Springer Handbook Of Glass 331993726X, 9783319937267, 9783319937281
This handbook provides comprehensive treatment of the current state of glass science from the leading experts in the fie
2,319 280 83MB
English Pages 1851 Year 2019
Polecaj historie
Table of contents :
Preface......Page 7
About the Editors......Page 8
About the Authors......Page 9
Contents......Page 14
List of Abbreviations......Page 25
1 The History of Glass......Page 33
1.1 Early Ages: The Invention of Glass......Page 35
1.2 Early Middle Ages......Page 39
1.3 A New Era, Late Middle Age and Renaissance: 13th to 16th Centuries......Page 43
1.4 Modern Times: 17th and 18th Century to Beginning of the 19th Century......Page 44
1.5 19th Century, the Century of Technical Revolutions......Page 48
1.6 The Revolutions of the Twentieth Century......Page 64
References......Page 78
Part A Fundamentals of Glass and the Glassy State......Page 80
2 Thermodynamics and Kinetics of Glass......Page 81
2.1 Definition of the Glassy State......Page 82
2.2 General Observations......Page 85
2.3 Fundamental Aspects of the Thermodynamics of Glasses......Page 91
2.4 Multicomponent Glasses......Page 99
References......Page 104
3 Viscosity of Glass and Glass-Forming Melts......Page 108
3.1 Shear Viscosity: General Remarks and Particularities of Glass......Page 110
3.2 Shear Viscosity – Measurement......Page 114
3.3 Shear Viscosity – Theory......Page 119
3.4 Bulk Viscosity......Page 137
References......Page 139
4.1 Tailoring Glass Crystallization for Glass-Ceramic Processing......Page 142
4.2 Theoretical Description of Glass Crystallization......Page 143
4.3 Design of Glass-Ceramics......Page 155
4.4 Structural Characterizations and Microstructures......Page 165
4.5 Glass-Ceramic Applications......Page 175
References......Page 186
5.1 Interaction of Light with Optical Materials......Page 197
References......Page 218
6 Nonlinear Optical Properties of Glass......Page 220
6.1 Polarization at the Microscopic Scale......Page 221
6.2 Polarization at the Macroscopic Scale......Page 222
6.3 Nonlinear Optical Susceptibility......Page 223
6.4 Third-Order Nonlinearity in Glass......Page 224
6.5 Second-Order Optical Properties in Glasses......Page 233
References......Page 246
7 Mechanical Properties of Glass......Page 253
7.1 Elasticity of Glass......Page 254
7.2 Plasticity of Glasses......Page 267
7.3 Fracture: Toughness, Strength and Fracture Mechanics......Page 278
7.4 Conclusion......Page 289
References......Page 290
8.1 Practical Use of Chemically Strengthened Glass......Page 298
8.2 Ion-Exchangeable Glass......Page 299
8.3 Ionic Interdiffusion......Page 302
8.4 Generation of an Ion-Exchange Stress Profile......Page 304
8.5 Application of Fracture Mechanics......Page 306
8.6 Frangibility......Page 310
8.7 Replication of Sharp Point Contact by Diamond Indentation......Page 311
8.8 Replication of Scratch Damage with a Diamond Indenter......Page 316
References......Page 319
9 Colors in Glasses......Page 322
9.1 Overview and Definitions......Page 323
9.2 Optically Active Centers......Page 336
9.3 Polyvalent Ions in Glasses......Page 339
9.4 Play Between Reflection, Scattering, and Absorption......Page 352
9.5 Glass Functionalization and Its Link with Colors......Page 359
9.6 Perspective and Outlook......Page 363
References......Page 364
10 Electrical Transport Properties of Glass......Page 368
10.A Appendix......Page 369
10.2 Ionic Transport Theory......Page 374
10.3 Experimental Results: Chalcogenide Glasses......Page 376
10.4 Experimental Results: Oxide Glasses......Page 383
10.5 Electrical Transport Property in Device-Related Materials......Page 388
10.6 Summary......Page 389
References......Page 390
11 Photosensitivity in Glasses......Page 393
11.1 Photothermal Interaction in Glass......Page 395
11.2 Photochemical Interaction in Glass......Page 402
11.3 Photophysical Interaction in Glass......Page 405
11.4 Anisotropic Photosensitivity of Glass......Page 419
11.5 Nonreciprocal Photosensitivity of Glass......Page 422
References......Page 424
12.1 Dissolution of Glass in Water......Page 431
12.2 Glass Corrosion in Aqueous Conditions......Page 434
12.3 Glass Vapor Hydration......Page 443
References......Page 454
Part B Glass Families......Page 463
13.1 Silicate Glasses: Historical and Industrial Importance......Page 465
13.2 Silica Glass......Page 473
13.3 Aluminum-Free Silicate Glasses......Page 477
13.4 Aluminum in Silicate Glasses......Page 489
13.5 Multivalent Elements in Silicate Glasses......Page 502
13.6 Volatile Elements in Silicate Glasses......Page 505
References......Page 512
14 Borate Glasses......Page 528
14.1 The Base Glass B_2O_3: Its Properties and Its Atomic-Level Structure......Page 529
14.2 The Binary Glasses RM_2OB_2O_3 and RMOB_2O_3......Page 531
14.3 Ternary Borosilicate Glasses......Page 539
References......Page 545
15 Chalcogenide Glasses......Page 548
15.1 Glass Compositions and Structures......Page 549
15.2 Glass Synthesis and Fabrication......Page 551
15.3 Thermal and Mechanical Properties......Page 554
15.4 Optical Properties......Page 556
15.5 Optical Components and Waveguides......Page 563
15.6 Selected Applications of Chalcogenide Glasses......Page 567
References......Page 569
16 Phosphate Glasses......Page 576
16.2 Research and Uses of Phosphate Glasses......Page 577
16.3 The Structure of Phosphate Glasses......Page 579
16.4 Properties and Applications......Page 589
References......Page 610
17 Halide Glasses......Page 618
17.1 Bonding in Halide Glasses......Page 619
17.2 Fluoride Glasses......Page 621
17.3 Chloride, Bromide, and Iodide Glasses......Page 632
References......Page 634
18 Metallic Glasses......Page 640
18.1 Fundamentals and a Brief History of Metallic Glasses......Page 641
18.2 Thermal Stability of Bulk Metallic Glasses......Page 645
18.3 Properties of Metallic Glasses......Page 650
18.4 Applications......Page 660
18.5 Conclusions and Prospects......Page 661
References......Page 662
19 Amorphous Selenium and Nanostructures......Page 667
19.1 Samples......Page 669
19.2 Noncrystalline Structure......Page 671
19.3 Structural Properties......Page 674
19.4 Electronic Spectra......Page 676
19.5 Electrical Properties......Page 682
19.6 Light-induced Phenomena......Page 684
19.7 Applications......Page 689
19.8 Nanostructures and Single Molecules......Page 691
19.9 Summary......Page 692
References......Page 693
20 Spin and Ferroic Glasses......Page 708
20.1 What is a Spin Glass?......Page 709
20.2 Brief Theoretical Introduction......Page 711
20.3 Phenomenological Taxonomy of Spin Glasses......Page 717
20.4 Other Ferroic Glasses: Materials with Glassy Relaxation......Page 726
20.5 Measuring Spin Glass Properties......Page 730
References......Page 734
21 Hybrid Glasses: From Metal Organic Frameworks and Co-ordination Polymers to Hybrid Organic Inorganic Perovskites......Page 740
21.1 Structure and Formation of Hybrid Glasses......Page 741
21.2 Phenomenology of Amorphization and Melting......Page 751
21.3 Pressure-Induced Amorphization and Mechanical Stability......Page 760
21.4 Extending the Range and Application of Hybrid Glasses......Page 775
21.5 Glass-Forming Ability......Page 780
21.6 Synopsis and Outlook......Page 785
References......Page 786
22 Natural Glasses......Page 792
22.1 Quenched Glasses......Page 802
22.2 Impact Glasses......Page 806
22.3 Obsidian......Page 812
22.4 Other Natural Glasses......Page 816
22.5 Insights into the Structure and Properties of Natural Glasses......Page 818
References......Page 825
23 Bioactive Glasses......Page 834
23.1 Bone Composition and Structure......Page 836
23.2 Bioactivity......Page 838
23.3 Composition versus Properties of Silicate Glasses......Page 842
23.4 Sol–Gel Silicate Bioactive Glasses......Page 847
23.5 Phosphate-Based Bioactive Glasses......Page 851
23.6 Borate-Based Bioactive Glasses......Page 852
23.7 Scaffolds for Tissue-Engineering Applications......Page 854
23.8 Bioactive Glasses in Clinics and Health Care......Page 860
23.9 Summary and Outlook......Page 862
References......Page 863
Part C Characterization of Glasses......Page 871
24 Thermal Analysis of Glass......Page 873
24.1 Differential Scanning Calorimetry (DSC)......Page 874
24.2 Differential Thermal Analyzer (DTA)......Page 885
24.3 Thermomechanical Analysis......Page 886
24.4 Thermogravimetric Analysis (TGA)......Page 890
24.5 Viscometry......Page 891
References......Page 896
25 Optical Spectroscopy of Glass......Page 899
25.1 Light–Matter Interactions......Page 900
25.2 Instrumentation......Page 911
25.3 Spectral Analysis and Interpretation......Page 922
References......Page 926
26 Terahertz Time-Domain Spectroscopy of Glasses......Page 929
26.1 THz Spectrometers......Page 930
26.2 Modeling and Experimental Validation......Page 935
26.3 Glass Systems......Page 937
26.4 Summary......Page 944
References......Page 945
27 Electron and Ion Beam Characterization of Glass......Page 949
27.1 Electron Beam Techniques......Page 951
27.2 Ion Beam Techniques......Page 961
References......Page 970
28.1 Magnetic Resonance Probes of Glass......Page 973
28.2 Theoretical Background......Page 974
28.3 Experimental Details......Page 978
28.4 Magnetic Resonance Studies of Glass......Page 987
References......Page 1004
29 Refractive Index of Optical Materials......Page 1014
29.1 Basic Parameters and Specifications......Page 1015
29.2 Main Properties of the Refractive Index......Page 1017
29.3 Measurement of the Refractive Index of Bulk Materials......Page 1027
29.4 Temperature Dependence of the Refractive Index......Page 1036
29.5 Spectrophotometric Determination of Refractive Indices......Page 1045
References......Page 1059
30 Neutron and X-Ray Diffraction of Glass......Page 1063
30.1 Diffraction by Noncrystalline Materials......Page 1064
30.2 Complementarity of Neutron and X-Ray Diffraction......Page 1069
30.3 Determination of the Structural Parameters......Page 1071
30.4 Difference Methods......Page 1072
30.5 Reverse Monte Carlo and Related Methods......Page 1075
30.6 Case Studies of Glass Investigation by Neutron and X-Ray Diffraction......Page 1079
30.7 In Situ High Temperature/High Pressure Diffraction......Page 1086
References......Page 1101
Part D Glass Modelling......Page 1111
31 First-Principles Calculation......Page 1113
31.1 Methods and Approach......Page 1115
31.2 First-Principles Calculation for Different Types of Glasses......Page 1118
31.3 Conclusions and Future Outlook......Page 1137
References......Page 1140
32.1 A Brief History of MD......Page 1147
32.2 Fundamentals of MD Simulations......Page 1148
32.3 MD Simulations of Glasses......Page 1153
32.4 Applications of MD Simulations in Oxide Glass Research......Page 1159
32.5 Outlook and Challenges......Page 1168
References......Page 1169
33.1 Data-Driven Glass Research......Page 1172
33.2 Development of Data-Driven Materials......Page 1178
33.3 Methods......Page 1183
33.4 Data-Driven Development for Glass Composition Design......Page 1188
33.5 Conclusions and New Glass Research Opportunities......Page 1202
References......Page 1205
Part E Glass Processing......Page 1208
34 Industrial Glass Processing and Fabrication......Page 1210
34.1 Brief Overview of Global Glass Production......Page 1211
34.2 Industrial Glass Compositions and Process Overview......Page 1215
34.3 Raw Materials and Batch Preparation......Page 1217
34.4 Importance of Redox in Glass Making......Page 1223
34.5 Glass Melting, Fining and Conditioning......Page 1225
34.6 Industrial Glass Furnaces......Page 1230
34.7 Modeling of Industrial Processes......Page 1236
References......Page 1244
35.1 Overview of the Batch Melting Process......Page 1247
35.2 Heat Transfer Processes......Page 1252
35.3 Different Types of Batch Reactions......Page 1255
35.4 Reaction Kinetics......Page 1259
35.5 Silica Conversion......Page 1260
35.6 Fining Reactions......Page 1261
35.7 Conclusions......Page 1269
References......Page 1270
36.1 Overview of the Glass-Shaping Process......Page 1273
36.2 Shaping of Glass at High Temperatures......Page 1274
36.3 Glass Shaping at Low Temperatures......Page 1291
36.4 Conclusions......Page 1303
References......Page 1304
37.1 Amorphous Film Processing and Coatings on Glass......Page 1307
37.2 Physical Vapor Deposition......Page 1313
37.3 Chemical Vapor Deposition......Page 1333
37.4 Comparison of PVD and CVD Techniques......Page 1334
37.5 Liquid-Based Film Fabrication......Page 1336
37.6 Contribution of Amorphous Thin Films and Coatings on Glass to 21st Century Development......Page 1338
References......Page 1340
38.1 The Role of Sol–Gel Processing in Glass Technology......Page 1347
38.2 Sol–Gel Processing......Page 1349
38.3 Gelation, Percolation and Syneresis......Page 1353
38.4 Drying and Removal of Solvent and Water......Page 1354
38.5 Consolidation and Sintering......Page 1356
38.6 Sol–Gel Fibers, Thin Films and Other Applications......Page 1358
38.7 Organic–Inorganic Hybrid Sol–Gel Glasses......Page 1361
38.8 Summary and Future Prospects......Page 1363
References......Page 1364
39.1 Why Recycle Glass?......Page 1369
39.2 Recycling Methods for Glass Products......Page 1376
39.3 Waste Cathode Ray-Tube Glass Recycling: A Case Study......Page 1382
39.4 Summary......Page 1388
References......Page 1389
Part F Optical and Photonic Glass Applications......Page 1392
40 Laser Glasses......Page 1394
40.1 Short Introduction to Lasers......Page 1395
40.2 Commonly Used Lanthanide Elements in Glasses for Lasers......Page 1399
40.3 Specification of Laser Glass Doping Level......Page 1400
40.4 Rules of Thumb in Glass Selection for Performance......Page 1401
40.5 Commercially Available Er3+-Doped Glasses......Page 1402
40.6 Estimating Refractive Index......Page 1403
40.7 Glass Melting and Measurements for Bulk Material Properties Characterization......Page 1404
40.8 Derivation of Laser Performance Related Properties......Page 1406
40.9 Laser Damage Testing......Page 1411
40.11 Summary......Page 1414
References......Page 1415
41.1 Theory of Light Guiding......Page 1418
41.2 Fiber Properties......Page 1428
41.3 Specialty Optical Fibers......Page 1439
41.4 Applications of Optical Fibers......Page 1446
References......Page 1451
42 Glass in Integrated Photonics......Page 1453
42.1 Processing of Planar Glass Photonic Components......Page 1455
42.2 Integrated Photonics Platforms Based on Glass Materials......Page 1462
42.3 Summary and Outlook......Page 1478
References......Page 1479
43 Amorphous Silicon in Microphotonics......Page 1494
43.1 Amorphous Silicon as a Photonic Material......Page 1495
43.2 Amorphous Silicon for Photonic Devices......Page 1498
43.3 Summary......Page 1502
References......Page 1503
44 Phase-Change Memory and Optical Data Storage......Page 1505
44.1 Conventional Ge-Sb-Te Phase-Change Films......Page 1507
44.2 Phase-Change Behaviors of Doped Ge_2Sb_2Te_5 Films......Page 1510
44.3 Doped Sb-Te Films for Phase-Change Memory Applications......Page 1512
44.4 Nanocomposite Films for Phase-Change Memory Applications......Page 1518
44.5 Crystallization Kinetics Studied by Ultrafast Calorimetry for Phase-Change Materials......Page 1522
44.6 Phase-Change Materials for Applications in Integrated Photonic Memory......Page 1525
44.7 Summary......Page 1526
References......Page 1527
45 Display Glass......Page 1531
45.1 Overview of Display Technologies......Page 1532
45.2 Display Glass Properties......Page 1536
45.3 Melting and Fining......Page 1541
45.4 Forming Precision Sheets for Displays......Page 1544
45.5 Glass Composition......Page 1548
45.6 Three-Dimensional (3-D) Upconversion Displays......Page 1557
45.7 Electronics on Glass......Page 1558
45.8 Flexible Glass and Displays......Page 1559
45.9 Conclusions......Page 1560
References......Page 1561
46 Scintillator Glasses......Page 1564
46.1 The Scintillation Process......Page 1565
46.2 Advantages and Disadvantages of Glass Scintillators......Page 1567
46.3 Synthesis......Page 1568
46.4 Basic Characterization of Scintillator Glasses......Page 1574
46.5 Ionizing Radiation and the Applicability of Scintillator Glasses......Page 1580
References......Page 1589
47 Mid-Infrared Molecular Sensing......Page 1594
47.1 Overview......Page 1595
47.2 Chalcogenide Glass Science and Technology Pertinent to MIR Molecular Sensing......Page 1597
47.3 MIR Molecular Sensing......Page 1603
47.4 Progress in Using Chalcogenide Glass Fibers for MIR Molecular Sensing......Page 1609
47.5 On-Chip MIR Molecular Sensing Using Chalcogenide Glasses......Page 1623
47.6 Highlights and Future Prospects......Page 1636
References......Page 1637
Part G Glass for Energy Applications......Page 1642
48.1 Photovoltaics......Page 1644
48.2 Flat Glass for Solar Applications......Page 1648
48.3 Anti-Reflective Surface Treatments on Glass for Solar Applications......Page 1652
48.4 Transparent Conductive Oxide Stacks for Solar Applications......Page 1661
48.5 Glass for Concentrated Solar Power Applications......Page 1670
References......Page 1681
49 Glass for Thermoelectric Applications......Page 1686
49.1 Basics of Thermoelectricity......Page 1687
49.2 Key Materials for Thermoelectric Applications......Page 1689
49.3 Chalcogenide Glasses......Page 1691
References......Page 1702
50 Glasses and Glass-Ceramics for Solid-State Battery Applications......Page 1706
50.1 Principle of an All-Solid-State Battery and Requirements......Page 1708
50.2 Solid Electrolytes......Page 1713
50.3 All-Solid-State Rechargeable Batteries......Page 1731
50.4 Conclusion......Page 1753
References......Page 1755
Part H Glasses in Art and Architecture......Page 1764
51 Art Glasses......Page 1766
51.1 Some Historical Milestones......Page 1767
51.2 Art of Glass, Trial of an Artistic Typology......Page 1775
51.3 Thinking Through the Glass......Page 1781
51.4 Conclusion......Page 1787
References......Page 1788
52 Architectural Glass......Page 1790
52.1 Flat Glass Products......Page 1791
52.2 Cast Glass Products......Page 1807
52.3 Glass in Architectural Applications......Page 1809
52.4 Connections......Page 1816
52.5 Numerical Modeling of Glass Components......Page 1822
References......Page 1824
Subject Index......Page 1829
Citation preview
Springer
Handbook Glass
oƒ
Musgraves Hu Calvez Editors
123
Springer Handbook of Glass
Springer Handbooks provide a concise compilation of approved key information on methods of research, general principles, and functional relationships in physical and applied sciences. The world’s leading experts in the fields of physics and engineering will be assigned by one or several renowned editors to write the chapters comprising each volume. The content is selected by these experts from Springer sources (books, journals, online content) and other systematic and approved recent publications of scientific and technical information. The volumes are designed to be useful as readable desk book to give a fast and comprehensive overview and easy retrieval of essential reliable key information, including tables, graphs, and bibliographies. References to extensive sources are provided.
H
Springer
Handbook of Glass
J. David Musgraves, Juejun Hu, Laurent Calvez (Eds.) With 1450 Figures and 224 Tables
K
Editors J. David Musgraves Rochester Precision Optics, LLC West Henrietta, NY, USA Juejun Hu Dept. of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA, USA Laurent Calvez UMR 6226 – Institut des Sciences Chimiques de Rennes University of Rennes I Rennes, France
ISBN 978-3-319-93726-7 e-ISBN 978-3-319-93728-1 https://doi.org/10.1007/978-3-319-93728-1 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG, part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
V
Dedicated to the memory of Neville Greaves
VII
Preface
As you’ll get a chance to see in Chap. 1 of this book, glass is a fascinating topic, in part because while we human beings have been manufacturing glass for thousands of years now, the discipline of glass science is only 100 years old. This means that humanity has developed the technology of glassmaking—the temperatures, times, ingredients, processes, etc., needed to make good window and plate glass—over the course of dozens or even hundreds of generations, and we have a great wealth of acquired knowledge of how to make glass. Compare this enormous amount of knowhow to the idea of glass science as a distinct scientific discipline, focused in part on why certain things make glass, and what exactly is a glass, which has only a few generations of students and masters contributing to its advance. What we see when we combine these two ideas of glass is fascinating: humanity knows quite a lot about how to make glass, but we are only just beginning to understand what makes a glass a glass, from the perspective of basic physics. Because of the sheer breadth of the discipline, there has been no single textbook in the glass science field that has attempted to cover all its aspects. There exist a handful of excellent basic glass science textbooks that will be referenced widely in this book, but these are all confined to their individual subdisciplines. The goal of this book is to serve as the starting point for any exploration into the field of glass science; indeed, we have chapters on the technical aspects of all of the major glassforming families, but we also have chapters devoted to the architectural, archeological, and geological aspects of glass science. No one textbook can hope to encompass the entirety of a modern scientific field, especially one as rapidly developing as glass science at the beginning of the 21st century, but the hope is that each of the chapters in the book serves as a place for the reader to get grounded, understand the basics (and the complications!), and find resources in the primary scientific literature where they can go and learn in more depth. The Springer Handbook of Glass is intended to be a comprehensive overview of the diverse field of glass science, with each chapter written by one or more work-
ing experts in the field. The handbook is aimed at senior undergraduate and graduate students, researchers, and professionals working in the field of glass science. The chapters provide the necessary background and up-todate knowledge in a wide range of topics, with in-depth references to the journal literature for those seeking greater depth in a particular subfield. In general, the book is structured to provide basic information on the particular glass families at the beginning, followed by specific applications later. Because each glass family has applications, and each application is associated with some glass family, there is necessarily a good deal of crossover between various chapters. For example, spectroscopic information regarding chalcogenide glasses can be found in the chapters on chalcogenide glasses, optical spectroscopy, and infrared sensing; the hope is that seeing these materials in a variety of contexts will help the reader grasp the interdisciplinary nature of glass science. The editors are very grateful to all of the authors who, out of the generosity of their scientific spirit, contributed their time and expertise to this handbook. We know this was a long process, and we’d like to thank each and every one of the authors for their participation in this journey together. Our deepest thanks go to Judith Hinterberg and Sara Kate Heukerott at Springer for their tireless efforts in keeping this project on track. During the process of making this book, we’ve had a few births, a near-death, and almost every other projectderailing experience you could imagine, and they have kept the program moving the entire way. Without them, the center could not have held, and we appreciate every bit of their effort. Finally, the editors would like to thank their families (Jessica, Di, Helius, Selena and Eos, Anne-Laure, Youna and Norah) for all of their support during this project. We do this for them, and we couldn’t do it without them. J. David Musgraves Juejun Hu Laurent Calvez
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About the Editors
J. David Musgraves received his bachelor’s degree in Physics from Pomona, followed by his PhD in Materials Science from the University of Arizona. His first time melting and quenching glass was in the laboratory of Kathleen Richardson at Clemson University, where he began a postdoc in 2010 and ultimately became a Research Assistant Professor. His research was focused on the integration of quantum computational modeling, optical spectroscopy, and thermal analysis as a means to evaluate the evolution of amorphous structure across multiple-length scales and to correlate this emergent structure with material properties. After founding IRradiance Glass, Inc. in 2012, he left Clemson University to become President and CEO of the company. IRradiance Glass was purchased in 2018 by Rochester Precision Optics (RPO), where Dr. Musgraves is now Chief Scientist. Dr. Musgraves moves to the frozen northlands with his wife and two dogs, who are his near-constant companions.
Juejun (JJ) Hu received his degrees in Materials Science and Engineering from Tsinghua University and Massachusetts Institute of Technology (MIT). He is currently Associate Professor at MIT’s Department of Materials Science and Engineering. His primary research interest is the field of integrated optics and photonics. Prior to joining MIT, he was Assistant Professor at the University of Delaware. He has been recognized with the National Science Foundation (NSF) Faculty Early Career Development Award, the Robert L. Coble Award from the American Ceramic Society, the Defense Advanced Research Projects Agency (DARPA) Young Faculty Award, the Gerard J. Mangone Young Scholars Award, and the University of Delaware Excellence in Teaching Award, among others. His research focuses on optical glass materials and their applications in integrated optics and photonics.
Laurent Calvez graduated from the University of Rennes and was awarded a DGA grant to pursue a PhD, which he obtained with honors. He completed a postdoc at the Arizona Materials Laboratory at the University of Arizona, before joining the faculty of the University of Rennes in 2007, where he currently heads the Energy Conversion and Storage group at the Institut des Sciences Chimiques de Rennes. His current research focuses on the generation of active nanoparticles in chalcogenide glasses and glass-ceramics to tailor material properties to accommodate specific optical and electrical designs and manufacturing. He was awarded the Young Brittany Research Award for his work on photosensitivity of glasses and innovative glass-ceramics. He received the French Academy of Sciences Lamb prize in 2016 and was recently accepted into the prestigious University Institute of France. Despite a lack of time, he is still improving his topspin in table tennis.
XI
About the Authors
Abdesselam Abdelouas SUBATECH IMT Atlantique, CNRS/IN2P3, Université de Nantes Nantes, France
Courtney Calahoo Dept. of Chemistry Dalhousie University Halifax, Canada
Jean-Luc Adam Institute of Chemical Sciences Rennes, UMR CNRS 6226 University of Rennes 1 Rennes, France
Thierry Cardinal Institute for Condensed Matter Chemistry of Bordeaux University of Bordeaux Pessac, France
Anuradha M. Agarwal Materials Research Laboratory Massachusetts Institute of Technology Cambridge, MA, USA
Michel Cathelinaud Institute of Chemical Sciences Rennes, UMR CNRS 6226 University of Rennes 1 Rennes, France
Ifty Ahmed Faculty of Engineering University of Nottingham Nottingham, UK
Thierry Chartier CNRS, Institute Foton University of Rennes 1 Lannion, France
Mathieu Allix University of Orléans Orléans, France
Yimin Chen Dept. of Microelectronic Science and Engineering, Faculty of Science Ningbo University Ningbo City, China
Christophe Bardin University Jean Monnet Saint-Etienne, France Jan Belis Dept. of Structural Engineering Ghent University Ghent, Belgium Elsa Branco Lopes Center for Nuclear Sciences and Technologies Instituto Superior Técnico, University of Lisbon Bobadela, Portugal Antoine Brient Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France Bruno Bureau Institute of Chemical Sciences Rennes, UMR CNRS 6226 University of Rennes 1 Rennes, France
Wai-Yim Ching Dept. of Physics & Astronomy University of Missouri – Kansas City Kansas City, MO, USA Marie-Hélène Chopinet Saint Gobain Research Aubervilliers, France Maria Rita Cicconi Dept. of Materials Science and Engineering Friedrich-Alexander University Erlangen-Nürnberg Erlangen, Germany Alexis G. Clare Center for Advanced Ceramic Technology Alfred University Alfred, NY, USA Reinhard Conradt uniglassAC GmbH Aachen, Germany
XII
About the Authors
Laurent Cormier IMPMC Sorbonne University – CNRS Paris, France Matt Dejneka Glass Research Corning Inc. Corning, NY, USA Gaëlle Delaizir Institute of Research for Ceramics (IRCER) Limoges, France Jincheng Du Dept. of Materials Science & Engineering University of North Texas Denton, TX, USA Marc Dussauze Institute of Molecular Sciences University of Bordeaux Talence, France Siamak Eqtesadi Abalonyx AS Oslo, Norway Steve Feller Dept. of Physics Coe College Cedar Rapids, IA, USA Ulrich Fotheringham Dept. of Materials Development SCHOTT AG Mainz, Germany Ashtosh Ganjoo Vitro Architectural Glass Cheswick, PA, USA Simi A. George SCHOTT North America, Inc. Duryea, PA, USA António Pereira Gonçalves Center for Nuclear Sciences and Technologies Instituto Superior Técnico, University of Lisbon Bobadela, Portugal Bernd Grambow SUBATECH University of Nantes Nantes, France
G. Neville Greaves (deceased) Timothy M. Gross Corning Inc. Corning, NY, USA Yann Gueguen Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France Jean-Pierre Guin Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France Akitoshi Hayashi Dept. of Applied Chemistry Osaka Prefecture University Osaka, Japan Joseph S. Hayden SCHOTT North America, Inc. Duryea, PA, USA Kazuyuki Hirao Dept. of Materials Chemistry Kyoto University Kyoto, Japan Juejun Hu Dept. of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA, USA Lili Hu Shanghai Institute of Optics and Fine Mechanics Chinese Academy of Science Shanghai, China Mathieu Hubert Dept. of Corning Glass Technologies Corning Research & Development Corporation Painted Post, NY, USA Leena Hupa Faculty of Science and Engineering Åbo Akademi University Turku, Finland Jacqueline A. Johnson Dept. of Mechanical, Aerospace, and Biomedical Engineering (MABE) The University of Tennessee Space Institute Tullahoma, TN, USA
About the Authors
Peter G. Kazansky Optoelectronics Research Centre University of Southampton Southampton, UK
Yegang Lv Laboratory of Infrared Materials & Devices Ningbo University Ningbo, China
T. J. Kiczenski Glass Research Corning Inc. Corning, NY, USA
Zhixun Ma Vitro Architectural Glass Cheswick, PA, USA
Lisa C. Klein Dept. of Materials Science & Engineering Rutgers University Piscataway, NJ, USA Erick Koontz Fisba LLC. Tucson, AZ, USA Romain Laniel Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France Charles Le Losq Research School of Earth Sciences The Australian National University Canberra, Australia Ronan Lebullenger Institute of Physics – Rennes (IPR), UMR CNRS 6251 Institute of Chemical Sciences Rennes (ISCR) UMR CNRS 6226 University of Rennes 1 Rennes, France Russell Lee Leonard Dept. of Mechanical, Aerospace, and Biomedical Engineering (MABE) The University of Tennessee Space Institute Tullahoma, TN, USA Martin Letz Dept. of Materials Development SCHOTT AG Mainz, Germany
Jacques Mangin Laboratoire Interdisciplinaire Carnot de Bourgogne Dijon, France John C. Mauro Dept. of Materials Science and Engineering The Pennsylvania State University University Park, PA, USA James McCamy Vitro Architectural Glass Cheswick, PA, USA John S. McCloy School of Mechanical & Materials Engineering Washington State University Pullman, WA, USA Jennifer McKinley Office of Research University of Central Florida Orlando, FL, USA François O. Mear Lille University Lille, France Paul A. Medwick Vitro Architectural Glass Cheswick, PA, USA Jean-Louis Meyzonnette Institut d’Optique Graduate School Palaiseau, France
Dominique de Ligny Dept. of Materials Science and Engineering Friedrich-Alexander University Erlangen-Nürnberg Erlangen, Germany
Jurgen Michel Materials Research Laboratory Massachusetts Institute of Technology Cambridge, MA, USA
Christian Louter Institute of Building Construction Technische Universität Dresden Dresden, Germany
Mathieu Miroir Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France
XIII
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About the Authors
Kiyotaka Miura Dept. of Materials Chemistry Kyoto University Kyoto, Japan Doris Möncke Inamori School of Engineering, Glass Science Alfred University Alfred, NY, USA Francisco Muñoz Institute of Ceramics and Glass (CSIC) Madrid, Spain J. David Musgraves Rochester Precision Optics, LLC West Henrietta, NY, USA Virginie Nazabal Institute of Chemical Sciences ISCR, UMR CNRS 6226 University of Rennes 1 Rennes, France James Neeway Pacific Northwest National Laboratory Richland, WA, USA Daniel R. Neuville Institut de Physique du Globe de Paris CNRS-IPGP-USPC Paris, France Jens H. Nielsen Dept. of Civil Engineering Technical University of Denmark Kgs. Lyngby, Denmark Petr Němec Faculty of Chemical Technology University of Pardubice Pardubice, Czech Republic Mehmet C. Onbasli Dept. of Electrical and Electronics Engineering Koç University Istanbul, Turkey Alexander L. Paterson Dept. of Chemistry Dalhousie University Halifax, Canada Jean-Marc Pelletier INSA-Lyon, MATEIS UMR 55140 University of Lyon Villeurbanne, France
Adam Polcyn Vitro Architectural Glass Cheswick, PA, USA Barrett G. Potter Jr. Dept. of Materials Science & Engineering University of Arizona Tucson, AZ, USA Annie Pradel Institut Charles Gerhardt Montpellier University of Montpellier Montpellier, France Jichao Qiao School of Mechanics, Civil Engineering & Architecture Northwestern Polytechnical Unviersity Xi’an, China Jianrong Qiu Dept. of Materials Science & Engineering Zhenjiang University Hangzhou, China Jean Rocherullé Institute of Chemical Sciences Rennes, UMR CNRS 6226 University of Rennes 1 Rennes, France Masaaki Sakakura Optoelectronics Research Centre University of Southampton Southampton, UK Jens Schneider Institute of Structural Mechanics and Design – Glass Competence Center Technische Universität Darmstadt Darmstadt, Germany Angela B. Seddon Mid-Infrared Photonics Group, George Green Institute for Electromagnetics Research University of Nottingham Nottingham, UK Vincent Seznec Laboratoire de Réactivité et Chimie des Solides (LRCS) Université de Picardie Jules Verne Amiens, France
About the Authors
Xiang Shen Laboratory of Infrared Materials & Devices Ningbo University Ningbo, China Koichi Shimakawa Center of Innovative Photovoltaic Systems Gifu University Gifu, Japan Masahiro Shimizu Dept. of Materials Chemistry Kyoto University Kyoto, Japan Yasuhiko Shimotsuma Dept. of Materials Chemistry Kyoto University Kyoto, Japan S. K. Sundaram Inamori School of Engineering Alfred University Alfred, NY, USA
Virginie Viallet Laboratoire de Réactivité et Chimie des Solides (LRCS) Université de Picardie Jules Verne Amiens, France Peter F. Wachtel Rochester Precision Optics, LLC West Henrietta, NY, USA Guoxiang Wang Laboratory of Infrared Materials & Devices Ningbo University Ningbo, China Xiaoju Wang Faculty of Science and Engineering Åbo Akademi University Turku, Finland Ulrike Werner-Zwanziger Dept. of Chemistry Dalhousie University Halifax, Canada
Keiji Tanaka Graduate School of Engineering Hokkaido University Sapporo, Japan
Lan Yang Dept. of Electrical and Systems Engineering Washington University in St. Louis St. Louis, MO, USA
Adama Tandia Science and Technology Division Corning Inc. Corning, NY, USA
Xiang-Hua Zhang Institute of Chemical Sciences Rennes, UMR CNRS 6226 University of Rennes 1 Rennes, France
Masahiro Tatsumisago Dept. of Applied Chemistry Osaka Prefecture University Osaka, Japan Oscar S. Verheijen CelSian Glass & Solar B.V. Eindhoven, The Netherlands
Josef W. Zwanziger Dept. of Chemistry Dalhousie University Halifax, Canada
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List of Abbreviations ............................................................. 1 The History of Glass Marie-Hélène Chopinet ......................................................... 1.1 Early Ages: The Invention of Glass ..................................... 1.2 Early Middle Ages........................................................ 1.3 A New Era, Late Middle Age and Renaissance: 13th to 16th Centuries.................................................. 1.4 Modern Times: 17th and 18th Century to Beginning of the 19th Century...................................... 1.5 19th Century, the Century of Technical Revolutions .................. 1.6 The Revolutions of the Twentieth Century ............................ 1.7 Conclusion ............................................................... References .......................................................................
XXIX
1 3 7 11 12 16 32 46 46
Part A Fundamentals of Glass and the Glassy State 2 Thermodynamics and Kinetics of Glass Reinhard Conradt................................................................ 2.1 Definition of the Glassy State .......................................... 2.2 General Observations ................................................... 2.3 Fundamental Aspects of the Thermodynamics of Glasses ........... 2.4 Multicomponent Glasses................................................ 2.5 Summary and Outlook .................................................. References .......................................................................
51 52 55 61 69 74 74
3 Viscosity of Glass and Glass-Forming Melts Ulrich Fotheringham ............................................................ 3.1 Shear Viscosity: General Remarks and Particularities of Glass ....... 3.2 Shear Viscosity – Measurement ........................................ 3.3 Shear Viscosity – Theory ................................................ 3.4 Bulk Viscosity ............................................................ References .......................................................................
79 81 85 90 108 110
4 Crystallization and Glass-Ceramics Mathieu Allix, Laurent Cormier ................................................. 4.1 Tailoring Glass Crystallization for Glass-Ceramic Processing ......... 4.2 Theoretical Description of Glass Crystallization ....................... 4.3 Design of Glass-Ceramics ............................................... 4.4 Structural Characterizations and Microstructures ..................... 4.5 Glass-Ceramic Applications ............................................. 4.6 Conclusion and Future Directions ...................................... References .......................................................................
113 113 114 126 136 146 157 157
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5 Linear Optical Properties Martin Letz ....................................................................... 5.1 Interaction of Light with Optical Materials ............................ References .......................................................................
169 169 190
6 Nonlinear Optical Properties of Glass Marc Dussauze, Thierry Cardinal ............................................... 6.1 Polarization at the Microscopic Scale .................................. 6.2 Polarization at the Macroscopic Scale ................................. 6.3 Nonlinear Optical Susceptibility ........................................ 6.4 Third-Order Nonlinearity in Glass ...................................... 6.5 Second-Order Optical Properties in Glasses ........................... 6.6 Conclusion ............................................................... References .......................................................................
193 194 195 196 197 206 219 219
7 Mechanical Properties of Glass Jean-Pierre Guin, Yann Gueguen .............................................. 7.1 Elasticity of Glass ........................................................ 7.2 Plasticity of Glasses ..................................................... 7.3 Fracture: Toughness, Strength and Fracture Mechanics .............. 7.4 Conclusion ............................................................... References .......................................................................
227 228 241 252 263 264
8 Chemical Strengthening of Glass Timothy M. Gross ................................................................ 8.1 Practical Use of Chemically Strengthened Glass....................... 8.2 Ion-Exchangeable Glass ................................................ 8.3 Ionic Interdiffusion...................................................... 8.4 Generation of an Ion-Exchange Stress Profile ........................ 8.5 Application of Fracture Mechanics ..................................... 8.6 Frangibility............................................................... 8.7 Replication of Sharp Point Contact by Diamond Indentation........ 8.8 Replication of Scratch Damage with a Diamond Indenter ........... 8.9 Conclusion ............................................................... References .......................................................................
273 273 274 277 279 281 285 286 291 294 294
9 Colors in Glasses Dominique de Ligny, Doris Möncke ............................................ 9.1 Overview and Definitions ............................................... 9.2 Optically Active Centers ................................................. 9.3 Polyvalent Ions in Glasses .............................................. 9.4 Play Between Reflection, Scattering, and Absorption ................ 9.5 Glass Functionalization and Its Link with Colors ..................... 9.6 Perspective and Outlook ................................................ References .......................................................................
297 298 311 314 327 334 338 339
10 Electrical Transport Properties of Glass Koichi Shimakawa............................................................... 10.1 Electronic Transport Theory ............................................. 10.2 Ionic Transport Theory .................................................. 10.3 Experimental Results: Chalcogenide Glasses .......................... 10.4 Experimental Results: Oxide Glasses...................................
343 344 349 351 358
Contents
10.5 Electrical Transport Property in Device-Related Materials ........... 10.6 Summary ................................................................. 10.A Appendix................................................................. References .......................................................................
363 364 365 365
11 Photosensitivity in Glasses Yasuhiko Shimotsuma, Masaaki Sakakura, Masahiro Shimizu, Kiyotaka Miura, Kazuyuki Hirao, Jianrong Qiu, Peter G. Kazansky .......... 11.1 Photothermal Interaction in Glass ..................................... 11.2 Photochemical Interaction in Glass .................................... 11.3 Photophysical Interaction in Glass ..................................... 11.4 Anisotropic Photosensitivity of Glass .................................. 11.5 Nonreciprocal Photosensitivity of Glass ............................... References .......................................................................
369 371 378 381 395 398 400
12 Chemical Durability of Glasses Abdesselam Abdelouas, James Neeway, Bernd Grambow ................... 12.1 Dissolution of Glass in Water ........................................... 12.2 Glass Corrosion in Aqueous Conditions ................................ 12.3 Glass Vapor Hydration................................................... 12.4 Conclusion ............................................................... References .......................................................................
407 407 410 419 430 430
Part B Glass Families 13 Silicate Glasses Charles Le Losq, Maria Rita Cicconi, G. Neville Greaves, Daniel R. Neuville . 13.1 Silicate Glasses: Historical and Industrial Importance ............... 13.2 Silica Glass ............................................................... 13.3 Aluminum-Free Silicate Glasses........................................ 13.4 Aluminum in Silicate Glasses ........................................... 13.5 Multivalent Elements in Silicate Glasses............................... 13.6 Volatile Elements in Silicate Glasses ................................... 13.7 Conclusion ............................................................... References .......................................................................
441 441 449 453 465 478 481 488 488
14 Borate Glasses Steve Feller ....................................................................... 14.1 The Base Glass B2 O3 : Its Properties and Its Atomic-Level Structure ......................... 14.2 The Binary Glasses RM2 O B2 O3 and RMO B2 O3 ....................... 14.3 Ternary Borosilicate Glasses ............................................ References .......................................................................
506 508 516 522
15 Chalcogenide Glasses Xiang-Hua Zhang, Jean-Luc Adam, Bruno Bureau........................... 15.1 Glass Compositions and Structures .................................... 15.2 Glass Synthesis and Fabrication ........................................ 15.3 Thermal and Mechanical Properties ................................... 15.4 Optical Properties ....................................................... 15.5 Optical Components and Waveguides .................................
525 526 528 531 533 540
505
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15.6 Selected Applications of Chalcogenide Glasses ....................... 15.7 Conclusion ............................................................... References .......................................................................
544 546 546
16 Phosphate Glasses Francisco Muñoz, Jean Rocherullé, Ifty Ahmed, Lili Hu....................... 16.1 Phosphorus and Glass Formation ...................................... 16.2 Research and Uses of Phosphate Glasses .............................. 16.3 The Structure of Phosphate Glasses .................................... 16.4 Properties and Applications ............................................ References .......................................................................
553 554 554 556 566 587
17 Halide Glasses Alexis G. Clare, Peter F. Wachtel, J. David Musgraves ......................... 17.1 Bonding in Halide Glasses .............................................. 17.2 Fluoride Glasses ......................................................... 17.3 Chloride, Bromide, and Iodide Glasses ................................ 17.4 Summary ................................................................. References .......................................................................
595 596 598 609 611 611
18 Metallic Glasses Jean-Marc Pelletier, Jichao Qiao ............................................... 18.1 Fundamentals and a Brief History of Metallic Glasses ............... 18.2 Thermal Stability of Bulk Metallic Glasses ............................. 18.3 Properties of Metallic Glasses .......................................... 18.4 Applications.............................................................. 18.5 Conclusions and Prospects.............................................. References .......................................................................
617 618 622 627 637 638 639
19 Amorphous Selenium and Nanostructures Keiji Tanaka ...................................................................... 19.1 Samples .................................................................. 19.2 Noncrystalline Structure ................................................ 19.3 Structural Properties .................................................... 19.4 Electronic Spectra........................................................ 19.5 Electrical Properties ..................................................... 19.6 Light-induced Phenomena ............................................. 19.7 Applications.............................................................. 19.8 Nanostructures and Single Molecules ................................. 19.9 Summary ................................................................. References .......................................................................
645 647 649 652 654 660 662 667 669 670 671
20 Spin and Ferroic Glasses John S. McCloy ................................................................... 20.1 What is a Spin Glass?.................................................... 20.2 Brief Theoretical Introduction .......................................... 20.3 Phenomenological Taxonomy of Spin Glasses ........................ 20.4 Other Ferroic Glasses: Materials with Glassy Relaxation ............. 20.5 Measuring Spin Glass Properties ....................................... 20.6 Outlook ................................................................... References .......................................................................
687 688 690 696 705 709 713 713
Contents
21 Hybrid Glasses: From Metal Organic Frameworks
and Co-ordination Polymers to Hybrid Organic Inorganic Perovskites G. Neville Greaves................................................................ 21.1 Structure and Formation of Hybrid Glasses ........................... 21.2 Phenomenology of Amorphization and Melting ...................... 21.3 Pressure-Induced Amorphization and Mechanical Stability ......... 21.4 Extending the Range and Application of Hybrid Glasses ............ 21.5 Glass-Forming Ability ................................................... 21.6 Synopsis and Outlook ................................................... References .......................................................................
719 720 730 739 754 759 764 765
22 Natural Glasses Maria Rita Cicconi, Daniel R. Neuville ......................................... 22.1 Quenched Glasses ....................................................... 22.2 Impact Glasses........................................................... 22.3 Obsidian.................................................................. 22.4 Other Natural Glasses ................................................... 22.5 Insights into the Structure and Properties of Natural Glasses ....... 22.6 Conclusions and Future Directions ..................................... References .......................................................................
771 781 785 791 795 797 804 804
23 Bioactive Glasses Leena Hupa, Xiaoju Wang, Siamak Eqtesadi.................................. 23.1 Bone Composition and Structure....................................... 23.2 Bioactivity................................................................ 23.3 Composition versus Properties of Silicate Glasses .................... 23.4 Sol–Gel Silicate Bioactive Glasses ...................................... 23.5 Phosphate-Based Bioactive Glasses ................................... 23.6 Borate-Based Bioactive Glasses ........................................ 23.7 Scaffolds for Tissue-Engineering Applications ........................ 23.8 Bioactive Glasses in Clinics and Health Care .......................... 23.9 Summary and Outlook .................................................. References .......................................................................
813 815 817 821 826 830 831 833 839 841 842
Part C Characterization of Glasses 24 Thermal Analysis of Glass Erick Koontz ...................................................................... 24.1 Differential Scanning Calorimetry (DSC)................................ 24.2 Differential Thermal Analyzer (DTA) .................................... 24.3 Thermomechanical Analysis ............................................ 24.4 Thermogravimetric Analysis (TGA) ...................................... 24.5 Viscometry ............................................................... References .......................................................................
853 854 865 866 870 871 876
25 Optical Spectroscopy of Glass Barrett G. Potter Jr. .............................................................. 25.1 Light–Matter Interactions............................................... 25.2 Instrumentation ......................................................... 25.3 Spectral Analysis and Interpretation................................... 25.4 Conclusions .............................................................. References .......................................................................
879 880 891 902 906 906
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26 Terahertz Time-Domain Spectroscopy of Glasses S. K. Sundaram .................................................................. 26.1 THz Spectrometers ....................................................... 26.2 Modeling and Experimental Validation ............................... 26.3 Glass Systems ............................................................ 26.4 Summary ................................................................. References .......................................................................
909 910 915 917 924 925
27 Electron and Ion Beam Characterization of Glass Jennifer McKinley ................................................................ 27.1 Electron Beam Techniques .............................................. 27.2 Ion Beam Techniques ................................................... 27.3 Conclusions .............................................................. References .......................................................................
929 931 941 950 950
28 Nuclear Magnetic Resonance
and Electron Paramagnetic Resonance Studies of Glass Josef W. Zwanziger, Ulrike Werner-Zwanziger, Courtney Calahoo, Alexander L. Paterson ........................................................... 28.1 Magnetic Resonance Probes of Glass .................................. 28.2 Theoretical Background ................................................. 28.3 Experimental Details .................................................... 28.4 Magnetic Resonance Studies of Glass.................................. 28.5 Summary ................................................................. References .......................................................................
953 953 954 958 967 984 984
29 Refractive Index of Optical Materials Jean-Louis Meyzonnette, Jacques Mangin, Michel Cathelinaud ............ 29.1 Basic Parameters and Specifications ................................... 29.2 Main Properties of the Refractive Index ............................... 29.3 Measurement of the Refractive Index of Bulk Materials ............. 29.4 Temperature Dependence of the Refractive Index .................... 29.5 Spectrophotometric Determination of Refractive Indices ............ References .......................................................................
995 996 998 1008 1017 1026 1040
30 Neutron and X-Ray Diffraction of Glass Laurent Cormier.................................................................. 30.1 Diffraction by Noncrystalline Materials ................................ 30.2 Complementarity of Neutron and X-Ray Diffraction .................. 30.3 Determination of the Structural Parameters .......................... 30.4 Difference Methods ..................................................... 30.5 Reverse Monte Carlo and Related Methods ........................... 30.6 Case Studies of Glass Investigation by Neutron and X-Ray Diffraction...................................... 30.7 In Situ High Temperature/High Pressure Diffraction .................. 30.8 Conclusion and Perspectives ........................................... References .......................................................................
1045 1046 1051 1053 1054 1057 1061 1068 1083 1083
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Part D
Glass Modelling
31 First-Principles Calculation Wai-Yim Ching................................................................... 31.1 Methods and Approach ................................................. 31.2 First-Principles Calculation for Different Types of Glasses............ 31.3 Conclusions and Future Outlook ....................................... References .......................................................................
1095 1097 1100 1119 1122
32 Molecular Dynamics Simulations of Oxide Glasses Jincheng Du...................................................................... 32.1 A Brief History of MD .................................................... 32.2 Fundamentals of MD Simulations ...................................... 32.3 MD Simulations of Glasses .............................................. 32.4 Applications of MD Simulations in Oxide Glass Research............. 32.5 Outlook and Challenges................................................. 32.6 Conclusions .............................................................. References .......................................................................
1129 1129 1130 1135 1141 1150 1151 1151
33 Machine Learning for Glass Modeling Adama Tandia, Mehmet C. Onbasli, John C. Mauro .......................... 33.1 Data-Driven Glass Research ............................................ 33.2 Development of Data-Driven Materials................................ 33.3 Methods .................................................................. 33.4 Data-Driven Development for Glass Composition Design ............ 33.5 Conclusions and New Glass Research Opportunities.................. References .......................................................................
1155 1155 1161 1166 1171 1185 1188
Part E Glass Processing 34 Industrial Glass Processing and Fabrication Mathieu Hubert.................................................................. 34.1 Brief Overview of Global Glass Production ............................ 34.2 Industrial Glass Compositions and Process Overview................. 34.3 Raw Materials and Batch Preparation ................................. 34.4 Importance of Redox in Glass Making ................................. 34.5 Glass Melting, Fining and Conditioning ............................... 34.6 Industrial Glass Furnaces ............................................... 34.7 Modeling of Industrial Processes....................................... 34.8 Conclusions .............................................................. References .......................................................................
1193 1194 1198 1200 1206 1208 1213 1219 1227 1227
35 Batch Chemistry and Reactions Oscar S. Verheijen, Mathieu Hubert ............................................ 35.1 Overview of the Batch Melting Process ................................ 35.2 Heat Transfer Processes ................................................. 35.3 Different Types of Batch Reactions ..................................... 35.4 Reaction Kinetics ........................................................ 35.5 Silica Conversion......................................................... 35.6 Fining Reactions ......................................................... 35.7 Conclusions .............................................................. References .......................................................................
1231 1231 1236 1239 1243 1244 1245 1254 1254
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36 Glass Shaping Romain Laniel, Mathieu Hubert, Mathieu Miroir, Antoine Brient ........... 36.1 Overview of the Glass-Shaping Process ............................... 36.2 Shaping of Glass at High Temperatures................................ 36.3 Glass Shaping at Low Temperatures ................................... 36.4 Conclusions .............................................................. References ....................................................................... 37 Amorphous Thin Film Deposition Virginie Nazabal, Petr Němec................................................... 37.1 Amorphous Film Processing and Coatings on Glass .................. 37.2 Physical Vapor Deposition .............................................. 37.3 Chemical Vapor Deposition ............................................. 37.4 Comparison of PVD and CVD Techniques ............................... 37.5 Liquid-Based Film Fabrication ......................................... 37.6 Contribution of Amorphous Thin Films and Coatings on Glass to 21st Century Development .......................................... References .......................................................................
1257 1257 1258 1275 1287 1288
1291 1291 1297 1317 1318 1320 1322 1324
38 Sol-Gel Glasses Lisa C. Klein ...................................................................... 38.1 The Role of Sol–Gel Processing in Glass Technology .................. 38.2 Sol–Gel Processing ...................................................... 38.3 Gelation, Percolation and Syneresis ................................... 38.4 Drying and Removal of Solvent and Water ............................ 38.5 Consolidation and Sintering............................................ 38.6 Sol–Gel Fibers, Thin Films and Other Applications ................... 38.7 Organic–Inorganic Hybrid Sol–Gel Glasses ............................ 38.8 Summary and Future Prospects ........................................ References .......................................................................
1331 1331 1333 1337 1338 1340 1342 1345 1347 1348
39 Glass Recycling Ronan Lebullenger, François O. Mear .......................................... 39.1 Why Recycle Glass? ...................................................... 39.2 Recycling Methods for Glass Products ................................. 39.3 Waste Cathode Ray-Tube Glass Recycling: A Case Study .............. 39.4 Summary ................................................................. References .......................................................................
1353 1353 1360 1366 1372 1373
Part F Optical and Photonic Glass Applications 40 Laser Glasses Simi A. George, Joseph S. Hayden .............................................. 40.1 Short Introduction to Lasers ............................................ 40.2 Commonly Used Lanthanide Elements in Glasses for Lasers ......... 40.3 Specification of Laser Glass Doping Level.............................. 40.4 Rules of Thumb in Glass Selection for Performance .................. 40.5 Commercially Available Er3C -Doped Glasses .......................... 40.6 Estimating Refractive Index ............................................
1379 1380 1384 1385 1386 1387 1388
Contents
40.7
Glass Melting and Measurements for Bulk Material Properties Characterization ......................... 40.8 Derivation of Laser Performance Related Properties.................. 40.9 Laser Damage Testing ................................................... 40.10 Storage and Handling of Laser Glass................................... 40.11 Summary ................................................................. References .......................................................................
1389 1391 1396 1399 1399 1400
41 Optical Fibers Thierry Chartier .................................................................. 41.1 Theory of Light Guiding ................................................. 41.2 Fiber Properties.......................................................... 41.3 Specialty Optical Fibers ................................................. 41.4 Applications of Optical Fibers .......................................... References .......................................................................
1403 1403 1413 1424 1431 1436
42 Glass in Integrated Photonics Juejun Hu, Lan Yang ............................................................ 42.1 Processing of Planar Glass Photonic Components .................... 42.2 Integrated Photonics Platforms Based on Glass Materials ........... 42.3 Summary and Outlook .................................................. References .......................................................................
1439 1441 1448 1464 1465
43 Amorphous Silicon in Microphotonics Anuradha M. Agarwal, Jurgen Michel ......................................... 43.1 Amorphous Silicon as a Photonic Material ............................ 43.2 Amorphous Silicon for Photonic Devices .............................. 43.3 Summary ................................................................. References .......................................................................
1481 1482 1485 1489 1490
44 Phase-Change Memory and Optical Data Storage Xiang Shen, Yimin Chen, Guoxiang Wang, Yegang Lv ....................... 44.1 Conventional Ge-Sb-Te Phase-Change Films ......................... 44.2 Phase-Change Behaviors of Doped Ge2 Sb2 Te5 Films ................. 44.3 Doped Sb-Te Films for Phase-Change Memory Applications......... 44.4 Nanocomposite Films for Phase-Change Memory Applications .............................. 44.5 Crystallization Kinetics Studied by Ultrafast Calorimetry for Phase-Change Materials ............................................ 44.6 Phase-Change Materials for Applications in Integrated Photonic Memory ........................................ 44.7 Summary ................................................................. References .......................................................................
1513 1514 1515
45 Display Glass Matt Dejneka, T. J. Kiczenski.................................................... 45.1 Overview of Display Technologies ...................................... 45.2 Display Glass Properties................................................. 45.3 Melting and Fining ...................................................... 45.4 Forming Precision Sheets for Displays ................................. 45.5 Glass Composition .......................................................
1519 1520 1524 1529 1532 1536
1493 1495 1498 1500 1506 1510
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45.6 Three-Dimensional (3-D) Upconversion Displays..................... 45.7 Electronics on Glass ..................................................... 45.8 Flexible Glass and Displays ............................................. 45.9 Conclusions .............................................................. References ....................................................................... 46 Scintillator Glasses Russell Lee Leonard, Jacqueline A. Johnson................................... 46.1 The Scintillation Process ................................................ 46.2 Advantages and Disadvantages of Glass Scintillators................. 46.3 Synthesis ................................................................. 46.4 Basic Characterization of Scintillator Glasses.......................... 46.5 Ionizing Radiation and the Applicability of Scintillator Glasses ................................................... 46.6 Outlook ................................................................... References ....................................................................... 47 Mid-Infrared Molecular Sensing Angela B. Seddon ............................................................... 47.1 Overview ................................................................. 47.2 Chalcogenide Glass Science and Technology Pertinent to MIR Molecular Sensing ................................... 47.3 MIR Molecular Sensing .................................................. 47.4 Progress in Using Chalcogenide Glass Fibers for MIR Molecular Sensing .............................................. 47.5 On-Chip MIR Molecular Sensing Using Chalcogenide Glasses ........ 47.6 Highlights and Future Prospects ....................................... References .......................................................................
1545 1546 1547 1548 1549 1553 1554 1556 1557 1563 1569 1578 1578 1583 1584 1586 1592 1598 1612 1625 1626
Part G Glass for Energy Applications 48 Glass and Coatings on Glass for Solar Applications Ashtosh Ganjoo, James McCamy, Adam Polcyn, Zhixun Ma, Paul A. Medwick .......................................................................... 48.1 Photovoltaics ............................................................ 48.2 Flat Glass for Solar Applications........................................ 48.3 Anti-Reflective Surface Treatments on Glass for Solar Applications ......................................... 48.4 Transparent Conductive Oxide Stacks for Solar Applications ......... 48.5 Glass for Concentrated Solar Power Applications ..................... References ....................................................................... 49 Glass for Thermoelectric Applications António Pereira Gonçalves, Elsa Branco Lopes, Gaëlle Delaizir .............. 49.1 Basics of Thermoelectricity ............................................. 49.2 Key Materials for Thermoelectric Applications ........................ 49.3 Chalcogenide Glasses ................................................... 49.4 Conclusion ............................................................... References .......................................................................
1633 1633 1637 1641 1650 1659 1670 1675 1676 1678 1680 1691 1691
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50 Glasses and Glass-Ceramics
for Solid-State Battery Applications Virginie Viallet, Vincent Seznec, Akitoshi Hayashi, Masahiro Tatsumisago, Annie Pradel ..................................................... 50.1 Principle of an All-Solid-State Battery and Requirements .......... 50.2 Solid Electrolytes ........................................................ 50.3 All-Solid-State Rechargeable Batteries ................................ 50.4 Conclusion ............................................................... References .......................................................................
Part H
1695 1697 1702 1720 1742 1744
Glasses in Art and Architecture
51 Art Glasses Christophe Bardin ............................................................... 51.1 Some Historical Milestones ............................................. 51.2 Art of Glass, Trial of an Artistic Typology............................... 51.3 Thinking Through the Glass ............................................ 51.4 Conclusion ............................................................... References .......................................................................
1755 1756 1764 1770 1776 1777
52 Architectural Glass Jan Belis, Christian Louter, Jens H. Nielsen, Jens Schneider ................. 52.1 Flat Glass Products ...................................................... 52.2 Cast Glass Products ...................................................... 52.3 Glass in Architectural Applications ..................................... 52.4 Connections .............................................................. 52.5 Numerical Modeling of Glass Components ............................ 52.6 Conclusions and Prospects.............................................. References .......................................................................
1779 1780 1796 1798 1806 1811 1813 1813
Subject Index ...................................................................... 1819
XXVII
XXIX
List of Abbreviations
0-D 1-D 2-D 2.5-D 3-D 3-DP 3Q-MAS 3R 5-D
zero-dimensional one-dimensional two-dimensional two-and-a-half-dimensional three-dimensional three-dimensional printing triple quantum MAS reduce, reuse, recycle five-dimensional
A A–A a-Si a-Si:H AB AC ACP ADF-STEM AES AFM AFM AFMI AG AGLAE AIMD AIST ALD ALP AM AM AM AM AMLCD AMOLED AOG AOPDF AOS AP APCVD APD APT AR ASB ASE ASM ASR ASSB ATR AWG
amorphous–amorphous amorphous silicon hydrogen passivation of dangling bonds within amorphous silicon acetylene black alternating current amorphous calcium phosphate annular dark-field scanning transmission electron microscopy Auger electron spectroscopy atomic-force microscopy antiferromagnetism antiferromagnetic insulating Adam–Gibbs Accélérateur Grand Louvre d’Analyse Elémentaire ab-initio molecular dynamics Ag-In-Sb-Te atomic-layer deposition alkaline phosphatase air mass additive manufacturing Avramov–Milchev active material active matrix liquid crystal display active matrix OLED alkali-containing OG acousto-optic phase dispersion filter amorphous oxide semiconductor annealing point atmospheric pressure chemical vapor deposition avalanche photo diode atom probe tomography anti-reflective aluminum–sec-butoxide amplified spontaneous emission asperomagnet alkali-silica reaction all-solid-state battery attenuated total reflection arrayed waveguide grating
AXRD AZS
anomalous x-ray diffraction alumina–zirconia silicate
B BAD BBO BBV bcc BCE BEI BER BGG BGO bIm BL BM BMG bMSC BO BO BO BP BPF BSA BSE BWO BZ
bond-angle distribution BaB2 O4 beam-bending viscometer body-centered cubic before common era backscattering electron image bit error rate barium gallogermanate crystalline scintillator Bi4 Ge3 O12 benzimidazolate bond length ball-milled bulk metallic glass bone marrow stromal cell Bayesian optimization bond order bridging oxygen boson peak band-pass filter bovine serum albumin backscattered electron backward oscillator Brillouin zone
C C2RMF CAD CAD-CAM CALPHAD CaP CAS CASS CASTEP CB CBH CBRAM CC CCD CCRN CCRN CD CE CEC CEM CF
Centre de Recherche et de Restauration des Musées de France computer-aided design Computer-Assisted Design Machining calculation of phase diagrams calcium phosphate Chemical Abstracts Service copper (chloride) acetic acid salt spray Cambridge Serial Total Energy Package conduction band correlated barrier hopping conductive bridging random access memory charge compensator charge-coupled device charge-compensated random network compensated continuous random network Cole–Davidson charge exchange configuration entropy change model correlated electron material color filter
XXX
List of Abbreviations
CFCG CFD CFL CG ChG CIGS CIP CMOS CMR CN CN CNC CNL CNT CNT CO CO-OO COD COF CoLOSSIS COx CP CP CPMD CPV CRG CRN CRT CS CSA CSH CSP CSP CSRO CSTP CT CT CT CTE CTRW CVD CW
continuous filament glass fiber computational fluid dynamics compact fluorescent lamp crushed glass chalcogenide glass copper indium (gallium) selenide cast in place complementary metal-oxide semiconductor colossal magnetoresistance chevron-notched coordination number computer numerical control conical nozzle levitation carbon nanotube classical nucleation theory carbon monoxide charge-ordered and orbital-ordered chemical oxygen demand covalent organic framework Confined Large Optical Scintillator Screen and Imaging System Callovo-Oxfordian coordination polymer cross-polarization Car–Parrinello molecular dynamics concentrated photovoltaics coarse recycled glass continuous random network cathode-ray tube compressive stress chemical shielding anisotropy calcium silicate hydrate concentrated solar power ceramic, stone, porcelain chemical short-range order concentrated solar thermal power charge transfer compact tension central transition coefficient of thermal expansion continuous-time random-walk chemical vapor deposition continuous wave
D DAC DAS DC DC DCB DCDC DCF DEX DFT DFTB DGD DGU
diamond anvil cell dynamic angle spinning direct current dielectric current double-cantilever beam double-cantilever drilled compression dispersion-compensating fiber dexamethasone density functional theory density-functional based tight binding differential group delay double-glazing unit
DGU DLC DLP DM DM DMA DNP DOE DOL DOR DOS DPhDES DPT DQ DQ-DRENAR DRG DSC DT DTA DTGS DVD
double-glass unit diamond-like carbon digital light processing Dzyaloshinky–Moriya dredged material dynamic mechanical analysis dynamic nuclear polarization Department of Energy depth of layer double rotation density-of-state diphenyl-diethoxysilane diffuse phase transition double quantum double-quantum dipolar recoupling effects nuclear alignment reduction dorsal root ganglia differential scanning calorimetry double-torsion differential thermal analysis deuterated triglycine sulfate digital versatile disc
E E-MORB EA EAM EBIC EBSD ECAE ECAP ECR ECR-PECVD ED EDFA EDS EDS EDS EDWA EDX EDX EEC EEE EELS EEM EFG EFISH EFTEM EGA EGFET EIS ELF ELV EM
enriched mid-ocean ridge basalt Edwards–Andersen embedded-atom method electron-beam-induced current electron backscatter diffraction equal channel angular extrusion equal channel angular pressing electron cyclotron resonance electron cyclotron resonance plasma-enhanced chemical vapor deposition electric dipole erbium-doped fiber amplifier energy-dispersive spectrometry energy-dispersive spectroscopy energy-dispersive x-ray spectroscopy Er-doped waveguide amplifier energy-dispersive x-ray analysis energy-dispersive x-ray spectroscopy equivalent electrical circuit electrical and electronic equipment electron energy loss spectroscopy electronegativity equilization method electric field gradient electric field-induced second harmonic effect energy-filtered transmission electron microscopy evolved gas analysis electrolyte-gated field-effect transistor electrochemical impedance spectroscopy energy loss function end-of-life vehicle electromagnetic
List of Abbreviations
emf EML EMT ENDOR EO EoW EP EPMA EPMA EPR EPR EPSR ERD ERDA ESA ESEEM ESEM ESR ETA ETAG ETEM EV EVA EXAFS
electromotive force electromagnetic levitation effective medium theory electron-nuclear double resonance electro-optical end-of-waste electroprecipitator electron probe microanalysis electron probe x-ray microanalysis electron paramagnetic resonance extended producer responsibility empirical potential structure refinement elastic recoil detection elastic recoil detection analysis excited-state absorption electron spin-echo envelope modulation environmental scanning electron microscopy electron-spin resonance European Technical Approval European Technical Approval Guideline environmental transmission electron microscopy electric vehicle ethylene vinyl acetate extended x-ray-absorption fine structure
F FAMOUS FAU FB FBG FC fcc FDA FDTD FE FE FE-SEM FEA FEWS FF FGF18 FIB FID FiM FIR FL FLS FM FO FOG FOG FOM FORS FP
French-American Mid-Ocean Undersea Study faujasites full basis fiber Bragg grating field-cooled face-centered cubic Food and Drug Administration finite-difference time-domain finite element fracture energy field-emission scanning electron microscopy field-emitter array fiber evanescent wave spectroscopy fill factor fibroblast growth factor 18 focused ion beam free-induction decay ferrimagnetism far infrared Fermi liquid fracture limit state ferromagnetism free oxygen fiber-on-glass fiber-optic gyroscope figure-of-merit fiber-optic reflectance spectrometry Fabry–Pérot
FPD FRG FSDP FT FT Ft FTIR FTO FWM
flat-panel display fine recycled glass first sharp diffraction peak fracture toughness Fourier transform Fourier transform Fourier transform infrared fluorine-doped tin oxide four-wave mixing
G G–R GA GB GC GEMT Gen gf GFA GFRP GGA GGA GHG GLAD GP GRIN GROMACS GSST GST GULP
generation–recombination genetic algorithm grain boundary glass ceramics generalized effective medium theory generation gram-force glass-forming ability glass-fiber reinforced plastic generalized Gibbs approach generalized gradient approximation greenhouse gas glancing-angle deposition gutta-percha gradient refractive index Groningen machine for chemical simulations Ge-Sb-Se-Te Ge-Sb-Te general utility lattice program
H HAADF HAP HAP HARP HCA hcp HD HDA HDL HDP HE-XRD HEBS HETCOR HF HIC HIP HiPIMS HiTUS HLW HMF HMFG HMO
high-angle annular dark field high average power hydroxyapatite high-gain avalanche rushing amorphous photoconductor hydroxyl carbonate apatite hexagonal close packed high density high-density amorphous high-density liquid high-density phase high-energy x-ray diffraction high-energy beam sensitive heteronuclear correlation hydrofluoric acid high index contrast hot isostatic pressing high-power impulse magnetron sputtering high target utilization sputtering high-level waste heavy metal fluoride heavy metal fluoride glass heavy metal oxide
XXXI
XXXII
List of Abbreviations
HMQC HN HOIP HOMO HPC HPLC HPPMS HPT HPXRPD HREM HRT HRTEM HS HSQ HSQC HTF HTSC HUP HUVEC HYSCORE
heteronuclear multiple quantum coherence Havriliak and Negami hybrid organic–inorganic perovskite highest occupied molecular orbital high-performance computing high-performance liquid chromatography high-power pulsed-magnetron sputtering high-pressure torsion high-pressure x-ray powder diffraction high-resolution electron microscopy high-resistivity transparent high-resolution transmission electron microscopy hard sphere model hydrogen silsesquioxane heteronuclear single quantum coherence heat transfer fluid high-temperature superconductivity hot uniaxial pressing human umbilical vein endothelial cell hyperfine sublevel correlation spectroscopy
I IBA IBAD IBD ICA ICCD ICME
ion-beam analysis ion-beam assisted deposition ion-beam deposition independent component analysis intensified charge-coupled device integrated computational materials engineering ICP inductively coupled plasma ICP-AES inductively coupled plasma atomic emission spectroscopy o ICP-OES inductively coupled plasma optical emission spectrometry ICSD Inorganic Crystal Structure Database IEP isoelectric point IFS ionic field strength IFT inverse Fourier transform IGF intergranular glassy film IGU insulating glass unit IGZO In-Ga-Zn-O IGZO indium-gallium-zinc-oxide IL ionoluminescence Im imidazolate INADEQUATE incredible natural-abundance double-quantum transfer experiment INS inelastic neutron scattering IO integrated optical IOG integrated optic glass IQE internal quantum efficiency IR internal resistance IR infrared IRO intermediate-range order IS individual section
IS ISG ISPM ISRO ITO IV-CT IVPD IW
impedance spectroscopy International Simple Glass interacting SPM icosahedral short-range order indium tin oxide intervalence charge transfer inside vapor-phase deposition iron-wüstite
J J–O JG JMA JMAK
Judd–Ofelt Johari–Goldstein relaxation Johnson–Mehl–Avrami Johnson–Mehl–Avrami–Kolmogorov
K K–K KCl KDP kgf KOH KWW
Kramers–Kronig potassium chloride KTiOPO4 kilogram-force potassium hydroxide Kohlrausch–Williams–Watts
L LA LA-ICP-MS LAGP LAMMPS LATP LATP LAW LBIC LC LCA LCD LD LDA LDG LDL LDP LDW LED LEFM LGP LGPS LI LIDAR LMJ Ln LO LOF LP LRO LSS
longitudinal acoustic laser ablation inductively coupled plasma mass spectrometry Li1:3 Al0:3 Ge1:7 (PO4 )3 Large-Scale Atomic/Molecular Massively Parallel Simulator Li1:3 Al0:3 Ti1:7 (PO4 )3 lithium aluminum titanium phosphate low-activity waste laser-beam induced current liquid crystal life-cycle assessment liquid-crystal display low density low-density amorphous Libyan desert glass low-density liquid low-density phase laser direct writing light-emitting diode linear elastic fracture mechanics light-guide plate Li10 GeP2 S12 localization index light detection and ranging megajoule laser lanthanide longitudinal optical Libbey–Owens–Ford linearly polarized long-range order limit state scenario
List of Abbreviations
LT LTO LTPS LUMO LVDT
low temperature Li4 Ti5 O12 low-temperature poly-silicon lowest unoccupied molecular orbital linear variable differential transformer
M MA MAD MAE MAF MAS MB MBG MC MCE MCR MCT CT MCVD MD MEMS MG MGI MH mid-IR MIMIC ML MME MMI MNR MO MO MOF MOF MORB MPC MQ MQ MQG MQMAS MRG MRN MRO MS MSD MSVD MTES MYEGA MZI
moving average multi-anvil device mixed alkali effect magic-angle flipping magic-angle spinning minimal basis mesoporous bioactive glass Monte Carlo mixed cation effect multivariate curve resolution mercury-cadmium-telluride x-ray microtomography modified chemical-vapor deposition molecular dynamics microelectromechanical system metallic glass Materials Genome Initiative magnetite-hematite mid-infrared micromolding in capillaries machine learning mixed modifier effect multimode interference Meyer–Neldel rule molecular orbital metal oxide metal-organic framework microstructured optical fiber mid-ocean ridge basalt muscle precursor cell multiple quantum melt-quenched melt-quenched glass multiple quantum magic angle spinning medium recycled glass modified random network medium-range order modified silane mean square displacement magnetron sputter vacuum deposition methyltriethoxysilane Mauro–Yue–Ellison–Gupta–Allan Mach–Zehnder interferometry
N NA NA NAMD NASICON NBF
numerical aperture Néel–Arrhenius nanoscale molecular dynamics Na superionic conductor nonbridging fluorine
NBO NBOHC NC NC ND NDIS NDR near-IR NEB NEP NIB NIL NLO NM NMF NMR NN NNH NNO NNPB NOBEC NODV NOMV NPT NRA NT NTCOP NTOC NYGGP
nonbridging oxygen nonbridging oxygen hole center nanocrystallite network connectivity neutron diffraction neutron diffraction with isotopic substitution normalized dissolution rate near-infrared nudged elastic band noise equivalent power sodium-ion battery nanoimprint lithography nonlinear optical network modifier N-methylformamide nuclear magnetic resonance neural networks nearest-neighbor hopping nickel-nickel oxide narrow-neck press–blow neonatal olfactory bulb ensheathing cell neutral oxygen divacancy neutral oxygen monovacancy constant pressure and temperature nuclear reaction analysis niobium-tellurite normalized thermal changes in optical path normalized thermo-optic coefficient Na1Cx Yy Gaxy Ge2x (PO4 )3
O OADM OCV ODE OES OG OLCAO OLED OM OPA OPD OQMD OSA OSL OTP OTP OVD OVITO O&M
optical add/drop multiplexer open circuit voltage ordinary differential equation optical emission spectroscopy oxide glass orthogonalized linear combination of atomic orbitals organic light-emitting diode optical microscopy optical parametric amplifier optical path difference Open Quantum Materials Database optical spectrum analyzer optically stimulated luminescence o-terphenyl o-terphenol outside vapor deposition Open Visualization Tool operating and maintenance
P PA PASS PBG
pair approximation phase-adjusted spinning sideband photonic bandgap
XXXIII
XXXIV
List of Abbreviations
PBO PBOD PbS PC PC PCA PCA PCD PCF PCL PCM PCT PCVD PDF PDF PDLC PDMS PDOS PDP PECVD PEL PET PFLS PFT PGEC PGF PHEV PhTES PIB PIGE PIXE PL PLD PLE PM PMD PMMA PMT PNP PNR POEC POHC poly-Si PPDF ppm PPV PRAM PRO PS PSB PSF PSL PT PTM PTR PV PVB PVC PVD
partial bond order partial bond order density lead-sulfide principal component partial charge photoconductive antenna principal component analysis perturbed cation distribution photonic crystal fiber polycaprolactone phase-change material product consistency test plasma-chemical vapor deposition pair distribution function planar deformation feature polymer-dispersed liquid crystal polydimethylsiloxane partial density-of-states plasma display panel plasma-enhanced chemical vapor deposition potential energy landscape polyethylene terephthalate post-fracture limit state pulse front tilt phonon-glass and electron-crystal phosphate glass fiber plug-in hybrid electric vehicle phenyl triethoxysilane polyisobutylene particle-induced gamma-ray emission particle-induced x-ray emission photoluminescence pulsed-laser deposition photoluminescence excitation polarization-maintaining polarization-mode dispersion poly(methyl methacrylate) photomultiplier tube Poisson–Nernst–Planck polar nanoregion phosphorus–oxygen electron center phosphorus–oxygen hole center polycrystalline silicon partial pair distribution function parts-per-million parallel-plate viscometer phase-change random access memory producer responsibility organization polystyrene phonon sideband point spread function photostimulated luminescence parity time pressure transmitting medium photo-thermo refractive photovoltaics polyvinyl butyral polyvinyl chloride physical vapor deposition
Q QCL Q-factor QCM QCPMG QED QENS QLED QM QPM
quantum cascade laser quality factor quartz-crystal microbalance quadrupolar Carr–Purcell–Meiboom–Gill quantum electrodynamics quasi-elastic neutron scattering quantum-dot light-emitting diode quantum mechanics quasi-phase-matching
R RBM RBS RCP RCS RDF RE RE REACH REAPDOR ReaxFF REDOR REE REV RF RFDA RGFM RH RI RIE RKKY RLP RMC RMS RMSE RN RNA ROC RP RPL RSF RT RW
random barrier model Rutherford backscattering spectrometry random close packing respirable crystalline silica radial distribution function rare-earth rare earth registration, evaluation, authorization, and restriction of chemicals rotational-echo adiabatic passage double resonance reactive force field rotational-echo double resonance rare-earth element representative elementary volume radio frequency resonance frequency and damping analyzer recycled glass filtration media relative humidity index of refraction reactive ion etching Ruderman–Kittel–Kasuya–Yosida random loose packing reverse Monte Carlo root mean square root mean-square error random network ribonucleic acid receiver–operator characteristic rapid prototyping radiophotoluminescence relative sensitivity factor room temperature random walk
S S=N SA/V SAD SANS SAV SAW
signal-to-noise surface area to volume selected area diffraction small-angle neutron scattering solvent accessible volume surface acoustic wave
List of Abbreviations
SAXS SBA-15 SBF SBS SBW SC SC-M SCCG SCF SCR SCW SDD SE SE SE SEDOR SEI SEM SEPB SERS SF SFF SFM SfP SHG SHGC SHO SIF SiM SIMS SK SLA SLM SLPL SLR SLS SLS SLS SM SME SMF SNB SONL SP SPD SPD SPFT SPM SPM SPr SPS SQ SR SRM SRO SRS SRSO SSB SSD
small-angle x-ray scattering Santa Barbara amorphous-type material-15 simulated body fluid stimulated Brillouin scattering sodium-bearing waste supercontinuum semiconductor metal subcritical crack growth surface crack in flexure selective catalytic reduction surface capillary wave silicon drift detector solid electrolyte secondary electron spectroscopic ellipsometry spin-echo double resonance secondary electron image scanning electron microscopy single-edge precracked beam surface-enhanced Raman spectroscopy strewn field solid freeform fabrication superferromagnet softening point second-harmonic generation solar heat gain coefficient simple harmonic oscillator stress intensity factor sperimagnet secondary ion-mass spectroscopy Sherrington–Kirkpatrick stereolithography spatial light modulator superlinear power law supercoooled liquid region serviceability limit state soda-lime silicate selective laser sintering speromagnet small and medium-sized enterprise single-mode fiber straight-notched beam second-order nonlinear strain point severe plastic deformation suspended particle device single-pass flow through superparamagnetic self-phase modulation stress profile spark-plasma sintering single quantum structural relaxation standard reference material short-range order stimulated Raman scattering silicon-rich silicon oxide spinning sideband subsurface damage
SSE SSE SSG SSGS SSIC SSL ST STE STEM STIM STM STP STZ sub-ppb SUS S=V SVHC SWE SZM SZP
sum of squared error solid-state electrolyte superspin glasses structural sealant glazing systems solid-state ion conductor solid-state laser satellite transition self-trapped exciton scanning transmission electron microscopy scanning transmission ion microscopy scanning tunneling microscopy standard temperature and pressure shear transition zone sub-parts-per-billion structural untreated steel surface area to volume ratio substances of very high concern Schrödinger wave equation surface zone model SnO-ZnO-P2 O5
T TAS TBO TBO TBOD TC TCO TCR TE TEDOR TEM TEOS TEOS TFMG TFT TGA TGU TGU THG THz-TDS TIR TIS TM TM TMA TMAH TMOG TMOS TMS TMT TNM TOC TOF TOSS TP TPA
total alkali versus silica total bond order three-bonded oxygen total bond order density technical committee transparent conductive oxide temperature coefficient of the resistivity transverse electric transferred-echo double resonance transmission electron microscopy tetraethoxysilane tetraethyl orthosilicate thin-film metallic glass thin-film transistor thermogravimetric analysis triple-glazing unit triple-glass units third-harmonic generation terahertz time-domain spectroscopy total internal reflection total integrated scattering transition metal transverse magnetic thermomechanical analyzer tetramethylammonium hydroxide transition-metal-oxide glass tetramethyl orthosilicate tetramethylsilane tetramethyltin Tool–Narayanaswamy–Moynihan thermo-optic coefficient time-of-flight total supression of spinning sidebands triethyl phosphate two-photon absorption
XXXV
XXXVI
List of Abbreviations
TPD TPPI TPV TRAPDOR TrL TRM TSC TSL TSRO TSSA TTT TzH
tons per day time-proportional phase incrementation total pitch variation transfer of populations with double resonance transient lens thermoremanent magnetization thermally stimulated depolarization current thermally stimulated luminescence topological short-range order transparent structural silicone adhesive time–temperature transformation 1,2,4-triazoles
U UD UDR UHV UHV-AFM ULS ULSI UPS URIS UV UV-Vis
unidirectional universal dielectric response ultrahigh vacuum ultra-high-vacuum atomic force microscopy ultimate limit state ultra-large-scale integrated ultraviolet photoemission spectroscopy ultraviolet to infrared refractive index measurement system ultraviolet ultraviolet–visible
V VACF VACSY VAD VAP VAP VASE VASP VB VDOS VDOS VEGF VFD VFT VGCF VGU VGU VHDA VIG VMD VOCS VOY VRH VRH
velocity autocorrelation function variable angle correlation spectroscopy vapor phase axial deposition Volunteer Contribution Point valence-alternation pair variable-angle spectroscopic ellipsometry Vienna Ab initio Simulation Package valence band Debye vibrational density-of-state vibrational density-of-state vascular endothelial growth factor vacuum fluorescent display Vogel–Fulcher–Tammann vapor-grown carbon fiber vacuum glass unit vacuum glazing unit very high-density amorphous vacuum insulated glass visual molecular dynamics variable-offset cumulative spectroscopy voices of youth Voigt–Reuss–Hill variable-range hopping
W W-MYEGA WAT WCMH WCPMG WDM WDS WDS WebFF WEEE WFD WGM WISE WLED WOM WRAP WSTZ WURST
Waterton–Mauro–Yue–Ellison–Gupta– Allan weak absorption tail weak coupling multiphonon hopping WURST Carr–Purcell–Meiboom–Gill wavelength division multiplexing wavelength-dispersive spectrometry wavelength-dispersive x-ray spectroscopy Web Force-Field waste of electrical and electronic equipment Waste Framework Directive whispering-gallery mode wideline separation white light-emitting diode weather-o-meter Waste And Resources Action Programme work for shear transformation zone wideband uniform rate smooth truncation
X XANES XAS XPM XPS XPS XPS XRD XRD XRF XRR XTEM
x-ray absorption near-edge structure x-ray absorption spectroscopy cross-phase modulation x-ray photoelectron spectroscopy x-ray photoemission spectroscopy x-ray photoelectron x-ray diffraction x-ray diffractogram x-ray fluorescence x-ray reflectivity cross-sectional transmission electron micrograph
Y YAG
yttrium-aluminum garnet
Z ZAFO ZBL ZBLAN ZFC ZIF ZT
zero attenuation fiber optic Ziegler–Biersack–Littmark zirconium barium lanthanum aluminum and sodium zero-field cooled zeolitic imidazolate framework zinc tellurite
1
Marie-Hélène Chopinet
Glass production is 5000 years old. Until the 1st century BC when blowing appeared in the Middle East, glass objects were mainly ornaments and small containers for cosmetics. Tiberius created a glass industry in Rome to satisfy the local customers more easily. Very soon, the western European glassmakers learnt to make glass themselves instead of importing ingots and processing them in secondary workshops. The collapse of the Roman Empire did not mean the disappearance of a product that has proved so useful. The art of glass was renewed during the Middle Age: stained glass windows appeared in numerous churches and cathedrals that were built all over Europe. The crusades enhanced the movement with new techniques coming from the East. Glass was still made with sand and a flux but the flux changed from sodium to potassium salts produced by combustion of land plants instead of the Mediterranean coastal plants containing mainly sodium. This composition was still used with a few improvements like purification of the ashes when industrial soda ash was invented at the beginning of the 19th century. The same century saw very important progress in glassmaking and it led to a huge decrease in price to the point where everyone could buy glass panes for their windows at the end of this period. Melting processes were also much improved. Use of coal was common since the 18th century, but the furnaces themselves had not really changed until the Siemens brothers invented the regenerative gas furnace where gas was produced with a gas producer. Ten years later, the tank furnace, a close ancestor of present-day melting furnaces, was introduced. The forming processes had been improved since antiquity but the major changes occurred at the end of the 19th century when the processes were mechanized. As a result, the output increased spectacularly even after the end of the First World War, which took the lives of many glassworkers. Throughout the 20th century, the trend towards automation accelerated and melting tanks were
applied to all types of glass. The middle of the century saw the revolutionary invention of float glass which laid the foundations for the modern glass industry.
1.1 1.1.1 1.1.2
1.1.3 1.1.4
Early Ages: The Invention of Glass ......... The Flux: Alkali Salts ............................. Glass Made in Two Steps, Melting and Remelting Before Processing.................................. The Romans Develop a Real Glass Industry ................ Window Glass.......................................
1.2 1.2.1
Early Middle Ages ................................. Situation in Western Europe After the Collapse of the Roman Empire ............... 1.2.2 Evolution of the Composition of Glass and Choice of the Alkaline Flux .............. 1.2.3 The Melting Process and the Furnace ...... 1.2.4 Window Glass: A Commodity Reserved for Wealthy People .................. 1.2.5 The Emergence of a New Production: Stained Glass Windows.......................... 1.2.6 A New Class of Noblemen, the Glassmakers ................................... 1.3
1.3.1 1.3.2
A New Era, Late Middle Age and Renaissance: 13th to 16th Centuries ........................... Emergence of Venice and its Cristallo in the Luxury Glass Market..................... Development of Glass in Other Parts of Europe ........................
Modern Times: 17th and 18th Century to Beginning of the 19th Century .......... 1.4.1 Use of Coal Instead of Wood in Furnaces: The First Trials in England ...................... 1.4.2 Flint Glass: A Revolution in England ....... 1.4.3 A New Player: Compagnie de Saint-Gobain with a New Process to Make Mirrors........ 1.4.4 Innovation in Container Glass Linked with Champagne Wine Development ......
3 4
4 5 5 7 7 7 8 10 10 10
11 11 11
1.4
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_1
12
12 13
13 14
History
The History o 1. The History of Glass
2
Introduction
History
1.5 1.5.1
1.5.2 1.5.3 1.5.4 1.5.5
19th Century, the Century of Technical Revolutions ..... Raw Materials: From Natural Soda-Ash to Artificial Soda and Sodium Sulfate...... The Development of New Furnaces ......... Progresses in Pyrometry......................... Innovations in Flat Glassmaking Around the End of the 19th Century ....... Container Glass Making at the End of the 19th Century ...............
1.6
16
16 19 24 27 30
Glass has always been the subject of various considerations about its quite special nature and influence on human life. It is interesting to recall an old one and a much more recent one, both providing an overall view of the interaction between glass and the human being. Who, when he saw the first sand or ashes, by a casual intenseness of heat, melted into a ‘metalline’ form, rugged with excrescences, and clouded with impurities, would have imagined, that in this shapeless lump lay concealed so many conveniences of life, as would in time constitute a great part of the happiness of the world? Yet by some such fortuitous liquefaction was mankind taught to procure a body at once in a high degree solid and transparent, which might admit the light of the sun, and exclude the violence of the wind; which might extend the sight of the philosopher to new ranges of existence, and charm him at one time with the unbounded extent of the material creation, and at another with the endless subordination of
The Revolutions of the Twentieth Century ...................... 1.6.1 Mechanization Mainly After the First World War ............. 1.6.2 Window Glass....................................... 1.6.3 Plate Glass ........................................... 1.6.4 Float Glass ........................................... 1.6.5 Container Glass..................................... 1.6.6 Textile Fiber Glass ................................. 1.6.7 Insulation Glass .................................... 1.7 Conclusion ........................................... References.....................................................
Around 2000 BP 500–1000
End of 17th century 19th century 1850–1870 1870–1890 1870–1910 1890–1930 1920–1930 1920–1950 1960
32 32 35 37 38 45 45 46 46
animal life; and, what is yet of more importance, might supply the decays of nature, and succour old age with subsidiary sight. Thus was the first artificer in glass employed, though without his own knowledge or expectation he was facilitating and prolonging the enjoyment of light, enlarging the avenues of science, and conferring the highest and most lasting pleasures; he was enabling the student to contemplate nature, and the beauty to behold herself. [1.1] What is special about glass is that it can provide shelter and storage and combines these and many other practical uses with the ability to extend the most potent of our senses, sight, and the most formidable of human organs, the brains. [1.2]
Glass is a very ancient material. It even exists as a natural one but it is not the subject of this chapter, which will be devoted to the history of its manufacture and uses along the centuries (Table 1.1).
Table 1.1 Milestones in the history of glass manufacturing Dates 5000 BP
32
Types of glass and products Jewels, small containers Blowing process to make containers Flat glass by casting Cylinder technique to make flat window glass Crown glass technique to make flat window glass Crystal glass invention Plate-glass casting New raw materials via chemistry developments Regenerator furnace Tank furnace New process to make window glass and roofing Mechanization of all processes Forehearth in container glass Textile fiber development Insulation glass development Float glass process
The History of Glass
1.1 Early Ages: The Invention of Glass
Glass was developed initially for aesthetic reasons: the most ancient glass objects discovered in excavations, beads for instance, date back to between 3000 and 2000 BC. It appeared most probably accidently as glazing on earthenware in the Middle East between Phoenicia (Lebanon), Syria and Egypt. The legendary Pliny the Elder [1.4] narrated in his Natural History claims that a ship laden with nitre moored upon the coast near the river Belus between Tyr and Sidon
(Lebanon). The Phoenician merchants, preparing their meal on the seashore and finding no stones at hand to hold their cauldrons, used for the purpose some lumps of nitre which they had taken from the vessel. After the fire burnt for the whole night, in combination with the sands of the beach, they observed transparent streams of a liquid hitherto unknown flowing from the hearth: this, it is said, was the origin of glass (Fig. 1.1).
Fig. 1.1 Glass is invented on a Middle-East beach by Phoenician merchants [1.3]
History
1.1 Early Ages: The Invention of Glass
3
4
Introduction
History
1.1.1 The Flux: Alkali Salts The main possible sources [1.5] of alkaline salts available to the ancient glassmaker were: (1) large-scale deposits resulting from the evaporation and drying up of former land-locked seas and lakes, and (2) vegetable matter ash. Deposits from former seas or lakes of interest to the glassmaker are illustrated by the impure carbonate and bicarbonate found in Wadi Natrun, in El Kab in Egypt and in Magadi in East Africa, and by sodium sulfate in Wadi Natrun and other locations all over the world. It is a natural conjecture that natron (nitre in Pliny) from Wadi Natrun may have been used for glassmaking. It had already been used from very early times as a detergent in medicine, and in embalming. Specimens of natron have been found in ancient Egyptian tombs. Analysis of the specimens and of modern soda obtained from Wadi Natrun show that both contain sodium carbonate and bicarbonate up to 95%, sodium chloride up to 40%, and sodium sulfate up to 30%. [1.5] All the ancient Egyptian glasses contain much more potash than can possibly be derived from natron or natural soda (Table 1.2). It shows that alkali derived from plant ash has long been an important ingredient in glassmaking. The alkali referred to in the tablets of Assurbanipal in the 7th century BC is derived from salicornia and the traditional glass-making mixture, sand plus ash, with a few other minor constituents, was essentially the same until the beginning of the 19th century. Plant ashes have over many centuries also been employed in medicines, detergents, and as the source of alkalis for manufacturing operations such as soap making. In the ashes, two kinds of alkaline elements can be found, sodium (soda) and potassium (potash). Plants that grow near the sea or in salted deserts are associated
with relatively high soda content, whilst those from inland region are relatively rich in potash. Nevertheless, the alkali in coastal and marine plant ash is not wholly soda, nor ashes of inland plants wholly potash, which explains the usual mixture of both alkalis observed in ancient glass samples. It is legitimate to deduce that the use of ashes as a flux to make glass might have originated from glazing on pottery. In primitive firing methods, the pots were stacked and covered by the fuel, chaff, straw, reeds, or wood, the ash from which reacted with the clay or siliceous material of the pot. The discovery that a crude glaze was thus produced might have given a natural impetus to further experimentation and initiated the long course of development, which ultimately led to the isolation of the glaze, or glass, as an independent material.
1.1.2 Glass Made in Two Steps, Melting and Remelting Before Processing The earliest glasses were not transparent. In addition to glazing on pottery, glass was mainly used to make replicas of semiprecious stones of various colors. It was processed as beads or as small containers for cosmetics by shaping the glass around a core of sand that is removed after cooling. It was also cast and pressed to make bowls or hollowware. According to Pliny, glass was considered to originate from a region known as Phoenice (present-day Lebanon), close to Judaea (present-day Israel) and enclosed between the lower ridges of Mount Carmelus, a marshy area where flows the river Belus, which, after a course of five miles, empties itself into the sea near the colony of Ptolemaïs. The tide of this river is slow, and the
Table 1.2 Glass compositions of various periods. Most of the glasses contain between 04 % MgO [1.5]
Thebes (1500 BC) Tell El Amarna (1370–1350 BC) Colored opaque Tell El Amarna (1370–1350 BC) Transparent clear Nimrude Assyria (800–850 BC) Babylon (250 BC) Alexandria (100 BC) Roman Salona (2nd century AC) Roman Cologne (1st–5th century) Merovingian (6th century) Reims stained glass (13th century English (16th–17th AC) Modern
Silica SiO2 (wt%) 65 62
Alkaline oxides Soda Na2 O (wt%) 14:3 1419
Potash K2 O (wt%) 2:0 1:57
Calcium oxide CaO (wt%) 6:5 710
Alumina Al2 O3 (wt%) 3:0 1:5
63
2022
0:40:8
79
1
71:5 65:8 68 64:5 67:6 67 54 5665 6874
12:7 12:1 1415:5 17 20 19.3 1:9 0:42 1216
0:9 2:3 0:1 1:5 0:6
4:8 6:6 710 6:8 6:7 7:5 1820 1520 714
0:5 2:1 45 3 3:2 3:2 34 1:2 0:33
1215 512 01
The History of Glass
Therefore, for centuries, glass was produced in primary Middle East workshops, shipped all around the Mediterranean Sea by the Phoenicians, and transformed in secondary workshops [1.6, 7]. This explains why glass has always been recycled throughout history, except perhaps in the middle of the twentieth century!
1.1.3 The Romans Develop a Real Glass Industry Around the first century BC, in the Middle East again, glass blowing was invented. It involved the use of a long iron pipe, which was dipped into the molten glass to gather a lump that was blown through the tube, the blowpipe, at first without a mold. It obviously required a good metallurgical technique, precise knowledge of molten glass behavior, and preparation of glass with reproducible chemical compositions. This new revolutionary technique made transparent thin glass possible and opened up new fields for its uses. This development did not escape the notice of Roman rulers, who were at that time the masters of the whole Mediterranean. Rome was traditionally supplied with glass from Egypt and Syria in large quantities. The emperor Tiberius imported glassblowers from the Middle East in 14 BC, and made them work in the Italian peninsula using crude glass imported from overseas, thus creating a real local glass industry. Very soon, glass was molded and various types of containers and drinking vessels were produced and sold all over the Roman Empire. Over time, Roman glassmakers learned that the sand from the Belus was not the only one which could be used: At the present day, a very white sand good for the purpose can be found at the mouth of the river Volturnus, in Italy. It spreads over an extent of six miles, upon the sea-shore that lies between Cumæ and Liternum, and is prepared for use by pounding it with a pestle and mortar; which done, it is mixed with three parts of nitre, either by weight
or measure, and, when fused, is transferred to another furnace. Here it forms a mass of what is called ‘hammonitrum’ which is again submitted to fusion, and becomes a mass of pure, white glass. Indeed, at the present day, even throughout the Gallic and Spanish provinces, we find sand subjected to a similar process. [1.4]
According to the accounts, the primary melting step was done in Italy. The process was still completed in two phases, one of melting, and one of remelting and working the glass to give it its shape.
1.1.4 Window Glass Casting The Roman glassmakers not only manufactured containers of various sizes and shapes, but also flat glass beginning in the first half of the 1st century AC, as was proven by the finding of window frames and pieces of window glass in Pompeii and Herculaneum excavations [1.8, 9]. The technique was to cast molten glass on a flat slab of stone and spread it as much as possible. The glass was translucent rather than transparent due to its large thickness and relative crudeness. Cylinder Method A second method (Fig. 1.2) to make flat glass emerged around the 2nd century [1.10]: the cylinder blowing method. This process involves blowing a large and long glass bottle and removing both ends. The resulting open-ended cylinder is then longitudinally slit and flattened to produce a rectangular sheet of glass. The details of the method were significantly improved over the centuries to come but its principle remained the same. The molten glass, cooled to the working consistency and kept at this consistency by reheating when required, was blown into a globe and formed into a shape which, when swung from side to side in a trench and upon being further blown, became a cylinder. The ends of the cylinder were subsequently removed. At first the cylinder was slit when still hot using a cold iron and clumsily opened out (or spread) on an iron plate at the mouth of the furnace. Following an improved method which was developed only around the 18th century, the cylinder was allowed to cool down before being slit from end to end with an iron or a diamond cutter. It was then reheated in a special kiln known as a flattening kiln to a temperature at which it could be opened out using a piece of polished refractory called a lagre with little damage to its surface [1.11, p.80]. Crown Method The disk blowing method (crown glass) (Fig. 1.3) appeared later around the 4th century, but became the
5
History
water unhealthy to drink, but held sacred in certain religious ceremonials. Full of slimy deposits, and very deep, it is only during the reflux of the tide that the river shows its sands; which, stirred by the waves, separate themselves from their impurities, and so become clean. It is generally thought that it is the acridity of the seawater that has this purgative effect upon the sand, and that without it no use could be made of it. The shore upon which this sand is gathered is not more than half a mile in extent; and yet, for many ages, this was the only spot that afforded the material for making glass. [1.4]
1.1 Early Ages: The Invention of Glass
6
Introduction
History Fig. 1.2 Flat glassmaking by the cylinder method [1.12]
a)
b)
c)
Fig. 1.3a–c Flat glass by the crown method. (a) Glass blown into a pear shape, (b) after the detachment of the blowpipe a punty is sealed on, (c) the
glass is spun in a flashing furnace
Blowing Tube
Punty
main process in the Middle East and in northern Africa during the 7th and 8th centuries. [1.10] The glass was first formed into the shape of a pear by blowing, heating, and rolling on a polished metal surface (known as a marver). The end of the pearshaped mass at the far end of the blowpipe was then flattened, and an iron rod called a punty was sealed to the center of this flattened surface. The blowpipe was detached and the piece was reheated at a flashing furnace. As the piece began to soften, it was rapidly spun on the punty. Through the action of centrifugal force, the glass was gradually opened out—or flashed—into a flat, circular plate that could extend up to sixty inches in diameter (in the 18th–19th centuries), depending on the rotation speed and amount of glass the gatherer orig-
inally collected on the blowpipe. This plate was known as a table of crown glass. The main advantage of this flat glass manufacturing method is that the glass never came into contact with any surface while it was still in a malleable state. As a result, the glass produced this way claims a remarkable polish and lustrous appearance. Conversely, only small panes could be cut from the circular table, and the central bull’s eye (where the punty was attached) and the selvage at the rim were wasted [1.11, p.51]. The cylinder method remained the cheaper alternative after the invention of crown glass, and both methods were used until the end of the 19th century. The cylinder method is still used in the Verreries de Saint Just in Loire.
The History of Glass
1.2 Early Middle Ages
1.2.1 Situation in Western Europe After the Collapse of the Roman Empire The collapse of the Roman Empire in the 5th century did not mean the complete elimination of glassmaking, simply because glassware was too utilitarian to be forgotten. Even luxury glass was still made on the borders of the Empire that had escaped the invasions from North-Eastern Europe. The idea that glass had disappeared within the Roman Empire was due to the facts that objects were progressively no longer being buried in graves during the first millennium, that glass was being recycled, and that broken pieces were not recovered during early archeological excavations. As a matter of fact, many medieval workshops have now been discovered all over Europe (Table 1.3—data for France). Glassmakers were mobile: they needed sands of good quality as well as large supplies of wood as fuel and possibly also ashes containing alkali in later periods. The need for wood was one of the major reasons to migrate once they had consumed all the local resources.
1.2.2 Evolution of the Composition of Glass and Choice of the Alkaline Flux Until the 9th century, at least in Italy, the glass produced was a soda-lime silica glass. Its composition is quite close to that of a modern glass. It was melted from a mixture of sand (containing impurities such as calcium carbonate, aluminum oxide, and iron oxide) and alkalis from the Middle East (rochetta or polverine, the plant ash imported from the Levant, Syria and Egypt [1.14], which had the advantage of being ex-
tracted from plants very rich in alkaline and mainly sodium salts). Calcium carbonate and aluminum oxide were present in the mixture due to their abundance in the earth’s crust, and were beneficial to glass because they improve its durability. Glassmakers of this period naturally did not understand these effects but optimal batching of raw materials was identified on a trial-anderror basis. As we can see from Table 1.2 [1.5], potassiumbased glasses appeared during the first millennium AD through the substitution of the traditional sodium flux by land plant ashes [1.15], especially in the north of Europe. Those ashes usually contain a few percent of potassium or sodium salts, carbonates, chlorides and sulfates, together with many other trace elements such as alkaline-earth, metal, phosphates, etc. In Mediterranean countries, areas where seawater is particularly rich in sodium salts, glasses were still prepared with ashes (soda ash) of plants growing in saline habitats (e. g., the well-known Barilla from Alicante in Spain, which refers to ashes of Salsola Kali, Salicornia, seaweeds and other marine plants). Seaweeds were also burnt in Brittany or England to prepare a kind of flux, Varech or kelp, which also contains mainly sodium salts, but is of lower quality than the Mediterranean Barilla and was considered to be less efficient to melt sand. Those ashes also contain potassium salts (Table 1.4). Table 1.3 Number of glass workshops discovered in
France dating before the 11th century [1.13] Period Protohistory 1st to 3rd century 4th to 9th century Total
North – 12 8 20
South 1 4 10 15
Table 1.4 Composition of a few alkalis containing ashes where it can be observed that land plants such as the Keli from Syria contains sodium and that marine plants such as seaweeds contain potassium [1.5] In wt% Sodium carbonate Sodium hydroxide Potassium chloride Potassium sulfide Calcium carbonate Calcium phosphate Magnesium carbonate Carbon Potassium sulfate Sodium sulfate Sodium chloride Sodium sulfite
Kali or ash from the Syrian desert plant Chinane 45 2:5 4:5 3:0 34:0 4:0 1:0 1:0
Kelp (combustion of seaweeds in Orkneys) 5:3
Varech (combustion of seaweeds, France 19th century) 09:5
19:3
4:120
6:4 10:5 6:8 4:5 3:6 26:5
18:641:5 030:9 2950:7 014:9
History
1.2 Early Middle Ages
7
8
Introduction
History
In other districts closer to forests, potash glasses were melted with additions of ashes from land plants like ferns, or from trees such as beeches. These two plants are the most often cited in the literature but many others were experimented with as well to determine their fluxing potential towards local sand (Table 1.5). The choice of raw materials for the glass composition was entirely empirical and dependent on the local resources, which is well exemplified in Agricola’s book published in 1556: To make glass, fusible stones are used and concrete ‘sucs’ which have a natural affinity with these stones. Among fusible stones, are preferred those which are white and transparent. That is why the first choice between them is crystal rock. The second choice is stones that do not have the same hardness but are nevertheless white and transparent. The third choice is stones that are neither white nor transparent. First they are burnt, ground and sieved in order to obtain sand. If river sand is available glassmakers are dispensed of calcination and sieving. Among the concrete ‘sucs’ the first rank goes to nitre, the fossil salt comes next. If neither is available, it is possible to use the leached salt obtained from the ashes of Anthyllis or any other plant containing salt. Some people place the last one on the second rank. . . Those who have no salt take two parts of oak, beech or pine ashes added with sea-salt. [1.16]
The resulting glasses were strangely similar, apart from the alkaline element used (sodium or potassium). This can be easily explained by the fact that glassmakers had two opposite aims: (1) melting in the furnace they have at moderate temperatures and keep it in working order as long as possible, (2) and introducing a minimum amount of flux to reduce the price and the work needed.
The result is that they usually arrived at similar ratios between sand and flux as being the best compromise. The compositions are quite often not so far from the present-day ones, for similar reasons. Mixture of both types of glass (sodium and potassium) can be found in excavations due to recycling of old local glass or glass coming from other countries, a practice which never ceased. Glass compositions remained of this type until the beginning of the 19th century, with or without purification of the flux, depending on the skill of the glassmaker and on the quality of the production his market needed. Agricola indicated that a purified form of flux could be obtained by extracting the water-soluble alkaline salts from the ashes, separating them from the alkaline earth or metal salts polluting the raw material for glass melting. Earlier in the period, the purification process remained the secret of some glassmakers, especially those of Venice [1.16].
1.2.3 The Melting Process and the Furnace The most important supply glassmakers needed was fuel, or more exactly at that time, wood. Until the end of the 19th century and the invention of the Siemens furnace, the consumption of fuel was 3 to 7 times more than the amount of glass melted (compared to 1=10 in modern times!). The melting process and working of the glass were usually done in the same place, and no longer in separate primary melting workshops and secondary rework shops. However, the melting process was very often carried out in two steps because the raw materials require a prereaction before being introduced into the final pot. The prereaction step, known as fritting, is necessary to obtain a glass of reasonable quality at the rather low temperatures accessible in the furnaces. The fritting process was still used, especially in container glass, during the 19th century for very difficult types of glass.
Table 1.5 Composition of land ashes [1.5] Ashes (%) Beech trunk Beech branches Beech leaves Oak Apple tree Fern Rush Willow Heather Barley straw
0:55 1:23 3:05 0:51 1:1 5:89 4:56 3:85 3:61 4:39
Chemical composition of ashes SiO2 CaO MgO (wt%) (wt%) (wt%) 5:4 56:4 10:9 9:8 48 10:6 33:8 44:9 5:9 2:0 72:5 3:9 2:7 70:9 5:5 6:1 14:1 7:6 11 9:4 6:3 71:4 6:0 1:3 35:2 18:8 8:3 53:8 7:5 2:5
Na2 O (wt%) 3:6 2:4 0:7 3:9 1:9 4:6 6:6 0:26 5:3 4:6
K2 O (wt%) 16:4 13:8 5:2 9:5 11:8 42:8 36:6 8:6 13:3 21:2
P2 O5 (wt%) 5:4 12:2 4:7 5:8 4:5 9:7 6:3 2:1 5:0 4:3
SO3 (wt%) 1:8 0:8 3:6 2:0 2:7 5:1 8:8 2:8 4:4 3:6
Cl (wt%)
0:3
10:2 14:2 2:2
The History of Glass
backside of the furnace, an orifice allows the heat to be passed to the third furnace, the annealing chamber. When there were only two furnaces and no furnace in which to conduct the first melting process, the glassmakers introduced the mixture of raw materials into the pots once they had finished working. It melted during the night with boys coming to maintain the fire with dry wood. In most workshops, while blowing was going on, other pots in the same furnace contained the mixture of raw materials currently melting for the next day’s work. If only one furnace was present, it had three chambers. The upper chamber was dedicated to cooling of the glass products and was not directly heated, only by the lower chambers. The furnaces were made from unfired, sun-dried bricks of refractory clay. Their construction was a rather complicated process even though no furnace lasted more than a few months before deteriorating too much and having to be rebuilt. The pots were also made of clay and their appropriate fabrication represented a large part of the technical skills required to be a glassmaker.
Fig. 1.4 Visit of the Venice Doge to a glass-making factory showing the glass-making furnace and the glass workers
(from L. Figuier, Les merveilles de l’industrie, around 1870)
9
History
Georg Agricola (1494–1555) explained that some glassmakers had three furnaces, a fritting furnace for prereaction, a glass-melting furnace, and the last one being what we would call the annealing lehr [1.17]. The raw material mixture was first fired in the vaulted fritting furnace, until it partly melted and eventually became a partially glassy material. It was extracted and broken after cooling down in order to be introduced into the pots already set in the melting furnace after having been heated up in the fritting furnace. The second furnace, the melting furnace was generally circular (Fig. 1.4), some ten feet in diameter and eight feet high. It consisted of two chambers, one for the fire (in the lower part) with a narrow orifice in the front to introduce wood into the firebox. In the middle of the vault of this lower part was a large round hole allowing the passage of flame into the upper chamber. Openings were created in the walls around the upper chamber. The larger ones were used to load the preheated pots into the chamber around the flame hole, whereas the smaller ones were designed for the workers to take gatherings of molten glass in the pots. On the
1.2 Early Middle Ages
10
Introduction
History
1.2.4 Window Glass: A Commodity Reserved for Wealthy People The Romans had made use of glass to enclose buildings. Logically, in the northern countries, glass should have been widespread to protect from the cold while letting light enter houses. However, it seems that glass was reserved for churches and a handful of rich people but did not reach the largest part of the population. Many quotations indicate that the use of sheet glass in dwellings was not common even in the 14th century or even later. For instance, in the counts of the silver of the kings of France in 1554, one can read: two yards of oil cloth with which was made a window frame set in the room of the queen in the castle of Melun, plus four chassis of wood to be arranged with paper on the windows of the said room and oil to cover them to make them clear. [1.17]
“In the 18th century, there still existed in Paris a job consisting in setting oiled paper in windows”, and as late as 1897, Henrivaux recalled that the paper window pane “begins to be unknown in our villages and the glass-mounted print replaces the rustic image glued to the wall”, illustrating the fact that window glass for everybody was a nineteenth century advance.
1.2.5 The Emergence of a New Production: Stained Glass Windows The Middle Ages are widely known for the huge number of churches that were built across Europe, most of them being decorated with stained glass windows. These windows were apparently produced mainly using the cylinder method, at least in Western Europe. Stained glass production began well before the end of the 1st millennium AD. Even if traces of it are rather rare nowadays, what is left is unquestionable. Progressively, as careful (because glass is not always immediately visible and has often been missed in the past) excavations are made on various sites, the flat glass-making landscape of those early centuries is revealed. Until the 7th century (perhaps as early as the 5th century in some places) only white glass was used in church windows and possibly rich settlements. Greenish white stained glasses dating back to the 7th and 8th centuries were found for instance in Notre-Dame de Bondeville, in Normandy, in Ile-de-France, or in the east of France. They are not yet painted but sometimes color appears and their manufacture is more sophisticated. Well-known examples of stained glass windows during the later period around 800–820 include those of the Abbey of San Vicenzo in Volturno in Italy, and at
the monastic sites of Jarrow (682–870) and Monkwearmouth in England. These glasses are not painted and not colored, except when recycled glass from the Roman period was used [1.18]. In the 8th century, it is evident that painted stained glass, a new step in the evolution of stained glass, had been developed. The main discoveries were made in Saint-Denis Abbey and in Normandy. The paint was a kind of enamel, usually dark brown or black, obtained from a mixture of pigments (ground copper or iron oxide), a frit (powdered glass), and a mixture of various substances (wine, urine or vinegar, and gum Arabic) as the medium. This paint was applied on the glass and the enamel was fixed by firing the glass in an annealing furnace around 600 ı C. By 1000 AD painted glass is mentioned quite frequently in church records [1.2, p. 20]. It was the Benedictine order in particular that gave the impetus for window glass. Churches used glass as a way of glorifying God and became involved in actual glass window production in their monasteries, injecting huge amounts of manpower and money into its development. The demand for colored glasses increased significantly during the period of Gothic cathedrals in the 11th and 12th century and reached its peak in the 14th and 15th centuries. This later history is much better documented than that of the 1st millennium, as it is still possible to see today the production of the glassmakers of the Middle Ages in cathedrals and churches all over Europe despite wars and destruction. Some of the largest cathedrals even had their own glass workshop operating on-site during the construction. Just as any other craft, glassmaking organized itself during this period into corporations.
1.2.6 A New Class of Noblemen, the Glassmakers Glass production underwent major changes during this period, perhaps not much from the technical point of view but its organization was transformed. During the 10th and 11th centuries, noblemen were granted special privileges by the European kings to make and trade glass without being deprived of their status as nobility. They were also granted relief from various taxes that further helped them to refill their treasury emptied by the Crusades. From another point of view, the production of glass in Europe was somehow enhanced during this period with the pilgrims bringing back beautiful objects as well as secrets from Constantinople and the Middle East glassmakers. It also means that glassmaking skills were increasingly passed down only in specialized glassmaker families.
The History of Glass
1.3 A New Era, Late Middle Age and Renaissance: 13th to 16th Centuries
At the end of the Middle Ages, with the onset of the Renaissance, many crafts experienced a boost to innovations and glass manufacturing and processing was not an exception.
1.3.1 Emergence of Venice and its Cristallo in the Luxury Glass Market During this medieval period, the Venetians had been well known for their glassware since the 13th century. The Venetian republic had wide connections with the East Mediterranean countries where luxury glass was still manufactured. From Constantinople where the glass tradition had been preserved, particularly for mosaics, came the renewal of the art of glassmaking. Venice possessed everything that was necessary to make glass: the very islands on which the city stood were composed of silica-rich sand. Beech forests on the Istrian Peninsula across the gulf of Venice provided the best fuel for the furnaces fires and, perhaps more importantly, as a skillful trader, the city was equipped to ship its production to the richest and most distant markets. The Venetian glassmakers discovered quite early how to purify the ashes by leaching the alkaline salts in water: this efficiently reduces the content of insoluble alkaline-earth elements and iron oxide, the main residual coloring agent of glass, giving its usual green color. Thus, they specialized in very clear glass, which referred to crystal rock which represented the archetype for whiteness in everybody’s mind. They called it cristallo and that was to be the name of various kinds of glasses as pure and white as crystal rock in the future. The secrecy that surrounded the making of Venetian glass was almost as strong a factor in its success as the beauty of the glass itself. The Venetian glassmaker was a master craftsman and a master at intrigue. Those who were not glass-workers came to believe that the glassmakers had knowledge of processes as mysterious as those of the alchemists. A glasshouse was therefore often regarded with the frightened awe that other people might have for houses they thought to be haunted by ghosts (Fig. 1.4). But in 1291, even the most careful restrictions—and the nervous caution of the public towards the risk of fire, related to the presence of glass furnaces—seemed inadequate to protect the secrets of the Venetian glassworkers. Consequently, the authorities decided that all the glassmakers would be moved into a single place, onto the island of Murano where they could be more
carefully guarded. For a long period, heavy penalties were still inflicted upon those who went abroad and taught their art to foreigners. Despite those precautions, Venetian glassmakers were able to escape their prison-island and proceeded to spread throughout Europe, not only the basic techniques that had survived in spite of history, but the tools and the very broad knowledge of Venice inherited from the east. Venice, which seemed everlasting until the middle of the 15th century, saw her trade strongly weakened by the Turks at sea on one hand and by the French on land on the other. By the beginning of the 17th century, Venice was rapidly losing her once magnificent role as maker of the world’s finest cristallo. There were other important glass-making centers in Italy [1.2, p. 23], particularly the northern town of Altare. Although smaller than those of Murano, the Altare works were particularly influential because their policy was to spread their techniques as widely as possible, rather than retain them as trade secrets as the Muranese attempted. Therefore the Italian techniques, as well as the glass itself, spread out throughout Western Europe, particularly beginning in the 16th century.
1.3.2 Development of Glass in Other Parts of Europe European glassmakers migrated frequently. The owner of a glasshouse would close up his workshop and move elsewhere because the local fuel supply had dwindled, because he had been offered subsidy somewhere else, or just for the love of traveling, being sure that he would have no difficulty to find work wherever he might go. Bohemia was the first to win a great reputation as a glass center, even before the fame of Venice began to decline. A local glass industry was created in the 13th century by Venetian glassmakers and was encouraged during the 16th century by the Bohemian rulers. Apart from the Venetian-type crystal, its specialty was gold ruby glass. Similar types of glass were made in many different parts of Europe: French, Dutch, Flemish, German, or Spanish glasses were largely the same, their specificity being more in uses and therefore in shapes and colors than in the nature of the material. In every country, for instance, drinking habits strongly influenced glass production. The only major variation was the type of ashes, either sodium-containing from marine plants or potassium-containing from terrestrial plants, obviously depending on the situation of the glass workshop.
History
1.3 A New Era, Late Middle Age and Renaissance: 13th to 16th Centuries
11
12
Introduction
History
1.4 Modern Times: 17th and 18th Century to Beginning of the 19th Century Many important evolutions characterized this period. In particular, a real glass industry was developed all over the European continent. These advances were largely due to the beginning of a real scientific mind and improved analysis of the problems, even if the most important revolutions in this domain were to occur in the 19th century. The raw materials were chosen with more care, the glass composition was more stable, the glassmaker dynasties were in place which brought about better transmission of glass-making skills, furnaces were more efficient, and transportation of men and merchandize was faster despite the numerous wars.
1.4.1 Use of Coal Instead of Wood in Furnaces: The First Trials in England By the early 17th century [1.11, p. 34] in England, attempts were already made in metallurgy to separate the coal from the iron ore by using the reverberatory principle of furnace design. In this type of furnace, the fuel and the ore are kept apart, and the flames were made to strike back from the arched roof of the furnace upon the materials to be smelted. The reverberatory furnace was found to meet the glassmaker’s needs. Using certain types of coal, and placing a cover over the pots, the batch could melt without filling the molten glass with impurities. By the early months of 1612, green glass for windows was being imperfectly made at a coal-fired furnace in Southwark. The new furnace and glasshouse design differed from its predecessors (Figs. 1.5 and 1.6) because it incorporated a long, underground tunnel feeding fresh air from outside the glasshouse to a grate for the coal in the center of the furnace. As this would often make the grate too long, a dividing wall (bridge) was built in the center of the trench, supporting the inner ends of the grates (Fig. 1.6). The furnace itself was built over this central grate in the shape of an inverted funnel with a curved crown to reflect the flame from the fire down on to the pots that were arranged around the waist of the furnace on a circular course of brickwork, or on two longitudinal ones on both sides of the grate in a rectangular furnace. This masonry part was called the siege or bench [1.19]. The pots were often covered to protect against soot, smoke, and black drops which fell from the crown. In the case of British window glass production, it was common practice to construct the outer building in the same shape as the furnace itself, in this case, a circular one.
With the appearance of the new furnace, which allowed use of a cheaper kind of fuel, the days of wood firing were numbered. The end came more rapidly than C Pot
A
B
Central trench
D
Crown
Working hole
Pot
A
B
Pot
C
D Sieges
Fig. 1.5 Wood-fired furnace (after [1.19])
Crown
Pot
Grate
Fig. 1.6 Coal-fired furnace (after [1.19])
The History of Glass
1.4.2 Flint Glass: A Revolution in England Glassmakers (and their customers) have always been attracted either by brilliantly colored glass or by very white glass similar to crystal rock. For years or centuries, new mixtures had been experimented with to find a glass as pure as the Venetian cristallo. About the year 1675, George Ravenscroft’s ingeniousness produced England’s famous “flint” glass by additions of more lead oxide than what had ever been done before. Chemically, this glass is based upon the usual potassium silicate glass with calcium oxide being replaced by lead oxide, most probably because the British Isles have always been a place for lead mining, at least since the Roman times. This new glass proved to be easier to work and engrave which allowed the production of very ornate glassware welcomed by the wealthy English upper class. Despite all its advantages, the continental glassmakers did not immediately embrace this new production: they were producing white cristallo glass themselves thanks to the very pure sand found in the north of Europe and the knowledge learnt from the Venetians. Lead crystal would only cross the Channel around one century after its discovery. Nevertheless, in time, English lead crystal, which lent itself so admirably to the production of high lustre and brilliancy when decorated by cutting, proved to have a greater attractiveness than the lime glass made
in Venice. From this time the fate of the Italian industry was sealed, and as the 17th century drew to a close, Venetian glass import into England declined.
1.4.3 A New Player: Compagnie de Saint-Gobain with a New Process to Make Mirrors The fame of Venetian glass was due not only to the cristallo glassware, but also to mirrors popular among all the aristocracy in Europe. In 1634, Louis XIII published the following edict: E. de Grammont and J.A. d’Anthonneuil travelled in foreign countries, and stayed there for several years, and searched secrets and rare and useful inventions, unknown in our realm, and concerning particularly the making of mirrors, their cutting and polishing; they are said to have succeeded so well that their work is beautiful, skill-rich and useful, the more so as the manufacturing of mirrors being not yet realized in France, is reserved to the Venetians who are the masters for this production and sell it at high prices in our realm, from where a lot of money escapes, which would not have happened if the manufacture was established in France [. . . We] allow them to establish in this city of Paris a manufacture making plate glass for mirrors . . . with special prerogative for a few years. [1.17]
It was only in 1665, during the reign of Louis XIV, that Colbert created the Manufacture Royale des Glaces with an impressive series of financial (the Manufacture was a privately owned company) and honorific (royal coat of arms on its gate, livery of the gate-keeper) privileges. In 1672, Colbert announced to his royal master: “Our mirrors are now more perfect than those of Venice.” [1.17] The manufacturing process relied on cylinders produced in Normandy (Tourlaville) with the silvering being made in Paris. The mirrors of the Galerie des Glaces in Versailles were made by this method in 1685. Why did the French glassmakers have such difficulties in making this glass with the same method as was used to make window glass? Mirror plate glass was made thicker than the window glass so that it could bear grinding, using sand, and polishing, using rouge (iron oxide), by which means an even, lustrous finish was imparted [1.11, p. 41]. While window glass was increasingly used during the 17th and 18th centuries, plate glass remained a luxury product. Only the purest ingredients, the best soda and lime, and thoroughly washed white sand, went into the manufacture of this kind of glass, and the whole batch was
13
History
even the most pessimistic would have ventured to forecast. On May 23, 1615, King James I passed a sort of death sentence on furnaces using wood. Anxious to preserve the forests, he decreed that, in future, glass was to be made in coal-fired furnaces. The control of the furnaces was already in the hands of those who held Letters Patent for their use. By the royal proclamation of 1615, the patentees were given monopolistic control not only of the furnaces but of the industry as well. One of them was Sir Robert Mansfield (or Sir Robert Mansell as he came to be known) and he soon bought out the other partners and thus gained absolute authority over most of the glass industry in England. From this time, English glassmakers and, later, their continental counterparts began to seek sites for their furnaces elsewhere than in forests, in places where coal was available. This was a major change in the glassmaking preoccupations. It was the birth of the glass industry in the North-East of England, near Newcastle, which became a great center for the manufacture of English window glass. The problem of plate glass was different because it was a different market and it has to be close to its customers, not too far from London or other big cities, for instance.
1.4 Flint Glass: A Revolution in England
14
Introduction
History
very carefully prepared and fritted before being placed into the melting pots. Being thick glass, any discoloration was readily noticeable. Any spots in the glass itself or unevenness of the surface meant that these glasses, chiefly used for mirrors, would fetch much lower prices. The emphasis, therefore, was always upon high quality. Although plate glass was made with much purer materials than window glass, the glassmaker manipulated his molten glass in much the same way when making both varieties. In both cases he blew the glass into a cylinder, which he slit along its length and then flattened out into a pane. This method had serious disadvantages, the main being the limit imposed upon the size: the cylinder could not be blown more than one meter long without a loss of thickness that would make grinding impossible. This disadvantage could however, be overcome if the glass, instead of being made into a pane via a cylinder, was cast straight on to a flat table, rolled out and allowed to cool. The resulting glass would not be transparent, but the usual finishing processes of grinding and polishing would remove these defects. Bernard Perrot, in Orléans, was probably the inventor of the process. As a result of his work, several Frenchmen, acting through Abraham Thévart, were granted Letters Patent in December 1688 which gave them a monopoly of plate-glass manufacture by the casting process for the French home market and later for export as well. They went to Saint Gobain where wood was plentiful and cheap as the Société des Grandes Glaces. The new company competed with the Manufacture and eventually threatened its life as the new process was able to produce plate glass of much larger size. In 1695, Louis XIV decided that the two companies were to merge: the new Company took the name of Manufacture des Glaces de France, which was to become much later Compagnie de Saint-Gobain. It kept using both methods of manufacturing plate glass until the 19th century when glass blowing was eventually abandoned. Plate glass (Fig. 1.7) was made by pouring the molten glass onto a large iron casting-table, and rolling it by means of a heavy iron roller driven by two workmen. The thickness of the plate was defined by the use of two iron slips laid along the edges of the table on which the roller rested. Thus, by using slips of different depths, glass plates of varying thickness were obtained. To adjust the width of the plate and to prevent glass from flowing onto the sideslips, two guides of cast-iron were set upon the table at the required distance apart. These guides were shaped to fit the front of the roller and were driven forwards by the roller, so determining
the width to which the glass spreads during the rolling process [1.20, p. 468]. After casting, the plate was cooled down in special kilns (carcaise) and polished. In this method, three distinct processes were carried out, grinding, smoothing, and the final polishing operation. The first two were identical in character, and consisted in rubbing down the surface of the glass with flat plates of iron, using sand as an abrasive. In grinding the main part of the excess glass was removed by the use of coarse sand, whilst finer sand grains employed in the smoothing process served to eliminate the larger defects left by the coarser particles preceding them. After grinding and smoothing, the glass surface had a dull grey appearance. Polishing consisted in rubbing tools shod with felt over the surface of the glass, iron oxide (rouge) being used as a polishing agent. While the first two operations removed large amounts of glass from the plate, the last actually took away nearly no material, but served to level the undulations, producing the smooth surface characteristic of plate glass [1.20, p. 475]. In theory, the casting process was far more straightforward than the complicated method of making a flat pane of glass by way of a cylinder. In practice, however, casting, grinding, and polishing required a large capital outlay. Instead of the small customary glasshouse, a large casting hall was needed, complete with an extensive melting furnace in the center, a number of sizeable annealing ovens around the walls (one for each plate made), a casting table upwards of 3 meters long and 2 meters wide, and cuvettes in which the molten glass could be transferred from the furnace to the casting table together with a crane to carry them. There was also the machinery required for grinding and polishing as well as the warehouse accommodation [1.11, p. 44]. It explains why Saint-Gobain did not have many competitors for a long time.
1.4.4 Innovation in Container Glass Linked with Champagne Wine Development Champagne wine appeared during the reign of Louis XIV with Dom Perignon, a monk of the Abbey of Hautvillers near Epernay [1.21]. Its particularity is to be aged directly in the bottle, at least since 1759, which leads to the pressure rising inside the container because of the carbon dioxide emitted during fermentation. Around this time, nearly half of the bottles broke during the process, making champagne a very expensive wine. The champagne industry therefore demanded bottles with much more mechanical resistance. Before the 19th century, the main quality of bottles was their strength. “As soon as they were of a neat
The History of Glass
1.4 Flint Glass: A Revolution in England
brown or green color, not cloudy, and without too many bubbles, the color intensity did not really matter” [1.19]. This color depended largely upon the nature of the raw materials, which in turn depended on the situation of the glass factory. Thus, near big cities, new ashes were used as well as charrées, the product of the leaching of wood ashes by laundry women. The other materials were sand that could be yellow, more or less clay containing, and crude soda ash from seaweeds. When the sand was very siliceous, clay was added. When sand and clay contained only a small proportion of limestone, chalk was added. Finally, broken bottles and residues from the fabrication could be part
of the mixture. Obviously bottle glass was not of the best quality compared to cristallo! The improvement of the Champagne bottle initially came from the improved regularity of its thickness, which was better mastered by the glassmakers and resulted in better mechanical resistance. The improvements in the glass composition did not occur until the end of the 19th century. No real evolution occurred as far as the container glass process is concerned until the beginning of the twentieth century and the beginning of mechanization: a semiautomatic process in 1895 and automation (feeder + machine) in 19151920.
History
Fig. 1.7 Casting plate glass (A. Bitard, Les arts et métiers illustrés, around 1890)
15
16
Introduction
History
1.5 19th Century, the Century of Technical Revolutions The end of the 18th century saw many evolutions in the sciences and thus the 19th century brought many important innovations in glassmaking.
1.5.1 Raw Materials: From Natural Soda-Ash to Artificial Soda and Sodium Sulfate Lavoisier died at the end of the 18th century but he had introduced the main laws of what we would now consider as real chemistry, beginning by weighing whatever entered a crucible, but also the results of the chemical process. More rational experimentation led to better controlled raw materials and glass. Soda in the 18th Century, a Variable and Expensive Product Before the French revolution, sodium carbonate or soda ash was prepared by means of the calcination of marine plants containing sodium as various salts, tartrate, oxalate, and chloride. The name soda comes from that of a family of plants, for instance salsola soda. The best soda ashes which came from Alicante (Spain) were called Barilla, because of the local name of the plant, barilla. The content in sodium carbonate was very variable in the ashes. Since chemical analysis was impossible at the time, the glassmakers usually had an empirical method to judge their quality: in addition to color, “he added the smell and the taste to determine their causticity which had to be frank and stinging without bitterness.” A small piece was put on his tongue to judge if it did not smell of sulfides, the sign for a bad quality soda ash [1.19]. The usual impurities in this natural raw material were alkaline salts soluble in water like sulfate or chlorides, calcium or magnesium insoluble salts, or charcoal coming from the calcination. Charcoal was partly eliminated by the fritting step that contributed to a faster melting operation because decarbonation and dehydration took place during the first firing. It also extended the life of the furnace. The drawbacks of natural soda inspired glassmakers and their suppliers to find a way to obtain a more stable flux. It began by the systematic purification of the natural soda ash and resulted in the invention of an industrial method to manufacture sodium carbonate from sodium sulfate. A third step was the discovery that sodium sulfate and even sodium chloride could be used as fluxes in glassmaking. The last step was the invention of Ernest Solvay, producing sodium carbonate directly from sodium chloride at the end of the nineteenth century (1865).
The Initial Improvement: Soda Ash Purification Venetian glassmakers knew how to obtain purer soda ash by water extraction. Pierre Delaunay Deslandes, the new manager of Saint Gobain factory, for plateglass manufacture, adopted this process in 1758. He obtained a much more stable and purer raw material, which considerably improved the quality of plate glass. In parallel, he observed that he had to compensate the CaO content in his glass brought by the unpurified soda ash by addition of limestone. He said in his memoirs: Lime was used in plate-glass fabrication without knowing; no attention was paid to the fact that natural soda ash contained more than half earth matters which, after having spent a considerable time in fritting furnaces had acquired the properties of lime. [1.22]
The experimental method used by Deslandes is interesting: “he took leached soda ash, fritted it to discolor it, made comparative mixture with this frit and with lime and observed that the result was the same.” [1.23] The comparative test was most probably the workability of the glass, as the viscosity of glass is highly dependent on its composition. Then he tried the stone with which lime was made, the limestone and found no difference. He does not indicate why, at this point of his trials, he did not perseverate in this direction and definitely adopted limestone instead of lime. We have to imagine that, his furnaces being less efficient than the modern ones, they needed a already prepared element instead of a product which had to be decomposed.
However, slightly later on, Deslandes understood that the unfritted mixture melted just as well as the fritted composition and he stopped this operation. This text is quite interesting: it illustrates the experimental process by trials and comparisons used at that time when no analytical process was available, and also shows that Deslandes was familiar with the chemical knowledge then available: water solubility of alkaline salts, filiation between CaCO3 , CaO and Ca(OH)2 , even if he did not have any conceptual tool to explain the reactions. It also brings to light the regularity problem related to the flux supply. Beside the supply security, the import of soda ashes from Spain was very expensive for French companies. In fact, the French Science Academy proposed a prize in 1775 for the solution to the transformation of marine salt (NaCl) into sodium carbonate without any success.
The History of Glass
Invention of Artificial Soda Ash According to P. Flamm, Chemistry had identified that marine salt, so widely spread on the earth, was a combination of two simple bodies, chlorine linked to soda. Hence it was natural that researches would deal with this so abundant salt, in order to find an economical process to isolate soda. [1.24]
This innovation was partly brought about for political reasons [1.19]. Until then, the price of natural soda alone had not been a sufficient incitement: the French science academy proposed a prize but France continued to give each year to Spain 20 to 30 millions of francs for the soda ash supply. The Revolution war having arisen, imports of soda ash and potash were hampered (by the continental blockade) and all the potash that France was producing was immediately consumed by saltpeter and powder manufactures. The ‘Comité de Salut Public’ in 1793, ordained that the most exact indications should be given about all the soda ash manufactures.
It was only then that the method to prepare soda ash advantageously from marine salt or rock salt was determined [1.12]. Nicolas Leblanc, supported by the Duke of Orléans, had invented a process to manufacture artificial soda ash in 1791 and the factory worked without interruption until November 1793 when the Duke of Orléans perished on the scaffold. His assets were sequestered, the factory was stopped, and the equipment sold. When the decree of the Comité de Salut Public was announced, Leblanc allowed the publication of his process, until then kept secret. The only reward he obtained was the restitution of the Saint Denis factory without any financing to make it work. Tired of his attempts to obtain justice, Leblanc committed suicide in January 1806 [1.9], but his invention remained. Artificial soda ash is obtained by calcination of a mixture of sodium sulfate, coal and chalk. . . . The exact mixture is introduced in an elliptical furnace at a temperature slightly higher than cherry red, the mixture is stirred every quarter of an hour. In time, the matter becomes thicker. Then it is
worked with an iron rod and extracted. This matter is artificial soda ash. [1.24]
According to Louis Figuier: It would be nearly impossible to estimate exactly the immense gains that industry made thanks to the discovery of Nicolas Leblanc, who made possible to extract soda ash from sodium chloride contained in sea-water. Whence did Nicolas Leblanc draw the countless riches with which he blessed Europe? From the application of a chemical fact the announcement of which would not have needed four lines in a scientific publication of the period, the decomposition of marine salt by chalk at high temperature. [1.9]
The artificial soda ash, richer in sodium carbonate than the natural soda ashes, but containing inconvenient impurities like calcium sulfide was used initially for container and sheet glass, but not for plate glass. However, producers rapidly managed to purify it and, in 1868, they were able to make a product containing 95% to 97% of sodium carbonate. In 1810, the soda ash manufacture was sufficient for all the needs of French industry: a decree of 11 July prohibited the import of foreign soda in France. At the same time, the Compagnie de Saint-Gobain, not being able to find a suitable supplier for its plate glass, decided to manufacture its own soda ash, on the site Charles-Fontaine bought for this purpose. In 1823 the soda factory was transferred to Chauny. The Direct Use of Sodium Sulfate or Sodium Chloride as a Flux One of the drawbacks of the Leblanc process is its cost. Glassmakers explored the use of the chemical precursor of sodium carbonate, sodium sulfate and even sodium chloride. In 1810, Clément Desormes from Saint-Gobain patented two processes, one of them using sodium sulfate and sodium chloride (sodium “muriate”) and the second, simply sodium chloride, which gave no interesting result, but indicated a trend. A fundamental chemical problem had to be overcome: in the beginning of the 19th century, sodium sulfate was not considered as a possible flux because unlike sodium carbonate, it does not easily combine with silica. In 1813, the German chemist Gehlen determined how to successfully use sulfate directly in furnaces, mixing it with limestone and coal [1.25]: For 100 of silica. 33 to 40 of sodium sulfate are necessary, 20 to 40 of calcium carbonate or its
17
History
By the time of the French Revolution, the problem of the flux supply had been plaguing the French glass industry for many years, for both technical and economical reasons.
1.5 19th Century, the Century of Technical Revolutions
18
Introduction
History
equivalent quantity in lime, from 1:65 to 2 of ground anthracite or 2:30 to 2:80 of charcoal.
tween silica and sodium chloride, which is difficult at high temperature.
Despite the success of Gehlen’s method, at first, manufacturers were not allowed, at least in France, to sell it because the government dreaded that sodium chloride, highly taxed, could be extracted from it. When it had been well-proved that sodium chloride produced from sodium sulfate would be much more expensive than marine salt, the government decided at last, in 1824, to allow the sale of sodium sulfate. It was first used to make sheet glass in Prémontré (Aisne). However, at first they fritted the mixture of sand, sulfate, chalk, and coal. Its use was very soon extended to other sheet glass manufacturers and even to half-white glass tableware fabrication. The use of sulfate for plate glass met a huge problem: the resulting glass was slightly green. Theoretically, there was no reason why the glass would not be as clear as with sodium carbonate. Chemists imagined that the light color obtained could be attributed to a reaction of part of the coal on soda ash. Gay-Lussac himself, who for several years was president of the Board of Saint-Gobain, was sure that, for this reason, it would be impossible to substitute sulfate for carbonate in plateglass manufacturing. It was Pelouze who corrected this error: in the 1850s, being convinced that the mixture of pure raw materials should yield a clear white glass, he determined that the color was due to a small quantity of iron oxide. As sand and lime used in Saint Gobain were free from iron, he looked more precisely at the sodium sulfate manufacturing process for a source of iron. Firstly, he discovered that, sodium sulfate usually contained a slight excess of sulfuric acid which reacts with the iron-rich clay of the pot. Secondly, that iron oxide came mainly from the bottom of the furnace where marine salt was decomposed by sulfuric acid, and remained in the sodium sulfate in more or less large proportions. Pelouze worked out the purification of sulfate and could entirely replace sodium carbonate by sodium sulfate in the plate-glass fabrication. This brought about large savings which allowed producers to drastically decrease the price of plate glass. (2.06 versus 4:63 F=m2 for the raw materials in 1868, the price of sodium carbonate being 5 times that of the sulfate) The bottle glassmakers, looking at whatever savings they could make, used sodium chloride together with sodium sulfate as soon as the end of the eighteenth century during the French revolution when sea salt was no longer taxed. The process included a previous fritting of the whole or part of the mixture and it seems that the incorporated water was enough to help the reaction be-
When sea salt was taxed again, container glass producers obtained from the government that a half decomposed salt would be processed for them, containing roughly half sulfate and half chloride, which is much cheaper than pure sulfate and could be advantageously used in bottle manufacturing. [1.19]
This product was used until the next generation of furnaces appeared, the Siemens regenerative tank furnaces, which were corroded too rapidly by chlorides. A New and Last Evolution: The Solvay Process The Leblanc process provided relatively expensive sodium carbonate, so that chemists persevered in their efforts to find a cheaper process. The ammoniac process was theoretically known since 1811, but devising an economical industrial process was difficult. E. Solvay, in Couillet, Belgium, used it for the first time in 1865. In this process sea salt is treated by ammonia, then by carbon dioxide, produced by limestone decarbonation, to yield sodium bicarbonate and ammonium chloride. When heated, bicarbonate yields carbonate. One of the advantages of this process is that ammonia can be recycled by reaction between ammonium chloride and limestone. Therefore, the process is economically more favorable and the sodium carbonate much cheaper. In spite of the fact that the sodium carbonate produced with the Solvay method was much cheaper, the substitution of sulfate by carbonate took a long time: partial substitution trials after 1887, in Saint Gobain plants, did not give any positive results [1.23]. One of the particularities of the sulfate glasses is their chemical activity at high temperature which leads to the liberation of gas at high temperature, which is useful for homogenization. This degassing happens either when the temperature is increased by spontaneous reduction of sulfate into sulfite, or, at lower temperature, following stirring with a wood rod or a potato, both being reducing agents which produce the same result. It is called maclage or shearing. A healthy boiling is obtained, which improves the homogeneity and the refining of the glass, but which also presents problems with installations. Shearing is not used everywhere with the same intensity; some plants use it as a help without decreasing the heat in the furnace; others, and especially those which have less strong pots, reduce heat and use this process, the chemical reduction of
The History of Glass
A too violent foaming induces an accelerated wear of the pots, and glassmakers always tried to obtain the same effect without heating too much or even without foaming, despite the fact that some work from the glass seems to be essential for homogenization. The economic advantage of Solvay carbonate did not allow the glassmakers to escape the question of replacing sulfate by carbonate in the beginning of the 20th century. In 1906, in the Montluçon plant of Saint Gobain, trials were conducted with carbonate and it was concluded that carbonate glass could not be refined at the usual temperature of furnaces, but that, if a small amount of sodium or calcium sulfate was added, it refined all right and that sulfuric acid seemed to have a real influence on the glass melting. [1.23]
In 1922 the Society of Glass Technology had discussions about the advantages and drawbacks of the use of sulfate and carbonate as raw materials in glass batches [1.26] “Should window glass made with sodaash be inferior to window glass made with salt-cake (sodium sulfate)?” It would seem apparent that the use of soda-ash as a constituent of the batch is less corrosive on the tank-blocks. Turner added: he hoped that someone might have referred to the difference in the working properties between glass produced from soda-ash and salt-sake containing batches? [1.26]
The viscosity is the same, but he understood the consensus of opinion among manufacturers of window glass was that the batch which contained at least a proportion of salt-cake was preferred, mainly because the glass, although being somewhat less fluid, had apparently a longer viscosity range. The salt-cake glass was often spoken of as being ‘sweeter.’ [1.26]
Hodkin added: “the salt-cake glass was a more readily worked material.” Rees mentioned: “the ordinary glass bottle-maker undoubtedly seemed to prefer glass which contains some salt-cake.” Dr. Travers said that when the glass-makers were unanimous in making a statement, there must surely be something definite about it, and although their mode of expressing
it might be somewhat puzzling to the man of science, the latter must make his business to try to find some explanation. [1.26]
Mr. Barker thought that “sweetness” in glass was closely associated with its homogeneity. It was possible to get a greater degree of homogeneity with a salt-cake batch than with soda ash. A thoroughly homogeneous glass could be blown out better, and because of this it was referred to as “sweeter.” Nevertheless, in 1927, W.E.S. Turner could say [1.27]: the weekly tonnage for some tanks has, since 1916, been increased six-fold. The four most important factors that have brought about this enormous advance are not directly associated with furnace design. They are: (1) the substitution of salt-cake by soda ash in glass batches, (2) the general reduction in the lime content employed and increase of the alkali content, (3) improved mixing of the batch, (4) the use of automatic machines. . . . Although in one or two instances the advantages of soda ash were recognized and employed before the war, the substitution of soda ash for salt-cake began to occur generally in this country about 1916/1917, and it would not be exaggerating, I think, to say that this change led to a speeding up of melting of quite 40 per cent.
This analysis did not escape the glassmakers, and the result was the usual glass batch with sodium carbonate, mixed with sodium sulfate to enhance its homogeneity, which they are still using today, one century later.
1.5.2 The Development of New Furnaces C.W. Siemens had invented a new process, combining a gas producer and regenerators [1.28, 29], and the first patent was taken in England in 1857 [1.30]. The fundamental idea was to make use of the enormous amount of heat lost up the chimney to preheat the ingoing combustion air and the gas [1.19]. The Regenerative Furnace A chamber full of bricks (Fig. 1.8) stacked to have as many interstices as possible between them is placed between the furnace and the chimney: the burnt gases release their heat in this chamber, the temperature decreasing towards the other end nearer to the chimney. After half an hour a valve is changed to close off the chimney and another one opened to allow the external air into the chamber: the air will be heated when flowing through the chamber previously heated and will reach the combustion chamber at high temperature.
19
History
sulfate inducing a sufficient degassing effect without the need to heat. [1.23]
1.5 19th Century, the Century of Technical Revolutions
20
Introduction
History
Fig. 1.8 The Siemens pot furnace
with regenerative chambers. Arrows indicate the circulation of gases: on the right, hot combustion gasses from the furnace, heating the right side regenerator; on the left, air and gas are heated when circulating through the previously heated chamber (after [1.12])
Pot
Regenerative chambers
Table 1.6 Number of Siemens regenerative pot-furnaces
built or ordered in 1863 [1.31] Great Britain Germany France
4 furnaces (Chance – Birmingham) 2 furnaces (British Plate Glass works – St. Helens) 1 furnace (Stevenson & Co – Glasgow) 2 furnaces (Siemens – Dresden) 2 furnaces (Broederson & Co – Hamburg) 2 furnaces (Montluçon) 5 furnaces ordered (Saint-Gobain)
At the same time other valves led the exhaust gases into a second set of chambers filled with bricks during another period of half an hour and the valve is reversed. This process saves a large part of the energy necessary to heat the fuel and the air up to the furnace temperature, and the furnace itself can more easily reach a higher temperature. Gas Producer. Beside the regenerative furnace principle, the process used gases produced by the partial combustion or distillation of coal, realized by the admission of steam and of a quantity of air insufficient to produce perfect combustion in the gas producer (Fig. 1.9). The Siemens system thus consists in removing the coal or other solid fuel from the furnace by supplying the furnace with gas and air already heated to a high temperature. Development of the Regenerative Furnaces. In England, a first regenerative glass furnace was built in Rotherham in 1860 to melt lead glass. In 1861, a new British patent was obtained (22 January) with special application to glass melting [1.28].
Chance Brothers in England were the first to decide to build a Siemens regenerative furnace to make window glass (cylinder method): the furnace, ready by the end of 1861, was quite successful. In 1862, they adopted the Siemens principle for three other sheet glass furnaces, and in 1863, for another two (Table 1.6). At this time, C.W. Siemens also had an address in Paris and took charge of the realization of the drawings and plans of the ordered furnaces and supervised the operation [1.31]. The royalties, calculated so as to represent 12 to 14 per cent of the profits registered during the application of this process, were to be paid by annuities, or all at once by a reasonable compensation. In 1862 (17 December), Saint-Gobain paid 200 000 francs for five plate-glass pot furnaces: three for SaintGobain, one for Cirey, and one for Mannheim. A first furnace was built in the Halle-Neuve in Saint-Gobain and blessed on May 21st 1863 by Mgr. Christophe, bishop of Soissons and Laon [1.23]. A Cost-Effective Process. The Saint-Gobain Glacerie of Cirey had its 16-pot gas regenerative furnace at the end of the next year (1864). This furnace consumed only 48 kg of coal per square meter of plate glass, representing 50% savings on fuel consumption compared to the previous furnaces without regeneration chambers, and produced 5793 m2 of plate glass in 33 castings. The application of the regenerative heating process, together with a gas producer brought substantial savings compared to direct coal-heating but moreover allowed the furnace to reach higher temperatures and consequently notably increased glass quality. The Siemens regenerative pot furnace of the first generation kept many characteristics of the older tradi-
The History of Glass
1.5 19th Century, the Century of Technical Revolutions
Fig. 1.9 Siemens gas producer
(after [1.20])
Coal
Air water
tional furnaces (Fig. 1.8): the burners were set in the siege, where the grates were previously placed, i. e., at each end of the trench, one or two meters from the wall. Gas and air arrived vertically in the furnace. The first furnace of Saint-Gobain (Aisne) was for 20 pots, 9 on each side and one at the wall. Its laboratory was 8:37 m long, 3:5 m wide, and 1:85 m high. The regenerative chambers situated under the furnace were 3:5 m long, 1:1 m wide, and 2:3 m high. Those first furnaces were progressively modified, with the help of Siemens, until they achieved a satisfactory design. For instance, the distribution, as well as the geometry, of the burners along the axis or in the corners, was studied so as to increase the homogeneity of the heating to obtain the same advancement of the melting process in all the pots along the furnace. The bottom was cooled by air circulation. These furnaces lasted 16 to 18 months. The success of the Siemens regenerative pot furnace was quite fast in England, France, and Belgium despite the fact reported by Bontemps that the operation of these furnaces was more difficult than that of the traditional furnaces. In the US, the first regenerative pot furnace was built in 1865 (O’Hara Glass Works, Pittsburgh, PA). Heat Transmission: Radiation Furnaces In 1884, Frederic Siemens published his paper about a new way to heat gas regenerative furnaces [1.31]: In all the types of furnaces designed until now, it was always considered that the first condition
of success was to make the heating chamber as small as possible, so that the flame can be in very close contact with the inside walls of the furnace, and more especially with the matter being heated. Lately M. Frederic Siemens asked himself if this design was correct and, after long and serious experiments, he convinced himself that the furnaces have to be designed so that the flame only radiates its ‘caloric’ on the matter to be heated and does not come into close contact with them. Having the flames travel horizontally above the melt and relying largely on radiant transfer decreased batch carry over and volatilization from the melt. In the furnaces he is now constructing, the gas and air inlets, instead of being placed so that the flame impinges on the batch placed in the furnace, are situated at a small distance of the crown of the heating chamber, and also of the walls of this chamber, so that gas and air, after the inflammation, have a large space for their combustion and for the free development of the flame. When there are crucibles they must be set with enough space between them so that the radiating heat has free access all around them. In gas regenerative furnaces, the temperature of the flame is sufficient to heat by radiation: the matters absorb most of the heat thus produced, and, consequently, there is no reason not to increase the laboratory of those furnaces. Experience shows that large fuel savings can be made and in many cases, indirect savings also come from the increased yield and the increased quality of the
History
Gas exhaust
21
22
Introduction
History
metal produced without contact with the flame. Finally furnaces have a much longer life.
(Essentially due to less volatilization from the batch— Fig. 1.10; see the new position of the burners.) New Design of the Furnace and Gas Producer System. The main characteristic of those furnaces is the position of the burners horizontally in the walls of the combustion chamber (Fig. 1.10). Two other changes were also proposed for the “Four Siemens Nouvelle disposition” [1.32]: to put the gas producer close to the furnace itself and have regenerators only for the air, the gas being directly injected in the furnace without being heated and burned in the regenerative chamber.
was melted much better in radiation furnaces but that the crown was too low and thus was attacked, at least in the Saint-Gobain-type furnaces, which still had a very low crown height at this time. In 1896, the following conclusions were drawn:
The new furnace is much smaller, usually half the old one, meaning considerable savings on the building cost. The savings on fuel can be evaluated between 25 and 30% compared to the first furnaces.
Data about the yield in these furnaces can be found in a Saint-Gobain document of 1911, where Mr. Boudin, the manager of the Saint-Gobain factory had to justify his yield compared to that of other Saint-Gobain factories: it was 0:4 t=day m2 in Saint-Gobain (Aisne), 0:48 t=day m2 in Montluçon and 0:36 t=day m2 in Pisa: this is not so far from what is done today! In 1893, a comparison was made between the traditional furnaces with burners in the siege and the new ones with burners in the wall [1.23] (Table 1.7). From those results one can draw the conclusion that the glass
Gas
Gas
Air
Air
The fuel consumption is the same. Until the beginning of the twentieth century, the Saint-Gobain plate-glass pot furnaces like the tank furnaces still had a regenerator chamber for gas, though it was smaller than that for air. A Revolution: Regenerative Tank Furnaces As Michael Cable said, the regenerative tank furnace (Fig. 1.11) was the greatest advance in glass technology since Roman times [1.28]. Siemens’s patent of 1870 reveals that the Siemens brothers were not sure of the possibility to use real tanks without pots. In the 1872 Pot
Crown
Gas
Furnace life: The burners in the walls are more advantageous. They are easily accessible, easier to maintain. Less deposits in the regenerative chambers: they last longer, the crown is less attacked. Pots are less violently attacked and the attack is more uniform among them. The refractories of the burners absorb a large quantity of heat and the beginning of the melting process is long and thus very regular. Glass quality: The old furnaces gave a good quality for a short period. Then the combustion was no longer optimal and the quality decreased. In a furnace with burners in the walls, the quality is more constant.
Cooling of the furnace bottom
Gas Regenerator chambers
Fig. 1.10 Siemens radiation pot furnace: Air and gas arrive into the furnace through the ports, alternately from left to right and right to left as the currents are reversed. Note the position of the ports above the melts and parallel to the vault (compare with air and gas coming upwards in Fig. 1.8). (After [1.20])
The History of Glass
1.5 19th Century, the Century of Technical Revolutions
Burners in the siege 2386 2405 2772 1.01 1.16
Number of plate-glass casting Number of unmolten sand particles Number of crown stones Number of sand stones per plate Number of crown stones per plate
Beaudoux burners in the wall 2432 460 5358 0.19 2.20
Fig. 1.11a,b Old Siemens crossfired (side-port) tank furnace ((a) cross section, (b) plan view) (after [1.20])
a) Siemens cross-fired furnace Air–gas burners
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Working holes ][
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To the chimney ][ ][
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Working area
Melting area
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b) Siemens cross-fired furnace front view
Crown Glass
Air reg.
Gas reg.
Gas reg.
patents, however, the use of pots had been forgotten in favor of tanks. The Siemens Brothers now had to solve the various problems due to inadequate refractory blocks. The first company to try the tank furnace was Pilkington Brothers. In May and July 1872, Windle Pilkington missed five successive Pilkington Board meetings.
Air reg.
The minutes record that he was in Switzerland, but he had also gone to Germany [1.11]. On his return, at a Board meeting held on July 10th, it was decided to put a continuous tank on the cylinder place upon the principles of the one that he has seen working at Dresden.
History
Table 1.7 Quality data comparisons between traditional furnaces and the new ones. Defects in plate glass melted in furnaces with burners in the siege (traditional) and in the wall (radiation furnace) [1.23]
23
24
Introduction
History
In April 1873, blowing of sheet glass began and an enthusiastic entry in the minutes on the 17th records that the metal at first was slightly seedy from the cullet but had continued to improve and at the present moment is beating any pot-furnace on the ground . . . Consider that we ought to seriously discuss the advisability of getting the patent secured to us by Siemens for our special use and will see Siemens if all be well next week
This exclamation was followed by 3 months silence, without a word about the tank or about negotiations with Siemens, until July 21st when the next reference occurs. Then, on August 14th the tank began to make glass “for the second time.” Obviously, soon after April 17th, something happened to the first attempt, which suddenly quenched the partner’s initial enthusiasm. What went wrong at the first attempt? James Taylor, then a young man working in the laboratory later recalled that the tank only worked one week before the bottom was eaten through; the metal leaked and set the place on fire. Nothing further was heard of this experiment for several months . . . The first tank failing at the end of the first week, MM Pilkington decided to abandon, but after several Board meetings and Mr. Windle Pilkington stating that, if they would not make another attempt, he would secure a piece of ground himself and erect one on his own account, they then gave way and agreed to another trial where he succeeded [1.33].
sides are worn thin, less glass is put in lest the sides should burst. The sides require renewal every 3 or 4 months. If they last 4 months it is good working. The bottom of the tank needed renewing every 10 or 11 months. In each case these renewals took about three weeks.
In May 1877, 12 tanks were at work and more were being built. The number of furnaces was so large that the Siemens Brothers agreed to receive royalties at a lower rate than the four shillings per ton of finished glass that they usually charged, itself much lower than the five shillings royalty on their pot furnaces. In the Compagnie de Saint-Gobain, the new tank technology was not perceived as being able to melt good quality plate glass. It was possibly the same at Chance & Co where rolled plate-glass production was fast increasing compared to the traditional window glass blowing. The first tank furnace was finally built at Saint Gobain to produce thin rolled glass No. 4 (see below for the development of this new production) in Saint-Gobain (Aisne) in 1881, in Stolberg in 1884 and a second furnace in 1888 (end-fired furnace). Their characteristics were close to our present-day furnaces: the superstructures and the tank itself were separately supported, room was provided under the furnace in case the bottom wore out because of the molten glass. Table 1.8 gives the characteristics of all the tank furnaces in use in 1913 in Saint-Gobain: New factories had been settled in Spain and Germany since the end of the nineteenth century [1.23].
1.5.3 Progresses in Pyrometry In fact, at the second attempt, the tank ran nonstop for 97 days. In the original version the side walls and crown of the furnace had been built on top of the side-blocks holding the molten glass. When the furnace bottom wore out, the whole furnace collapsed. In the second attempt they were independently supported. Having built one successful tank, Pilkington began to substitute tanks for pots at a rapid rate. A second tank was in use in February 1874. At the end of August 1876, there were nine tank furnaces in operation and the ground was being cleared for a tenth. Chance & Co. “anxious to find out every detail about their rival’s progress,” [1.33] kept a record of statements made by anyone who came to them from St Helens. Early in 1877, they had the information that Pilkington was at that time using tanks nine feet wide and 36 feet long whereas formerly their tanks had been 12 feet wide and rather shorter in length. These held 20 600 of melted glass when the tank is new. When the
In 1782 Wedgwood observed that ceramic products often have their beauty or value considerably depreciated by too much or not enough heat during the firing process [1.34]. What is more, with no determination of the conditions of firing, the artists could not use even their own experiments to improve their production. This problem was quite true as well for glassmaking where temperature is as important as in ceramics. One of the major innovations in the 19th century was the measurement of high temperatures. Wedgwood created a very simple pyrometer which used clay retraction during firing. It consisted of refractory clay cylinders and could be used to indicate the reproducibility of the temperature from one experiment to another. Instead of following the variations in dimension of a crystallized material like clay, the progressive melting of a partly vitreous body can be used to indicate temperature. Lauht and Vogt in the Manufacture de
The History of Glass
1.5 19th Century, the Century of Technical Revolutions
Furnace Saint-Gobain 1
Surface (m2 ) 61
Depth (m) 1.2
Saint-Gobain 2 Montluçon 1 Montluçon 2 Stolberg 1 Stolberg 2 Mannheim 1 Mannheim 2 Pise 1 Pise 2 Arija Altwasser 2 Altwasser 41 Altwasser 42
37 46 49 52 34 42 24 34 46 19 30 48 30
1.4 1.25 1.6
Bilin Dux
50 84
1.2 1.2
1.25 1.2 1.33 1.45 1.65 1.2 1.35 1.3 1.35
Number of burners and distribution 1 at the doghouse 5 side port 3 side port 4 side port 4 side port 4 side port 3 side port 5 side port 2 side port 2 end port 5 end port 2 side port 4 side port 2 end port 2 side port 2 end port 4 side port 6 side port
Sèvres developed this idea, before 1882. They established a series of small prisms constituted of various mixtures presenting variable melting points, adapted to the Sèvres porcelain manufacture. Seger, the manager of a ceramic research laboratory in Berlin published in 1886 a paper where he presented a series of montres fusibles covering the range between 600 and 1800 ı C every 25 ı C. In the continuous furnaces they could be introduced into the furnace during the firing. A Scale for Temperature Since Wedgwood, many scientists tried to measure high temperatures although not very successfully. Until the end of the 19th century the confusion was considerable. For instance, the estimated temperature of a steel furnace varied, following the operator and the system he used, between 15002000 ı C, that of the sun between 10001 000 000 ı C! H. Le Châtelier explained the major difficulty of the problem: to measure a length or a weight is to count how many unit bodies have to be added to make an equivalent either of the length or of its weight of the
Air chamber volume (m3 )
Gas chamber volume (m3 )
22 47 45 20
16 23 31 17
27 35 27 21 20 26 27
17 16 26 14 14 18 16
30 38
24 34
studied body. This idea supposes two physical laws: equivalence and additivity. The first law is respected by temperature, but the second one is not. It is possible to identify the temperature by comparison with that of a chosen body but temperature is obviously not additive. Consequently, temperature has to be determined by the measurement of a phenomenon varying with temperature; for instance, the expansion of mercury counted with reference to the temperature of ice melting, with a unit equal to 1=100 of the expansion between the melting temperature of ice and its boiling temperature at atmospheric pressure. Four data have to be chosen to define temperature: the phenomenon, the body, the origin of the scale, and the unit. Consequently the number of thermometric scales is unlimited and very often the scientists chose their own as the best. For instance, a few thermometric scales are given in Table 1.9. The enormous differences that could be found in the literature of this period were mainly due to the choice of a scale rather than to problems of measurement. In order to escape this confusion, a unique temperature scale
Table 1.9 Thermometric scales [1.34] Authors Fahrenheit Réaumur Celsius Wedgwood Pouillet Thermodynamic scale Siemens
Underlying phenomenon Expansion Expansion Expansion Permanent contraction Expansion at constant pressure Reversible heat exchange Electrical resistance
Material Mercury Mercury Mercury Clay Air Any Platinum
Origin/zero point Hard winter Ice Ice Dehydration Ice Zero heat Ice
Unit 1=180 1=80 1=100 1=2400 1=100
History
Table 1.8 Tank furnaces working in Saint-Gobain in 1913 according to Document Saint-Gobain Archives
25
26
Introduction
History
Table 1.10 Fixed points used to establish the thermometric scale [1.34] Melting Boiling
Sn 232
Naphthalene
Zn 420
218
S
Sb 630
Al 655
445
Zn
Ag 962
Au 1065
Pt 1780
930
Table 1.11 Color of bodies versus temperature Color Red beginning Dark red Beginning cherry red Cherry red Light cherry red
Temperature (ı C) 525 700 800 900 1000
had to be chosen: at the end of the 19th century, it was that of the gas thermometer. Their expansion was large enough to be very precisely measured. A reference gas pyrometer using the measure of the pressure change of a gaseous mass maintained at constant volume was designed. (Pouillet, Becquerel, Saint-Claire-Deville). Its volume and fragility made it unsuitable for everyday measurements. It was only used to scale other pyrometers. The reference thermometer chosen by the International Bureau of Weight and Measures (BIPM) to define the practical scale of temperatures was the hydrogen thermometer, at constant volume and loaded with gas at 1000 millimeters of mercury pressure at the temperature of melting ice. Practically, at high temperatures, nitrogen is easier and its expansion is quite close to that of hydrogen. Any other pyrometer can be used as soon as it has been scaled with this thermometer. According to Le Châtelier, the fix points that could be used for the indirect scaling of a thermometric range were the ones shown in Table 1.10. Invention of the Thermocouple Becquerel, Barus, and Le Châtelier invented the electrical pyrometer at the end of the 19th century. It used the measurement of the emf (electromotive force) developed by the temperature difference between two similar thermoelectric soldering joints. This pyrometer was widely used in laboratories and factories. Becquerel used the discovery of Seebeck (1830) to derive this pyrometer, with a platinum/palladium couple. Le Châtelier restudied the problem to solve errors observed which were due to the lack of homogeneity of some metals and their oxidation at high temperature. The best couple he chose was Pt=Pt C 10% Rh, rhodium being possibly replaced by iridium. This pyrometer was not robust enough to be used in factories at this time [1.17] (contrary to what is done at present in modern installations).
Color
Temperature (ı C) 1100 1200 1300 1400 1500
Dark orange Light orange White Soldering white Blazing white
Optical Pyrometer The use of radiation emitted by glowing bodies to evaluate the temperature was not new at the end of the 19th century: in all periods, glassmakers driving their furnace took those emissions into account and their optical variations, intensities, color. For instance, Pouillet established a scale with reference to the air thermometer [1.34] (Table 1.11). In 1859, Kirchhoff showed that an incandescent body emitted radiation, the intensity of which increases with temperature, and that the maximum of intensity goes from red to blue in the spectrum when temperature is increased. Estimation of the temperature can be done by measurements of the total intensity of the luminous radiation, the intensity of a radiation of a particular wavelength, or the relative intensity at different wavelengths. The problem is to have a device robust enough to be used in industrial situations. The optical pyrometer designed by Le Châtelier uses the measurement of the intensity of a precise radiation emitted by the heated body by comparison with that of a known flame the image of which is projected on the image of the body to be measured with an optical device. Le Châtelier used this apparatus to measure the highest temperatures he could find in nature or industry. Those data are interesting because they are probably among the first exact available measurements (Table 1.12). This measurement indicates that the furnaces of the end of the 19th century were probably heated one hundred degrees lower than the present-day furnaces. We Table 1.12 Various
industrial
temperature
ments [1.34] Siemens Martin Furnace (steel) Glass furnace Hard porcelain furnace Incandescence lamp Arc lamp Sun
14901580 ı C 13751400 ı C 1370 ı C 1800 ı C 4100 ı C 7600 ı C
measure-
The History of Glass
1.5 19th Century, the Century of Technical Revolutions
Date 1806 1839 1844 1855 1867 1878 1889
Surface area (m2 ) 4.25 8.73 11.66 18.40 21.80 26.50 34.20
Length (m) 2.50 3.80 4.30 5.40 5.90 6.40 8.10
Price for 1 m2 (F) 226 (1805) 127 (1835)
Width (m) 1.70 2.30 2.70 3.40 3.70 4.10 4.20
61 (1856) 47.75 (1862) 40.30 (1884) 30.23 (1889)
Table 1.14 Time necessary to make plate glass: evolution between 1765 and 1889 in hours [1.17, p. 447] Preparation of the batch Melting and casting Annealing Cutting Grinding Smoothing Polishing Total
1765 3 28 96 6 36 5 72 246
shall see that this increase was made possible by a considerable change in the refractories (and the furnace design and insulation) during the 20th century.
1.5.4 Innovations in Flat Glassmaking Around the End of the 19th Century Evolution of Plate Glass, the Most Expensive Product At the end of the 19th century Saint-Gobain produced plate glass for mirrors by casting. In 1868, Bontemps thought that no “other factory has ever been the model for all others to the degree that had been achieved by Saint-Gobain.” It has not only been the model for all others created in France or in foreign countries but hardly any other has been established without the cooperation of the directors of SaintGobain or workers coming from that company. [For instance] the first cast plate glass works in England was set up at Ravenhead only in the summer of 1773; this company had the assistance of a M. Delille from Saint-Gobain; it was the British Plate Glass Company. [1.19]
Heretofore, the practice used in making plate glass was to ladle the molten glass from its melting pot into a casting pot, according to the size of sheet to be made, and then to heat the casting pot for some hours, and pour the glass on to a table and roll it out. The ladling and heating of the intermediate pot were laborious and costly.
1862 3 24 84 6 28 5 24 174
1889 3 24 72 6 28 22 22 127
Rough (unpolished) plate glass had come largely into use at railway stations and other buildings, made by this process of glassmaking. Thus, plate glass was beginning to have new uses in architecture, but it was too expensive to be used polished. That being said, many improvements were made during the 19th century on plate-glass production. The tendency was to an increased demand towards the production of larger and larger sheets of polished plate glass [1.20, p. 469]. Along with the decrease of prices, the market was widening: in 1897, Henrivaux wrote that it had doubled in twenty years and that plate-glass manufacturing was no longer a luxury industry (Table 1.13). In 1897, seven plate-glass factories worked in France, five in Belgium, six in Germany, six in England, one in Russia, one in Italy, and four in the US. In 1893, 2 400 000 m2 of plate glass were manufactured in Europe. In 1897, the surface was 3 600 000 m2 . During this period, the US production increased from 500 000 m2 in six factories to 1 200 000 m2 made in 13 factories. The time to make plate glass was diminished by a factor of two since 1765 (Table 1.14). This evolution in price and volume was for a large part due to the introduction of new mechanical means of working to operate casting, grinding, and polishing [1.17, pp. 414–425]. The end of the 19th century saw the reign of mechanical engineers. One of them was Lucien Delloye, who, after having successfully dealt with grinding and polishing machines became the Plate-glass General Manager of Saint-Gobain and
History
Table 1.13 Evolution of the maximum size and price of plate glass manufactured in Saint Gobain [1.17, p. 444]
27
28
Introduction
History
earned the consideration of all the European glassmaking community of this time through the creation of the International Plate Glass Convention [1.35]. Up to 1900, plate glass was always cooled in special kilns, but the following years saw the introduction of annealing lehrs. Movement along the lehr was obtained by means of mechanically worked rods. Improvements in Window Glass Production In 1872, sheet glass [1.11, p. 146] works benefited from two recent innovations: the first innovation, the Bievez lehr enabled sheets rapidly cooled by being raised successively on iron bars and so kept apart, to be annealed in twenty-five to thirty minutes as compared to seven or eight hours in the piling kilns. The other innovation was an appliance to assist glassmakers in blowing the heaviest of cylinders. It had been invented by Windle Pilkington and was patented in 1871. Four such machines were in use by the beginning of the following year [1.11, p. 446] The major advance was the development of tank furnaces. To feed in raw materials at one end of a tank, melt them as they passed along, and then cool the molten glass to the correct consistency for working by the time it reached the other end, would allow window glass manufacture to become a continuous process. The twenty-four hour interval while the molten glass was prepared, inevitable with the existing pot furnaces, could be avoided and time, fuel, and labor saved. Therefore, sheet glassmakers were among the first (along with container glassmakers) to adopt the new Siemens tank furnace, as we saw above. At Pilkington Brothers, the largest recorded weekly output of window glass before the introduction of tank furnaces was 350 000 ft [1.11]. The weekly average throughout the year 1877 was just over 500 000 feet (Note the expression of the surface in linear feet, making the data impossible to translate! The reader will consider only the increase in output) and throughout 1887, just over 900 000 ft. The 1 250 000 ft mark was passed in the early 1890s and, by the end of the century, production exceeded 1 600 000 ft per week. A New Type of Glass: Hartley’s Patent Rolled Plate Glass Various molded glassware, lighthouse parts for instance, were also produced. In the Chauny factory, Saint-Gobain had been manufacturing thin plate glass by blowing, according to the Nuremberg process, since 1839. In 1852, the new Director, Hector Biver had previously worked in the British Plate Glass Company. He brought from England the idea of manufacturing this thin roofing glass by the new Hartley’s patent rolled plate glass method instead of blowing. On October 28th
1854, the Board allowed the production of the “verre de toiture cannelé” [1.23]. The process, derived from the casting of plate glass (which has never been patented), was much simpler and cheaper than the cylinder window-glass process, giving the possibility of new applications. Besides, this production, being of a lesser quality than the plate glass, opened up the possibility of experimenting with new processes and among them new furnaces such as tank furnaces. Hartley’s invention [1.36] consisted of dispensing with the costly processes of receiving the melted metal into a crucible, instead ladling the metal directly from the pot on to the table and then rolling it out in the ordinary manner. He applied one, two, or more ladles full to make each sheet, and found that the several ladles did not need to be poured on at the same time, but may be added towards the end of the previous quantity. This was a way to produce long sheets of rough plate glass that were comparatively narrow, at a considerable saving of labor and cost; when made they were annealed by piling in the same manner as was practiced in annealing crown and sheet glass, which avoided the use of the costly furnaces employed to anneal plate glass [1.23]. The glass produced in this way was considerably thinner than standard size plate glass. Hartley’s patent rough-plate glass has been recommended for conservatory and hothouse roofs. It was strongly recommended by Dr Lindley who said: ‘this glass is prepared by rolling which destroys transparency without diminishing translucency. It is slightly rough on the surface, which has the important effect of dispersing the sun’s rays instead of concentrating them. The roughness however, renders it less agreeable to the eye, and would make it objectionable for the perpendicular sides of glass houses’ [1.37].
The thinness made the glass roofing much lighter. One of the main features of Hartley’s Glass Works is the glass covering. It is glazed over its whole extent with Hartley’s Patent Rough Plate, one-eighth of an inch-thick, the kind now almost universally used for conservatory and railway station roofs, and which was supplied by Mr. Hartley in the instance of the immense roof erected at the Great Western Railway Station at Paddington; the new baths at Buxton are also glazed with this same material. The size of the squares is 76 inches by 20. They amount to no less than 1560 in number (equal to 16 400 superficial feet), and yet to no more than fourteen tons in weight! — An extraordinary lightness, if we contrast it with the glass roofing of
The History of Glass
When the Crystal Palace was built for the Great Exhibition of 1851 Hartley offered to provide all the glass necessary of 1=8th inch (3:175 mm) thickness at £18 13s 4d=t. Glass of that thickness weighs 7:94 kg=m2. The offer was not accepted because there was insufficient experience of that kind of glass: it was feared that this glass would be more fragile than blown glass and it was absolutely necessary to avoid accidents in covering with glass a building in which so many people and valuable objects were to be gathered together. Siemens tanks furnaces were also used for making rolled plate glass and the output of rolled plate glass grew at a pace comparable with that of sheet glass, although the increase was not as regular because of an irregular market. In England there were three factories making rolled plate with Hartley’s license (Pilkington’s, Chance’s, and Hartley’s) and their combined annual production was certainly at least 25003000 t or 200 000300 000 m2 . Hartley’s process had also been adopted by Saint-Gobain who used the name “patterned glass” [1.19]. The Saint-Gobain Company made only one grade of this patterned glass, which was 56 mm thick and pieces below half a square meter sold at a net price of 6 F in half-white or 6:80 F in white glass. Sizes up to a square meter cost 6:80 F in half-white and 7:60 F in white glass. The prices fell considerably as its consumption increased. Saint-Gobain sold patterned glass for the glasshouses in Jardin des plantes (1854), for the Halles de Paris (1855), 4500 m2 for the Milan railway station in 1862, and 40 000 m2 of roughly ground patterned glass for the glazing and roofing of the Palace of the permanent Exhibition in Auteuil (1862) [1.39]. Thus, by the end of the 19th century, in addition to molded glassware, two different types of plate glass were manufactured in Saint-Gobain: the usual thick plate glasses which were polished for making mirrors (two grades: No. 1, thick, and No. 3, half-thick), and the thin plate glass (No. 4) which was used without polishing for roofing (Table 1.15).
Molten glas Rollers
Printing rollers
Fig. 1.12 Chance’s rolled glass
Chance’s Rolled Glass In the late 1980s George and Edward Chance successfully developed a machine (Fig. 1.12), patented in 1884, whereby the molten glass was poured down an inclined plane and passed between a pair of iron rollers [1.11, p. 150]. In 1890, Edward Chance perfected the machine by adding a second pair of rollers, one of this second pair impressing a pattern when required. A further short inclined platform carried the still soft glass onto a horizontally moving table whence it was drawn at the rate at which it was pressed. The first cylinders were water-cooled, since they come into contact with the hot glass. The manufacture of rolled plate glass became of primary importance to the Chances and the royalties from other companies, including Saint-Gobain operating under license, were considerable. Wired Glass One of the earliest machines [1.20] to make wired glass was due to Tenner, with Appert designing a later machine (Fig. 1.13). The casting table is mounted on a wagon running on rails and passing between two rollers upon the fixed frame. Above the first roller is a cylinder having a rough surface tapering somewhat from center to sides and provided with a brake arrangement. Above this cylinder and a little to the side of it is the roller for holding the wire net. Before rolling is begun, wire is run over the rough surface cylinder and beneath the rollers, then finally
Table 1.15 Plate glass production in Saint Gobain (Aisne) before and after the arrival of Hector Biver Production (m2 ) Plate glass No. 1 Plate glass No. 3 Thin glass No. 4
1851 25 568 6666 20 373 (hand-blown)
1855 98 324 24 549 27 931 (thin plate)
29
History
the Great Northern Railway Station in London, in which the plates are half an inch thick, and consequently, enormously heavier. In equal areas of roofing, the difference between the rough-plate of MM. Hartley would be that between fourteen tons and fifty-six! [1.38]
1.5 19th Century, the Century of Technical Revolutions
1856 88 095 34 479 40 579 (thin plate)
30
Introduction
History
left behind its Gold Age of the 1860s: our company, that of Oignies and Floreffe in Belgium, that of Aniche in France, and the English companies, shared the world market and lived in good intelligence; they prudently harmonized their production means with the consumer needs and wisely developed. [1.39]
Wire net roll
Wire net
Casting table
Rollers
Table
Fig. 1.13 Wired rolled glass
clamped to the end of the table at a height above the casting table equal to that at which it is desired it be embedded in the glass. Glass is now poured onto the table, which has been set beneath the roller. Then, after translation of the casting plate, a new charge of molten glass is poured upon the already rolled but still soft plate, in front of the second roller and this completes the plate by rolling out a glass layer above the wire. The two layers unite to form a single plate. A later process was much simpler: the wire was clamped above the table at the correct height and glass poured on and rolled in the usual way. The roller forces the fluid glass through the meshes of the wire, to unite again beneath it, thus giving in one simple operation the required result. State of Manufacturing of Flat Glass Products at the End of the 19th Century The technical progress in processes during the second half of the nineteenth century brought about a considerable increase over the old production in plate glass but also a diversification which would allow new changes during the twentieth century. One of the most important ones was the revolution in furnaces, the transfer of at least a part of the production of flat glass to a potentially continuous process through the use of radiationtank furnaces. During those years, the plate glass world had completely changed. In 1878, the Duc de Broglie, in his report to the assemblée générale of Saint-Gobain, spoke about the complete transformation of the plate glass industry which has
The reasons for this change were numerous: the new American plate-glass makers were making one third of the global production in 1870. Several new companies had appeared in Belgium: Auvelais (1876), Moustiers (1883), Saint-Roch (1889), and Charleroi (1890). The new plate glass factories created in Belgium and in the United States did not conform to the previous European agreements: the combination of larger and larger production with higher and higher importation taxes, strongly cut down the exportations to the US, causing a disorder which had proved fatal to the plate-glass makers in England, leaving only Pilkington Brothers among the previous plate-glass companies. In France, new players had appeared beside SaintGobain: Aniche, Maubeuge (Pilkington 1891), and Boussois (Charleroi 1899). In Germany, the Glas und Spiegel Manufaktur (1872), Herzogenrath (1877), and Altwasser (1872) factories were created. In 1870, the global production was 1 100 000 m2 plate glass (26% in Saint-Gobain factories). In 1913, it was 13 500 000 m2 (17% Saint-Gobain with 30% in France). As a consequence of those major technical improvements but also of the increased competition on the market, the price of plate glass and other types of glasses had significantly decreased during this period: 54 F=m2 in 1855, 33 F=m2 in 1865, and 14 F=m2 in 1895.
1.5.5 Container Glass Making at the End of the 19th Century At the end of the 19th century, bottles were still hand made but their fabrication had been largely improved since the early days. Use of the Siemens Tank Furnace One of the major improvements was the use of the Siemens end-port tank furnace (Fig. 1.14) that allowed continuous work and thus a much larger output than with the old pot furnaces. On the side of the furnace were the working holes, just above the glass level. A secondary wall situated on the outside of the furnace wall somewhat protected the workers from the heat radiated by the furnace thanks to the air space between it
The History of Glass
1.5 19th Century, the Century of Technical Revolutions
31
History
Furnace
Working area
Regenerator chambers Melting area
Dog house
Fig. 1.14 End-port (horse-shoe) tank furnace, (Top) side view, (bottom) plan view (after [1.20])
and the furnace itself. An opening in this wall gave the men access to the molten glass. Inside the furnace and immediately in front of the working hole was a ring, made of fire-clay, floating on the melt and preventing the gathering of surface scum. The gatherer used his previously slightly heated blowpipe to collect the desired amount of glass from the tank and after examination for the presence of drops, blisters, or stones from the furnace, the blower took the pipe from the gatherer and proceeded to roll the glass upon the marver while rotating the pipe. Then he applied his lips to the end of the pipe and, by blowing, distended the gathering into a hollow globe known as the parison. The bottom of the parison was flattened on a plate, its neck rolled to the desired diameter and the parison was adjusted by holding the pipe vertical and allowing the glass to lengthen by virtue of its own weight. The parison was then blown to shape in the mold.
After blowing had been continued for a sufficient length of time to allow the bottle to become set enough, the bottle was removed from the mold and separated from the pipe by a slight thermal shock. It was taken by means of the punty (in the form of a split cylinder of iron fixed upon the end of an iron rod) with the diameter of the cylinder being such as to allow it to gently grip the bottle. Then, the finisher gathered a little glass on a small iron rod and ran it evenly around the rim of the bottle neck, and pressed it with tongs on the bottle neck rim while revolving the punty to mold the thread of glass to form a collar on the neck-ring of the bottle. The finished bottle was then taken to the lehr. Bottle-Making by Machine In 1886 Ashley, of Castleford in England, thought that much of the preliminary work in shaping parisons for mold-blown bottles might be mechanically performed.
32
Introduction
History
He introduced a first mold, the parison mold, to replace the first blowing step. A further improvement was the use of compressed air for blowing up the bottle in the finishing or “blow” mold. Finally, the machine worked with three molds, the parison (or blank) mold, the mold for the neck-ring of the bottle, and finally the finishing or blow mold. The parison was made in three steps: the glass was introduced into a parison mold equipped with the neck-ring mold, upside down, the neck of the bottle being down. Air was introduced to press the glass inside the neck-ring mold. The system was then returned so that the neck-ring mold would be situated under the compressed air admittance, and another air injection pierced the neck and formed the hollow parison. Then the mold opened and the parison was transferred to the finishing mold to be blown into a bottle. This machine was soon adopted in England. In France, in 1894, Claude Boucher also designed a manual compressed air machine, capable of replac-
ing the glassblower in all of the operation except the gathering of the molten glass in the furnace [1.40]. The invention was improved until 1898, when it appeared that its use required a much simplified training for the glassworkers (a few months instead of 10 years) to be able to produce glass bottles with a much better output (2.5 times), even better than the Ashley machine (2 times) thanks to the presence of two alternating parison molds. While one was filled, the other one could shape the parison. As soon as the parison was finished in the second mold and transferred into the finishing mold, the system was inversed to blow the glass already injected in the first mold. This machine was the cause for a strong disquiet among the glass blowers. Nevertheless, the first mechanically created bottles were made and sold in 1898. In 1906, 108 machines were currently working in most factories (except Champagne bottles makers!). Claude Boucher received a prize from the Académie des Sciences in 1902.
1.6 The Revolutions of the Twentieth Century Rationalization, also as a result of the reduced available workforce after World War I, led to the development of new techniques and processes.
1.6.1 Mechanization Mainly After the First World War The beginning of the 20th century was important for the development of mechanization of glass manufacturing in all branches of the activity, except for plate glass (which will come later, at the end of the 1920s). Industrial developments could not keep up with the rate technical progresses were made: not only did it mean a drastic change in factory organization, which did not please the very specialized glassworkers, but also because it needed rather heavy capital investments and the beginning of the century was not very bright from the economical point of view in Europe. This was for a large part due to the fast development of the glass industry in America. Because of the American glass industry, and because of the high taxes imposed by the American government on glass imports, the traditional export market of European companies evaporated within a few years, and the crisis lasted until they organized the market between them via two (at least) International conventions, one for special glass and one for plate glass [1.35]. They had considerably improved their results when the War was declared.
In 1918, when the war ended, the needs of the market for glass were huge and factories had to produce again as rapidly as possible. Thousands of glassworkers had disappeared during the war and many of the factories, especially the continental ones, had to a large part been destroyed. They were reconstructed with integration of mechanical processes that had mostly been designed before the war.
1.6.2 Window Glass The increased demand for flat glass in buildings and the more economic processes to prepare it went hand in hand. Drawn Cylinder Process, an Improvement but not a Breakthrough The beginning of the 20th century was to see considerable changes in the fabrication of sheet/window glass. One of the most spectacular inventions was the drawn cylinder process, invented by John H. Lubbers in the early 1890s with financing from the American Window Glass Company. It began with the introduction of a mechanical, but not continuous process [1.11, p. 192]. A large pipe was dipped into molten glass in a specially constructed pot that was filled with sufficient glass to make a single cylinder. As it was slowly raised, it drew up the glass with it. Compressed air, passed through the blowpipe, was blown at such a rate as would main-
The History of Glass
Direct Drawing of Glass Sheets The previous methods to make sheet glass are not only labor-intensive but also gave a product liable to have many defects, while the size of the sheets is also limited. Therefore, it was natural that the idea of producing glass by machinery in longer lengths than could be obtained by hand working should have been conceived. The initial idea was simple, and was patented in 1857 by William Clark of Pittsburgh [1.20, p. 458]: it was to dip a bait into the molten glass to which the glass would attach itself, and gradually withdraw this from the molten glass. The method had one major defect,
which could not be overcome for half a century: when a sheet of glass is so drawn, the second stratum is somewhat shorter than the first, the third less still, and so on, so that, instead of a parallel-sided sheet, the two bounding edges approach each other and a triangular sheet is obtained. To solve the problem several workers tried the method of drawing the sheet downwards, allowing the glass to flow through a slit of suitable size. The same difficulty occurred: the sheet becoming heavier, the weight drew thinner the portion that was not yet set and rupture finally occurred. Fourcault Method. E. Fourcault obtained the first success at the Dampremy glassworks in Belgium in 1903: his method consisted in drawing the sheets vertically from a tank of molten glass (Fig. 1.15). Overcoming of the surface tension of the sheet by gravitational pull caused a narrowing of the sheet of glass. If the liquid were given an upward velocity at the drawing point counteracting the gravitational tendency, the uniform width of the sheet would be maintained. To produce this upward movement, Fourcault used a float, a long trough of refractory material having, along its base, a slit parallel to the length of the trough. In the process, the trough was caused to sink somewhat in the glass at a definite depth of penetration. Molten glass was therefore forced through the slit at the desired rate. The glass was seized as it emerged from the opening by means of a bait and drawn off in sheet form, which remained uniformly of the same size as the slit. Two water-cooled tubes against the sides of the slit chilled the glass when it emerged. Above the troughs were placed the drawing machines, sort of rectangular towers four meters high, through which passed a framework with a series of rollers set in pairs. Their rotation served to draw the sheet as it is formed. The rate of working was 30 m=h for glass that was 2 mm thick. Sheets of glass made by this method are 11:25 m wide. The slow, even, cooling with no contact with chilling materials gives a glass free from strain which can be cut without trouble. Several machines could be placed around the end of a tank furnace. In 1912, the S.A. des Verreries de Dampremy began the production of sheet glass with eight machines. The production improved but the glassmakers adopted this process for sheet glass only, due to the numerous defects caused by contacts with the refractories of the trough. In France, in 1928–1929, sheet glass was produced mainly with this process; hand blowing had definitely been abandoned. The process was still in use after the float glass process had revolutionized the production of flat glass, until the patent expired, especially in Eastern Europe.
33
History
tain the diameter constant. This way a cylinder of 10 m in length and 0:70 m in diameter could be drawn. Afterward, the giant cylinders had to be cut into smaller lengths, flattened in the usual way, and annealed. Around 1905, Windle Pilkington went to America to see the cylinder process and returned with the opinion that the glass produced was not yet of sufficient quality for the British market. In 1908, Pilkington Brothers decided to consider a proposition from American Window Glass Company and an agreement was signed in April 1909. An experimental machine was set up at the end of the same year and commercial machines in May 1910 and April 1912. The quality was poor and could not replace the hand-blown glass process. “The machines make poor glass, but they make so much more glass that they can pick out a great deal of good glass and sort it very carefully.” [1.11] In 1910, Lucien Delloye, General Manager of Glass in Saint-Gobain decided to buy the process from American Window Glass and the first machine was set up in the Aniche factory between 1911 and 1912 with an 8-machine tank furnace. The second factory was established in Chalon-sur-Saône in 1914 for the market in the south of France, and two others in Bilin (Germany) in 1911, in Rome in 1911–1912, and in Spain. Except in Italy, the process could not compete with hand-made sheet glass blowing. The Aniche factory was destroyed during the First World War and in the end, sheet glass was made by the old hand-blowing process until the end of the 1920s [1.39, p. 426]. The process was exploited only in Chalon with poor economical results. It was the same for Pilkington’s factory in Canada. In Saint Gobain, and even in Italy, the hand-blowing process was replaced by another method (Fourcault process) around 1926–1927, which directly draws sheets of glass. Nevertheless, Damour reports in 1936 [1.41] that, in America, the Window Glass Company was still making sheet glass with this method and actually obtained sheets of quite a good quality.
1.6 The Revolutions of the Twentieth Century
34
Introduction
History
1 to 1.25 m wide sheet Drawing machine: 30 m/min for glass 2 mm thick
Pairs of asbestos rollers
Inclined sheets to prevent radiation from the molten glass
Tank furnace D
D
Extension curtain Drawing float: trough
Fig. 1.15 Fourcault method (after [1.20])
Colburn Process. I.W. Colburn began his researches in 1900 but Libbey & Owens who acquired his patent rights developed his process and they perfected the machine at their works in Toledo (Fig. 1.16). Several improvements in the method of keeping the width of the glass sheet were tried and the last one was to set a pair of water-cooled, channeled rollers placed at each end of the sheet just above the level of the molten glass in the pot. These rollers gripped the edges of the sheet as it was drawn and so maintained the width. When the sheet had risen vertically to a height of 1 m, it was softened by gas jets and turned over rollers until it lay horizontally, after which it passed through an annealing lehr. The bending roller must be cooled as it came into contact with the glass, or else deterioration would have ensued. The marking of the glass by this bending roller constituted one of the difficulties of the method, but in 1915, a factory of the new Libbey Owens Sheet Glass
Company was using this process. It was quite successful in Europe and competed with the Fourcault process, promoted by Saint-Gobain for sheet glass. Pittsburgh Process. This process was developed [1.11, p. 207] during the 1920s by the Pittsburgh Plate Glass (PPG) Company, already the giant of the American plate glass industry before 1914, but not at that point particularly interested in sheet glass manufacture. The process differed from those of Fourcault and Colburn in an essential feature: the method of drawing the ribbon of glass from the tank. But it was like the Fourcault machine in that it had a vertical lehr, thus being economical in the use of ground space. In this process, like in the Libbey–Owens (Colburn) process, the sheet of glass was drawn from the molten glass without any contact with another surface and it gave a sheet with a very bright firepolished surface. In order to do that, the process
The History of Glass
1.6 The Revolutions of the Twentieth Century
35
History
Hollow rollers Burner
Damper opening
Annealing chamber
Drawing chamber Curtain Drawing tank Cooling off tank
Burners Melting tank
Exit flute
Fig. 1.16 Sheet-drawing: Libbey–Owens (Colburn) process (after [1.20])
used a refractory device immersed in the molten glass roughly 8 cm under the surface. It protected the drawn glass against radiation from the melt and kept its viscosity constant. The width of the glass ribbon was maintained by a pair of rollers placed on each end of the sheet similarly to the Libbey–Owens process. The sheet of glass then rose in the same kind of rectangular tower as in the Fourcault process and was progressively cooled down until it was cut. This process was perceived as interesting but SaintGobain perfectly understood that its implementation was more complicated than that of the Fourcault process and needed a real team of engineers to ensure a smooth start of this process in plants [1.39, p. 430]. An agreement was signed with PPG in May 1929. A new company was created to deal with the patents, bringing together Saint-Gobain, PPG, Saint-Roch, and Boussois. An operational team of five engineers was commissioned from Saint-Gobain to make the connection between the European and American factories, and to install and improve the process. Even Pilkington Brothers used the services of this organization when they decided to use the PPG process in Britain. The first experimental attempts to draw glass at St. Helens were made in March 1930; and as early as April 1931 Austin Pilkington could describe the PPG machine as “really a winner” [1.33]. In the following November the first
four machines went into commercial operation and the drawn cylinder process was then rapidly abandoned at Pilkington Brothers. The Pittsburgh process turned out to be the most profitable window glass process for years, until the float glass process appeared in the 1960s.
1.6.3 Plate Glass In 1919, most plate glass factories were equipped with the same installations as they had been at the end of the 19th century: melting of glass in pots containing around 2:5 t of glass in regenerative gas furnaces, casting and annealing in static furnaces (carcaises). In a few SaintGobain factories (Franière in Belgium or Pisa in Italy) a tunnel furnace had been introduced where plate glass passed through decreasing temperature zones, from 650550 ı C, the annealing being performed in space instead of time. Thence, the casting table (10 m 5 m) could be fixed and reinforced, which was much more favorable in terms of product quality. Bicheroux Process Between 1910 and 1914, trials were made by Bicheroux, in Herzogenrath (Germany), a factory that SaintGobain had bought in 1905. This process (Fig. 1.17), derived from the Chance process, consisted in casting the molten glass contained in its pot after extraction
36
Introduction
History
Evolution of the plate-glass processes
Pot containing the molten glass
Roller Casting table Bicheroux Rollers
Pot containing the molten glass Moving casting table
Boudin Rollers
Furnace end Rollers supporting the glass
Fig. 1.17 Plate glass: Evolution of the process
from the furnace between two cast iron rollers on a moving table. This approach gave two nearly parallel sides so that less material had to be removed before polishing (less than 2 mm instead of 3:5 mm with the classical process). It was generalized in the 1920s in most plate-glass works in Saint-Gobain and in other companies. The license was sold to all European and American plate-glass makers in the framework of the Plate-glass International Convention, during the interwar years. Boudin Process This was derived from a combination of the Bicheroux process and the continuous tank furnace: hot glass was directly introduced into the machine from the end of the furnace (Fig. 1.17). The use of the tank furnace in plate-glass production came about 50 years after that of sheet glass because the refractories used
in tank furnaces were very rapidly damaged and stones appeared in the glass sheet [1.39, p. 399]. It was easy to replace a pot (after 1520 castings) but not the whole furnace. The tank furnace began to be used for plate glass after the development of new refractories in 1925–1930, the electrocast refractories. Saint-Gobain, Saint-Roch, and Corning wanted to manufacture electrocast refractories in Europe and created the Société Française de l’Electro-Réfractaire in 1928. The first factory was settled in Modane where Saint-Gobain already worked a hydroelectric plant and a chemical products factory. In 1932, Boudin set his first machine in Chantereine (near Compiègne), the model plate glass works of Saint-Gobain. Despite the fact that, when the glass is still hot, it subsides between two rollers, the continuous sheet is at least as good as that obtained by the Bicheroux process. This process is still used at present to manufacture printed glass. Continuous Grinding and Polishing of Plate Glass At the Cowley Hill factory of Pilkington Brothers, a continuous grinding and polishing system was being developed [1.11, p. 204]. A continuous sequence of cast iron tables carried the rectangular plates of glass under a series of grinding heads with subsequent polishing under the same continuous line. One side of the glass was dealt with at a time. The first experimental model was running at the beginning of 1920, but much development lay ahead; it was not until May 1923 that this machine finally went into service. This gave Pilkington Brothers an international advantage in plate glass manufacture by the middle of the 1920s. Lucien Delloye visited the installation in April 1923. An agreement (January 1924) was negotiated between the Plate Glass International Convention, Pilkington, and Heuze-Malevez-Simon, one of the developers of the technique together with Pilkington, the content of which was that the only licensees on the European continent would be the members of the Plate Glass International Convention. The first continental installation occurred in Herzogenrath, a Saint-Gobain factory in Germany, and improved in the years 1927– 1929. Full-size machines were then settled in Franière (1932) and Chantereine (1935). Only three other factories outside of Saint-Gobain ever used this set up: Boussois, Auvelais, and Moustiers. What was further needed was a machine that could grind and polish the ribbon of glass on both sides simultaneously as it emerged from the lehr and before it was cut into plates. Twin grinding was finally developed in the early 1930s and came into service in 1935 at the Doncaster works and in Cowley Hill in 1937.
The History of Glass
Automotive Glass and Safety Glass During the 1920s the growing motor industry provided a new market for glass. At first the few open cars required only a small amount of plate glass (never sheet glass which was not of a sufficient optical quality) for their windscreens. But, as the number of cars multiplied and the closed saloon became more popular, much larger quantities of glass were bought by the car manufacturers and eventually sales of plate glass to them exceeded those for building. Moreover, the car industry began to require safety glass, first laminated and then toughened. The fitting of safety glass in windscreens of British cars became compulsory from the beginning of 1932. The research team in the Saint-Gobain laboratory searched for a process to improve the flatness and polish of the plate of glass. The idea was to homogeneously reheat the previously cut up plate hung in an electrical furnace at 680 ı C (the softening point), and cool it down symmetrically with controlled compressed air streams. Together with Boussois for Securit glass, they took patents that were exploited in the whole world. In September–October 1930, Pilkington became a licensee. In the US, Saint-Gobain and Boussois created American Securit with Corning in 1933 (to bring an American-like air to the society) and important agreements were concluded with the two American plate-glass giants PPG and LOF (Libby–Owens–Ford). Another type of safety glass was the Triplex glass, a sandwich of a plastic foil between two glass plates [1.39, p. 411]. The inventor, Edouard Benedictus, started in 1909 the Société du Verre Triplex and Delpech the English Triplex Company. This society was profitable thanks to war supplies, and developed during the 1920s. Pilkington bought shares in the society in 1925. After having tried to launch a new fabrication of Triplex glass in the Cirey factory, Saint-Gobain decided to enter the small Société du Verre Triplex, as well as Boussois, Aniche, and the Société Franco-
Belge pour la Fabrication Mécanique du Verre (Libbey– Owens process), members of the association of various French plate glassmakers: this was in agreement with the general political principles of Saint-Gobain at that time. The glassmaker’s society was completely reorganized. A new factory was built in Longjumeau, near Paris, in order to be closer to the car manufacturers: for instance, in 1928, Citroën bought 600 m2 =day. Various modifications were made and new patents taken, which much improved the quality. It is interesting to note that, contrary to Securit glass, the Triplex plates could be cut according to any dimensions the customer wanted. Pilkington Brothers, by failing to acquire the Triplex Safety Glass Company Ltd. when that processing company was still a small concern, lost an opportunity to control the supply of glass to their most promising market. Nevertheless, Triplex soon became Pilkington’s largest customer and, in 1929, the two companies joined forces to create a subsidiary under the name of Triplex (Northern) Ltd. In 1955, Pilkington surrendered control of this subsidiary in return for a greater interest in Triplex itself.
1.6.4 Float Glass A discontinuous process of casting-made plate glass, followed by grinding and finally polishing on the same discs. Glass manufacturers had long looked forward to the day when they could flow a ribbon of glass from a tank. Experiments at the Ford Motors Company in Detroit did not succeed in the 1920s because of the poor glass quality coming from the tank furnace. The problem began to attract the attention of a newcomer to the Pilkington Company, Alastair Pilkington, a member of a branch of the family that had not previously been connected with the glass industry [1.11, p. 208]. He joined Pilkington in 1947 after completing a Mechanical Science degree in Cambridge, and, in 1950, took charge of production at one of the plate-glass factories. In October 1952, he began to explore the possibility of using liquid metal as a means of supporting the uneven and rough ribbon of glass that emerged from the rollers. In his own words: the basic idea is a continuous ribbon of glass moving out of the melting furnace and floating along the surface of molten metal at a strictly controlled temperature. Because the glass has never touched anything while it is soft except a liquid, the surface is unspoiled, it is the natural surface which molten glass forms for itself when it is cooled from liquid to solid. Because the surface of the metal is dead flat, the glass is dead flat too. Natural forces
37
History
The twin grinder first ran at 1 m=min but it was later improved until the ribbon of glass passed through it at the rate of 5 m=min. It came to be used by all the main manufacturers in the world for the greater part of their plate-glass production. In 1937, Saint-Gobain and Pilkington negotiated directly and, from this date to 1950, the former was the only licensee for the twin grinder. The polishing step was still performed as before until Saint-Gobain invented a complementary polishing machine, the Jusant at the end of the 1950s, which allowed working the glass ribbon emerging from the furnace in a continuous way: it came too late and was soon replaced by the float glass process.
1.6 The Revolutions of the Twentieth Century
38
Introduction
History
of weight and surface tension bring it to an absolute thickness. [1.11, p. 208]
In March 1953, it was proved that the glass could be fire-finished by floating on liquid metal. Could a glass of good quality be produced? A new plant was built early in 1954 to produce a 40 cm ribbon but, although the surface was considerably better than that of the pilot run, it was still far from perfect. Nevertheless, in September 1954, it was agreed to design and build a plant capable of making a ribbon 80 cm wide, with promising results. In April 1955, the Pilkington Board decided to take the decisive step and build a full-scale production unit to make float glass 2:30 m wide. It was started up at Cowley Hill in April 1957, but difficulties of formidable proportion appeared, which needed more than a year of struggle to be solved, with the big continuous plant swallowing vast sums of money all the time. Finally, the first good float glass was at last made in July 1958. This early output went to Triplex, Pilkington’s largest single customer, who agreed to use it in the manufacture of their safety glass. Despite this success, in January 1959, Sir Harry Pilkington stressed that they had not seen the best float glass, nor the cheapest. Years of development still lay ahead before the full commercial advantages of the new product could be fully realized. Between 1952 and the end of 1958, Pilkington had spent over four million pounds on the development of the float process.
1.6.5 Container Glass Until the end of the 19th century container glass was still mainly hand-made. Glass blowing was a source of illnesses for the workers, but also opposed evolution. The end of World War I—with many factories destroyed and a significantly reduced workforce—gave rise to the design of more rationalized and automatic manufacturing. The First Automatic Machines Several types of machines were used until the last evolution around the middle of the 20th century. Press and Blow Machines. Press and blow machines were the first and the easiest machines to set up: molten glass was gathered and dropped into the parison mold, the neck-ring mold was placed on this mold and the plunger was entered into the molten glass forcing it into the shape of the mold and also up into the neckring mold where it was chilled and able to keep its shape [1.20, p. 412]. The plunger was removed and the neck-ring mold plus the parison (blank) lifted from the mold and transferred in one of the finishing molds.
The blowing head was put into position and the bottle was blown to shape, removed from the molds, and annealed. Narrow-neck bottles could not be made by this method. Narrow-Neck Bottle Machines. The general solution was to invert the parison mold, the neck-ring mold and the plunger being placed at the bottom. Glass was dropped in at the top as before, the requisite quantity being cut off with the shears, plugged to shape the neck-ring, given a preliminary blow to form the parison (blank), and then transferred to the blow mold. Multiple-mold Machines. Desire for an increased rate of production led manufacturers to design machines with several sets of parison and blowing molds. Two turntables were generally used, one set with the parison molds, the second the blow molds and these were rotated mechanically. As each mold approached the gatherer it received its quota of glass, after which the blank was formed. Further rotation brought it into juxtaposition with one of the blow molds, when a boy seized the ring-mold, and the parison was rapidly transferred from one mold to the other. Rotation of the blow mold table brought the parison under a blowhead timed to descend at the correct moment and blow the bottle. On passing further stages in its journey, the mold was opened and the bottle removed. Three people, one to gather, one to transfer, and one to remove could keep a number of molds working without undue effort. Machines with Automatic Transfer and Take-out Devices A further improvement in bottle machines of the multiple mold type was a device for the transfer of the blank to the blow mold, and an apparatus for removing the finished bottle from the blow mold [1.20]. A number of these machines were invented, for instance, the Hartford-Fairmont, Lynch, and O’Neill machines to cite the best known among them. The Hartford-Fairmont was designed for wide-neck bottles and the parison molds were placed neck uppermost and did not invert. The other ones were designed for either narrow- or wide-mouth ware and glass was fed into an inverted parison mold. Those machines were designed to reinvert the parison mold between filling the glass and delivering the blank to the blow mold. The O’Neill Machine. This machine was comprised of two circular tables, each equipped with six molds (Fig. 1.18). Glass gathered was dropped into the mold through a pouring ring. When sufficient glass had been run in, a trigger was touched and this set in operation
The History of Glass
1.6 The Revolutions of the Twentieth Century
History
O’Neill machine Paraison (blank) molds
Conveyor Finishing mold
Step 5
Step 3 Table with finishing molds
Table with blank molds Blank inverted
Step 2
Step 4
Step 1
Table with finishing molds
Table with blank molds
Fig. 1.18 O’Neill bottle machine
the shears that cut off the glass. The parison mold was in an inverted position and as shears opened, a head was forced down upon the pouring ring, a valve was opened and compressed air blew the glass down around the plunger situated below in the neck of the mold. The head rose and the plunger pulled out of the neck, when the mold advanced to the second position. At this point a solid head was pressed down upon the mold to close the opening and air was admitted from below, thus blowing the glass into the shape of the mold. The head rose and the mold advanced into position three, rotating as it moved, until the charge had been inverted. In
39
this position the mold opened, leaving the blank suspended by the ring-mold: it moved across until it was in position over the corresponding blow mold set on the second rotating table. This blow mold closed over the blank and, as it did so, the ring mold opened and freed the glass entirely from contact with the first table. In the next position of the blow mold, compressed air was released and the bottle was blown. At nextto-last position, the finishing mold was opened and a pair of automatic pincers seized the bottle at the same instant, carried it from the table, and placed it on a suitable conveyor, whence it was transferred to the lehr.
40
Introduction
History
Lynch Machine. The Lynch machine was introduced in 1928 in Cognac. In this machine (Fig. 1.19), the ringmold opened independently of the rest of the parison mold and served to sustain the blank during the transfer from the parison mold to the blow mold. Like in the O’Neill machine, the inversion of the parison took place during the process. The Lynch machine was, in the beginning, 1.5 times faster than the O’Neill. It received many improvements until it was dethroned by the Hartford IS (Individual Section) machine.
We saw that container glassmakers obtained a mixture of sodium chloride and sodium sulfate as a flux to be mixed with the sand in the beginning of the 19th century. Except possibly in very few markets (Champagne for instance), glass bottles had to be cheap to be attractive to customers. Therefore the flux, which was the most expensive element of the batch, was limited as much as possible. This trend was enhanced by the development of Siemens regenerative tank furnaces, which presented an increased melting efficiency compared to the traditional furnaces. At the end of the 19th century, the chemical compositions of container glasses were quite peculiar [1.17, 42] for French container glasses (Table 1.16). The compositions were very rich in alkaline-earth oxide and were therefore quite easy to melt: the very fluid glass was easily homogenized. The problem was that devitrification (tendency to crystallize) occurs most readily in glasses containing the largest proportion of alkaline-earth oxides. Bontemps observed that:
Completely Automatic Machines. Patents addressing this problem were numerous in the beginning of the 20th century. There were two schools, one thinking that it was easier to feed the molds with very hot glass, which had just to flow or be sucked from the furnace, and the other one estimating that it would be better to cool down the glass sufficiently to be able to form a kind of parison which could be sheared and introduced into the mold. In both systems, a subsidiary compartment was then added to the working end of the furnace to stabilize the temperature of the glass corresponding to the subsequent process [1.20, p. 426].
if ones examines the glass remaining in the bottom of pots used for bottle glass, when they have been removed from the furnace, it is seen that this glass is completely devitrified and very like coarse pottery . . . All bottle glasses are to some degree subject to this defect and it can only be prevented by keeping the furnace at a sufficiently high temperature and completing working out as quickly as possible. [1.19, p. 149]
Problems Due to the Chemical Composition of the Bottle Glass. At first it was easier and more economical to supply the molten glass to the machines by hand because the conditions for an automatic gathering were numerous and not at all met by the glass process. The source of molten glass had to be constant and steady, with an invariable surface level and, more important, the glass must not devitrify under the condition of working. This last point was not at all fulfilled by the type of chemical composition used for bottle glass at the beginning of the 20th century.
Therefore, this type of composition was not compatible with the use of tank furnaces and inclusion in an automatic process, where devitrified glass could not be eliminated from the installation, as was possible with the use of pots.
Blow air adjustable on
Blank turnover Mold cooling
Mold cooling
6
5
5
6 Blow
Blow
Blank table Transfer
1
Charge and blowdown
Neck-ring open as
4
Blow mold closes
2 – 8 RPM
2 Blowback Blank turnover
1
Blow table
3
3 Blank open wide
Blank cracked open
Adjustable blow off
2 Cooling cleanout
Takeout
Conveyor
Fig. 1.19 Lynch bottle machine (plan)
The History of Glass
1.6 The Revolutions of the Twentieth Century
In (wt%) Silica Alumina Iron oxide Lime Magnesia Sodium oxide Potassium oxide
Clear glass Cognac 1897 62:5 4:4 1:3 20:5 5:4 4:7 0:9
Champagne < 1897 61:9 4:4 1:8 18:0 6:4 6:2 1:1
Data from Henrivaux, in a later book (1904), shows that the composition had a much higher content in alkaline oxide than before (Table 14 in that book, later compositions): the ratio between alkaline-earth and alkaline oxides had been reduced and the behavior of the glass was certainly much improved and made compatible with the modern processes [1.43]. In fact, during the 20th century, the composition of bottle glass progressively got in line with the soda-lime silica glass used by tableware or flat glass productions. Fluid Glass Feeding Devices. In the bottom of this compartment a hole was provided through which glass flowing from the tank could run in a stream into the parison molds, which passed below (on the rotating machines). One of the difficulties was to hold up the stream of glass during the period of substitution of a full mold to an empty one. Another problem came from the coiling of the stream of glass, giving charges not very suitable for entering the mold, and presenting a tendency for the formation of bubbles. The Homer Brooke Feeder. The Homer Brooke feeder was of this very earliest type: a continuous stream of molten glass issues from the orifice below which is the table supporting the parison molds. A cup was introduced between the stream of glass and the molds to collect the glass and in time it turned over and delivered the molten glass into the parison mold. A Suction Feeder, the Owens Bottle Machine (1903). This machine operated adjacent to an auxiliary furnace, and consisted of a revolving pot with a combustion chamber of 3 m in diameter and 20 cm deep, this being supplied continuously from the tank. A portion of the revolving pot projected beyond the walls of the combustion chamber, exposing a segment of the glass surface. The gathering molds of the machine dipped into this exposed molten glass consecutively as the machine rotated, and as each mold dipped into the glass a vacuum was automatically created in the mold, sucking the glass up to it and thereby forming the parison. As the mold rose up and moved away from the glass a knife automat-
Vauxrot < 1897 59:7 2:4 2:2 21:4 8:0 6:1 0
Fourmies < 1897 62:5 2:9 2:2 21:3 4:0 6:8 0:5
Cognac 1899 69:5 2 1 16
Lynch machine 1929 Damour 1929 70 3 2 13:5
10:5
11:5
ically cut off the string of glass that remained attached, dropping that portion back into the furnace. This machine was one of the first automatic machines after the Ashley and Boucher semiautomatic ones. It did not meet with great success in France, considering the cost of the installation and the difficulties linked with the suction: the quality of the glass was destroyed by the periodic suction step despite the rotation of the furnace. Even if it could widely increase the productivity, in most places glassmakers preferred to keep their Boucher machines while waiting for the probable development of the gravity feeder. In the beginning, another machine used this type of suction to feed the mold, the Roirant machine of 1923, which was not very successful either. Cooled-down Glass. The Hartford-Fairmont Gravity Feeder (1915). The particularity of this feeder is that it delivers glass at the working temperature at the end of a long chamber allowing it to cool down from the furnace temperature. Its first design was described as follows in 1925 [1.20, p. 429]: the feeder ends up in a lip beyond which is situated the extrusion orifice. Into the chamber dipped a paddle that drove successive waves of glass of uniform size over the lip by a regular vertical and horizontal back and forth motion. The successive waves of glass were forced through the orifice by a plunger (or needle) moving vertically (Fig. 1.20). The glass, being at working temperature, formed gobs of a size and shape very accurately determined by the length of the paddle stroke and its depth of immersion, the shape of the plunger, and the timing of the various motions. This feeder might be used to supply a single forming machine but it could serve three or four machines using a hinged receiving trough below the orifice. This trough moved in turn in step with water-sprayed, inclined, cast-iron troughs leading to the machines. The hot gob created a water-vapor cushion on which it rested as it slid down the trough, so tending to prevent deformation. A major improvement in the Hartford-Fairmont feeder was the disappearance of the paddle, replaced by a cavity created by a rotating refractory cylinder (tube)
History
Table 1.16 Chemical compositions of bottle glass at the end of the 19th century before and after mechanization
41
42
Introduction
History
Fig. 1.20 Hartford-Fairmont feeder: first device with a paddle (after [1.20])
Plunger Paddle
Hole
Glass in forehearth
To machine Trough
set over the orifice (Fig. 1.21): when the plunger rises in the tube, glass is drawn up in the tube above the hole; when the plunger goes down, a definite quantity of glass is expulsed through the hole forming the gob. The appearance of the Hartford-Fairmont feeder turned out to be the encouragement necessary for the development of automatic machines: the gathering problem was finally solved. The Lynch and O’Neill machines were adapted to the Hartford-Fairmont feeder gathering. The Hartford Individual Section (IS) Machine. This machine (Fig. 1.22) was revolutionary insofar as there is no real limit to the number of molds that could be set on a single machine. It is no longer a machine with two rotating tables. The sections are arranged in line, each of them consisting of a parison mold above a neck-ring mold and of a finishing mold in front of the machine, all of them fixed. The transfer of the parison, processed neck down from the blank mold to the finishing mold is operated by a mobile arm, inverting the parison. The limitation of the movements allows this machine to be run at a very high rate. They can also make two or three bottles per section. The Hartford-Fairmont device
ensured the delivery of the glass gob into the parison mold. The machine was only 10% faster than the Lynch machine but its flexibility determined its success. It was installed for the first time in 1952 in Lagnieu (SaintGobain Company). Saint-Gobain Invests in Container Glass Making In the 1920s, Saint-Gobain finally decided to invest in bottle glass making, after a technical journey of the General Manager Eugène Gentil, sent by Lucien Delloye to the US in order to perform a large review of the situation of glass making in that country (not only sheet or plate glass). He was impressed by the technical quality of American plants using automatic machines, thus reducing handwork. Eugène Gentil went back there in 1921 and came back with a good opinion of the Lynch machine, using the Hartford-Fairmont feeder. In 1924–1925, the Company decided to undertake manufacturing of the Lynch machines, the feeders, and the annealing lehr in order to centralize their conceptions and more easily generalize the best innovations in all the factories.
The History of Glass
1.6 The Revolutions of the Twentieth Century
Reciprocating plunger
Rotating tube
Molten glass
Shear Gob
In 1927, the production of the first Lynch machine equipped with a Hartford feeder was of 60 million bottles in the Verreries à Bouteilles du Nord in which Saint-Gobain had a 15% share in the 1920s and eventually became a majority shareholder a few years later. At the end of the same decade, Saint-Gobain had 70% of the shares in the Etablissements Boucher and they convinced them to use the Lynch machine with the Hartford feeder instead of developing their own process. The other French participations of Saint-Gobain were in Verreries du Saumurois (1924), Verreries mécaniques de l’Anjou (1927), the Verrerie d’Hirson (1928), the Verreries de Carmaux, the Verreries of the group Paul-Laurent (Saint-Romain-le Puy, Saint-Yorre, Pont-St-Esprit) from 1925 to 1930, the Verreries Aupècle (1936), and the Etablissements Deviolaine (1937 with Vauxrot).
A new plant was built in 1925 (Société d’Exploitation Verrière du Bugey) in Lagnieu (Ain) to make glass pots and various containers for perfumery, pharmacy, and food. This society, in which Saint-Gobain had a 56% share, built a new plant in Sucy-en-Brie (1926), also equipped with the Lynch machine. In 1930, a new plant was built in La Chapelle-SaintMesmin, near Orléans by a company, which would in time sell it to Saint-Gobain (1936). The production of bottles taking place in this plant was transferred and La Chapelle would produce tableware in pressed glass. Toughening was adapted to this kind of glass in 1936– 1937 in the Central Laboratory of Saint-Gobain and it was the beginning of a famous product, Duralex. At the same time, other glassworks allied with the Souchon Company but they mainly bought the O’Neill machine.
History
Fig. 1.21 Hartford-Fairmont feeder: new device with a rotating tube and a plunger
43
44
Introduction
History Delivery
Settle blow
Counter blow
Transfer from blank mold to blow mold
Reheat
Fig. 1.22 IS machine process
Final blow
Take out
The History of Glass
The 20th century saw the emergence of numerous technical glass products: all of them will not be described in this part, simply because they will be dealt with in other chapters. Two of them, at least, have had a sufficiently long history, textile fiber glass and insulating fiber glass, to be briefly described here. The reader will find more precise details in the corresponding chapters. At the end of the 19th century, E.D. Libbey produced fibers by softening glass rods with a burner and winding them [1.44]. They were occasionally used to make materials but it did not really work. From 1938, the company Owens-Corning-Fiber Glass began to draw glass fibers from molten glass, with a device pierced with holes of 12:5 mm diameter: filaments are extruded because of the hydrostatic pressure in the crucible, and they are wound on a drum, with the speed (1050 m=s) determining the size of the filaments, between 525 m. Then the filaments are brought together to form a thread. Those threads of glass were at first used to realize printed circuits and to reinforce plastics. The initial need for these fibers was for printed circuits, and more generally for electrical uses. This process makes use of a different type of glass without sodium oxide, the electrically conductive element in the soda-lime silica glass, E-glass. It is therefore a much more complicated and very technical glass to manufacture because no flux is introduced in the batch. Instead of any alkaline oxide, boron oxide, an oxide with a very low viscosity and a very low melting point (300 ı C) was used to help the melting process, in addition to using silica of very small grain size, calcium borate, and alumina. Nevertheless, the melting temperature of this glass is quite high. Containing a few percent of boron oxide, it has never been made with the regenerative furnaces, the regeneration chambers of which would have been destroyed too fast by the low melting boron oxide fumes, but with another type of furnace, the recuperator furnace, equipped with a metallic heat exchanger in the exhaust gas flow, thus heating the air or oxygen supplied for the combustion.
1.6.7 Insulation Glass Insulation wool was most probably produced accidentally in small quantities before any industrial process had been studied, just with a powerful stream of very warm air or gas on a stream of molten glass. Many different processes were later developed to produce these types of products.
Two of these processes are gas processes, either with a flame or with vapor. The first was the Ohio Insulation Company process (1935), which attacked a stream of molten glass with a high-pressure vapor stream oriented in the same direction. The result is an unwoven material, which can be used to reinforce asphalt shingles for roofing. The second process was invented at the end of the Second World War in Owens-Corning-Fiber Glass: the Aerocor process consists in producing rods of glass 1 mm thick and pushing them into a stream of hot gases emerging from a burner. The glass is then stretched and forms filaments of a fine glass-wool on which is deposited a binder to make a sort of porous and insulating blanket which was used at first for plane insulation. The third process is purely mechanical: it was invented in 1955 at the Johns Manville Company. Molten glass falls on a very fast horizontally rotating wheel. The glass drops ejected by the first wheel arrive on a second one turning in the opposite direction and on a third one turning in the same direction as the first one. The projections issuing from the last wheel are a mixture of drops and filaments and are then processed as in the previously described system, giving what is usually called Rock wool because the batch was initially made with basalt rocks having a very low viscosity adapted to this process when melted at high temperature. The furnace used mostly for this production is an unusual one in the glass industry: a cupola, a device more frequent in metallurgy, where the compacted batch is introduced into alternate layers together with coke as a fuel. In 1931, Hager invented an original process using centrifugal force to stretch molten glass falling on a circular refractory device having radial slots. Streams of glass are ejected by the centrifugal force through the slots and stretching is produced by friction between the high-speed streams of molten glass and the surrounding air. In 1957, Saint-Gobain (Isover) achieved the development of the process: the molten glass is supplied to the fiberizing machine, it flows into the spinner, where it is ejected by centrifugal force through the band of this spinner in refractory steel drilled with a multiplicity of holes of about 1 mm diameter each, creating the fibers. A strong annular burner situated outside and above the spinner completes the stretching of the filaments down to a very small size around 1 m in diameter and projects them into the reception zone. In between they are sprayed with a binder, arrive on the conveyor and are shaped into a blanket. Then the glass fiber blanket passes through a curing oven and can be compressed to achieve its final thickness.
45
History
1.6.6 Textile Fiber Glass
1.6 The Revolutions of the Twentieth Century
46
Introduction
History
1.7 Conclusion scientists, artists, and industrialists would not be reduced to regrettable inaction without the indispensable aid of their spectacles. However, these are not the only important results of the admirable properties of this material. It is to glass that the natural sciences owe their most notable discoveries; by its use they have been increased, clarified and placed on solid principles. It is by means of glass that man has been able to investigate the two limits of infinity (microscopy and telescope). Glass allows us to decompose light, to analyze and weigh the atmosphere, measure heat, study electricity and all aerial fluids, the invisible agents that influence so powerfully the great phenomena of Nature and by which man passes over the seas against the winds, shrink distances by locomotion, rises into the skies, and communicates instantaneously with all corners of the world. The multiplicity and importance of these advantages, exclusively due to glass, ensure a legitimate interest in researches into its invention. One should be curious about who first made it, how it was improved and the uses to which it has been put.
Despite all the misadventures which could have occurred within five thousand years, glass has survived and developed to be an essential material in our lives today. I would like to recall a few words from Georges Bontemps at the beginning of his famous book, the Guide du Verrier, in 1868 [1.19]: Among the numerous and varied products that attest to the industrial genius of mankind, few others have as many uses as glass or possess such marvellous properties. No other material could replace glass in its most important applications; only iron could dispute the pre-eminence of this diaphanous substance that, above all, while protecting us from the intemperance of our climates, allows us to enjoy the clarity of daylight. If our most fastidious habitations are ornamented with mirrors and chandeliers, the facets of which prismatically refract and reflect the light with such brilliance, it is also true that few humble thatched cottages are without some window panes, a small mirror and a few drinking glasses. Not being subject to decomposition by acids (other than fluorhydric) glass is eminently suitable for the storage without alteration of liquids of all kinds and, by its transparency, allows us to appreciate their condition. Glass has also prolonged the active career of many a man, who without it would be condemned to predictable old age: how many of our statesmen,
This is what was tried in this chapter, even if many properties or applications have not been treated, such as optical properties and optical glass for instance, which would be part of other chapters in the book.
References 1.1 1.2 1.3 1.4 1.5
1.6
1.7
S. Johnson: The fondness of every man for his profession, The Rambler April 17th (1750) A. MacFarlane, G. Martin: The Glass Bathyscaphe (Profile Books, London 2002) A. Bitard: Les arts et métiers illustrés (Jules Rouff et Cie éditeurs, Paris around 1890) Pliny the Elder, Natural History, Vol. 36 W.E.S. Turner: Studies in ancient glasses and glassmaking processes. Part V Raw materials and melting processes, J. Soc. Glass Technol. 8 (1929) J.F. Cubells: Le verre à vitre de l’épave romaine de Porticcio (Golfe d’Ajaccio, Corse), Verre et Fenêtre de l’Antiquité au XVIIIème siècle, Les cahiers de Verre et Histoire n°1, 39–45 (2005) M.-P. Jézégou, H. Bernard: Epave Ouest-Embiez I – Agencement de la cargaison: quelques pistes pour l’étude du commerce du verre au début du IIIème siècle après J.C, Verre et Fenêtre de l’Antiquité au XVIIIème siècle, Les cahiers de Verre et Histoire n°1, 25–28 (2005)
1.8
1.9
1.10
1.11
1.12 1.13
P. Vipard: L’usage du verre à vitre dans l’architecture romaine du Haut-Empire, Verre et Fenêtre de l’Antiquité au XVIIIème siècle, Les cahiers de Verre et Histoire n°1, 15–24 (2009) L. Figuier: Industrie du verre et du cristal. In: Les merveilles de l’industrie (Librarie Furne, Jouvet et Cie, Paris 1880) pp. 7–158 S.D. Fontaine, D. Foy: La modernité, le confort et les procédés de fabrication des vitrages antiques. In: De transparentes speculations, vitres de l’antiquité et du haut Moyen-Age (Occident-Orient), exposition du Musée départemental de Bavay (2005) pp. 15–24 T.C. Barker: Pilkington Brothers and the Glass Industry (Ruskin House, George Allen & Unwin, London 1961) R. Wagner, F. Fischer, L. Gautier: Chimie Industrielle (Librairie F. Savy, Paris 1892) p. 42 D. Foy, G. Sennequier: A travers le verre du Moyen Age à la Renaissance (Rouen exhibition 1989)
The History of Glass
1.15
1.16
1.17 1.18
1.19
1.20 1.21
1.22
1.23
1.24 1.25
1.26 1.27 1.28
A. Neri: The Art of Glass (Society of Glass Technology, Sheffield 2006), original published in 1662, ed. by M. Cable, translated into english by C. Merrett M. Verita: Italian window glass chemical composition from the roman time to the 18th century, Verre et Fenêtre de l’Antiquité au XVIIIème siècle, Les cahiers de Verre et Histoire n°1, 11–16 (2009) G. Agricola: De Re Metallica, Book XII (Dover, New York 1986), original published 1556, translated by H.C. Hoover and L.H. Hoover, http://farlang.com/books/ agricola-hoover-de-re-metallica J. Henrivaux: Le verre et le cristal (Vicq-Dunod, Paris 1897) D. Foy: La suprématie du verre soufflé en cylindre, panneaux et vitraux du Vème au IXème siècle. In: De transparentes speculations, vitres de l’antiquité et du haut Moyen-Age (Occident-Orient), exposition du Musée départemental de Bavay (2005) pp. 59–64 G. Bontemps: Le Guide du verrier (Society of Glass Technology, Sheffield 2010), original published in 1868, translated by M. Cable F.W. Hodkin, A. Cousen: A textbook of glass technology (Constable, London 1925) N. Fiérobe: La champenoise, outil de champagnisation. In: Champenoises, Champagne 2000 (Ateliermusée du Verre de Trélon, Écomusée de la région de Fourmies-Trélon, Trélon 2000) p. 79 Delaunay-Deslandes: Mémoires, unpublished Internal Report, Archives de la Compagnie de Saint Gobain H. de Coqueréaumont: Compagnie de Saint Gobain – Fabrication des glaces 1665–1914, Internal Saint Gobain report by 1920 (Archives de la Compagnie de Saint Gobain, Blois 1920) P. Flamm: Le verrier du XIXème siècle (Eugène Lacroix, Paris 1863) A.F. Gehlen: Über das Glasmachen ohne Pottasche vermittels des Glaubersalzes, Ann. Chem. 1816(97), 216–218 (1813) W.E.S. Turner: General discussion, Trans. Soc. Glass Technol. (1922) W.E.S. Turner: Discussion, J. Soc. Glass Technol. (1927) M. Cable: The advance of glass technology in the nineteenth century. In: Proc. Int. Congr. Glass, Edinburg, Vol. 1 (2001) pp. 121–130
1.29
1.30
1.31
1.32 1.33
1.34 1.35
1.36
1.37 1.38
1.39
1.40
1.41 1.42 1.43 1.44
M.-H. Chopinet: Developments of Siemens regenerative and tank furnaces in Saint-Gobain in the XIXth century, Glass Technol. 53(5), 177–188 (2012) C.W. Siemens: Improvements in furnaces and in the application of heated currents, patent A.D. 1857, May 11, No. 1320 (1857) C.W. Siemens, F. Siemens: Four à gaz et à chaleur régénérée inventé par M. C.W. Siemens et son frère Frédéric Siemens (Dunod, Paris 1863) F. Siemens: Four Siemens Nouvelle Disposition, document Archives Saint-Gobain T.C. Barker: The Glassmakers – Pilkingtons: The Rise of an International Company 1826–1976 (Weidenfied & Nicolson, London 1976) H. Le Châtelier: La mesure des températures élevées (George Carré et C. Naud, Paris 1900) M.-H. Chopinet: Lucien Delloye, ou comment un ingénieur mécanicien régna sur l’industrie européenne du verre à glaces pendant plus d’un quart de siècle, Mat. Tech. 103(4), N9, 1 (2015) J. Hartley: Specification of the Patent granted to James Hartley, of Sunderland, Glass Manufacturer, for Improvements in the Manufacture of Glass, Sealed 7 Oct. (1847) C. MacIntosh: The Book of the Garden, Vol. 1 (W. Blackwood & Sons, Edinburgh 1853) J.B. Langley: The Illustrated Official Guide and Tourist’s Handbook to the Northern Railway (Lambert, Newcastle 1863) J.P. Daviet: Un destin international, la compagnie de Saint Gobain de 1830 à 1939 (Editions des archives contemporaines, Paris 1988) M. Boagglio: Evolution des technologies de fabrication de la champenoise. In: Champenoises, Champagne 2000 (Atelier-musée du Verre de Trélon, Écomusée de la région de Fourmies-Trélon, Trélon 2000) pp. 92–113 E. Damour: Cours de verrerie. Part 3 (Librairie polytechnique Ch. Béranger, Paris 1936) E. Damour: Cours de verrerie. Part 1 (Librairie polytechnique Ch. Béranger, Paris 1929) J. Henrivaux: La verrerie au vingtième siècle (E. Bernard & Cie, Paris 1904) J. Barton, C. Guillemet: Le verre, science et technologie (EDP Sciences, Les Ulis 2005)
Marie-Hélène Chopinet Saint Gobain Research Aubervilliers, France [email protected]
Marie-Hélène Chopinet received her PhD in 1978 from the University of Paris VI. She worked as a Research Engineer for Saint Gobain for over 35 years (until her retirement). Her main scientific activities included the development of glass formulations, the melting process, and the improvement of glass durability and color.
47
History
1.14
References
49
Part A
Fundame Part A Fundamentals of Glass and the Glassy State
2
Thermodynamics and Kinetics of Glass Reinhard Conradt, Aachen, Germany
3
Viscosity of Glass and Glass-Forming Melts Ulrich Fotheringham, Mainz, Germany
4 Crystallization and Glass-Ceramics Mathieu Allix, Orléans, France Laurent Cormier, Paris, France 5 Linear Optical Properties Martin Letz, Mainz, Germany 6 Nonlinear Optical Properties of Glass Marc Dussauze, Talence, France Thierry Cardinal, Pessac, France 7
Mechanical Properties of Glass Jean-Pierre Guin, Rennes, France Yann Gueguen, Rennes, France
8 Chemical Strengthening of Glass Timothy M. Gross, Corning, NY, USA
9 Colors in Glasses Dominique de Ligny, Erlangen, Germany Doris Möncke, Alfred, NY, USA 10 Electrical Transport Properties of Glass Koichi Shimakawa, Gifu, Japan 11 Photosensitivity in Glasses Yasuhiko Shimotsuma, Kyoto, Japan Masaaki Sakakura, Southampton, UK Masahiro Shimizu, Kyoto, Japan Kiyotaka Miura, Kyoto, Japan Kazuyuki Hirao, Kyoto, Japan Jianrong Qiu, Hangzhou, China Peter G. Kazansky, Southampton, UK 12 Chemical Durability of Glasses Abdesselam Abdelouas, Nantes, France James Neeway, Richland, WA, USA Bernd Grambow, Nantes, France
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_1
51
Reinhard Conradt
This chapter gives an overview of the thermodynamics of the glassy state and the kinetics of glass formation and relaxation. The emphasis is placed on thermodynamics. First, several characteristic features of glasses are discussed in relation to earlier definitions of the glassy state. Then, the glassy state is contrasted to equilibrium states by discussing glass formation versus crystallization, the glass transition versus equilibrium phase transitions, and relaxation phenomena typical of glasses. A major part is devoted to fundamental aspects of the thermodynamics of glasses, comprising a detailed discussion of enthalpy, entropy, and the kinetics of glass formation as derived by nonequilibrium thermodynamics. Another significant part focuses on the quantitative treatment of multicomponent glasses and glass melts by using the formalism of thermodynamics of mixed phases. Tools and models are presented allowing one to approach the properties of glasses relevant to industry. In terms of examples, the emphasis rests on oxide glasses, in specific, silicate glasses. The chapter closes with an outlook on future developments and on challenges for future research work.
The topic of thermodynamics and kinetics of glass has been covered in depth by many excellent monographs [2.1–7], book chapters [2.8, 9] and review papers [2.10–12], which are highly recommended for further reading. This chapter gives a brief overview of only a few of the main aspects of the topic. The emphasis is placed on the thermodynamic treatment of glasses and their melts. Kinetic aspects are addressed chiefly in their relation to thermodynamics. It is true that crystallization phenomena and the issue of viscosity are core topics related to kinetics, but these issues will be treated in detail in the following two chapters of the handbook. So, only a brief introduction to crystallization and viscosity of glass-forming systems will be given here. In terms of examples, the emphasis rests on oxide glasses, more specifically silicate glasses.
2.1
Definition of the Glassy State................
52
2.2 General Observations ........................... 2.2.1 Glass Formation versus Crystallization..... 2.2.2 The Glass Transition versus Phase Transition ......................... 2.2.3 Relaxation Phenomena .........................
55 55
Fundamental Aspects of the Thermodynamics of Glasses ........ 2.3.1 Enthalpy .............................................. 2.3.2 Entropy ................................................ 2.3.3 Thermodynamic Treatment of Glass Formation Kinetics....................
56 58
2.3
2.4 2.4.1
61 61 64 67
Multicomponent Glasses....................... Review of Thermodynamics of Mixed Phases.................................... 2.4.2 Model Approaches ................................
69 69 70
2.5
Summary and Outlook ..........................
74
References.....................................................
74
In Sect. 2.2, general observations are compiled. They refer to the nature of the glass transition as compared to phase transitions, to glass formation versus crystallization, and to phenomena typically observed in the glass transition. Section 2.3 is devoted to fundamental aspects of the thermodynamics of the glassy state. The essential facts are demonstrated for one-component systems. The topics of enthalpy, entropy, and the consequences for glass formation kinetics are discussed in detail. Section 2.4 deals with the challenge of transferring the above general findings to multicomponent glasses. It is the purpose of this section to render the methods of thermodynamics useful for the treatment of typical industrial glasses, most of which contain five to ten oxide components. The chapter closes with an outlook on future developments and on challenges for future research work.
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_2
Part A | 2
Thermodynam 2. Thermodynamics and Kinetics of Glass
52
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.1
2.1 Definition of the Glassy State Different definitions of the glassy state have been given. These definitions are compiled, supplemented, and briefly discussed here. Earlier definitions read like this: “In the glassy state, there are solid non-crystalline materials” [2.1], and, “Glass is an inorganic product of fusion which has been cooled to a rigid condition without crystallization” [2.13]. As much as these definitions grasp some essential facts, they also have some weaknesses. First, there are solid noncrystalline materials like xerogels that are definitely not glasses. Second, glasses are not necessarily inorganic materials, and although producing glasses by cooling their melt is the most widespread method, it is not the only way. Glasses may also be formed along the pressure coordinate, by polymerization, or by precipitation from the gas phase. Therefore, the above definitions are supplemented by the author in the following way: Glasses are dense (nonfractal) isotropic and homogeneous noncrystalline solids characterized by the absence of any internal phase boundaries. It is true, the latter statement also applies to single crystals, but these are not isotropic. It is also true that thermally or chemically strengthened glasses display density gradients, hence, a distinct unisotropy. But this requires specific measures of secondary production. By their very nature, well annealed glasses are isotropic. The absence of internal phase boundaries has far-reaching consequences for the optical and mechanical properties, like transparency, stiffness, lack of ductility, brittleness, and fracture behavior. On the basis of groundbreaking work by Zachariasen [2.14], later modified by Greaves [2.15], the following definition is added: “At the atomic scale, glasses are characterized by the absence of any translational symmetry.” No unit cell of a glass can be given. Therefore, glasses have been termed amorphous. This is, in fact, a poor statement. The term means absence of a defined structure, thus expressing what we do not know
about glass structure only. In Table 2.1, features of gases, crystals, liquids, and glasses are compiled. While well elaborated theories are available for the former two states, we still lack the formulation of a concise theory for liquids and glasses alike. As Landau [2.16] pointed out, this is chiefly attributed to the fact that both liquids and glasses lack a small parameter: both atomic interaction and displacement are large. Yet, there is no complete absence of order. The degree of order is grasped by the categories of short-range order (SRO) and medium-range order (MRO). For silicate glasses, SRO chiefly consists in the nature of the cation coordination polyhedra, and MRO in the nature of linkage among these polyhedra. Frenkel [2.17] stated that, in view of the small energetic and entropic differences between glasses and isochemical crystals (as compared to the energies and entropies of formation from the elements), the structural disorder of glasses and even liquids cannot be dramatic. The residual degree of order (SRO and MRO) is clearly reflected by the similarity of phononic properties of glasses and their crystalline counterparts, like heat capacity, thermal expansion, and elastic moduli. The sketch in Fig. 2.1 shows the x-ray diffraction pattern of the polycrystalline state of phases cristobalite SiO2 , sodium disilicate Na2 Si2 O5 , and devitrite Na2 Ca3 Si6 O16 in proportions corresponding to a glass composition of 74 SiO2 , 10 CaO, 16 Na2 O (by wt%). Very tiny crystals (phenocrystals) would show a broadening of the diffraction peaks; their average size b can be derived from the width B of the peaks at halfheight given as B D . =180ı/1=2.2max 2min / by using Scherer’s formula
bD B cos
1 2 2
;
(2.1)
where is the x-ray wavelength and 2 the diffraction angle. There is no doubt that the diffraction pattern
Table 2.1 Comparison of structural and dynamic features of gases, crystals, liquids, and glasses in general State Gas Crystal
Order Dynamic disorder Static order
Interaction !0 Large
Displacement Very large !0
Liquid
Static and dynamic disorder; SRO, MRO
Large
Moderately large
cV .T/ 3=2 Nk 3 Nk 3 3 !!DF Nk
Glass
Static disorder; SRO, MRO
Large
Moderately large
3 Nk
The expression of cV .T/ for liquid follows a proposition by [2.18]; !F D Frenkel frequency of positional hopping of atoms, !D D Debye frequency; this scenario does not take into account any configurational degrees of freedom thus that cV .T/ might take the form cV D aNk with a > 3.
Thermodynamics and Kinetics of Glass
with chemical composition 74 wt% SiO2 , 10 wt% CaO, 16 wt% Na2 O; polycrystalline state with cristobalite, devitrite, and sodium disilicate crystals, phenocrystalline state of identical constitution, and glass J
(Poly)crystalline state
Phenocrystals
Glass
10
15
20
25
30
35
40
45
50 2θ (°)
a)
of the glass still bears the signature of the crystalline state. This led earlier scientists to the conclusion that, based on the observed peak broadening, the glass structure should consist of 23 nm-sized nanocrystals. Recent high-resolution TEM (transmission electron microscopy) images [2.19] (Fig. 2.2), however, clearly show that there is no crystallinity at all, not even at the nm scale. On the basis of a statistical evaluation of atom positions determined at the surface of a silica glass (Fig. 2.3) by UHV-AFM (ultra-high-vacuum atomic force microscopy) [2.20] assigning bonds to any distances approximately corresponding to the crystallographic Si–O distances, and accidental neighborhood only to the rest, a distinct clustering at the nm scale is revealed. The final definition of the glassy state reads “Glasses are undercooled frozen-in liquids” [2.21–23]. In thermodynamic terms, this is the most concise definition. It is valid even if a glass has not been formed by cooling from a melt. For example: silica glass can be produced by sintering pyrogenic silica particles. The b)
MgTi2O5 nanocrystal
BPO4 nanocrystal
4 nm
10 nm
Fig. 2.2a,b High-resolution transmission electron microscope images of two different glasses in the early stage of crystallization: (a) MgO-Al2 O3 -TiO2 -SiO2 ; (b) BPO4 -SiO2 glass. The presence and absence of translational order in the crystallites and in the glass matrix, respectively, is clearly seen. Reprinted with permission from [2.19]
53
Part A | 2.1
Fig. 2.1 Sketch of x-ray diffraction patterns of samples
Intensity (arb. u.)
5
2.1 Definition of the Glassy State
54
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.1
a) Abundance
c) ≡Si–O–Si≡
O–Si–O
≡Si–O
0.1
0.2
0.3
0.4 Distance (nm)
b) nm
2
1
0
0
1
2
nm
Fig. 2.3a–c High-resolution vacuum atomic force microscope image of a fracture surface of silica glass with illustration of the evaluation procedure of atomic distances (c) yielding the abundance distribution as shown in (a); an evaluation in terms of crystallographic Si–O distances yields the image of connectivity at the atomic scale as shown in (b). Reprinted
from [2.20] with permission from Elsevier Fig. 2.4 Didactic illustration of
Traffic direction Fluid, low viscosity
High-T limit
Onset of cooperative effects Independent motion, full access to degrees of freedom velocity and change of lane Loss of degree of freedom velocity, strictly correlated cooperative motion, onset of deviation from Arrhenius behavior Loss of degree of freedom Frozen-in state, rigid change of lane, and noncrystalline fluid, high viscosity
a freezing-in process occurring upon gradual loss of configurational degrees of freedom; example of a traffic jam
Thermodynamics and Kinetics of Glass
SiCl4 .g/ CO2 .g/ C2H2.g/ ! SiO2 .am/ C4HCl.g/ (2.2)
has been sintered to monolithic silica glass [2.24]. The resulting material is an undercooled frozen-in melt ex-
perimentally not distinguishable from silica glass prepared via the melting route. The sintering of pyrogenic silica is the preferred production route for ultrapure communication fibers. Figure 2.4 presents a pedagogical illustration of a freezing-in process. In a most general way, freezing-in occurs as a sudden transition upon a continuous loss of configurational degrees of freedom. Eventually, a rigid noncrystalline state (traffic jam) is reached.
2.2 General Observations In this section, three phenomena with importance for glass formation are addressed, namely, crystallization (which is to be avoided), equilibrium phase transitions (in contrast to the glass transition), and relaxation phenomena.
2.2.1 Glass Formation versus Crystallization When a one-component melt is cooled down below its melting temperature Tm , it assumes a metastable undercooled state. It is true, the stable state at T < Tm is a crystalline state, typically with polycrystalline microstructure (the growth of a single crystal requires highly specialized procedures not discussed here). But the actual occurrence of crystals requires a critical undercooling Tcrit . For water, Tcrit =Tm 0:85. A compilation of data for close to 60 different systems [2.2] yields an average of Tcrit =Tm D 0:81 ˙ 0:05, with the largest value D 0.88 and smallest value D 0.66, respectively. Crystallization from a homogeneous melt requires the foregoing formation of nuclei from which the crystals start to grow. If the local growth of individual crystals proceed at a constant velocity vCG (m=s), then the volume of a dendritic, planar, or spherulitic crystal increases in proportion to (vCG t/n with n D 1; 2; 3, respectively. For diffusioncontrolled local growth, it increases like .Dt/n with n D 1=2; 1; 3=2, respectively; D (m2 =s) is the diffusion coefficient. The dimensionless number density NV of nuclei develops like NV / tm with m D 0 for a constant number of nuclei, and m D 1=2, 1 for diffusion-controlled and linear nucleation kinetics, respectively. The volume fraction XV of crystalline matter in the system increases like XV D 1 exp.CtnCm / ;
(2.3)
and depending on the geometry and kinetics of nucleation and crystal growth, the exponent n C m may assume values between 1=2 and 4 (Kolmogorov–
Johnson–Mehl–Avrami mechanism [2.25–30]). In the case of linear spherulitic growth and constant nucleation rate J0 (s1 ), and at very small volume fractions XV , XV
1 3 J0 .T/vCG .T/t4 ; 3 V0
(2.4)
where V0 (m3 ) is the total volume of the system. The quantities vCG .T/ and J0 .T/ depend on temperature [2.1, 23, 31] like T vCG / Hm 1 ; Tm ˝ J0 .T/ / 1 exp .T=Tm /.1 T=Tm / 1
(2.5a) (2.5b)
(see insert in Fig. 2.5); ˝ D .16 =3/ 3VX2 = .Hm2 kTm /, where .N=m/ D interfacial tension between melt and crystal, VX .m3 =mol/ D molar volume of the crystal, and Hm .kJ=mol/ D heat of melting. For a fixed threshold XVı , (2.4) yields a relation T.t/. If plotted as T versus log t, a TTT (time-temperature-transformation) curve is obtained (Fig. 2.5). The curve marks the boundary at which the threshold XVı is reached. TTT curves are powerful tools allowing one to design cooling procedures in such a way that crystallization is safely avoided. The straight line in Fig. 2.5 does, of course, not represent a constant cooling rate. But the rate q.ttp / at the tangential point tp marks a critical value which must be exceeded to keep the degree of crystallization below XVı . Typically, XVı D 1 106 is quoted as a threshold to obtain a noncrystalline material. This would, however, amount to 1 cm3 =m3 . If expressed as the number of defects of 250 m size in a standard float glass sheet of dimensions 3 6 0:004 m3 , this would mean 8800 defects per sheet, which is completely unacceptable. In industrial production, values of XVı D 5 1012 would still lead to a reject rate of 45%.
55
Part A | 2.2
commercial product OX50, a powder of pore-free beads of 3050 nm size precipitated in an amorphous state (am) from the gas phase by the reaction
2.2 General Observations
56
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.2
T
Tm Tm
vCG
J0
Critical cooling rate at tp
vCG, J0
log (t)
Fig. 2.5 Sketch of a time-temperature-transformation
(TTT) curve of a glass-forming system in a plot of temperature versus log time; the bold curve marks the boundary beyond which (to the right) a given volume fraction XVı of crystals in the volume is exceeded; the cooling rate at the tangential point tp marks the critical cooling rate keeping the crystal volume fraction below XVı ; insert: Tammann curves (after [2.1]) showing the temperature dependence of the crystallization velocity vCG and of the nucleation rate J0 (arb. u.); Tm is the melting temperature
2.2.2 The Glass Transition versus Phase Transition Phase transitions are transformations between equilibrium phases. They occur at well-defined temperature or pressure fixpoints Teq or peq , respectively. The elementary school examples are the ice–water and the water–steam transitions at Teq D 0 and 100 ı C, respectively, and peq D 1 atm D 1:013 25 bar. At a constant temperature of T D 25 ı C, the water–steam transition occurs at peq D 0:032 bar. Let the indices X and L denote a crystal and an isochemical liquid, respectively. Then, in a general way, the heterogeneous equilibrium between both phases is defined by the condition j;L .T; p/ D j;X .T; p/
(2.6)
for each component j in the system; is the chemical potential. For one-component systems, G , hence, GL .T; p/ D GX .T; p/. Thus, in equilibrium, dG D .SL SX /dT C .VL VX /dp D 0 ;
(2.7)
yielding the Clausius–Clapeyron equation SL SX QX!L dP D : D dT VL VX T.VL VX /
(2.8)
QX!L is a finite amount of heat transferred to the system during melting. At Tm , QX!L D Hm (heat of melting) and Sm = Hm =Tm (entropy of melting). Phase transitions of this type are termed 1st-order transitions because the first derivatives of the G function, i. e., (@G=@T/p D S and (@G=@p/T D V display finite and sharp discontinuities. By contrast, 2nd-order phase transitions are characterized by finite and sharp discontinuities in the second derivatives of G. The matrix .G/T;p of second derivatives reads c=T ˛V (2.9) .G/T;p D : ˛V =V For any phase in internal equilibrium, det.G/T;p > 0, hence, c > VT˛ 2 > 0. Here as in the rest of the chapter, c shall denote the heat capacity at constant pressure, ˛ the volume expansion coefficient at constant p, V the molar volume, and the isothermal compressibility. Material scientists prefer the use of the isothermal compression modulus KT D 1= . For 2nd-order phase transitions between two phases I and II, two separate relations for dp=dT are obtained, namely dp 1 cII cI D D dT TV ˛II ˛I dp ˛II ˛I 1 D D dT
II I TV
1 c ; TV ˛ ˛ :
(2.10a) (2.10b)
Equating dp=dT yields Ehrenfest’s relation 1 c
dp D D1: dT TV .˛/2
(2.11)
Distinct jumps c, ˛, and are characteristic of a 2nd-order phase transition. In Fig. 2.6, the changes observed in the glass transition are compiled. The glass transition is also characterized by jumps of c, ˛, and . These jumps, however, do not occur at a distinct temperature, but extend over an—albeit narrow—temperature interval (Fig. 2.6a). The reality of undercooled liquids is more complex than suggested by this simple sketch. Depending on the glass-forming system, heat capacities beyond the jump of c may remain constant, or increase, or decrease [2.31, 32, 32]. Figure 2.6b shows that no heat of transformation is involved in the glass transition. At glass transition temperature Tg , G, H, S, and V show changes of their slopes which also extend over a narrow temperature interval. Figure 2.6c,d shows that the approach towards Tg from high temperatures goes along with a dramatic increase of viscosity (Pa s) over many
Thermodynamics and Kinetics of Glass
b)
cp, α, κ
H, S, G; V
H; V
S
G Tg
Tg T
c) log η (Pa s)
T
d) log η (Pa s) 12
12 10 Long
Working range
8
8 4
6
Strong 0 Length
2 Tg 0
Fragile
Long
4
Very fragile Short
very short
–4 T
0.0
0.2
0.4
0.6
0.8
1.0 Tg/T
Fig. 2.6a–d Phenomena observed during glass formation as a function of temperature; Tg D glass transition temperature; (a) jump of heat capacity cp , expansion coefficient ˛, and compressibility ; (b) enthalpy H, molar volume V, Gibbs energy G, and entropy S; (c) viscosity curves for three glasses with very different working range “length”; (d) Angell’s plot (after [2.33]) for the same glasses, showing strong, fragile, and very fragile behavior; dashed diagonal: perfect Arrhenius behavior; dashed tangent: fragility slope of the very fragile glass
orders of magnitude. The steepness of the increase differs for different glass-forming systems. Technologically, it is quantified by the so-called length of the glass denoting the temperature difference between viscosity levels log D 3 and 5. This is the temperature range within which a macroscopic shape may be imposed on the undercooled melt during technical glass forming. In scientific terms, the slope at which log approaches Tg in a log versus Tg =T plot is taken as the measure of steepness (Fig. 2.6d; Angell’s plot [2.33]). It is termed the fragility of the glass. Systems with slopes close to the diagonal are termed strong glasses; their viscosity shows an Arrhenius-type temperature dependence. Systems with large slopes are termed fragile glasses. The reader is cautioned that these terms have nothing to do with the strength of a glass. For the high-T limit Tg =T ! 0 the sketch involves an oversimplification. In
57
Part A | 2.2
a)
2.2 General Observations
fact, there is no universal high-T limit for the viscosity at log D 5. Rather, experimental data of different glass-forming systems extrapolate to values between 1 and 6. Figure 2.7 shows that experiments are rarely performed below Tg =T D 0:2, which corresponds to inaccessibly high temperatures in most cases. Freezing-in occurs in an approximately universal way at log D 12. It is true, the glass transition displays some faint similarities to a 2nd-order phase transition. But when (2.11) is evaluated, then dp 1 c
D D PD > 1 dT TV .˛/2
(2.12)
is found. In (2.12), PD denotes the Prigonine–Defay ratio. A compilation for PD rations is given in [2.34].
58
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.2
merization) represented here by a vector nj comprising the molar amounts of components j. Combined formation paths are possible, too. The following discussion shall be restricted to glass formation via cooling. The sketch in Fig. 2.8a illustrates how the glassy state depends on the cooling rate in principle. At temperatures well below the glass transition, it bears the signature of the temperature Tf at which the system drops out of thermodynamic equilibrium. Tf is termed the fictive temperature. Thus, for a glass, G D G.T; p; nj ; Tf /. For alternative formation routes, a fictive pressure or a fictive degree of polymerization play an analogous role. As a direct consequence, the glass transition temperature Tg of a glass shifts with the cooling rate q (K=s or K=min). Among several other approaches [2.39], the following relations between Tg and q have been proposed [2.40, 41]
log η (Pa s)
11 9 7
Nepheline NaAl 2Si 2O8 Anorthite CaAl 2Si 2O8
5
SiO2
3 1
7BeF2·3NaF
–1
2BiCl 3·KCl
ZnCl 2
–3 –5 0.0
0.2
0.4
0.6
0.8
1.0 Tg/T
Fig. 2.7 Angell’s plot (log viscosity versus reduced tem-
perature Tg =T) for different glass-forming systems; data after [2.33]
They range from approximately 2.0 to 2.7 for technical silicate glasses, to 2.5 for bulk metallic glasses, 4.7 for B2 O3 , 9.4 for glycerol, and 103 105 for different kinds of pure silica. The deviations PD > 1 have been interpreted by the action of more than one order parameter in the freezing-in process [2.35–37]. In any case, the glass transition cannot be interpreted as a special case of a 2nd-order phase transition. Gundermann et al. [2.38] identified tetramethyl-tetraphenyltrisiloxane as a nearly perfect van der Waals system (absence of molecular association or any network forming tendency), with PD D 1:1 ˙ 0:3 and 1:2 ˙ 0:6 as determined by different methods. Until today, this remains a rare example for PD 1. In view of the above facts, we may conclude that the glass transition is not a phase transition according to Ehrenfest’s classification, and the glassy state is not a classical aggregate state [2.2].
2.2.3 Relaxation Phenomena As stated above, a phase transition is a transformation between equilibrium phases. Both phases involved represent a path-independent equilibrium state determined by T, p, and composition only. By contrast, the state of a glass at a given temperature and pressure also depends on the path along which it was formed. In fact, a glass can be formed along any variable of the Gibbs function G.T; p; nj /, i. e., along the T-axis (cooling), the p-axis (jamming), or a compositional axis (e. g., poly-
dTg DC; d ln q q D A exp
(2.13a)
Eq RTg
:
(2.13b)
The constants C, Eq , and A are glass specific; the equations are useful tools for the evaluation of experiments. The sketch in Fig. 2.8b, shows how the viscosity of a glass-forming system behaves in the temperature regimes ranging from high temperatures to temperatures well below Tg [2.4]. At very high temperatures (I), viscosity displays an Arrhenius-type dependence on temperature, ln / E =.RT/ (E D activation temperature of viscous flow), followed by a range with nonArrhenius behavior characterized by fragility (compare to Fig. 2.6). Below Tg , the range of isostructural viscosity is reached. In this range, .T/ shows Arrhenius behavior again, but it bears the signature of its thermal history given by the fictive temperature Tf . Different cooling scenarios yield different viscosities in this range. At this point, the reader may be puzzled concerning the difference between the meaning of fictive temperature Tf and glass transition temperature Tg . A detailed discussion of the matter is given in [2.3]. On first glance, there is no objection to using Tf and Tg as synonyms; but on a second look, one must acknowledge the different concepts behind Tf and Tg . Tg denotes a quantity determined by experiment, preferentially by the inflection point of the c.T/ or ˛.T/ curve in Fig. 2.6a (calorimetric and dilatometric Tg , respectively). Glass samples should be prepared at a cooling rate qcool , then measured in heating mode at a rate qheat > qcool . For technical glasses, qcool D 2 K=min and qheat D C5 K=min are recommended. Calorimetric and dilatometric Tg values agree within experimental accuracy.
Thermodynamics and Kinetics of Glass
2.2 General Observations
20
Undercooled melt
Tf2
15 Tf1
Tf2
10 Glass High cooling rate
5
II
III
0
Tf1
Low cooling rate
I
–5 0.0
T
0.2
0.4
0.6
0.8
1.0
1.2
1.4 Tg/T
Fig. 2.8 (a) Molar volume and enthalpy of a glass-forming system as a function of temperature and cooling rate; dashed lines: extrapolations of the undercooled liquid state and the glassy states obtained at different cooling rates, respectively; intersections of the dashed lines mark the corresponding fictive temperatures Tf ; (b) viscosity of a glass-forming system, temperature extended to the region below Tg (after [2.4]); I: Arrhenius-type high-temperature behavior; II: nonArrhenius behavior characterized by fragility; III: isostructural viscosity of the nonrelaxed frozen-in liquid at different fictive temperatures; the dashed curve is an extrapolation of the relaxed equilibrium state to T < Tg
Technically, Tg has been defined as the temperature at which a viscosity of 1012 Pa s is reached. In contrast to Tg , the fictive temperature Tf is used as a parameter in relaxation theory. Tool’s equation [2.42] reads T Tf dTf D ; dt
(2.14)
where is a relaxation time. By identifying dTf d D ; T Tf eq
(2.15)
Tool’s equation can be cast into the form of a general relaxation equation eq d D ; dt
eq d D : dT q
(2.16)
In (2.15) and (2.16), is a reaction coordinate in the sense of de Donder’s theory [2.43, 44]. The Gibbs energy of a nonequilibrium system changes like dG D SdT C VdP Ad :
.A=T/d along the coordinate . In equilibrium, A D 0. If the relaxation time in (2.14) and (2.16) has a constant value, then shows an exponential relaxation behavior / exp.t= /, and shows an Arrhenius-type temperature dependence D 0 exp.Ea =kB T/, where 0 is a high-T limit and Ea is an activation energy. By contrast, glass formation is characterized by Three Big Non’s, comprising:
(2.17)
The affinity A D .@G=@ /T;p determines the change of internal entropy (Sect. 2.3.2) of a system: dSint D
A non-Arrhenius temperature dependence of A nonlinear relaxation behavior as a result of the fact that explicitly depends on , too A nonexponential relaxation behavior as a consequence.
Much scientific work has been invested to find adequate formulations for D .T; /. Among the different propositions, Narayanaswami’s model [2.45] has received wide recognition. A detailed compilation of earlier approaches is found in [2.46]. When taking into consideration the relation between relaxation time and viscosity , / [2.47], then the non-Arrhenius temperature dependence of is represented in the best way by well-established viscosity models. Let g D .Tg /, 0 D .T ! 1/, and y D Tg =T. Then is given by ln D ln 0 C .ln g ln 0 /f .y/ :
(2.18)
Part A | 2.2
b) log η (Pa s)
a) V, H
59
60
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.2
The different viscosity models differ by the type of the function f .y/ only. More specifically, we find the following relations: The VFT (Vogel–Fulcher–Tammann) type [2.48– 50] or free-volume type [2.51] has f .y/ D
.1 aVFT /y : 1 aVFT y
(2.19)
With aVFT D T0 =Tg , f .y/ assumes the familiar form f .y/ D const=.T T0 /. The AG (Adam–Gibbs) type [2.52] reads f .y/ D
y 1 aAG ln y
(2.20)
where aAG has a direct thermodynamic meaning: aAG D c=Svit . Svit is the frozen-in configurational entropy of the glass (Sect. 2.3.2). The KWW or Avramov–Milchev type [2.53] reads f .y/ D yaKWW ;
(2.21)
which is basically a stretched exponential or KWW equation. For network-forming glasses, aKWW is approximately given by the molar fraction xMOD of network modifiers, aKWW 1:2 C 6xMOD . The MYEGA type [2.54] has f .y/ D y exp .aMYEGA .y 1// ;
(2.22)
with aMYEGA D aAG D c=Svit like in the AG model. The VFT-type model is the one most widely used in glass technology with significant success over many decades. It stands out because of its formal simplicity. Its familiar form log D A C B=.T T0 / with three empirical fit constants A, B, T0 may be deduced from a free-volume model approach with a free volume V0 .T/ vanishing at T D T0 . This causes, however, log to diverge at T D T0 , which is unphysical and constitutes the major weakness of this model. Viscosities below Tg are systematically overestimated by VFT. But for T > Tg , it yields a highly accurate representation of .T/. Viscosity of standard float glass DGG-1 [2.55] as measured by the National Metrology Institute (PTB) of Germany (46 data points between Tg D 538 and 1400 ı C) were fitted by a least square fit to the four models in (2.19)–(2.22), yielding mean standard deviations ˙ı log of 0.016, 0.016, 0.082, and 0.029, for VFT, AG, KWW, and MYEGA, respectively. This corresponds to a mean temperature error of ˙ıT D
3; 3; 11, and 6 K, respectively. The result is typical of technical glasses with moderately high fragility. For systems with high fragility, AG and MYEGA are more accurate than VFT. MYEGA stands out in accurately describing the range below Tg . For a thorough discussion of the physical background of the viscosity models, as well as the options to generically derive the viscosity-temperature relation from glass composition please refer to [2.56]. It has been a matter of discussion whether or not the high-T limit 0 in (2.18), and hence, the high temperature intercept log 0 in Fig. 2.7, is a universal feature of liquids in general. In fact, the numerical fits to experimental data by (2.19)–(2.22) yield systematically different intercepts log 0 , with KWW typically giving the highest and VFT the lowest value. The models also differ with respect to the slopes (i. e., the activation energies E of viscous flow) at which they approach the limit Tg =T ! 0. For AG and KWW, E ! E0 D 0 (like for a gas-like fluid), while VFT and MYEGA maintain a finite value of E0 > 0. These are major differences in the physical concepts behind the individual models. When equating the high-T limit of a diffusion coefficient in condensed matter D0 D .kB T=h/2 =3 with the Stokes–Einstein–Eyring equation [2.17], D0 D kB T=.6 0 /, then 0 D h=.2 3/ follows; is the atomic distance to bring about a positional change; k and h have their usual meaning. This simple rationale suggests that 0 is probably not a universal constant but depends on the length typical of an individual glass-forming system. A yet unpublished analysis of viscosity data of glycerol and ZnCl2 by a free-volume approach (VFT) yielded log 0 D 5:0 and 3:74 ( in Pa s), respectively, matching very well with the size of the neutral glycerol molecule of approximately 5 Å and the radius of the Cl ion of 1:8 Å, respectively. To summarize: VFT still maintains its role as an excellent model for the temperature range above Tg . Both AG and MYEGA offer the possibility to assess one fit constant by the quantity c=Svit as derived by independent thermodynamic experiments. Thus, with Tg known, only the high-T intercept log 0 remains as the fit constant. MYEGA specifically opens up the possibility for a quantitative treatment of relaxation processes below Tg . This has very important practical consequences, enabling a precise control of annealing and cooling processes, of thermal and chemical strengthening, a precise adjustment of refractive indices of optical glasses, and an approach to the properties of hyperquenched glasses like reinforcement fibers.
Thermodynamics and Kinetics of Glass
2.3 Fundamental Aspects of the Thermodynamics of Glasses
In the following section, the energy of a system is presented in terms of the function of state of enthalpy H. Most thermodynamic textbooks start with the concept that the energy of a system is given by its internal energy U. When the system is isolated from the environment, then U remains constant. Changes dU are brought about by transferring heat or matter, or by performing work on the system. The internal energy U is closely related to the volume V as working coordinate, and hence to the condition dV D 0 in the absence of volume work. This is a convenient boundary for computer simulation. For condensed phases in the real world, however, conditions dV 0 can be maintained under extreme experimental effort only. For this reason, the enthalpy H D U C PV turns out to be a quantity with more practical relevance. At constant pressure, a change dH denotes the amount of heat reversibly exchanged with the environment (hence the symbol H for heat). This is the basis for any industrial heat balance. At environmental pressure p D 1 bar, and with molar volumes
of condensed phases typically ranging from 5 106 to 20 106 m3 =g-atom, the term pV assumes values of 0:52 J=g-atom only, whereas the standard enthalpies of substances are of the order of many kJ=g-atom. Thus, H may even be taken as a fairly accurate representative of the internal energy U.
2.3.1 Enthalpy Figure 2.9 shows the c.T/ function of the onecomponent system CaMgSi2 O6 in the states X D crystal, GL D glass, and L D liquid as determined by different calorimetric methods [2.57–61]. The number of citations shows just how much work has to be invested in the accurate characterization of a single system. The general observation that the onset of the glass transition coincides with the Dulong–Petit value cp D 3NR is well substantiated experimentally, here as well as in many other cases [2.7]. Attention is also drawn to the fact that at temperatures sufficiently > 0 K, the heat b) cp (J/(mol K))
a) cp (J/(mol K))
180 Glass
400
160 140
350
Tm = 1665 K
120 100
300
∆cp 80 Glass
Crystal
Crystal
60 250 40
3NR
20
200 Tg = 981 K 500
1000
0
1500 T (K)
0
100
200
300 T (K)
Fig. 2.9a,b Calorimetric data of heat capacities of the system CaMgSi2 O6 in the crystalline state (bold lines) and in the states glass, undercooled, and stable liquid (big symbols), data from [2.57, 59–61]; glass transition range (small symbols), data from [2.58]; data from; (a) high-temperature range from ambient temperature beyond the melting point Tm ; the jump of heat capacity and the Dulong–Petit value are marked; (b) low-temperature range from 0 K to ambient temperature; Tg D glass transition temperature
Part A | 2.3
2.3 Fundamental Aspects of the Thermodynamics of Glasses
61
62
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.3
capacities of the glass and its isochemical crystalline counterpart are nearly identical. This is attributed to the fact that the wavelengths of thermal phonons are short enough to probe the SRO of the glass structure only. Obviously, GL and X have the same type of SRO. From the data in Fig. 2.9, the enthalpies of GL and X are determined by ZT HX .T/ D
cX dT C CX ;
respectively. The enthalpy values of all elements i at 298 K, 1 bar are defined as zero 298 Z K
ci .T/dT D 0 : 0
Then, the enthalpy of a compound X composed of i moles of elements i is given as 298 Z K
(2.23a)
HXı .298 K/
0
D
ZT HGL .T/ D
cX .T/dT 0
cGL dT C CGL :
(2.23b)
0
Since the branches of X and GL reach an identical state at T D Tm , the branch of GL has to match the value HL .Tm / D HX .Tm / C Hm . Thus, the integration constants CX and CGL in (2.23a) and (2.23b) are related by CGL D CX C HGL .0/; HGL .0/ is the frozen-in configurational enthalpy of the glass at T D 0. CX remains unknown in principle, because energies cannot be defined in an absolute way, but relative to a reference level only. A reference level widely accepted is the state of the elements in their terrestrial isotope mixture at T ı D 298 K, pı D 1 bar. Thus, for example, Fe(fcc), Hg(liq), or O2 (g) represent the elements Fe, Hg, O, a)
(2.24)
H (kJ/mol) 500
0 @ i
1
298 Z K
ci .T/dT A :
The right-hand ordinate of Fig. 2.10a presents the values H ı .T/ for CaMgSi2 O6 . The H ı .T/ are termed standard enthalpies. Most thermodynamic tables [2.62– 64] use this reference system. Some [2.65], however, use an alternative reference system, assigning zero to the enthalpies of the elements at any temperature. The resulting enthalpy values are termed enthalpies of formation from the elements Hf .T/. At 298 K, H ı D Hf ; for other temperatures, the relation X
i Hiı .T/ (2.26) Hf .T/ D H ı .T/
HL(Tm) –2800
b)
S (J / (mol K)) 700
SL(Tm)
600
Sm
T
400
(2.25)
0
H° (T) (kJ/mol)
Hm
X
HGL(0) + ∫ cGL dT
T
0
c G SGL(0) + ∫ GL, dT T 0
500 –2900
300
400 –3000
T
∫ cX dT
200
300
T
c
∫ TX dT
0
0
–3100
200
100 Tg
HGL(0)
Tm –3200
0
0
500 298 K
1000
1500 T (K)
Tg
100
H°X (298 K)
Tm
SGL(0) 0
0
500
1000
1500 T (K)
Fig. 2.10a,b Enthalpies (a) and entropies (b) of the system CaMgSi2 O6 in the solid (X), glassy (GL), and liquid (L) state, obtained by integration of the data shown in Fig. 2.9
Thermodynamics and Kinetics of Glass
a) HGL – HX, GGL – GX (kJ/mol)
the same value p0 . In this state, N spheres with diameter d occupy a total volume Vtot D .N=p0/. =6/d 3. This state is assigned a temperature T D 0. Upon thermal vibrations, an individual sphere occupies a space corresponding to a diameter dT > d. Thus, the total volume increases and the packing density p.T/ < p0 decreases. Upon increasing temperature, such a system shows a phase transition at a distinct temperature from the fcc type to a liquid-like condensed state with nonpercolating free volume. When the free volume starts to percolate, a noncondensed (gas-like) fluid state is reached. An even more interesting phenomenon is found upon cooling of the liquid-like state. At high cooling rates, the rearrangement to the fcc structure does not take place. Rather, random close packing (RCP) occurs which, at T D 0, eventually reaches a well-defined noncrystalline ground state with a packing density p0;rcp D 2= 0:637. The similarity between the curves in Figs. 2.12 and 2.10a are striking. Investigations of this kind shed some light on the mechanisms of glass formation at the atomic scale. They may be adopted as a scientific version of the pedagogical traffic jam illustration in Fig. 2.4. The entropy of the b) SGL – SX (J/(kJ mol))
140
100 Hm
120
Sm HGL – HX
80
100 GGL – GX 60
80
Simon’s approximation
Hvit Svit
60
40
HGL(0)
Tm
40 SGL(0) 20 20 Tg 0
0
500
1000
Tg 0
1500 T (K)
0
500
1000
Tm 1500 T (K)
Fig. 2.11a,b Differences between (a) the enthalpies H and Gibbs energies and (b) entropies S of crystal (X) and glass (GL) for the system CaMgSi2 O6 ; the average value obtained from the shaded areas (Simon’s approximation) yields the enthalpy and entropy of vitrification, Hvit an Svit , respectively; data derived from Fig. 2.9
63
Part A | 2.3
holds, where Hiı .T/ are the (nonzero) standard enthalpies of elements i at temperature T. Figure 2.11a shows the enthalpy difference between GL and X for the system CaMgSi2 O6 . For many practical purposes, we are interested in the enthalpy values of GL for T > 298 K only. In this range, a glass differs from its isochemical crystalline counterpart by a constant enthalpy value Hvit in very good approximation. As a rule of thumb, Hvit 1=2Hm . Unlike Hm , Hvit is not a fixed value. It depends on the fictive temperature Tf of the glass and slightly increases with the cooling q like dHvit / d ln q. According to Fig. 2.8, the enthalpy and molar volume show the same kind of temperature dependence. From this point of view, it is interesting to invoke some theoretical and experimental results from systems composed of monosized rigid spheres (see one of the first approaches in [2.66]). Some recent findings [2.67] are illustrated in Fig. 2.12. The equilibrium state of the system investigated is face-centered cubic (fcc) packing. Maximum volume packing p density p0 is reached at the well-known value p0 D 2 =6 0:740. The hexagonal polymorph (hcp) would reach
2.3 Fundamental Aspects of the Thermodynamics of Glasses
Fundamentals of Glass and the Glassy State
Gas-like
fcc becomes the equilibrium phase
0.3
behavior of a system of monosized rigid spheres (after [2.67])
li k e
Part A | 2.3
Fig. 2.12 Result of a simulation of the
ρ 0.2
0.4
= 2⋅
ρfcc T→ 0
0.5 ρrcp
= T→ 0
2
id -
Part A
6
Li qu
64
Free volume percolation threshold
rcp
0.6 Glass-like
fcc
0.7
0.8 –3
–2
–1
fcc and rcp ground states are 0 and 1 kB per sphere, respectively.
2.3.2 Entropy The issue of entropy is more complex than the issue of enthalpy. For the reader with scientific interest in general, entropy may be perceived as a somewhat cryptic quantity. For this reason, a few fundamental considerations are given first. The term entropy was introduced in 1865 by Clausius as SD
Qrev ; T
(2.27)
where Qrev is the reversibly exchanged heat and T the absolute temperature. In his original work, Clausius used the symbol N instead of S. S is a (pathindependent) function of state. For irreversible processes, S > Q=T. The difference Qrev Q was termed uncompensated heat. According to Prigogine [2.43, 44] and other scientists [2.22], the entropy exchange in nonequilibrium processes is given by dS D dSext C dSint :
(2.28)
Here, Sext denotes the entropy exchange with the environment due to heat, mass, or momentum transfer; Sint denotes the intrinsic entropy production due to dissipation processes (equilibration of internal temperature, pressure or concentration gradients, chemical reactions, etc.). The exchange dSext may assume positive or negative values—the latter at the expense of an entropy
0 log(k B T/(p d3))
increase of the environment. This is the basis for the dramatic entropy increase of growing biological systems and of industrial processes transforming raw materials into sophisticated products. By contrast, dSint 0 always. At the time scale, dSint =dt 0; dSint =dt ! 0 when equilibrium is approached. Statistical interpretations of entropy shall not be discussed here. For further reading, an overview given in [2.68] is recommended. Nonequilibrium thermodynamics plays a key role in the description of glass formation kinetics. The issue will be resumed in Sect. 2.3.3. In 1906, Nernst presented his work on “the calculation of chemical equilibria from thermal measurements” [2.69] and “on the relation between heat evolution and maximal work in condensed systems” [2.70] with the principal conclusion dA dQ D lim D0: T!0 dT T!0 dT lim
(2.29)
A denotes the maximum available work and Q the heat evolution. Today, we would write G instead of A, and H instead of Q. The term entropy was not used explicitly in the original formulation. Equation (2.29) nevertheless led to a fundamental statement on entropy, i. e., the 3rd law of thermodynamics. The formulation of the 3rd law goes back to Planck [2.71] who in 1910 interpreted Nernst’s theorem as follows: Upon infinitely decreasing temperature, the entropy of any pure condensed substance approaches a limit which is independent of pressure, aggregate state, and chemical modification.
Thermodynamics and Kinetics of Glass
The entropy of all factors within a system which are in internal thermodynamic equilibrium disappears at absolute zero.
Here, the term factor, later also called category [2.77], denotes one of various mechanisms like configuration, vibration, orientation, rotation, etc., known to contribute to the entropy of a system. Individual categories may drop out of internal equilibrium and make
a nonzero contribution to the entropy at 0 K, while the rest of the categories remain in internal equilibrium. This goes together well with the experience that the heat content and molar volume of a glass assume an internal equilibrium with respect to the temperature T and pressure p of the environment while its atomic configuration remains in the state frozen-in at the fictive temperature Tf . An earlier description of glasses based on statistical mechanics [2.79] agrees with the above result. For the reader with a general scientific background, the following brief and simplified introduction to the methods of statistical mechanics is given: In statistical mechanics, the so-called phase space of a system containing N atoms is a 6N-dimensional space put up by three space coordinates q.i/x , q.i/y , q.i/z plus three momentum coordinates p.i/x D m.i/v .i/x , p.i/y D m.i/v .i/y , p.i/z D m.i/v .i/z per atom; v D velocity, m D mass. Thus, a system at a given time t occupies exactly one point (one microstate) in phase space. When a sufficiently high number of points is visited during observation time , then the time average and the ensemble average (i. e., the average of individual microstates weighted by their probability to occur) are identical. Such a system is termed ergodic. The average provides access to the macroscopic properties of the system. A recent treatment of the glassy state in terms of statistical mechanics is given in [2.80]. It starts from the concept of broken ergodicity as developed by Palmer [2.81]. The glassy state as a nonequilibrium state is treated as a system with broken ergodicity. Phase space is made up of disparate subspaces ˛ with internal ergodicity, however, confining subgroups of atoms N˛ in such a way that they visit the states of adjacent subspaces at very low probability during observation time only. In the limiting case of zero temperature, each individual atom constitutes a subspace of its own and all transitions are strictly forbidden. Hence, the glass is confined to a single microstate. Consequently, its entropy is zero. This line of reasoning must, of course, hold for the simple frozen-in systems like CO etc. discussed above, too. At elevated temperatures, the dynamics of the system is characterized by internal equilibria within the subspaces (vibrational dynamics) and very slow (low probability) transitions between them (configurational dynamics). Above Tg , all subspaces merge and the (metastable) equilibrium state of the undercooled liquid is reached. It is the latter slow dynamics which is evaluated with respect to the relaxation behavior of glasses below Tg . Phenomena like density fluctuations and the nonequilibrium viscosity (Fig. 2.8b) have been predicted correctly in agreement with experimental data [2.80]. Let us turn again to the c.T/ curves of the system CaMgSi2 O6 shown in Fig. 2.9a, which shows an
65
Part A | 2.3
This statement is most conveniently accounted for by defining this universal limit as zero. Since, scientists have been wrestling with the possibility of a finite positive entropy difference to the universal limit at absolute zero temperature for certain types of materials. The debate focused on the concept of internal equilibrium and was fueled by the pioneering experimental work by Giauque and coworkers [2.72, 73], Simon et al. [2.2, 74, 75], Clusius and Bartholomé [2.76] and others. More specifically, Giauque devoted much of his work to experimentally investigating the entropies of substances at very low temperatures. He was focused on experimentally validating the 3rd law of thermodynamics, which was in fact fully proved by his work. The proof was based on a comparison of low-T calorimetric data (yielding the so-called calorimetric entropy) with data calculated from the partition function derived from the IR band spectra of substances (yielding the so-called spectroscopic entropy). Just for the sake of demonstration: The calorimetric entropy of N2 (g) at its boiling point Tb D 77:32 K, given in units of cal=.mol K/ at 1 atm like in the original paper, amounts to 36:3 ˙ 0:1 as compared to a spectroscopic entropy calculated as 36.416 [2.73]. A similarly accurate agreement was found for Ar, O2 , Cl2 , CH4 , C2 H4 , and many other substances (see the compilation of earlier literature results by Wilks [2.77]). In specific cases, however, significant differences beyond any experimental error were found. Miscalculations of the partition functions of the simple molecules investigated were very unlikely as well. For example, the calorimetric and the spectroscopic entropy of deuterated methane CH3 D deviated by 11:59 J=.mol K/. A frozen-in random position of D at one of the four possible sites in the structure of the methane molecule provides a straight-forward explanation for the observed discrepancy. In fact, S D R ln.1=4/ D 11:53 J=.mol K/ matches exactly with the observed entropy difference. Other substances with frozen-in molecular configuration at very low T are: CO, NO, N2 O, H2 O, and D2 O (see again the compilation of Giauque’s results in [2.77]). In view of such observations, and in retrospect of his own work, Simon specified the 3rd law of thermodynamics in the following way [2.78]
2.3 Fundamental Aspects of the Thermodynamics of Glasses
66
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.3
excess of the heat capacity of the glass GL to the crystal occurring at low T. This is a typical feature of the glassy state, first found by Simon for glycerol [2.82]. The phenomenon is termed the calorimetric Boson peak; it agrees well with the peak found spectrometrically [2.83, 84]. Upon integration of c.T/=T, the entropies for the crystal X, the glass GL, and the liquid L are determined as ZT SX .T/ D
cX dT C SX .0/ ; T
(2.30a)
0
ZT SGL .T/ D
cGL dT C SGL .0/ : T
(2.30b)
0
The results for SX .T/ and SGL .T/ are shown in Fig. 2.10b. As for the integration constants in (2.30a) and (2.30b): By virtue of the 3rd law, SX .0/ D 0. Since both states merge into an identical state at Tm , the relation SGL .Tm / D SX .Tm / C Sm must hold, and SG .0/ assumes a nonzero value given by ZTm SGL .0/ D Sm
cGL cX dT : T
(2.30c)
0
When interpreting the meaning of the experimental value SGL .0/, one has to keep in mind that a calorimetric experiment records the reversibly exchanged heat between sample and calorimeter only, i. e., the term dSext in (2.28). For a material in internal equilibrium (the crystal X), the term dSint in (2.28) is zero; it does not make any contribution to (2.30a). By contrast, the glass GL is not in internal equilibrium with respect to its atomic configuration, hence dSint > 0. Thus, the calorimetric value SGL .0/ does not comprise the effects of internal dissipation and relaxation during the measurement. For frozen-in systems, this part is principally inaccessible to calorimetric experiments. However, following the approach by Bestul and Chang [2.85, 86] and by Sethna [2.87], and the theoretical analysis by Gutzow and Schmelzer [2.88] and Guijrati [2.89], the experimentally observed entropy SGL .0/ is a strict lower bound for the true residual entropy SR .0/, and the difference SGL .0/ SR .0/ > 0 is small as compared to the absolute value of SGL .0/. In industrial practice, we are primarily interested in thermodynamic data for glasses and glass melts between 25 ı C and high temperatures. Then the difference between SGL SX below Tg may be approximated by a constant value Svit (Fig. 2.11b, Simon’s approximation). For an approximately constant difference c D
cGL cX between Tg and Tm , Tg Svit c 1C ln Sm Sm Tm
(2.31a)
is obtained. This is in fair agreement with the rules of thumb Svit =Sm 1=3, c=Sm 3=2, Tg =Tm 2=3, and goes together with the corresponding approximations Tg c Hvit 1 1 (2.31b) Hm Sm Tm and Hvit =Hm 1=2. Like Hvit , Svit is not a fixed value. It depends on the fictive temperature Tf of the glass and slightly increases with the cooling rate q like dSvit / d ln q. For standard cooling conditions, data for Hvit and Svit of a large number of silicate compositions are compiled in [2.90]. In contrast to enthalpy values, because of the 3rd law, entropy values can be tabulated as absolute values. The definition of a reference state referred to the elements is not required. This, however, involves some difficulties for the G function: Standard Gibbs energies Gı .T/ are given in a straight-forward way by Gı .T/ D H ı .T/ TS.T/, but Gibbs energies of formation from the elements Gf .T/ are given by X Gf .T/ D Gı .T/
i Hiı .T/ TS.T/ ; Gf .T ı / D Gı .T ı / C T ı
X
(2.32a)
i S.T ı / ;
(2.32b)
T ı D 298 K. The Gibbs energies of species dissolved in aqueous solutions, for example, are tabulated in terms of Gf .T ı / only. Therefore, the reader is cautioned to carefully check the nature of tabulated thermodynamic values, especially, when data from different tables are used. Conversely, the above formalism allows one to assess G, H, and S of glasses, and to treat any chemical reactions comprising a glass as an educt or product in a quantitative way. Recent publications [2.91–93] have challenged the physical reality of a nonzero value of SGL .0/ as given by (2.30c). As already explained above, the challenge is based on the nonergodicity of the glassy state. Ergodicity denotes the fact that the average of the positions and momentums of an ensemble of atoms sampled over long observation times (time average) is equal to the momentary average sampled over a large number of atoms (ensemble average). This requires that a system visits a sufficiently large number of microstates such that the ensemble average of a property is equal to the time average of that property. This is definitely not the case for glasses where the frozen-in states are inaccessible. Hence, glasses are nonergodic systems. For such
Thermodynamics and Kinetics of Glass
2.3.3 Thermodynamic Treatment of Glass Formation Kinetics Let us recall (2.15)–(2.17) from Sect. 2.2.3, describing the relaxation of a de Donder-type reaction coordinate in a most general way, and relating it to the concept of fictive temperature Tf . In the following, the reaction coordinate is specified as a degree of structural disor-
der, ranging from D 1 for complete disorder (like in an ideal gas) to D 0 for perfect order (like in a single crystal at T D 0). At this point already, one might interject that, in view of the experimental values of the Prigogine–Defay ratio PD > 1, the use of a single reaction coordinate is unsuitable for the description of glass formation kinetics. This contradiction, however, appears only if the glass transition is approximated as occurring at a distinct temperature Tg . If a gradual transition within an interval Tg ˙ ıT is taken into account in an explicit way, then the use of a single parameter is sufficient [2.2]. The dependence of on temperature has been quantified by a simple lattice-hole model. Let D 0 correspond to the molar volume VX .0/ of a chemically pure single crystal at T D 0. VX .0/ confines exactly NA atoms (or molecular units); NA .mol1 / D Avogadro’s number. At T > 0, the crystal forms thermally induced defects (vacancies or holes) resulting in a slightly larger than 0. For simplicity, Schottky-type vacancies are taken into account only, where Nh atoms are moved to the surface leaving behind Nh randomly distributed vacancies. The molar volume thus increases from VX .0/ to VX .0/.NA CNh /=NA . The molar fraction of vacancies in thermal equilibrium is given by xh D NA =.NA C Nh /, and the entropy of the crystal increases from zero (3rd law) to S D kB ŒNh ln xh C NA ln.1 xh / xh D R ln xh C ln.1 xh / : 1 xh
(2.33)
The volume increase of the crystal is given by VX D VX .0/Nh=NA . Now let the crystal expand in a different way to be an increasingly random distribution of atoms. This leads to an increase of its volume by Vrandom > VX . Then Nh =NA is replaced by D Vrandom =VX .0/, where is a measure of degree of order of the new structure in the same way as xh is a measure of the degree of order of the crystal. Hence, the entropy of the random structure is ln C ln.1 / : S D R (2.34) 1 In a simplified approach valid for T > 298 K, is taken as
VGL .Tg / VXı ; VGL .Tg /
(2.35)
and an estimate of the frozen-in entropy Svit per g-atom is readily obtained. In (2.35), VXı denotes the molar volume of the crystal at 298 K. For lack of reliable data
67
Part A | 2.3
systems, it was claimed that residual entropies cannot be measured in principle—which is true within the bounds discussed below (2.30c)—, and Planck’s universal law S.0/ D 0 holds for any condensed substances at T D 0. This view was, in turn, contested by several other authors [2.94, 95]. In the discussion, the so-called Kauzmann paradox plays an important role. In 1946, Kauzmann had published a widely recognized paper on the nature of the glassy state and the behavior of liquids at low temperatures [2.96], from which the scientific world later deduced a paradox, wherein the entropy of an undercooled liquid extrapolated to low temperatures apparently approaches a value below the one of the iso-chemical crystalline state. Hoffmann [2.97] points out that this paradox is readily resolved by the fact that, in contrast to phase transitions (Sect. 2.2.3), the glass transition at constant p cannot occur under isothermal conditions (like melting at Tm /; the glass transition can be brought about by continuously passing through a temperature interval only. This is demonstrated in the H.S/ plot in Fig. 2.13; the data of the system CaMgSi2 O6 are used again. The graph consists of two branches, one for the states GL-L, one for X. The branches are smooth monotonous curves. More specifically, the branch GL-L does not display any deflection at Tg . This is because both slopes and curvatures of the branches follow fundamental rules, i. e., @H=@S D T 0 and @2 H=@S2 D T=c 0, which are consequences of the 1st and 2nd law of thermodynamics. Both branches possess a common tangent with a slope denoting the melting temperature Tm . At Tm , the heat and entropy of melting are exchanged isothermally with the environment. By contrast, the slope representing the glass transition temperature Tg does not constitute a common tangent to the branches. Thus, the glass transition does not occur isothermally. Any attempt to bend the branch GL towards S D 0 by an unaccounted or principally not measurable entropy loss in the glass transition while maintaining the common tangent at Tm would violate the condition T=c 0, hence the 2nd law. Beyond any fundamental consideration, from a practical point of view, and with respect to the quantitative treatment of chemical reactions involving glasses, the clarification of the issue of residual entropies of glasses is of utmost importance.
2.3 Fundamental Aspects of the Thermodynamics of Glasses
68
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.3
H (kJ/mol) –2700 ∂H –2800
Melting =T
∂S 137.7
∂ 2H T = ≥0 cp ∂S 2
–2900
82.7
Glass transition Glassy and liquid state
–3000
85.1 45.8
–3100
–3200
Fig. 2.13 Plot of enthalpy H versus entropy S for the system CaMgSi2 O6 in the glassy (GL) and liquid (L) state (upper branch) and the crystalline state (X, lower branch); data derived from Fig. 2.9; the thin rectangles connect states at identical temperatures, i. e., melting temperature Tm , glass transition temperature Tg , and 0 K, respectively; the sides of the rectangles mark the enthalpy and entropy differences at these temperatures
0K 81.4 24.8
–3300 0
Crystalline state 100
200
300
400
500
600 S (J/(mol K))
Table 2.2 Volumes and entropies of glass-forming systems; N D number of atoms in formula; calc D calculated from (2.34) and (2.35); exp D experimental values [2.2, 7, 32]; all values at p D 1 bar System SiO2 CR MgSiO3 proto CaSiO3 CaMgSi2 O6 CaAl2 Si2 O8 NaAlSi3 O8 ZnCl2 mono Glycerol
N
Tg
Tm
VXı
ı VGL
3 5 5 10 13 13 3 14
(K) 1607 1063 1065 981 1160 1096 378 183
(K) 1999 1834 1817 1665 1830 1381 598 292
(cm3 =g-atom) 8.577 9.087 6.488 7.272 8.017 8.067 6.606 7.564 7.768 7.947 7.728 8.515 15.626 17.884 4.928 5.214
of VX .0/, VXı serves as an estimate of VX .0/. In view of the fact that the thermal expansion coefficient ˛ ! 0 for T ! 0, this approximation is adopted. Table 2.2 shows results of calculated entropies Svit for different glass-forming systems (mostly silicates) from volumetric data. The data are compared to residual entropies determined by calorimetry as well as to the rule-of-thumb values Svit 1=3Sm . Data agree fairly well for systems reaching the glassy state at moderate cooling rates. For systems requiring rapid cooling, as well as for systems possessing strong and extended network structures difficult to structurally rearrange (like SiO2 ), larger deviations are found. This is attributed to the fact that upon cooling at a constant rate q, the actual value of lags behind the equilibrium value eq of the undercooled melt, especially for the above cases. The
ı VGL (Tg )
9.095 7.452 8.265 7.760 8.151 8.533 18.098 5.204
VL (Tm )
Svit calc
9.154 7.996 8.813 8.347 8.309 8.552 19.086 5.221
(J=.mol K/) 5.3 5.1˙1 14.4 8.7˙ 5 5.5 8.5˙3 33.4 24.8˙3 21.5 36.8˙2 32.5 36.7˙6 6.4 8.0˙1 27.6 24.1˙1
Svit exp
1=3Sm exp 1.6 13.6 15.2 25.7 30.5 14.2 9.1 21.1
exact determination of .Tg / is explained in [2.34] and extended to D .T; p/ in [2.35]. The approach allows one to correctly predict the behavior of glass-forming systems in the glass transition as sketched in Fig. 2.14. Heat capacity
Cooling
Heating Temperature
Fig. 2.14 Sketch of the behavior of the heat capacity of a glassforming system in the glass transition range during heating and cooling, arb. u.
Thermodynamics and Kinetics of Glass
2.4 Multicomponent Glasses
First, a review is given of some fundamentals of the thermodynamics of mixed phases in general. Then, models are introduced that have the power to apply the principles of thermodynamics to multicomponent glasses and their melts.
2.4.1 Review of Thermodynamics of Mixed Phases Many of the facts compiled and discussed in Sect. 2.3 have been investigated for chemically simple systems, mostly one-component systems. By contrast, industrial glasses—with the exception of fused silica—typically contain five to ten different oxide components. So there is a challenge to render the results from Sect. 2.3 useful for such glasses, too. The following text starts with a short review of the fundamentals of the thermodynamics of mixed phases in general, then specifies the approach for multicomponent glasses and their melts. In view of the share of glasses produced worldwide, the emphasis is placed on oxide glasses, more specifically silicate glasses. Let us start with the functions Z D G; H; S (G D Gibbs energy, H D enthalpy, S D entropy) as before. In the following, p is kept at pı D 1 bar. This is by no means a principle restriction. In fact, geochemistry essentially rests on the treatment of Z D Z.T; p/. For most industrial processes, however, the thermochemical approach with p D pı is sufficient. Let nj be the molar amount of oxide j in the glass composition. Since chemical compositions of industrial glasses are typically communicated in terms of wt% or g=100 g, it is advisable to normalize nj to a total mass of 100 g. The nj are given by nj D wt%.j/=Mj ; Mj (g=mol) are the molar masses of oxides j. Thus, the nj have the dimension mol=100 g. By this definition, one avoids the futile discussion of what constitutes 1 mol of a multicomponent glass, which arises, for example, when considering expressions like exp.G=RT/. With G given in kJ=100 g, the correct P term to be inserted in the exponent reads G=.RT nj /. The values Z D G; H; S are obtained by the weighted sums ZD
X
nj zj ;
(2.36)
j
where the zj are the partial molar quantities zj D gj , hj , sj , respectively. They are composed of the tabulated values Zj of the pure oxides and a mixing term zjMIX , zj D Zj C zjMIX :
(2.37)
Thus, the functions Z of the entire mixture are given by a weighted sum of the contributions of the pure oxides plus a mixing term comprising the overall effect of mixing: X (2.38a) ZD nj Zj C Z MIX ; X Z MIX D nj zjMIX : (2.38b) Among the zj , gj has a special meaning. It is the socalled chemical potential of oxide j in the mixture, often also labeled as j . It is given as j D gj D Gj C gjMIX D Gj C RT ln aj ; X X GMIX D nj gjMIX D RT nj ln aj :
(2.39a) (2.39b)
Here, aj denotes the activity of oxide j (relative to its equilibrium state at temperature T); aj is expressed as a product of the molar fraction xj and the activity coefficient fj , aj D xj fj ; fj depends on temperature and composition. A mixture containing N oxides, is described by N 1 independent coefficients fj ; the N-th one is determined by the relation X xj d.ln fj / D 0 .Gibbs–Duhem relation/ : The set of fj .T; p/ carries all relevant information for the description of a multicomponent system. As to the temperature dependence, the following relations hold @ ln fj sjMIX D R ln aj C (2.40a) ; @ ln T @ ln fj ; hjMIX D RT (2.40b) @ ln T gjMIX D hjMIX TsjMIX D RT ln aj ; (2.40c) which is consistent with (2.39a) and (2.39b). An ideal mixture is defined by identical interaction among all its constituents and merely statistical mixing. Then, all fj 1, hence, sjMIX D R ln xj and hjMIX D 0. As a consequence of the latter relation, H MIX D 0, i. e., no caloric effect upon mixing is observed. Unfortunately, oxide glasses and their melts turn out to be extremely nonideal mixtures of their oxide components. This is very different from, for example, aqueous solutions where the fj take the role of correction factors to the molar fractions only. Without knowledge of the fj , the functions G, H, S of an oxide mixture cannot be determined by the oxide amounts even in a rough approximation. This is the intrinsic problem and challenge in transferring the findings from Sect. 2.4 to
Part A | 2.4
2.4 Multicomponent Glasses
69
70
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.4
a) Phase content (wt.%)
b) Phase content (wt.%)
100
100 Tg = 740 °C
Tg = 540 °C
Tsol = 929 °C
80
80
Melt
60
40
NCS5
Melt
60
Ca-Ti-Fe-O CAS2
Tliq = 1209 °C
40
NS2 Tliq = 973 °C
N3S8
S
CS 20
Tsol = 721 °C
NC3S6
S
20 S
CMS2 NC3S6
(Na,K)AS6 0
800
1000
0
1200
600
800
NC3S6 1000 T (°C)
T (°C)
Fig. 2.15a,b Phase content in equilibrium for (a) an alumosilicate reinforcement fiber glass composition and (b) a model float glass composition (74 wt% SiO2 , 10 wt% CaO, 16 wt% Na2 O) obtained via thermochemical calculation (after [2.101, 102]); the positions of the glass transition, solidus, and liquidus temperature Tg , Tsol , and Tliq are marked; short-hand notation: A D Al2 O3 , C D CaO, M D MgO, N D Na2 O, S D SiO2
multicomponent systems. Unfortunately again, experimental data for fj are scant. The Slag Atlas [2.98] reports data for 24 binaries, 22 ternaries, and 7 quaternaries in total, comprising 4 binaries and 4 ternaries only which contain alkali oxides. A compilation of data for 7 alkalicontaining glass-forming binaries is given in [2.99]. In view of this situation, three different approaches to the determination of fj in homogeneous multicomponent mixtures are outlined in Sect. 2.4.2. All of them make use of the evaluation of available phase diagrams. The outstanding meaning of phase diagrams in glass science has been emphasized by many authors for a long time. A large database is found in [2.100].
2.4.2 Model Approaches Commercial Software Few commercial software packages are available [2.101, 102] that allow one to calculate solid–liquid equilibria in multicomponent systems. The approach to the thermodynamic functions rests on the evaluation of liquidus lines and surfaces taken from known phase diagrams. In a binary with j D 1; 2, the liquidus temperature Tliq .x1 / at a composition (molar fraction) x1
starting from the pure compound 1, is given by Tliq .x1 /
Tm;1 : 1 .Sm;1 =R/ ln.x1 f1 /
(2.41)
Tm;1 and Sm;1 denote the melting point and entropy of the pure component 1, respectively, and f1 is its activity coefficient at composition x1 and temperature Tliq .x1 /. Equation (2.41) is only given to illustrate the fact that liquidus temperatures reflect mixing behavior in a sensitive way. The actual determination and compilation of an accurate and consistent set of fj as a function of composition and temperature is highly sophisticated. Consequently, in view of the large amount of work required to compile them, they are not free to public access. Typically, the databases for multicomponent liquid mixtures are combined with available data of pure substances. Information regarding their constitutional relation at a given composition is not required. Via a suitable algorithm minimizing the overall Gibbs function of the system (typically using the Lagrange multiplicator method), the equilibrium of coexisting phases for a given composition is determined. This comprises the identity of coexisting solids and
Thermodynamics and Kinetics of Glass
Constitutional Model This approach is comparatively simple. It can be performed with the help of any spread sheet calculator. It rests on the observation that oxide melts maintain a memory of their underlying solid state constitution even at temperatures well above liquidus temperature. An early observation of this kind was communicated by Turner [2.103]; it was obtained from an investigation of sodium oxide evaporation losses from binary sodium silicate melts at 1400 ı C. This is clearly reflected by the data in Fig. 2.16. With sodium oxide chiefly evaporating as NaOH(g) and Na(g), the net vapor pressure of Na-bearing species above the melt is 1=2 1=2 1=4 1=2 p[Na] D a1=2 ; Na2 O KNaOH pH2 O C KNa pO2
(2.42)
q (mg/cm 2) 200
200 h 160 h
180
120 h
160
100 h 140
80 h
120 60 h 100 40 h 80 60
20 h
40 20 0
0.1
0.2
0.3
0.4
0.5 x Na2O
Na2Si 2O5
Fig. 2.16 Evaporation losses q from binary sodium silicate melts (Na2 O-SiO2 ) at 1400 ı C as a function of composition (expressed in molar fraction of Na2 O) and exposure time (after [2.103])
K D equilibrium constant of the evaporation reaction, pH2 O and pO2 D water and oxygen partial pressure, respectively, above the melt. The evaporation rates observed are directly proportional to p[Na] , hence, a direct measure of aNa2 O . Calorimetric measurements on binary and ternary melts with components CaAl2 Si2 O8 , CaMgSi2 O6 , NaAlSi3 O8 , and SiO2 [2.104] revealed that the heats of mixing H MIX are negligibly small against the contributions of the pure phases (Tab. 2.3). In conclusion, these systems, although extremely nonideal mixtures of their oxide components j, are nearly ideal mixtures of their constitutional components k. In view of the number Nk
Table 2.3 Equimolar mixtures of binary and ternary glasses with components k D CaAl2 Si2 O8 , CaMgSi2 O6 , P NaAlSi3 O8 , and 4SiO2 D Si4 O8 , the sum of molar amounts nk is n D nk D 1 mol; HMIX determined calorimetrically at T D 712 ı C in liquid 2PbO B2 O3 melt; H MIX [2.104]; Hk [2.64] Molar composition 1=2CaAl2 Si2 O8 -1=2CaMgSi2 O6 1=2CaAl2 Si2 O8 -1=2NaAlSi3 O8 1=2NaAlSi3 O8 -1=2CaMgSi2 O6 1=2Si4 O8 -1=2CaAl2 Si2 O8 1=2Si4 O8 -1=2NaAlSi3 O8 1=3CaAl2 Si2 O8 -1=3NaAlSi3 O8 -1=3CaMgSi2 O6 1=3Si4 O8 -1=3CaAl2 Si2 O8 -1=3NaAlSi3 O8
P
nk Hk (kJ=mol)
3433:3 3804:3 3318:0 3683:4 3567:2 3508:9 3675:0
HMIX (kJ=mol) 6:8 8:6 C5:9 2:2 ˙0 5:2 6:2
71
Part A | 2.4
their amounts, as well as the amount and composition of the coexisting liquid phase. As a result, the constitutional relations in the multicomponent solid state, the phase distribution in the liquid–solid coexistence range, and the liquidus temperature of the system are obtained. This is extremely valuable information for the glass technologist. It allows one to draw conclusions on the ultimate melting of raw materials, the occurrence of glass defects, and Tliq as the lower temperature threshold above which the melt has to be safely kept when conveying it to the working stations. Figure 2.15 gives examples of a commercial reinforcement fiber glass and a simple model container glass. In the former case, the fiber drawing tips must be kept safely above the liquidus temperature of 1209 ı C. In the latter case, a liquidus temperature of 973 ı C does not impose any critical constraint on the forming process. However, complete sand dissolution cannot be expected to be reached below this temperature. Typical glass defects (not discussing any origin from raw materials or refractories, but from cold spots only) are S D cristobalite and NC3 S6 D devitrite. As a drawback, this type of software has not been designed to calculate the glassy state.
2.4 Multicomponent Glasses
72
Part A
Fundamentals of Glass and the Glassy State
Part A | 2.4
a) cp (J/(g K)) 1.6
b) cp (J/(g K)) Tliq = 1209 °C
Tg = 740 °C
1.6
by Calvet
1.5
Tg = 543 °C
Tliq = 965 °C by DSC up-scan
1.5
by Calvet 1.4
1.4
∑ ck, L nk
1st DSC down-scan
∑ ck, L nk
∑ ck, X nk 1.3
1.3 by Calvet; ∑ ck, X nk
3R/g-atom
1.2
1.2
3R/g-atom 2nd DSC up-scan
1.1
1.1 by Calvet
1st DSC up-scan 1.0
1.0 400
600
800
1000
1200 T (°C)
400
600
800
1000 T (°C)
Fig. 2.17a,b Heat capacities of (a) an alumosilicate reinforcement fiber glass (same composition as in Fig. 2.15) and (b) standard float glass DGG-1 measured by Calvet calorimetry (bold lines) and DSC (differential scanning calorimetry)
(symbols), and calculated (thin lines) by the constitutional model (Sect. 2.4.2)
of atoms in the ideally mixing components, the entropy of mixing SMIX D R
X nk ln xj Nk
X
nk Hkı C Hk;vit ;
(2.44a)
nk HL;k;1673 ;
(2.44b)
nk Skı C Sk;vit ;
(2.44c)
nk SL;k;1673 ;
(2.44d)
nk cX;k .T/ ;
(2.44e)
nk cL;k ;
(2.44f)
HL .T/ D HL;1673 C cL .T 1673/ ;
(2.44g)
k
HL;1673 D
X k
ı SGL D
X k
SL;1673 D
X k
cGL .T/ D
X k
cL D
X
(2.44h) (2.44i)
(2.43)
becomes negligibly small, too [2.105]. Thus, the thermodynamic properties of multicomponent glasses and their melts are determined by [2.106] ı HGL D
T ; SL .T/ D SL;1673 C cL ln 1673 ı HL .T/ D HL .T/ HGL :
k
With the help of these equations, the properties of a reinforcement insulation fiber with nine oxide components and a standard float glass with ten oxide components have been calculated (Fig. 2.17). The results agree well with experimental data. On the basis of (2.44i), the amount of heat drawn from a glass furnace can be calculated as a function of production rate and pull temperature, thus allowing one to judge the energy efficiency of the melting process. Table 2.4 presents Gibbs energies of formation from the elements Gf (298 K) of a commercial insulation glass wool from the system SiO2 -TiO2 -Al2 O3 -Fe2 O3 -FeOP2 O5 -MgO-CaO-Na2 O-K2 O. These data are key for the development of fibers with a sufficiently high solubility in human lung fluid so as to avoid a carcinogenic effect of inhaled fibers. The approach has been used in a successful way for the calculation of the elastic properties of glasses, too [2.107]. What needs to be known in this approach is the solid state constitution of a given oxide composition, i. e., the stoichiometric identity of the compounds formed from the oxides j. The information is taken from available
Thermodynamics and Kinetics of Glass
2.4 Multicomponent Glasses
Glass a Glass b Glass c Glass d
Gfel (kJ=mol) exp 852:0 865:0 880:8 885:4
Gfox (kJ=mol) exp 12:9 35:4 34:0 44:1
calc 849:6 867:2 881:8 882:7
phase diagrams for the main constituents (they typically amount to > 90% of the mass content even in complex industrial glasses), and estimated by a CIPW norm calculation [2.108] for the minor constituents. This type of calculation is still used as an auxiliary tool in geochemistry. By virtue of Gibbs’ phase rule, the number of oxide and constitutional components is equal. For convenience, let us write the composition in vector form as line or column vectors nj> , n> k , or nj , nk , respectively, and the their thermodynamic function in the analogous way as Zj> , Z> k , or Zj , Zk . Then the sums of the P form Z D nk Zk etc. may be written as scalar products n> k Zk . Let M be the coefficient matrix linking the stoichiometries of the j and k. For example, within the constitutional range Na2 O 2SiO2 -Na2 O SiO2 , nj and M take the form nSiO2 nj D ; nNa2 O 2 1 MD : (2.45) 1 1 The composition in terms of compounds is readily cal> 1 > culated as nk D M1 nj or n> k D nj .M / , where 1 1 > M and .M / are the inverse and the transposed inverse coefficient matrix, respectively. Oxide activities aj , (2.39b), are derived by equating G D nj> .Gl C GMIX / D n> l k Gk . Then, ln aj for each oxide component is given by ln aj D
1 .Jj Gj / ; RT
(2.46)
where Jj denotes a value related to j in a vector calculated as Jj D .M1 /> Gk . The aj thus determined represent average values valid within a given constitutional range. Associated Species Model This approach to multicomponent systems rests on the work by [2.109, 110]. In this model, no information on the constitutional relations in the solid state are required. Rather, the formation reactions of all possible compounds occurring within an oxide system are
calc 10:6 37:7 35:0 41:4
evaluated simultaneously. This results in a large nonlinear equation system. Its solution requires considerable numerical skills, especially when it comes to a large number of components. Most published results making use of this approach refer to binary and a few ternary systems. As a special feature of this approach, the socalled chemical structure of a system is calculated. This is the molar distribution of molecular building blocks in the liquid with stoichiometries identical to the compounds formed in the solid state. Figure 2.18 presents the example of the system CaO-SiO2 in the liquid state at 1400 ı C. In view of the high liquidus temperatures of individual compounds formed in the system, Fig. 2.18 must be interpreted as referring to an undercooled liquid state within the entire composition range. As a verification of the model, x-ray and neutron diffraction studies have been performed on the so-called Q group distribution within many silicate, borate, and phosphate systems [2.111]. Recall: the Qn group in a silicate system, n D 4; 3; 2; 1; 0, refers to SiO4 tetrahedra with n Si–O–Si bonds to adjacent tetrahedra. Q4 denotes the
1.0
xi C
C3S C2S
C3S2
CS
S
0.8 0.6 0.4 0.2 0.0 0.0 CaO
0.2
0.4
0.6 x
0.8
1.0 SiO2
Fig. 2.18 Species distribution (symbols) in an undercooled melt of the system CaO-SiO2 at 1400 ı C calculated by the associated species model (Sect. 2.4.2); short-hand notation: C D CaO, S D SiO2 ; thin lines mark the distribution of constitutional solid phases in the corresponding binary sections
Part A | 2.4
Table 2.4 Gibbs energies of formation Gfel and Gfox from the elements and oxides, respectively, of four industrial mineral fiber glass compositions, each containing 12 different oxides; experiments by P. Richet, private communication
73
74
Part A
Fundamentals of Glass and the Glassy State
Part A | 2
Fig. 2.19 Oxide activities a(Na2 O) and a(SiO2 ) in melts of the system Na2 O-SiO2 at 1000, 1200, and 1400 ı C, calculated by the associated species model (Sect. 2.4.2); symbols denote experimental data (after [2.112, 113]) I
log (a) 0 –2
log a(Na2O)
–4
structural entity ŒSiO4 0 , and Q0 the entity ŒSiO4 4 , respectively. Experimental values agree very well with the predictions by the associated species model. The molar fractions of the pure oxides in the chemical structure represent their activities aj , which is again in good agreement with experimental data [2.112, 113] (see Fig. 2.19 for the binary system Na2 O-SiO2 ). As a shortcoming, the results refer to liquid and undercooled liquid states only; values of Svit and Hvit are not encompassed in the approach.
–6 –8 –10
log a(SiO2) 1400 °C
–12
1200 °C
–14
1000 °C
–16 0.0 Na2O
0.2
1400 °C 1200 °C 1000 °C
0.4
0.6 x
0.8
1.0 SiO2
2.5 Summary and Outlook Thermodynamics is a powerful tool helping us to understand essential features of glass formation of the glassy state, and to predict the properties of glasses and their melts. It is true, the methods of thermodynamics do not appeal to the imagination; the correlations to glass structure are indirect only. This is because the categories of thermodynamics are stoichiometry, energy, and entropy, which represent a quite abstract perception of degree of order of the distribution of matter and energy. The lack of imaginary power is compensated very well by the fact that thermodynamics always yields quantitative results. This is an advantage over several empirical views of the glass structure that have with an air of persiflage been described as “explaining everything but predicting nothing.” The application of thermodynamics of irreversible processes allows one to invoke time as a parameter, and to explain and predict most of the phenomena observed in the glass transition as well as the relaxation behavior of undercooled melts and glasses. With respect to relaxation phenomena, statistical mechanics in combination with topological constraint theory are approaches
essentially supplementing and extending the approach by phenomenological thermodynamics. The application of the method of thermodynamics of mixed phases allows one to invoke chemical composition and to extend the above results to multicomponent systems with relevance to industry. Much needs to be done to render the methods useful for a broader community of glass scientists and technologists. Thermodynamics and statistical mechanics are perceived as “difficult” and as an issue for specialists. This is primarily a pedagogical challenge. Beyond this, the issue of a universal understanding of the nature of the glassy state and the glass transition, highlighted in 1995 by Anderson, 1977 Nobel prize laureate in Physics, “as one of the deepest and most important unsolved problems in condensed matter science” [2.114] is still a pending issue, in spite of the outstanding work performed since then by many scientists. We may add: Much of what we do not understand about the glassy state may be attributed to the lack of a concise and universal theory of the liquid state.
References 2.1 2.2 2.3 2.4 2.5
G. Tammann: Der Glaszustand (Leopold Voss, Leipzig 1933) I. Gutzow, J. Schmelzer: The Vitreous State (Springer, Berlin 2013) J.W.P. Schmelzer, I.S. Gutzow: Glasses and the Glass Transition (Wiley-VCH, Weinheim 2011) S.V. Nemilov: Thermodynamic and Kinetic Aspects of the Vitreous State (CRC Press, Boca Raton 1995) E. Donth: The Glass Transition (Springer, Berlin 2001)
2.6 2.7 2.8
L. Leuzzi, T.M. Nieuwenhuizen: Thermodynamics of the Glassy State (Taylor & Francis, New York 2007) B.O. Mysen, P. Richet: Silicate Glasses and Melts (Elsevier, Amsterdam 2005) G.W. Scherer: Glass formation and relaxation. In: Glasses and Amorphous Materials, ed. by J. Zarzycki, Materials Science and Technology, Vol. 9, ed. by R.W. Cahn, P. Haasen, E.J. Kramer (Wiley VCH, Weinheim 1991) pp. 119–173
Thermodynamics and Kinetics of Glass
2.10
2.11
2.12 2.13
2.14 2.15 2.16 2.17 2.18
2.19
2.20
2.21
2.22 2.23 2.24
2.25
2.26 2.27
2.28
2.29
2.30
P.H. Gaskell: Models for the structure of amorphous solids. In: Glasses and Amorphous Materials, ed. by J. Zarzycki, Materials Science and Technology, Vol. 9, ed. by R.W. Cahn, P. Haasen, E.J. Kramer (Wiley VCH, Weinheim 1991) pp. 175–278 C.A. Angell, K.L. Ngai, G.B. McKenna, P.F. McMillan, S.W. Martin: Relaxation in glassforming liquids and amorphous solids, Appl. Phys. Rev. B 88, 3113–3157 (2000) P.G. Debenedetti, F.H. Stillinger: Supercooled liquids and the glass transition, Nature 410, 259–267 (2001) C.A. Angell: Formation of glasses from liquids and biopolymers, Science 267, 1924–1935 (1995) ASTM C162-05: Standard Terminology of Glass and Glass Products (ASTM International, Conshohocken 2015) W.H. Zachariasen: The atomic arrangement in glass, J. Chem. Soc. 54, 3841–3851 (1932) G.N. Greaves: EXAFS and the structure of glass, J. Non-Cryst. Solids 7, 203–217 (1985) L.D. Landau, E.M. Lifshitz: Statistical Physics (Pergamon, Oxford 1969) J. Frenkel: Kinetic Theory of Liquids (Oxford Clarendon, Oxford 1946) V.V. Brazhkin, K. Trachenko: Collective excitations and thermodynamics of disordered states: New insights into an old problem, J. Chem. Phys. B 118, 11417 (2014) L. Stoch: Real glass crystallization high resolution electron microscopy (HREM) study and classic nucleation theory, Opt. Appl. 35, 819–827 (2005) J.-F. Poggemann, G. Heide, G.H. Frischat: Direct view of the structure of different glass fracture surfaces by atomic force microscopy, J. Non-Cryst. Solids 326/327, 15–20 (2003) F. Simon: Fünfundzwanzig Jahre Nernst’scher Wärmesatz, Ergeb. Exakt. Naturwiss. 9, 222–274 (1930) R. Haase: Thermodynamik der Irreversiblen Prozesse (Steinkopff, Darmstadt 1963) H. Scholze: Glass – Nature, Structure, and Properties (Springer, Berlin 1990) R. Clasen: Preparation and sintering of high-density green bodies to high-purity silica glasses, J. Non-Cryst. Solids 89, 223–244 (1987) A. Kolmogorov: A statistical theory for the recrystallization of metals, Akad. Nauk. SSSR, Izv., Ser. Mat. 1, 355 (1937) M. Avrami: Kinetics of phase change. Pt. I. General theory, J. Chem. Phys. 7, 1103–1112 (1939) M. Avrami: Kinetics of phase change. Pt. II. Transformation-time relations for random distributed nuclei, J. Chem. Phys. 8, 212–224 (1940) M. Avrami: Kinetics of phase change. Pt. III. Granulation, phase change, and microstructure kinetics of phase change, J. Chem. Phys. 9, 177–184 (1941) W.A. Johnson, R.F. Mehl: Reaction kinetics in processes of nucleation and growth, Trans. Metall. Soc. AIME 135, 416–442 (1939) D.R. Uhlmann: A kinetic treatment of glass formation, J. Non-Cryst. Solids 7, 337–248 (1972)
2.31 2.32
2.33
2.34 2.35
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2.37
2.38
2.39
2.40
2.41
2.42
2.43 2.44 2.45 2.46 2.47 2.48
2.49
2.50
2.51
D. Turnbull: Under what conditions can a glass be formed?, Contemp. Phys. 10, 473–488 (1969) P. Richet, Y. Bottinga: Rheology and configurational entropy in silicate melts. In: Reviews in Mineralogy, Vol. 32, ed. by J.F. Stebbins, P.F. McMillan, D.B. Dingwell (Mineralogical Society of America, Washington D.C. 1994) C.A. Angell: Glass-formers and viscous liquid slowdown since David Turnbull: Enduring puzzles and new twists, MRS Bulletin 33, 544–555 (2008) J.W.P. Schmelzer, I. Gutzow: The Prigogine-Defay ratio revisited, J. Chem. Phys. 125, 184511 (2006) J.-L. Garden, H.G. Guillou, J. Richard, L. Wondraczek: Configurational Prigogine–Defay ratio, J. Non-Eq. Thermodyn. 37, 143–177 (2012) C. Mauro, C. Ribeiro, T. Scopigno, G. Ruocco: Prigogine–Defay ratio for an ionic glass-former: Molecular dynamics simulation, J. Phys. Chem. B 113, 3099–3104 (2009) U. Buchenau: Structural interpretation of the Prigogine-Defay ratio at the glass transition, Phys. Rev. B 86, 184105 (2012) D. Gundermann, U.R. Pedersen, T. Hecksher, N.P. Bailey, B. Jakobsen, T. Christensen, N.B. Olsen, T.B. Schrøder, D. Fragiadakis, R. Casalini, C.M. Roland, J.C. Dyre, K. Niss: Predicting the density-scaling exponent of a glass-forming liquid from Prigogine-Defay ratio measurements, Nat. Phys. 7, 816–821 (2011) H.N. Ritland: Density phenomena in the transformation range of aborosilicate crown glass, J. Am. Ceram. Soc. 37, 370–378 (1954) C.T. Moynihan, A.J. Easteal, M.A. De Bolt, J. Tucker: Dependence of the fictive temperature of glass on cooling rate, J. Am. Ceram. Soc. 59, 12–16 (1976) G.M. Bartenev, N.N. Scheglova: High-temperature relaxation mechanisms in inorganic glasses, J. Non-Cryst. Solids 37, 285–298 (1980) A.Q. Tool: Relation between inelastic deformability and thermal expansion of glass in its annealing range, J. Am. Ceram. Soc. 29, 240–253 (1946) I. Prigogine: Thermodynamics of Irreversible Processes (Ch. Thomas, Springfield 1955) I. Prigogine, D. Kondepudi: Modern Thermodynamics (Wiley, Chichester 1998) O.S. Narayanaswami: A model of structural relaxation in glass, J. Am. Ceram. Soc. 54, 491–498 (1971) W. Scherer: Theories of relaxation, J. Non-Cryst. Solids 123, 73–89 (1990) O.V. Mazurin: Relaxation phenomena in glass, J. Non-Cryst. Solids 25, 130–169 (1977) H. Vogel: Das Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten, Phys. Z. 22, 645–646 (1921) G. Fulcher: Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8, 339–355 (1925) G. Tammann, W. Hesse: Die Abhängigkeit der Viscosität von der Temperatur bei unterkühlten Flüssigkeiten, Z. Anorg. Chem. 156, 245–257 (1926) M.L. Williams, R.F. Landel, J.D. Ferry: The temperature dependence of relaxation mechanisms in
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2.9
References
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Fundamentals of Glass and the Glassy State
Part A | 2
2.52
2.53
2.54
2.55
2.56 2.57
2.58
2.59
2.60
2.61
2.62
2.63
2.64 2.65
2.66 2.67
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amorphous polymers and other glass-forming liquids, J. Am. Chem Soc. 77, 3701–3703 (1955) G. Adam, J.H. Gibbs: On the temperature dependence of cooperative relaxation properties in glassforming liquids, J. Chem. Phys. 43, 139–146 (1965) I. Avramov, A. Milchev: Effect of disorder on diffusion and viscosity in condensed systems, J. NonCryst. Solids 104, 253–260 (1988) J.C. Mauro, Y. Yue, A.J. Ellison, P.K. Gupta, D.C. Allan: Viscosity of glass-forming liquids, Proc. Natl. Acad. Sci. USA 106, 19780–19784 (2009) G. Meerlender: Viskositäts-Temperaturverhalten des Standardglases I der DGG (Deutsche Glastechnische Gesellschaft), Glastechn. Ber. 47, 1–3 (1974) Q. Zheng, J.C. Mauro: Viscosity of glass forming systems, J. Am. Ceram. Soc. 100, 6–25 (2017) P. Richet, Y. Bottinga: Anorthite, andesine, wollastonite, diopside, cordierite and pyrope: Thermodynamics of melting, glass transitions, and properties of the amorphous phases, Earth Planet. Sci. Lett. 67, 415–432 (1984) R.M. Martens, M. Rosenhauer, H. Büttner, K. von Gehlen: Heat capacity and kinetic parameters in the glass transition interval of diopside, anorthite, and albite glass, Chem. Geol. 62, 49–70 (1987) K.M. Krupka, R.A. Robie, B.S. Hemingway, D.M. Kerrick, J. Ito: Low-temperature heat capacities and derived thermodynamic properties of anthophyllite, diopside, enstatite, bronzite, and wollastonite, Am. Mineralogist 70, 249–260 (1985) K.M. Krupka, B.S. Hemingway, R.A. Robie, D.M. Kerrick: High-temperature heat capacities and derived thermodynamic properties of anthophyllite, diopside, dolomite, enstatite, bronzite, talc, and wollastonite, Am. Mineral. 70, 261–271 (1985) P. Richet, R.A. Robie, B.S. Hemingway: Lowtemperature heat capacity of diopside glass (CaMgSi2 O6 ): A calorimetric test of the configurational entropy theory applied to the viscosity of liquid silicates, Geochim. Cosmochim. Acta 96, 1521–1533 (1986) R.A. Robie, B.S. Hemingway, J.R. Fisher (Eds.): Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 bar (105 Pascals) Pressure and at High Temperatures (Geol. Survey Bull. U.S. Gov. Printing Office, Washington 1978) O. Knacke, O. Kubaschewski, K. Hesselmann (Eds.): Thermochemical Properties of Inorganic Substances, Vols. I–III (Springer, Berlin 1991) O. Kubaschweski, C.B. Alcock, P.J. Spencer: Materials Thermochemistry (Pergamon, London 1993) M.W. Chase Jr., C.A. Davies, J.R. Downey Jr., D.J. Frurip, R.A. McDonald, A.D. Syverud (Eds.): JANAF Thermochemical Tables (The Am. Ceram. Soc., Westerville 1985) S.F. Edwards, R.B.S. Oakeshott: Theory of powders, Physica A 159, 1080–1090 (1989) L.V. Woodcock: Thermodynamic description of liquid-state limits, J. Phys. Chem. B 116, 3735–3744 (2012) A. Takada, R. Conradt, P. Richet: Residual entropy and structural disorder in glass: A review of history
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and an attempt to resolve two apparently conflicting views, J. Non-Cryst. Solids 429, 33–44 (2015) W. Nernst: Über die Berechnung chemischer Gleichgewichte aus thermischen Messungen, Nachr. Kgl. Ges. Wiss. Gött. 1, 1–40 (1906) W. Nernst: Über die Beziehung zwischen Wärmeentwicklung und maximaler Arbeit bei kondensierten Systemen, Ber. Kgl. Preuss. Akad. Wiss. 52, 933–940 (1906) M. Planck: Vorlesungen über Thermodynamik (Veit, Leipzig 1911) G.E. Gibson, W.F. Giauque: The third law of thermodynamics. Evidence from the specific heats of glycerol that the entropy of glass exceeds that of a crystal at the absolute zero, J. Am. Chem. Soc. 45, 93–104 (1923) W.F. Giauque, J.O. Clayton: The heat capacity and entropy of nitrogen. Heat of vaporization. Vapor pressure of solid and liquid. The reaction 1/2 N2 + 1/2 O2 = NO from spectroscopic data, J. Am. Chem. Soc. 55, 4875–4889 (1933) F. Simon: Zum Prinzip von der Unerreichbarkeit des absoluten Nullpunktes, Z. Phys. 41, 806–809 (1927) F. Simon: Über den Zustand der unterkühlten Flüssigkeiten und Gläser, Z. Anorg. Allg. Chem. 203, 219–227 (1931) K. Clusius, E. Bartholomé: The heat of rotation of the molecule HD and D2 and the nuclear spin of D atoms, Z. Elektrochem. Angew. Phys. Chem. 40, 524–529 (1934) J. Wilks: The Third Law of Thermodynamics (Oxford Univ. Press, Oxford 1961) F. Simon: The third law of thermodynamics – A historical survey. 40th Guthrie Lecture (The Physical Society, Oxford 1956) J. Jäckle: On the glass transition and the residual entropy of glasses, Philos. Mag. B 44, 533–545 (1981) J.C. Mauro, M.M. Smedskjaer: Statistical mechanics of glass, J. Non-Cryst. Solids 396/397, 41–53 (2014) R.G. Palmer: Broken ergodicity, Adv. Phys. 31, 669– 735 (1982) F. Simon, F. Lange: Zur Frage der Entropie amorpher Substanzen, Z. Phys. 38, 227–236 (1926) B. Champagnon, C. Chemarin, P. Richet: Fictive temperature and medium range order in silicate glasses: Comparison between heat capacity measurements and the Boson peak, Philos. Mag. B 77, 663–669 (1998) E. Duval, A. Boukenter, T. Archibat: Vibrational dynamics and the structure of glasses, Phys. Condens. Matter 2, 10227–10234 (1990) A.B. Bestul, S.S. Chang: Excess entropy at glass transformation, J. Chem. Phys. 40, 3731–3733 (1964) A.B. Bestul, S.S. Chang: Limits on calorimetric residual entropies of glasses, J. Chem. Phys. 43, 4532–4533 (1965) J.P. Sethna: Statistical mechanics: Entropy, Order Parameters, and Complexity (Oxford Univ. Press, Oxford 2006) I. Gutzow, J.W.P. Schmelzer: The third principle of thermodynamics and the zero-point entropy of
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W.E.S. Turner: Studies on volatilization from glass melts, Glastechn. Ber. 12, 409–413 (1934) A. Navrotsky, R. Hon, D.F. Weill, D.J. Henry: Thermochemistry of glasses and liquids in the systems CaMgSi2 O6 -CaAl2 Si3 O8 -NaAlSi3 O8 , SiO2 -CaAl2 Si2 O8 NaAlSi3 O8 and SiO2 -Al2 O3 -CaO-Na2 O, Geochim. Cosmochim. Acta 44, 1409–1423 (1980) R. Conradt: Chemical structure, medium range order, and crystalline reference state of multicomponent oxide liquids and glasses, J. Non-Cryst. Solids 345/346, 16–23 (2004) R. Conradt: The industrial glass melting process. In: The SGTE Casebook. Thermodynamics at Work, ed. by K. Hack (CRC Press, Boca Raton 2008) pp. 282–303 K. Philipps, R.P. Stoffel, R. Dronskowski, R. Conradt: Experimental and theoretical investigation of elastic moduli of silicate glasses and crystals, Front. Mater. 4, 1–9 (2017) W. Cross, J.P. Iddings, L.V. Pirrson, H.S. Washington: A quantitative chemico-mineralogical classification and nomenclature of igneous rocks, J. Geol. 10, 555–590 (1902) B.A. Shakhmatkin, N.M. Vedishcheva, M.M. Shultz, A.C. Wright: The thermodynamic properties of oxide glasses and glass-forming liquids and their chemical structure, J. Non-Cryst. Solids 177, 249– 256 (1994) N.M. Vedishcheva, B.A. Shakhmatkin, M.M. Shultz, A.C. Wright: The thermodynamic modeling of glass properties: A practical proposition?, J. Non-Cryst. Solids 196, 239–243 (1996) B.A. Shakhmatkin, N.M. Vedishcheva, A.C. Wright: Thermodynamic modeling of the structure of glasses and melts: Single-component, binary and ternary systems, J. Non-Cryst. Solids 293–295, 312– 317 (2001) W.G. Dorfeld: Structural thermodynamics of alkali silicates, Phys. Chem. Glasses 29, 179–186 (1988) D.N. Rego, G.K. Sigworth, W.O. Philbrook: Thermodynamic study of Na2 O-SiO2 melts at 1300° and 1400°C, Metall. Trans. B 16, 313–323 (1985) P.W. Anderson: Through the glass lightly, Science 267, 1615–1616 (1995)
Reinhard Conradt uniglassAC GmbH Aachen, Germany [email protected]
Reinhard Conradt received a PhD in Physical Chemistry (1981) and a Habilitation (1996) at RWTH Aachen University, Germany. He worked at the Fraunhofer Institute of Silicate Science, Würzburg, Germany, Chulalongkorn University, Bangkok, Thailand, and as Chair of Glass and Ceramic Composites at RWTH Aachen University. His work focuses on building bridges between science, especially chemistry, thermodynamics and kinetics, and industrial engineering.
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glasses. History and new developments, J. NonCryst. Solids 355, 581–594 (2009) P.D. Guijrati: Hierarchy of relaxation times and residual entropy: A non-equilibrium approach, Entropy 20, 149 (2018) R. Conradt: Thermodynamics of glass melting. In: Fiberglass and Glass Technology, ed. by F.T. Wallenberger, P.A. Bingham (Springer, Berlin 2010) J.C. Mauro, P.K. Gupta, R.J. Loucks: Continuously broken ergodicity, J. Chem. Phys. 126, 184511 (2007) J.C. Mauro, P.K. Gupta, R.J. Loucks, A.K. Varshneya: Non-equilibrium entropy of glasses formed by continuous cooling, J. Non-Cryst. Solids 355, 600–606 (2009) J.C. Mauro, R.J. Loucks, S. Sen: Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems, J. Chem. Phys. 133, 164503 (2010) M. Goldstein: On the reality of residual entropies of glasses and disordered crystals, J. Chem. Phys. 128, 154510 (2008) G.P. Johari: Configurational and residual entropies of nonergodic crystals and the entropy’s behavior on glass formation, J. Chem. Phys. 132, 124509 (2010) W. Kauzmann: The nature of the glassy state and the behavior of liquids at low temperatures, Chem. Rev. 43, 219–256 (1948) H.-J. Hoffmann: Energy and entropy of crystals, melts and glasses or what is wrong in Kauzmann’s paradox?, Materialwiss. Werkstofftech. 43, 528–533 (2012) M. Allibert, R. Parra, C. Saint-Jours, M. Tmar: Thermodynamic activity data for slag systems. In: Slag Atlas, ed. by M. Allibert, et al. (Stahleisen, Düsseldorf 1995) R. Conradt: On volatilization from glass melts, Glastechn. Ber. 59, 34–52 (1986) Phase Equilibria Diagrams PC Database Ver. 2.1, Ver. 4.2. (The American Ceramic Society, Westerville 1998, 2017) G. Eriksson, K. Hack: ChemSage – A computer program for the calculation of complex chemical equilibria, Metall. Trans. B 21, 1013–1023 (1990) Thermfact Montreal and GTT Technologies Aachen, FACTSAGE Software Ver. 5.2 (2004)
References
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Viscosity of G
3. Viscosity of Glass and Glass-Forming Melts
Ulrich Fotheringham
With respect to glass manufacturing, viscosity, together with its temperature course, is definitely the most important glass property. First, it determines the temperature range in which glass is molten. This temperature range has to be such that there is enough convection to make batch particles quickly spread and dissolve in the glass bath so that a homogeneous glass melt will result. Viscosity also determines the temperature range in which a glass is refined. It has to be such
3.1
Shear Viscosity: General Remarks and Particularities of Glass ................... 3.1.1 Definition of Shear Viscosity................... 3.1.2 Shear Viscosity of Glass-Forming Melts ... 3.1.3 Viscosity Fix Points ................................ 3.1.4 Types of Viscosity Curves: Short and Long Glasses ......................... 3.2 3.2.1 3.2.2 3.3 3.3.1 3.3.2 3.3.3
3.3.4 3.3.5
81 81 81 82 84
Shear Viscosity – Measurement ............. 85 ISO Standards ....................................... 85 Further Methods ................................... 87 Shear Viscosity – Theory ....................... 90 Kinetics of Viscous Flow in the Viscoelastic Regime ..................... 91 Viscous Flow Beyond Upper Limit of Viscoelastic Regime ........................... 97 Temperature Dependence Approaches: Arrhenius versus Non-Arrhenius (Adam–Gibbs) ...................................... 98 Fragility ............................................. 102 Practical Viscosity Formulas.................. 104
3.4 3.4.1
Bulk Viscosity ..................................... Bulk Viscoelasticity in the Case of Linear Response.............................. 3.4.2 Permanent Compression by a Multianvil Device .........................
108 108
References...................................................
110
110
that the mobility of gaseous inclusions (bubbles) is so high that they quickly leave the melt. Further, viscosity determines the temperature range of glass forming. In this range, the viscosity has to be low enough to allow forming yet high enough so that the glass piece will maintain its shape after the process. The steeper the course of viscosity with temperature is, the more sensitive hotforming becomes with respect to temperature control. Last, viscosity also determines the annealing
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_3
Part A | 3
Beginning with a selection of commercial glasses, the typical temperature course of the shear viscosity of inorganic glasses is discussed. The significance of the different temperature ranges for the different production steps (melting, hotforming, annealing) is explained. The viscosity-based typology of glasses as long or short is introduced and discussed with respect to glass composition. The glass viscosity measurement methods conforming to ISO 7884 1-7 are described. This includes the individual rules for the determination of the shear viscosity fix points. Special shear viscosity measurement techniques applying to extremely high or low viscosity values are also described. Concerning viscosity theory and modeling, Adams–Gibbs theory, Angell’s fragility concept, and the semiempirical models after Vogel– Fulcher–Tammann (VFT), Avramov–Milchev (AM), and Waterton–Mauro–Yue–Ellison–Gupta–Allan (W-MYEGA) are presented, applied to different glasses, and compared. Viscoelastic behavior is discussed with respect both to shear and bulk deformation, including Boltzmann’s superposition principle, the particular effect of delayed elasticity, the special viscoelastic models after Maxwell, Kelvin–Voigt, Burger etc. as well as special mathematics, i. e., the stretched exponential or Kohlrausch(–Williams– Watts) function. Viscoelastic characterization by dynamic mechanical analysis and by reversible compression in a quasi-isostatic device are discussed considering experimental data.
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Part A | 3
temperature range where glass is cooled in a particular way in order to, for instance, allow possible stresses in the glass to relax and finally obtain a stress-free product. This having been said, it is clear that both the exact experimental determination of viscosity and its theoretical description, in particular with respect to the temperature dependence, as well as the knowledge of how viscosity is affected by composition are all essentials of applied glass science. For a standardized experimental determination, certain viscosity fix points have been defined. These are temperatures where the viscosity has particular values which mark the above temperature ranges (in particular the so-called annealing point, softening point, and working point). How the locations of these ranges are spread over the temperature scale sensitively depends on the glass type, for instance vitreous silica, borosilicate glass, soda-lime glass, or aluminosilicate glass. For both vitreous silica and borosilicate glasses, the difference between working point and annealing point is usually high (so-called long glasses), whereas for aluminosilicate glasses, it is usually small (so-called short glasses). Soda-lime silicate glasses are usually in the middle between short and long glasses. As the viscosities belonging to the above fix points differ by many orders of magnitude, there is no single solution for the experimental determination. According to ISO standards, there are three methods: beam bending for the annealing range, fiber-drawing for the softening range, and rotational cylinder for the range of the working point and above. There are, however, also other methods which may be preferred with respect to either ease of sample preparation (parallel plate instead of fiber-drawing) or to applicability in the ultrahighviscosity range (helical spring). Most measurement methods derive the viscosity values from observing a steady-state viscous flow. There are, however, also dynamic test methods. They offer an insight into the kinetics of viscous flow and are of particular importance in the viscoelastic regime which is identical to the temperature range around the annealing point. In this temperature range, the shortterm response of a sample exposed to shear will be elastic whereas the long-term response will be viscous. Concerning the theoretical description, said kinetics of viscous flow in the temperature range around the annealing point is challenging. The critical issue is to describe the time-dependence of the material response between the onset of the viscoelastic process and before the final steady state. Starting with mechanical models for the combination of short-term elastic and long-term viscous response (Maxwell, Kelvin– Voigt, Burger, and combinations of them), a set of formulas has been developed whose core is commonly
a so-called Kohlrausch(–William–Watts) approach. The final steady state is either equal to a stress-free deformation (case of stress response to an imposed strain, with gradual stress relaxation) or to a continuous deformation (case of strain response to an imposed stress, gradually turning into continuous viscous creep). Between the annealing point and the softening point, there is a breakdown of the short-term elastic response to almost zero so that the viscoelastic behavior in the annealing range essentially turns into a purely viscous one at higher temperatures. To describe the temperature course of viscosity is a challenge, too. For a small temperature interval, the thermal activation model by Arrhenius may be applied. For the whole temperature range, more sophisticated models are required. For the last 50 years, the most popular has been the one by Adam and Gibbs. It combines the thermal activation ansatz by Arrhenius with the number of atoms involved in an elementary step of viscous flow thus finally establishing a link between viscosity and configurational entropy. It is this link which allows one to understand why there are short and long glasses and how this is affected by composition. The rule of thumb is: the higher the number of configurational degrees of freedom, the shorter the glass is. The number of configurational degrees of freedom, in return, is linked to the composition. In a glass in which there are mostly covalent bonds between, e. g., silicon and oxygen dominate, it is low. In a glass with lots of ionic bonds between, e. g., sodium and oxygen, it is high. A quantitative measure of the shortness of a glass which is an excellent starting point for further physicochemical considerations has been provided by Angell’s concept of fragility. If the required knowledge about the configurational entropy has been provided by a measurement of the specific heat, the Adam–Gibbs model allows an excellent representation of a measured viscosity curve. Particularly in case this knowledge does not exist, other models are applied. For almost 100 years, the one named after Vogel, Fulcher, and Tammann has been the most popular. In recent years, new models have been developed by Avramov and Milchev as well as by Mauro, Yue, Ellison, Gupta, and Allen (MYEGA), the latter coinciding with an empirical function from Waterton. All three models give excellent fits. With this, the essential experimental and theoretical issues concerning viscosity of oxide glasses have been discussed. There is, however, an additional one that has to be mentioned. Referring to viscosity or viscoelasticity, usually shear viscosity or viscoelasticity is addressed. There is, however, also bulk viscosity or viscoelasticity which is far less frequently discussed because of, first, the much
Viscosity of Glass and Glass-Forming Melts
smaller technical importance (so far), and, second, the experimental challenges involving high-pressure devices. Its kinetics are controlled by the so-called second
3.1 Shear Viscosity: General Remarks and Particularities of Glass
81
or bulk viscosity. In contrast to shear which is volume conserving it involves permanent densification of the material.
3.1 Shear Viscosity: General Remarks and Particularities of Glass temperature (the melting point in the case of stoichiometric glasses) from above, see Fig. 3.2. It is this substantial increase in shear viscosity that suppresses the atomic motions required for crystallization and thus enables glass formation. See the shear viscosity curve of a non-glass-forming system for comparison, see Fig. 3.3. In the vicinity of the melting point, the viscosity of vitreous silica is higher by eight orders of magnitude than that of sodium chloride.
y Boundary plate (2-D, moving)
Velocity, υ Shear stress, τ
Fluid
∂υ Gradient, — ∂y
3.1.1 Definition of Shear Viscosity The common textbook definition of shear viscosity begins by considering fluid layers moving parallel in the same direction, but at different velocities. In this case mutual forces are exerted between neighboring layers. Those fluids (or, to be precise, those combinations of fluids and velocities) for which linear response theory holds, i. e., for which said forces are proportional to the velocity gradient perpendicular to the flow direction (x), are called Newtonian [3.2]. The constant of proportionality is called shear viscosity f D
@v : @y
x Boundary plate (2-D, stationary)
Fig. 3.1 Definition of shear viscosity
log η (dPa s) 14
(3.1)
10
f is the friction per unit area, v is the velocity (Fig. 3.1).
8
3.1.2 Shear Viscosity of Glass-Forming Melts
6
Remarkably, it is the course of viscosity with temperature which is one of the essential features of glassforming systems. Compared to other inorganic melts (only inorganic glasses are considered here), glassforming systems are characterized by a strong viscosity increase as the temperature approaches the liquidus
Melting point of high temperature polymorph of silica (cristobalite)
12
4 1000
1200
1400
1600
1800
2000 2200 2400 Temperature (°C)
Fig. 3.2 Viscosity of natural vitreous silica. Courtesy of
HERAEUS QUARZGLAS GmbH & Co. KG, Hanau, Germany
Part A | 3.1
In fluid mechanics, viscosity describes the effect which “energy dissipation, occurring during the motion of a fluid, (has) on that motion itself” [3.1]. In general, viscosity is a measure for one part of the inhibiting response of a body to an imposed deformation, namely the part due to energy dissipation by internal friction [3.2]. Consider, for instance, a drop of a liquid in a capillary. If the drop has an initial momentum, it will first move; the combination of the boundary conditions at the interface to the capillary and the internal friction in the liquid, however, will soon bring this motion to a standstill. There are two orthogonal types of deforming a piece of matter, i. e., either volume conserving or shape conserving, meaning two different types of viscosity have to be dealt with. The one considered first is the one associated with a volume-conserving deformation, i. e., to the response to shear stress.
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The background of the different behavior of these two inorganic liquids is the different nature of the chemical bonds involved. Silicon dioxide consists of tetrahedral units with a silicon in the middle and four surrounding oxygens at the corners; the latter are shared by neighboring tetrahedrons [3.4]. The silicon–oxygen bonds are almost covalent and very strong. Any deformation of the silicon dioxide network—such as by viscous flow—implies the breakage and reclosure of those bonds. This picture is supported by the following fact. If one fits an Arrhenius function to the viscosity so that one gets .T/ 1 eE=.RT/ , 1 : high temperature limit of viscosity (first fit parameter), E: activation energy (second fit parameter), R: gas constant, one will find that E is almost equal to the single-bond strength of one mole of silicon–oxygen bonds in the temperature range of Fig. 3.2 [3.4]. (Note that the fit will not be exact because the temperature-dependence of the viscosity of silicon dioxide comes close to an Arrhenius function but is not perfectly Arrhenius-like.) The (approximate) Arrhenius behavior of the viscosity means that the lower the temperature is, the less thermal energy is there for bond breaking and the closer the stirring of molten silicon dioxide comes to “stirring a heap of fishhooks.” In contrast to silicon dioxide, a sodium chloride melt consists of positive sodium ions and negative chloride ions. Bonding does not involve the structural constraint of bond angles. Perpendicular to the bond axis to their neighbors, the ions are moveable. Therefore, shear deformation does not require thermal activation which is supported by the below Fig. 3.3 showing almost no temperature dependence of the viscosity. So the essential property of a glass-forming system is the ability to form a covalently bonded network [3.4]. Said ability is high for silicon dioxide and zero for sodium chloride. With respect to this, silicon dioxide
may be called a network former whereas sodium chloride may not. As most inorganic glasses consist of oxides only so that there is one single type of anion, i. e., oxygen, said anion is not named in the nomenclature and silicon alone is called a network former. Sodium which, if it enters a covalently bonded network, will partially destroy it, is called a network modifier, see Fig. 3.4. Other network formers are, for instance, boron and phosphorus; other network modifiers are potassium, magnesium, and calcium. One can assess the role a cation will play in a network a priori by Dietzel’s field strength approach [3.5] or Sun’s bond strength approach [3.4]. According to either the so-called field strength or the single bond strength of the corresponding cation-oxygen bond(s), they classify the cations as either network formers (high field strength/high bond strength), network modifiers (low field strength/low bond strength), or intermediates. Aside from vitreous silica, all technically important inorganic glasses are mixtures of glass formers, intermediates, and modifiers. As will be discussed in the next paragraph, a certain amount of network modifiers is necessary to lower the temperature at which glass melting is practically carried out.
3.1.3 Viscosity Fix Points During further cooling, in the metastable state below the liquidus temperature, the viscosity of a glass-forming system continually rises, usually in a super-Arrhenius way. To characterize the change of the viscosity with temperature, commonly the temperatures at which the viscosity equals 104 dPa s (working point), 107:6 dPa s (softening point), 1013 dPa s (annealing point) are pro-
η (dPa s) 0.1 Si4+ Na+ O2–
0.01
0.001 800
850
900
9500 1000 Temperature (°C)
Fig. 3.3 Viscosity of sodium chloride. Data from [3.3, Ta-
ble 24.2]
Fig. 3.4 Entering a covalently bonded silicon dioxide net-
work, sodium destroys a part of the oxygen bridges and generates nonbridging oxygens. Note that the fourth bond of a SiO2 4 -tetraeder is assumed to be perpendicular to the drawing level and is not shown here
Viscosity of Glass and Glass-Forming Melts
Casting on a blowpipe (tube drawing) Pulling of flat glass.
The working point itself approximately marks the viscosity at which glass leaves a feeder, is cut into pieces (gobs) and is provided to classical hotforming processes. These comply to:
Hot pressing/blowing (i. e., at temperatures just below the working point) Cold pressing/blowing (i. e., at temperatures just above the softening point).
Below the softening point, forming has usually come to its end. Only very special forming processes are carried out between the softening point and the annealing point, that is:
Grain dissolution Homogenization by stirring Refining.
Between the temperatures of the actual melting processes and the working point, there are the starting points of processes like:
Sintering Precision molding.
log η (dPa s) 15 Strain point
14 Beam bending
13
Annealing point
12 11 10 9 8
Fiber elongation Softening point
7 6 5 4
Working point
Rotating cylinder 3 2 1 0 300
400
500
600
700
800
900
83
1000
1100
1200
1300
1400
1500 1600 1700 Temperature (°C)
Fig. 3.5 Viscosity of former television bulb glass 8056 from SCHOTT. Viscosity measurements by ISO 7884-2, -3, -4-comform self-built devices at the accredited laboratories of SCHOTT AG, Mainz
Part A | 3.1
vided. Sometimes, the temperature at which the viscosity equals 1014:5 dPa s (strain point) is provided also. The unit dPa s conforms with the corresponding ISO norm [3.6], and is equal to the non-SI unit Poise, which is commonly used. All temperature ranges defined by these characteristic temperatures have a special significance for glassmaking, see Fig. 3.5, [3.7]. Above the working point, namely at the temperatures where the viscosity is ca. 102 dPa s and below, the actual melting processes take place involving, for example:
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Part A | 3.1
The latter takes place at so low temperatures in order to make the glass piece in the mold keep the imposed shape as precisely as possible. In the temperature range between the annealing point and the strain point, the exact positions of the atoms become fixed. Macroscopic hotforming is over when the temperature has already fallen so low, but there are some processes which may be called microscopic hotforming that are preferably carried out in this temperature range. If properly chosen, an according temperature treatment will allow:
Stress relaxation Structural relaxation.
Stress relaxation means the compliance of the glass to an external or internal stress field by viscous flow which finally results in reduced or even totally eliminated stress. As will be discussed in detail below, the typical timescale of stress relaxation becomes seconds to minutes in the range of the annealing point and rises sharply with further decreasing temperature. So if, for instance, an internal stress field has been generated during hotforming, a properly dimensioned soak time or slow cooling in the range between annealing point and strain point will significantly reduce it. Structural relaxation is a related effect, but not identical. Structural relaxation means that the atomic structure (which is not unique in an amorphous material) adapts to the environmental temperature by choosing a configuration that minimizes Gibbs’ free energy. Manufacturing glass by melting, hotforming, and subsequent cooling implies a permanent change of the atomic structure which, however, comes to a standstill in the temperature range between the annealing point and the strain point. This is due to the fact that the timescale of structural relaxation is similar, although not identical, to the timescale of stress relaxation. The proper choice of thermal treatment in said temperature range allows the fine-tuning of the refractive index and other properties which sensitively depend on the atomic configuration [3.8]. During further cooling, the (desired) resulting structure will not change. This position at the threshold to fixed atomic configurations defines the uniqueness of the temperature range between the annealing point and the strain point and this explains why fine-annealing in order to allocate, e. g., a desired value to the refractive index is carried out there. Also the result of stress relaxation will not change. Any build-up of permanent internal stress requires a change of the atomic configuration which is not possible during further cooling. (This statement does not
log η (dPa s) 14 6
5
12
4
2 3
1
10 7 8 8 6 4 2 0 200
400
600
800
1000
1200 1400 1600 Temperature (°C)
Fig. 3.6 Typical viscosity versus temperature curves. 1: natural vitreous silica, 2: 8253 (Aluminosilicate glass for halogen lamps), 3: 8252 (same application field as 8253), 4: BOROFLOAT33® 8330 (low thermal expansion, chemically inert Borosilicate glass), 5: AR-GLASS 8350® (soda-lime-silicate glass for tubing), 6: 8248 (low dielectric loss Borosilicate glass), 7: 8095 (electrically highly insulating Lead-Silicate glass), 8: 8465 (lead Aluminoborate solder glass). 1 from HERAEUS QUARZGLAS GmbH & Co. KG, Hanau, Germany. 2–8 from SCHOTT AG, Mainz, Germany [3.9]
apply to intermediary stresses due to intermediary internal temperature gradients.) Not that in the nonequilibrium case, i. e., when structural state and environmental temperature do not fit, the structural state is often characterized by the value which the environmental temperature would have to have if the glass was at equilibrium. This value is called fictive temperature Tf [3.8].
3.1.4 Types of Viscosity Curves: Short and Long Glasses There is a very remarkable general feature of the course of all glass-forming systems which becomes nicely visible in a log..T// versus Tg =T plot (Angell plot, [3.10]; Fig. 3.31). Tg shall denote the annealing point, not the dilatometric glass transition temperature. At high temperatures (typically at Tg =T < 0:5), the slope of .T/ versus Tg =T becomes smaller if the network formers are mixed with network modifiers, see, for instance, the slope of vitreous Na2 O 2SiO2 and the one of vitreous SiO2 in [3.10]. This is in accordance to what has been observed above considering SiO2 and NaCl melts. At comparatively low temperatures (typically 0:8 < Tg =T < 1), the opposite holds. The two effects almost mutually compensate so that altogether, all
Viscosity of Glass and Glass-Forming Melts
In accordance to what has been said above, silicon (network former) alone gives a long glass (1); silicon and boron (network former) together also give long glasses (4, 5), silicon and aluminum (intermediate) together give short glasses (2, 3), lead (intermediate) and aluminum (intermediate) and boron (network former) together give a very short glass (8). For a quantitative understanding, in particular to find out why the soda-lime-silicate glass (5) is comparatively long, one needs to consider the exact composition. It is 69 wt% SiO2 , 1 wt% B2 O3 , 4 wt% Al2 O3 , 3 wt% MgO, 5 wt% CaO, 2 wt% BaO, 13 wt% Na2 O, 3 wt% K2 O so that the SiO2 content is comparatively large which results in a comparatively long viscosity curve.
3.2 Shear Viscosity – Measurement 3.2.1 ISO Standards It is not possible to measure the entire viscosity– temperature curve with one universal apparatus. According to the recommendation of ISO (International Organization for Standardization, Geneva, Switzerland), three different devices are commonly used which are designed such that the optimum performance is in the viscosity range of the above crucial points on the viscosity-temperature curve, i. e., either the working, the softening, or the annealing point. Rotating Cylinder In the temperature range of the working point, the friction between either a rotating cylinder in a fixed axisymmetric crucible with molten glass (Searle-type set-up) or a fixed cylinder in rotating axisymmetric crucible with molten glass (Couette-type set-up) is measured (Fig. 3.7), see ISO 7884-2 [3.11]. The advantage Inner (rotating) cylinder Molten glass Outer (fixed) cylinder
H
D R
Fig. 3.7 Viscosity measurement by rotating cylinder
of the Searle-type set-up is its self-alignment feature. It comes from the centrifugal forces acting on the volume elements of the molten glass, which in return drive the cylinder (which is usually hollow and therefore has a comparatively low moment of inertia) in the center of the set-up. The advantage of the Couette-type set-up is its stable motion since it is the outer, high-momentof-inertia part of the set-up which is moving whereas the inner, low-moment-of-inertia part of the set-up is fixed. If the gap between the crucible wall and the cylinder surface is small, the viscosity follows from D
MD ; 2 R3 H!
(3.2)
with M: angular moment, D: gap thickness, R: cylinder radius, !: angular frequency, H: height of molten glass. Depending on the way the device is constructed, either the torque or the angular frequency is imposed. Data collection starts when a steady state characterized by constant values for both torque and angular frequency has been reached. To take into account the flow at the bottom of the inner cylinder (which, for instance, may have a conical shape in order to allow bubbles to disappear from there), (3.2) has to be extended. To the height H of the glass volume, a value is added which shall represent an effective height of the cylinder bottom D
MD : 2 R3 .H C / !
(3.3)
can be determined by measuring for different values of H and extrapolation to H D 0.
85
Part A | 3.2
viscosity curves do not only end at the same point for Tg =T D 1 (which is by design) but also start at almost the same point for Tg =T D 0 (which is remarkable). This common behavior (the background of which will be discussed below) results in viscosity curves which for glasses with a high modifier content are comparatively steep in the vicinity of the annealing point. Figure 3.6 shows the viscosity curves of some important technical glasses. Glasses with steep gradients are called short glasses and glasses with shallow gradients are called long glasses. This is historical wording and goes back to the times when glass hotforming was mainly done by hand. A long glass would offer a suitable viscosity range to the glassmaker for a comparatively long time during cooling in open space whereas a short glass would not.
3.2 Shear Viscosity – Measurement
86
Part A
Fundamentals of Glass and the Glassy State
Part A | 3.2
In order to ensure precise temperature monitoring, which is essential for all viscosity measurements, the temperature of the melt may be recorded directly via a thermocouple plunge sensor. Confusion concerning the exact location of the working point on the temperature scale may arise from the fact that a second, slightly different definition of the working point exists. Alternatively to the 104 dPa s criterion, the working point may be defined via measuring the time a platinum-rhodium rod of defined weight and geometry requires to penetrate a glass melt down to a certain depth, see ISO 7884-5 [3.12]. The working point temperature after said ISO 7884-5 may differ slightly from that obtained via ISO 7884-2 and the 104 dPa s criterion. Consequently, the viscosity measured by ISO 7884-2 at the working point temperature determined according to ISO 7884-5 may differ a little from 104 dPa s, too. Fiber Elongation The natural high-viscosity limit of the above rotating cylinder device is reached once the angular velocity becomes so small that it is hardly detectable. A typical upper limit is the range 105 106 dPa s. So for measuring higher viscosities, devices have to be used where the force that may be applied leads to a larger deformation of the sample. In the temperature range of the softening point, viscosity can be determined via the elongation of a fiber which is loaded with a constant weight (Fig. 3.8), see ISO 7884-3 [3.13]. The viscosity follows from D
FL2 ; 3V v
(3.4)
with F: load (gravitational force), L: fiber length, V: fiber volume, v : elongation speed. Again, data collection starts once a steady state has been reached, which here means creep at a constant elongation speed. Note that (3.4) suggests that there is a one-to-one relation between elongation speed and viscosity. Reality, however, is more complex than (3.4) and also involves a surface tension contribution. It is because of this that the alternative definition of the softening point (which exists as well as the one above of the working point) is exactly equivalent to the definition of the softening point via the viscosity value of 107:6 dPa s only for glasses with a density of 2500 kg=m3 and a surface tension of 300 mN=m. According to said alternative definition, the temperature is determined at which a 235 mm fiber, with the upper 100 mm exposed to the temperature load and the whole fiber exposed to its own weight, reaches 1 mm=min elongation speed, see ISO 7884-6 [3.14]. Commonly, this issue is neglected. It is, however, responsible for the fact that in some literature, one will find D 107:65 dPa s as the softening point definition instead of D 107:6 dPa s. Because of its geometry, the set-up of the fiber elongation method is particularly sensitive to temperature inhomogeneities. To suppress the latter, the fiber is sometimes encased in a hollow bloc of highly conductive metal, e. g., silver, see again ISO 7884-3 [3.13]. Beam Bending To increase the proportion between sample deformation and force applied, one may make use of the lever effect. In the temperature range of the annealing point, threepoint bending is used (Fig. 3.9), see ISO 7884-4 [3.15]. The sample rests on two edges. In the middle, a load is applied.
Fixturing I
A
Glass fiber Elongation
Transducer Transducer
Fig. 3.8 Load F
Viscosity measurement by fiber elongation
Load F
Fig. 3.9 Viscosity measurement by beam bending
Viscosity of Glass and Glass-Forming Melts
FL3 : (3.6) 12dh3v As the annealing point is situated in the center of the temperature range of the glass transition, care has to be taken concerning structural relaxation. To obtain the equilibrium viscosity, the sample has to be kept long enough at the measurement temperature to allow for almost complete structural relaxation. (In other words: one has to wait until the fictive temperature Tf of the glass has reached the measurement temperature T.) In addition to structural relaxation, delayed elasticity has to be taken into account. When the load is applied, the steady state of constant deformation speed (so-called creep) is not reached immediately even in the case of an imaginary absence of structural relaxation. Instead, a transition period is passed for which delayed elastic effects are characteristic [3.16]. Commonly, the measurement is evaluated once a constant deformation speed has been reached which is considered as both an indicator of complete structural relaxation and finished delayed elastic effects. Note that delayed elasticity does not play a role in a temperature run if it is started at higher temperatures and carried out on one and the same sample without any removal of the load. At the start temperature, delayed elastic effects do not take much time and creep is reached quite soon. Any subsequent temperature decrease will only affect creep velocity, not the already-finished delayed elastic effects. Also for the annealing point, there is an alternative definition which may lead to a slightly different result, i. e., a difference between the annealing point defined above—as the temperature where the equilibrium viscosity is equal to 1013 dPa s—and the alternative one. The reason is incomplete structural relaxation (as discussed in the previous paragraphs). The alternative definition is given in ISO 7884-7 [3.17], according to which the annealing point is the temperature where a certain sample-geometry-dependent value for the deformation speed is reached during cooling at 4 K=min. D
Said deformation speed is equivalent to a viscosity of 1013 dPa s which, however, is a nonequilibrium viscosity in this case. The equilibrium viscosity at the corresponding temperature is somewhat higher, e. g., 1013:2 dPa s or else. For the same reason as above, delayed elasticity does not play a role in this type of annealing point measurement.
3.2.2 Further Methods Ultrahigh Viscosities: Helical Spring To increase the proportion between sample deformation and force applied even further and allow viscosity determination even below the annealing point, at least down to the temperature where the viscosity amounts to 1015 dPa s, the ingenious device shown in Fig. 3.10 has been developed [3.18, 19]. The core piece is a helical spring made of the glass being investigated. Axial elongation of such a spring will result in pure shear deformation so that the set-up is generally suited to the measurement of shear viscosity. By choosing optimum values for the diameter of the glass fiber or rod from which the helical spring is made as well as for diameter and length of the helix, tiny shear deformations will lead to measurable spring elongations allowing the determination of ultrahigh viscosities. For the same reason as for the beam-bending device above, delayed elasticity does not play a role in a temperature run if it is started at higher temperatures and carried out on one and the same sample without any removal of the load. The viscosity value follows from D
8FD3 N ; v d4
(3.7)
with F: load, D: coil diameter, N: number of coils, d: wire diameter, v : elongation or deflection speed (D speed at which the sample bottom moves).
Fixture
Extensometer
Fig. 3.10
Load
Viscosity measurement by helical spring
87
Part A | 3.2
The viscosity value follows from gAL L3 FC 1:6 ; (3.5) D 144I v with F: load, : glass density, A: cross-section area, L: distance between the two edges, I: geometric moment of inertia (for a sample with rectangular cross-section and width d, height h: I D dh3 =12), v : deformation speed (D speed at which the sample bottom moves), g: standard gravity. For thin samples with a rectangular cross-section, (3.5) reduces to
3.2 Shear Viscosity – Measurement
88
Part A
Fundamentals of Glass and the Glassy State
Part A | 3.2
Since descriptions of the helical spring elongation method are scarce in the literature, the derivation of (3.9) is briefly summarized here. In general, the elongation or deflection ı of any glass piece exposed to shear (so in particular also a helical spring) as a response to an applied load F consists of three parts, namely a spontaneous elastic response, a delayed elastic response, and creep [3.16] ı D ıelasticity C ıdelayed elasticity C ıcreep :
(3.8)
Provided that the coil diameter D is considerably bigger than the wire diameter d, the elastic part is given by [3.20] ıelasticity D
8FD3 N ; Gd 4
(3.9)
G is the instantaneous shear modulus. To obtain the long-term creep response instead of the short-term elastic response, one only has to replace 1=G with t= [3.16] ıcreep D
8FD3 N t ; d4
(3.10)
With the long-term limit of the elongation speed v being dıcreep =dt, one may obtain (3.7) from (3.10). Alternative in the Medium Viscosity Range: Parallel Plate In the range 106 1011 Pa s, a parallel plate viscosimeter [3.21, 22] may be used alternatively to the fiber elongation method. The viscous body deposited between the parallel plates is exposed to load and responds by deformation (Fig. 3.11). Experimentally, the plate separation h is measured at a given temperature as a function of time. According
Transducer
Load F
Load rod
Sample
h
Parallel mold plates Pedestal
Fig. 3.11
Viscosity measurement by parallel plate
to Gent [3.22] who has considered the case of a frictionless contact between the glass and the parallel mold plates, the viscosity follows from D
Fh2 30V
dh dt
1 ;
(3.11)
F is the load applied, V is the volume, and h is the height of the glass sample. Joshi and Joseph have considered a more general case and found a more precise approach which requires some more mathematical effort but is still easy to handle [3.23]. Compared to fiber elongation, the sample preparation effort is easier (no fiber manufacturing required). However, the resolution of the elongation measurement is lower due to the much smaller sample height. Alternative in the Ultralow Viscosity Range: Falling Sphere The set-up of, e. g., Shartsis and Spinner [3.24] is as follows. A platinum sphere is suspended by a thin platinum wire in the glass melt to be measured which in return is contained by a crucible. The platinum wire is fastened to one pan of an analytical balance. To impose very low forces, the other pan of the balance may contain a counterweight almost completely balancing gravitational force. The velocity of the sphere is indicated by the motion of the balance pointer, which is observed through a Brinell microscope. Viscosity is calculated from Stokes’ law [3.24]. Dynamic Mechanical Analysis (DMA) All measurement methods introduced so far are steadystate. However, the beam-bending device may also be run in a dynamic mode if modified accordingly. By imposing both a constant and an overlaid alternating load on the sample, the latter is both fixed (by the constant or static load) and tested in an oscillating mode (by the alternating or dynamic load; mechanical spectroscopy by dynamic mechanical analysis, DMA) [3.25]. The viscosity range being addressed by DMA is the same as for beam bending. The crucial quantity of the measurement is the phase shift between the alternating part of the total load and the alternating part of the displacement of the moveable part of the sample holder, usually its upper piece. Assume that the alternating part of the load follows a cosine function F D F0 cos.!t/. For small loads, the alternating part of the displacement follows a cosine function, too, but with a phase shift ı: s D s0 cos.!t ı/. Making use of the theorems for the cosine function one may partition the alternating part of the displacement into two components,
Viscosity of Glass and Glass-Forming Melts
! is the angular frequency. A derivation of (3.12) will be given below. A reasonable procedure to obtain the viscosity from (3.12) is to make a so-called frequency sweep at the temperature under consideration, i. e., to carry out the dynamic mechanical analysis at different frequencies, typically in the range 0:1100 Hz, and take the value for which gives the best fit of the theoretical tan.ı.!// versus the experimental tan.ı.!// curve. There is one issue concerning the experimental set-up. Three-point bending as shown in Figs. 3.9, 3.12 implies uniaxial strain which is not pure shear but a mixture of shear and compressional/dilatational strain. This does not play a role in steady-state beam bending above because “steady state” means waiting for so long that before data sampling starts, all effects have attenuated, with the sole exception of shear viscositydriven creep. Shear viscosity is the only effect that allows long-lasting constant creep [3.16]. Fortunately, uniaxial strain is not pure shear but “almost pure shear.” One may quantify this considering the displacement s of a thin, purely elastic sample as a response to three-point bending by a force F [3.26] sDF
L3 1 / : 4Edh3 E
(3.13)
With typical values for glass, i. e., Young’s modulus E D 60 GPa and Poisson number D 0:2, and [3.16] E GD ; 2 .1 C / 1 1 1 D C E 3G 9K
E KD ; 3 .1 2 / (3.14)
89
Fig. 3.12 Sample
fixture for dynamic mechanical analysis in three-point bending mode
Load F
Part A | 3.2
sin-phase D s0 cos.ı/ cos.!t/ which is in phase with the load and soff-phase D s0 sin.ı/ sin.!t/ which is off phase to the load. In mechanics, force and displacement in phase means no energy dissipation; the energy introduced into the system is stored as potential energy, e. g., as elastic energy. On the contrary, force and displacement off phase is equal to force and velocity (i. e., the time derivative of displacement) in phase which in return means energy dissipation, see Fig. 3.13. So the quotient sin-phase =soff-phase D tan.ı/ gives the proportion between dissipated and stored energy in such a set-up. As energy dissipation is via internal friction which in return means viscous flow, tan.ı/ is a measure for viscosity. For most oxide glasses, the relation is approximately p =2 tan .ı/ D p (3.12) sin : 4 !2=G
3.2 Shear Viscosity – Measurement
Displacement s
F, s δ
Time
Force F
Displacement s
Fig. 3.13 Phase shift between force and displacement in dynamic mechanical analysis
a
b
h c Core of sample (subject to shear)
Fig. 3.14 Asymmetric four-point bending
one arrives at the fact that about 80% of the elongation is due to shear and only the remaining 20% is due to compression=dilatation. K is the bulk modulus. This ratio may even be increased by a finite-element-optimized asymmetric four-point bending [3.27], see Fig. 3.14.
90
Part A
Fundamentals of Glass and the Glassy State
Vertical displacement 8 mm 4 mm 6 mm
16 mm
Part A | 3.3
+ 0.19 + 0.15 + 0.11 + 0.07 + 0.03 – 0.01 – 0.13 – 0.17 – 0.21 – 0.25 – 0.29
Fig. 3.15 Finite element calculation to determine the optimum asymmetric four-point bending geometry. The vertical displacement indicated by colors shown is in arbitrary units and largely overscaled. With respect to the assumed linearity, only very small deformations need to be calculated
Fig. 3.16 Principal stresses for an optimized asymmetric four-point bending
smax in-plane smin in-plane s out-of-plane
The geometry can be optimized by a linear finite element analysis [3.28]. With respect to the symmetry of the problem, this analysis is 2-D. Two calculations are carried out. First, the mutual displacement of the top sample holder and the bottom sample holder as a response to a force F is calculated with E and taking the above typical values E D 60 GPa and D 0:2. With (3.14), this is equivalent to G D 25 GPa and K D 33:33 GPa. This calculation provides the linear overlay of the shear response of the sample and its response due to compression or dilatation. Second, the mutual displacement of both sample holders as a response to the same force F is calculated with E D 75 GPa and D 0:5. With (3.14), this is equivalent to G D 25 GPa and K D 1. This calculation provides the pure shear response of the sample. Because of the assumed linearity, the ratio of both calculated displacement values gives the ratio of shear deformation to total deformation.
For the three-point bending of a thin plate one gets a ratio of 80%, as expected. For an asymmetric four-point bending, the ratio depends on the exact geometry. For the geometry shown in Fig. 3.15, i. e., a D 8 mm, b D 16 mm, c D 6 mm, h D 4 mm, the ratio is 86%. The corresponding principal stresses are shown in Fig. 3.16. The vanishing trace of the stress tensor in the center of the sample indicates pure shear in this area. Another way to subject the sample to (almost) pure shear is by torsion [3.25]. The actual motivation to introduce dynamic mechanical analysis into glass research, however, has not been the desire for another viscosity measurement method but the fact that, compared to steady-state beam bending, dynamic mechanical analysis offers far more insight into the kinetic details of viscous flow. This will be discussed in the next paragraph after an introduction into the corresponding theory.
3.3 Shear Viscosity – Theory The general ansatz for a shear viscosity formula is the product of an assumed high-temperature limit 1 of the shear viscosity and a temperature-dependent (or inversely temperature-dependent) function that approaches Unity in the high-temperature limit ˇ 1 ˇˇ 1 ; f D 1 f !1: (3.15) T T ˇ T!1
Particularly concerning the form of f .1=T/, there are numerous theories which will be discussed below.
The ansatz (3.15), however, refers to a steady-state viscosity as measured by the above methods. For a comprehensive picture of viscosity, a detailed knowledge of the kinetics of viscous flow has to be developed. This is of great practical importance in the viscoelastic regime which is identical to the temperature range around the annealing point. In this temperature range, the short-term response of a sample exposed to shear will be elastic whereas the long-term response will be viscous.
Viscosity of Glass and Glass-Forming Melts
3.3.1 Kinetics of Viscous Flow in the Viscoelastic Regime
Maxwell Model If exposed to constant shear strain by, e. g., an asymmetric four-point-bending set-up, glass will respond by elastic counterforces which, however, will decrease with time in the glass transition range (relaxation); so will the forces necessary for keeping up the constant strain. If exposed to constant shear stress, the glass will respond by a combination of instantaneous and continuous elongation. Maxwell has described this behavior by a model which consists of a spring and a dashpot in a series. Viscoelastic behavior according to this model means that the material considered responds like an elastic body on short timescales and like a viscous fluid on long timescales [3.25], see Fig. 3.17. Consider the case of continuously increasing elongation caused by a constant force F which is applied for t 0, the following equation holds zD
F F C t: D Ad
(3.16)
F1 F2 z1
z2
F z
Fig. 3.17 Maxwell model for viscoelasticity: spring in se-
ries with a dashpot (piston moving in a hollow cylinder filled with a viscous fluid). x; y: dislocations of spring/piston, z: total dislocation, F: force measured along the set-up
91
D is the spring constant, the viscosity, A the outer surface of the piston assumed to be (almost) equal to the inner surface of the hollow cylinder, and d the distance between piston and hollow cylinder. The above equation may be derived with the following intermediary steps F1 D Dz1 A dz2 F2 D d dt F1 D F2 D F z1 C z2 D z :
Part A | 3.3
The starting point of the following theoretical considerations is the essential feature of the glassy state, namely the existence of configurational degrees of freedom. At room temperature, most of those degrees of freedom may be considered as frozen-in on any realistic timescale. If reheated into and above the glass transition range, however, the glass will regain its ability to reconfigure its atomic structure and will use this ability to acquire a state of minimum Gibb’s free energy, with respect to said configurational degrees of freedom. It will also use this ability to yield to an imposed stress or strain by viscous flow, for instance, to change its shape to adapt to an imposed deformation. This links viscosity to the timescale of atomic reconfiguration or—more commonly—relaxation. A simple relation between shear viscosity and the corresponding relaxation time in the viscoelastic regime has been derived by Maxwell.
3.3 Shear Viscosity – Theory
(3.17)
The transition from elastic to viscous behavior occurs instantaneously in this simple case (in general, the transition is smooth). In an infinitesimally short time the elastic energy .1=2F 2/=D is deposited in the spring; all further energy introduced into the system is dissipated. Viscoelastic relaxation is observed if a constant elongation z D const. is imposed. In this case, the force F required for keeping up the elongation is t.Dd/
F.t/ D D const. e .A/
D D const. et= :
(3.18)
The time constant D .A/=.Dd/ is called relaxation time. Equation (3.18) may be derived with the following intermediate steps dz1 dz2 C D0 dt dt 1 dF1 d F2 C D0 D dt A F1 D F2 D F :
(3.19)
Summarizing, the above mathematical discussion of the Maxwell model [3.25] shows that essentially, it may both describe the relaxation of the stress response to an imposed elongation, with a single exponential time response function, and the combination of spontaneous elastic elongation/deformation and continuously progressing elongation/deformation (creep by viscous flow) as a response to an imposed stress. Kelvin–Voigt Model (Delayed Elasticity) For a comprehensive description of viscoelastic behavior, delayed elasticity must also be taken into account. This phenomenon may be represented by a Voigt model according to which the material responds like a rigid body on short timescales and like an elastic body on long timescales such as a combination of the spring and dashpot set-up in parallel will do [3.25], see Fig. 3.18.
92
Part A
Fundamentals of Glass and the Glassy State
Fig. 3.18 Voigt model F1 z1
F
Part A | 3.3
F2 z2
for viscoelasticity: spring in parallel to a dashpot. z: dislocation, F1 : force measured at spring, F2 : force measured at dashpot, F: total force measured
A
F ε
Fig. 3.19
Definition of shear angle "
ε'
d γ
γ' z
Below, it will be shown that a realistic representation of glass viscoelasticity requires at least one Maxwell and one Voigt model. In case of a constant force the response is t.dD/ i Fh 1 e .A/ : zD D
(3.20)
This time, the time constant involved is called retardation time. Equation (3.20) may be derived with the following intermediate steps
To describe the deformation, mostly not the angle "0 describing the change of 0 is referred to but the angle " describing the change of . In this case, one has to introduce a factor of 2 for compensation. F1 D Dx ! 1 D G2"1 A dz2 d2" ! 2 D 2 : F2 D d dt dt
(3.25) (3.26)
Assuming glass to behave according to the simple Maxwell model this leads to: 1. In the case of constant shear stress 0
F1 D Dz1 A dz2 F2 D d dt z1 D z2 D z F D F1 C F2 :
0 0 C tD "D 2G 2
1 t C 0 DW J.t/0 2G 2 (3.27)
(3.21)
This leads to the following inhomogeneous differential equation that may be solved by the variation of the constant. Dz C
x, y, z
(with J.t/ being called compliance), and 2. In the case of constant shear strain "0 .t/ D 2G"0 et.G=/ D .2Get.G=/ /"0 DW .2Get= /"0 DW 2G.t/"0
A dz DF: d dt
(3.28)
(3.22)
The case of an instantaneous, fixed elongation may not be realized with a Voigt model. Summarizing, the above mathematical discussion of the Voigt model [3.25] shows that essentially, it describes the delayed response to an imposed stress, with a single exponential time response function. Shear in Glass Consider a glass volume element under shear stress [3.16], see Fig. 3.19. The link between the above models and the glass behavior is found by a transformation from (force, elongation) to (stress, strain). G"01
F1 D Dz1 ! 1 D A dz2 d"0 ! 2 D 2 : F2 D d dt dt
(3.23) (3.24)
(with D =G being the thus-defined relaxation time and G.t/ the thus-defined time-dependent shear modulus). Assuming glass to behave according to the simple Voigt model and constant shear stress this leads to 1
0
1 et.G=/ D 1 et.G=/ 0 2G 2G 1 DW 1 et= 0 DW J.t/0 2G
"D
(3.29)
(with D =G being the thus-defined retardation time and J.t/ again being called compliance). Note that G is assumed to be temperatureindependent which is true in the viscoelastic regime around the annealing point, see, e. g., [3.29, 30].
Viscosity of Glass and Glass-Forming Melts
Fig. 3.20 Typical response of glass to constant shear stress
ε Creep
3.3 Shear Viscosity – Theory
with 1 , 2 relaxation times and v1 , v2 coefficients which shall fulfill the condition v1 C v2 D 1. C is a small negative number compared to G1 =1 and is a big negative number compared to G1 =1 so that both
v1 D
Delayed elastic shear
C C G11
Part A | 3.3
C
and Instantaneous elastic shear t
v2 D
Simplest Realistic Representation of Shear Relaxation: Burger Model However, the behavior of inorganic glasses is more complicated and cannot be described with either the Maxwell or the Voigt model alone [3.16], see Fig. 3.20. The simplest representation of the above behavior is by a Burger model [3.25], see Fig. 3.21. In case of constant stress one gets G 1 t 1 t 1 "D 1 e 1 0 C C 2G2 22 2G1 DW JBurger .t/0 : (3.30)
This corresponds to the general features shown above. The first term in (3.30) represents instantaneous response, the second one represents long-term creep, and the third one represents delayed elasticity. The case of constant strain is more complicated 2G2 "0 G1 C t D C C e .C / 1 G1 t e : C (3.31) 1 C , are the roots of the equation G1 G2 C .G2 2 C G1 2 CG2 1 /C1 2 2 D 0. C , are negative numbers with different amounts, so that one might also write t t (3.32) D 2G2 "0 v1 e 1 C v2 e 2
C G11 C
are positive numbers. Thus, (3.31) or (3.32), resp., becomes comparable to (3.28). The single exponential relaxation in (3.28) has been replaced with a double exponential with two relaxation times. As will be shown below, the single exponential will be replaced with a whole spectrum of relaxation times in the general case. The derivation of (3.31) is as follows "1 C "2 C "3 D "0 d"1 d"2 d"3 C C D0 dt dt dt d 2 "1 d 2 "2 d 2 "3 C 2 C 2 D0 dt2 dt dt d"1 d 2 "1 d"2 d 2 "2 C 21 2 C 2G1 C 21 2 2G1 dt dt dt dt d"3 d 2 "3 C 21 2 D 0 C2G1 dt dt 1 d 1 d2 1 d C 2G1 C 21 C 2G1 dt 2G2 dt 2G2 dt2 22 1 d D0 C21 22 dt d G1 G2 C .G2 2 C G1 2 C G2 1 / dt d2 C1 2 2 D 0 dt (3.33)
G1 η2 G2
η1
93
Fig. 3.21 Burger model
94
Part A
Fundamentals of Glass and the Glassy State
Ansatz D et G1 G2 C .G2 2 C G1 2 C G2 1 / C 1 2 2 D 0 ˙ D
.G2 2 C G1 2 C G2 1 / 21 2
Part A | 3.3
p G2 2 .G2 2 C 2G1 2 C 2G2 1 / C .G1 2 G2 1 /2 ˙ 21 2 D C eC t C e t (3.34)
Initial conditions ) Š
.0/ D C C D 2G2 "0 D ˇ ˇ ˇ d ˇˇ d"1 ˇˇ d"2 ˇˇ .0/ D 21 ; D 2G ; 2 dt ˇ tD0 dt ˇ tD0 dt ˇ tD0 ˇ d"3 ˇˇ ; .0/ D 22 dt ˇ tD0 ˇ 1 d ˇˇ .0/ .0/ C C D0; 1 G2 dt ˇ tD0 2 G2 G2 0 D .C C C / ; 1 2 0 G2 G2 C D ; C 1 2 G2 G2 0 C C C ; D C 1 2
Improved Representation of Shear Relaxation: Kohlrausch(–Williams–Watts)-Kinetics A better coincidence of theoretical and experimental data is obtained, if the single exponential function from above is replaced with a stretched exponential or Kohlrausch(–Williams–Watts) function [3.16], see Fig. 3.22. For constant stress this gives 1 1 t 1 "D C C 2G0 2 2G1 2G0 t b . / 0 DW J.t/0 : 1e (3.36) 1=.2G0 / represents the instantaneous elastic response, 1=.2G1 / represents the sum of instantaneous and delayed elastic response, and t=.2/ represents the longterm creep. J.t/ is the time-dependent compliance, and is a retardation time. The expression resembles very much the one for the Burger model with the exception of the detailed kinetics of delayed elasticity (single exponential for the Burger model and stretched exponential here). For computational purposes, the Kohlrausch function may be represented by a number of single exponentials (Prony series) [3.16] " 1 1 t 1 "D C C 2G0 2 2G1 2G0 # X t vi 1 e i 0 i
X
G2 G1 G2 ; 1 1 2 0 G1 C D C C ; C 1 0 G1 D C C 1
C C D
DW J.t/0 ; vi D 1 :
(3.37)
i
σ/σ(0) 1 Single exponential function e –t/τ
(3.35)
Combining the results for C , derived in (3.35) with the result of (3.34), one arrives at (3.31). Summarizing, the above mathematical discussion of the Burger model [3.25] shows that essentially, it may both describe the relaxation of the stress response to an imposed elongation/deformation, in which it does with a double exponential time response function, in contrast to the Maxwell model, as well as all elements of the response to an imposed stress, i. e., spontaneous elastic elongation/deformation, delayed elastic elongation/deformation, and creep.
0.5 Kohlrausch
1
2
3 t/τ
Fig. 3.22 Single exponential function exp.t= / versus Kohlrausch- or stretched exponential function exp..t= /b /, b D 0:3
Viscosity of Glass and Glass-Forming Melts
3.3 Shear Viscosity – Theory
Fig. 3.23
For constant strain the change to the Kohlrausch kinetics gives .t/ D 2G"0 e. / DW G.t/"0 : t
Oscillating shear
b
(3.38)
G.t/ is the time-dependent modulus, and is a relaxation time. Again, the Kohlrausch function may be represented by a number of single exponentials (Prony series) X t vi 1 e i DW G.t/"0 : (3.39) .t/ D 2G"0
F
Part A | 3.3
i
The determination of relaxation kinetics by dynamic mechanical analysis will be shown below. The determination of retardation kinetics including the value of G1 can be made, for instance, by a detailed analysis of fiber elongation, not only in the steady state. Note that G without index is identical to G0 . Boltzmann’s Superposition Principle In general (not only for shear) it is assumed that the stress effects arising from strain contributions imposed at different times overlay without interfering [3.25] X b 0 .t/ D 2G ".at time t0 / e..tt /= / Zt
0
b
e..tt /= /
2G 1
d".t0 / 0 dt : dt0
(3.40)
Boltzmann’s superposition principle is the starting point of the derivation of an important connection between the responses to stress and strain [3.16]. Consider the case of constant strain rate which is comprehended by both the constant stress case, i. e., (3.36), and Boltzmann’s superposition principle for a continuous sequence of infinitesimal strain steps, i. e., (3.40). In (3.36), the case of constant strain rate is reached once the value of the time t has exceeded a certain limit so that the Kohlrausch term can be neglected. Above that time, the strain rate d"=dt is given by d" 0 D : dt 2
(3.41)
t0 has been substituted by x via x D .t t0 /= . is the Gamma function. (t) turns out to be constant as expected. Comparing (3.41) and (3.42), one arrives at 1 ; D G 1 C b
(3.43)
which relates the relaxation time from (3.40) to the steady-state viscosity [3.16]. Determination of Kohlrausch(–Williams–Watts) Relaxation Kinetics by DMA Boltzmann’s superposition principle as defined in (3.40) is also the starting point of the determination of the parameters of the Kohlrausch(–Williams–Watts) kinetics by mechanical spectroscopy or dynamic mechanical analysis (DMA) [3.31], see Fig. 3.23. With the following equation for the oscillatory part of the strain " .t/ D "0 cos .!t/ ;
! D 2
.t/ D 2G
D 2G
d" dt
one may rewrite (3.40) for the oscillatory part of the stress as Z1 ) .t/ D 2Gi!"0 e
i!t
..tt0 /= /b
e 1 Z1
d" dt
xb
e
or " .t/ D "0 ei!t (3.44)
In (3.40), the case of constant strain rate means Zt
95
dt0
e.t
00 = /b
00
ei!t dt00 : (3.45)
0
1 d" : dx D 2G 1 C dt b
0
(3.42)
We may write this also as 0 .t/ D @2Gi!
Z1
00 b t i!t00
e 0
e
1 dt00 A "0 ei!t
(3.46)
96
Part A
Fundamentals of Glass and the Glassy State
and call the term in brackets the complex modulus. Rewriting leads to 20 1 1 Z b i$ t 4@ . y / e sin .!y/ dyA D !2G"0 e 0
Part A | 3.3
Ci @
0
Z1
13
e. / cos .!y/ dyA5 : y b
(3.47)
0
This means for the phase shift R1 tan .ı/ D
. y / cos .!y/ dy 0 e R 1 . y /b sin .!y/ dy 0 e b
Z1
00
F.!/ D F .!/ C iF .!/ D i
(3.48)
F.y/ei!y dy
0
Z1 Di
e. / ei!y dy ; y b
(3.49)
0
F 00 .!/ : ) tan.ı/ D 0 F .!/
(3.50)
One remark on the identification of this issue here as a Laplace Transform issue. Because of the exponential decrease of the Kohlrausch function, the following equation holds Z1 )
. y /
e 0
b
i!y
e
Z1 dy D lim
!0
F.y/ D 1
y b
CO
y 2b
:
(3.52)
Carrying out the integration in (3.49) after inserting (3.52), one arrives at the integral representation of Euler’s gamma function with the argument .1 C b/ .1 C b/ 1 1 1 )F.!/ D CO ! .i! /b .! /2b .1 C b/ i b 1 1 2 1 ; e O D ! .! /b .! /2b (3.53)
:
According to (3.48) and the theorems for the Laplace Transform, tan.ı/ is a monotonous function of and ! for fixed b with tan(ı) ! 0 for !1 and for !!1 and with tan.ı/!1 for !0 and for ! ! 0. There is, however, no general analytic solution of this so that in general, and b may only be determined numerically. In the temperature region of the glass transition, however, where takes values of the order of magnitude of 10 s, and for frequencies above 1 Hz there is a very good approximation [3.28, 32]. See also [3.33]. The starting point is the Laplace transform of the Kohlrausch function. We define 0
series
e. / e y ei!y dy : y b
0
(3.51)
In the following, the !0-limit should be considered as present also if not stated explicitly. According to the Tauber theorems for Laplace transforms, the !!1-behavior is determined by the y!0behavior of F.t/ ) replace F.y/ by its 1st-order Taylor
b .1 C b/ 1 1 )F.!/ D cos ! 2 .! /b 1 b .1 C b/ C O ; sin Ci 2 .! /b .! /2b .1 C b/
(3.54)
b sin 2 1 .! /b CO ) tan.ı/ D .1 C b/ b .! /2b 1 cos b 2 .! / 1 b .1 C b/ C O ; sin D 2 .! /b .! /2b (3.55)
Setting b D 0:5 which Rekhson found to be a good estimate for many glasses [3.16] allows one to derive the above formula (3.12) from (3.55). For an exact determination, one has to apply dynamic testing, see below. In such a case, i. e., if a high precision is required, it is also preferable to use a 2nd-order Taylor series. This analysis leads to .1 C b/ b ) tan.ı/ D sin b 2 .! / Œ .1 C b/2 .1 C 2b/ C 2 .! /2b 1 sin . b/ C O ; (3.56) .! /3b If tan.ı/ is known as a function of frequency from dynamic mechanical analysis, both and b may be determined via (3.56). If temperature is varied as well, also H can be obtained. In that case the ansatz for is usually an Arrhenius ansatz D 0 eH=.RT/ . (The data set taken for parameter evaluation is limited to data from above the glass transition range so that equilibrium can be assumed.) Figure 3.24 shows a DMA on Borofloat33® .
Viscosity of Glass and Glass-Forming Melts
tan(δ) 0.30 1.0 Hz 0.25 1.8 Hz 0.20 0.15
6.0 Hz
0.10 0.05
displacement s as a response to a uniaxial load with a force F is equal to the change of the sample height H and—provided that jsj H holds—may be written as sDF
H 1 / : 2 E R E
(3.57)
R is the sample radius. Applying Boltzmann’s superposition principle on subsequent dislocation steps s one obtains for the relationship between the alternating part of the load— herein called F.t/—and the alternating part of the sample response—herein called s.t/ b .tt0 / R2 X F.t/ D E s.at time t0 / e H 2 Z t .tt0 / b R ds.t0 / 0 E e dt : H dt0
0 560
580
600
620 640 Temperature (°C)
Fig. 3.24 DMA on Borofloat33® (Annealing point 570 ı C,
Young’s modulus 64 GPa, Poisson number 0.2, shear modulus 26:67 GPa) in the asymmetric four-point-bending mode with a GABO EPLEXOR® . Geometry: a D 10 mm, b D 12 mm, c D 4 mm, h D 7 mm. Ratio of shear deformation to total deformation 0.82. Static load 400 N. Dynamic load 200 N. In addition to the customary compliance correction referring to standard sample holders, the data have been corrected comparing equal measurements on the sample holders alone and on the sample holders plus sample. Measurement: dots. Fit: solid lines
For the borosilicate Borofloat33® , a fit combining the Arrhenius ansatz for and (3.56) leads to b D 0:323191, 0 D 2:25644 1026 s, H=R D 52 725:8 K. Note that in the annealing range, the material may not be at equilibrium, i. e., it may be that the fictive temperature is different from the environmental temperature. The application of the Arrhenius ansatz D 0 eH=.RT/ is restricted to the equilibrium case, however. In the nonequilibrium case an ansatz which is dependent both on the environmental temperature and the fictive temperature has to be used, e. g., the so-called Tool–Narayanaswamy–Moynihan model [3.16].
3.3.2 Viscous Flow Beyond Upper Limit of Viscoelastic Regime In the middle between the annealing point and the softening point, the shear modulus almost completely collapses, see, e. g., [3.34, 35]. One may determine the corresponding temperature range by DMA in the uniaxial loading mode (constant or static plus alternating or dynamic load) with the sample being, for instance, cylinder-shaped. In that case the
97
(3.58)
1
Note that with respect to uniaxial load being almost pure shear (see above) it is assumed that the kinetics is the same as for shear. In particular, the parameters and b are assumed to be the same. With s.t/ D s0 cos .!t/
(3.59)
and following the above derivation, one arrives at the same expression for tan.ı/, namely (3.56). This expression is independent from the values of E, R, and H which have been assumed to be constant so far. It only depends on b, , and !. With the set-up as described (uniaxial compression of a cylinder), the above independence from E, R, and H is a weak condition only. It has to hold during the time intervals when the alternating force is applied and data are recorded. It need not hold in the time intervals required to heat the sample up from one temperature to the next during a temperature run. Under the static load (which is continuously applied throughout the whole measurement in order to keep the sample in position), the sample will change its R and H values in the latter time but this will not affect the measured value of tan.ı/. This is different for the bending set-ups where reasonable measurements are not possible once the sample has been substantially deformed and this is why the uniaxial compression of a cylinder is particularly suited to obtain a qualitative picture of what happens at temperatures significantly above the annealing point. The disadvantage of uniaxial cylinder compression is of course the tiny amount of dislocation even for very high forces applied. This makes it difficult to separate
Part A | 3.3
3.3 Hz
3.3 Shear Viscosity – Theory
98
Part A
Fundamentals of Glass and the Glassy State
3.3.3 Temperature Dependence Approaches: Arrhenius versus Non-Arrhenius (Adam–Gibbs)
tan(δ) 0.020 0.016 4 Hz
0.012 0.008
Part A | 3.3
8 Hz
0.004 0 500
520
540
560
580
640 600 620 Temperature (°C)
Fig. 3.25 DMA on former television bulb glass 8056 from
SCHOTT (annealing point 515 ı C) on a cylinder-shaped sample (height 10 mm, diameter 10 mm) under uniaxial load. Static load 800 N, dynamic load 400 N. No extra compliance correction for these particular sample holders
the actual measurement data from the contribution of the machine compliance. This is why one may forego an extra compliance correction for the corresponding set of sample holders. The loss angle values thus obtained have to be called apparent loss angles values then. Figure 3.25 shows such a measurement which has been carried out on the former television bulb glass 8056 from SCHOTT. For the first 3040 K above the annealing point, the apparent loss angle or its tangent, resp., follows the principle temperature course as already shown in Fig. 3.24. At about 60 K above the annealing point (when the sample height has already dropped to 60% of its initial value), the viscoelastic response of the sample collapses. With further increasing temperature, the sample reduces to zero and the apparent loss angle to the loss angle of the machine compliance. Consequently, the viscoelastic picture involving multiple springs and dashpots collapses and reduces to a single dashpot, at least on the timescale of a glass practitioner. The question if there is a viscoelastic response of inorganic glass melts in the range of the softening point has been investigated in [3.36]. Analyzing different types of soda lime glass, they found a nonzero shear modulus in the melt whose value is, however, three orders of magnitude smaller than the one in the viscoelastic regime around the annealing point. The corresponding relaxation times are in the 0:1 s range so that this effect is of concern only for ultrafast processes. In the case of ultrafast processes, also the issue of non-Newtonian flow arises which has been discussed, e. g., in [3.37].
For small temperature intervals, the most common way to describe the temperature dependence of viscosity follows the general ansatz by Arrhenius. The most common theory used to explain the non-Arrhenius temperature dependence of viscosity which is found for large temperature intervals has been established by Adam and Gibbs [3.38]. Simple Ansatz for Temperature Dependence of Relaxation Time: Arrhenius The simplest model allowing relaxation is a doublewell potential, Fig. 3.26. The atomic structure of the material under consideration shall be such that the material consists of small units which may choose between two different configurations. The change from one configuration to the other shall be hindered by a potential barrier of constant height h. Reconfiguration steps shall be such that each of them contributes to a macroscopic motion (viscous flow in the case of imposed stress) or relaxation of the macroscopic stress (stress relaxation in the case of imposed strain). According to the Arrhenius law, the probability p of a successful attempt of the material unit to jump over said potential barrier is given by k hT
pDe
(3.60)
B
The frequency at which the material unit makes an attempt to jump over said potential barrier shall be given by a constant value 0 . In that case the relaxation frequency p 0 has the same temperature dependence as p alone and the relaxation time D 1=.p 0/ also follows Potential
h
∆ x
Fig. 3.26 Double-well potential. The positions of the
small spheres mark configurational states of an atomic ensemble
Viscosity of Glass and Glass-Forming Melts
an Arrhenius law D
1 k hT eB
0
(3.61)
Sophisticated Ansatz for Temperature Dependence of Relaxation Time: Adam–Gibbs Recall the above double-well potential. A piece of glass is considered as consisting of groups of atoms. Each group has two different possible configurational states at two different energy levels. Each group has a fixed, temperature-independent size. According to Adam and Gibbs, this model is too simple. In reality, one will find that the size of the groups of atoms which can relax, i. e., which may exist at a given temperature T at least in two different configurational states, depends on this temperature. Consider an atomic ensemble with possible configurations having energy levels 0, , , : : : with 0 < < < : : : At low temperatures, kB T , and, a forteriori, kB T holds. Therefore, only level 0 will be populated. No significant transition from one state to another will occur, i. e., there will be no relaxation. At high temperatures, both kB T , kB T hold. All levels will be equally populated. No significant transition from one state to another will occur, i. e., again there will be no relaxation. Between low and high temperatures, there are different temperature regions. There are some regions where due to the value of kB T, only configurational changes involving either level 0 or level are possible, and others, where level is accessible, too. The more configurations are accessible, the more possibil-
ities an atomic ensemble has to relax, i. e., to undergo configurational changes. Reversely, this means that an atomic ensemble which originally has more than one possibility of relaxation at its disposal may be reduced in number of atoms until a minimum group is reached which has only one possibility of relaxation. Let the glass have a temperature T. Let z be the number of atoms of the minimum group size which allows relaxation, i. e., which is effectively a double-well potential at T. Consider the thermal activation necessary for relaxation of this double-well potential. Since all z atoms are affected, the probability p for a successful attempt to change from one configurational state to the other is (with h0 being the activation enthalpy for a single atom, compare (3.60) above) 0 z 0 h zh D e kB T : (3.62) p D e kB T If there is one mol, the number n of such groups is NA =z. This gives for the molar configurational entropy Sc,molar the number Sc,molar D
NA Sc,group : z
(3.63)
Sc,group is the minimum configurational entropy a group must have in order to allow relaxation. According to the above argument (“the minimum group [. . . ] which allows relaxation [. . . ] is effectively a double-well potential”), this means that there have to be two distinct configurational states so that Sc,group kB ln .2/ :
(3.64)
With this, the following substitution is possible 0
kzhT
pDe
B
N Sc,group h0 c,molar kB T
SA
De
S
De
Q c,molar T
:
(3.65)
Q is a new constant. Next, we neglect all relaxation processes involving larger groups of atoms than the minimum group, i. e., groups with atom numbers z0 > z. This is justified because the corresponding relaxation probability p0 is very much smaller 0 0
kz hT
p0 D e
B
0
kzhT
z :
(3.66)
Multiplication by the above elementary frequency
0 gives the Adam–Gibbs result for the relaxation frequency. The inverse is the relaxation time . 0 D 1= 0 / Q
D 0 e Sc,molar T :
(3.67)
99
Part A | 3.3
kB is Boltzmann’s constant. With the Arrhenius law being valid, a log. / versus 1=T plot (and, approximately, also a log. / versus T plot) should show a linear dependence between the two quantities. Comparing to measured values one finds that generally viscosity follows an Arrhenius law over a limited temperature range only. This non-Arrhenius behavior is an essential feature of systems with configurational degrees of freedom and therefore one of the key issues of relaxation theory. The most common explanation has been given by Adam and Gibbs. Originally, it had been developed to explain structural relaxation but was soon generally applied to all relaxation phenomena including the underlying mechanism of viscous flow [3.39]. (Of course, the fact that the non-Arrhenius behavior is linked to the existence of configurational degrees of freedom somehow questions the theoretical justification of the above Arrhenius-based theories. For this and other reasons they are called semiempirical.)
3.3 Shear Viscosity – Theory
100
Part A
Fundamentals of Glass and the Glassy State
Although the parameters may differ, it is assumed that the functional form of this temperature dependence is the same for all relaxation time constants. As viscous flow is related to relaxation, it is also assumed that D 1 e
Q Sc,molar T
or D 1 10
B0 Sc,molar T
cp (J/(g K)) 3.0
2.0
:
Part A | 3.3
(3.68)
1.5
As Sc,molar is not a constant, this formula is capable of reproducing the non-Arrhenius temperature dependence in the range of the supercooled liquid, between glass transition and liquidus temperature. As structural relaxation is so fast in this temperature range that Tf is always equal to T, the glass is always at equilibrium there.
1.0
Arrhenius and Adam–Gibbs Approach Compared to Experimental Data The capability of the Adam–Gibbs model of reproducing the non-Arrhenius temperature dependence can be demonstrated by considering a glass for which both the viscosity and the specific heat cp are available as functions of temperature. In this case, the temperaturedependent molar configurational entropy can be calculated this way ZT Sc,molar D Sc,molar;max C M
cp;config 0 dT : T0
(3.69)
Tmax
M is the molar mass. Tmax is the upper boundary of the temperature range of the cp measurement. Sc,molar,max is the corresponding (at this stage unknown) configurational entropy. Both a short and a long glass will be demonstrated, see [3.40]. The short glass is the high-index, low-dispersion optical glass N-LAK12® from SCHOTT AG (approximate composition: 4050 wt% BaO, 1020 wt% B2 O3 , 1020 wt% La2 O3 , 1020 wt% SiO2 , see Table 1 below). As for all optical glasses, the DSC (differential scanning calorimeter) measurement in heating mode displays a sharp overshoot peak of the measured apparent cp at the glass transition which is due to the careful (slow) previous cooling (Fig. 3.27). To provide a consistency check and to obtain data without the large overshoot peak, the measurement is carried out in cooling mode as well. The nature of the overshoot peak and further details of cp measurements on glass are discussed elsewhere [3.8, 41]. Here, only the following items are of interest:
Heating (8 K/min) Cooling (10 K/min) Einstein
2.5
Below the glass transition, the DSC signal comes from the vibrational degrees of freedom only.
cp, config
0.5 0
0
200
400
600
800
1000 1200 Temperature (°C)
Fig. 3.27 Determination of cp;config for N-LAK12® from
SCHOTT AG in the T > Tg regime via DSC measurements carried out in both heating and cooling mode by a SETARAM Multi-HTC 96® device at the accredited laboratories of SCHOTT AG
All configurational degrees of freedom are frozen due to the lack of thermal activation. The measured cp -values at low T may be represented by an Einstein model E 2 TE 3NA e kB M T cp .T/ D C cp cV : 2 e
E T
1 (3.70)
E is the Einstein temperature, an adjustable parameter which has been found to be 920 K for N-LAK12® . M is the mass per mole of particles which is 31:9 g for N-LAK12® . As the Einstein model is essentially a model for the specific heat at constant volume, not constant pressure, cp cV correction has to be made. According to fundamental thermodynamics, said correction is given by cp cV D 9˛ 2 T=. /, ˛: linear thermal expansion coefficient, compressibility, density, see again [3.8]. For N-LAK12® , the corresponding values are: ˛ D 10:85 ppm=K, D 1=68 GPa, D 4:1 g=cm3 . Note that for ˛, the slope of the linear thermal expansion curve just below the glass transition is taken here. Note also that the Einstein model was originally developed for crystals. This is, however, not a point of concern here where it is applied close to its high-temperature limit. (The latter is identical to the Dulong–Petit model.) The glass transition marks the temperature where there is sufficient thermal energy to unfreeze the configurational degrees of freedom. Above the glass transition, the measured cp is the sum of a vibrational
Viscosity of Glass and Glass-Forming Melts
Sc,molar,max Sc,molar .1003:6 ı C/ D D 0:2772 J=.g K/ ; M M 1 D 103:6592 dPa s, B0 =M D 1840:71 J=g and Sc,molar calculated by (3.69), one gets a precise representation of the measured viscosity data by the Adam–Gibbs model. The optimum Arrhenius fit D 1 eH=.RT/ with 1 D log η (dPa s) 9 8 7 6 5 4 3 2 1 0 600 700
cp (J/(g K)) 3.0 Heating (8 K/min) Cooling (10 K/min) Einstein
2.5 2.0 1.5
cp, config
1.0 0.5 0
0
200
400
600
800
1000 1200 Temperature (°C)
of cp;config for K7® from SCHOTT AG in the T > Tg regime via DSC measurements carried out in both heating and cooling mode by a SETARAM Multi-HTC 96® device at the accredited laboratories of SCHOTT AG Fig. 3.29 Determination
1018:7568 dPa s, H=R D 58 219:5 K, does not fit well— as expected. The long glass investigated is a regular crown optical glass, namely K7® from SCHOTT AG (Fig. 3.29) (approximate composition: 6070 wt% SiO2 , 110 wt% B2 O3 , 110 wt% Na2 O, 1020 wt% K2 O, 110 wt% ZnO, see Table 3.1 below). The Einstein temperature E has been found to be 810 K for K7® . M is 21:6 g. The material parameters for the cp cV correction are: ˛ D 10:34 ppm=K, D 1=40 GPa, D 2:53 g=cm3 . Note again that for ˛, the slope of the linear thermal expansion curve just below the glass transition is taken here. Again, with cp;config thus obtained and the remaining unknown parameters of (3.68) determined by a fit, one may represent the viscosity values measured by the Adam–Gibbs model at a very high precision. As above, the calculation with an Arrhenius model is shown also for comparison in the following (Fig. 3.30). One finds that with Sc,molar .1003:68 ı C/ Sc,molar,max D D 0:3458 J=.g K/ ; M M
800
900
1000 1100 Temperature (°C)
Fig. 3.28 Representation of the viscosity curve of
N-LAK12® by the Adam–Gibbs model (solid line); Arrhenius model (dashed line) for comparison. Viscosity measurement (symbols) by ISO 7884-2, -3, -4-conform self-built devices at accredited laboratories of SCHOTT
101
1 D 101:698 dPa s, B0 =M D 2585:85 J=g and Sc,molar calculated by (3.69), one gets a precise representation of the measured viscosity data by the Adam–Gibbs model. The optimum Arrhenius fit D 1 eH=.RT/ with 1 D 108:625 dPa s, H=R D 37279:5, fits much better than in the above case of N-LAK12® yet not equivalently well as the Adam–Gibbs model—as expected. The differences between the two glasses investigated illustrate that the measurement of both viscosity and specific heat allows a deeper understanding of the underlying physicochemistry. This will be discussed further below.
Part A | 3.3
and a configurational contribution. The latter, cp;config, may be separated from the former by extrapolating the Einstein model to higher temperatures: cp;config D cp;measured cp;vib . The following application of the Adam–Gibbs model is restricted to the temperature ranges of the softening point and the working point. To extend the application into the range of the annealing point, one would need cp data where the overshoot peak occurs at significantly lower temperatures. Because of the kinetics of the glass transition, such cp data would require DSC measurements carried out at significantly lower heating or cooling rates, see again [3.8, 41]. From the different heating rates discussed there, one may (very roughly) conclude that a 20 K peak shift would require a factor of 10 in the heating rate. Moving the peak to lower temperatures by 100 K would require a heating rate of 0:0001 K=min, plus a device that would still be able to detect a signal under these circumstances. Such a heating rate is unrealistic. With cp;config thus obtained and the remaining unknown parameters of (3.68), i. e., 1 , Q or B0 , and Sc,molar,max determined by a fit, one may represent the viscosity values measured at N-LAK12® by the Adam– Gibbs model at a very high precision. In the following Fig. 3.28, the calculation with an Arrhenius model is shown also for comparison. One finds that with
3.3 Shear Viscosity – Theory
102
Part A
Fundamentals of Glass and the Glassy State
Table 3.1 Approximate composition in wt% of glass types investigated K7® 2.53 528
Part A | 3.3
Sample (g=cm3 ) Annealing point (ı C) Aluminum oxide Antimony trioxide Arsenic trioxide Barium oxide Boron oxide Lanthanum oxide Lead oxide Niobium pentoxide Potassium oxide Silica Sodium oxide Titanium oxide Zinc oxide Zirconium oxide
N-BaF10® 3.75 652 110 h blue ;
5.1
Interaction of Light with Optical Materials ........................ Dielectric Function .............................. Linear Refraction ................................ Absorption ......................................... Microscopic Origin of Absorption .......... Emission ............................................ Volume Scattering ...............................
169 169 175 182 183 185 187
References...................................................
190
5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6
with h blue D hc=blue D 3:18 eV, where h is Planck’s constant, c is the speed of light in a vacuum (or air), is the wavelenght and is the frequency. The energy is given here in units of eV (1 eV D 1:602 1019 J). The (nearly) complete absence of light scattering in glasses has its origin in the fact that as opposed, e. g., to most ceramic materials, glasses are isotropic and extremely homogeneous on all length scales relevant for the interaction with visible light. Also, while glasses have well-defined structure on the atomic scale, a few ångstroms (Å), they are completely disordered and therefore homogeneous and isotropic on the larger length scales relevant for the interaction with visible light.
5.1 Interaction of Light with Optical Materials In this section the general physics of the interaction of light with matter is briefly presented. A detailed insight into theoretical electrodynamics cannot be given here. The interested reader might refer to standard textbooks on electrodynamics, e. g., [5.1, 2].
5.1.1 Dielectric Function The starting point for an analysis of any interaction between electromagnetic waves with matter are Maxwell’s equations. The static interaction for the dielectric displacement and the magnetic induction is described by r DD ; r BD 0 ;
(5.1)
whereas the dynamic interaction of the electric and magnetic fields is given by P; r E D B P : r H D jCD
(5.2)
E and B are the electric and magnetic fields; D and H are the electric displacement and the auxiliary magnetic fields; and j are the charge and the current density. Material equations are needed to complete Maxwell’s equations and turn them into a closed set of equations D D "0 E C P ; B D 0 H C M ;
(5.3)
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_5
Part A | 5.1
This chapter provides an extended overview of the optical properties of glasses. In Sect. 5.1 the underlying physical background of light–matter interaction is presented, where the phenomena of refraction, reflection, absorption, emission and scattering are introduced. Most oxide glasses are transparent in the visible spectral range. This obvious fact, confirmed by every look through a window, is based on two highly nontrivial principles: (i) the existence of an electronic bandgap and (ii) the (nearly) complete absence of light scattering. Although transparent solid materials like single crystals and glasses have been known for thousands of years, understanding the existence of an electronic bandgap, an energy range where practically no absorption of electromagnetic radiation occurs, requires quantum mechanics, which just became 100 years old. If such a forbidden zone is larger than the photon energy of blue photons, the photons with the largest energy quantum in the visible spectral range, the material is visibly transparent.
170
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where P and M are the polarization and magnetization densities. The vacuum permittivity (in SI units) is "0 D 8:854 1012 A s=.V m/ and the vacuum permeability is 0 D 4 107 V s=.A m/. The complete optical properties for any spatial combination of matter are included in the solution of (5.1), (5.2), which are closed by using the material equations (5.3) and by using appropriate boundary conditions. For only a few special cases such a solution can be written down directly. In the following we give a few examples. Wave Equation in a Vacuum If we want to solve (5.1) and (5.2) in an infinite vacuum we have the following boundary conditions and material equations P.r/ D 0 ;
M.r/ D 0 ;
.r/ D 0 ;
j.r/ D 0 ; (5.4)
Part A | 5.1
where r D .x; y; z/ are the three spatial coordinates. With these simplest possible boundary conditions the material equations (5.3) read D D "0 E ; B D 0 H :
(5.5)
After applying a few vector operations, one gets the wave equation for the electromagnetic field E in a vacuum R D0: E 0 "0 E
(5.6)
An identical wave equation can be derived for the magnetic field B. (5.6) immediately defines the speed of light c (in a vacuum), then s 1 cD : (5.7) 0 "0
Wave Propagation in an Ideal Transparent Medium We can describe an ideal material by simply replacing the speed of light in a vacuum by that of the medium, cmed !
c ; n
(5.9)
where n is the (in this case only real) refractive index of the material. Wave propagation in a dispersing or weakly absorbing medium is considered at the end of the present section. In fact, most parts of an optical design can be done by treating optical glasses as such ideal transparent materials (Sect. 5.1.2). Even though such an ideal material cannot exist in reality, optical glasses come very close to it (for electromagnetic radiation in the visible range). For such an ideal material the wave equation (5.6) reads E
n2 R ED0: c2
(5.10)
It is solved again by plane transverse waves, where the speed of light is now reduced to the speed of light in the transparent medium cmed D c=n and the wavelength of the light wave is reduced to med D =n. Refraction and Reflection We now derive the laws of refraction and reflection for the ideal transparent medium just described. They are obtained by solving Maxwell’s equations at the (infinite) boundary between two materials of different refractive indices n1 and n2 (Fig. 5.1). As boundary conditions one obtains that the normal component of
kr
||
E 0i
E0r
E 0i
||
E0r
α1 α1 ki
Equation (5.6) is generally solved by all fields that fulfill E.r; t/ D E0 f .kr ˙ !t/ involving any arbitrary scalar function f . The most common systems of function f are plane waves Es .r; t/ D E0 Re.ei.kr!t/ /:
(5.8)
These plane waves, with a time and spatial dependent phase D kr !t, are described by a wave vector k, an angular frequency !, and a corresponding wavelength D 2 =k D 2 c=!, where k D jkj is the absolute value of the wave vector. Describing an arbitrary field E in terms of plane waves is identical to decomposing this electrical field into its Fourier components.
n1 n2
α2 ||
E0t
E 0t
kt
Fig. 5.1 The polarization directions of the E and B fields
for reflection and refraction at an interface between two optical materials of different refractive indices are shown. A circle indicates that the vector is perpendicular to the plane shown. The B fields (not shown) are always perpendicular to k and E
Linear Optical Properties
the electric displacement (and magnetic induction) and the tangential component of the electric (and magnetic) field have to be continuous at the interface Dn1 D Dn2 ;
E1t D E2t :
(5.11)
r D i ;
(5.12)
where r,i are the phases of the reflected and incident wave respectively. If we solve Maxwell’s equations for an incoming plane wave (applying the boundary conditions stated above), Snell’s law of refraction is obtained n1 sin ˛1 D n2 sin ˛2 ;
(5.13)
together with that of reflection ˛r D ˛1 :
(5.14)
k
r? D
k E0i ? E0r ? E0i
R? WD jr? j2 I
Rk WD jrk j2 ;
T? WD jt? j2 I
Tk WD jtk j2 :
(5.17)
The angular-dependent coefficients of reflection from (5.16) are displayed in Fig. 5.2. In Fig. 5.2a the case of light propagating from an optically thin medium with refractive index n1 to an optically thicker medium with refractive index n2 > n1 is plotted. At the so-called Brewster angle ˛B the reflected light is completely polarized; ˛B is given by the condition ˛1 C ˛2 D =2. Therefore, the Brewster angle ˛B results as a solution of n2 cos ˛1 ; (5.18) ˛1 D arccos 2 n1
Part A | 5.1
Now the electric field E is decomposed into its components, which are defined relative to the plane outlined by the three beams of incoming, transmitted and reflected light. This decomposition is shown in Fig. 5.1. The coefficients for reflection and transmission are defined as E0r
a) R 1
k
I I
tk D
E0t
k E0i E? t? D 0t ? E0i
171
order to indicate back-traveling of light. The quantities that are measured in an experiment are intensities. The relationship between the intensities defines the reflectivity (R) and transmissivity (T) of a material
Further, a phase shift of an incoming wave occurs upon reflection
rk D
5.1 Interaction of Light with Optical Materials
R
; :
R ||
(5.15)
The Fresnel formula for these coefficients can be derived as n1 cos.˛1 / n2 cos .˛2 / sin.˛1 ˛2 / DC ; r? D n1 cos.˛1 / C n2 cos.˛2 / sin.˛1 C ˛2 / tan.˛1 ˛2 / n2 cos.˛1 / n1 cos .˛2 / D ; rk D n1 cos.˛2 / C n2 cos.˛1 / tan.˛1 C ˛2 / 2n1 cos.˛1 / t? D n1 cos.˛1 / C n2 cos.˛2 / 2 sin.˛2 / cos.˛1 / DC ; sin.˛1 C ˛2 / 2n1 cos.˛1 / tk D n1 cos.˛2 / C n2 cos.˛1 / 2 sin.˛2 / cos.˛1 / DC : sin.˛1 C ˛2 / cos.˛1 ˛2 / (5.16)
Here the usual convention has been used that the coefficients of reflectivity obtain an additional minus sign in
0
αB
b) R
π /2 α1
1
R R ||
0
αB
αT
π /2
Fig. 5.2a,b The reflection coefficients are plotted as a function of incident scattering angle for light propagating from a medium of (a) smaller refractive index into a medium of larger index and (b) larger refractive index into a medium of smaller index. Here, total reflection occurs at an angle ˛T and ˛B is the Brewster angle
172
Part A
Fundamentals of Glass and the Glassy State
which gives ˛B D arctan n2 =n1 . In Fig. 5.2b the case of light propagating from an optically thick to an optically thin medium is plotted. Here an additional special angle occurs—the angle of total reflection ˛T . All light approaching the surface at an angle larger than ˛T is totally reflected. At ˛1 D ˛T the angle for refraction in the medium with refractive index n2 is ˛2 D =2. For ˛T it follows that n2 : (5.19) ˛T D arcsin n1 Evaluating (5.16) for the special case of normal incident light as lim˛!0 allows one to calculate the reflectivity for normal incidence ˇ ˇ ˇ n 1 n 2 ˇ2 ˇ : ˇ (5.20) Rnorm D ˇ n1 C n2 ˇ
Part A | 5.1
Note that polarization with respect to a plane of refraction loses its meaning at normal incidence. Therefore (5.20) is valid for all polarization directions. For practical applications it is important to note that the Fresnel equations remain valid in the case of weakly absorbing media discussed at the end of the present section. In this case, only the refractive indices have to be replaced by the complex quantities of (5.36). It is further helpful to define a transmittivity and reflectivity for unpolarized light k2
Runpol D
?2 E0r C E0r k2
?2 E0i C E0i
k2
I
T unpol D
?2 E0t C E0t k2
?2 E0i C E0i
: (5.21)
Inserting the expressions for the reflection coefficients we obtain, for example, the total reflectivity as a function of the incident and refracted angular unpol Rall
D
k2 tan2 .˛1 ˛2 / tan2 .˛1 C˛2 / k2 E0i
E0i
?2 sin .˛1 ˛2 / C E0i sin2 .˛ C˛ / 2
1
?2 C E0i
2
:
With the definitions from (5.21) the following sum rule must be fulfilled unpol
R
n2 cos ˛2 unpol C T D1: n1 cos ˛1
(5.22)
The rule provides an easy check for transmitted and reflected total intensities, especially for normal incidence.
isotropic material, which is further a perfectly linear optical material. Considering time dependence, including retardation in the materials, (5.2) leads to D.r; t/ D "0 E.r; t/ C P.r; t/ :
The polarizability is related to the electric field via the susceptibility (5.24). In the case of a homogeneous isotropic material is a scalar function. In optically anisotropic media becomes a second-rank tensor Z P.r; t/ D
dr
0
Zt
dt0 .r r0 ; t t0 /E.r; t0 / : (5.24)
1
Fourier transformation in time and space deconvolutes the integral and leads to P.k; !/ D .k; !/E.k; !/ ;
(5.25)
where .k; !/ is, in general, a complex analytic function of the angular frequency !. The complex function .k; !/ unifies the two concepts of (i) a lowfrequency polarizability 0 and (ii) a low-frequency conductivity of mobile charges to a single complex quantity lim .!/ D 0 .!/ C 4 i
!!0
.!/ : !
(5.26)
At larger frequencies the separation of the two concepts breaks down. A bound charge can have a dielectric response that does not differ from the response of a mobile charge when it is probed at large enough frequencies. For example, above the frequencies of optical phonon modes in the infrared (IR) the bound charges are unable to follow the electric field, whereas below the phonon modes the charges can follow this motion (Sect. 5.1.3). The usual form in which the susceptibility enters the equations for optical purposes is via the dielectric function ".k; !/ D 1 C .k; !/ :
(5.27)
The dielectric function can now be identified with the square of the refractive index by comparing (5.10) and (5.29). This is done in (5.37). Inserting the dielectric function into the material equation (5.23) after a Fourier transformation in time and space gives D.k; !/ D "0 ".k; !/E.k; !/ :
Wave Propagation in an Isotropic, Homogeneous Medium We now consider wave propagation in an ideal optical material. This is a nonmagnetic, homogeneous,
(5.23)
(5.28)
Here, we restrict ourselves to ideal optically isotropic materials by neglecting the nature of the dielectric function as a second-rank tensor. Glasses are isotropic but
Linear Optical Properties
nearly all lose their isotropy when, e. g., uniaxial stress is applied. With the same steps as in (5.5) and (5.6) a wave equation can be derived, which has the following form in Fourier space !2 k2 ".k; !/ 2 E0 D 0 ; c
(5.29)
where the relations @2 =@t2 Es .r; t/ ! ! 2 Es .r; t/ and Es .r; t/ ! k2 Es .r; t/ have been used. The index s refers, as in (5.8), to the system of plane waves. The expression in brackets in (5.29) defines the dispersion relation for an optically linear, homogeneous, isotropic material. Poynting Vector and Energy Transport The energy flux density of the electric field is obtained via the Poynting vector, given by SD EH :
(5.30)
I D hjSji D 12 jE Hj
(5.31)
and is the energy flux density of the electromagnetic radiation. In the special case of propagation of transverse plane waves (as given in (5.8)), it simplifies to ID
1 n jE0 j2 ; 2 c 0
(5.32)
General Form of the Dielectric Function For most optical materials the dielectric function has a form in which a transparent frequency (or wavelength) window is bounded at the high energy side by electron– hole excitations (dominating the ultraviolet (UV) edge) and at the low energy site by IR absorptions given by optical phonon modes (lattice vibrations). The general form of the dielectric function is given by the Kramers– Heisenberg equation [5.3] ".k; !/ D 1 C
X j
˛k;j : 2 2 ! !k;j i!k;j
A schematic view of the dielectric function is plotted in Fig. 5.3. Here we use a model for a transparent, homogeneous, isotropic solid (such as glass) with one generic absorption at low energies (!IR in the infrared, IR) and another one at large photon energies (!UV in the ultraviolet spectral range, UV). In the following this model solid is used to discuss optical material properties. Dispersion Relation Solving (5.29) gives two frequency-dependent solutions for the wave vector k as a function of ! since the left-hand side of (5.29) is quadratic in k. Far away from absorptions the dielectric function is real and positive. Here only one solution exists, which describes the wave propagating with the speed of light in the medium. Close to an absorption two solutions exist, which are even more complicated. This means that near a resonance the dispersion of the light cannot be considered independently from the dispersion of the excitations in the material. They both form a composite new entity propagating in the medium. This is called the polariton [5.4]. For our model solid with two generic absorptions (!IR and !UV /, the dispersion is plotted in Fig. 5.4. Figure 5.4 shows the solution of (5.29) for the dielectric function ".k; !/ plotted in Fig. 5.3. The frequency ! is plotted as a function of the real and imaginary part of the the wave vector k. The dashed line is the dispersion in a vacuum with the speed of light as a derivative ! D ck. In the regions where the imaginary part of k is small there are propagating modes with a speed of light that is smaller than the vacuum speed of light. In the vicinity of absorptions anomalous propagation occurs together with strong damping. Dielectric function ε IR
where in a vacuum n D 1 is valid.
Vis
UV
Re(ε) Im(ε) ωIR
ωUV Frequency ω
Fig. 5.3 Dielectric function ".!/ for the model optical
(5.33)
Here ˛k;j is the amplitude, !k;j is the frequency and k;j is the damping of the particular excitation j.
173
solid with one generic absorption in the infrared !IR and a second one in the ultraviolet !UV . The dielectric function is plotted on a logarithmic energy scale. The solid line is the real part and the dashed line is the imaginary part of ".!/
Part A | 5.1
It gives the rate at which electromagnetic energy crosses a unit area and has the unit W m2 . It points in the direction of energy propagation. The time average of the absolute value of the Poynting vector hjSji is called the intensity I of the electromagnetic wave
5.1 Interaction of Light with Optical Materials
174
Part A
Fundamentals of Glass and the Glassy State
ω
v IR
Vacuum
Vis
UV
Im(k) ωUV
vph Re(k) vgr
ωIR ω IR
k
Fig. 5.4 Dispersion relation !.k/ for the model optical solid on a double logarithmic scale. The solid line is the real part of k and the dashed line is the imaginary part of k. For comparison the simply linear dispersion relation for light propagating in a vacuum ! D ck is shown with a long-dashed line
Part A | 5.1
Wave Propagation, Phase and Group Velocity When an electromagnetic wave propagates through a medium one can define two velocities. The phase velocity is the speed with which a certain phase propagates. It is, for example, the velocity of the wavefront maxima moving through the medium. The phase velocity is given as
vph D
! : k
(5.34)
In Fig. 5.5 the phase velocity of the model solid is plotted on a logarithmic frequency scale. Close to the absorption edges of the material it loses its meaning because attenuation due to the absorption processes will dominate most processes. Far away from absorptions it reaches a nearly constant value. The second velocity is the group velocity
vgr .k/ D
@! : @k
(5.35)
This is the velocity at which a complete wave packet travels through the medium and is, hence, the speed with which information can travel through the system. The phase and group velocities are plotted in Fig. 5.5 for the model solid. Reasonably far away from material absorptions the group and phase velocities approach each other. However, the group velocity is always smaller than the phase velocity. Refractive Index The refractive index n is the most widely used physical quantity in optical design. It is the square root of
ω UV
ω
Fig. 5.5 The group velocity vgr .k/ D @!=@k (solid line) and the phase velocity vph .k/ D !=k (dashed line) are plotted on a logarithmic frequency scale. Far away from absorptions both velocities approach each other while the group velocity is always smaller than the phase velocity
the dielectric function. The dynamic refractive index is generally a complex quantity nQ .!/ D n.!/ C i .!/
(5.36)
and must fulfill the Kramers–Kronig relations [5.3]. The refractive index for our generic model solid is plotted as a function of logarithmic frequency in Fig. 5.6. In practical use, the wavelength dependence is often exploited s 2 c nQ .k; / D " k; :
(5.37)
With a few basic steps, (5.33) can be rewritten as a function of wavelength alone. If one further restricts consideration to wavelengths that are far away from 2 absorptions, .! 2 !k;j / !k;j , the Sellmeier formula (Sect. 5.1.2), which is widely used for characterizing optical materials, is obtained n./2 1 C
X Bj 2 ; 2 j2 j
(5.38)
where i D 2 c=!i with i 2 f.k; j/g is used and Bj D ak;j k;j =.2 c/2. It describes the dispersion of a material by infinitely sharp absorption lines (ı functions), which are far away from the visible range at wavelength j and have the absorption strength Bj . Normally Bj and j are just fitting constants to describe the dispersion of the refractive index over a certain wavelength range.
Linear Optical Properties
175
is
Refraction index n IR
5.1 Interaction of Light with Optical Materials
Vis
I2 D 12 jE2 H2 j ;
UV
!
D 12 jE1 H1 je2 c l ; !
Re(n)
D I1 e2 c l D I1 e˛l :
(5.41)
The absorption coefficient ˛ is connected to the complex refractive index by Im(n) ωIR
ωUV Frequency ω
Fig. 5.6 The complex refractive index n.!/ D n .!/ C
i .!/ is plotted on a logarithmic frequency scale. The real part is plotted with a solid line and the imaginary part with a dashed line
Wave Propagation in a Weakly Absorbing Medium In this subsection the link between the attenuation of a wave and the imaginary part of the refractive index is given. A weakly absorbing medium is defined by the imaginary part of the refractive index (5.36) as being much smaller than the real part
n
(5.39)
(5.42)
˛ can easily be measured and its importance for optical properties is discussed in Sect. 5.1.3. Equation (5.41) is also called Lambert–Beer law. It is also important to note that the Fresnel equations (5.16) remain valid in the case of a weakly absorbing medium if the complex refractive indices are used. As an example, we plot the reflectivity resulting from (5.20) (at the interface air–model solid) near an absorption for a complex refractive index n2 ! nQ 2 . In Fig. 5.7 the reflectivity is plotted on a logarithmic frequency scale. Note that the absorption seems to be shifted compared to the plots of the complex dielectric function or the complex refractive index. This is due to the fact that the poles of the function Rnorm in (5.20) are shifted from the poles of n. Measurement of the reflectivity is of importance for reflection spectroscopy or ellipsometry.
5.1.2 Linear Refraction As already introduced in Sect. 5.1.1, two phenomena occur when light impinges upon the surface of any optical material: reflection and refraction [5.5]. The reflected light bounces off the glass surface, while the refracted light travels through the material. The amount of light that is reflected depends on the refractive index of the sample, which also affects the refractive behavior of the sample [5.6]. The refractive index of optical Reflectivity R IR
Vis
UV
(the coefficient =n is also called the attenuation index). In this case light propagates as transverse waves through the medium. We consider two points in our medium: P1 and P2 . Between these points the light travels the distance l. In the absence of absorption, the electric and magnetic fields at point P2 are given by !
E2 D E1 ei c nQ l ;
!
H 2 D H1 ei c nQ l :
(5.40)
Using (5.31) we obtain for weak absorption the radiation intensity at point P1 . The radiation intensity at P2
ωIR
ωUV Frequency ω
Fig. 5.7 Reflectivity R for normal incidence plotted on
a logarithmic frequency scale
Part A | 5.1
The Sellmeier formula (5.38) uses three infinitely sharp absorption lines. One in the infrared wavelength range and two in the ultraviolet range of of the spectrum to fit the dispersion of material in the range of optical wavelengths. Even if only used as fitting parameters, the absorptions are connected to the microscopic fundamental absorptions of the material. In some cases n./ and not n./2 is approximated with a Sellmeier formula. Since n./ as well as n./2 are complex differential (analytic) functions both formulae give refractive indices and dispersions with the same accuracy. However, care has to be taken over which quantity is expressed when using a Sellmeier formula.
! ˛D2 I c
176
Part A
Fundamentals of Glass and the Glassy State
materials turns out to be one of the most important factors that must be considered when designing systems to transmit and modulate light [5.7]. The refractive index is a complex material property that depends on thermodynamic parameters, e. g., temperature and on wavelength [5.8]. The wavelength dependence of the refractive index is the dispersion [5.5].
θi
n2
Law of Refraction When a light ray impinges upon a smooth glass surface, a portion is reflected and the rest is either transmitted or absorbed. The material modulates the light upon transmission. The light travels at a different velocity as it is transmitted through the glass as compared to a vacuum. As introduced in Sect. 5.1.1, the index of refraction (n) is defined as the ratio of the speed of light in a vacuum (c) to that in the material, (cm ) [5.9] nD
c : cm
(5.43)
Part A | 5.1
Most commonly, the reported refractive indices are relative to the speed of light in air, rather than in a vacuum, no matter which technique is used to measure the refractive index [5.10]. The index of refraction for a vacuum is defined as 1. The index of refraction of air is 1:00029 at standard temperature (25 ı C) and pressure (1 atm) (STP). Therefore, the index of refraction of optical matter (nrel ) relative to air (nair ), rather than a vacuum is [5.9] nrel D
nm : nair
(5.44)
The STP indices of some common compounds, and classes of compounds, are shown in Table 5.1 [5.11]. As discussed in Sect. 5.1.1, when light hits a glass surface at an angle i , it is Fresnel-reflected back at an angle t . The angle of incidence is equal to the angle of reflection (i D r ), as shown in Fig. 5.8 [5.12]. The Table 5.1 Indices of common materials at standard temperature and pressure at 587:56 nm (helium d line) (after [5.11]) Material Vacuum Air Water Acetone Ethanol Sugar solution (30 wt%) Fused silica Sugar solution (80 wt%)
nd 1 1.00029 1.33 1.36 1.36 1.38
Material Crown glass Sodium chloride Polystyrene Carbon disulfide Flint glass Sapphire
nd 1.52 1.54 1.55 1.63 1.65 1.77
1.46 1.49
Heavy flint glass Diamond
1.89 2.42
θr
n1
θt
Fig. 5.8 Ray tracings of incident, reflected, and transmit-
ted light from one medium to another representing the angles and indices necessary to apply Snell’s law (after [5.12])
percentage of light reflected for i D 0 at each interface (R) relative to the incident intensity (Sect. 5.1.1) is dependent on the index of refraction of the two media the light is passing through, typically air (n2 ) and glass (n1 ) (Fig. 5.8 and (5.20)) [5.12] n1 n2 2 : (5.45) Rnorm D 100 n1 C n2 Fresnel’s formula (5.45) assumes smooth surfaces that produce only specular reflection. Diffuse reflection occurs when the surface is rough, so the incident light is reflected through a range of angles, thereby reducing the intensity of the specular reflected light at any given angle [5.12]. The specular reflection that is taken into consideration by Fresnel’s relationship can be monitored and used to estimate the refractive index of samples in situ [5.13]. The angle of the light transmitted within the material (˛t ), relative to the incident light transmitted through air, is dependent on the refractive indices of the air (nair ) and solid (nm ) and the incident light angle (˛i ) [5.12] nair sin ˛i D nm sin ˛t :
(5.46)
This is the general form of Snell’s law of refraction to predict transmitted angles in media [5.14]. Dispersion Relationships in Glass The refractive index of a medium is dependent upon the wavelength of the light being transmitted (Sect. 5.1.1).
Linear Optical Properties
nF = 0.486 μm 1.52
nD = 0.589 μm nC = 0.656 μm
1.51
1.50
0.4
0.6
0.8
1.0
most common wavelengths at which n is measured are reported in Table 5.2. These wavelengths most often correspond to common sharp emission lines of gas discharge lamps. The index can be determined most accurately .˙1 106 / by measuring the angle of minimum deviation of light in a prism [5.15]. However, a Pulfrich refractometer .˙1 105 / is most commonly used in industry. Details of measurement techniques are given in [5.16] and in Chap. 29. The index at various wavelengths is commonly referred to by the designations in Table 5.2: i. e., nd is the refractive index measured at the yellow helium d line of 582:5618 nm. The dispersion is often given as a difference in n at two wavelengths. For instance, the primary dispersion is given by nF nC (hydrogen lines) and nF0 nC0 (cadmium lines). The most commonly reported measure of dispersion is the Abbe number ( ), which is commonly given for two sets of conditions
d D
nd 1 ; nF nC
1.2
1.4
1.6
1.9 2.0 λ (μm)
Fig. 5.9 Dispersion present in BK7 optical glass. Com-
mon index of refraction measurement wavelengths are indicated
e D
ne 1 : nF0 nC0
(5.47)
The Abbe number is a measure of the ratio of the refractive power to the dispersion. In most optical materials catalogs, a six-digit number is assigned to the solid that is dependent upon the index and the Abbe number: the first three digits are 1000.nd 1/ and the next three digits are 10 d . Using this property, optical glasses, for example, are divided into two general categories: crowns and flints (Fig. 5.10). Crown glasses typically have a low index of refraction and a high Table 5.2 Wavelength of spectral lines used for measuring index of refraction, with the common designation and spectral line source (after [5.9]) Wavelength (nm) 2325:4 1970:1 1529:6 1013:98 852:1101 706:5188 656:2725 643:8469 632:8 589:2938
1.53
177
587:5618 546:074 486:1327 479:9914 435:8343 404:6561 365:0146
Designation
t s r C C0 D d e F F0 g h i
Spectral line Hg IR line Hg IR line Hg IR line H IR line Cs IR line He red line H red line Cd red line He–Ne laser line Na yellow line (center of doublet) He yellow line Hg green line H blue line Cd blue line Hg blue line Hg violet line Hg UV line
Part A | 5.1
This wavelength dependence is dispersion, which means that different wavelengths of light will be modulated differently by the same piece of matter [5.12]. Each wavelength of light will be subject to a different index of refraction. Our model solid in Sect. 5.1.1 shows dispersion due to the fact that the transparent wavelength range of a solid is bounded by absorptions. One ramification of dispersion is that white light can be separated into its principal visible components through a glass prism, or a simple raindrop. It is the dispersion of white light through raindrops that causes rainbows. The dispersion of light through optical materials results in the light being refracted at various angles because of Snell’s law (5.46). The various components of white light experience different indices of refraction, which leads to different angles of exiting light. The difference in refractive index with wavelength is illustrated in Fig. 5.9 for BK7 optical glass, which is a highdispersion material. In normal dispersion, the index increases for shorter wavelengths of light [5.15]. Normal dispersion is valid only far away from absorption bands in the infrared wavelength range (Fig. 5.6). Water has a normal dispersion response in the visible, so the red light is refracted by a lower index, and thus a greater angle, which is why red is on top in a rainbow. Discussion of rainbow formation is presented elsewhere in depth [5.12]. Anomalous dispersion is an increase in refractive index with an increase in wavelength. Anomalous dispersion typically occurs when one approaches a long wavelength absorption like an IR vibration mode. This is also seen in our model solid in Fig. 5.6 and is further discussed in [5.9]. Due to dispersion, the index of refraction must be reported with the wavelength of measurement. The
5.1 Interaction of Light with Optical Materials
178
Part A
Fundamentals of Glass and the Glassy State
Abbe number (nd < 1:60 and d > 50), whereas flint glasses have high indices and low Abbe numbers (nd > 1:60 and d < 50) [5.15]. The terms crown and flint have historical significance in that flint glasses typically had lead oxide added to them to increase the
refractive index (Fig. 5.10) and crown glasses were typically blown and had curvature – a crown. Typically, to make an achromatic optical system crown and flint lenses are combined in series (Fig. 5.10, Table 5.3).
nd 1.95
Schott Ohara Hoya
E-FDS 1 N-SF 66 S-NPH 2
1.90
TaFD 25 N-LaSF 46 S-LAH 78 N-LaSF 31A S-LAH 58 TaFD 30
1.85
S-TIH 53 PBH 53W
N-LaSF 9
N-SF 57 SF 57HHT
N-LaSF 41 S-LAH 55 TaFD 5
Part A | 5.1
1.80
FDS 90
E-FD 60 FD 60 N-SF 6 SF 6HT S-TIH 6
S-LAH 65 N-LaSF 44 TaF 3
S-TIH 11 N-SF 11 E-FD 110 S-LAH 66 N-LaF 34 TaF 1 N-LAK 33B
1.75
N-LaF 2 S-LAM 2 LaF 2
LAM 7 N-LaF 7 E-LaF 7
N-LAK 34 N-LaK 10 S-LAL 10 LaC 10
1.70
BaFD 15
S-LAL 14 N-LaK 14 LaC 14
N-Lak 23
N-BaSF 64
N-BaF 10 S-BAH 10 N-BaF 10 BaF 10
N-LAK 22
1.65
SF 2 S-BSM 18 N-SK 18 BaCD 18 PCD 4
1.60
N-PSK 53 S-PHM 52
S-TIM 22 FD 2
S-TIM 2 F2 N-KZFS 4 F2 BPM 51 E-ADF 10 N-BaF 4 S-BAM 4
N-SSK 8
S-BSM 28
S-BSM 2 N-SK 2 BaCD 2
LF 5 S-TIL 25 E-FL 5
N-BaLF 4 S-BAL 14 N-BaK 4 BaC 4 N-PSK 3
1.55
S-TIL 1 LLF 1 E-FEL 1 N-PK 51 N-KF 9 N-BK 7
1.50
S-BSL 7 BSC 7 N-ZK 7
S-FPL 51 N-PK 52A FCD 1
N-FK 5 S-FSL 5 FC 5
N-FK 51
1.45 νd
90
85
80
75
70
65
60
55
50
45
40
35
Fig. 5.10 Abbe diagram showing index of refraction versus the Abbe number for optical glasses
30
25
20
Linear Optical Properties
5.1 Interaction of Light with Optical Materials
179
Table 5.3 Commercially available optical glasses by code, glass type and manufacture (H D Hoya, O D Ohara, and S D SCHOTT) (after [5.17–19]) Glass type N-FK 56 S-FPL 53 S-FPL 52 FCD 10 S-SL 5 FC 5 N-FK 5 N-FK 51 FCD 1 S-FPL 51 N-PK 52 N-BK 10 K 10 N-ZK 7 K7 S-BSL 7 E-CF6 S-NSL 36 BSC 7 N-BK 7 E-C 3 S-NSL 3 N-K 5 S-NSL 5 N-KF 9 N-PK 51 E-FEL 6 S-TIL 6 N-LLF 6 S-BAL 12 N-BAK 2 E-FEL 2 S-TIL 2 N-BALF 5 E-FEL 1 S-TIL 1 LLF 1 N-LLF 1 SBF 1 N-PSK 3 N-KZFS 2 S-BAL 41 BACD 11 N-SK 11 E-FL 6 PBL 26 BAC 4 N-BAK 4 S-BAL 14 N-PSK 58 S-BAL 2 S-PHM 52
nd 1.43430 1.43875 1.45600 1.45650 1.48749 1.48749 1.48749 1.48656 1.49700 1.49700 1.49700 1.49782 1.50137 1.50847 1.51112 1.51633 1.51742 1.51742 1.51680 1.51680 1.51823 1.51823 1.52249 1.52249 1.52346 1.52855 1.53172 1.53172 1.53169 1.53996 1.53996 1.54072 1.54072 1.54739 1.54814 1.54814 1.54814 1.54814 1.55115 1.55232 1.55836 1.56384 1.56384 1.56384 1.56732 1.56732 1.56883 1.56883 1.56883 1.56907 1.57099 1.61800
d 95.0 95.0 90.3 90.3 70.2 70.4 70.4 84.5 81.6 81.6 81.6 67.0 56.4 61.2 60.4 64.1 52.2 52.4 64.2 61.2 59.0 59.0 59.5 59.8 51.5 77.0 48.8 48.9 48.9 59.5 59.7 47.2 47.2 53.6 45.8 45.8 45.8 45.9 49.5 63.5 54.0 60.7 60.8 60.8 42.8 42.8 59.0 56.0 56.3 71.2 50.8 63.4
Producer S O O H O H S S H O S S S S S O H O H S H O S O S S H O S O S H O S H O S S H S S O H S H O H S O S O O
Code 571530 573575 573578 575415 580539 581407 581408 581409 581409 583464 583466 583594 583595 583595 589612 589613 589613 589613 592684 593353 593355 596392 596392 603380 603380 603380 603606 603607 603607 603655 606437 606437 606637 607567 607567 607568 609466 613370 613370 613443 613443 613444 613445 613586 613586 613587 614550 617366 618498 618498 618634 667330
Glass type S-BAL 3 N-BAK 1 S-BAL 11 S-TIL 27 N-BALF 4 S-TIL 25 N-LF 5 E-FL 5 LF 5 BAM 3 N-BAF 3 S-BAL 42 BACD 12 M-BACD 12 S-BAL 35 BACD 5 M-BACD 5N N-SK 5 N-PSK 57 S-FTM 16 FF 5 E-F 8 S-TIM 8 E-F 5 S-TIM 5 F5 N-SK 14 BACD 14 S-BSM 14 S-PHM 53 S-BAM 4 N-BAF 4 LBC 3N BACD 2 N-SK 2 S-BSM 2 N-BAF 52 E-F 3 PBM 3 BPM 51 KZFSN 4 E-ADF 10 N-KZFS 4 BACD 4 N-SK 4 S-BSM 4 BSM 9 F4 S-BSM 28 N-SSK 8 PCD 4 S-TIM 39
nd 1.57135 1.57250 1.57250 1.57501 1.57956 1.58144 1.58144 1.58144 1.58144 1.58267 1.58272 1.58313 1.58313 1.58313 1.58913 1.58913 1.58913 1.58913 1.59240 1.59270 1.59270 1.59551 1.59551 1.60342 1.60342 1.60342 1.60311 1.60311 1.60311 1.60300 1.60562 1.60568 1.60625 1.60738 1.60738 1.60738 1.60863 1.61293 1.61293 1.61340 1.61340 1.61310 1.61336 1.61272 1.61272 1.61272 1.61405 1.61659 1.61772 1.61773 1.61800 1.66680
d 53.0 57.5 57.8 41.5 53.9 40.7 40.8 40.9 40.9 46.4 46.6 59.4 59.5 59.5 61.2 61.3 61.3 61.3 68.4 35.3 35.5 39.2 39.2 38.0 38.0 38.0 60.6 60.7 60.7 65.5 43.7 43.7 63.7 56.7 56.7 56.8 46.6 37.0 37.0 44.3 44.3 44.4 44.5 58.6 58.6 58.7 55.0 36.6 49.8 49.8 63.4 33.0
Producer O S O O S O S H S O S O H H O H H S S O H H O H O S S H O O O S H H S O S H O O S H S H S O O S O S H O
Part A | 5.1
Code 434950 439950 456903 457903 487702 487704 487704 487845 497816 497816 497816 498670 501564 508612 511604 516641 517522 517524 517642 517642 518590 518590 522595 522598 523515 529770 532488 532489 532489 540595 540597 541472 541472 547536 548458 548458 548458 548459 551495 552635 558540 564607 564608 564608 567428 567428 569560 569560 569563 569712 571508 618634
180
Part A
Fundamentals of Glass and the Glassy State
Table 5.3 (continued)
Part A | 5.1
Code 620363 620363 620364 620364 620603 620603 620603 620622 620635 621603 622532 622533 623569 623570 623570 623580 623581 623582 624471 626357 626357 638424 639449 639509 639554 639555 640345 640346 640601 640601 640602 648338 648338 648338 649530 649530 650557 651562 651669 652450 652584 652585 652585 654396 654396 654397 658509 658509 658509 664360 717479 717480 717480
Glass type E-F 2 S-TIM 2 F2 N-F 2 BACD 16 S-BSM 16 N-SK 16 ADC 1 N-PSK 53 SK 51 BSM 22 N-SSK 2 E-BACD 10 S-BSM 10 N-SK 10 N-SK 15 BACD 15 S-BSM 15 E-BAF 8 E-F 1 S-TIM 1 N-KZFSN 11 S-BAM 12 S-BSM 18 N-SK 18 BACD 18 S-TIM 27 E-FD 7 S-BSM 81 N-LAK 21 LACL 60 E-FD 2 S-TIM 22 SF 2 E-BACED20 S-BSM 71 LACL 2 S-LAL 54 N-LAK 22 N-BAF 51 LAC 7 S-LAL 7 N-LAK 7 E-ADF 50 KZFSN 5 BPH 5 BACED 5 S-BSM 25 N-SSK 5 N-BASF 2 S-LAM 3 LAF 3 N-LAF 3
nd 1.62004 1.62004 1.62004 1.62005 1.62041 1.62041 1.62041 1.62000 1.62014 1.62090 1.62230 1.62229 1.62280 1.62280 1.62278 1.62296 1.62299 1.62299 1.62374 1.62588 1.62588 1.63775 1.63930 1.63854 1.63854 1.63854 1.63980 1.63980 1.64000 1.64049 1.64000 1.64769 1.64769 1.64769 1.64850 1.64850 1.65020 1.65100 1.65113 1.65224 1.65160 1.65160 1.65160 1.65412 1.65412 1.65412 1.65844 1.65844 1.65844 1.66446 1.71700 1.71700 1.71700
d 36.3 36.3 36.4 36.4 60.3 60.3 60.3 62.2 63.5 60.3 53.2 53.3 56.9 57.0 57.0 58.0 58.1 58.2 47.1 35.7 35.7 42.4 44.9 55.4 55.4 55.5 34.5 34.6 60.1 60.1 60.2 33.8 33.8 33.8 53.0 53.0 55.7 56.2 55.9 45.0 58.4 58.5 58.5 39.6 39.6 39.7 50.9 50.9 50.9 36.0 47.9 48.0 48.0
Producer H O S S H O S H S S O S H O S S H O H H O S O O S H O H O S H H O S H O H O S S H O S H S O H O S S O H S
Code 667483 667483 670393 670471 670472 670473 673321 673322 673322 673323 678506 678507 678549 678552 678553 678555 689311 689312 689313 691547 691547 691548 694508 694508 694532 694532 694533 694533 697485 697485 697554 697555 697555 699301 699301 699301 699302 700481 702402 702412 702412 704394 706302 713538 713539 713539 717295 717295 717295 717296 762401 773496 773496
Glass type BAF 11 S-BAH 11 BAH 32 N-BAF 10 BAF 10 S-BAH 10 S-TIM 25 E-FD 5 SF 5 N-SF 5 LACL 9 S-LAL 56 LAKL 12 N-LAK 12 S-LAL 12 LAC 12 S-TIM 28 E-FD 8 N-SF 8 LAC 9 N-LAK 9 S-LAL 9 LACL 5 LAL 58 M-LAC 130 S-LAL 13 LAC 13 LAKN 13 LAFL 2 LAM 59 N-LAK 14 LAC 14 S-LAL 14 E-FD 15 S-TIM 35 SF 15 N-SF 15 S-LAM 51 BAFD 15 BAFD 7 S-BAH 27 N-BASF 64 N-SF 64 N-LAK 8 LAC 8 S-LAL 8 E-FD 1 PBH 1 SF 1 N-SF 1 S-LAM 55 TAF 1 S-LAH 66
nd 1.66672 1.66672 1.66998 1.67003 1.67003 1.67003 1.67270 1.67270 1.67270 1.67271 1.67790 1.67790 1.67790 1.67790 1.67790 1.67790 1.68893 1.68893 1.68894 1.69100 1.69100 1.69100 1.69350 1.69350 1.69350 1.69350 1.69350 1.69350 1.69700 1.69700 1.69680 1.69680 1.69680 1.69895 1.69895 1.69895 1.69892 1.70000 1.70200 1.70154 1.70154 1.70400 1.70591 1.71300 1.71300 1.71300 1.71736 1.71736 1.71736 1.71736 1.76200 1.77250 1.77250
d 48.3 48.3 39.3 47.1 47.2 47.3 32.1 32.2 32.2 32.3 50.6 50.7 54.9 55.2 55.3 55.5 31.1 31.2 31.3 54.7 54.7 54.8 50.8 50.8 53.2 53.2 53.3 53.3 48.5 48.5 55.4 55.5 55.5 30.1 30.1 30.1 30.2 48.1 40.2 41.2 41.2 39.4 30.2 53.8 53.9 53.9 29.5 29.5 29.5 29.6 40.1 49.6 49.6
Producer H O O S H O O H S S H O S S O H O H S H S O H O H O H S H O S H O H O S S O H H O S S S H O H O S S O H O
Linear Optical Properties
5.1 Interaction of Light with Optical Materials
181
Table 5.3 (continued) Glass type BPH 8 LAM 58 S-LAM 52 LAM 61 S-LAL 10 LAC 10 N-LAK 10 S-TIH 18 BAFD 8 S-BAH 18 BASF 51 E-FD 10 SF 10 S-TIH 10 N-SF 10 TAC 8 S-LAL 18 M-LAF 81 TAC 4 S-LAL 59 PBH 3 E-FD 13 S-TIH 13 TAC 2 S-LAL 61 NBF 1 M-NBF 1 S-LAM 60 S-LAM 2 LAF 2 N-LAF 2 N-LAF 7 E-LAF 7 LAFN 7 LAM 7 FF 8 N-LAK 33 N-SF 4 E-FD 4 S-TIH 4 SF 4 TAC 6 S-YGH 51 NBF 2 S-LAM 54 S-TIH 14 SF 14 FD 140 SF 57 N-LASF 31 S-LAH 58 E-FDS 1 PBH 71
nd 1.72047 1.72000 1.72000 1.72000 1.72000 1.72000 1.72003 1.72151 1.72342 1.72342 1.72373 1.72825 1.72825 1.72825 1.72828 1.72916 1.72906 1.73077 1.73400 1.73400 1.74000 1.74077 1.74077 1.74100 1.74100 1.74330 1.74330 1.74320 1.74400 1.74400 1.74397 1.74950 1.74950 1.74950 1.74950 1.75211 1.75398 1.75513 1.75520 1.75520 1.75520 1.75500 1.75500 1.75700 1.75700 1.76182 1.76182 1.76182 1.84666 1.88067 1.88300 1.92286 1.92286
d 34.7 42.0 43.7 46.0 50.2 50.3 50.6 29.2 38.0 38.0 38.1 28.3 28.4 28.5 28.5 54.7 54.7 40.5 51.1 51.5 28.3 27.8 27.8 52.6 52.7 49.2 49.3 49.3 44.8 4.9 44.9 34.8 35.0 35.0 35.3 25.1 52.4 27.4 27.5 27.5 27.6 52.3 52.3 47.7 47.8 26.5 26.5 26.6 23.8 41.0 40.8 20.9 21.3
Producer O O O O O H S O H O S H S O S H O H H O O H O H O H H O O H S S H S O H S S H O S H O H O O S H S S O H O
Code 773496 785257 785257 785258 785261 785261 785261 785263 786439 786441 786442 788474 788475 788475 795454 795455 800422 800423 801350 801351 804396 804465 804465 804466 805254 805254 805254 805255 805396 806333 806406 806407 806407 806409 808228 815370 816445 816466 816466 834372 834373 834373 835427 835430 835431 847236 847238 847238 850322 883408 901315 923209 1022291
Glass type N-LAF 34 FD 110 S-TIH 11 SF 11 FDS 30 N-SF 56 SF 56A S-TIH 23 NBFD 11 N-LAF 33 S-LAH 51 S-LAH 64 TAF 4 N-LAF 21 TAF 2 N-LAF 32 S-LAH 52 NBFD 12 S-LAM 66 N-LASF 45 S-LAH 63 TAF 3 N-LASF 44 S-LAH 65 S-TIH 6 N-SF 6 SF 6 FD 60 NBFD 3 NBFD 15 N-LASF 43 M-NBFD 130 NBFD 13 S-LAH 53 S-NPH 1 M-NBFD 82 TAFD 10 TAF 5 S-LAH 59 S-LAH 60 NBFD 10 N-LASF 40 S-LAH 55 TAFD 5 N-LASF 41 SFL 57 FDS 90 S-TIH 53 LASFN 9 TAFD 30 LAH 78 SF 66 N-LASF 35
nd 1.77250 1.78472 1.78472 1.78472 1.78470 1.78470 1.78470 1.78470 1.78590 1.78582 1.78590 1.78800 1.78800 1.78800 1.79450 1.79457 1.79952 1.79950 1.80100 1.80100 1.80440 1.80420 1.80420 1.80400 1.80518 1.80518 1.80518 1.80518 1.80450 1.80610 1.80610 1.80610 1.80610 1.80610 1.80809 1.81474 1.81550 1.81600 1.81600 1.83400 1.83400 1.83404 1.83481 1.83500 1.83501 1.84666 1.84666 1.84666 1.85025 1.88300 1.90135 1.92286 2.02204
d 49.6 25.7 25.7 25.8 26.1 26.1 26.1 26.3 43.9 44.1 44.2 47.4 47.5 47.5 45.4 45.5 42.2 42.3 35.0 35.1 39.6 46.5 46.5 46.6 25.4 25.4 25.4 25.5 39.6 33.3 40.6 40.7 40.7 40.9 22.8 37.0 44.5 46.6 46.6 37.2 37.3 37.3 42.7 43.0 43.1 23.6 23.8 23.8 32.2 40.8 31.5 20.9 29.1
Producer S H O S H S S O H S O O H S H S O H O S O H S O O S S H H H S H H O O H H H O O H S O H S S H O S H O S S
Part A | 5.1
Code 720347 720420 720437 720460 720502 720503 720506 722292 723380 723380 724381 728283 728284 728285 728285 729547 729547 731405 734511 734515 740283 741278 741278 741526 741527 743492 743493 743493 744448 744449 744449 749348 750350 750350 750353 752251 754524 755274 755275 755275 755276 755523 755523 757477 757478 762265 762265 762266 847238 881410 883408 923209 923213
182
Part A
Fundamentals of Glass and the Glassy State
Often it is desirable to have a mathematical representation of the index as a function of wavelength. A considerable number of models exist for just this purpose. Perhaps the best known, and most widely used, is the Sellmeier formula [5.15] B1 2 B2 2 B3 2 C 2 C 2 : (5.48) n2 ./ 1 D 2 C1 C2 C3
Part A | 5.1
Most major optical material manufacturers supply the Sellmeier coefficients for their glasses on the product data sheets. Note that the coefficients C1 , C2 and C3 have the physical unit of a squared length and are usually given in units of m2 . With the six Sellmeier coefficients it is possible to estimate the index of refraction at any wavelength around the visible spectral range, given that it is not near a strong absorption. Numerous other dispersion models have been developed and are presented elsewhere [5.12, 15]. The index of refraction is also dependent on temperature, and similar formulas and tables of constants have been developed for the differential change in n with temperature [5.15]
2 n .; T0 / 1 dnabs .; T/ D dT 2n.; T0 / E0 C 2E1 T 2 D0 C 2D1 T C 3D2 T C ; 2 2TK
log10 AD
(5.51)
The microscopic origin of the absorption coefficient is discussed in Sect. 5.1.4. The second view on absorption comes from the experimental side. We place a sample, e. g., a parallel plate, between a light source and a detector. The attenuation of the light is now related to surface reflection, surface scattering, bulk absorption in the material and bulk scattering in the material. (In addition complicated light paths occur, which include multiple internal reflections as sketched in Fig. 5.11. Figure 5.11 shows multiple reflections followed by multiple partial transmissions and reflections in a plane parallel slab of material, e. g., glass.) The reflectivity on a surface between two media is related to the complex refractive index as ˇ ˇ 2 ˇ nQ nQ 0 ˇ2 ˇ n1 ; R D ˇˇ nQ C nQ 0 ˇ nC1 (5.52) for k n and n0 D 1 : If we can neglect surface and volume scattering together with interference effects, the total reflectivity Rt and transmission Tt can be expressed as an infinite series Rt D R C R.1 R/2
(5.49)
where T0 is 20 ı C, T is the temperature in ı C, T is T T0 , is the wavelength in m, and TK is the average effective resonance wavelength for the temperature coefficients in m. The constants E0 , E1 , D0 , D1 , and D2 are provided on the manufacturer’s product data sheets for each composition. The index of refraction must be measured at a temperature of 20 ı C.
˛d : ln.10/
Tt D .1 R/2
e2˛d 1 R2 e2˛d
(5.53)
Œ2: 0 e˛d .1 R/2 e˛d : 1 R2 e2˛d
(5.54)
The transmission can be approximated by its secondorder term, which is a good approximation for most materials where r2 1. As n and ˛ are usually unknown, two independent measurements have to be performed, either a transmission and a reflectivity
5.1.3 Absorption Absorption in a material can be viewed from two sides. Inside the glass the absorption follows the Lambert– Beer law I.d/ D I0 e˛d ;
(5.50)
which means that the light intensity, I is reduced by a factor of e˛d after traveling a distance d through a homogeneous absorbing medium. The quantity ˛ is called the absorption coefficient and was already introduced in Sect. 5.1.1. The absorption coefficient has the physical unit inverse meter, m1 . Sometimes the absorbance, A, is also used, which is based on the decadic logarithm,
θ 1 d
Φ
n
2 3
Fig. 5.11 Schematic view of light transmission through a transparent plate, where multiple reflection on both sides becomes important
Linear Optical Properties
measurement (Tt ; Rt ) or a combination of two transmission measurements of different thickness (T1 ; T2 ). The absorption coefficient can then be determined by ˛.Tt ; Rt / D ( ) p .1 Rt /2 Tt2 C 4Tt2 C ŒTt2 .1 Rt /2 2 1 ln d 2Tt
˛.T1 ; T2 /Œ2:O D
1 T1 ln d2 d1 T2
(5.55)
:
(5.56)
5.1.4 Microscopic Origin of Absorption Light absorption in glass is mainly caused by the excitation of electron–hole pairs, which can form bound states as excitons that are either delocalized or bound to local impurities. Absorption can be caused by electronic transitions within the absorbing specimen, such as transition metal ions, rare earth ions or even nanosized semiconducting particles. If electrons and holes originate from different ions, the term charge transfer is also used for a particular absorption line. This is due
183
to the fact that the excitation of an electron–hole pair transfers a charge from one ion to a second one. The 4f electron systems like the rare earth ions have very well-defined absorption lines, since the electronic transitions within the 4f shell couple only weakly to phonon modes. A quantity that is microscopically related to the absorption of a single well-defined specimen is the absorption cross-section abs .; T; : : :/. It is connected to the absorption coefficient ˛.; T; : : :/ as X i abs .; T; : : :/ ; (5.57) ˛.; T; : : :/ D i
where the sum over i is the summation over all absorbing transitions, i is the density in units of m3 of the specimen to which the absorbing transition belongs, and abs .; T; : : :/ is the individual absorption cross-section of a given electronic transition. The absorption cross-section is a microscopic property of an absorbing specimen (in a given crystal field), which is wavelength dependent and has the physical unit of an area, m2 . A frequency D c= (or wavelength) integration of the absorption cross-section of a particular well-defined absorption peak gives the oscillator strength, P, of the particular transition when divided by the integrated cross-section of a classic excitation Z 1 . /d ; (5.58) PD int-classic peak
with int-classic D
e2 2:65 106 m=s : 40 m0 c
The oscillator strength is therefore the relation between the measured absorption and the absorption of a given transition expected by a classical theory. The value P takes into account the quantum-mechanic matrix elements of ground state and excited state as well as the multiplicity of particular spin and momentum configurations in an atom. The value P therefore takes into account all spin rules and selection, rules which have a deep quantum-mechanical origin. For optically allowed transitions for the total spin S and total momentum L of a many-electron system the quantummechanic selection rules of spin conservation and parity change apply:
Russel–Sounder selection rule: S D 0 Laporte selection rule: L D ˙1.
Violations of these rules are called forbidden transitions and are of comparatively weaker intensity. The Russel–Sounder rule can be partially circumvented by
Part A | 5.1
For the combination of two transmission methods no analytical solution exists, but the second-order approximation (neglecting all multiple reflections > 2) is accurate enough for many purposes (n 2 , r2 D 0:012). Often a combination of two transmission methods turns out to be more suitable, as reflectivity measurements always have a worse signal-to-noise ratio and therefore a comparatively higher error and lower resolution. An important criterion for the quality of a transmission measurement is the sample homogeneity (which means no striae inside the two samples). An important question concerning absorption is: What happens to the absorbed radiation energy? In most cases the energy is released into lattice vibrations via a cascade of different microscopic processes like electronic transitions and multiphonon absorption processes. This means the electromagnetic radiation that is absorbed is finally heating the glass. There are a number of important exceptions where the absorbed radiation is either instantaneously released as electromagnetic radiation or is released after a certain time and with a shift in energy. This is the case when fluorescence or luminescence occurs, which is discussed in Sect. 5.1.5. Usually the fluorescence or luminescence occurs at lower photon energies (longer wavelengths) than the absorbed light. There are rare cases when many photon processes lead to upconversion, where radiation of shorter wavelength (higher photon energy) occurs. An example for this is the infrared to green upconversion in Er3C -doped glasses.
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Table 5.4 Oscillator strengths for various types of transitions [5.21] Type of transition Spin-forbidden, Laporte-forbidden Spin-allowed, Laporte-forbidden Spin-allowed, Laporte-allowed (e. g., CT)
Approximate P 107 102 105 101
the influence of spin-orbit coupling (e. g., enables 4f– 4f transitions) and Laporte forbidden transitions due to vibronic coupling (e. g., enables 3d–3d transitions in octahedral environments) or ligand field interaction causing a lower symmetric environment (e. g., enables 3d–3d transitions in tetragonal environments) [5.20] (Table 5.4). Numerous mechanisms exist for the creation of colors in glasses. Color is usually created by absorption of a particular part of the visible spectrum. In the following we discuss different types of absorption.
Part A | 5.1
Absorption From Single Ions Most commercial glasses are colored by intraionic transitions between the 3d or 4f energy levels of dissolved transition-metal or lanthanide ions [5.22–24]. Among the sharpest and most well-defined electronic transitions are the 4f electron systems. The electronic transitions within the 4f electron systems are both spin-forbidden and Laporte-forbidden. Therefore a relatively large concentration of these ions is needed to color a glass. Most of these transitions merely decay into phonons and therefore lead to strong fluorescence, which finds numerous applications in laser active materials, optical amplifiers and lighting technology. One example are Nd3C glasses for laser applications. A second example is the transition within the Er3C spin system at the IR wavelength of optical telecommunication. Er-doped glass fibers are widely used as optic amplifiers for telecommunication applications. d-Electron systems are often used to color glasses. The electronic transitions are symmetry-allowed but strongly couple to phonons. Therefore they only give a small contribution to fluorescence but are efficient coloring agents in glasses. For example the blue color of glasses can be created by adding the oxides of Co or Cu to a glass compositions, and green colors can be obtained by doping glasses with Fe or Cr3C . Very efficient optic transitions are obtained by 4f– 5d transitions. An example is Ce3C , which creates red colors in glasses. Here the one electron of the Ce3C that is in the 4f shell is excited into the 5d shell. Absorption by a Combination of Ions Efficient coloration can also be provided by a combination of two coloring ions. An example is the coloration
of brown glasses using Fe and V. Here the excitation of a Fe3C ,V3C pair to a Fe2C ,V4C pair causes light absorption. Such mechanisms are often called charge transfer mechanisms (CT). Absorption by Conducting Particles The coloration of glasses due to small conducting particles in the glass is a combination of both absorption and scattering effects. For small metallic particles, the scattering is governed specifically by Mie’s theory but can also be treated in general with the Rayleigh scattering theory [5.12]. Mie scattering and Rayleigh scattering are covered in Sect. 5.1.6. For understanding the Mie scattering of metallic, conducting particles the absorptions need to be taken into account. In particular, the resonance surface plasmon is important for coloring glasses, since its absorption line depends on the size of the metal particle. For several hundred years glass makers have known how to create beautiful colored glasses with nanosized particles of gold or silver inside. For gold and silver the surface plasmon mode extends well into the visible range. The gold ruby glasses in church windows, which are colored using nanometer-sized gold colloids in the glass, are wellknown examples of this. Absorption by Semiconductor Particles Semiconductor particles in glass can be made so small (110 nm) that the scattering of visible light plays a minor role, however they absorb light over a continuum of wavelengths corresponding to energies greater than the bandgap (Eg ) of the semiconductor particles [5.12]. The bandgap of the semiconductor particles is controlled by the size of the particle and the chemical composition. Typically, semiconductor glasses are melted with Zn, Cd, S, Se and Te raw materials in the batch and upon casting the glasses cool colorless [5.15]. Secondary heat treatment (striking) results in the crystallization of various semiconductor crystal phases in the glass, or a mixture thereof: ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe. The size and distribution of the semiconductor particles can be controlled by the heat treatment and thus so can the optical properties of the resulting glasses. With the proper heat treatment, one glass can be struck into multiple glasses with absorptions leading to red, yellow and orange coloration [5.15]. When the bandgap of the particles is large enough, the absorption edge is shifted into the UV and the glass appears colorless. The opposite can also occur when the bandgap energy is so low that it absorbs all visible light, and the sample appears black [5.15]. Semiconductor-doped glasses are often used as lowpass filter glasses because of their sharp absorption cutoff.
Linear Optical Properties
5.1.5 Emission
Absorption
6 5 4 Emission 3 2 1 1500
1550
1600 1650 Wavelength (nm)
Emission Cross-Section Although absorption has a well-defined meaning with respect to attenuation of light and can be measured quantitatively via the absorption coefficient ˛ (Sect. 5.1.1) it has a quantum-mechanical origin. In particular, when making absorption (and emission) quantitative the quantum-mechanical concept of transition probabilities is needed. It is also usually expressed via oscillator strengths of certain transitions. The fact that light is absorbed at certain frequencies ! (or energies „!) means that light is portioned in packages (photons) of energy Ephoton given by Ephoton D „! D
(5.59)
where h is Planck’s quantum and „ D h=.2 /. The absorption cross-section (Sect. 5.1.4) is connected to the transition probability Rij , which is the probability for absorbing a photon to induce a transition in the medium from state i to state j. In general the transition probability depends on the detailed wavelength dependence of the transition and on the wavelength dependence of the incoming light. Therefore the transition probability is related to the cross-section as follows Z Z 2 c Rij D .!/˚.!/d! D ./˚./d ; 2 (5.60)
where ˚ is the photon flux measured in units of m2 , which is related to the light intensity I D „!˚. Quantum Emissions Furthermore, emission and emission cross-sections have a quantum-mechanical nature. Historically the work of Einstein not only brought its author a Nobel prize but also laid the foundation of laser physics. Einstein introduced the fundamental concepts of stimulated and spontaneous emission. The stimulated emission process produces copies of photons with identical energy and – more importantly – phase as the incident photon. This is the process behind laser activity and amplification. While stimulated emission is just the opposite process of absorption, spontaneous emission is caused by the finite lifetime of an excited state. This lifetime is responsible for noise in a laser or optical amplifier. The lifetime 2 of the upper, excited level with only one transition 2 ! 1 is the inverse of the transition probability A21
Fig. 5.12 Plot of the emission and absorption cross-section
for an Er3C -doped glass
hc ;
2 D
1 : A21
(5.61)
Part A | 5.1
Intensity (arb. u.)
0 1450
185
the approach to treating spectral emission of an excited material is more sophisticated.
For numerous applications of active optical materials the interrelation between specific absorption and emission processes [5.25] is of crucial importance. One example is a laser or an optical amplifier, where a specific absorption on a well-defined level in the optically active material is needed for pumping. This leads to the buildup of an inversion in a lower laying state with a lower energy level compared to the pump level. The inversion can either be emptied by spontaneous emission, which causes noise, or by stimulated emission, which amplifies a laser (or signal) mode. The microscopic processes between these absorption and emission levels can have different origins, for example several levels of 4f electron systems of a rare earth. These levels only interact weakly with lattice vibrations and therefore barely show thermal broadening (zero phonon lines). Examples for laser materials are Nd3C -doped yttrium aluminate garnet (YAG) single crystals and Nd3C -doped phosphate glasses. Examples of optical amplifier materials are Er3C -doped fused silica and Er3C =Yb3C -doped multicomponent glasses (Fig. 5.12). Here the optical emission of Er3C in the wavelength range of optical telecommunication is used. Further laser systems are, e. g., ruby lasers (Cr3C C doped Al2 O3 ); semiconductor lasers, where the pumping is done electronically; gas lasers such as the helium–neon laser, where the energy levels of He are used for pumping and the inversion is built up in the energy levels of Ne; or dye lasers where broad -electron systems of organic molecules are used to provide the necessary tunable energy levels. For more details on laser physics see also [5.25]. The absorption and the absorption cross-sections can be directly measured and are described in Sect. 5.1.3. As we will see,
7
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Fundamentals of Glass and the Glassy State
In the case of different decay channels the lifetime is the inverse of a sum over all transition probabilities 1 : m A2m
2 D P
Part A | 5.1
The upper as well as the lower laser level are composed of an ensemble of sublevels. Especially in disordered systems such as glasses an inhomogeneous broadening of the energy levels can become important. Therefore an effective density of states for each level has to be taken into account. The spacing of the sublevels is such that thermal occupation has to be considered, i. e., where E D h! < kB T, where kB is the Boltzmann constant. Different degeneracies of the energy levels are involved. If the upper level has a degeneracy of g2 and the lower level a degeneracy of g1 , the emission and absorption probabilities have to be multiplied by these degeneracy factors. If an energy state is connected with a magnetic moment, a canceling of degeneracies due to crystal field splitting can occur, which leads to an ensemble of sublevels (see above). There exist nonradiative processes that empty the upper state and decrease the radiative emission cross-section. At high enough energies lattice vibrations (phonons) can empty an excited state in a nonradiative way.
For these reasons the effective emission crosssection for a real system deviates from the absorption cross-section in a nontrivial way abs ./ ¤ emis ./ :
(5.63)
An ideal two-level system and a real system are sketched schematically in Fig. 5.13a,b. The emission cross-section is related to the transition probability by emis ./ D
2 A21 c S ; 8
b)
(5.62)
We now want to define an emission cross-section. If we consider an ideal system with a single nondegenerate transition and no nonradiative decay channels, the emission and absorption cross-sections are identical abs D emis . Real systems deviate from this in the following ways:
a) Energy (arb. u.)
(5.64)
where S.c=/ D S. / is the lineshape Rfunction. The lineshape function is normalized to unity S. /d D 1. The question remains if and how it is possible to measure the emission cross-section. While for the absorption cross-section such a measurement is straight-
Fig. 5.13a,b In (a) the schematic terms for an ideal, only
lifetime-broadened emission process from an excited state to the ground state is plotted. Many real systems sketched in (b) show a splitting into different sublevels, and different degeneracies and nonradiative transitions
forward, it is far more complicated to complete this process for an emission cross-section. The lineshape can be determined by saturating a transition with a light source then switching off the light and measuring the resulting fluorescence, which is decaying exponentially in time, with a spectrometer. The wavelength-dependent signal of the spectrometer is proportional to the emission cross-section. If a sample of volume V is irradiated with light until a stationary state is reached, the inversion level 0 < N2 .x/ < 1 is a measure of the density of the excited optical centers. The probability for an emission process to occur in the wavelength range between and C is emis ./ W./ D R emis : ./d
(5.65)
Therefore the light intensity emitted by an infinitesimal volume element dV.x/ is given by dI.; x/ D NN2 1 dV.x/h W./ :
(5.66)
Here again N is the concentration of optical centers, h D hc= is the energy of each emitted phonon with Planck’s constant h and is the lifetime of the excited state. For a measurement of W./, this intensity, which is emitted with equal probability in all spatial directions, has to be collected in a spectrometer that normally covers only a small part of the spatial angle in which the emission takes place. On the way to the spectrometer the light may also travel through other volume elements causing absorption or stimulated emission. Therefore the absolute signal measured in the spectrometer is related in a nontrivial way to the emission cross-section. For measuring cross-sections the following special conditions are thus used:
Linear Optical Properties
Excitation and measurement are done close to the surface of a sample to avoid the emitted light traveling through large parts of the sample. This is done either in a backscattering geometry or at a corner of the material. The excitation is so strong (e. g., with a laser) that saturation is reached N2 1. In this way absorption of emitted light traveling through the sample is suppressed. Standards are used for a comparison. These are, e. g., rare-earth ions of well-defined concentration in single crystals, glasses with well-controlled compositions or fluid organic dyes.
Even if it is a nontrivial task to measure the emission cross-sections, it is the most important microscopic quantity for the laser activity of a transition.
5.1.6 Volume Scattering
man scattering or Brillouin scattering are not discussed in this section. The origins of light scattering are spatial fluctuations of the complex refractive index. From this point, volume scattering is diffraction of an electromagnetic wave at particles in a certain volume. Obviously scattering is strongly related to diffraction, as seen from the definition of scattering. Indeed, diffraction is scattering by a flat particle [5.26]. In the following, volume scattering is subdivided into (Fig. 5.14):
Single scattering Multiple scattering Coherent scattering.
Volume scattering can be regarded as the sum of single scattering events as long as the density of scattering particles is not too high. Mathematically this is expressed with the packing fraction defined by WD
Nscat Vscat ; Vvol
(5.67)
where N is the number (integer) of the single scatterer, Vscat is the volume of a single scatterer, and Vvol is the whole volume in which the N identical scatterers are located. Before discussing these three different subdivisions of volume scattering a few basic items must be described. Scattering attenuates light, as does absorption by the medium itself. Both effects together are referred to as extinction, where extinction D absorption C scattering [5.26]. The total (over all directions) scattered power Pscat (in units of W) can be calculated from the scattering
η < 0.3
Incident light
Scattered light η > 0.3
This section deals with the interaction of light with particles inside a certain volume leading to light scattering. Before going into details the term scattering must be defined and explained. Afterwards scattering is subdivided into single scattering, multiple scattering, and coherent scattering. Definition and Basics Scattering is defined here as energy absorption of incident light followed by reemission of part of this light at the same frequency. Thus inelastic effects such as Ra-
187
η > 0.3
Fig. 5.14 Illustration of the subdivision of volume scatter-
ing: single scattering (top), multiple scattering (middle), and coherent scattering (bottom)
Part A | 5.1
Example for Er Ions As an example we show here the emission and absorption cross-sections of Er3C for the transition around 1550 nm. This transition is important for telecommunication applications since it takes place in the wavelength range where silica fibers exhibit minimum light attenuation. The states involved in this transition have the spectroscopic symbols E1 ! 4 I15=2 and E2 ! 4 I13=2 , which stand for spin, angular and total moment of the correlated eleven 4f electron systems that forms the Er3C system. In Fig. 5.12 we plot an example of this transition of Er3C , which is of high technological importance. The value of the emission cross-section is influenced by the fact that the ground state is eightfold degenerate whereas the degeneracy of the excited state is sevenfold. It is further influenced by nonradiative decay channels due to lattice vibrations. The spectral shape of the cross-sections is formed by the level splitting in the local crystal field formed by the glass environment and the thermal occupation of the different sublevels. In addition there is inhomogeneous broadening due to the disordered structure of the glass.
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cross-section scat (in units of m2 ) by Pscat D scat Iin ;
(5.68)
where Iin is the incident light intensity (in units of W m2 ). Typically one wants to know the power scattered in a certain direction (Fig. 5.15) and this is described by the differential scattering cross-section dscat =d˝ (˝: solid angle) Iscat dscat D R2 ; d˝ Iin
(5.69)
where R is the distance from scatterer to observer and Iscat is the scattering intensity. The scattering crosssection can be obtained from the differential scattering cross-section by Z dscat d˝ : scat D (5.70) d˝
that completely describes the scattering from a (conducting or nonconducting) sphere embedded in a nonconducting medium. A compact survey of the formulas can be found in [5.28]. Many basic characteristics of scattered power can be obtained by studying scattering by a sphere. The calculated scattering cross-section normalized to the geometric cross-section of a glass sphere (D a2 where a is the sphere radius) can be seen in Fig. 5.16. Figure 5.16 demonstrates the different wavelength dependence of the scattering cross-section and thus of the scattered power according to (5.68). Depending on the geometric sphere size (characterized by the diameter 2a) relative to the wavelength, three important regions can be identified:
2a=nmedium, region of geometric optics. Surprisingly the term scat =. a2/ D 2. This effect is called the extinction paradox and the factor 2 is due to diffraction effects [5.29, 30]. In Fig. 5.17 the factor of 2 is approached only approximately since at small wavelengths (or large scattering particles) the Mie solution becomes numerically instable. 2a=nmedium, resonance effect, the term scat =. a2 / has its maximum. Therefore the highest scattered power can be measured if the geometric size of an object is of the order of the wavelength. 2a=nmedium, Rayleigh scattering. The scattered power is proportional to 1=4 . This effect is responsible for the blue sky and red sunsets, where small
4
Part A | 5.1
Unfortunately the scattering cross-section and the differential scattering cross-section can only be calculated for a few geometries, such as spheres (Mie scattering). The attenuation of light due to scattering is related to the scattering cross-section and the packing fraction of scatterers as follows scat scat D Nscat scat D ; (5.71) Vscat which has the unit of inverse meter (m1 ) and occurs in the exponent when light with starting intensity I0 travels a distance d through a scattering medium and is attenuated as I D I0 e scat d :
(5.72)
In the case when scat d 1 optic imaging is possible and only weak scattering is present. In the case when scat d 1 a sample is turbid and cannot be used for optical imaging. In this case multiple scattering is present. Single Scattering (Mie Scattering) A very important geometry of single scatterers is the sphere. In 1908 Mie [5.27] derived an analytic theory
Geometric Resonance optics region Cscat /(πa2)
Region of Rayleigh scattering
5.0 4.5
Rayleigh scattering
4.0 3.5 3.0 2.5 2.0
dCscat Area at detector: R2dΩ
1.5
Scattering at a sphere
1.0 0.5
Incident light
0 0
R
250
500
750 1000 1250 1500 1750 2000 2250 2500
Wavelength (nm) Scattered light: observer
Fig. 5.16 Scattering cross-section per sphere area (crossFig. 5.15 Scattering in a certain direction described by the
scattering cross-section
section) versus wavelength for a glass sphere (nsphere D 1:50) of radius a D 400 nm in air (nmedium D 1:0)
Linear Optical Properties
E τ1 Pump Stimulated
(u) Spontaneous τ2 (1)
Fig. 5.17 Schematic plot of a three-level laser system via
a pump level with a very short lifetime 1 2 where the upper laser level (u) is populated. Depopulation can either occur via stimulated emission, where copies of photons are made or via spontaneous emission, where the probability is determined by the lifetime 2
particles inside the atmosphere scatter blue light ( 400 nm) more than red light ( 750 nm).
Multiple Scattering In the preceding section scattering at a single isolated particle was described. Now, multiple scattering is discussed, which is the weighted superposition of many single scatterers without interference effects. Multiple scattering with interference effects is called coherent scattering and is discussed below. Multiple scattering is present whenever the product of turbidity and sample thickness is much larger than 1 ( scat d 1) and can be described by diffusive light transport [5.28]. An approximation that treats scattering analytically is the Kubelka–Munck theory [5.31], which approximates light transport in a strongly scattering medium as a diffusive phenomenon in one direction. Based on the knowledge of the scattering function (described by the differential scattering cross-section) of a single scatterer, the overall scattering function can be calculated by tracing rays throughout the volume, if the scattering centers are large enough to allow for use of classical optics. Coherent Scattering Coherent scattering is scattering where the phase relation of the electromagnetic wave on different scattering centers is important and interference plays an important
role for the scattered light. When dealing with materials containing scatterers separated by distances greater than the coherence length (the distance necessary for propagating waves to lose their coherence), the scattering events can be treated as independent occurrences even under multiple scattering conditions. Such scattering is called incoherent, and the resulting intensity of such radiation is simply a summation of the intensity contributions of all the independent scattering centers. However, when the distances between scatterers are on the order of or less than the coherence length, coherent scattering effects must be considered [5.32]. In this case, wave packet interference takes place as the packet is capable of interacting with more than one scattering center at a time; several scatterers distort the photon packet simultaneously. Thus, a relationship exists between the phases of the light signals arising from the different scatterers. The events are no longer separate; they are correlated, and the resulting intensity of transmitted light is no longer a simple sum. Thus, in coherent scattering, wave packets experience a combined interaction with several scattering centers that affects their transport through the medium. In photon group interference (a quantum effect), the wave packet comes apart upon scattering but the different sinusoidal components meet again and interfere. This interference affects the intensity of light transmitted through the sample; thus, coherent scattering studies can yield valuable structural information. As discussed, scattering is coherent when the phases of the light signals arising from different scattering centers are correlated and incoherent when the phases are not. Hence, the propagation of coherently scattered light depends strongly on the direction of the scattering vector q – the difference between the incident and outgoing wave vectors, kin kout (Fig. 5.18, right) – whereas incoherently scattered light can propagate in any direction regardless of the phase relation S(q)
k0 = kin α k1 = kout
q
1
2π/d
q
Fig. 5.18 Left: an example of the static structure factor, for
the case of hard spheres. Right: the scattering vector q
189
Part A | 5.1
These basic characteristics of a single scatterer – here shown for the special case of a sphere – are typical for all single scatterers of arbitrary geometry. As discussed and shown in Fig. 5.16 different behaviors of the scattered power can be observed based on the size of the scatterer relative to the wavelength.
5.1 Interaction of Light with Optical Materials
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Part A
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between waves from different scattering centers [5.33]. When the average distance between scattering centers (d) is on the order of the coherence length or less, the interference effects are significant and quantitatively describable by the static structure factor S.q/, which gives correlations in the positions of particle centers (Fig. 5.18, left). S.q/ is the link between the theoretical description of structural inhomogeneities and the actual experimental scattering measurements [5.34]. An extreme case of coherent scattering is a strictly periodic configuration of scattering centers. The scattering intensity shows maxima at Bragg peaks and the structure factor consists of sharp ı peaks. Note that the relation between incoherent and coherent scattering terms is usually expressed via the Debye–Waller factor. The plot of the structure factor in real space is the pair correlation function, g.r/, which gives the probability of finding a pair of centers at a specific distance r apart in a sample. The relationship between g.r/ and S.q/ is
Part A | 5
Z1 S.q/ D 1 C 4
r2 Œg.r/ 1
sin.kr/ dr ; kr
(5.73)
0
where is the density of scattering centers. There is a mathematical connection between the cross-section of the scatterers and the structure factor. For the general
case of scattering from a correlated group of particles the scattering cross-section is 1 scat D 2 k0
2k0 a Z F.y; k0 a/S.y/ydy ;
(5.74)
0
where y D qa, F.y; k0 a/ is the form factor, a is the radius of the scatterer, and k0 is the incident wave vector [5.35]. Coherently scattered photons have a phase relationship and consequently exhibit more wavelike behavior. In experiments in which coherent scattering is a prominent effect, the interference between scattering paths must be considered – and can be exploited. For example, light from a monochromatic coherent source scatters from a sample and exhibits a characteristic speckle pattern – an array of bright, nonoverlapping spots due to interference effects – based on the composition and structure of the sample, as long as single scattering is the dominant effect [5.33]. Thus, such patterns contain structural information. An additional field is the analysis of backscattering cones. Another example of coherent scattering effects is evidenced by the unexpectedly high transparency of a glass ceramic – a phenomenon that cannot be explained by Rayleigh or Mie scattering theories.
References 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12
J. Jackson: Classical Electrodynamics (Wiley, New York 1975) L.D. Landau, E.M. Lifshitz: The Classical Theory of Fields (Addison Wesley, New York 1971) C. Kittel: Introduction to Solid State Physics (Oldenbourg, Munich 1988) H. Haken: Quantum Field Theory of Solids (Teubner, Stuttgart 1973) A. Sommerfeld: Optics: Lectures on Theoretical Physics, Vol. IV (Academic Press, New York 1954) A.C. Hardy, F.H. Perrin: The Principles of Optics (McGraw-Hill, New York 1932) C.S. Williams, O.A. Becklund: Optics: A Short Course for Engineers and Scientists (Wiley, New York 1972) W.G. Driscoll, W. Vaughan (Eds.): Handbook of Optics (McGraw-Hill, New York 1978) E. Hecht: Optics, 4th edn. (Addison Wesley, New York 2002) S. Singh: Refractive index measurement and its applications, Phys. Scr. 65(2), 167–180 (2002) D. Halliday, R. Resnick, J. Walker: Fundamentals of Physics, 4th edn. (Wiley, New York 1993) J.H. Simmons, K.S. Potter: Optical Materials (Academic, New York 2000)
5.13
5.14
5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23
S. Tominaga, N. Tanaka: Refractive index estimation and color image rendering, Pattern Recognit. Lett. 24(11), 1703–1713 (2003) J.E. Shelby: Introduction to Glass Science and Technology (The Royal Society of Chemistry, Cambridge 1997) H. Bach, N. Neuroth (Eds.): The Properties of Optical Glass (Springer, Berlin, Heidelberg 1998) J.V. Hughes: A new precision refractometer, J. Rev. Sci. Instrum. 18, 234 (1941) Hoya Corporation: Hoya Optical Glass Catalog, http:// www.hoyaoptics.com Ohara Corporation: Ohara Optical Glass Catalog (Ohara, Brandsburg 1995) Schott AG, Advanced Optics: Schott Optical Glass Catalog (Schott, Mainz 2001) F. Gan: Optical and spectroscopic properties of glass (Springer, Berlin 1992) A. Paul: Chemistry of Glass (Chapman Hall, New York 1990) C.R. Bamford: Colour Generation and Control in Glass (Elsevier, Amsterdam 1977) R.G. Burns: Intervalence transitions in mixed valence minerals of iron and titanium, Annu. Rev. Earth Planet. Sci. 9, 345–383 (1981)
Linear Optical Properties
5.24
5.25 5.26 5.27
5.28 5.29
J.E. Shelby: Introduction to Glass Science and Technology (The Royal Society of Chemistry, Cambridge 2005) W. Koechner: Solid-State Laser Engineering (Springer, Berlin, Heidelberg 1976) H.C. Van de Hulst: Light Scattering by Small Particles (Dover, New York 1981) G. Mie: Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, Ann. Phys. 25, 377–445 (1908), Vierte Folge, in German A. Ishimaru: Wave Propagation and Scattering in Random Media (IEEE, Piscataway 1997) C. Bohren, D. Huffman: Absorption, Scattering of Light by Small Particles (Wiley, New York 1983)
5.30 5.31 5.32 5.33 5.34
5.35
References
191
M. Born, E. Wolf: Principles of Optics, 7th edn. (Cambridge Univ. Press, Cambridge 1999) P. Kubelka, F. Munck: Ein Beitrag zur Optik der Farbanstriche, Z. Tech. Phys. 12, 593–601 (1931) P. Debye, A.M. Bueche: Scattering by an inhomogeneous solid, J. Appl. Phys. 20, 518 (1949) C.S. Johnson, D.A. Gabriel: Laser Light Scattering (Dover, New York 1981) A. Dogariu: Volume scattering in random media. In: Handbook of Optics, Part 1 Classical Optics, Vol. III, ed. by M. Bass (McGraw-Hill, New York 2001), Chap. 3 P.D. Kaplan, A.D. Dinsmore, A.G. Yodh: Diffusetransmission spectroscopy: A structural probe of opaque colloidal mixtures, Phys. Rev. E 50, 4827 (1994)
Martin Letz Dept. of Materials Development SCHOTT AG Mainz, Germany [email protected]
Martin Letz works with SCHOTT AG as a Senior Principal Scientist for the physics of glasses and glass ceramics. He received his PhD in 1995 in Solid State Physics from the University of Stuttgart, Germany, and joined SCHOTT in 2001. He is also an external faculty at the Graduate School of Materials at Mainz University.
Part A | 5
193
Nonlinear Op 6. Nonlinear Optical Properties of Glass
Marc Dussauze, Thierry Cardinal
Numerous innovations in photonics have been realized on the basis of nonlinear optical properties, notably in information technologies. To take advantage of the nonlinear optical properties of glass, multidisciplinary research efforts were necessary, combining optics, glass chemistry, material science, as well as development of optical or electrical polarizations processes. This chapter addresses both fundamental aspects of nonlinear optical responses and also the exploitation of nonlinear optical phenomena in glassy material. It starts by a general introduction to nonlinear optical phenomena and concepts. Then, the specific cases of second and third optical responses in glasses are treated separately and described in detail as a function of the corresponding optical phenomena, the various glass families, and their applications.
6.1
Polarization at the Microscopic Scale ...
194
6.2
Polarization at the Macroscopic Scale ..
195
6.3
Nonlinear Optical Susceptibility ..........
196
6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.4.5
Third-Order Nonlinearity in Glass........ Transparent Media (Out of Resonance) .. Absorbing Medium (Resonance) ........... Kerr Effect in Glass .............................. Raman Gain ....................................... The Specific Case of Supercontinuum Generation .........................................
197 197 197 198 201
Second-Order Optical Properties in Glasses .......................................... 6.5.1 Second-Order Optical Response by Optical Poling................................. 6.5.2 3-D Optical Poling by fs Laser Irradiation 6.5.3 Second-Order Optical Response in Glasses by Thermal Electrical Poling ..
206 207 207 209
Conclusion .........................................
219
References...................................................
219
appeared with the development of high-power lasers and the growth of the optical information transmission in the telecom sector. The main objectives were to investigate the light propagation and the perturbation of the wave front while limiting the detrimental effects of NLO phenomena in waveguides where a high density of photons occurs. For instance, the Kerr effect (third-order nonlinearity), at the origin of a change in the refractive index with the laser intensity, is responsible for a spectacular self-focusing phenomenon due to the formation of a photo-induced lens directly linked to the intensity-spatial profile of the beam. This lensing could result, at worst, in an optical breakdown or in an alteration of the wave front propagation. Such effects are still of importance for laser ignition facilities such as the megajoule laser (LMJ) in France or the National Ignition Facility in the USA. In the telecommunications sector, the issue was raised by the current use of small fiber core diameter of a few micrometers in which the power density of the optical
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_6
Part A | 6
6.6
The investigations of nonlinear optical (NLO) properties of glass are intimately related to the discovery of lasers [6.1]. In the early age of lasers, most of the investigations were devoted to crystals and especially to noncentrosymmetric materials such as quartz, LiNbO3 , KTiOPO4 (KDP), and ˛-BaB2 O4 (BBO) [6.2]. Numerous innovations in photonics were realized, such as frequency conversion, which allows expansion of the range of accessible wavelengths by taking advantage of second and third harmonic generation or frequency sum or difference using only one or a few monochromatic laser lines due to the highpower laser material interaction. Glasses, due to their isotropic nature, do not exhibit second-order nonlinearity such as second harmonic generation (SHG) or electro-optic effects (Pockels effect). In contrast to the field of crystalline compounds for which the NLO properties have led to a rapid scientific and technological revolution, NLO phenomena in glass have been considered more like a constraint for practical use. Indeed, the interest in NLO properties of glass
204
6.5
194
Part A
Fundamentals of Glass and the Glassy State
signal over a long distance can give rise to prolonged laser material interaction. In that case again the choice was made to select materials exhibiting the lowest NLO effects to prevent any optical signal distortion. In the last 25 years, NLO properties have been exploited in optical fibers to generate soliton wave propagation to minimize signal attenuation during its propagation. In the scientific community, it was mainly in the late 1980s that articles mentioning the opportunity of NLO properties in inorganic glass began to appear [6.3, 4]. Once again, the interest was related to the development of a novel light source able to deliver energy in a short
time and able to generate a high electric field in matter. These short-pulse lasers brought the possibility to laboratories to access an electric field (1010 V=m) on the order of that between outer-most electrons and the atom. The field rapidly became important, and numerous articles have been published on the investigation of NLO properties of glasses. Indeed, the short-pulse laser has developed interest in the nonlinear optical properties of glasses, such as the ultrafast intensitydependent index, third harmonic generation, stimulated Raman, second harmonic generation, and multiphoton absorption.
6.1 Polarization at the Microscopic Scale
Part A | 6.1
To describe the nonlinear optical response of a medium, we will first introduce the concept of polarization. Light is an electromagnetic wave described by an electric (E) and a magnetic (B) field. The direction of light propagation is perpendicular to these two fields, and Maxwell’s equations permit a full description of its propagation. In dielectric media (such as glasses), the magnetic field part of light can generally be neglected. The electric field can be written as E.r; t/ D E0 e.ikri!t/ ; (6.1) with ! being the angular frequency of the electromagnetic field also equal to 2 ( being the frequency), !t a time-dependent phase term, and kr a space-dependent phase term; k is the wave vector that indicates the direction of light propagation and is equal to 2 n= (n being the refractive index, being the wavelength), and r is the position vector. Matter can be described as an association of a positive point charge (core) surrounded by a cloud of negative charges (electrons) which, in a first approximation, is described as a dipole characterized by its dipole moment M, which is a vector describing the separation of the positive and negative charges. Once an electric field is applied to the medium, the core tends to move in the direction of the field, and the electrons in the opposite direction. Due to their lower mass, the movement of the electrons is much more significant and leads to a faster response. The deformation of the electron cloud causes a charge separation characterized by a microscopic dipole moment . Under illumination, the microscopic dipole moments oscillate at the fre-
quency of the incident electric field. Dielectric dipole moments at the microscopic scale result in a macroscopic polarization of the medium described as the sum of all the microscopic dipoles. If the illumination is of high intensity, i. e., of the order of the atomic cohesion forces, the cloud of electrons oscillates with a higher amplitude, deviating from a harmonic oscillation. The resulting nonlinear polarization is described in a power series as a function of the local electric field. The induced dipole moment at the microscopic scale can be written in a first approximation as ind .!/ D .1/ .!/ C .2/ .!/ C .3/ .!/ C : : : D ˛F.!/ C ˇF.!/F.!/ C F.!/F.!/F.!/ C : : : ; (6.2)
with ˛ the molecular first-order polarizability or linear polarizability, while ˇ and are, respectively, the second and third-order polarizability terms that describe the nonlinear induced polarization, and F the local field. It is important to note that because of interactions between dipoles at the microscopic scale, the local field F is not equal to the electric field E of the incident light. A local field factor (f ) is thus necessary to account for interactions between neighboring dipoles. A common form of the local field factor is given by the Lorentz– Lorenz approximation and takes into account these interactions [6.5]. The local field F can be written as F D fE :
(6.3)
Nonlinear Optical Properties of Glass
6.2 Polarization at the Macroscopic Scale
195
6.2 Polarization at the Macroscopic Scale Macroscopic polarization, as a function of time and space, of a material under the influence of an applied electric field can be described in terms of a power series of the field: .0/
.n/
ij::: .! I !1 ; !2 ; : : : ; !n / ZC1 .n/ D Rij::: .t1 ; t2 ; : : : ; tn /
.1/
Pi .rI t/ D Pi .rI t/ C Pi .rI t/ .2/
the Fourier transform of the response function of the material
.n/
C Pi .rI t/ C C Pi .rI t/ C : : : ;
1
(6.4)
expŒi.!1 t1 C !2 t2 C C !n tn /dt1 dt2 dtn ; (6.8)
.0/
where Pi .rI t/ represents the static polarization (null .1/ .2/ in glass), Pi .rI t/ is linear in the field, Pi .rI t/ is quadratic, and so on. The most general expression for linear polarization, with the assumptions of homogeneity of the material and invariance by time translation and the causality principle, is Z1
.1/
Pi .rI t/ D "0 D
.1/
Rij .rI t t1 /Ej .rI t1 /dt1
0 .1/ "0 Rij .t/ ˝ Ej .t/
(6.5)
:
Pi .!/ D
.1/ "0 ij .! I !/Ej .!/ ;
.n/
Pi .rI t/ Zt Zt Zt .n/ D "0 : : : Rij::: .rI t t1 ; t t2 ; : : : ; t tn / 0
0
Ej .rI t1 / Ek .rI t2 / E .rI tn /dt1 dt2 dtn ; (6.7)
where Rij : : : .n/ is the total response function of the material taking into account the time response. As we will see, later the time response of the material can have an important impact on the NLO properties; .n/ can be defined as the nth-order susceptibility obtained by
"0 D .2 /2
ZC1 ZC1 .2/ ijk .! I !1 ; !2 / 1 1
Ej .rI !1 / Ek .rI !2 / (6.9) expŒi.!1 C !2 /td!1 d!2 ; ZC1 ZC1 ZC1 "0 .3/ .3/ Pi .rI t/ D ijkl .! I !1 ; !2 ; !3 / .2 /3 1 1 1
Ej .rI !1 / Ek .rI !2 / El .rI !3 / expŒi.!1 C !2 C !3 /td!1 d!2 d!3 ;
(6.6)
R C1 .1/ .1/ where ij .! I !/ D 1 Rij .t1 / exp.i!t1/dt1 is the first-order susceptibility of the material, a second-rank tensor. In these equations, ! D !. With the same assumptions as in the previous paragraph (homogeneity, time invariance, locality, and causality), the quadratic, cubic, and higher-order polarizations are expressed as
0
.2/ Pi .rI t/
(6.10)
where .n/ is the nth-order susceptibility defined as the Fourier transform of the response function of the material .2/
ijk .! I !1 ; !2 / ZC1 (6.11) .2/ Rijk .t1 ; t2 / expŒi.!1 t1 C !2 t2 /dt1 dt2 ; D 1 .3/
ijkl .! I !1 ; !2 ; !3 / ZC1 .3/ Rijkl .t1 ; t2 ; t3 / D
(6.12)
1
expŒi.!1 t1 C !2 t2 C !3 t3 /dt1 dt2 dt3 : One can observe that the nonlinear response is a function of multiple wavelengths, and the response is also time dependent. The laser wavelengths and pulse wave duration selected to conduct measurements thus have
Part A | 6.2
Since this last expression is a convolution product, it is natural to pass into the frequency domain, where the linear polarization is a simple product
.n/
where Rij::: is an .nC1/-rank tensor denoted as the nthorder response function of the material. By expressing the response functions and the electric fields with their respective Fourier transforms, the equations can be rewritten as
196
Part A
Fundamentals of Glass and the Glassy State
a strong influence on the material’s response, since different nonlinear terms of the tensors can be involved. For simplicity, at the macroscopic scale in the Fourier space, the polarization is usually seen as the sum of all the induced microscopic dipole moments. The material polarization is thus similarly described at the macroscopic scale by P D 0 Œ.1/ E C .2/ EE C .3/ EEE C : : : ;
(6.13)
where 0 is the vacuum permittivity, .1/ the linear susceptibility that is directly linked to the linear refractive index n0 , .2/ and .3/ , respectively, the second and third-order nonlinear susceptibilities, and E the electric field; .2/ and .3/ nonlinear optical susceptibilities are tensors of the third and the fourth rank and contain 27 and 81 components, respectively. The susceptibilities exhibit various types of symmetry, which are of
fundamental importance in nonlinear optics: permutation symmetry, time-reversal symmetry, and symmetry in space. The time-reversal and permutation symmetries are fundamental properties of the susceptibilities themselves, whereas the spatial symmetry of the susceptibility tensors reflects the structural properties of the nonlinear medium. The more general symmetry requirement that is currently used, called the overall permutation symmetry, is an approximation that applies when all of the optical fields involved in the susceptibility formulae (excitations and response) are far from any transition. This was first formulated by Kleiman [6.6, 7]. For centrosymmetric materials, all components .2/ tensor are null. As a consequence, second-order nonlinear optical effects as well as first-order electro-optical effects are not observed in glasses, and additional treatments of the material should be considered to break the centrosymmetry of glasses.
6.3 Nonlinear Optical Susceptibility
Part A | 6.3
Second-order, .2/ , and third-order, .3/ , terms of the polarization have to be considered to describe nonlinear effects under intense optical excitations that may also be combined with strong static electric fields. These interactions are, respectively, called nonlinear-optical
(NLO) effects, which require only optical excitations, and electro-optical (EO) effects, where optical and electrical excitations are combined. A brief description of the basic EO and NLO effects and susceptibilities are gathered in Table 6.1.
Table 6.1 Basic electro-optical and nonlinear-optical effects observed in dielectrics Order 2
Tensor .2/ (!; !, 0)
2
.2/ (0; !, !)
Effect Linear electro optical effect (Pockels effect) Optical rectification
2
.2/ (2!; !, !)
Second harmonic generation
2
.2/ (!3 ; !2 , !1 )
3
.3/ (!; !, 0, 0)
Generation of light with frequency equal to the sum of frequencies of incident radiations. !3 D(!2 C !1 ) Kerr effect
3
.3/ (!; !, !, !)
3
.3/ (3!, !, !, !)
Nonlinear refractive index also called Kerr effect, self phase modulation. Third harmonic generation.
3
.3/ (!4 ; !1 , !2 , !3 )
Multiwave mixing.
Description Under an electric field there is a change of refractive index in the NLO medium. A static electric field occurs in the NLO medium under illumination. The emission of light with double frequency happens under illumination of the NLO medium. It is observed at illumination of the NLO medium by two light sources with different frequency. The frequency of emission equals the sum of the two excitation source frequencies. Under the action of two electric fields there is a change of refractive index in the NLO medium. The refractive index of the medium changes with intensity according to the formula: n D n0 C n2 I. Self-focusing and self-defocusing of a laser beam are special cases. There is an emission of light with triple frequency under illumination of the medium. When illuminated with three light sources with different frequencies a generation of light occurs whose frequency equals the sum of the three excitation frequencies.
Nonlinear Optical Properties of Glass
6.4 Third-Order Nonlinearity in Glass
197
6.4 Third-Order Nonlinearity in Glass In the absence of poling, or some other treatment to eliminate glass’s isotropy, the first nonlinear term in vitreous material is .3/ . In the relation 6.13 the electric field E appear three times in the third-order NLO term, introducing the possibility to combine three excitations at different frequencies !i (with different field polarization). The .3/ susceptibility, which is described as shown in 6.12, the mixing of four electric field components (three excitations and one response), is a tensor of 3 3 3 3 with 81 terms (taking into account the combination of the electric field polarization). Indeed, the third-order polarization can be written, without taking into account the degeneracy from the polarization state for clarity, in the frequency space as P.! / D "0 .3/ .! I !1 ; !2 ; !3 / E.!1 /E.!2 /E.!3 / :
6.4.2 Absorbing Medium (Resonance) (6.14)
The material can respond at a ! frequency different from the excitation frequencies, while satisfying the two fundamental rules: energy preservation (E D h!=2. /, where h is the Planck constant) and the preservation of momentum (p D hk=2. /) as described in Fig. 6.1. These figures express all the richness of high .3/ materials that allow four-wave mixing phenomena.
At least one intermediate state 1, 2, or 3 in the example corresponds to a real electronic or vibrational state of the material. For instance, in the case of two-photon absorption or the stimulated Raman effect, the imaginary term of the .3/ susceptibility is involved:
When considering transparent materials (out of any resonance), none of the intermediate states 1, 2, or 3 in our example correspond to an electronic or vibrational state of the materials. Two responses can be identified: the Kerr effect and the third harmonic generation (THG): The Kerr effect: In the degenerate case for which the NLO response is observed at the same frequency as that of the excited beam, the term .3/ .!I !; !; !/ can be considered. This term gives rise to the nonlinear Kerr effect in glass and results in the refractive index variation, n D n0 C
Two-photon absorption: In a transparent spectral region, far from a possible linear absorption, two photons can be simultaneously absorbed if the density of photon is sufficient (Fig. 6.3). In most cases, such a criterion is only fulfilled in the focalization volume. The nonlinear absorption is commonly used for 3-D control of the laser induced modification. Stimulated Raman effect: Raman amplification, or Raman gain, is a nonlinear optical process that is based on the stimulated emission of a photon at a frequency that is down-shifted by the vibrational modes of a medium (Fig. 6.4). Two laser beams, presenting a frequency difference matching a vibrational state of the material, interact in the volume of the medium, and light intensity can be transferred from the first beam (!1 ) ω
a) State 2
b) ω2
k3
k2
ω3
ω
State 3 State 1 ω1
ωσ
ωσ = ω1 + ω2 – ω3
k1
ω
3ω
Fig. 6.2 Schematic energetic diagram
of the third harmonic generation phenomenon
kσ kσ = k1 + k 2 + k 3
Fig. 6.1a,b General case of four-wave mixing: preservation of energy (a) and momentum (b)
ω ω
Fig. 6.3 Energetic diagram of twophoton absorption
Part A | 6.4
6.4.1 Transparent Media (Out of Resonance)
n2 I, with I being the light intensity, n0 the linear refractive index, and n2 is called the nonlinear refractive index. The Kerr effect is responsible for the self-focusing phenomenon and the self-phase modulation, which leads to the spectral broadening of the pulse. Such an effect can be used for soliton wave propagation or fast optical switches. The third harmonic generation: For intense excitation with a monochromatic wave, the generation of a triple-frequency signal can be observed due to the term .3/ .3!I !; !; !/ (Fig. 6.2). Such a response can be used for imaging in space the third-order nonlinearity by coupling the measurement with an optical microscope for instance [6.3].
198
Part A
Fundamentals of Glass and the Glassy State
Fig. 6.4 Energetic diagram of the ω1
ω2
stimulated Raman effect involving a vibrational excited state
to the second beam (!2 ). The difference (!1 !2 ) of the pump beam and the beam to amplify (signal) corresponds to the frequency ˝ from the fundamental state to the excited vibrational state.
6.4.3 Kerr Effect in Glass Physical Phenomena Contributing to the Nonlinear Index Historically, the optical Kerr effect is the nonlinear optical property that has been the most studied in glass. Four main phenomena contribute to the nonlinear refractive index with different origins and with different time responses: thermal, electrostrictive, nuclear, and electronic n2 D nelectronic C nnuclear C nelectrostrictive C nthermal : 2 2 2 2 (6.15)
Part A | 6.4
The electronic and nuclear responses originate from the oscillation of the electronic cloud combined, or not, respectively with the vibration of the nucleus. While the electronic response is related to the spontaneous nonlinear distortion of the electronic distribution around the nuclei, the nuclear response is due to a slower opticalfield-induced change arising from the motions of the nuclei. The nuclear-associated response has led to limited investigations. It is usually considered to contribute 1015% of the total n2 , but such an assumption has to be taken with precaution, depending on the glass composition and the laser characteristics [6.8]. Far from a resonance, the pure electronic cloud contribution is the fastest with a characteristic time less than 1 femtosecond. For isotropic materials, the thirdorder susceptibility tensor far from resonance can be fully defined by the measurement of only one term of the .3/ tensor due to the following relation [6.7]: .3/ .3/ .3/ .3/ xxxx D 3xxyy D 3xyxy D 3xyyx :
of this timescale, the impact of the nuclear contribution will then be highly correlated to the laser pulse duration. The electrostrictive contribution corresponds to the material density variation when submitted to an electric field. This effect has a response time of the order of tens of nanoseconds, similarly to that of an acoustic wave in the material. The thermal response is due to the absorption of the electric field by the material and its dissipation by heat. The response time of thermal effects is on the order of tens of microseconds. When a fast response time is considered below a few hundred picosecond regime, within the Born– Oppenheimer approximation, only the electronic and the nuclear contributions contribute to the Kerr effect. Third-Order Nonlinearity Scale in Glass The nonlinear refractive index evolution tendency versus the different glass families (selenide, sulfide, oxide, fluoride) has now been established, due to almost 30 years of continuous investigations (Fig. 6.5). Due to the four-wave mixing-based phenomenon, it is necessary to pay special attention while selecting the laser wavelengths for measuring the nonresonant nonlinear response. For instance, when evaluating the third-order nonlinearity by THG, it is necessary to not only select a fundamental wavelength ! far from any absorption but also to pay attention to the third harmonic wave 3!, which should also be out of resonance. For materials with a band gap in the visible range, this requires selecMeasured at 1.5 μm n2/n2 SiO2
Sulfide, selenide
100
Chalcogenide
Tellurite Oxide
10
1 Fluoride
d0 ions (Ti4+, Nb5+, W6+) in silicate, borate, phosphate Lead silicate Germanate, gallate Silicate, borate, phosphate Fluoride
(6.16)
The nuclear contribution to .3/ originates from the rearrangement of the position of the nuclei during the excitation. This effect is much slower than the electronic one; it is on the order of several hundreds of femtoseconds to a few picoseconds. Because
0.1
Fig. 6.5 Scale of third-order nonlinearity (Kerr effect) among various glass compositions. (The color coding from blue to red is a qualitative indication of the magnitude of nonlinear materials’ response for the eye)
Nonlinear Optical Properties of Glass
n2 ( 10 times that of SiO2 ). For titanium oxide, chains of distorted TiO6 have been evidenced, while for niobium oxide the network organizes as a tridimensional corner shared NbO6 skeleton. Such a high nonlinear index can be also obtained by incorporating a high concentration of ions with a lone pair of electrons ns2 , such as Pb2C in silicate-based glass composition. Nonlinear optical responses more than 10 times greater than silica can be obtained in lone pairs of electron ns2 oxide-based compounds. This is the case, for instance, with tellurite glass composition in which the tellurium oxide amount can reach 99% TeO2 [6.13]. The Te4C ion occupies a TeO4 disphenoid site where the tellurium ion is at the center of a trigonal bipyramid TeO4 E in which the electronic doublet E forms the third equatorial corner. When the concentration of TeO2 decreases by the addition of modifiers such as Al2 O3 , for instance, the TeO4 entities are progressively replaced first by asymmetric groups TeO3C1 corresponding to TeO4 disphenoids with a Te–O axial long bond and by trigonal pyramids TeO3 for the largest modifier concentration. The origin of the nonlinear optical properties has been related to the strong optical hyperpolarizability of the TeO4 entities forming a chain-like structure [6.14, 15] The effect of a glass modifier on the chain-like structure will then have a strong influence on the nonlinear optical response of the materials. Modifiers such as ZnO tend to rapidly break the tellurite chains and to decrease the magnitude of the nonlinear response. The highest nonlinear indices observed in tellurite glass were obtained when the TeO2 is combined with other ions also having a ns2 lone pair of electrons such as TlC , Pb2C or Bi3C [6.16, 17]. Table 6.2 gives the nonlinear third-order susceptibilities measured at 1:5 m on various tellurite glass compositions. Depending on the glass modifier, different values can be observed with the following evolution d10 < ns2 np6 < d0 < ns2 . As explained by Jeansannetas et al. [6.18], the largest nonlinear response is generated by heavy cations with ns2 electron pairs such as Bi3C , Pb2C , or also TlC ions. The addition of Tl2 O in the tellurite glass matrix Table 6.2 Nonlinear susceptibility of different tellurite
glass measured at 1:5 m Glass composition (mol%) 90 TeO2 -10 Tl2 O 90 TeO2 -10 Nb2 O5 90 TeO2 -10 WO3 90 TeO2 -10 Al2 O3 90 TeO2 -10 Ga2 O3 90 TeO2 -10 Sb2 O4 SF59 (lead silicate)
Third-order susceptibility .3/ (1023 SI) ˙20% 141 115 97 78 72 58 57
199
Part A | 6.4
tion of a laser wavelength ! as high as possible in the near infrared. It has been established that the fast response time Kerr effect (1 ps) out of resonance, in a first approximation, follows the evolution of the glass polarizability and more precisely the polarizability of the anions (F < O2 < S2 < Se2 ) (Fig. 6.5). Several studies have also established a correlation between the decrease of the material band gap and the increase of the nonlinear optical behavior. For instance, SiO2 has a band gap of about 9 eV, niobium phosphate around 3:5 eV, and As2 S3 around 2:3 eV. One notices that this progression is accompanied with a strong reduction of the damage threshold for measurement in the NIR. Several models have been proposed to estimate the nonlinear response of glasses. The model proposed by Sheik Bahae et al. for crystalline materials has been applied, for instance, to estimate the values of n2 using a simple Kramers–Kronig analysis by the approximation of the two-photon-absorption spectrum by a two-parabolic-band model (semiconductor model approximation) [6.9]. This model allows determination of the order of magnitude of the glass response even if, as mentioned by Harbold et al., precaution needs to be considered, since this model does not take into account the exponential Urbach tail of amorphous materials [6.10]. When considering a specific glass family, it appears that the evolution is complex, and the impact of the glass structure and composition has a huge impact on the nonlinear optical responses of the material. Different investigations have been conducted by different research groups in order to establish the structure– property relationship. Regarding oxides, silicates, phosphates, and borates, the introduction of alkali and alkaline earth ions by forming nonbridging oxygen between the glass formers increases the linear and the nonlinear indices. In 1995, Nasu et al. clearly established that in silicates, the introduction of alkali or alkaline earth ions increases the nonlinear optical response due to the formation of nonbridging oxygens with higher hyperpolarizability than bridging oxygens [6.11]. The introduction of d0 transition ions (with empty d orbitals) in silicate, phosphate, and borate glass matrices allows a drastic increase in the nonlinear optical response without the resonance phenomenon [6.4, 12]. It has been demonstrated that the arrangement of the structural units formed mainly of MO6 octahedra, with M the transition metal ions, has an important impact on the nonlinear response of the glass. In the specific case of niobium and titanium, the formation of a 2-D or 3-D network of MO6 octahedra for high concentration of transition metal oxide leads to a strong increase of the
6.4 Third-Order Nonlinearity in Glass
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Part A
Fundamentals of Glass and the Glassy State
Part A | 6.4
leads to a high magnitude of optical nonlinearity [6.16, 18] but at the expense of depolymerization of the glass network and a reduction in the glass’ stability [6.19, 20]. Chalcogenide glass (sulfide, selenide) present the largest nonlinear index with n2 above 80 to more than 500 times the SiO2 value for measurement in the near infrared range; As2 S3 glass has a n2 at 1:5 m, for instance, 80 times higher than the SiO2 value. In such materials, the materials’ composition and structure also have an impact on the nonlinear optical properties. First of all, the substitution of sulfur by selenium leads to a continuous increase of the nonlinear optical properties for measurement at 1:5 m. A strong increase can be observed when the Se=S ratio is above 1 with n2 four times higher in As2 Se3 glass than in As2 S3 [6.10, 21]. Such an increase has to be related to a decrease of the band gap of the materials, which should lead to a dispersion of the nonlinear optical response and the appearance of a two-photon-absorption resonance. In such materials, when the concentration of .S C Se/=As is above 1:5, an increase of the nonlinear optical properties has been noticed in various studies of rich selenium content materials even if the evolution of the band gap structure is not significant. This effect has been related to the formation of highly hyperpolarizable Se–Se bonds [6.21]. A similar increase of the nonlinear optical properties for substitution of sulfur for selenium has been measured in the glass system Ge-Sb-S-Se. Germanium selenide glass has a n2 at 1064 nm 350 times the n2 of SiO2 . Correlations have been established by x-ray photoelectron (XPS) between the nonlinear optical response and the presence of Ge-Se and Sb-Se bonds. The nonlinear response within the glass system Ge-Sb-S can be increased by substituting germanium for gallium [6.22]. Even if the nonlinear response of chalcogenide is large, when considering applications, the issue remains the ratio between the nonlinear response and the absorption. Early in 1989, a figure of merit was proposed: FOM D n2 =ˇ, with ˇ the nonlinear absorption coefficient and the wavelength [6.23]. It has been proposed that selenium containing glasses in the system As-S-Se or Ge-Se-Sb could offer a large Kerr effect with n2 =n2;SiO2 , respectively of 500 and 360, while satisfying an optimized FOM for use in the near infrared range [6.10, 24]. Influence of the Nuclear Contribution in Glass In 1975, Hellwarth et al. showed that the nuclear contribution to the nonlinear refractive index of some glasses is not negligible and can reach as high as up to 1530% of the total nonlinear response depending on the glass composition [6.25]. Later, Smolorz et al., for instance, demonstrated that the relative nuclear contribution to
the nonlinear refractive index increases upon addition of GeO2 in a SiO2 optical fiber from 13% to 18% for respectively molar percentage of GeO2 in SiO2 , ranging from 0% to 16% in molar percentage [6.26]. In 1992, Stolen and Tomlinson pointed out that such a nuclear contribution is highly dependent on the pulse width and decreases below 100 fs [6.27]. Several groups actually experimentally showed that the nuclear contribution is definitely dependent on the laser pulse duration and especially for the ultrafast laser regime [6.27, 28]. The time-dependent observation of the nuclear motion has to be fully taken into account in (6.7). This Raman contribution to the nonlinear refractive index constitutes a noninstantaneous nonlinear response in a femtosecond regime. The effect is clearly seen when the optical pulse width becomes comparable to the molecular resonance period. Based upon the Born–Oppenheimer approximation, several measurements of the nuclear contribution in glasses have been performed in the femtosecond regime using timeresolved techniques to separate out the electronic and the vibrational contributions [6.8, 29, 30]. The nuclear contribution can be obtained by integrating the overall Raman cross-section while taking into account the depolarization ratio as proposed by [6.31] ¯! Z1 1 e kB T @2 k .P ; !/ 2 c nnuclear d! ; D 2 3 n0 ¯P @˝@! S ! 4
0
(6.17)
where P is the pump frequency, S is the signal frequency, ! is the Raman frequency (Stokes shift), ˝ is the frequency shift, and @2 k .P ; !/ @˝@! is the parallel polarization component of the spontaneous Raman cross-section. Heavy metal oxide and chalcogenide glasses have been investigated, since they offer the largest nonlinear response. For instance, S. Smolorz et al. reported for 57:2PbO-24:9Bi2 O3 17:8Ga2 O3 and 7:5BaS-17:5Ga2 S3 -70GeS2 , respectively, 9% and 18% of the nuclear contribution to the total n2 [6.26]. Among the different glass families, glasses containing transition ions with empty d orbitals and especially niobium oxide have been widely studied. They can exhibit high nonlinearity in various glass matrices for the incorporation of a large amount of Nb2 O5 [6.32, 33]. The increase of the third-order nonlinear optical response has been directly related to the atomic density
Nonlinear Optical Properties of Glass
Borophosphate (niobium) Borophosphate (titanium) Silicate (titanium) Silicate (niobium) Electronic contribution
12 10 8 6 4 2 0
0
2
4
6
8
10
12 14 16 18 20 Ti or Nb (103 mol/cm 3)
Fig. 6.6 Evolution of the relative third-order nonlinearity
to SiO2 of the d0 transition ion containing glass versus titanium or niobium volume concentration
6.4.4 Raman Gain C.V. Raman first discovered the spontaneous Raman scattering process in 1928, for which he received the Nobel Prize in 1930 [6.34]. More than three decades later, stimulated Raman scattering was discovered by b) Nuclear contribution to n2 (%)
7
40
40% Nb2O5
6 30
5 4
20% Nb2O5
20
3
10% Nb2O5
2
10
1 0 10 0
101
102
103 104 Pulse width (fs)
0 10 0
101
102
103 104 Pulse width (fs)
Fig. 6.7 (a) Nuclear contribution to the nonlinear response for SiO2 versus the laser pulse width, (b) nuclear contribution to the nonlinear response for a NaPO3 glass matrix with various amounts of niobium oxide (for clarity, the error bars of 20% on the nuclear contribution are not displayed on the graph (a))
Part A | 6.4
of transition ions in glass. In addition, a particular behavior of the nonlinear refractive index has been shown, with a clear enhancement of the nonlinear optical response for a large amount of niobium ions in the glass network (Fig. 6.6). In the specific case of the introduction of niobium oxide in phosphate or borophosphate glass matrices, the optical nonlinear response has been related to the specific three-dimensional corner-sharing arrangements of NbO6 octahedra, which enables the formation of a tunga) Nuclear contribution to n2 (%)
201
sten bronze-like local structure for high niobium oxide concentration. Lipovskii et al. observed a similar behavior of the electro-optical Kerr effect, with the successive addition of Nb2 O5 into silicate-based glasses [6.32]. All these investigations have illustrated the correlation between the increase of both the Raman spectral density and the Kerr response of the materials with an increase of NbO6 tungsten bronze crystal motifs within the glass structure. The enhancement of the nonlinear response in niobium oxide-containing glass belongs to the nuclear contribution to the nonlinear response, which can reach 40% of the overall Kerr effect for high niobium oxide concentration (Fig. 6.6). The nuclear contribution, as was mentioned before, is definitely dependent on the laser pulse width. As shown in Fig. 6.7a,b for, respectively, silica and niobium oxide phosphate glass, the nuclear contribution drops rapidly when pulse widths are below 100 fs to become negligible for laser pulse widths below 10 fs. On the contrary, the phenomenon is clearly at its maximum for the picosecond laser regime. Niobium oxide-containing glasses illustrate the importance of taking into account the laser regime when evaluating the nonlinear response of the glass. This also illustrates the variety of the magnitude of the nuclear contribution to the nonlinear index among different glass compositions.
χ(3)/χ(3) SiO2 14
6.4 Third-Order Nonlinearity in Glass
202
Part A
Fundamentals of Glass and the Glassy State
Part A | 6.4
Woodbury and Ng in 1962, but it was not until 1973 that the first experimental evidence of stimulated Raman process, or Raman amplification, in an optical fiber was actually observed by Stolen and Ippen [6.35]. Raman amplification is a nonlinear optical process that is based on the stimulated emission of a photon at a frequency that is down-shifted by the vibrational modes of a medium. From a classical mechanics point of view, the Raman gain process is described by the imaginary part of a nonlinear susceptibility .3/ , in which a signal beam becomes amplified by a pump beam, given that the difference in energy between the two beams goes into the vibrational modes of the Raman gain medium. The gain magnitude depends on the pump wavelength and on the material properties (e. g., the frequency of the Stokes shift and Raman spectral intensity), as shown with the example of SiO2 in Fig. 6.8. The selection of various pumps at different wavelengths permits amplification within the transparency windows of glasses. Already in the early days of fiber optics [6.36], the fundamental advantages of Raman amplifiers were evident even if, for telecommunication, erbium-doped fiber amplifiers (EDFA) have been rapidly adopted due to the requirement of much lower pump power for operation [6.37]. Traditionally, there are several types of Raman amplifiers, one of which is the distributed Raman amplifier. In this case, the gain is accomplished along the propagation length throughout the optical fiber itself; hence, the trade-off between the gain and the optical losses becomes an essential factor to achieve high performance. This category can be g R (10 –13 m/W) 5 1.6
10
15
Frequency shift (THz) 20 25 30
1.4 Raman gain bandwidth for maximum gain
1.2 1.0 0.8
λexcitation = 1064 nm
0.6 0.4 0.2 0.0
1075
1100
1125
1150
1175 1200 Wavelength (nm)
Fig. 6.8 Raman gain spectra of silica glass with a pump
laser at 1064 nm. Here, the gain bandwidth is defined by the full width at half maximum (FWHM)
further expanded into cascaded or diode pumped distributed Raman amplifiers, respectively. Such Raman amplifiers are primarily used in long-haul network systems. These types of amplifiers require a gain medium with high gain coefficients and broad bandwidth; and in this case, low loss is a desirable property but not a crucial issue. Another type of application is Raman fiber lasers, in which the device operates as a typical laser system [6.38]. Several glass families were studied during the 1970s and 1980s with the purpose of increasing the scattering cross-section [6.39–42]. Among the main oxide glass systems studied were silica, germanium-doped silica glasses, and multi-component glasses such as heavy metal oxide glasses. Fused silica has been the key material used for longhaul transmission of optical signals, due to their good optical properties and low loss characteristics, which give an attractive figure of merit (described as the tradeoff between Raman gain and losses). Indeed, the most studied Raman gain media have been fused silica and germanium-doped silica glasses [6.43–46]. However, fused silica offers a limited usable bandwidth for Raman amplification of 5 THz and has one of the lowest Raman cross-sections among glasses (with a Raman gain magnitude of gR D 0:89 1013 m=W at 1 m). Another glass matrix that has been investigated as a Raman fiber amplifier is phosphosilicate, which provides a peak Raman gain of 40 dB at 1:3 m [6.47, 48]. Heavy metal oxide glasses have been proposed for Raman gain applications due to their enhanced nonlinearity and transparency over the telecom window for fabricating short components [6.42, 49]. Tellurite fiber has been also evaluated for its high Raman gain performance (gain over 10 dB) with relative low loss of 20 dB=km [6.50]. Glass families that primarily include TeO2 -based glasses for high-gain applications have recently been reported in the literature [6.51–55]. In 2005, Stegeman et al. demonstrated that direct Raman spontaneous cross-section measurement can be used for estimating the Raman gain coefficient after careful correction using the Bose–Einstein factor [6.35, 54]. Using such an approach, it has been demonstrated that the introduction of transition ions in phosphate or borophosphate glass matrices allows reaching a Raman gain coefficient close to 10 times the value of silica (Fig. 6.9). A broad-band amplification window has also been shown by introducing small amounts of d0 ions in the phosphate, due to the disruption of the phosphate chains and the formation of multiple phosphate units with various vibration signatures such as in Fig. 6.10 leading to a Raman gain bandwidth of 38 THz as compared to the 5 THz of fused silica [6.56].
Nonlinear Optical Properties of Glass
g R (10 –13 m/W) 0 10 10
Frequency shift (THz) 30 40
20
x = 10 x = 20 x = 30 x = 40
8
g R (10 –13 m/W) 0 10 4
6.4 Third-Order Nonlinearity in Glass
203
Frequency shift (THz) 30 40
20
3
6 2 4
2
0
1
200
400
600
800
1000 1200 1400 Wavenumber (cm –1)
0
1100
1150
1200 1250 Wavelenght (nm)
Fig. 6.9 Calculated Raman gain curve from spontaneous
Raman cross-section measurements of phosphate .100 x/NaPO3 -xNb2 O5 glass system (extracted from VV polarized spontaneous Raman spectra), normalized to SiO2 , along with experimentally measured Raman gain coefficient data points (squares) of composition 70% NaPO3 30% Nb2 O5 , using the direct NLO technique at 1064 nm
to the vibration at around 665 and 750 cm1 ; respectively assigned to the presence of TeO4 bi-pyramids and to the TeO3C1 or TeO3 trigonal pyramids vibrational units. In the case of d0 transition ions, the most intense contribution is the 665 cm1 vibration. It was recently demonstrated that in such glass the existence of the Te– O–Te chains formed with TeO4 units is the source of the nonlinear optical response. The introduction of zinc oxide into the composition, resulting in the disruption of those chains, induces a fast drop of the nonlinear optical response [6.59]. For tellurite glass compositions with lone pairs of electrons, such as thallium, TeO3 vibration can become the most intense and lead to a Raman gain coefficient 50 times the value of fused silica at 1064 nm, as reported in Table 6.2 and Fig. 6.11. Special attention should be paid while measuring or estimating the Raman gain coefficient. As demonstrated by Rivero et al., a large decrease in the relative inten-
Table 6.3 Composition of different binary TeO2 glasses, Raman gain measurement at 1064 nm Glass composition 85% TeO2 -15% WO3 85% TeO2 -15% TiO2 85% TeO2 -15% NbO2:5 85% TeO2 -15% PbO 85% TeO2 -15% GaO1:5 xTeO2 -.100 x/TIO0:5
x D 75% x D 70% x D 50%
TeO4 ( D 665 cm1 ) gR 1013 .m=W/ ˙ 20% 43 39 44 36 26 25 21 14
TeO3 ( D 750 cm1 ) gR 1013 .m=W/ ˙ 20% 25 16 17 31 13 19 23 52 ˙ 3
Part A | 6.4
Heavy metal oxides can provide a high Raman cross-section. Among such materials, tellurites have been widely investigated. Pure TeO2 glass cannot be obtained using classical melting methods, requiring minor (a few mol%) additions of modifiers to avoid crystallization. Previous investigations have shown that the introduction of d0 -transition ions (W6C , Nb5C , Ta5C , Ti4C , etc.) or ions with a lone pair of electrons such as TlC or Pb2C to the TeO2 glass network former, allows one to maintain high optical nonlinearity, high Raman gain and to improve the processing conditions required to make high-quality glass [6.54, 57, 58]. Several glass compositions have been investigated. Table 6.3 reports binary glass compositions for the introduction of different intermediate compounds. The main contributions to the Raman spectrum correspond
Fig. 6.10 Calculated (black) and experimental (red) Raman gain spectra of glasses 90% NaPO3 -5% Na2 B4 O7 5% TiO2
204
Part A
Fundamentals of Glass and the Glassy State
tions but also to the dispersion phenomenon. Tohoutek et al. reported high Raman gain for sulfide in the glass system Ge-Ga-Sb-S [6.63]. Within the vibration mode domain between 250500 cm1 , for measurement at 1064 nm by comparing the measured Raman scattering intensities with the Raman intensity of the silica glass, peak gains of 296 and 140 have been measured, respectively, for As2 S3 and GeS2 . Nevertheless, one has to keep in mind that the use of such glasses requires the selection of pump wavelengths at > 2 m in order to avoid detrimental nonlinear absorption phenomena. For selenides, at 1550 nm, using As2 Se3 fiber, Slusher et al. reported a Raman gain of 780 times the value of SiO2 . However, as reported by various authors, the issue of the material stability for use in the near infrared should be taken into account [6.64].
Relative Raman intensity (arb.u.) x = 75 x = 70 x = 50
100
80
60
40
20
0
200
400
600
800 Wavenumber (cm –1)
6.4.5 The Specific Case of Supercontinuum Generation
Fig. 6.11 Parallel/parallel polarized (VV) spontaneous Ra-
man spectra of the xTeO2 -.100 x/TlO0:5 glass system, normalized to SiO2 . Excitation wavelength 514 nm
Part A | 6.4
Supercontinuum generation in glass fiber, which is a wide spectral broadening of a intense laser beam due to an addition of multiple nonlinear processes, has become a hot topic during the last decades. The nonlinear optical phenomena at the origin of the spectral broadening can be multiple, depending on the material and the adopted optical and material configuration. Alfano and Shapiro first reported supercontinuum generation in glass [6.66, 67]. In the final years of 1990s, the discovery of the photonic crystal fiber, which allows taking advantage of nonlinear optical properties and managing group velocity dispersion and the position of the zero wavelength dispersion, led to the demonstration of broad spectral generation out of fiber systems [6.68]. Supercontinuum generation has found numerous ap-
sity of the Raman scattered signal with an increasing excitation wavelength between 458 and 752 nm is clear (Fig. 6.12) [6.60]. Since all the spectra have been normalized to SiO2 , this result clearly illustrates a strong dispersion dependence of the Raman susceptibility tensor. This effect has to be taken into account while comparing Raman gain measurements in the literature measured at different wavelengths. Chalcogenide glasses offer the largest Raman gain coefficient in the near infrared. Chalcogenide fibers (As2 S3 and As-Se fibers), can provide Raman gain coefficients several hundred times that of SiO2 [6.61, 62]. Such an effect is directly linked to the high nonlinear third-order susceptibility of such composia) Relative Raman intensity
b) Relative Raman intensity
85 TeO2-15 WO3
λexc =
40
20
0
λexc =
85 TeO2-15 NbO5/2 458 nm 514 nm 752 nm 1064 nm
60
458 nm 514 nm 752 nm 1064 nm
60
40
20
500
600
700
800
900
1000
1100
1200 λ (nm)
0
500
600
700
800
900
1000
1100
1200 λ (nm)
Fig. 6.12a,b VV polarized experimentally-obtained spontaneous Raman spectrum for (a) 85% TeO2 -15% NbO2:5 and (b) 85% TeO2 -15% WO3 tellurite glass composition normalized to SiO2 traducing the dispersion of the Raman response
for different excitation wavelength
Nonlinear Optical Properties of Glass
6.4 Third-Order Nonlinearity in Glass
205
a)
b)
10 μm
2 μm
3 μm
Fig. 6.13a,b SEM images of various tellurite glass microstructured fibers. (a) Core diameters varying from 1:6 to 2:2 m. (b) The same fiber at different scales. Reprinted from [6.65] with permission from Elsevier
agement using suspended core technology, as shown in Fig. 6.13. In the case of tellurite glasses, large spectral broadening has been demonstrated with bandwidths exceeding 2500 nm while managing zero dispersion by microstructured fiber in tellurite suspended core fiber [6.71–75]. In chalcogenide glasses, using suspended core As38 Se62 fiber, Moller et al. used a laser source exciting in the mid-IR, emitting at 4:4 m and in 2015 demonstrated a supercontinuum spanning from 1:7 to 7:5 m with an average output power of 15:6 mW [6.76]. Suspended core fibers can present drawbacks, since surface contamination can become an important issue with formation, for instance in chalcogenides, of oxide impurities, which dramatically reduce the transmission window of the fiber [6.74]. Recently, major efforts have been conducted to engineer step index fibers that prevent air contact with the core using newly available mid-IR lasers close to the minimum dispersion wavelength of the core materials [6.77]. Using such an approach, mid-infrared supercontinuum covering the 1:413:3 m spectral range has been demonstrated using a chalcogenide step-index fiber formed of a As40 Se60 core surrounded by a Ge10 As23:4 Se66:6 cladding pumped at 6:3 m (Fig. 6.14) [6.78].
Part A | 6.4
plications such as spectroscopy, pulse compression, and in the use of tunable ultrafast femtosecond laser sources. The physics of spectral broadening is complex. When seeded by femtosecond pulses, for instance, in the early stages, self-phase modulation takes place and later, various phenomena occur, such as stimulated Raman scattering, four-wave mixing etc. [6.69]. Even if silica remain the best materials for the visible range, when the near infrared or mid infrared range is required, novel materials with low phonon energy need to be developed. Again, the loss issue is crucial but so is the transmission window of the glass. Silica-based photonic crystal fiber offers supercontinuum generation with flat spectral power densities; however, SiO2 is not transparent above 2400 nm. Recently, Jiang et al. demonstrated that fluorides allow extended use in the infrared but also in the ultraviolet range, spanning more than three octaves in the spectral range 2002500 nm [6.70]. Heavy metal oxide glass or chalcogenide glasses are an interesting alternative for transmission in the mid-IR, since they have high nonlinear optical response for shortening the final device and they allow expending the transmission spectrum in the infrared due to their low phonon energy. Much effort has been deployed to improve the optical quality of the glass and to engineer group velocity dispersion man-
206
Part A
Fundamentals of Glass and the Glassy State
a) Intensity (dB)
b)
0 –10 –20 –30 1
2
3
4
5
6
7
8
9
10
11
12 13 14 Wavelength (μm)
c) Pump peak power (MW)
d)
2.0 1.6 1.2 0.8 0.4 0.0
1
2
3
4
5
6
7
8
9
10
11
12 13 14 Wavelength (μm)
Fig. 6.14a–d Experimental supercontinuum generation with the pump laser centered at 6:3 m. (a) Input pump spectrum (dashed line) and spectral profile at maximum pump power (solid line). (c) Spectral evolution with increasing pump peak power, showing the gradual redshift of a distinct spectral peak at the long-wavelength edge and the corresponding formation and blueshift of dispersive waves. Fiber output near-field beam profile corresponding to the spectrum in (a) for all wavelengths (b) and beam profile for wavelengths above 7:3 m only (d). From [6.78]
Part A | 6.5
6.5 Second-Order Optical Properties in Glasses Second-order nonlinear (SONL) optical responses are of utmost importance in photonic applications. The most common uses are notably for electro-optical signal conversions and optical frequency control. At a first level of description, if one considers a centrosymmetric material and only the electric-dipolar optical response, it implies that the even nonlinear dielectric susceptibility, .2/ , is zero. Under this approximation, symmetry requirements do not allow nonlinear optical response of the second order in any homogeneous glassy material. However, several second harmonic optical signals, with different origins, can be observed in glasses. First, the second harmonic elastic scattering or hyper Rayleigh, which can be measured in all kinds of inorganic glass. This harmonic diffusion signal can be linked to the second-order molecular hyperpolarizability, ˇ (6.2). This signal is commonly used as a spectroscopic tool to study isotropic media such as liquids or glasses [6.79, 80]. Second, at the glass surface, a structural loss of the inversion symmetry at the interface allows the observation of a coherent second harmonic generation with an electric-dipolar origin. Third, even in the bulk, second-
order optical response have been measured and linked to electric-quadrupole and magnetic-dipole contributions [6.81–83]. Please note that such origins of optical nonlinearity were not described in the previous sections, which were only focused on the electric-dipole contribution. The understanding of these optical signals is of a great importance for the development of second harmonic generation as a tool for interface characterizations or structural studies. Nevertheless, the efficiency of second-order optical responses observed in homogeneous glasses remains very weak and can hardly be considered for photonic applications. To implement effective .2/ in glasses, poling treatments have been widely used to break the centrosymmetric nature of a glass structure. Poling can be based on the action of laser irradiation, called optical poling; [6.84], on the action of an external electric field, called thermal (electrical) poling or corona poling; [6.85, 86] and also on the action of electron beam irradiation [6.87] or proton implementation [6.88]. Within all these different kinds of poling methods, optical and thermal electric poling to induce efficient second-order
Nonlinear Optical Properties of Glass
optical properties in glasses are the most studied approaches in the literature and will be reviewed in the next sections.
6.5.1 Second-Order Optical Response by Optical Poling In 1981, Sasaki and Ohmori were the first to report the observation of a second-order optical response in an inorganic oxide glass. A peak pump power of 0:8 kW at 1064 nm from a Q-switched and mode-locked Nd:YAG laser was injected in germanosilicate fibers. As shown in Fig. 6.15, the authors demonstrated two-wave sumfrequency responses between the laser pump (!p ) and the two first Raman stokes signal (!1 and !2 ), resulting in the signals !s1 and !s2 [6.84]. After 5 years, an efficient second harmonic generation response was observed in single-mode germanosilicate optical fibers illuminated by a Nd:YAG laser producing up to 70 kw peak power of 100130 ps pulses with a 1250 Hz Q-switched rate. Within the first 9 h of the illumination procedure, the SHG efficiency grew exponentially over more than four orders of magnitude and finally saturated after approximately 12 h. In this experiment, Österberg and Mar-
Si-APD Ge-APD
ω2 4 ω1 3
2
1 ωs1 ωs2 0 0.5
ωP 0.7
0.9
1.1
1.3
1.5 1.7 Wavelength (μm)
Fig. 6.15 Two-wave sum-frequency response spectrum
measured with two different avalanche photodiodes (APD) by Sasaki and Ohmori for injection in a germanosilicate fiber of a signal at 1064 nm from a Q-switched modelocked Nd:YAG laser. The measurements were carried out using two detectors: silicon and germanium avalanche photodiodes (Si-APD and Ge-APD as noted in the figure’s legend). Reprinted (adapted) from [6.84] with the permission of AIP Publishing
gulis observed a peak power-conversion efficiency of 3% [6.89]. Stolen and Tom demonstrated the importance of coillumination with a strong power at the fundamental frequency with a second weak seeding illumination at the harmonic wavelength, in order to greatly increase the speed of the second-order optical response implementation in the fiber. Moreover, these authors demonstrated the utmost importance of a self-induced periodic static polarization linked to a third-order process mixing the fundamental and the harmonic waves, allowing for possible dipole orientation and phase matching conditions [6.90]. In the same period, Ouelette et al. reported the erasure of such self-organized .2/ gratings in optically poled fibers by ultra-violet irradiation or strong green light. The origin of the second-order response was explained by the presence of periodic domains in which charge separation have occurred and charge defects were trapped, as concluded by the time dependence of the erasure process [6.91]. This conclusion regarding the electro-optical origin of the second-order optical response was confirmed by Mizrahi et al., who studied the SHG polarization properties in optically poled Gedoped silica glass optical fibers [6.92]. Similarly, Driscoll and Lawandy demonstrated on optically poled bulk silicate glasses that the symmetry and tensor components of the SHG response were consistent with a periodic implementation of an internal static electric field interacting with the third-order nonlinearity, .3/ , through an electric field-induced second harmonic effect (EFISH) [6.93]. In addition, using chemical attack by hydrofluoric acid, Margullis et al. and Kyung and Lawandy, recorded direct images of the periodic gratings resulting from macroscopic separation of charge in the silicate glass matrix. The charge separation was mainly located at the core–clad interface of the optically poled fiber [6.94, 95]. Later, the research activity on optically poled silicate glasses significantly decreased. The mechanisms involved have been well described experimentally and theoretically, but both the low stability and effectiveness of the second-order optical response induced are certainly the main reasons of this loss of interest by the community.
6.5.2 3-D Optical Poling by fs Laser Irradiation Laser-induced crystallization of second-order nonlinear crystals has been developed by various several research teams. Homna et al. and Komatsu et al. developed an approach allowing local crystal precipitation
207
Part A | 6.5
Power output (arb.u.) 5
6.5 Second-Order Optical Properties in Glasses
208
Part A
Fundamentals of Glass and the Glassy State
Part A | 6.5
by the incorporation in the glass composition of transition or rare earth ions absorbing at infrared continuous wave (CW) laser wavelength. The selected ions exhibit a strong nonradiative relaxation that induces an increase of the local temperature of the glass above the glass transition temperature and the precipitation of the second-order nonlinear crystal. Nonlinear optical crystals such as ˇ-BaB2 O4 , Ba2 TiGe2 O8 , Smx Bi1x BO3 , (Sr,Ba)Nb2 O6 , and LiNbO3 crystals have been obtained in borate, tellurate, phosphate, or silicate-based glass systems [6.96]. Femtosecond laser irradiation is a promising tool to achieve second-order nonlinear optical functionality in glasses with three-dimensional and submicrometer spatial resolution when no element is introduced in the glass matrix for sensitization. Two main approaches have been studied to achieve nonlinear optical functionality structuring in glasses by femtosecond laser irradiation. Several authors have reported on threedimensional control of the precipitation of nonlinear optical crystalline phases within a glassy matrix [6.97, 98]. At certain high repetition rates (e. g., > 200 kHz), thermal accumulation effects occur within the irradiated volume and reach the melting temperature of the glass matrix, allowing for the crystalline phase formation. In addition, by adjusting the femtosecond laser irradiation parameters, such as writing direction and speed, pulse energy, and the polarization state of the light, it is possible to control the crystalline growth, and notably its orientation [6.99]. Finally, the objective of this laser-structuring method is to produce optical-quality single-crystal structures suitable for waveguiding. As an example, in Fig. 6.16, we depict some promising results reported on direct laser-writing of ferroelectric LaBGeO5 single-crystal waveguides in a glass matrix of the same composition.
The second approach for femtosecond laser writing in glasses of 3-D optical second-order nonlinear microstructures is linked to the use of photosensitive glasses, as reported for the first time by Choi et al. [6.100]. Compared to the previous approach, the irradiation process does not modify the glassy state of the optical material treated. The photosensitive glasses studied were zinc phosphate glasses containing few mol% of silver oxide. Such structuring of silver containing phosphate glass needs a high repetition rate and near infrared femtosecond laser sources. Careful polarization-dependent SHG characterizations have demonstrated the EFISH origin of the second-order optical response. The second-order nonlinearity efficiency was evaluated at about 2:5 times the quartz value. One particularity concerns the fact that the inscribing of the nonlinear optical response is achieved together with the creation of silver ionic clusters exhibiting strong visible luminescence [6.101]. The formation mechanisms of both SHG response and silver clusters within the glass matrix by femtosecond laser irradiation involves multiphoton absorption leading to generation of free electrons, electron diffusion, and trapping but also to ionic motion forming (i) a silver depletion at the center and (ii) silver ionic clusters at the border of the voxel of interaction. For one single line inscribed by a sample translation during the irradiation, the original spatial distribution of the nonlinear pattern is composed of four lines, two lines at each side of the beam voxel (Fig. 6.17). By SHG/luminescence correlative microscopy the locations of fluorescent and SHG signals have been characterized (Fig. 6.17). On the basis of the EFISH origin of the signal, the electric field and electric potential distributions have been estimated. This has allowed us to point out a clear correlation between the electric poten-
a) Fig. 6.16a,b Birefrin-
10 μm
b)
25 μm
gence micrographs of crystal junctions written inside a LaBGeO5 glass by a femtosecond laser showing (a) independent lattice orientations developed in each branch, (b) merging of the two branches back to a single line. The angle of either the fast or slow axis of birefringence is indicated by the color wheel. From [6.98]
Nonlinear Optical Properties of Glass
Fig. 6.17 (a) Spatial distributions of the fluorescence and SHG signal induced after femtosecond irradiation of photosensitive silver-doped phosphate glass. (b) Electric field and potential profiles deduced from the EFISH origin of the second-order optical nonlinearity. (c) Correlation between the calculated electrical potential and the fluorescence signal originating from the silver cluster stabilized within the glass matrix (after [6.102]) I
6.5 Second-Order Optical Properties in Glasses
209
a) Intensity (arb.u.) 30
SHG lines Fluo lines
25 20 15
tial of the induced space charge and the formation and stabilization of the luminescent silver clusters. Finally, the SHG lines are explained by the two electric field components of opposite sign, as shown in Fig. 6.18b. Remarkably, the second harmonic generation signal has been found to be stable for temperatures close to the glass transition temperature [6.101].
6.5.3 Second-Order Optical Response in Glasses by Thermal Electrical Poling
0 –4
–3
–2
–1
0
1
2
3 4 Width (μm)
2
1
1
0
0
–1
–1
–2 10–4
–2 –3
–2
–1
0
1
2
3 4 Width (μm)
c) Fluorescence intensity (arb.u.) Electric potential (arb.u.) 12 10 1 8
(6.18)
6
The first term is connected to the existence of a static electric field (EDC ) frozen within the sample after poling and a coupling with the intrinsic third-order susceptibility .3/ of the glass matrix. This is considered as an EFISH response linked to a space charge within the glass. The second term corresponds to the contribution of an oriented structure, which was approximated by an oriented dipole where N is the number of dipoles
4
0
–1
2 0
–2 –4
–3
–2
–1
0
1
2
3 4 Width (μm)
Part A | 6.5
Thermally Poled Silica SHG response in thermally poled glasses was reported for the first time by Myers et al. [6.85]. A .2/ response of 1 pm=V was measured and related to two possible origins as expressed in (6.18) [6.103] Npˇ Eloc : 5kB T
5
b) Electric field amplitude (arb.u.) Electric potential (arb.u.)
A thermal electrical poling procedure consists of applying a DC electric field at the sample to an elevated temperature before cooling, while the DC field is kept (Fig. 6.18). Such a simple process was largely studied to induce second-order optical response in polymers and inorganic glasses. If one focuses on thermally poled glasses, research efforts come form both physicist and glass chemist communities. This interdisciplinary approach of the problem has demonstrated the potential but also the restriction and the complexity of polarization processes in a large range of glassy systems. The next sections will treat the achievements reported on silica, ionic, and nonoxide glasses separately.
.2/ 3.3/ EDC C
10
210
Part A
Fundamentals of Glass and the Glassy State
a)
+
Depletion zone
b) T
+ + + + + High voltage Time
Part A | 6.5
per volume, p is the dipole moment, ˇ the microscopic hyperpolarizability, and Eloc corresponds to the local electromagnetic field. At the same time, Kazansky and Russel demonstrated that the origin of SONL properties in thermally poled silica is due to an EFISH process by characterizing the relative values of the nonlinear tensor components [6.104]. The depletion zone in mobile cations at the origin of the space charge implementation were observed experimentally for the first time by SIMS (secondary ion mass spectrometry) by Alley et al. [6.105]. They observed the depletions of lithium and sodium cations over thicknesses of 17 and 25 m, respectively. In the same report, these values were shown to be dependent on the poling time. Several studies have characterized both the second-order optical response efficiency and the thickness of the SHG-active layer as a function of the treatment conditions (temperature, voltage, duration, atmosphere) [6.106–111]. Polarization mechanisms in poled silica were described by Quiquempois et al., who developed a model taking into account charge dissociation and charge recombination occurring during the poling process [6.112]. This description is based on the model first developed by Proctor and Sutton in 1959. It predicts the electric field distribution and a poling voltage threshold [6.113]. Experimental observations are in good accordance with the model. Finally, poling mechanisms in silica are well described by a competition between charge dissociation and charge recombination leading to the appearance of a voltage threshold above which the internal electric field can be implemented. Nevertheless, depending on the type of silica (purity, fabrication process etc.), differences up to two orders of magnitude have been reported for secondorder optical efficiency [6.114]. As an example, Fig. 6.19 compares the SHG efficiency measured for two poled silica (Infrasil® and Suprasil® ) using the Maker fringe technique. Such a technique simply consists of measuring the SHG signal in transmission as a function of the angle of incidence between the incident laser and the sample. The rota-
Fig. 6.18a,b Thermal electrical poling of glass: (a) formation of a mobile cation depleted zone during the poling; (b) description of the procedure of poling corresponding to the application of a DC electric field during heat treatment and its preservation during cooling
tion of the sample permits us to induce a change of the optical path inducing the observation of interference fringes. In Fig. 6.19, the two poled silica plates exhibit completely different SHG patterns, mainly due to differences in the thickness of the SHG active layer, but the key point concerns the SHG efficiency that shows a difference greater than one order of magnitude. It is now believed that the SONL efficiency is highly dependent on the initial glass composition and notably the amount of both mobile alkali cations and hydroxyl impurities. The best results were obtained for the Infrasil® silica type with alkaline content (NaC , LiC , KC ) in the order of few ppm [6.115]. Optical Devices Based on Thermally Poled Silica-Based Glass Planar Devices. As opposed to natural birefringent crystalline materials like the standard KDP (KH2 PO4 ) and BBO (BaB2 O4 ) used for frequency conversion, phase matching conditions cannot be achieved in thermally poled glasses. Nevertheless, quasi-phasematching (QPM) conditions are possible if a spatial distribution of the induced electric field can be inscribed in the material. The principal methodologies used to spatially structure the embedded electric field in thermally poled silica are based either on a local erasure of a macroscopic poled surface or on the use of periodic electrodes. As the coherence length of silica is rather large (on the order of 3040 m for a harmonic wave at 532 nm), the spatial resolution needed to obtain the QPM condition can be reached quite easily by the use of classical lithography methods, for example, to fabricate either masks or periodic electrodes. We will focus now on some devices designed from poled silica-based planar waveguides, on their performances, and on the fabrication methods. Chao et al. polarized planar waveguides (14 mm of length) fabricated from a silica glass film doped with germanium oxide. Aluminum masks and 266 nm UV light exposure (46 ns pulse width and 8 mJ pulse power) were used for a local erasure of the implemented static electric field. The low second-order nonlinearity achieved
Nonlinear Optical Properties of Glass
a) SHG peak power (W) 3 ×10
6.5 Second-Order Optical Properties in Glasses
211
b) SHG peak power (W)
–8
1.5 ×10 –9
1.5 ×10 –8
5 ×10 –10 5 ×10 –9
0
–40
–40 θ (°)
0
–40
–40 θ (°)
Fig. 6.19a,b Second harmonic generation Maker fringe patterns as a function of the internal angle of propagation measured for Infrasil® (a) and Suprasil® (b) poled silica types (after [6.114]) .2/
Thermally Poled Optical Fibers. To compensate the intrinsically low nonlinear coefficient of poled silica, electro-optical modulators or frequency convertors have also been developed using poled silica glass fibers, with the idea of increasing the length of the light path. Two methods to apply a thermal electrical poling treatment to optical fibers have been tested: (i) using a D-shaped fiber on which a periodical electrode can be applied [6.120, 121] and (ii) by incorporating two electrodes within a twin-hole fiber [6.122, 123]. With respect to the first approach, an efficient frequency doubling of 20% has been reported, but rather limited
SiO2 SH + F Electrode BPSG SiON SiO2 Si F
Fig. 6.20 Device containing three waveguides with different quasi-phase-matching periods (after [6.118])
additional results have been published to confirm this performance. By designing composite optical fibers with embedded electrodes several electro-optical modulators were successfully designed, and the poling treatment was modeled (Fig. 6.21). Particular attention was paid to the electrode/clad geometry, as well as to the electrical configuration of the treatment. It was notably found that using a two-anode configuration i. e., both internal electrodes of a twin-hole fiber at the same anodic potential resulted in strong nonlinearity comparable with the conventional bulk cases [6.124–127]. Finally, important technological efforts have been made and are still in progress to use poled silica in
Part A | 6.5
(eff D 0:03 pm=V) limits the conversion efficiency of this particular device [6.116]. Similarly, a second-order nonlinear grating has been fabricated using uniform thermal poling followed by periodic erasure inside an e-beam deposition. Nevertheless, the overall performance of this device remains insufficient, with a very low effective nonlinear coefficient of 0:0075 pm=V [6.117]. Fage-Pedersen et al. obtained the best results so far with SiO2 films using periodical electrodes. A precise control of the quasi-phase-matching wavelength and bandwidth was observed due to the high periodic contrast of the nonlinearity with an effective .2/ of 0:13 pm=V [6.118]. The same authors related good performance of their device with the use of encapsulated periodic electrodes positioned as close as possible to the core layer (Fig. 6.20) [6.119].
212
Part A
Fundamentals of Glass and the Glassy State
Fig. 6.21
Example of a microstructured optical fiber designed for electrical poling. In black: the holes for electrode insertion; in white the core of the fiber. Reprinted from [6.128]
photonic devices, but their use as frequency converters turns out to be limited because of the weakness of their intrinsic SONL responses.
Part A | 6.5
Thermal Poling of Cation-Rich Glasses The pioneer work concerning electrical polarization processes of cation-rich glasses was published by Carlson et al. in the 1970s, [6.129–132], but the first report concerning SONL in thermally poled ionic glasses was published in 1998 on soda lime and borosilicate commercial glasses [6.133]. In these first works, it was notably demonstrated that a complete depletion of mobile cations can be formed at the anode side of the poled ionic glass, which involves a very large displacement of matter and significant composition variations. Within this depletion layer, large SONL responses have been observed for a large variety of oxide glasses such as silicate, borate, phosphate, and germanate [6.134–140]. As an example, a .2/ up to 5 pm=V was obtained on sodium niobium borophosphate (Fig. 6.22). Polarization Mechanisms in Cation-Rich Oxide Glasses and SONL. As was shown in the previous example, the complete charge dissociation process occurring during thermal poling treatment involves large displacements of mobile cations towards the cathode. To counterpart this cation departure, two main compensation processes have been proposed. First, most authors have agreed on the role of protonic species injection from air, which could be described as an ion-exchange process driven by an electric field and corresponding to an open-anode poling configuration. Second, if one considers a blocking anode, the conductivity of negative charge carriers, involving large structural rearrangements, have to be taken into account. In order to describe the relative influence of these two compensation mechanisms in cationic glasses, an important number of studies have dealt with the influence of the treatment atmosphere on the structural rearrangements within the glass matrix [6.139, 142–144].
Two examples of this methodological approach, combining a state-of-the-art correlative technique with Raman spectroscopy and SHG microscopy is shown in Figs. 6.23 and 6.24. The Raman maps show the different structural rearrangement attributed to the two main compensation mechanisms for the cation depletion, which is the hydroxyl injection and the network reticulation that can lead to the formation of molecular oxygen, as shown, respectively, in Fig. 6.23a–c for silicate and in Fig. 6.24 for a sodium germano-niobate oxide glass. This modified layer at the anode side can be easily correlated to the space charge location using second-harmonic generation mapping (Fig. 6.23d). The nature of the negative charge carriers involved during the poling process to compensate the cation depletion is a complex problem that has been the subject of several studies. The respective roles of electronic and/or anionic contributions have notably been discussed on the basis of a large range of experimental data [6.140, 146–152]. Recently, a new description of these compensation mechanisms was been proposed. In the case of a semi-blocking anode, redox reactivity between different positive and negative charge carriers was proposed to explain the observation of nitrogen oxide molecular species trapped within the polarized glassy matrix by Raman spectroscopy. Second, for a blocking anode configuration, the mechanism proposed by Redkov et al. for a silicate glass describes an electronic conductivity involving (i) peroxide radical formation during the charge dissociation mechanism and (ii) their reactivity to form the new glass structure and trapped molecular oxygen [6.153–155]. Finally, as the strength of the internal electric field implemented controls the SONL efficiency, one should definitely focus on the influence of the mechanisms compensating the formation of the cation depletion. This was notably shown by comparing the .2/ values obtained for two poling treatments of a soda lime glass done in argon or in air atmosphere. The blocking
Nonlinear Optical Properties of Glass
a) I(2ω) (arb.u.)
6.5 Second-Order Optical Properties in Glasses
213
b) I(2ω) (arb.u.)
5 2.0
pp
pp
4 1.5 3 1.0
2
0.5
1
sp
sp 0 –80
–60
–40
–20
0
20
40
60
80 θ (°)
c) Na+ (at.%)
0.0
–80
–60
–40
–20
0
20
40
60
80 θ (°)
d) d33 (pm/V) 4
12 10
3
Rescaled
8
∫
(ρ(x) – n) e dx ε
2
6
1
d33 (SHG)
2 0 0
5
10 15 Depth under anode (μm)
0
0
1
2
3
4 5 6 Depth under anode (μm)
Fig. 6.22a–d Maker fringe analysis performed on thermally poled sodium niobium borophosphate glass in transmission (a) and reflection (b) mode. The experimental data are shown with bullets, the simulation with a line. (c) Depth profile of the sodium concentration measured at the anode side of the poled sample, showing a complete depletion of 12 at:% of NaC cations. (d) Depth profile comparisons of (i) the SONL active layer calculated from the Maker fringe analysis and (ii) the static electric field implemented estimated from the sodium depletion data (after [6.141])
electrode configuration (no charge injection within the glass matrix at the anode poling under argon), allows the generation of an SONL response ten times higher than the poling done in air, promoting protonic injections [6.115]. The EFISH origin of SHG signals was confirmed by careful Maker fringe analysis and modeling. The internal electric field strength was estimated to be 3108 V=m for the argon-poled soda lime glass. This value is similar to the one estimated for the Infrasil® silica-poled sample. It proves that, if the poling procedure prevents any charge injection from the atmosphere, in a cation-rich silicate glass it is possible to achieve the implementation of an internal electric field as strong
as that for poled silica. On the other hand, if hydroxyl group injection is predominant, the space charge can be almost totally compensated. .2/ Structuring in Cation-Rich Glasses Regarding thermal electric treatment and cation-rich glasses, the main advantage is linked to the possibility of using the poling process as an imprinting approach by the use of structured electrode. Such an imprinting process was notably reported for submicrometer scale structuring of surface relief [6.156, 157] and linear optical properties. One example is given in Fig. 6.25 in which the topology profile of the electrode, used
Part A | 6.5
4
214
Part A
a)
Fundamentals of Glass and the Glassy State
Fig. 6.23 (a) Raman
Raman intensity (arb.u.) 350
spectra measured from the anode surface towards the bulk of a poled soda lime glass. The silica spectra is shown as a reference for the spectral assignments. (b,c) Raman mapping showing (i) the reticulation of the silicate network and (ii) the injection of hydroxyl group. (d) SHG image measured within the same exact zone. Adapted from [6.145]. Copyright (2010) American Chemical Society
SiO2 Layer 1 Layer 2 Layer 3 bulk
D1 300 D2
250
3000
200
3500
4000
150 Y = 1 μm 100 Y = 5 μm
50
Y = 14 μm
0 400
b) Si–O–Si
y (μm)
Part A | 6.5
–1 –2 –3
1200
c) Si–OH map
–2 0 2 4 6 8 10 12 14
0 4 8 12 14
0 x (μm)
800
y (μm)
2000 cm –1
d) SHG map
–2 0 2 4 6 8 10 12 14
0 4 8 10
0 x (μm)
1600
–1 –2 –3
y (μm) 0
6 μm
5 0 2 4 6
3 2 x (μm)
as a stamp during the poling process, is compared to the poled glass relief after treatment. This process has been linked to changes of the glass composition inducing density modifications and mechanical constraints governed by the electrode design. The validity of the method was demonstrated by the fabrication of diffraction grating [6.158–162]. In addition, a few reports exist on the use of this kind of imprinting process for structuring SONL response [6.164, 165]. Using micropatterned silicon substrates, microstructured second harmonic generation responses have been achieved on sodium-phosphoniobate glasses. Submicrometer-sized patterns of both surface relief and second-order optical responses were fabricated on the anode glass surface. The authors pointed out that in their poling conditions the SHG patterns do not simply follow the electrical potential expected from the anode topology [6.166]. The possibility of field enhancement effects within the microstructured electrode
1
0
10 15
–1
is proposed to play a key role to govern the charge density on the glass surface during the process. This could finally control the amplitudes of both the implemented static electric field for the SONL response and Maxwell stresses for the topology. A more advanced set of results recently showed that this kind of imprinting process allows for spatial and geometric control of second-order optical properties at the micrometer scale [6.165]. As shown in the upper part of Fig. 6.26a–c, the geometry of the optical anisotropy was characterized by SHG microscopy using a radial or azimuthal polarization state of the incident laser to probe the respective longitudinal and in-plane components: (i) at each border of the electrode, the SHG response is two orders of magnitude higher and (ii) one in-plane component is localized in between two longitudinal components (Fig. 6.26b,c). A simple electrostatic model taking in account local field enhancement and lateral poling effects allows repro-
Nonlinear Optical Properties of Glass
a) Raman intensity (VV + VH) (arb.u.)
6.5 Second-Order Optical Properties in Glasses
215
b) SHG intensity (arb.u.) Before poling Poled anode cross section
8
6
4 475
715
2
845
420 0
0
2
4
Raman intensity ratio
6
8
10 d (μm)
Raman intensity (arb.u.)
3 1550
2 1525
200
1550
400
1575
600
800
0
2
4
6
8
10 d (μm)
Fig. 6.24a,b Example of correlated SHG/Raman study done on a sodium germano-niobate oxide glass. (a) Spectral variations induced at the anode side of the glass and notably the occurrence of a band 1550 cm1 linked to the formation of molecular oxygen within the glass matrix. (b) Spatial correlation between location of the SONL response (top) and the structural rearrangements (bottom). In the Raman profile part of the figure, triangles (gray dashed curve) are linked to the intensity of the Raman band 1550 cm1 ; diamonds (brown full curve) correspond to the intensity ratio of the bands at 715 and 845 cm1 (after [6.138])
a) nm
Fig. 6.25a,b
b) nm
120
20
80
10
40
0 0
0 0
2
4
6 μm
2
4
6 μm
Topology picture and profiles of the structured anode (a) and the polarized soda lime glass surface (b). From [6.163]
Part A | 6.5
1000 1200 Wavenumber (cm –1)
216
Part A
Fundamentals of Glass and the Glassy State
a) z→
b) μm
c) SHG intensity (arb.u.)
I2ω
Edges of imprinted line
–5 x → ||x
200 0
I2ω I2ω ||y
80
5
100
0.4 μm –4
y → ||y
–2
0
60
μm
2
I2ω ||y 200
μm –5
40
150
0
20
100 5 50 μm
0.4 μm –4
d)
–2
0
2
0
50
μm
e)
0
2
4
6
8
10
12
14
16 μm
f) SHG (arb.u.) 0 200 400 600 μm 0.8 0.6
20 μm
0.4
Part A | 6.5
–60 –40 –20 0 μm
0.2 20 40 0.0 60
–0.6
–0.3
0.0
0.3
0.6 sin(θ)/λ
Fig. 6.26a–f Geometry control and micrometric localization of the electro-optical anisotropy. (a) Optical image of the surface of glass after a thermal poling imprinting process. (b,c) Longitudinal and in-plane SHG signal measured for one imprinted line. (d–f) Periodical and long-range .2/ structuring. (d) Optical image of an imprinted grating and (e) the SHG response of the grating measured in microscopy. (f) SHG diffraction pattern measured for this 4 mm2 -sized grating. From [6.165] reprinted with permission by John Wiley & Sons
ducing the experimental data. It denotes that a control of the location and the geometry of the electro-optical anisotropy can be obtained. As it can be described by simple electrostatic models, this opens the way to accurate designs of SONL response in glass by managing electric field distribution on microstructured electrodes. The potential of such a process to fabricate largescale micro-structured periodical design of secondorder optical properties has been demonstrated [6.164, 165]. The example given in Fig. 6.26d–f is a SHGgrating inscribed by poling on phosphoniobate bulk glass. The period of the SONL pattern is 5 m on a surface of several mm2 . The micrometric dimension of the pattern, as well as the long-range periodicity, was confirmed by SHG microscopy (Fig. 6.26e) and SHG diffraction (Fig. 6.26f) measurements, respectively.
SONL in Thermally Poled Chalcogenide Glasses Considering the possible use of poled glasses in photonic devices, the two main issues to be targeted are (i) an increase of the efficiency of the second-order optical response and (ii) ensuring a real temporal stability. If one consider an EFISH origin of the nonlinearity, as the magnitude of the static electric field cannot be increased in classical oxide glassy systems, high .3/ glasses should be considered to improve poling-induced .2/ values (6.18). Chalcogenide amorphous materials are based on chalcogens (S, Se, and Te) covalently bound to other suitable elements like Ge, As, and Sb used as network formers. These glasses are well known for their high third-order susceptibility .3/ , which can be a thousand times larger than that in silica glass (Fig. 6.5,
Nonlinear Optical Properties of Glass
Guignard et al. compared poling currents and SONL response as a function of the treatment duration, temperature, and voltage for two sulfur germanate systems with or without gallium [6.172]. SHG signals were generated within the first 15 m under the anode side in both glasses for different optimized poling parameters. Two distinct behaviors were clearly observed upon poling. For the gallium-containing glasses, the poling current slightly increased during the treatment, and the SHG signal increased continuously with the increase of the poling temperature until the appearance of damage. Without gallium in the Ge–S-based glasses, the poling current exhibits a severe decrease from about ten to few A and the second-order nonlinear susceptibility is maximal for a poling time of few minutes at about 170 ı C (Fig. 6.27) These behavior variations upon poling were linked to a higher electronic conductivity in galliumcontaining glasses, and two mechanisms were proposed to explain the creation of a nonlinear layer under the anodic surface. The formation and migration of charged defects towards the anode was proposed for glasses containing gallium and exhibiting a higher electronic conductivity, whereas the migration of cationic species, NaC , which was observed by SIMS analysis, may play a more important role for of the accumulation of negative charges under the anode in germanium-based sulphide glasses. For a similar glassy system, Gu et al. proposed that the mechanism of SHG in GeS2 -Ga2 S3 -CdS glasses is related to the reorientation of dipoles originating from the structural defects within the glasses. Under given poling conditions (5 kV, 280 ı C, 30 min), differences of .2/ efficiency as a function of the composition are proposed to be due to changes of the dipole’s reorientation ability with the evolution of glassy structure [6.177]. Considering arsenic-based glasses, the creation of a second-order nonlinearity was first achieved by using thermal-electric but also optically-assisted poling treatments of As2 S3 chalcogenide thin film [6.178]. As2 S3 amorphous films of about 4 m were deposited onto an indium tin oxide transparent thin electrode on a BK7 substrate. The .2/ coefficient was estimated to be greater than 0:6 pm=V whatever the used poling method. It is worth mentioning that high photosensitivity was observed induced by near band gap illumination (488 and 514 nm, 5 J=mm2, and 2:5 mW=mm2), which influenced the SONL efficiency and stability considerably. More accurate studies of the links between (i) the alkali content of the chalcogenide glass compositions, (ii) the photosensitivity, and (iii) the thermal poling-induced SONL stability have been reported [6.179, 180]. Careful Raman and SHG signal characterizations were carried out in order to improve
217
Part A | 6.5
Sect. 6.4.3). Thus, chalcogenide glasses can be considered as potential candidates to generate, after thermal poling treatment, large second-order susceptibility, which theoretically could compete with highly nonlinear single crystals in optical devices [6.10, 21, 24, 167– 171]. In addition, their large domain of transparency opens up unique possibilities for the development of new devices for promising applications of parametric frequency converters and electro-optic modulators in the IR spectral region. One should notice that in the literature, SONL induced by thermal poling in chalcogenide has been studied only for sulphide compositions and mainly for germanium or arsenic-based sulphide glasses [6.172] because of their transparency in visible and near-IR, allowing second harmonic generation measurements from near-IR and mid-IR laser sources, which is not possible for selenide or telluride glasses. Guignard et al. were the first to report strong second-order coefficients .2/ up to 8 pm=V for a Ge25 Sb10 S65 thermally poled glass [6.172]. This value was obtained using simulation based on accurate knowledge of the thickness of the nonlinear layer, ensuring the reliability of the quantitative measurement. In addition, the performance of the same glass system was found to be significantly increased by femtosecond laser irradiation [6.173]. The highest .2/ value was found to be 11:4 pm=V, 4050% larger than before laser exposure. Raman spectral changes seem to indicate that defects were created, enhancing the third-order optical nonlinearity of the glass, and as a result its second-order nonlinearity. Large SHG efficiency was also shown in chalcohalide glassy systems. Compositions 0:56GeS2 -0:24Ga2 S3 0:2KI and 60GeS2 -20Ga2 S3 -20KBr were studied by Jing et al. [6.174], and for an optimized thermal poling process (5:2 kV, 260 ı C for 120 min), the coefficient .2/ was as strong as 3:74 pm=V. Dong et al. worked on a similar system modified by silver chloride: (100 x)(80GeS2 -20Ga2 S3 )-xAgCl [6.175]. The polarization of the glass was achieved by irradiation with an electron beam with moderate energy (25 kV, 25 nA, 15 min). The SHG intensity of the irradiated glass was assumed to be about 1:5 times larger than that of z-cut quartz as a reference, and the .2/ was estimated to be greater than 6:1 pm=V. These different reports clearly demonstrate that large second-order optical response can be achieved in thermally poled chalcogenide glasses. However, these studies have also shown a restriction due to the low temporal stability of the poling effects in these glass systems, which reiterates the need for an accurate description of the poling mechanisms for these compositions [6.176].
6.5 Second-Order Optical Properties in Glasses
218
Part A
Fundamentals of Glass and the Glassy State
Fig. 6.27 Maximum SH intensity versus the temperature used for the poling process of Ge25 Sb10 S65 glass and MF patterns recorded for different temperatures from 170 to 310 ı C (after [6.172])
SHG Intensity (arb. u.) 16 310 °C 270 °C 230 °C 200 °C 170 °C 140 °C
14 12 10 8 6 –80 –60 –40 –20
0
20
40
60
80
4 2 0
150
170
190
210
230
250
270
a) SHG Intensity (arb. u.)
290 310 Temperature (°C)
b) SHG Intensity (arb. u.)
0.00020 0.00006 0.00015
Part A | 6.5
0.00004 0.00010 0.00002
0.00005 0.00000
As34Ge6Na2S58
As36Ge6S58 0
250
500
750
1000
1250
1500 1750 Time (s)
0.00000
0
10
20
360 Time (d)
Fig. 6.28a,b Kinetics of SHG signal stability for poled glasses of compositions (a) As36 Ge6 S58 and (b) As34 Ge6 Na2 S58
(after [6.179])
the understanding of SONL stability of poled chalcogenides. The discussion was based on the nature of the trapped charges within the glass matrix and was rationalized in agreement with the model proposed by Shimakawa [6.181, 182]. For a nondoped As2 S3 glass, the displacement of positive charges is four orders of magnitude lower than for the NaC -doped composition. The space formation is, thus, mainly formed by charged defects (also called self-trapped excitons), which are not stable in time and accelerate the creation of structural rearrangements upon light irradiation. On the other hand, for the NaC -doped As2 S3 compositions, the electrical current during the poling treatment is nonnegligible, and the formation of trapped charges is accompanied by structural rearrangements. Such
trapped charges are called random pairs, the SONL responses are found to be stable, and the photosensitivity within the space charge layer is almost totally reduced. As an example, in a germano-arsenic composition, the poling-induced SHG response was found to decrease rapidly in few minutes, whereas the same glass doped with 1 mol% of sodium showed a stable response for more than 1 year (Fig. 6.28). These studies on thermal electrical poling in chalcogenides have demonstrated the importance of a rearrangement of the glass matrix induced by the polarization treatment in order to stabilize the SONL properties. Nevertheless, the .2/ values achieved in these stable poled chalcogenides are very low, on the order of
Nonlinear Optical Properties of Glass
5 102 pm=V. This leads to an estimate of the static field strength on the order of a few 104 V=m, which is four orders of magnitude lower than that for oxide glasses. Both explanations of (i) the low value of the optical nonlinearity and (ii) the low stability for effective polarized chalcogenide glasses should be linked to
References
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the electronic conductivity of these glasses. This opens the route for glass chemists to prepare compositions that could have limited electronic conductivity to optimize the second-order optical susceptibility induced by thermal electrical poling in such promising glassy systems.
6.6 Conclusion In the last 30 years, the development of lasers, glass science, and associated technologies has allowed us to take advantage of numerous nonlinear optical properties of glass. Investigations have dealt with the fundamental aspects of glass response, but also innovative technologies for exploiting nonlinear optical phenomena and bringing them to practical life. These discoveries are the basis of information technology and are nowadays invading sectors such as security or health. In terms of materials, even if silica or silicatebased materials often exhibit low nonlinear optical response, the extremely low loss achieved in these materials has allowed the exploitation of nonlinear optical phenomena, often using long-distance propa-
gation. New compositions may allow reduction in the size of optical systems due to high nonlinear optical performance, if high-quality optical materials can be optimized and developed, as demonstrated in recent years. Acknowledgments. The authors gratefully acknowledge P. Canioni and Dr. Royon for their help to setup this chapter. This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Programme IdEx Bordeaux— LAPHIA (ANR-10-IDEX-03-02)
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R. Jing, Y. Guang, Z. Huidan, C. Guorong, K. Tanaka, K. Fujita, S. Murai, Y. Tsujiie: Second-harmonic generation in thermally poled chalcohalide glass, Opt. Lett. 31(23), 3492 (2006) G. Dong, H. Tao, X. Xiao, C. Lin, X. Zhao, S. Mao: Mechanism of electron beam poled SHG in 0.95GeS2 0.05In2 S3 chalcogenide glasses, J. Phys. Chem. Solids 68(2), 158 (2007) H. Zeghlache, M. Guignard, A. Kudlinski, Y. Quiquempois, G. Martinelli, V. Nazabal, F. Smektala: Stabilization of the second-order susceptibility induced in a sulfide chalcogenide glass by thermal poling, J. Appl. Phys. 101(8), 084905 (2007) S. Gu, Z. Ma, H. Tao, C. Lin, H. Hu, X. Zhao, Y. Gong: Second-harmonic generation in the thermal/electrical poling (100-x)GeS2 x(0.5Ga 2 S3 0.5CdS) chalcogenide glasses, J. Phys. Chem. Solids 69(1), 97 (2008) Y. Quiquempois, A. Villeneuve, D. Dam, K. Turcotte, J. Maier, G.S. Stegeman: Lacroix: Secondorder nonlinear susceptibility in As2 S3 chalcogenide thin glass films, Electron. Lett. 36(8), 733 (2000) W.T. Shoulders, J. Novak, M. Dussauze, J.D. Musgraves, K. Richardson: Thermal poling behavior and SHG stability in arsenic-germanium sulfide glasses, Opt. Mater. Express 3(6), 700 (2013) M. Dussauze, X. Zheng, V. Rodriguez, E. Fargin, T. Cardinal, F. Smektala: Photosensitivity and second harmonic generation in chalcogenide arsenic sulfide poled glasses, Opt. Mater. Express 2(1), 45 (2012) K. Shimakawa, S. Inami, S.R. Elliott: Reversible photoinduced change of photoconductivity in amorphous chalcogenide films, Phys. Rev. B 42(18), 11857 (1990) K. Shimakawa, S. Inami, T. Kato, S.R. Elliott: Origin of photoinduced metastable defects in amorphous chalcogenides, Phys. Rev. B 46(16), 10062 (1992)
Marc Dussauze Institute of Molecular Sciences University of Bordeaux Talence, France [email protected]
Marc Dussauze is a CNRS Researcher at the Institute of Molecular Science (ISM), University of Bordeaux. He received a PhD in Physical Chemistry of Condensed Matter from the University of Bordeaux (2005) and was a Postdoctoral Fellow at the National Hellenic Research Foundation of Athens, before entering the CNRS in 2009. He specializes in glass chemistry, nonlinear optics, as well as structural characterizations by vibrational spectroscopy.
Thierry Cardinal Institute for Condensed Matter Chemistry of Bordeaux University of Bordeaux Pessac, France [email protected]
He is specialized in new inorganic materials for photonics and laser structuring. He investigated nonlinear optical properties in glass, demonstrating the advantage of implementing noble ion-containing glass using the direct femtosecond laser writing process, local luminescence, and second-order nonlinearity.
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Mechanical P 7. Mechanical Properties of Glass
Jean-Pierre Guin, Yann Gueguen
For nonspecialists, glasses are brittle materials (in the usual sense, easy to break) devoted to optical applications or used as containers, and not as materials to be exposed to severe mechanical loading. However, glasses have been used for many years in some applications only for their mechanical properties (reinforcing fibers in composites as an example). Over the past several decades, the mechanical properties of conventional glasses (silica-based) have been largely improved to find application in probably the worst situations: be-
7.1 7.1.1 7.1.2 7.1.3 7.1.4 7.1.5 7.1.6 7.1.7
Elasticity of Glass ............................... Stress and Strain ................................. Linear Elasticity .................................. Nonlinear Elasticity in Glasses .............. Measurement of Elastic Moduli ............ Elastic Moduli and Glass Structure ........ Temperature Dependence of Elastic Moduli ................................. Pressure Dependence of Elastic Moduli .
238 240
7.2 7.2.1 7.2.2 7.2.3 7.2.4
Plasticity of Glasses ............................ Permanent Deformation of Glass .......... Hydrostatic Behavior of Glass ............... Mechanical Loading ............................ Indentation and Glasses......................
241 242 242 243 244
7.3
7.3.3 7.3.4
Fracture: Toughness, Strength and Fracture Mechanics ...................... Fracture Toughness ............................. Fracture Mechanics from Strength Considerations ............... Usable Strength: Fracture and Fatigue .. Subcritical Crack Propagation ...............
253 256 259
7.4
Conclusion .........................................
263
References...................................................
264
7.3.1 7.3.2
228 228 229 229 230 235
252 252
Part A | 7
This chapter focuses on the mechanical properties and behavior of glasses below their glass transition temperature. In this temperature range, they are usually seen as perfectly brittle materials: materials that deform only elastically, until they break. This chapter explores the behavior of glasses from the domain from elasticity to fracture. We first review the most widely used methods for measuring the elastic moduli of glasses, and the state of the art regarding knowledge of the relationship between elastic moduli and short- to medium-range order in glasses. We then discuss nonlinear elasticity in glasses, and how temperature and pressure impact on elastic moduli. But glasses can also deform plastically under high levels of compressive stress, particularly under sharp contact (indentation), because of high pressure and shear stress. This plastic deformation is highly dependent on glass composition; it results from densification and shear flow, two mechanisms that are affected by the loading path, temperature and strain rate. We examine how plasticity occurs under sharp contact (e. g., indentation, scratch), until damage appears (cracks). Finally, we examine the practical strength of glasses, which is highly dependent on resistance to surface damage as well as to crack propagation (fracture toughness). The important role of moisture is also discussed, as it is responsible for subcritical crack propagation, and thus lower durability of glass parts.
ing touched and hit every few seconds, scratched by keys in pockets and bags, dropped on the floor, or even placed in the hands of small children (e. g., as screens for smartphones). These improvements were even made initially to ensure that the windshields of planes could withstand the impact of large birds at high speeds. Nonconventional glasses (metallic glasses) have now been developed and are among the best materials for mechanical applications (high resistance to fracture). As a matter of fact, the mechanical properties of glasses
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_7
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are a critical factor in many applications. Before breaking or before being scratched, glasses deform elastically (reversibly): everything starts with an elastic deformation. This underscores the importance of understanding the elasticity of glasses. Additionally, even if we are still far from being able to predict the elastic moduli of glasses simply based on their composition, our understanding of the elasticity of glasses may provide a clue as to the structural peculiarities of glasses. Elasticity is strongly connected to the short- and medium-range order of glasses. A simple measurement of the elastic moduli of a glass can be the first step in analyzing its structure, and the first part of this chapter will focus on
glass elasticity. We typically think that once the glass can no longer withstand additional elastic deformation, it breaks (at low temperatures). Glasses are indeed brittle materials, materials that can withstand elastic deformation only to the point of breaking. Nevertheless, under sharp contact (e. g., scratch, impact, indentation), glasses can behave in a ductile way and can undergo permanent deformation, which will be the subject of the second part of this chapter. Once the ductility has reached its limit, however, sharp contact will also initiate cracks. These cracks, under mechanical loading, will propagate until fracture, as will be discussed in the last part of this chapter.
7.1 Elasticity of Glass 7.1.1 Stress and Strain We will first introduce stress as defined for a tensile test, and the corresponding strain. Consider a cylinder made of a given material (Fig. 7.1), having a cross section S. We apply a load F on this cylinder. The stress is defined as D
F : S
(7.1)
Under this stress, the cylinder will be lengthened. If the elongation is L and the initial length L, the strain " is "D
L : L
(7.2)
Part A | 7.1
The stress unit is the Pascal (Pa), and the strain has no unit. These concepts of stress–strain can be generalized for any kind of mechanical loading using stress F
and strain tensors. We consider now a cube of a given material. The normal of one of its surfaces is x, forming an orthonormal basis with y and z (Fig. 7.2). We apply a load (F) on this surface; its area is S. This load has three components F D Fx x C Fy y C Fz z :
(7.3)
We can define three corresponding stress components xx D
Fx I S
xy D
Fy I S
xz D
Fz : S
(7.4)
With the other surfaces, their normal vectors being y and z (the other surfaces have as normal vectors x, y and z), we can define six other stress components constituting the stress tensor 3 2 xx xy xz : (7.5) ¢ D 4yx yy yz 5 zx zy zz x;y;z The equilibrium of the moment of the forces inducing the stresses implies that (Cauchy’s second law) the
∆L y
σxy
L x σxx
Fig. 7.2 F
Fig. 7.1 Tensile
test
z
σxz
Components of the stress tensor
Mechanical Properties of Glass
stress tensor is symmetric: ij D ji . When only xx or yy or zz is not null, it corresponds to a tensile/compression test. When only ij for i ¤ j are not null, it corresponds to a pure shear test (such as torsion), and when xx D yy D zz D p, p is called isostatic pressure. Under stress, the surface having x as a normal vector can move in the direction of x (the displacement is ux ), y (uy ) or z (uz ). In the framework of small strain assumption, the strain tensor is defined as 2
"xx © D 4"yx "zx
"xy "yy "zy
3 "xz ; "yz 5 "zz x;y;z
(7.6)
(7.7)
Because of their inherent disorder, glasses made by the conventional melt-quenching method are expected to be homogeneous and isotropic. When only a small strain– stress is applied, most inorganic glasses behave as linear elastic bodies. The relationship between the stress tensor and the strain tensor is
"yy D "zz D "xx :
(7.11)
K is called the bulk modulus. "xx C"yy C"zz corresponds to the relative volume change (V=V). For a pure shear test, as an example, if xy D yx ¤ 0, all other stress components being null, and if ux D 0 xy D
E E duy "xy D : 1C 2.1 C / dx
(7.12)
duy ; dx
(7.13)
is the shear modulus and is given by D
E : 2.1 C /
(7.14)
When materials such as glasses undergo deformation, their atomic distance is increased or reduced. To understand why the relationship between stress and strain is or is not linear, let us consider a simple interatomic potential, proposed by Morse [7.2] and simplified here U.r/ D U0 .1 exp Œa.r re //2 ;
(7.15)
where U0 is the energy of dissociation, r the interatomic distance, and re the interatomic distance at rest (at T D 0 K and with no load applied). We can now approximate U around re using the second-order Taylor series U.r/ D U0 a2 .r re /2 :
(7.16)
(7.9) x
All other strain components are null. E is the Young’s modulus (Pa), and the first relationship is known as Hooke’s law [7.1]. is the Poisson ratio (1 < < 0:5). These two elastic parameters are sufficient to describe all the elastic deformations under any kind of stresses. When a pure isostatic pressure () is applied E ."xx C "yy C "zz / D pI "xx D "yy D "zz : 3.1 2 / (7.10)
σxy duy γ
dx
y
Fig. 7.3 Shear σxy
stress and resulting distortion
Part A | 7.1
(7.8)
where tr.¢/ D xx C yy C zz and I is the identity tensor (its diagonal terms are 1, all others are 0). For a pure tensile test, in the direction of x xx D E "xx I
E 3.1 2 /
KD
7.1.3 Nonlinear Elasticity in Glasses
7.1.2 Linear Elasticity
1C
¢ tr.¢/I ; E E
All other strain components are null, and
tan
In particular, for a tensile test "xx D dux =dx, and since the displacement is a linear function of x, with ux .x D 0/ D 0 W "xx D ux .L/=L D L=L.
©D
229
The shear stress induces a shear distortion angle ( see Fig. 7.3). In the framework of a small strain assumption
where 1 dui duj "ij D "ji D ! "xy C 2 dxj dxi 1 dux duy C : D "yx D 2 dy dx
7.1 Elasticity of Glass
230
Part A
Fundamentals of Glass and the Glassy State
The Morse potential and this approximation are plotted on Fig. 7.4. The load (F) required to expand the interatomic distance derives directly from U (F D dU=dr) and is consequently a linear function of r, around re , and only around re , and it can be seen in Fig. 7.4. Accordingly, Hooke’s law is only valid when the glasses undergo a small strain (.r re /=re 1). All solids are assumed to exhibit nonlinear elasticity as soon as they can support a sufficiently large strain (without breaking or undergoing plastic deformation) to make this nonlinearity detectable. Since nonlinear elasticity occurs under large strain, let us introduce true strain. We consider a cylinder having an actual length L under a given tensile stress. The stress is increased, inducing an elongation dL. The corresponding strain increment is dL : L
d" D
(7.17)
The true strain is thus given by ZL
ZL d" D
"D L0
L0
L dL D ln ; L L0
(7.18)
where L0 is the initial length of the cylinder (at zero stress). For inorganic glasses, the relationship between tensile stress and true strain proposed by Gupta and Kurkjian [7.3] is E1 E2 ."/ D E0 " C "2 C "3 2 6
(7.19)
Part A | 7.1
E0 is the conventional Young’s modulus, E1 is called third-order Young’s modulus and E2 fourth-order U(r)
U(r)
0.98
1.00
1.02 r/re
Young’s modulus. The values of these moduli are given for some glasses in Table 7.1. According to (7.19) and to the data of Table 7.1, the stress–true strain curve of fused silica (SiO2 ) deviates from Hooke’s law by 1% when the strain reaches 0:184% and the stress 131 MPa. For the Na2 O-Al2 O3 SiO2 , the deviation will be 0:1% at 12 GPa. We can observe that the apparent Young’s modulus (d=d") of most glasses decreases when the stress increases, as expected from the interatomic potential plotted in Fig. 7.4. However, the apparent Young’s modulus of fused silica and GeO2 first increases when the stress increases: they are called anomalous glasses. Mallinder and Proctor [7.4] interpret this anomaly in terms of free volume. Fused silica has a large free volume, so that bond angle distortions are easily produced when the stress is applied, and the Young’s modulus is relatively low. But once this deformation mode has reached its limit, the glass deforms mainly through bond stretching, a more rigid mode of deformation, and Young’s modulus increases. Normal glasses have a reduced free volume, so the effect of bond angle distortion is limited. This anomaly could also be due to a polyamorphic transition we will discuss later. All glasses are assumed to have a zero Young’s modulus at a given stress (and a negative one above) according to (7.19), but this stress has never been reached experimentally.
7.1.4 Measurement of Elastic Moduli For isotropic material such as inorganic glasses, it is sufficient to measure two elastic parameters (such as E and ) to deduce all the others. Since Young’s modulus (E) is defined as the ratio between the tensile stress and the strain induced in the direction of loading, and Poisson’s ratio ( ) by the ratio between the strains, it seems obvious that a tensile test would be the best way to measure the elastic properties. Nevertheless, while this method is widely used for metals or polymers, it is rarely used for brittle materials such as inorganic glasses, because samples for tensile tests are much more difficult to prepare, and less expensive and less timeconsuming techniques exist. Table 7.1 Values of the elastic moduli of nonlinear elastic-
ity at room temperature for some glasses [7.3] Glass composition
0.0
0.5
1.0
1.5
2.0
2.5
3.0
r/re
Fig. 7.4 Interatomic potential (Morse potential, solid line) and its approximation around the equilibrium position, using the Taylor series (dashed line)
SiO2 Na2 O-Al2 O3 -SiO2 B2 O3 GeO2 As2 S3
E0 (GPa) 72:3 74:1 14:3 43:9 15:3
E1 (GPa) 772:4 0:9 34:3 210:7 132
E2 (GPa) 11 084 0 0 0 0
Mechanical Properties of Glass
Cantilever Beam-Bending Test for Fibers The Young’s modulus of a fiber can only be measured by recording its curvature when it is fixed at just one end, positioned horizontally and subjected to its own weight [7.7]. The Young’s modulus is given by ED
2gL4 fd 2
(7.20)
g is the acceleration of gravity, the density of the fiber, L the horizontal projected length of the fiber, d its diameter, and f the deflection of the end of the fiber. This method only requires good measurement of the
231
density and the diameter, a long enough fiber (L d), and a method to measure the deflection (camera). When sufficiently large strains are achieved (i. e., when fibers with sufficient length are used [7.7]), the uncertainty is acceptable (< 10%). If the fiber is naturally bent, for example because of the process used to prepare it, everything becomes more complicated. Young’s Modulus Measurement Using a Mechanical Test While the tensile and compression tests are rarely used to measure the elastic properties of brittle materials, the three-point beam-bending technique is still used [7.8], although not widely, for glasses. This method consists of taking a beam of glass supported by two cylinders on the bottom (the distance between the cylinders is L); a load is applied on the top through another cylinder, exactly in the middle (exactly between the two bottom cylinders). The relationship between the deflection induced in the middle (f ) and the load (F) is fD
FL3 ; 48EIG
(7.21)
where IG is the second moment of area: d 4 =64 if the beam is a cylinder of diameter d, bh3 =12 if the beam has a rectangular section of height h and thickness b. Compared to a tensile test, with a sample of similar geometry the displacement (elongation/deflection) is considerably higher with the bending method, for an equivalent stress. However, the length L must be at least ten times that of all other dimensions (Euler–Bernoulli beam theory [7.9]), but not so great that the deflection of the sample, due to its own weight, becomes negligible. Additionally, to reduce the uncertainty regarding the determination of E, large deflection must be achieved (much larger than the uncertainty associated with f ), so again, surface flaws must be avoided to increase the failure stress. Finally, this test provides only Young’s modulus and no other elastic moduli (at least one is missing to obtain all others). Ultrasonic Measurements The strain tensor derives only from the displacement fields, and the stress tensor from the load applied (7.4), (7.7) and (7.8), so that in the framework of linear elasticity, we can directly write a relationship between the load and the displacement field irrespective of the mechanical loading and the sample geometry. Consequently, by converting the load into the associated elastic displacement, Newton’s second law becomes, when the displacement field is u.x; y; z; t/ D ux .x; t/x and when the gravity is neglected (known as the Navier–
Part A | 7.1
First of all, for a tensile test, large stresses (and strain) must be reached to obtain a low uncertainty of measurement on the elastic moduli: a large load and elongation, compared to their respective uncertainty, must be reached. For inorganic glasses, it can be achieved only with a well-prepared sample, free from any consequent surface defects; in other words, with well-prepared surfaces to avoid failures at low stresses. Obviously, compression tests could be done instead; but for compression tests, the geometry must be carefully chosen to avoid buckling [7.5] (long sample) or barreling [7.6] (short sample: it takes the form of a barrel under compression because of the surface friction). Additionally, under compression, the sample is still very sensitive to surface flaws because of the positive strain in the transverse direction. Secondly, tensile or compression tests must be performed under quasistatic conditions. A tensile test makes sense here only if the stress and strain are homogeneous. Under dynamic loading, they are not: it seems obvious that during an impact, the stress–strain are first larger close to the impact, until the mechanical wave propagates inside the sample, at the speed of sound. A fast tensile test is nothing less than a slow impact. Strain and stress are considered as homogeneous only during quasi-static loading, typically achieved when the strain rate is lower than 104 s1 . In this situation, when moduli are measured at high temperatures, for oxide glasses or at room temperature for low-Tg glasses, the strain rate becomes too slow and viscous flow impacts the measurement of elastic moduli. Finally, tensile and compression tests can be seen as destructive tests, since larger stresses are targeted to increase measurement reliability (i. e., failure stresses). These are all reasons why other, typically nondestructive techniques requiring less sample preparation are preferred. Please note that most of the methods presented here also allow the measurement of viscoelastic properties, but we will focus only on the measurement of elastic moduli.
7.1 Elasticity of Glass
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Fundamentals of Glass and the Glassy State
Lamé equation) . C 2 /
@2 ux @2 ux D 2 ; 2 @x @t
(7.22)
where D E =.1 2 2/. (C2 ) is also called longitudinal modulus (noted CL ). Considering a standing longitudinal wave ! ux .x; t/ D A cos x cos.!t/ ; (7.23) vL where A is the maximum amplitude of displacement, ! the pulsation of the wave, and vL the velocity of the longitudinal wave form. Equation (7.22) gives CL D vL2 :
(7.24)
It is important to note that since the equation involved is Newton’s second law, the velocity always depends on the density, which must be known or deduced. Now, considering a standing transverse wave ! uy .x; t/ D A cos x cos.!t/ : (7.25) vT The corresponding Navier–Lamé equation gives
@2 uy @2 uy D ! D vT2 ; @x2 @t2
(7.26)
Part A | 7.1
where vT is the velocity of the transverse (or shear) wave form. Consequently, by measuring the longitudinal and transverse velocities, we obtain two elastic moduli (CL and ), and all the other moduli can be calculated. In particular 3v 2 4v 2 E D L 2 T : vL 1 vT
(7.27)
These sound velocities are usually measured by a pulseecho technique [7.10, 11]. The method is called ultrasonic echography or ultrasonic spectroscopy. A pulse is produced at the surface of the sample using a piezoelectric transducer, typically at frequencies larger than MHz. The pulse propagates through the sample to reach the opposite surface, parallel to the first one, is partially reflected and goes back to the transducer, acting also as a receiver. By measuring the transit time of the pulse, thanks to the piezoelectric transducer, and if the thickness is known, the velocity is deduced. Two transducers are used separately, one producing longitudinal waves and the other producing shear waves. Ultrasonic pulses are typically used, because the corresponding
wavelength is short. For fused silica, at ambient conditions, the wavelength of shear waves is D vT =f D 3740 m s1 =f , where f is the frequency, and thus is lower than 1 mm at 3:8 MHz. When the sample size is lower than the wavelength, the waves cannot propagate under proper conditions. Additionally, if the glass has at least one small stress relaxation time ( ), as compared to f 1 , viscoelastic effects influence the wave propagation, and elastic moduli are no longer properly measured. When the frequency is larger than 1 MHz, the measurements will be affected only by relaxation time in the range of 1 s: typically, in inorganic glasses, the measurements are not affected by viscoelastic effects below and even slightly above the glass transition temperature. This is why elastic moduli are also referred to as moduli at infinite frequencies or unrelaxed moduli, because if the condition f ! C1 could be reached, the measurements would never be affected by viscoelastic relaxation and would always provide the elastic moduli. Ultrasonic spectroscopy is nondestructive, requires a small amount of glass (the dimensions only need to be larger than the wavelength), typically a few cubic centimeters, and theoretically works even at high temperatures [7.12]. However, it does not work when the glass is not homogeneous (at the scale of the wavelength), that is, if the glass contains many bubbles, defects or crystals. Ultrasonic spectroscopy is used elsewhere to detect these defects, but cannot be used to measure the elastic properties. The wave interacts with the defect (reflection, diffraction) so that the transit time cannot be measured. To solve this problem, one can focus on the surface waves instead of the bulk ones, which interact with defects. Surface waves (Rayleigh waves) can be produced by a focused piezoelectric transducer (acoustic microscopy [7.13], developed mainly for imaging) or by laser irradiation (laser-generated surface acoustic wave technique [7.14]). Basically, the latter method still consists in measuring ultrasonic wave velocities to determine the elastic moduli. It must be underlined that the mechanical waves induced in the glass with these methods produce a ridiculously small stress, so that if the glass undergoes nonlinear elasticity, the methods only provide the elastic moduli at low stress (E0 , not E1 and E2 ). Resonance Techniques Who has never passed a finger around the top of a glass to make it ring? The musical note produced by the glass depends on its geometry (and the wine/water level inside) and on its physical properties, including the elastic moduli. Let us consider a beam made of an isotropic material, in the framework of linear elasticity. The length of the beam is L. Three kinds of free vibra-
Mechanical Properties of Glass
tions can be induced in the beam: elongation, torsion and bending (just like a xylophone bar). The natural frequencies of these modes, if the beam is free (no limited displacement at any point of the beam), are given by the following relationship s i fi D 2L
E ;
i 2 f1; 2; 3; : : : g
(7.28)
for elongational (or longitudinal) vibration (i D 1 the first mode, i D 2 the second) i fi D 2L
r
;
i 2 f1; 2; 3; : : : g
(7.29)
for the torsional vibration, and k2 fi D i 2
s E IG ; S L4
i 2 f1; 2; 3; : : : g
(7.30)
E D 1:26189
fi2 L4 T1 ; d2
(7.31)
where f1 is the frequency of the first mode of bending vibration and T1 is a correction factor (D 1 if no correction), basically to take into account the approximation made using the Euler–Bernoulli beam theory. The problem is that T1 not only depends on the sample
233
dimension, but also on Poisson ratio, which is assumed to be unknown by the user, since he wants to measure it. For a long beam (L=d > 20), the Euler–Bernoulli beam theory is quite accurate and the correction factor is lower than 1:01235 [7.15], so that the error on E is assumed to be lower than 1%. For a rectangular beam (length L, height h, width b), we have (using (7.29) and (7.30)) E D 0:946415
f12 L4 0 T1 and D 4 f12 L2 B ; (7.32) h2
where f1 is the frequency of the first mode of bending vibration and the first mode of torsional vibration. T10 is again a correction factor (not equal to T1 , because it depends on the sample geometry). Again, T10 corresponds to a correction of almost 1% if L is at least 20 times as large as b and h. B is also a correction factor that depends only on the sample geometry [7.15] BD 4
h b
C hb h 2
b h
2:52
b
C 0:21
h 6 :
(7.33)
b
A vibration can be easily induced in a sample just by disturbing its equilibrium state. Various methods exist to do so. A method conventionally used is the impulse excitation technique [7.16, 17]. Basically, the sample is impacted by a projectile shot by a pneumatic gun (obviously, a lightweight projectile at low speed). A microphone close to the sample records the sound produced (Fig. 7.5), and using a fast Fourier transform, the resonance frequencies are extracted and the moduli calculated. The technique used to analyze the signal is called resonance frequency and damping analyzer (RFDA). Obviously, the sample cannot be free, as assumed by the equations used: it is supported by wires (made of platinum, as an example) placed at the node of the first mode of bending vibration in order not to disturb this mode (used to determine the moduli) [7.16, 17]. For the beam-bending vibration, the nodes of the first mode are at 0:224 L from the ends of the sample (it is also where the bars of a xylophone are fixed). This method can be used at high temperatures [7.16]. The practical limit for glasses is due to the viscosity: above Tg , first the glass will start to deform under its own weight, and the damping becomes too large to obtain a good signal. Measurements can typically be done up to 1:1 Tg . Because the density of the sample comes into play in the calculation of elastic moduli, the thermal expansion must be taken into account to calculate the actual density at a given temperature. The elastic moduli (M D E or ) can be
Part A | 7.1
for the bending vibration according to the Euler– Bernoulli beam theory. S is the cross section and IG the second moment of area of the beam. ki are values depending on the mode i. It cannot be calculated analytically for a free beam (ki is the i-th solution of cos.x/ cosh.x/ D 1 for a free beam), but the numerical values for the four first modes are: k1 D 4:73004, k2 D 7:8532, k3 D 10:9956, k4 D 14:1372. Consequently, by inducing a vibration of a beam and by measuring the vibration frequencies induced (the musical note), the elastic moduli can be easily deduced. For fused silica, at room temperature, for a beam of 50 mm in length, the frequency of the first torsional mode will be around 3:8 kHz. The first bending mode, will be around 100 Hz, if the beam is a cylinder of diameter 5 mm. Again, this frequency is assumed to be large enough to consider that the measurement is not affected by viscoelastic processes below the glass transition range of usual inorganic glasses. Various geometries of samples can be used, such as rectangular beam, cylinder or even disk. For a cylinder (length L, diameter d), the torsional vibration is quite difficult to induce, but for the bending vibration, the Young’s modulus is given by (using (7.30)) [7.15]
7.1 Elasticity of Glass
234
Part A
Fundamentals of Glass and the Glassy State
by [7.19, 21]
To computer: FFT Microphone
f D ˙
Furnance
Waveguide
Sample
Wire
Projectile
Pneumatic gun
Fig. 7.5 Schematic of a RFDA
corrected using the following equation [7.15] MT D MRT
fT fRT
2
.1 C ˛ T/1 ;
(7.34)
Part A | 7.1
where the index T represents the temperature of the measurement, RT is the room temperature, ˛ is the linear thermal expansion coefficient, and T the temperature difference between T and the room temperature. However, considering that T D 1000 K, and even if ˛ D 105 K1 , the correction is lower than 1%. Brillouin Scattering Brillouin scattering is an inelastic scattering of light in a solid or liquid medium induced by acoustic waves (photon–phonon interaction). Brillouin explained that the scattering is due to a periodic variation in the density of the medium acting as a diffraction grating [7.18, 19]. The scattering is inelastic: the radiation energy of a scattered photon is not equal to the energy of the incident photon. The energy of the photon can decrease because a phonon (or other quasi-particle) is created (Stokes event), or can increase because a phonon is absorbed (anti-Stokes event) [7.20]. Consequently, a frequency shift (f ) of the photons occurs (between the incident and the scattered photons): the frequency increases for a Stokes event (positive shift) and decreases for an anti-Stokes event (negative shift). This shift is given
2n sin v; 2
(7.35)
where is the wavelength of the incident light, n the refractive index of the glass (at the wavelength ), v the acoustic wave velocity and the scattering angle. Basically, this relationship between the frequency shift and the acoustic wave velocity can be seen as a Doppler shift. It can be measured using a Fabry–Pérot interferometer [7.22], and the acoustic wave velocity thus deduced. With oxide glasses, for a wavelength around some micrometers, the typical shift is between 1 and 100 GHz (far below the Raman shifts). For isotropic materials such as normal glasses, four peak shifts are observed on the Brillouin scattering spectrum: two symmetric shifts (Stokes and anti-Stokes: Brillouin doublet) for the longitudinal acoustic waves (called LA), and two symmetric shifts for the transverse wave (TA) [7.23]. The shifts due to the TA are smaller. In backscattering mode ( D 0), the wave vectors of the phonon and the light point in the same direction [7.24], and only the LA shifts are observed. Once the longitudinal and transverse waves velocities are deduced (n must be known), the longitudinal and shear modulus can be calculated using (7.24) and (7.26), but the density must also be known. Although commercial equipment is available for ultrasonic spectroscopy and resonance frequency measurements, Brillouin spectroscopy is clearly less pushbutton, and is thus less commonly used for measuring simple elastic properties. Nevertheless, Brillouin spectroscopy enables the measurement of elastic moduli of very small samples (a few cubic millimeters or less [7.25]) and is particularly well suited for measurements at high temperatures [7.25, 26] and under high pressure (under diamond anvil cells as an example [7.27]), mainly because this is a contactless measurement. Very large pressure can be reached (> 50 GPa), as has been achieved for fused silica [7.28]. Obviously, the refractive index is required to determine the elastic moduli, and is assumed to be known at a given pressure/temperature. To obtain the refractive index, one technique consists of combining the results of two Brillouin scattering geometries (symmetric 90ı and backscattering geometries [7.29]). Nowadays, Brillouin scattering is probably the only method for measuring the elastic moduli of oxide glasses in situ during their densification at high pressure [7.30]. Another advantage of using this method is the ability to probe natural elastic acoustic waves, so that the elastic moduli can even be measured in the liquid state, and thus at higher tem-
Mechanical Properties of Glass
peratures than in ultrasonic spectroscopy or resonance techniques. We must also emphasize here the difference between isothermal and adiabatic moduli. Basically, when the material has time to release the mechanical energy provided during the measurement into heat, the elastic moduli are isothermal. When it does not have enough time to do so, it is adiabatic. The Brillouin scattering allows the measurement of adiabatic moduli (because it corresponds to high frequencies). However, for most inorganic glasses, especially oxide glasses, the difference between adiabatic and isothermal moduli is negligible. Instrumented Indentation and Elastic Moduli Nowadays, micro- or even nano-indentation devices are increasingly used in laboratories or industry. Consequently, it is increasingly common in publications to see values of Young’s modulus measured by instrumented indentation using the Oliver and Pharr methods [7.31]. It is important to note that the conventional indentation techniques do, indeed, enable the measurement of an elastic modulus (and only of one modulus), but this is not Young’s modulus. This is the reduced or indentation modulus E D
E : 1 2
(7.36)
7.1.5 Elastic Moduli and Glass Structure The bulk modulus (K) of a material represents the ratio between the isostatic pressure applied and the relative volume change induced (V=V). This volume change is due to bond length and bond angle changes. K is in Pascal, so that it corresponds also to Joules per unit volume (Pa D J m3 ). In other words, the bulk modulus can be related to a density of energy. Bulk moduli of usual inorganic glasses typically range between 10 (a-Se: 9:6 GPa [7.32]) and 160 GPa (Pd40 Cu30 Ni10 P20 : 159:1 GPa [7.33]). The bulk moduli of soda-lime or alumina-silica glasses range between 30 and 40 GPa [7.34]. First Grüneisen Rule and Bulk Modulus According to the work of Grüneisen, the bulk moduli of a solid can be related to the interatomic potential, the bonding energy and the molar volume [7.35]. The first
235
Grüneisen rule gives pV C U.V/ D E ;
(7.37)
where V is the volume, E is the energy of atomic vibrations (E D 0 at 0 K) and the dimensionless Grüneisen parameter. U is the interatomic potential. If a Mie– Coulomb potential is used, h r n n r m i m e e : (7.38) U0 U.r/ D nm r m r U0 and re are already defined in (7.15), and m and n are the exponents for the attractive and repulsive forces, respectively; it gives [7.34, 36], at 0 K (see also [7.37]) KD
mn U0 ; 9 V0
(7.39)
where V0 is the equilibrium volume per mole if U0 is per mole. Consequently, the bulk modulus is proportional to the density of energy. It implies that solid materials have large bulk moduli not only if their bonding energies are high, but also there is a large density of bonds. As an example, the bulk modulus of the hexagonal selenium is 22:45 GPa, the bonding energy of the Se– Se bond is 330 kJ mol1 (V0 D 16:42 cm3 mol1 ) [7.38] and the coordination number of Se is 2. The bulk modulus of the face-centered diamond cubic germanium is 77:2 GPa [7.39], even if the bonding energy is only 265 kJ mol1 (V0 D 13:65 cm3 mol1 ), because the germanium is four-fold coordinated and presents a more compact structure. However, while U0 and V0 can be estimated [7.34, 40], m and n are unknown for glasses, since they depend on the atomic bond and its type (van der Waals, ionic, covalent), and in most inorganic glasses various bond types are present (ionic and covalent at least for soda-lime glasses as an example). Additionally, if V0 can be calculated according to the molar mass and the density of the glass, U0 for a multiple-component glass is the average bonding energy: in order to calculate U0 , we must first know which bonds are present (between which atoms) and their relative fractions. When phase separation occurs, or any unexpected structural change leading to unexpected atomic bonds, U0 is quite difficult to estimate [7.40, 41]. Nevertheless, it has been observed that in most families of inorganic glasses, the bulk modulus typically increases with the calculated volume density of energy (U0 =V0 ) [7.34]. Basically, the bulk modulus of chalcogenide glasses such as As–Se glasses ranges between 10 and 15 GPa, with a U0 =V0 ratio of around 1214 kJ cm3 [7.40], whereas oxynitride glasses have a bulk modulus larger than 90 GPa, with a U0 =V0 ratio larger than 80 kJ cm3 [7.34]. The fused silica is in the middle, with K D 33:3 GPa and U0 =V0
Part A | 7.1
Accordingly, the reduced modulus is assumed to be larger than the Young’s modulus. For glasses with a large Poisson ratio, such as chalcogenide glasses or even borosilicate glasses, the reduced modulus is more than 10% larger than the Young’s modulus. If the Poisson’s ratio is unknown, the instrumented indentation does not allow a precise evaluation of the Young’s modulus.
7.1 Elasticity of Glass
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Part A
Fundamentals of Glass and the Glassy State
70 kJ cm3 . This illustrates that the elastic moduli is strongly connected to what for glasses is usually called the short-range order (SRO: the scale of atomic bonds). It is important to note that there is currently no general model that can accurately predict the elastic moduli of glasses across a wide range of compositions, as compared to solid crystals. This is mainly because glasses have structural peculiarities that are not known without comprehensive structural investigation. As an example, in the As-Se system, an estimation of U0 based on a continuously reticulated glassy network yields an incorrect estimation of the bulk modulus, since U0 and K are expected to increase when the arsenic content increases. Actually, when the As content is greater than 40%, the bulk modulus K decreases: this is because nanophase separations occur, breaking the continuity of the network and leading to an inaccurate estimation of U0 [7.40]. Therefore, the SRO is not sufficient to interpret the elasticity of a glass, and a better understanding of the medium-range order is required (MRO: the scale of the arrangement of structural units such as SiO2 rings in fused silica). On the other hand, if no structural investigation has been conducted on a given glass family, a simple estimation of the bulk moduli based on a first model of the glass structure compared to the measured moduli will quickly show whether the prediction of K using this model is or is not far from reality.
Part A | 7.1
Young’s Modulus Various models have also been developed to correlate the Young’s modulus to the glass structure. Two parameters are usually introduced: the average dissociation energy G of the components of the glass (G D xi Gi , xi being the molar fraction of the i-th component and Gi its dissociation energy) and the atomic packing density Vt . The atomic packing density is the ratio between the volume occupied by the atoms of the glass and the corresponding volume of glass. So it ranges virtually between 0 and 1. Makishima and Mackenzie [7.42] have shown that the Young’s modulus is theoretically given by E D 2Vt G :
where r is the ionic radius and N is Avogadro’s number, to have a volume per mole. Therefore the atomic packing density is [7.42] P xi Vi ; (7.42) Vt D P xi Mi where is the density of the glass, xi the molar fraction of the i-th component, and Mi its molar mass. Makishima and Mackenzie [7.42] revealed good agreement between the calculated Young’s modulus (using (7.40) and (7.42)) and the measured modulus for silicabased glasses, as shown in Fig. 7.6. However, when the Young’s moduli are large (> 100 GPa), there is no longer good agreement. Rocherullé et al. [7.43] have proposed another formulation for the atomic packing density, more suitable for glasses with large Young’s moduli and those with nonoxide components (nitride as an example) [7.43, 44] P X xi Vi Vt D xi i P ; (7.43) xi Mi where i is the density of the i-th components. When this correction is taken into account, some parameters are rather difficult to know. The ionic radii must be known, and correctly chosen, as well as the dissociation energies corresponding to the real component as present in the glass (AlO5 instead of Al2 O3 in aluminosilicate, as an example [7.44]). If (7.40), regardless of the Vt used, provides reasonably good predictions of Young’s moduli of silica-based glasses, it fails dramatically in predicting the Young’s moduli of phosphate and borate glasses. Measured Young´s modulus (GPa) 160 140 120
(7.40)
100
Let us consider an oxide glass such as .SiO2 /x1 .Al2 O3 /x2 . The packing factor of the i-th component of the glass (SiO2 or Al2 O3 here) is given by
80 60 40
4 3 Vi D .XrM C YrO3 /N 3 4 3 C 3rO3 /NI ! VAl2 O3 D .2rAl 3 4 3 VSiO2 D .rSi C 2rO3 /N ; 3
40
60
80 100 120 140 Calculated Young´s modulus (GPa)
Fig. 7.6 Comparison between the Young’s modulus mea(7.41)
sured for various aluminosilicate glasses and the Young’s modulus calculated using (7.43) (after [7.42])
Mechanical Properties of Glass
Young’s modulus is probably not as suitable as the bulk modulus for investigating the relationship between glass structure and elasticity, as it seems to be sensitive to various structural peculiarities that could have compensating effects. As an example, the Young’s moduli of fused silica and standard windows glasses (sodium aluminosilicate) are very similar (70 and 72 GPa respectively [7.34], but it is possible to obtain fused silica and window glasses having exactly the same Young’s modulus just by playing with their fictive temperature), whereas their bulk moduli are significantly different (33:3 and 44:4 GPa). Their Poisson ratios are also very different (0:15 and 0:23, recalling 1 < < 0:5).
237
when the average coordination number per structural unit is 2, it is one-dimensional (1-D; made of chains); when the average coordination number per structural unit is 3, it is two-dimensional (2-D; made of layers, such as As2 Se3 ), and when the structural units are mainly four-fold, it is three-dimensional (3-D). The Poisson ratio increases when the dimensionality decreases: it is low for 3-D networks and high for 0-D networks. This is illustrated in Fig. 7.7 for two chalcogenide binary systems (Ge-Se and As-Se): Poisson’s ratio decreases when the connectivity increases (i. e., when the dimensionality increases). The Poisson ratio increases again for these two systems when a nanophase separation occurs [7.40], associated with a connectivity loss. The Poisson ratio also seems to increase continuously with atomic packing density [7.34, 45]. This is consistent with what we discussed earlier. Strongly connected networks (3-D) are usually less densely packed (fused silica presents a relatively large free volume) than lightly reticulated networks (0-D, 1-D . . . ). Elasticity and Topology Since 30 years [7.46, 47], the physical properties of glasses have been largely investigated through topological aspects (constraint theory or rigidity theory). The basic premise of this approach is that we can schematically consider a glassy network made of covalent bonds as a mechanical truss, and count the constraints and degrees of freedom per atom. For those who use to deal with mechanical trusses, it basically consists in calculating the degree of hyperstaticity of the truss (the glassy network). This theory has been developed largely over recent decades and has been used to predict variPoisson´s ratio 0.340 Ge-Se As-Se
0.330 0.320 0.310 0.300 0.290 0.280 0.270 0.260 2.0
2.2
2.4 2.6 2.8 3.0 Average coordination number
Fig. 7.7 Poisson’s ratio of Ge-Se and As-Se glasses at
room temperature as a function of the average coordination number per atom
Part A | 7.1
Poisson’s Ratio of Glasses Poisson’s ratio ( ) has no unit and cannot be related to bonds or the density of bond energies. The Poisson ratio is the ratio between the transverse and longitudinal deformations during a tensile test. When it is negative (to our knowledge, there are no conventional glasses with a negative Poisson ratio), the sample tends to increase its transverse dimensions when it is elongated. When the Poisson ratio is 0, there is no transverse deformation. If it is positive, the transverse dimensions decrease when the sample is elongated. The relative volume change is defined as "xx C "yy C "zz . Therefore, if the initial length is L and the elongation L > 0, the relative volume change will be V=V D .12 /L=L. Since 1 < < 0:5, the volume of the sample always tends to increase under elongation, but the larger the Poisson ratio, the smaller the change in volume. In other words, materials with a large Poisson ratio tend to distort when they are stressed, and materials with a low Poisson ratio tend to change in volume [7.45]. We can take two examples of covalent glasses: fused silica and amorphous selenium. Their Poisson ratios at room temperature are 0:150 and 0:322, respectively [7.34]. The structural units of fused silica are the SiO4=2 tetrahedra, four-fold coordinated (the four bridging oxygens), whereas the structural units of amorphous selenium are mainly two-fold selenium. Fused silica is one of the conventional glasses with the lowest Poisson ratios. Oxycarbide glasses can have a lower Poisson ratio [7.34], and they have a larger average coordination number (two-fold oxygen is substituted by four-fold carbon). These examples illustrate that Poisson’s ratio is strongly correlated to the reticulation/connectivity of the glassy network: strongly connected covalent glasses have low Poisson ratios. Metallic glasses, having no covalent bonds, show very high Poisson ratios, typically 0:320:40 [7.34]. Poisson’s ratio can be seen as an indicator of the dimensionality of the glassy network [7.34]: when the glass has no covalent bond, it is zero-dimensional (0-D);
7.1 Elasticity of Glass
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ous physical properties of glasses, including the glass transition temperature [7.48], the hardness [7.49] (although hardness is better related to packing density) and the glass-forming ability, to name but a few. This theory has been successfully used to describe many glass peculiarities/properties during the last decade, and this is the reason why we have to discuss here its ability to explain the elasticity of glasses. The name of this theory (rigidity theory), by itself, suggests that we could predict the elastic moduli of glasses only using topological considerations. The rigidity of a mechanical truss is indeed—partially—defined by its hyperstaticity. This is actually what He and Thorpe proposed 30 years ago [7.50]. Tested a few years later [7.51] for predicting the elastic moduli of Ge-Se glasses, this theory has shown its limit in this domain. Up to now, to our knowledge, there is no model based on topological aspects that succeeds in predicting elastic moduli or at least that provides the relationship between elasticity and topology. This is, maybe, a good illustration of the complexity of the relationship between glass structure and elasticity.
7.1.6 Temperature Dependence of Elastic Moduli
Part A | 7.1
As discussed previously, elastic moduli are also called unrelaxed moduli, as opposed to relaxed moduli, affected by viscoelastic relaxation processes (storage and loss moduli). As soon as the timescale for measuring the elastic moduli (i. e., the inverse of the frequency if a dynamic technique is used) approaches the viscoelastic relaxation time of the glass, the measured moduli deviate from the true elastic moduli (actually, only storage moduli are measured; moduli are equivalent to elastic moduli only at an infinite frequency). For most oxide glasses, their relaxation times at room temperature are orders of magnitude larger than the inverse of the frequency used. Nevertheless, if the temperature increases, the viscosity and thus the relaxation time decreases (the relaxation time being basically the ratio between the viscosity and the shear elastic modulus), and the frequencies used are not large enough to consider the moduli measured as the unrelaxed moduli. Consequently, Brillouin scattering is probably the best technique for investigating the elastic properties of glasses up to and above the glass transition temperature (Tg ), because the measurement will be only affected by relaxation times lower than a few nanoseconds (relaxation times reached far above Tg ). For other techniques such as RFDA, we must always keep in mind that apparent elastic moduli changes observed when the temperature increases can also be due to viscoelastic effects, especially the small fluctuations that
could actually only result in ˛ and ˇ relaxations. Here we discuss the global trends observed regarding the elastic moduli measured, and not this type of small fluctuations. Glasses undergo expansion under heating, as do most materials. Consequently, the density of energy decreases, and the elastic moduli are expected to decrease when the temperature increases. However, this thermal expansion induces a very small volume change (smaller than 1% for most oxide glasses over a temperature increase of 400 ı C, below Tg ). Consequently, if elastic moduli change during heating, it would be mainly because of bond changes (nature, energy, etc.). Intuitively, when, during heating, thermal energy is provided to a glass, we expect structural changes that occur through bond breakage, ultimately reaching the liquid state, where the connectivity becomes very low. Consequently, we expect the average bond energy to decrease, leading to a decrease in the elastic moduli. This trend is actually observed for most glasses (e. g., oxide, oxynitride, chalcogenide, metallic glasses): the Young’s and shear modulus (E) decrease slowly up to Tg and dramatically fall down above Tg . For glasses with E > 10 GPa at Tg , the temperature dependence of the Young’s modulus above Tg is given by: E.T/ D E.Tg / Tg =T [7.34]. The typical evolution of elastic moduli is illustrated in Fig. 7.8 with the shear elastic modulus of a window glass. The evolution is qualitatively similar for most glasses and for all the moduli. According to the strong–fragile classification of glasses [7.52], strong glasses retain their structure upon heating, whereas fragile glasses do not. Consequently, fragile glasses should undergo a rapid decrease in their elastic moduli, at least above Tg , while strong glasses Shear elastic modulus (GPa) 30 29 28 27 Glass transition range
26 25 24
0
100
200
300
400
500 600 700 Temperature (°C)
Fig. 7.8 Evolution of the shear elastic modulus of a silica-
soda-lime glass (window glass) upon heating, measured by RFDA. Data provided by F. Célarié
Mechanical Properties of Glass
In other words, it seems obvious that thermal energy always allows glasses to explore new states with different short- or intermediate-range order. But for fragile glasses, these states would correspond to lessconnected networks, with lower elastic moduli (or at least a network with lower average bond energies). For strong glasses, the network connectivity change will be lower or even null if only polyamorphic transitions occur. Since we interpret the decrease in the elastic moduli upon heating as induced by connectivity loss, Poisson’s ratio, strongly related to the connectivity, must increase when the elastic moduli decrease. This is actually observed [7.34, 45]. Fragile glasses undergo a large increase in the Poisson ratio associated with this connectivity loss (C30% between Tg and 1:05 Tg for amorphous selenium [7.54]). On the contrary, the Poisson ratio of fused silica increases only slightly and slowly upon heating (< C4% between 0:5 and 1:1 Tg [7.34]). However, only very fragile glasses exhibit a significant increase in the Poisson ratio. If this ratio is strongly connected to the connectivity of the glassy network, it is probably not sensitive enough to highlight the relatively small connectivity changes occurring at T < 1:1 Tg . Additionally, there is no relationship between fragility and connectivity (fragility can be seen as the effect of connectivity loss upon heating, not as an effect of the connectivity itself). Therefore, because glasses with low connectivity already have a high Poisson ratio at room temperature, they would demonstrate only a small increase in this ratio (it is physically limited to 0:5) even if they were very fragile. Glasses below their Tg are metastable materials, out of their thermodynamic equilibrium. They can reach this state of equilibrium through structural relaxation. This relaxation process is thermally activated, thus becoming slower and slower as the temperature decreases. The sharp (usually along a few degrees Celsius) change in the slope of elastic moduli versus T observed at Tg reflects the transition from a nonequilibrium modulus below Tg , to an equilibrium modulus above Tg . During isothermal treatment (aging), below Tg , glasses will relax and their elastic moduli evolve. Since structural relaxation is usually associated with volume compaction, elastic moduli are assumed to increase during aging. If the fictive temperature has the same impact qualitatively as the actual temperature, reducing the fictive temperature will increase the elastic moduli for normal glasses and decrease the moduli for abnormal glasses. As an example, the bulk modulus of fused silica is 37:4 GPa when the fictive temperature (Tf ) is 1500 ı C, but only 35:0 GPa when Tf D 985 ı C [7.58]. Thus, we must keep in mind that most glasses, with Tg larger than the ambient temperature, could have a potentially much larger
239
Part A | 7.1
should maintain their elastic moduli [7.34, 53], because they retain their structure. Ge-Se glasses typically illustrate this trend [7.54]. Strong liquids also show slow viscosity changes, around Tg , upon heating, whereas fragile liquid shows a rapid change (this is the first definition of fragility). This is consistent with the shoving model of Dyre et al. [7.55], in which the temperature dependence of the viscosity is governed mainly by the shear elastic modulus: when rapid changes in elastic moduli occur upon heating, a rapid decrease in viscosity is expected. Nevertheless, some glasses present extreme behavior. The fused silica does not undergo any Young’s modulus decrease but rather a smooth increase when the temperature increases (almost C10% over 1000 ı C) [7.34]. The fused silica crosses its glass transition domain without any drastic change in its Young’s and shear moduli [7.53], and even without a drastic change in the slope of E versus T, whereas most other glasses undergo a large slope change. The elastic moduli of the GeO2 glass also continuously increase upon heating, even above Tg , but the Tg is marked by a small change in the slope [7.53]. SiO2 and GeO2 are strong glasses, so a very small decrease in elastic moduli could be expected, but they even increase. This behavior of fused silica is known as a thermomechanical anomaly. Besides this anomalous elastic moduli increase, fused silica also exhibits a negative thermal expansion coefficient (over a limited range of temperatures) and an anomalous elastic moduli decrease under pressure (to be discussed later) [7.56]. This anomalous behavior has been interpreted recently through the observance of two (at least) distinct amorphous states coexisting, but varying in proportion, during heating (this polyamorphic transition is thermally activated). These states are still not well-identified, but the transition is assumed to be due to Si–O–Si bond rotation [7.53, 56] as observed during the ˛ ! ˇ cristobalite phase transition. This is in agreement with the interpretation of Mallinder and Proctor [7.4] (Sect. 7.1.3), if we assume that free volume promotes ease of bond rotation. The transition is gradual upon heating and can occur without changing the nature of the bonds and without changing the connectivity of the network, but just impacts on the SiO4=2 ring geometry [7.56]. This specific geometry change will induce an increase in elastic moduli not compensated by bond breaking or thermal expansion. This anomalous behavior, typical of fused silica, is also observed in SiO2 -rich sodium silicates (< 15% Na): their elastic moduli (bulk, shear, Young’s moduli) increase upon heating, at least below Tg . This is interpreted also through the polyamorphic transition of the SiO2 network [7.57]. In sodium-rich sodium silicates (> 20% Na), a normal behavior is observed.
7.1 Elasticity of Glass
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Part A
Fundamentals of Glass and the Glassy State
K' (p = 0), μ' (p = 0) 9.0
nvL (km/s) 11.5 K' μ'
8.5
11.0
8.0
10.5
7.5
10.0 9.5
3.0
9.0
2.5
8.5
2.0
8.0
1.5
0
5
10
15
20
25
30 Ge (at.%)
Fig. 7.9 Initial variation rate (in Pa=Pa) of the bulk modulus (K 0 ) and the shear elastic modulus ( 0 ) at p D 0, in Ge-Se glasses. Data from [7.59]
elastic moduli if they were aged long enough or cooled at slower rates (if Tf is low). This effect has largely been investigated in metallic glasses [7.60, 61]. Most oxide glasses do not age at room temperature at human, geological or even universe timescales, because their relaxation times are too large, and their elastic moduli will not evolve. On the contrary, low-Tg glasses, such as some chalcogenide glasses, can experience significant elastic moduli increases, even at room temperature and at timescales corresponding to weeks or months [7.62].
7.1.7 Pressure Dependence of Elastic Moduli Part A | 7.1
Once again, we can imagine, intuitively, how the elastic properties of glasses will evolve under hydrostatic pressure. Under pressure, the volume will decrease, increasing the density of bond energies, thus increasing the elastic moduli. Using the classical equations of thermodynamics and the Mie–Coulomb potential (7.38), we can actually show that [7.63] K 0 .p D 0/ D
mCnC6 ; 3
(7.44)
where K 0 .p D 0/ is the pressure derivative of the bulk modulus at p D 0, and m and n are defined in (7.38), and are positive. Consequently, the bulk modulus should, at least initially, increase when pressure is applied. We also imagine, intuitively, that the bulk modulus would tend to be virtually infinite at very high pressure, when the glass will have reached a maximum compactness. Nevertheless, this compactness will never be reached without structural changes, and (7.44) implies that no structural change occurs (this is an equation at constant entropy). The bulk modulus could thus decrease
7.5
0
2
4
6
8
10
12
14 16 p (GPa)
Fig. 7.10 Anomaly of fused silica: the product of the
refractive index and the longitudinal sound velocity measured by Brillouin scattering (backscattering mode) as a function of the applied pressure (in situ). Data from [7.30]
if a specific structural change (in the broad sense) occurs. When K increases with pressure, the behavior is said to be normal, and many glasses exhibit normal behavior. Once again, the fused silica is abnormal: its bulk modulus decreases at relatively low pressure before increasing. As an example, the bulk modulus of As2 S3 goes from 13 GPa at ambient pressure to 26 GPa at pressure of 2 GPa (its shear modulus increases from 5:7 to 8:8 GPa) [7.64]. This normal behavior (moduli increase) is also observed for relatively low pressures in Ge-Se glasses (Fig. 7.9) [7.65] and various chalcogenide glasses [7.66], in fluoride glasses [7.65], Na2 OTiO2 -SiO2 glasses [7.67] or B2 O3 -Na2 O glasses [7.68]. However, in the two latter glass systems, if the bulk modulus always increases under pressure, for some compositions the shear modulus decreases. In contrast, an anomalous behavior (bulk modulus decrease) is observed in K2 O-SiO2 glasses [7.69]. The moduli of fused silica all decrease (the bulk modulus becomes lower than 30 GPa) when the pressure increases to p D 23 GPa (at room temperature), and then increases at greater pressure (see [7.58] and refs therein). This is illustrated here in Fig. 7.10 by Brillouin scattering. It is known that silica undergoes permanent densification under large pressure, but this densification starts at pressure larger than 58 GPa. In other words, the anomaly of fused silica is not due to the structural changes associated with the densification. In the domain of the anomaly (0 < p < 23 GPa), the deformation is reversible (the volume recovers its initial value if the pressure is released; see [7.58] and refs
Mechanical Properties of Glass
therein). Consequently, it is believed that the anomaly is also (like the anomaly observed when the temperature increases) due to a polyamorphic transition from a low-density phase (LDP ˇ-like) to a high-density phase (HDP ˛-like) [7.58]). At ambient pressure, the glass has a given ratio of LDP/HDP (it depends on the fictive temperature). Under pressure, this displacive
7.2 Plasticity of Glasses
241
transition occurs but is reversible (by definition), and the LDP/HDP ratio decreases; when the pressure is released, the LDP/HDP ratio recovers its initial value. Glasses with high silica content could also undergo this polyamorphic transition [7.30]. The anomaly is observed in B2 O3 glass as well, and it is believed that this is also due to a polyamorphic transition [7.70].
7.2 Plasticity of Glasses the oxide glass community, plasticity describes a nonreversible deformation through a more complex mechanism, where dislocation theory is not applicable, and volume may not be a conservative value, as will be illustrated. Please note that plasticity will hereafter include both densification and shear flow deformations! Because of their diverse composition, structure and bonding nature (from metallic to covalent), not all glass families are equal regarding permanent deformation. For instance, some metallic glasses (bulk metallic glasses; BMG) act in a similar way as metallic alloys, exhibiting a large amount of plastic deformation before fracture happens when being tested under tensile conditions. When plasticity occurs in BMGs, the plastic deformation is localized into shear bands, which remembers the preferential slipping plane mechanisms in metals. For iono-covalently bonded glasses such as oxide-based glasses (SiO2 -based glasses, for example) or chalcogenide glasses, the term brittle illustrates very well the nature of their mechanical behavior when tensile stress is applied. Far from their transition temperature (Tg ), fracture happens suddenly without evidence of permanent deformation prior to rupture (although this aspect could also be debated; see crack propagation Sect. 7.3.4). Regarding the behavior of glasses under compression, this is a totally different story: Those properties are of importance regarding both the use and lifetime prediction of glass parts. Plasticity is a milestone on the pathway to understanding why glass parts break at low stress values (tens of megapascals), while the theoretical strength of the material is two orders of magnitude larger or strength of the material is 100 times (about 20 GPa) as plasticity provides the conditions for crack nucleation. It is therefore the last brick before surface damage nucleation induced by sharp contact in glass. A better understanding of the creation of surface defects by contact would definitely help to develop better strategies to improve resistance to surface damage and subsequent crack propagation. The final goal would be to identify the constitutive law for the plastic regime of any glass (relation between stress and strain, Hooke’s
Part A | 7.2
Oxides glasses being the archetype of brittle behavior from linear elastic fracture mechanics (LEFM), the juxtaposition of the two words plasticity and glass may seem incongruous or curious to the reader. Yes, even a brittle material such as glass exhibits a plastic behavior, especially at high levels of compressive stress (GPa). However, a frame of reference is necessary in order to understand what is hidden here behind the word plasticity. From a semantic perspective, a speaker employing this word in the context of oxide glasses in front of different audiences might expect feedback ranging from no reaction to one of arousing controversy. This is why some definition with a quick historical background may provide the reader a fair understanding of the situation. Plasticity may be defined as the nonreversible deformation a solid undergoes under applied force. Following this simple definition, the fact that, for instance, a permanent deformation may be left behind on the surface of a material by a sharp, hard diamond tool after an indentation test is proof that some plastic (nonreversible) deformation occurred during the test. Now, for the history. The theory of plasticity [7.71] was developed after the theory of elasticity [7.72], and as is well described in the introduction to The Mathematical Theory of Plasticity by R. Hill, it was intended to first describe experimental observation in order to develop a mathematical framework from which to compute nonuniform stress–strain distributions. This theory began to develop in 1864 (Tresca) for metallic materials, because for this type of material, plasticity is easily observed with the naked eye at room temperature. Since then, a tremendous amount of work, catalyzed and accelerated by the two world wars and their respective postindustrial eras, has been undertaken on the plasticity of metallic materials, which refers to a specific mechanism based on dislocation theory for which plasticity occurs by slipping along specific atomic planes. It is a volume-conservative or isochoric mechanism of shear flow. This is certainly why, for a portion of the scientific community, speaking of plasticity refers to a volume-conservative mechanism through which nonreversible deformation occurs, while for others, such as
242
Part A
Fundamentals of Glass and the Glassy State
law for elasticity) in order to identify the conditions of stress and strain for crack initiation under sharp contact.
7.2.1 Permanent Deformation of Glass
Part A | 7.2
In glass, permanent imprints are left behind at the surface after an indentation test (Fig. 7.15). This is by now a well-known phenomenon, but to our knowledge, the first traces of such permanent imprints made on a glass surface may be found associated with the term sleek [7.73]: a kind of scratch that looks like a fine groove, as opposed to a larger and irregular scratch exhibiting conchoidal splintering. In this century-old work by J.W. French, such fine residual imprint was attributed to the Beilby layer, or surface flow layer, generated by the polishing process (see [7.74–76] for more information on the Beilby layer) rather than to the bulk glass, the behavior of which was considered brittle in nature. Taylor [7.77], followed later the same year by Custers [7.78], described the permanent marks left behind on different glass-type surfaces made by a sharp Vickers or cube-like-shaped diamond tool using small loads (tens to hundreds of meganewtons) as possibly resulting from some degree of plastic deformation. Both authors qualitatively described their respective optical observations (indentation imprint, scratch groove, shavings or turnings) by a direct comparison with the behavior of metallic materials from which they used the semantic. It was in 1953 that Bridgman and Simon [7.79] showed the common properties of oxide glasses, which is their capacity, under high levels of hydrostatic pressure, to permanently densify—in other words, to be permanently compacted. For sufficiently high pressure levels, glass will endure structural rearrangements at the short- (coordination number, tetrahedral to octahedral) and medium-range order (inter-tetrahedral bond angle Si–O–Si, n-fold rings statistics). He also showed the existence of two thresholds, the first of which needed to be overcome for the permanent densification to set in (near 10 GPa for silica glass), and the second (near 20 GPa for silica) above which a saturation of the densification ratio upon pressure application is observed (Fig. 7.11). Between those two thresholds, the permanent densification of the glass increases as the pressure increases. By x-ray measurement, almost no modification of the short-range order (Si–O bond distance) was observed in the densified amorphous phase, which was attributed to an atomic-scale mechanism leading to some sort of local folding of the glass network upon compression.
7.2.2 Hydrostatic Behavior of Glass From this preliminary work by Bridgman, numerous studies have since been carried out. Nowadays, high-
∆ρ/ρ 0 (%) 25 Soda-lime-silica window glass (Ji et al. (2006)) B2O3 (Bridgman et al. (1953)) FBaEuZr (Miyauchi et al. (1999)) SiO2 (present data) GeSe 4 (present data) ZrCuAlNi (present data)
20 15 10
F57Ba15Eu 5Zr 3
SiO2
Window glass
B2O3
5 GeSe 4
0
0
10
Zr55Cu 30Al10Ni5
20
30 p (GPa)
Fig. 7.11 Evolution of the relative variation in density ver-
sus hydrostatic pressure level illustrating the existence of the two thresholds reported for different glass families. Reprinted with permission from [7.80]. Copyright 2008 by the American Physical Society
pressure tests can be coupled with in situ Raman or Brillouin spectroscopy, which allows one to follow in situ structural variations or physical property variations (sound wave speed for Brillouin spectroscopy). Under purely hydrostatic loading conditions, it is admitted that oxide glasses start to permanently densify above a pressure threshold, then gradually densify upon pressure increase before reaching a second threshold above which a saturation level in density increase is reached. This general behavior of the relative density variation (after pressure release) versus the applied hydrostatic pressure can be well described by a sigmoidal-like curve. The different pressure thresholds and saturation level, which translates the capability of the glass structure to be permanently compacted, do depend on glass composition. The capacity of a glass network for compaction will depend on both the structural organization and the existence of free volume (the two are linked); for pure silica glass, the free volume represents 30% of the total volume of the bulk. This capability may also depend on other properties such as, for example, the coordination number evolution under pressure [7.81]. Silica glass and window glass start to permanently densify above 10 GPa then reach a saturation level above a pressure of 20 GPa [7.80, 82], whereas silica has a saturation level of permanent densification ratio of 21%. Soda-limesilica glass, such as a window glass, saturates at a 6:5% densification ratio (Fig. 7.12). This saturation level was shown to be linked in some way to the Poisson ratio of the glass, which provides a convenient way to rapidly estimate this parameter from the elastic property. Raman spectroscopy has proven to be an efficient tool for studying and understanding the mechanical
Mechanical Properties of Glass
243
Fig. 7.12
∆ρ/ρ 0 (%) 25
GeSe 4
Maximum density relative variation after high hydrostatic pressure testing at room temperature reported as a function of the Poisson ratio of the pristine glass. The atomic packing density Cg for some compositions is also given. Reprinted with permission from [7.80]. Copyright 2008 by the American Physical Society
SiO2 Cg ≈ 0.454 20
15
GeO2
10
SiO2-Na2O (10%) B2O3 F57Ba15Eu 5Zr 3
5 Window glass Cg ≈ 0.516 0 0.1
7.2 Plasticity of Glasses
0.2
Zr55Cu 30Al10Ni5 Cg ≈ 0.81
0.3
7.2.3 Mechanical Loading The Importance of Shearing on Densification Although the hydrostatic loading condition is by far the simplest stress condition, it is not easily achieved experimentally, as it requires specific sets of equipment such as simple diamond or multi-anvil systems [7.87]. Real-life conditions usually provide more complicated mechanical loading conditions through the presence of shearing. The importance of shearing with respect to the mechanical response of glass has been nicely illustrated by Roy and Cohen [7.88] from an examination of discrepancies between experimental results reported in the literature in the mid-1950s to mid-1960s [7.79, 88, 89]
0.5 v
regarding the room temperature densification of silica glass as a function of hydrostatic pressure (Fig. 7.13). Christiansen et al. [7.89] suggested that the discrepancy observed between studies was probably due to some shearing effect. He noted that a larger amount of shearing was certainly present in his experiment when compared to the study by Bridgman and Simon [7.79]. Roy and Cohen did not use disks but instead powdered silica glass to conduct their study; it was thus suggested that a large amount of shearing was introduced by the ∆ρ/ρ (%) 16
a
b
12
8
c
4
0 0
100
200 p (kbar)
Fig. 7.13 Evolution of the permanent densification of silica
glass at 25 ı C as a function of pressure. Data from Roy and Cohen [7.88] (curve a), Christiansen et al. [7.89] (curve b) and Bridgman and Simon [7.79] (curve c) (after [7.89])
Part A | 7.2
behavior of glasses under high-pressure conditions. Indeed, it provides both in situ and ex situ qualitative as well as quantitative data regarding the evolution of the glass structure as a function of pressure or permanent densification level, respectively [7.83]. From a mechanical viewpoint, constitutive laws are needed to describe the mechanical behavior of a material by providing a relation between the applied stress tensor and the deformation tensor. For purely hydrostatic conditions, it was only recently that a constitutive law was provided for silica glass [7.84]. This constitutive law takes into account the anomalous variation in the elastic properties of silica as reported in Fig. 7.10, and presents a rather good matching with experimental data extracted from [7.85, 86].
0.4
244
Part A
Fundamentals of Glass and the Glassy State
contact between the different grains. A thorough study of the shearing effect on densification of silica glass was subsequently reported in 1963 by Mackenzie [7.90], which provided a well-grounded explanation for those discrepancies. As a conclusion, shearing has an impact on both pressure thresholds: the one at which permanent densification sets in, and the one corresponding to saturation. It also has an impact on the level of permanent densification reached for a given hydrostatic pressure level. The Effect of Loading Path and Temperature on Densification Recent studies [7.91, 92] have definitely revealed the importance of both load and temperature paths by comparing the Raman spectra of silica glass samples having the same densification ratio (density equal to 2:5 g=cm3 ), with one densified at room temperature under pure hydrostatic conditions (16 GPa) using a diamond anvil cell set-up (DAC), and the other loaded in a belt (5 GPa) set-up at 750 ı C. Although those two glasses have the same density, differences are visible in the R (Si–O–Si bond angle value statistic), D1 (fourfold rings) and D2 (three-fold rings) regions of the Raman spectra (Fig. 7.14). Hydrostatic densification at room temperature provides a densified glass structure with more three-fold rings which are more strained (D2 band shifted to higher wave numbers) than the glass densified at high temperature under shear + hydrostatic loading conditions. Intensity (arb. u.)
Part A | 7.2
Belt DAC
The Effect of Strain Rate on Densification The strain rate may also be an important parameter in the densification process, especially as it relates to the high-velocity impact resistance to damage of the material. Arndt [7.93] and then Okuno et al. [7.94] studied the densification of silica glass through flyer plate-induced shock wave compression (compression of up to 43 GPa). From refractive index measurement and postmortem Raman spectroscopy investigations, they show that for low pressure levels, permanent densification increases with pressure, reaching a maximum value of 11% for a pressure of 26:3 GPa; then a decrease in the permanent densification level is reported for higher pressure values (0:5% for 43 GPa). The decrease in permanent densification at high pressure levels was attributed to the relaxation of the glass due to the temperature increase generated by the shock. Molecular dynamics simulation, because of its timescale compatibility with high-velocity shock events, is a well-suited tool for studying the effect of shock loading on the structure of a material. A recent study [7.95, 96] was able to quantitatively describe the experimental results from Arndt and Okuno et al.
7.2.4 Indentation and Glasses Hardness The indentation test is an extremely popular mechanical test used to generate plasticity at the surface of a material. Moreover, its principle is very simple and easy to put into practice. It involves having a physical contact between two surfaces in a controlled way so that an indenter of a given yet well-defined geometry made of a hard material is applied normally to the flat surface of the tested material with a chosen load P. If the contact is purely elastic, no permanent imprint is left behind on the surface; if plasticity occurs, a permanent imprint (Fig. 7.15) of the projected area A will be observable. H, the Meyer hardness (equivalent to the mean pressure), may eventually be computed following the well-known relation H .GPa/ D
200
400
600
800 Raman shift (cm –1)
Fig. 7.14 Effect of loading path on the Raman spec-
troscopy signature of permanently densified silica glasses having similar densities (2:5 g=cm3 ). The continuous line indicates the press belt sample (hydrostatic + shear), and the dashed line indicates the diamond anvil cell (DAC)densified sample (hydrostatic loading). After [7.92]
P .N/ : A .m2 /
(7.45)
Instrumented indentation offers the opportunity to record, as a function of time, both the load applied to the surface and the penetration depth of the indenter into the surface (h) of the material. Thus, if the geometry of the indenter is well defined (A is known for any h), hardness (H) and the indentation elastic modulus (also called reduced modulus D E=.1 2 /) may be computed from the penetration depth at maximum load and from the unloading part of the load
Mechanical Properties of Glass
a)
7.2 Plasticity of Glasses
245
b) nm 500 μm
400
0.05 300 –0.50 200 10 μm
10 μm
100 0
0
1
2
3
4
5
6
7
8
9
10 μm
Fig. 7.15a,b Atomic force microscopy 3-D image of a 100 mN Vickers indentation imprint and its profile extracted along
the black dotted line. Indentation made on a soda-lime-silicate glass. Prepared with the Gwyddion software [7.97]
displacement curve, respectively (see Oliver and Pharr method [7.98]); for more information regarding the indentation test, please refer to [7.99]. Among its advantages, instrumented indentation does not require the observation of the residual imprint in order to compute H, which gives access to very small loads in the millinewton to sub-millinewton range. Yet this simple test is trickier than it seems, as measurements will be affected by numerous parameters such as:
Usually, hardness of glasses lies in the range of 0:4 (pure selenium glass) to 11 GPa, depending on the glass composition as reported in numerous works available in the scientific literature. Based on the temperaturedependent constraint theory [7.49], values of H for multicomponent glass systems can be a priori computed with knowledge only of the glass composition, which is of great help regarding the engineering of glass composition [7.101]. Short Note on Hardness and Its Meaning. The hardness number was firstly used as a fast, easy and nondestructive test making it possible to compare materials between each other and to characterize and control an industrial process (quality of an alloy, effectiveness of a thermal treatment for example). In this case, its use relates more to engineering than to science. In 1956, Tabor [7.100] established a link between hardness and yield stress y .H D y =3/ (7.46) first for nonhardening perfectly plastic materials then extended to hardening materials. In this paper, he also devoted a few lines to brittle materials, such as minerals (rock salt), and noted that the local yield pressure equals roughly three times the yield stress. He concluded that even for glass, the indentation hardness value computed from a well-defined residual imprint, provided it is done in a geometrically similar regime, is a measure of plasticity. From those statements and the definition of H given by (7.45), it is concluded that when measurements are done in the geometrically similar regime of the indenter, away from
Part A | 7.2
Surface preparation (see, e. g., Beilby layer, residual stress) Tilt of the surface (indenter–surface angle ¤ =2) Indenter shape imperfection: conical- and pyramidal-shaped indenters are not infinitely sharp. They do have a finite probe size, which may be seen as a missing part of the indenter usually called the truncated length. This truncated length increases over time as the indenter wears out. Note that conical and pyramidal indenters are geometrically similar; the ratio a=h between a lateral dimension of the imprint a and the penetration depth h stays constant with load. This means that for very small loads, the geometrical similarity will be lost, as the material will start to feel the truncated length. The shape evolves from a pyramid toward a paraboloid as the load decreases. Spherical indenters are not geometrically similar, as the radius of the imprint does not vary in proportion to the penetration depth [7.99]. The microstructure of the material will also have an impact; this is usually described by the notion of representative elementary volume (REV), the smallest volume above which the mechanical answer of the material will be representative of the bulk. This is no problem for glass, as this material can usually
be considered homogeneous above tens of nanometers; on the other hand, for peculiar inhomogeneous systems (polymorphism, phase separation, presence of nanophases), this notion may become important.
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Composition Indenter dependent dependent
Composition and indenter shape dependent
Finite size of the sample
σy REV: representative elementary volume FPSE: finite probe size effect
Geometrical similarity
H σy = cste
Damage (fracture)
Plasticity 0 Probably wrong
Load Measured H value = correct
Questionable
Fig. 7.16 Schematics of the behavior of glasses as measured by indentation as a function of indentation load. The green zone indicates a domain for which H can be measured in a safe way and eventually linked to a material’s property according to Tabor [7.100]. Red areas are related to an unwanted effect that may lead to artifacts that will cause the measured H value to be questionable or incorrect
any REV considerations and for loads at which only plasticity is expressed (no fracture damage), then H is a constant independent of the applied load (Fig. 7.16).
Part A | 7.2
Plasticity of Glass Under Sharp Contact For sharp indenters, such as a pyramidal-shaped indenter (Vickers, Berkovich, cube corner), plasticity will occur right under the indenter as the elastic deformation of the surrounding material will provide the required confinement for densification to occur. As was shown by Raman spectra or cartography collected at indentation sites [7.86, 102], it is acknowledged that glasses under sharp contact loading deform plastically through two concomitant mechanisms: on the one hand, shear flow, which is a volumeconservative deformation, and on the other hand, densification, a non-volume-conservative mechanism. Shear flow may be compared to what is classically thought of as the plasticity of metals, except that the amorphous structure of glass makes the dislocation mechanisms inappropriate to provide a satisfying explanation. Nowadays, the intimate mechanism for shear flow is still not clearly understood despite the many different strategies developed relatively recently to gather more information regarding the plastic deformation of glass. For instance, mapping the densification landscapes under indentations using either Raman or Brillouin spectroscopy may be conveniently used as a benchmark to test constitutive laws [7.103–105]. Nevertheless the resolution of those techniques (about 1 m) needs a large enough volume affected by densification which leads experimenters to use high indentation loads (20 N) which may cause large fracture damage at the indentation site [7.102]. Plasticity-induced structural modi-
fications may be advantageously used to probe, with a nanometer-scale resolution, the densified volume underneath an imprint by looking at small variations of dissolution rate [7.106]. A rather complex stress state is to be found under a pyramidal indenter; this is why other mechanical testing geometries have been adapted to glass, such as the uniaxial compression testing of silica micropillars [7.107]. It was developed because it ideally provides a stress test similar to that for uniaxial compression (hydrostatic pressure D zz =3, maximum shear stress D zz =2). Nonetheless, at the microscale, misalignment, coupled with the compliant substrate and friction, provides departure from the ideal case. For such a mechanical test, although densification occurs during the test, it was shown that shear flow must exist to describe in an adequate way the experimental observations. Furthermore, no strain hardening of silica glass was observed experimentally; as a consequence, once shear flow initiates, no higher shear stress will be handled by the glass structure which will eventually lead to damage initiation [7.108]. Uniaxial compression testing on nanoscale silica spheres was also performed under TEM or SEM for which densification was reported [7.109–111]. Furthermore, the electron beam interaction with the silica network may be utilized to generate athermal e-beam-assisted quenching while being under load by switching off the e-beam [7.110]. From instrumented indentation testing performed on fully densified silica glass [7.112], it was shown that the fully densified glass behaves as a von Mises material, with a yield strength of 6:5 GPa, a value close to those (about 7 GPa) reported in previous studies [7.105, 107]. Molecular dynamics simulations, based on recent results, have proved to be a pertinent
Mechanical Properties of Glass
method for investigating the plastic behavior of silicate glasses, suggesting possible scenarios for plasticity at the local scale. The stress multiaxiality effect on plasticity can also be studied more easily than in experimental study; for instance, the shear yield strength was shown to be unaffected by densification [7.113]. The latest work provides also tangible elements toward a multiscale modeling of the plastic behavior of silica glass, proposing a method usable for other glass compositions [7.114]. Contact-Induced Damage When indentation load is further increased, a transition occurs in the behavior of the glass, from ductile at small loads (i. e., small scale), toward a brittle behavior at higher loads (i. e., larger scale; Fig. 7.17). When the latter regime is reached, fracture events are observable at the free surface of the sample around the indentation imprint. Contact-induced fracture has been studied now for more than a century. It started with the study of the Hertzian cone crack formation [7.115] that is typically encountered for glass when a spherical indenter is used (see also the historical overview by B. Lawn [7.116]). It was only in the 1950s that scientists started to study the fracture mechanisms under contact loading, trying to decipher when, how and where the cracks initiate. For pyramidal indenters, and more specifically for Vickers indenters (squared-based pyramid), two different principle cracking systems do develop. The first one is called the median/radial crack system: median cracks are first formed at the corners of the imprint and are parallel to the loading axis. They have a shallow depth and can sometimes be called Palmqvist radial cracks. Median cracks nucleate below the plastic deformation
7.2 Plasticity of Glasses
zone while under load. They do need a certain load threshold to be overcome in order to nucleate. Then they propagate in a stable way as the load increases; they have a circular shape [7.117]. Those cracks do close down upon the release of the load. Half-penny cracks are formed at unloading, while tensile residual stress at the imprint corners builds up and reaches a high enough level for the two systems to merge down, leading to the famous star-like cracking system. Lateral cracks are subsurface cracks that form during loading at much higher loads than the other crack systems (about 50 N for soda-lime-silicate glasses) and further propagate during unloading; they find their origin underneath the plastic zone and propagate quasi-parallel to the free surface of the sample. When they merge to the surface, they form chips that may detach form the surface. For glasses exhibiting a large densification ratio, such as silica glass and some borosilicate glasses, Hertzian cone-like cracks can be observed. An exhaustive description of the different types of cracks (Fig. 7.18) that can be encountered is described in [7.118]. Cracking behavior has been shown to depend on glass composition: glass deforming essentially by densification, such as silica glass, has been classified as anomalous glass (Hertzian-like crack system) [7.119], while those for which the plasticity is essentially composed of shear flow are called normal glasses, the latter of which do exhibit the famous half-penny crack system. This apparent dichotomy in the indentation cracking behavior of glasses [7.120] must be tempered by two considerations: First, starting with an anomalous glass such as SiO2 , infinitesimal modifications of the glass composition can be made by adding sodium and calcium oxides until, finally, a glass exhibiting normal
Part A | 7.2
Anomalous behavior: silica 25 μm Ductile to brittle transition 5 μm
Normal behavior: window glass
50 μm
50 μm
10 mN
247
1N
10 N
Indentation load
Fig. 7.17 Illustration of the ductile to brittle behavior of an anomalous (silica) and a normal (soda-lime) glass under pyramidal indentation with applied load increase. 10 mN and 1 N are atomic force microscopy pictures, 10 N are optical pictures
248
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Fundamentals of Glass and the Glassy State
a)
b)
d)
Fig. 7.18a–e
c)
Most commonly observed contactinduced crack systems in glass materials: (a) radial crack, (b) median crack, (c) halfpenny crack, (d) lateral crack and (e) Hertzian cone crack (after [7.118])
e)
Part A | 7.2
behavior is obtained. Intuitively, a smooth transition is to be expected between the two behaviors [7.121]. Second, it has been shown that indenter shape plays a major role in the development of the cracking system. The modification of the equivalent apex angle of pyramidal indenters toward sharper values causes silica glass to act as a normal glass (i. e., to exhibit a median/radial crack system) [7.122]. Indeed, the sharper the indenter, the more important the shear component, which in time favors shear flow at the expense of densification. At this point, the critical load (Pc ), which is the load below which no radial crack is observed, is an important parameter that enables a comparison of glasses in terms of their resistance to the initiation of contact-induced surface damage [7.121, 123]. Scratch Scratch is in some ways a more natural aggression of a surface, yet it is even more complex and difficult to understand than the indentation test. The only difference with indentation is that the indenter is slid onto the surface while a normal load is applied, thus increasing the shear strain (Fig. 7.19). The instrumented scratch test gives access to the X–Y–Z displacements, the longitudinal one from which the scratch velocity is computed, the lateral one (normal to the sliding direction) and the vertical displacement or penetration depth into the surface and to the corresponding forces (Fx , Fy , Fz ), the tangential force (sliding direction), the lateral one and the applied normal force, respectively. The friction coefficient may be computed from the ratio Fx =Fz . If the normal load increases progressively from zero, similar regimes as those reported for indentation are observed. For a soda-lime-silicate glass,
Fz Indenter Groove
x z Fx
Plastic zone
Fig. 7.19 Schematic of cross-sectional view of scratch test-
ing in the ductile regime (after [7.124])
scratches with a Vickers indenter Ahna et al. [7.124] describe first at low loads (050 mN) a microductile regime where a hardly visible to the naked eye plastic tray (no cracks) is left behind at the surface; as the load increases (50800 mN), cracks will set in (Fig. 7.17). At first, shallow lateral cracks on the sides of the plastic groove will appear, forming a chevron-like pattern. Then, as they grow in size with increasing load, median cracks will form underneath the groove perpendicular to the surface and parallel to the scratch direction. Lateral cracks will also form in this range of load before reaching the surface at higher loads, typically between 0:8 and 3 N. Above 36 N, crushing will act as a machining regime (i. e., pieces of glass are ejected from the surface). Those different regimes (microductile, fracture, grinding) are marked by load thresholds, the position of which will vary by glass composition, as expected from indentation studies [7.125], and en-
Mechanical Properties of Glass
a)
7.2 Plasticity of Glasses
249
b)
2c 2a
2c 2a
100μm
100μm
Fig. 7.20 (a) Top view of Vickers indentation (10 N) on a chalcogenide glass exhibiting the median/radial crack system of what is referred to as normal behavior. 2c and 2a are the crack length and the diagonal of the imprint, respectively. Reddish colors are due to the lateral crack system underneath the surface. (b) Cross-sectional view of the imprint and the half-penny crack arrest mark line Fig. 7.21 (a) Effect of molar volume on the brittleness parameter as defined by the ratio H=Kc , (b) Vickers indentation response of a soda-lime glass (left) and a scratchresistant one (right) to a 3 N indentation. Reprinted with permission from [7.127] I
7.5 Simple soda-lime-silica glass New low-brittleness glass Commercial soda-lime-silica glass
7.0 6.5 6.0 5.5 5.0 23.5
24.0
24.5
25.0 25.5 Molar volume (cm 3)
b)
Indentation Fracture Toughness For normal glasses presenting a well-developed median/radial crack system (Fig. 7.20), it is possible to compute what is called an indentation toughness value (Kc ). A relation between hardness (H), Young’s modulus (E), the crack length c and the applied load P was first proposed by Anstis et al. [7.128]. Kc D
P 3
c2
with
Dı
E H
50μm
12 (7.46)
ı is a constant equal to 0:016 for Vickers indentations made on soda-lime-silicate glass of the window type (Fig. 7.21). Other values of ı are reported in the literature for other glass systems; as a matter of fact, if the mode I fracture toughness of the tested glass is known, ı
can be computed from the material’s other parameters. This equation may be used provided a well-developed median/radial crack system is obtained, or c=a > 2:5. Although Kc values are close to mode I fracture toughness values KIc , the indentation fracture method is not recognized as a standardized method for measuring the
Part A | 7.2
vironmental parameters such as humidity level [7.125] or temperature [7.126]. A dry environment (50 ppm of water molecules) will make the lateral cracks almost disappear, while at 30% relative humidity, large chipping is observed around 1 N. In contrast, the grinding regime is barely reached at 3 N in a humid environment, whereas at 1 N it is well developed for dry conditions. Both friction coefficient and subcritical crack growth, which are humidity-dependent, do play a major role (see Chap. 36 for related information).
a) Brittleness (μm–1/2)
250
Part A
Fundamentals of Glass and the Glassy State
mode I fracture toughness of a brittle material [7.129]. The fracture indentation test includes inelastic deformation processes, nucleation of the defect, and then propagation of the cracks, whereas fracture toughness is a measure of the resistance that a material offers against crack propagation. Moreover, as will be seen later, in oxide glasses, materials suffer from a subcritical crack growth phenomenon due to the humidity present in the surrounding environment. The crack length for glasses characterized as intermediate to anomalous can be very short due to the increasing role of densification and the accompanying lowering of residual stress. This lower residual stress level is a major contributor to unrealistically high fracture toughness values reported for intermediate to anomalous glasses [7.130]. Brittleness Index: Resistance to Cracking The brittleness index, defined by the ratio of hardness to indentation fracture toughness (B D H=Kc ), was proposed by Lawn and Marshall [7.131] in order to provide a useful engineering parameter allowing for an easy comparison between materials for design purposes. B is computed from two material properties measured using the same experimental set-up. This parameter is related to the competition between plastic deformation and crack nucleation threshold; it allows one to predict the behavior (cracking event occurrence) for any glass if H and Kc are known. As shown by Sehgal et al. [7.132], the ratio c=a may also be used to classify the brittleness of glasses. B and c=a are linked by the following relation c 2 1 D .B/ 3 P 6 (7.47) a
Part A | 7.2
with being a calibration factor to be determined in the experiment [7.131]. For soda-lime-silica glass, it was shown [7.127] that B is linked to the molar volume of the glass (Fig. 7.21), with the former decreasing linearly as the molar volume increases. (In some cases, the addition of oxide components with higher formula unit weights may lead to high molar volume, which may result in greater packing density. Therefore, the molar volume approach must be used with caution.) This enables the development of a strategy regarding the synthesis of a glass composition more resistant to surface damage (see also [7.133]). Other approaches have been developed to improve damageresistant glasses. For example, in [7.134–136], based on the work of Yoffe [7.137] and Boussinesq [7.138], the notion of a driving force for the different crack systems (radial, lateral, cone crack) is developed from the
expression of the stress field that develops on loading at Vickers indentation sites. The components of the stress field in spherical coordinates can be conveniently expressed as a function of the material properties (E, , H) Young’s modulus, Poisson ratio and hardness, respectively; indenter geometry through the equivalent cone angle (Yoffe’s model was originally developed for conical indenters); a distance from the load application point and a tunable parameter. This enables the production of cartographies of the stress field component values as a function of the material’s related parameters (E=H, ; Fig. 7.22). From this work, two main conclusions were drawn: first, as the ratio E=H is roughly equal to 10 for most oxide glasses (varies from 10 to 13), D 0:22 is a critical value at which the indentation stress field components are less favorable for cracking events (near zero value); second, a classification of glasses as a function of with respect to their resistance to radial-median cracks was proposed by the authors as follows:
Resilient glasses: 0:15 < < 0:20 Semi-resilient glasses: 0:20 < < 0:25 Easily damaged glasses: 0:25 < < 0:33 Highly resilient glasses: 0:33 < .
Although some of the questions regarding highpressure behavior of glasses and sharp contact-induced damage have been open for more than 50 years, it is still a very active topic throughout the world’s glass community, in both the academic and industrial fields. Progress realized over the last 15 years in obtaining more resistant glass composition with regard to contact-induced damage has had a strong impact on our everyday lives, as anyone with a smartphone or a tablet owns a part of that fruitful progress. To finally resolve the contactinduced damage issues, it is clear from the recent literature that the next steps will come from a combined approach: mechanical, with better knowledge of the stress state under sharp contact, and thus to the determination of a constitutive law for plasticity and then damage nucleation, from the structure of the glass and especially from its possible evolution under a high level of compressive stress (local buckling, change in coordination number), as was shown recently for lithium aluminosilicate glasses, which were revealed to be ultraresistant to damage thanks to their adaptive network under high pressure [7.139] (see also [7.140] for calcium aluminoborosilicate glasses). This knowledge can also bear fruit in the context of improving post-processing treatments such as chemical tempering [7.141].
Mechanical Properties of Glass
a) E/H
7.2 Plasticity of Glasses
251
b) E/H
30
30 –6
26
26 1
22
Metallic
18 14
18
–2 –1
0 0.3
Silicates
10 6
22
–4
Borosilicates a-SiO2
14
0.5
10
0.3
6 –0.3
σrr(θ = /2)/H 2 0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45 ν
2 0.1
c) E/H
d) E/H
30
30
0.15
–0.1 0.2
0.25
9 26
0.3
σϕϕ(θ = /2)/H 0.35
0.4
0.45 ν
–1.3
26
22
0.1 0
–1
22 6
18
18
–0.5
3 14
14
1
–0.2
0
10
0
10
–1
0.1
6
6
2 0.1
0.15
0.2
0.25
0.3
0.35
0.4
σϕϕ(θ = 0)/H 0.45 ν
2 0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45 ν
Fig. 7.22a–d Maps of stress field components rising on loading at a Vickers indentation site as a function of and the E=H ratio. Stress fields are computed at a distance a from the initial contact point at the surface along the vertical axis ( D 0) and the surface ( D =2). The red contour highlights the region where the stress reaches a zero value. (a) rr . D =2/=H governs the formation of ring cracks; (b) . D =2/=H is a driving force for radial cracks, (c) rr . D 0/=H is the driving force for lateral cracks, (d) . D 0/=H is assumed to govern the formation of median cracks (after [7.136])
Part A | 7.2
0.15
σrr(θ = 0)/H
252
Part A
Fundamentals of Glass and the Glassy State
7.3 Fracture: Toughness, Strength and Fracture Mechanics 7.3.1 Fracture Toughness The toughness of a material is an intrinsic material property defined by a rather simple concept, which is the resistance the considered material offers to crack propagation. Note that this parameter does not provide any information as to how the crack was created. It only tells one how easy or difficult the propagation is: the higher the KIc , the more difficult the propagation of the crack. Yet, it is a quite difficult property to measure for brittle materials, and especially for glasses, as external parameters such as temperature, chemical environment or even light may affect the behavior of the material, and thus the measured property. Toughness Measurement Several techniques have been used to measure KIc . They include the double-cantilever beam (DCB), the double-cantilever drilled compression (DCDC) [7.142], the double-torsion (DT)—for a review see [7.143], the straight-notched beam (SNB), the surface crack in flexure (SCF), the single-edge precracked beam (SEPB), the chevron-notched (CN) or the compact tension geometries (CT) [7.144, 145], and references therein. The SEPB or CN specimen geometries seem to be better suited for brittle materials. Beams are loaded using either a three- or four-point bend loading set-up. The critical stress intensity factor KIc can be computed from the load at failure using the relation KIc D
Pc p Yc B W
(7.48)
Part A | 7.3
where B and W are the width and the thickness of the beam, respectively, Yc is a geometrical factor function of (a=W), and a is the length of the crack. a) Load
Note that the three-point bending geometry requires the chevron or the pre-crack to be perfectly aligned with the upper loading roll. The latter, when under loading conditions, gives rise to a Hertzian-like contact compression stress, which will cause the crack to deviate strongly from the mean propagation plane at the end of the test. The SEPB and CN methods correspond to standardized tests and are well described in ASTM C1421 [7.146]. The most difficult part lies in the specimen preparation (machining and polishing), which requires accurate geometries of the beam on the one hand, and a well-controlled and well-defined defect geometry (semi-elliptical crack geometry (SCF), straight crack (SEPB), chevron) on the other. For the chevronnotched geometry dimensions of the beam, chevron size and shape as well as loading geometry will depend on the compliance of the loading machine. The goal is to have the stored elastic energy in the system while under load be released and used to break the last ligament of material before complete rupture. Some help regarding the choice of geometry to obtain this mandatory stable crack propagation may be found in [7.147, 148]. Stable and unstable crack propagation are illustrated in Fig. 7.23. For the chevron-notched method, the mode I critical stress intensity factor under plane-strain conditions is given by (7.48), where Yc is the minimum value of a geometrical factor at the maximum load Pc for which a critical defect size ac is obtained. Munz et al. [7.149] provided an expression for the geometrical factor Y that depends on the chevron geometry, the actual size of the defect and a term C0 related to the compliance of the system (i. e., a sample having a crack of length a plus the loading frame). Additional information regarding the technique may be found in the related ASTM document as well as
b) Load Stable
Displacement
c) Load Semi-stable
Displacement
Unstable
Displacement
Fig. 7.23a–c Load displacement curves from the chevron notched three-point bend test done on a soda-lime-silicate glass at room temperature and 55% relative humidity. Crosshead speed was set to 0:005 mm=min. (a) Illustration of a stable crack propagation, and (b) a semi-stable and (c) an unstable crack propagation, respectively
Mechanical Properties of Glass
7.3 Fracture: Toughness, Strength and Fracture Mechanics
in [7.149, 150]. Although mechanical testing is quite straightforward, the nature of the tested material may be important with regard to the validity of the toughness values obtained. For example, oxide glasses are prone to subcritical crack growth due to the presence of moisture in the test environment; the crack selfhealing phenomenon may also have an impact. Fracture toughness (Table 7.2) values for borate, germanate and phosphate as well as silicate glasses may be found in [7.151].
Orowan [7.152] also later considered the elastic energy needed to create new surfaces by propagating the crack to estimate roughly the molecular cohesion of a solid from its specific surface energy (Fig. 7.24). He expressed the maximum sustainable stress as a function of the Young’s modulus (E), the fracture surface energy ( ) and the interatomic distance (d0 )
7.3.2 Fracture Mechanics from Strength Considerations
For silica glass (E D 70 GPa, D .4:6 ˙ 0:2/ J=m2 [7.153] and d0 D 0:16 nm), a value of 45 GPa is there-
The strength of a material is a characteristic with important societal impact, as it is the ultimate maximum stress value that a structure may sustain before catastrophic rupture. It is used for dimensioning any structural part (e. g., civil engineering, transportation, energy) in order to prevent any rupture while in use. It is even more important for brittle materials, as in this case, fracture will occur suddenly in a catastrophic manner, without warning (i. e., plastic deformation). Thus, the ability to characterize this property takes on critical importance, especially for glass.
E d0
12
:
(7.49)
F E Fmax
γ d0 Distance Distance
Fig. 7.24 Theoretical resistance to decohesion between two atoms: cohesive force as a function of the interatomic spacing. The solid extends uniformly in a stable and reversible way under applied tensile forces until the maximum force Fmax is reached, then fracture occurs. The elastic energy stored in the material must provide the energy needed to create the new surfaces by crack propagation (2x). is the specific surface energy, also called fracture surface energy
Table 7.2 Toughness values for different glass compositions and the measurement conditions. DCB: double-cantilever beam, NB: notched beam, MDC: moment double-cantilever, DT: double-torsion. From NIST website Molar composition SiO2 71:3%SiO2 + 1:16%Al2 O3 + 7:4%CaO + 0:63%K2 O + 5:9%MgO + 13:4%Na2 O
71%SiO2 + 29%Na2 O 62:5%SiO2 + 37:5%BaO 58:4%SiO2 + 12:0%Al2 O3 + 3:5%B2 O3 + 6:6%CaO + 18:3%MgO + 1%Na2 O 70%B2 O3 + 20%Na2 O + 10%SiO2 50%P2 O5 + 20%CaO + 30%Na2 O
Toughness (MPa m1=2 ) 0:740:75 0:87 0:76 0:77 0:75 1:04 0:5 0:91 0:84 0:46
Experimental conditions Vacuum (DCB, NB) N2 liquid (MDC) Air (DT) Oil (DT) N2 gas (DCB) N2 liquid (DCB) Air (DCB) N2 gas (DCB) Air (NB) Air (short bar)
Part A | 7.3
Strength: Theoretical Values and the Reality Fracture strength may be seen as the maximum tensile stress a structure is able to sustain before catastrophic rupture occurs. For an ideal material (i. e., without any surface defects such as impurities, bubbles, cracks or nano-heterogeneities), and in the absence of environmental effects, this maximum stress value is called the intrinsic strength of the glass. It is in this case a material property. Orowan [7.152], by estimating the maximum energy required to separate two atomic planes and using Hooke’s law, found the intrinsic strength of silica to range between E=10 and E= , thus between 7 and 22 GPa (E, Young’s modulus, 70 GPa).
m D
253
254
Part A
Fundamentals of Glass and the Glassy State
Part A | 7.3
fore obtained. This is quite a high value, but remembering the specific n-fold ring structure of silica (3 < n < 10), the most probable ring structure is five to six tetrahedra; thus a final distance of 4 d0 before rupture seems to be a fair mean value, which leads to a value of 22:5 GPa. More recently, molecular dynamics simulations have provided several values of intrinsic strength for pure silica glass [7.154–157]. Most of the values reported in the literature are rather close to one another (22 to 30 GPa) and on the same order as the estimated values previously discussed. It is important to note that, as mentioned by the authors, the results may strongly depend on the chosen interaction potential as well as on both the numerical experimental set-up and the hypothesis. For instance, Ochoa et al. [7.156] showed that thermal vibrations play an important role, as they weaken the structure. By suppressing them (a nonrealistic situation), a value of 72 GPa was obtained. Ochoa also noted that for silica, the large amount of free volume (up to 30%) results from the presence of large voids that reduce the maximum strength. Although these are numerical studies, they nevertheless establish a direct link between the intimate glass structure (medium-range order) and its ultimate strength. A number of attempts have been made to characterize the intrinsic strength of glasses. Proctor et al. [7.158] were among the first to study this aspect, and obtained flawless samples by drawing fibers from silica rods. They obtained a strength value of 14 GPa for pure silica fibers (diameter of 4060 m) that were tested under tensile conditions in liquid helium (4 K). More recently, Brambilla and Payne [7.159] studied the ultimate strength of silica nanowires (radii ranging from 300 to 60 nm), although a strength value of 11 GPa was reported; for the smaller radii, maximum values above 20 GPa were measured. Proctor et al. observed that an increase in testing temperature or the presence of moisture had a drastic and negative impact on the measured strength value. For silica, the same type of fibers tested under vacuum conditions at room temperature gave a strength value of 8 to 9 GPa (6 to 7 GPa in the presence of moisture). This is even worse if one performs a strength test on a glass sample taken from the shelf, as in this case, values in the range of tens of megapascals are to be expected [7.160]. This low value essentially results from surface defects (micro-cracks) generated either during the manufacturing process or later when manipulating the sample. Thus there is an important difference between the intrinsic strength of the glass and the practical or usable strength of a glass structural part. The latter will depend on numerous parameters such as the manufacturing process (see Chap. 36 on glass shaping), which includes the way surfaces are
generated, and relates to the surface defect population, roughness and the thermal history of the glass (fictive temperature, residual stress) [7.161]; environmental effects (e. g., temperature, humidity); strain rate effects, even under vacuum conditions; aging or storage time; and condition after manufacturing [7.160]. These points are addressed in the paragraphs that follow. Practical Strength of Glass: The Inglis and Griffith Theories Both Inglis [7.162] and Griffith [7.163] knew that a piece of glass is never perfect and that pre-existing flaws such as micro-cracks do exist and are responsible for the low practical strength values one can measure. Those cracks act as stress concentrators; when far from the flaw, the mean stress lies well below that required for the crack to propagate. Inglis solved the elastic problem of an elliptical crack under tensile stress in an infinite plate. The choice of using an elliptical form of the major axis c and minor axis a was convenient (Fig. 7.25), as it describes a large variety of defect geometries: from the circular hole when a D c to the fine straight crack when c a. The hole is subjected to a tensile stress perpendicular to the major axis. The radius of curvature at the ends of the major axis of the ellipse is given by D a=c2 . For a hole far from the plate edges and within the elastic behavior of the material, the stress at the extremities A and A0 of the hole is expressed as r c c ; (7.50) tip D 1 C 2 D 0 1 C 2 a r tip c : KD D 1C2 (7.51) 0 If the stress intensity concentration is defined as the ratio K D tip =, the thinner the crack (i. e., a is low), the higher the value of the SIF. When c=a D 100, the tensile stress at the edge A is 201 times the stress applied to the sample. However, the work of Inglis poses a problem for ideally sharp cracks. In this case, a D 0 and so is , which implies that the stress at the tip of the crack tends toward infinity (Fig. 7.25). This situation is far from realistic; as a matter of fact, at least one interatomic bond would bridge the two lips of the crack at its tip. Griffith was aware of Inglis’ work, and instead of focusing on the crack tip stress concentration, he utilized an energy balance approach. Griffith considered a straight crack that passes normally through a flat homogeneous isotropic plate of uniform thickness when tensile stress is loaded in its plane at edges far from the crack. In simple words, in order to propagate the crack, energy is consumed. At the least, this energy is needed for the creation of new surfaces. Within the
Mechanical Properties of Glass
a)
b)
σ0
7.3 Fracture: Toughness, Strength and Fracture Mechanics
crack propagation and is expressed as
σ0
@W @Uel @ D @S @S @S Three different cases are then considered: GD
Stress σ(r) c
c
a A
A'
σ0
ρ
255
r
σ0
Fig. 7.25 (a) An elliptical crack in an infinite elastic body subjected to remote tensile stress 0 and (b) stress intensity
variation as a function of the distance to the crack tip for a crack length of c and curvature radius in a semi-infinite elastic body subjected to a remote tensile stress 0
framework of linear elasticity, Griffith considered that an elastic body containing a crack loaded under tensile stress conditions can be considered a reversible thermodynamic system. From the first law of thermodynamics, for an adiabatic system for which the load is applied in a quasi-static way (no kinetic energy) .U C / D W ;
(7.52)
@ .U C / D W : @t
(7.53)
@S @ @c @ @ D D @t @t @S @t @c @Upl @ @W @U @ @Uel D C D C C @S @S @S @S @S @S @W @Uel @ D C : @S @S @S
1. G < 2 : there is not enough energy available in the system to propagate the crack 2. G D Gc D 2 : there is just enough energy for the creation of new surfaces for infinitesimal crack propagation (actually, the instability will be determined by the sign of the derivative of G with dS or dc .@G=@c D 0/, see Fig. 7.26) 3. G > 2 : the crack propagation is unstable. Thus @W @Uel @ D0D C : (7.56) @S @S @S From Inglis’ work, for a surface crack of length c and unit thickness, c2 2 ; 2E @Uel @Uel c 2 D D dc : @S @c E Thus Uel D
(7.57)
cc2 dc E and at fracture r r 2 E EGc D c c c 2 dc D
(7.58)
(7.59)
Energy Surface energy
Uγ = ∫ ГdS = 2γc
Unstable equilibrium cc
Crack length (c) Uγ + Us
Elastic energy (7.54) Us = –
In the case of brittle fracture, there is no energy dissipation through plastic or viscoelastic deformation, and D 2 dS, where (J=m2 ) is the fracture surface energy. While the crack propagates, two new surfaces are generated. G is introduced as the strain energy release rate. It represents in this particular case the energy per unit crack area that is available for an infinitesimal
σ 20c2 2E
Fig. 7.26 Energies plotted as a function of crack length c. The blue line is the elastic energy, the straight black line is the surface energy, and the green line is the sum of the two W external work values. For a critical length cc W reaches an unstable equilibrium above which the crack propagation becomes unstable
Part A | 7.3
where U is the total internal strain energy (elastic plus plastic): U D Uel CUpl , the surface energy and W the external work. All changes with respect to time result from a modification of the crack surface (S); usually, a unit thickness sample is considered so that only the crack length (c) becomes a variable
(7.55)
256
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Fundamentals of Glass and the Glassy State
finally, p
x1
c c D
p
p EGc D 2Ec D const :
r
(7.60) θ
As E and are material properties that can be measured experimentally, Griffith established the first relation between the size (length) of the flaw and the measured strength: the longer the crack length, the smaller the strength value. The smallest possible crack size would be on the order of d0 D 0:16 nm, the Si–O bond length. Furthermore, for silica glass, D .4:6 ˙ 0:2/ J=m2 , E D 70 GPa, which gives a 36 GPa ultimate strength value. If taking a 4d0 value for c, the strength value falls to 18 GPa. Now, using the critical strength value c D 14 GPa measured experimentally for pristine silica fibers, one obtains a flaw size of 1 nm. Note that Griffith’s work was intended for engineers, to provide them with an estimation of the strength of a material, given a crack size and the material’s properties. The strength is an important parameter that allows for a better design and reliability of structural parts while in service. Both Inglis and Griffith are considering an isotropic material in a linear elasticity framework, which even for brittle materials might not be totally true near the crack tip. To stay valid, any nonlinear effect (plasticity, for example) has to stay confined to the near-crack-tip region so the global behavior of the structure may be considered as linear elastic. If the material is not perfectly brittle, Griffith’s work may be generalized by introducing a globalized fracture energy parameter f that includes (by the addition of the relevant contributions to the elastic one) nonlinearities such as plasticity, viscoelasticity, viscoplasticity and other effects.
Part A | 7.3
Linear Elastic Fracture Mechanics: Stress Intensity Approach The stress state near the crack tip, which introduces the notion of stress intensity factor (SIF) at the crack tip, is preferred. Three types of fracture modes, referred to as modes I, II and III, are treated in the literature. Mode I, which is the most dangerous with respect to structural integrity, is the opening mode, and modes II and III are pure shearing modes. For mode I, from the work of Irwin [7.164] and then Westergaard [7.165], Williams [7.166] obtained an asymptotic expression of the stress in the near region of an infinitely sharp crack tip (7.61) (Fig. 7.27) ij D
KI 1
.2 r/ 2
fij . / :
(7.61)
where ij is the stress tensor, r the distance from the crack tip, KI the mode I stress intensity factor and fij . /
x2
Fig. 7.27 Schematics of an idealized crack tip (light brown
area) and its associated Cartesian and cylindrical coordinate systems; x2 is the crack propagation direction. For a pure mode I loading (opening mode), remote stress would be applied along the x1 direction
a geometrical factor that depends on the crack geometry and loading conditions. Most encountered situations and associated SIF expressions are given in Table 7.3. When r tends toward zero, the stress at the crack tip becomes infinite, which is not physically sound. This is because no process zone including nonlinear effects such as plasticity and viscoelasticity is considered here.
7.3.3 Usable Strength: Fracture and Fatigue From the previous paragraph it becomes obvious that the strength value obtained from a glass part is intimately linked to the largest defect, or at least the one that saw the highest stress level (orientation of the defect with respect to the applied stress has to be considered). This is why the theory of the weakest link best describes the rupture of glass, as from fracture mechanics theory, the largest defect will be responsible for the rupture of the whole glass part. Glass rupture most often occurs from surface defects whose origin may either be found in the fabrication process or result from postfabrication use. Intrinsic Strength The intrinsic strength should be understood as the ultimate value obtainable for a material, which means that it should not be related to the fabrication process, but rather to the material itself and its intrinsic structural defects. These considerations make the measurement of such a property very difficult. Two settings have primarily been used in the literature to measure the intrinsic tensile strength of glasses. The geometry and size of the sample is driven by the need for defect-free surfaces loaded under tensile stresses. Thus, carefully drawn fibers are usually used in order to test pristine glass surfaces. The main difficulty with this technique lies in obtaining a good clamping of the extremities of the fiber. This was successfully done recently [7.159] for loading nanoscale fibers using modern techniques. For this simple loading configuration, the stress is given by the ratio between the maximum applied load before rupture and the section of the fiber. Strength values
Mechanical Properties of Glass
7.3 Fracture: Toughness, Strength and Fracture Mechanics
257
Table 7.3 Expressions of the stress intensity factor for a few crack geometries [7.167] σ
p
Center crack of length 2c in an infinite plate
KI D
Edge crack of length c in a semi-infinite plate
p KI D 1:12 c
c
c
σ σ c
σ σ
Center crack of length 2c in an infinite plate of width W
c W σ σ
Edge crack of length c in a semi-infinite plate of width W
c W
c p KI D c f W c 4 r c c c 2 C 0:06 sec f 1 0:025 W W W 2W
c p KI D c f W c c 4 c c 2 f C 30:082 D 1:122 0:231 C 10:550 W W W W
σ
Face plates
Guide plate Fiber
Fig. 7.28 Schematic drawing of the two-point bending
technique set-up used to measure the strength of optical fibers (after [7.168])
ments. Its main drawback lies in its very localized maximum tensile stress region at the surface of the fiber, which is three orders of magnitude smaller in size than that of a classical tensile test. Therefore, strength values measured by the two techniques may be difficult to compare [7.168]. Nonetheless, France et al. [7.170] managed to measure the strength of coated silica and borosilicate fibers at room and liquid nitrogen temperatures using both techniques. As a matter of fact, tensile tests and two-point bend tests do not give the same results, because of a difference in gauge length, which could be taken into account by a proper correction. For silica and borosilicate, a strain at rupture of 21 and 12% was reported, respectively, which corresponds to approximately 14 GPa of strength for silica (Hooke’s law provides a linear elastic behavior for silica). This value is equivalent to the value reported by Proctor et al. in 1967 for liquid helium and nitrogen temperatures [7.158]. According to ASTM C158-02 [7.171], the most appropriate and suitable method for measuring a strength value is based on the equibiaxial flexure test (ring-on-ring bending test), which provides the best option with regard to the in-surface stress isotropy (no specific orientation) on the tensile loaded surface added to a large surface of homogeneous stress level. This is important with respect to the size of statistical defect
Part A | 7.3
above 10 GPa were obtained for fibers with a radius ranging from 300 to 60 nm: the smaller the radius, the higher the measured strength value, near 15 GPa for the thinner ones. Maximum values in the range of 25 GPa were also reported for some of the smallest radii. Nonetheless, most of the experimental data reported in the literature were obtained using a twopoint bend test loading geometry (Fig. 7.28), which was first developed by Murgatroyd [7.169] and commonly used throughout the years. It is a convenient technique that can rapidly generate a large quantity of results for strength and fatigue parameter measure-
258
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Fundamentals of Glass and the Glassy State
distribution. Practically, to obtain a good estimation of a strength value, numerous fracture tests (whatever the chosen loading geometry) must be carried out; strength measurements are usually associated with a Weibull statistics treatment [7.172, 173]. Size of the Defect: Fabrication Process While reporting on a new method for measuring the tensile strength of glass, and knowing the work of Inglis and Griffith, T. Littleton [7.174] was looking at the discrepancies between strength results reported in the literature, and noted: The most obvious conclusion to be drawn from the work of these investigators is that all experiments made to date, with the exception of that of Griffith, have served to measure only the surface condition of the glass.
This can be of great use when one needs to characterize the quality of an industrial fabrication process or a method of surface preparation. Indeed, experimental evidence has since validated the fracture mechanics approach. Holloway [7.176] showed that three sets of the same glass but having different handling history (off the book shelf, free from abrasion cracks and free from both abrasion cracks and surface inclusions), were giving three distinctive statistical populations of strength values. Mould [7.177] proposed a classification (Fig. 7.29) aimed at providing useful insight toward safe design
of glass parts which links the effective flaw depth to strength ranges and types of flaws. Effect of the Environment: Temperature and Humidity Interestingly, Proctor et al. [7.158] measured the strength of silica under various conditions, notably by varying temperature while ensuring vacuum conditions during the test. A decrease in strength was observed as temperature increased from 196 to 80 ı C, whereas it stayed constant up to 200 ı C at 9 GPa. The same trend was observed when fibers are tested in air, but the plateau value was degraded to roughly 6 GPa. The degradation of the measured strength with both temperature and humidity was attributed to the rate of reaction of water molecules at the stressed crack tip, the mobility of water molecules toward the crack tip and the availability of water molecules. pH also has an impact on the measured strength value; in particular, extreme values of pH acidity (pH < 2) and basicity (pH > 13) decrease and increase the measured strength, respectively, for abraded microscope slides [7.178]. Static Fatigue: Effect of Time The phenomenon of static fatigue was first reported in 1899 by Grenet [7.175], who experimentally observed a decrease in measured strength with a decrease in the loading rate. But the static fatigue effect was long known among champagne makers, who never used a bottle twice, despite their elevated price. Because of
Strength (GPa) 70
Part A | 7.3
Theoretical strength
20
Pristine glass, as drown
Static
2 0.7
Fig. 7.29 Strength versus
Instantaneous strength
7
Endurance limit
Pristine glass, heat treated Fatigue Formed glass Effect
0.2
Used glass 0.07
Damaged glass
0.02 0.007
Inherent flaws
0.002 10 –9
10 –8
Structural flaws 10 –7
Fabrication Microscopic damage 10 –6
10 –5
Visible damage 10 –4 Effective flaw depth (m)
effective flaw depth for glass, indicating general strength ranges associated with various surface conditions and types of flaws. Instantaneous strength refers to measurements made while minimizing the environmental effect (vacuum conditions, low temperature, high-strainrate loading), while the endurance limit refers to a stress that the specimen will withstand for an infinite amount time without breaking under fatigue conditions (after [7.175])
Mechanical Properties of Glass
Relative strength (σ/σ N) 1.0 Test condition 0.5% RH 43% RH Water
0.9 0.8 0.7 0.6 0.5 0.4 10 –3
10 –2
10 –1
1
10
104 100 1000 Load duration (s)
Fig. 7.30 Reduced strength as a function of load dura-
tion (log scale) for specimens tested: immersed in distilled water (triangles) and in nitrogen atmospheres of 0:5% (circles) and 43% relative humidity. Adapted with permission from [7.178]
7.3.4 Subcritical Crack Propagation As we saw earlier, the mode I fracture toughness value KIc is a critical value below which the crack should not
259
move, and when KI,tip KIc , the crack propagates catastrophically and rapidly at a fraction of the Rayleigh wave speed in the material (about 40% theoretically). This brutal process is usually assisted by a typical sound (acoustic wave emission), and photons as well as particles can be emitted from the crack tip [7.184]. However, through the action of the environment—such as water molecules, for instance, in the present case—crack propagation becomes possible below the KIc value. This is called subcritical crack growth (SCCG). Although crack velocity may be as low as a few angstroms per second, it has a tremendous impact on the lifetime of glass parts, as we saw previously. Catastrophic failure of engineered glass structures can happen hours, days, months or even years after their first use. The Mechanism This phenomenon is rather common to all oxide glasses, and will depend mainly on the nature of the glassforming network (e. g., SiO2 , GeO2 , B2 O3 , P2 O5 ) as well as the mobile ion content, such as LiC , NaC . The greater the number of network modifiers in the glass composition, the more sensitive to subcritical crack growth the glass will be. As silicate-based glasses have been the most studied, the following paragraph is focused on the SiO2 network. However, the reader may satisfy their curiosity regarding phosphate glasses [7.185], borosilicate glasses [7.186] and germanate glasses [7.187] in the scientific literature. To understand the origin of the phenomenon, which has a macroscopic impact, one must go to the molecular level and look at the bonding nature of the glass network (sometimes networks). Glasses are made of strong and highly directional iono-covalent bonds. From fracture mechanics, we saw that an important stress singularity rises at the tip of the crack. As a result, the silica network in the vicinity of the crack tip will be highly deformed. This deformation is likely to mainly impact the Si–O–Si inter-tetrahedral bond angle [7.188–190] (the O–Si–O tetrahedral bond angle will also be affected, but to a much lesser extent). The deformation of the network will modify the dipolar moment of the Si–O bond (an iono-covalent bond), which for a polar solvent such as H2 O molecules will indeed have a strong impact on the energy required for the molecule to approach a Si–O–Si bridge and then react with via hydrolysis. Michalske proposed a three-step mechanism for the hydrolysis reaction of the silica network: 1. The water molecule is adsorbed to the glass surface 2. Two hydrogen bonds are created, one between the silicon atom belonging to the Si–O–Si bridge and the oxygen atom from the water molecule, and the other between the oxygen atom belonging to the
Part A | 7.3
the effect of the environment, strength is no longer a constant, and may further decrease over time, especially if the sample is aged in the presence of water at a stress below failure. Static fatigue describes the time to failure as a function of a given constant load or stress applied to a specimen. One of the important outputs of this phenomenon is that a piece of glass will be able to withstand a higher load for a shorter time than it will for longer times [7.179]. This is illustrated in Fig. 7.30 [7.178], where the reduced strength (=N ) is reported as a function of load duration in three different media: distilled water, and 43 and 0:5% relative humidity. Strength decreases both as load duration increases and as the water content of the medium increases. For low-content media, the strength value at the shorter time is almost equal to the nitrogen value. As was proposed by Charles [7.180, 181] and then Hillig [7.182, 183], static fatigue was explained by the following concept: in the presence of mechanical stress, defects present at the surface grow under the action of the corrosive environment through a surface stress-enhanced chemical reaction. While growing slowly, the defect size may eventually reach a critical size, given the applied stress, which will lead to fracture. As any chemical reaction, its rate will depend on temperature and concentration or availability of water molecules, as well as stress level.
7.3 Fracture: Toughness, Strength and Fracture Mechanics
260
Part A
Fundamentals of Glass and the Glassy State
siloxane bridge and the hydrogen atom from the water molecule 3. The Si–O bond is broken, and two silanols (–Si–OH function) are created. SiO2 C H2 O $ 2Si–OH :
Part A | 7.3
The study of the effect of strain upon silica network hydrolysis by molecular orbital computation [7.188] revealed that a decrease in the inter-tetrahedral angle (Si–O–Si), coupled with a slight decrease in the tetrahedral angle O–Si–O, results in a tremendous increase in the reaction rate. This was also confirmed more recently in [7.189] using quantum mechanical and classical simulations to study the action of a single water molecule on a pure silica nanorod under tensile stress. The authors further showed that the activation energy barrier for siloxane bond rupture was highly strain- (and thus stress)-dependent: the higher the strain, the lower the energy barrier. At this point, it must be noted that some schemas proposed in the literature to illustrate the effect of water on crack propagation tend to lead the reader to a misinterpretation of the origin of the phenomenon. It is not the increase in the Si–O–Si bond angle that causes the lowering of the total energy barrier for hydrolysis to occur, but instead it is a decrease in this bond angle that may occur through a local pinching of the glass network that may exist locally within edge-sharing structures or resulting from the deformation of the 3-D glass network as a consequence of the high strain gradient that exists in the vicinity of a loaded crack tip. This effect has been experimentally observed at indentation sites in silica glass, where an increase in the dissolution rate of the glass is seen for the densified glass [7.106], for which a decrease in the mean Si–O–Si bond angle by up to 5:7ı for a 21% densification rate is reported from Raman spectroscopy measurements [7.83]. V –K Curves: Crack Velocity as a Function of Applied Stress Intensity Factor The subcritical crack growth phenomenon is usually studied in mode I crack propagation and is characterized by the well-known log(V)–K curves, where V is the crack velocity and KI the mode I applied stress intensity factor. In such a mechanical test, the crack propagation velocity is followed as a function of the applied stress intensity factor. More practically, this is done by measuring the crack length over time for a given load applied remotely to the sample. From the crack length, the applied load, a given sample geometry and the linear elastic fracture mechanics, the applied stress intensity factor at the crack tip may be computed. Thus this requires a proper mechanical set-up and a well-defined sample and crack geometry in order
to compute the applied KI from the crack length and the applied remote stress. The first V–K curve was reported in the literature in the late 1960s [7.191], and various sample geometries may be used to study this phenomenon. The most common geometries are the DCB (double-cantilever beam) [7.192] and the DCDC (double-cantilever drilled compression) [7.193], but DT (double-torsion) and CT (compact tension), as well as spherical indentation [7.194], have been used. While being loaded by a dead weight or by a conventional testing machine, the sample can be placed in various environmental conditions (controlled humidity enclosure, liquid cell, ultrahigh vacuum, temperature) in order to characterize the impact of the environment on SCCG. A typical V–K curve is shown in Fig. 7.31; depending on glass composition and environment, these curves may exhibit four different regions, usually labeled 0, I, II and III. Region III. Region III corresponds to a fast crack propagation regime that becomes environmentindependent as water molecules no longer have time to reach the crack tip. Stress intensity tends rapidly toward the critical value KIc , for which crack velocities as high as 1500 m=s are reported [7.195]. Nonetheless, a pseudo-stable crack propagation regime is observed in this region regardless of whether it is under humidity-controlled conditions [7.191, 196, 197]. Also, the mechanism responsible for it is still not well understood. Although the stress intensity factor level at which region III occurs is weakly dependent on humidity level, the latter has a strong impact on the crack velocity at which region III is reached (i. e., lower V values when RH decreases). The liquid in which the crack propagates also has an impact on region III. For alcohols, the chain length of the constituent molecules plays a role in this region: the longer the chain length, the lower the crack velocity. Viscosity of the liquid is log(V) III
Fig. 7.31 II
I
0
K0
KIc KI
Schematic of a typical crack velocity (V) versus mode I applied stress intensity factor (KI ) for oxide glasses, illustrating the different regions
Mechanical Properties of Glass
thought to play a role as the crack reaches its terminal velocity.
7.3 Fracture: Toughness, Strength and Fracture Mechanics
261
Crack velocity (m/s) 100%
Region II. Region II is characterized by a horizontal plateau and is usually observed for a gaseous environment with a controlled humidity level, its existence in liquid water being rather limited (Fig. 7.32). In this region, the crack velocity is almost independent of the applied stress intensity factor, as it results from the equilibrium between the diffusion of the water molecules from the surrounding environment to the crack tip, and the kinetics of the reaction between the water molecules and the deformed glass network at the crack tip. The crack velocity VII as a function of KI can be described by [7.191, 198] VII D 0:0275
X.H2 O;medium/ D.H2 O;medium/ nı
pH2 O p0
exp
Ea C bKI RT
:
III 10 –5 1.0% 0.2% 10 –6
H 2O(l)
0.017%
(7.63)
II
I 0.6
0.7
0.8
0.9
1.0 1.1 Applied force (kg)
Fig. 7.32 Effect of relative humidity on subcritical crack
growth velocity as a function of the applied stress. Adapted with permission from [7.191]
where pH2 O and p0 are the partial pressure of the water phase in the atmosphere and the total atmospheric pressure, respectively, T is the temperature (in K), R is the ideal gas constant, KI is the applied stress intensity factor and Ea is the experimental activation energy. A, m, Ea and b are four empirical and adjustable parameters. Region I may also be fitted by a Paris–Erdogan law (7.63) [7.202], which expresses a power law dependence of VI over KI VI D AKIn :
(7.64)
where VI is the observed crack velocity, KI is the applied mode I stress intensity factor, A is a constant and n is defined as the stress corrosion susceptibility parameter and ranges typically from 10 to 50. The latter equation is more practical from an engineering point of view, as it is often used to estimate the lifetime of glass parts under a certain stress level and given a population of sized defects. Region 0. The fatigue limit occurs at low KI values when the V–K curve cannot be described by the exponential or power law dependency. As KI decreases
Part A | 7.3
VI D A
10%
10 –7
Region I. Region I is characterized by a linear dependence of log.V/ as a function of KI (Fig. 7.32); this region is essentially governed by the kinetics of a chemical reaction, the hydrolysis of the deformed silica network at the crack tip. Therefore, this region will be dependent on parameters such as the concentration of the reactive chemical species, the temperature and the glass composition. The RH level has an important effect on the V–K curves (Fig. 7.33): all three regions are observed, so the curve keeps its general shape, but as the RH rises from 0:017 to 100%, the curves are shifted to higher velocities [7.191]. From a reaction-rate theory developed initially by Charles and Hillig [7.182], Wiederhorn [7.191, 201] suggested that the exponential dependence of VI , the crack velocity in region I, upon KI the stress intensity factor can be described by (7.63), which takes into account the effects of humidity level, temperature and glass composition m
30%
(7.62)
where X.H2 O;medium/ and D.H2 O;medium/ are the molar concentration of water and the diffusion coefficient of water molecules in the considered medium (air, liquid), respectively, n is the order of the chemical reaction and ı is the diffusive boundary layer thickness in front of the crack tip. The molecular flow rate of water molecules toward the crack tip may be a rather complicated process [7.199, 200]; for instance, as reactive molecules approach the crack tip, the distance between the crack walls will, at some point, become smaller than the free path between intermolecular collision. For dilute gases, this may inhibit the progression of reactive species toward their reaction site.
10 –4
262
Part A
Fundamentals of Glass and the Glassy State
Crack velocity (m/s) Borosilicate Silica 10
–5
10 –6
10 –7 Aluminosilicate I
Soda-lime 10 –8
10 –9
10 –10
3
limit is usually observed for alkaline-containing glasses (presence of mobile ions such as LiC or NaC ), but if the proportions of these mobile ions in the glass composition becomes too important, instead of the drop-off of the crack velocity near K0 , a plateau of constant V is observed, while KI tends toward zero. In this later case, a self-propagation of the crack is observed. The environment is also of importance, as dependence on the pH value of the solution K0 value will vary (higher values from basic pH toward acidic pH). Explanations for the existence of the fatigue limit are still a hot topic. Three theories have been put forth:
4
5
6 KI (105 × N/m 3/2)
Fig. 7.33 Illustration of the effect of the glass composition on the region 0 and region I behavior. Borosilicate and soda-lime exhibit a departure from (7.62), a sign of the existence of a fatigue limit. Adapted with permission from [7.192]
Part A | 7.3
to a threshold value below which crack displacement is no longer observed, this threshold value is noted as K0 (Fig. 7.31). The fatigue limit is of importance from an engineering point of view, as it provides through LEFM considerations a stress level limit below which a crack is no longer dangerous. The fatigue limit has been widely studied over the years [7.203–207], as it is a quite complicated phenomenon, the origins of which are still being debated. Typical and interesting behaviors have been observed experimentally near the fatigue limit [7.203]. Gehrke et al. [7.203] and then Michalske [7.204] reported that when a crack is held for a certain time while under load at or below the K0 value, it takes time before the crack propagation can be observed when reloaded to higher KI values. The closer to K0 the holding KI , the longer the holding time, and the lower the reloading KI (yet KI > K0 ), the longer the time delay before crack propagation. Glass chemical composition has a tremendous effect on the threshold behavior (value of K0 and the relative strength of the associated effects observed experimentally); a fatigue
1. Ion exchange process: In this process, the mobile ions from the glass (such as KC , NaC and LiC ) and the hydronium ions (H3 OC ) from the solution may be exchanged. The important stress gradient near the crack tip acts as a driving force for alkaline ions to diffuse toward the crack tip. Due to this ion exchange, an exchanged surface layer is created, with thickness varying linearly with the square root of time. As exchanged ions do not have exactly the same size, stresses can be generated in this layer; in the case of H3 OC $ NaC exchange, it was shown that compressive stresses of up to 2:5 GPa could be generated [7.208]. Stresses developed in this ion-exchanged layer add a stress intensity factor component to the total stress intensity factor seen by the crack (KI,tot D KI,LFEM C KI,layer ). If KI,layer < 0 (compressive stress state), a crack tip shielding effect is obtained, which provides conditions for the existence of a fatigue limit. The interdiffusionbased semi-analytical model proposed in Fett et al. [7.209] quantitatively describes most of the behavior observed experimentally; only the time to restart crack propagation does not provide the finest details of experimentation. Nonetheless, in the case of the potassium ion, which has a size similar to that of H3 OC , a limited fatigue effect is expected for potassium aluminosilicate glasses (RO-Al2 O3 SiO2 , R D KC , NaC , LiC ). In fact, Gehrke reported that potassium ions are the most effective in pushing the fatigue limit value to a higher percentage of KIc , followed by NaC then LiC . 2. Crack tip blunting [7.210]: At low KI values, the sides of the crack tip are expected to dissolve away faster than the crack tip. Moreover, because of the confined environment, a reprecipitation phenomenon of the products of dissolution is expected [7.211]. Those two mechanisms will contribute to the blunting of the crack tip, which in time will reduce the stress intensity value (from LFEM, KI is linked to crack tip radius). From a blunt crack tip, the crack would need higher stress intensity val-
Mechanical Properties of Glass
ues and longer time (stress induces a resharpening process) to repropagate [7.212]. See also [7.213, 214] for complementary discussion regarding this theory. 3. More recently, an interesting alternative explanation was proposed which is based on surface stress relaxation resulting from water diffusion in the glass network. The relaxation of the tensile stress present at the crack tip will, upon release of the remotely applied stress, turn into compressive stresses, the level of which was shown to be in the gigapascal range for silica glass fibers [7.215]. Stress relaxation should follow a diffusioncontrolled process, and stress relaxation during aging time may be computed. For crack tip stress intensity factor, as for the work of Fett et al. (initially used by McMeeking and Evans for crack tip shielding in zirconia [7.216]), the superposition principle is applied, and the total stress intensity factor at the crack tip is the sum of two contributions: one from the remote applied stress, and a second and negative one from the relaxed stress that acts as a shielding component. This model quantitatively describes experimentally observed behaviors in terms of decreased crack velocity near the fatigue limit value, as well as time delay to restart crack propagation.
quenching: the higher the Tf , the lower the density of the glass. Raman spectra of silica glasses having different Tf show that three- and four-fold ring concentrations increase as Tf increases. Those rings are more strained than larger rings (i. e., smaller Si–O–Si bond angle), which can have an impact on the kinetics of the hydrolysis reaction. This chapter about cracks in glass would not be complete without a word about recent techniques that have provided a considerable amount of useful knowledge regarding either in situ crack propagation [7.193, 220–225] or postmortem observation of fracture surfaces [7.226–230]. Atomic force microscopy (AFM) has a lateral resolution of a few nanometers, coupled with a vertical resolution better than 0:1 nm; as such, it is almost the only tool that glass scientists can use to investigate, at the relevant (nanometer) scale, the fracture behavior of glass. In situ studies have confirmed that the deformation of the free surface of a glass sample around the crack tip follow the LFEM prediction down to a 10 nm zone around the crack tip which was the estimated limit of resolution of the technique. Studies have related the existence of plasticity event at the crack tip arguing that the crack propagates in the subcritical regime through nucleation–growth– coalescence of nanocavities. Nonetheless, if so, their size would have to be smaller than the process zone. From postmortem study [7.231, 232], no traces of such cavities were observed on the fractured surfaces (like for metallic glasses [7.233]), meaning that if they exist, they have to be smaller than the experimental resolution. In situ observation has also evidenced the migration of mobile ions while the crack is moving in region I of the subcritical regime [7.234]. AFM also allowed, under ultrahigh vacuum conditions, to image the atomic structure of glass surfaces for silica and borosilicate glasses revealing the boroxole ring structure for the latter glass. The evolution of the roughness of glass fracture surfaces over 13 decades of crack velocity allowed linking the surface corrugations to the nanoscale heterogeneities of the glass (polyamorphism, local variation of density, elastic modulus, stress state resulting from quenching) as initially stated by Kurkjian et al. [7.235].
7.4 Conclusion From a practical perspective, the usable strength of a glass structure is what matters. As a customer, one understands its importance, but unfortunately only perceives its negative result: the failing of a device or a structural part. The usable strength is directly connected to the whole glass science, as it is the result of
a glass composition being able to resist crack initiation and then propagation—whether it is during manufacturing or later when in use. Oxides glasses are the archetype of homogeneous isotropic brittle behavior, so it may seem like only three parameters would be sufficient to characterize the
263
Part A | 7.4
Subcritical crack growth is a rather complex phenomenon, the mechanisms of which take place at the nanometer scale and may vary with subtle glass compositional or structural modifications, for instance, water content and thermal history, usually characterized by the fictive temperature (Tf ) [7.217]. Water in glass is known to decrease the mean connectivity of the network, thus leading to a decrease in properties such as Young’s modulus, viscosity [7.218] and Tf [7.219] as its content rises. It will therefore have an impact on the subcritical propagation of the crack. The fictive temperature is also an important parameter, which is an artificial temperature in the sense that it cannot be measured. Tf represents the temperature at which the structure of the glass was frozen, and Tf may be varied by applying a different temperature in the transformation range for a long enough time span before a rapid
7.4 Conclusion
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Part A | 7
whole mechanical behavior of a glass: two elastic moduli and fracture toughness. Accordingly, it seems that the only thing we have to do to understand and predict the mechanical behavior of glasses is to correlate the glass structure to these three parameters. Alas, nothing is that simple: many more parameters are required, and this correlation is rather difficult to establish. Indeed, glasses are disordered materials. Consequently, it is always difficult to analyze their structure. The elastic moduli are strongly connected to the shortand medium-range order (SRO and MRO) of glasses. Nowadays, even if no universal model exists for predicting the elastic moduli of glasses based on their composition alone, a simple measurement of the elastic moduli—something that is not very complicated— provides important information regarding their structure. Importantly, for a given glass family, we are able to predict how the moduli will qualitatively evolve with the composition if we have good knowledge of the SRO and MRO. Conversely, if the structure is completely unknown, we can simply try to provide a model of the structure and then check it by comparing the experimental elastic moduli with that predicted by the model. The discrepancies will highlight all the structural peculiarities that are not taken into account, including nanophase separation or unexpected coordination changes. Elastic moduli depend on the temperature, pressure and the fictive temperature. Consequently, measuring these moduli—something that is, again, not terribly complicated, and is not really time-consuming—allows us to track structural changes in the SRO and MRO versus temperature, pressure or thermal history. But glasses do not behave as pure elastic solids until they break. Inorganic glasses, despite their brittleness, undergo plasticity, especially during sharp contact, by shear flow and/or permanent densification. Although the constitutive law of this ductile behavior is still not well established and the physical mechanisms not clearly understood (especially regarding shear flow in oxide glasses), significant progress has been made in recent decades, thanks to new approaches, new techniques for investigating densified volume, and molecular dynamics simulations. Nevertheless, we are still far from a predictive model of glass ductility, especially since investigations up to now have been focused
mainly on silica glasses. But ways are open for the development of glasses with ideal plasticity, that is, for which the contact load required for crack nucleation is very high. The mechanical behavior of glasses offers a rather more complex world than it is expected from its usual elastic-brittle definition. Physical parameters such as E, , H, KIc are very useful parameters from an engineering point of view, nonetheless they do not transcribe neither the complexity nor the large variety of mechanisms at stake either during plasticity or crack propagation. Subcritical crack growth occurs in glasses (crack propagation at a stress intensity factor lower than the fracture toughness) because large stress and deformation at crack tips favor chemical reactions with water as well as ionic mobility. As chemical reactions are thermally activated processes, the fatigue resistance of glasses is strongly temperature-dependent, and of course depends on the humidity and the glass composition. Consequently, it is also very difficult to predict the in-service strength of a glass structure based on the glass composition, as it is not an intrinsic property, and furthermore is highly dependent on external parameters such as manufacturing processes and postmanufacturing handling. For practical applications, it is important to develop glasses with high elastic moduli (especially reinforcing fibers in composites), or at least with specific moduli. Our knowledge of the relationship between the SRO and MRO of glasses and their elasticity is now sufficient to efficiently design new glasses for this purpose. It is also clearly important to develop glasses with high mechanical strength (e. g., glasses in civil engineering, windshields, screens, reinforcing fibers, bullet-proof windows), and thus to develop new glasses with high resistances to crack initiation and propagation. Many efforts have been made in recent decades to understand the relationship between glass structure and crack resistance. While there is still a long way to go to obtain glass structures with strength close to the intrinsic strength, these efforts have paved to way for the development of glasses with better crack resistance thanks to both adapted and newly developed glass composition and improved glass processing and manufacturing.
References 7.1 7.2
R. Hooke: Lectures de Potentia Restitutiva (John Martyn, London 1931) P.M. Morse: Diatomic molecules according to the wave mechanics. II. Vibrational levels, Phys. Rev. 34(1), 57 (1929)
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P.K. Gupta, C.R. Kurkjian: Intrinsic failure and nonlinear elastic behavior of glasses, J. Non-Cryst. Solids 351(27–29), 2324–2328 (2005)
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E. Gross: Change of wave-length of light due to elastic heat waves at scattering in liquids, Nature 126(3171), 201 (1930) W. Hayes, R. Loudon: Scattering of Light by Crystals (Courier Corporation, Chelmsford 2012) S. Speziale, H. Marquardt, T.S. Duffy: Brillouin scattering and its application in geosciences, Rev. Mineral. Geochem. 78(1), 543–603 (2014) G. Hernández: Fabry–Perot Interferometers (Cambridge Univ. Press, Cambridge 1988) S.M. Shapiro, R.W. Gammon, H.Z. Cummins: Brillouin scattering spectra of crystalline quartz, fused quartz and glass, Appl. Phys. Lett. 9(4), 157–159 (1966) E.S. Zouboulis, M. Grimsditch, A.K. Ramdas, S. Rodriguez: Temperature dependence of the elastic moduli of diamond: A Brillouin-scattering study, Phys. Rev. B 57(5), 2889 (1998) S.V. Sinogeikin, J.M. Jackson, B. O’Neill, J.W. Palko, J.D. Bass: Compact high-temperature cell for Brillouin scattering measurements, Rev. Sci. Instrum. 71(1), 201–206 (2000) J.A. Bucaro, H.D. Dardy: High-temperature Brillouin-scattering in fused quartz, J. Appl. Phys. 45(12), 5324–5329 (1974) C.H. Whitfield, E.M. Brody, W.A. Bassett: Elastic moduli of NaCl by Brillouin scattering at high pressure in a diamond anvil cell, Rev. Sci. Instrum. 47(8), 942–947 (1976) C. Zha, R.J. Hemley, H. Mao, T.S. Duffy, C. Meade: Acoustic velocities and refractive index of SiO2 glass to 57.5 GPa by Brillouin scattering, Phys. Rev. B 50(18), 13105–13112 (1994) H. Shimizu, E.M. Brody, H.K. Mao, P.M. Bell: Brillouin Measurements of Solid n-H2 and n-D2 to 200 kbar at room temperature, Phys. Rev. Lett. 47(2), 128 (1981) C. Sonneville, D. De Ligny, A. Mermet, B. Champagnon, C. Martinet, G.H. Henderson, T. Deschamps, J. Margveritat, E. Barthel: In situ Brillouin study of sodium alumino silicate glasses under pressure, J. Chem. Phys. 139(7), 074501 (2013) W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7(06), 1564–1583 (1992) A.N. Sreeram, A.K. Varshneya, D.R. Swiler: Molar volume and elastic properties of multicomponent chalcogenide glasses, J. Non-Cryst. Solids 128(3), 294–309 (1991) W.H. Wang, C. Dong, C.H. Shek: Bulk metallic glasses, Mater. Sci. Eng. R Rep. 44(2/3), 45–89 (2004) T. Rouxel: Elastic properties and short-to mediumrange order in glasses, J. Am. Ceram. Soc. 90(10), 3019–3039 (2007) L.C.E. Struik: Integration of polymer science and technology? In: Integration of Fundamental Polymer Science and Technology 3, ed. by P.J. Lemstra, L.A. Kleintjens (Springer, Dordrecht 1989) pp. 3–16 C. Zwikker, R. Smoluchowski: Physical properties of solid materials, Phys. Today 8, 17 (1955)
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F.P. Mallinder, B.A. Proctor: Elastic constants of fused silica as a function of large tensile strain, Phys. Chem. Glasses 5(4), 91–103 (1964) L.H. Donnell: A new theory for the buckling of thin cylinders under axial compression and bending, Trans. ASME 56(11), 795–806 (1934) J.K. Banerjee: Barreling of solid cylinders under axial compression, J. Eng. Mater. Technol. 107(2), 138–144 (1985) V. Chean, E. Robin, R. El Abdi, J.C. Sangleboeuf, P. Houizot: Use of the mark-tracking method for optical fiber characterization, Opt. Laser Technol. 43(7), 1172–1178 (2011) R.J. Angel, J.M. Jackson, H.J. Reichmann, S. Speziale: Elasticity measurements on minerals: A review, Eur. J. Mineral. 21(3), 525–550 (2009) S. Timoshenko: History of Strength of Materials: With a Brief Account of the History of Theory of Elasticity and Theory of Structures (Courier Corporation, Chelmsford 1953) H.J. McSkimin: Measurement of elastic constants at low temperatures by means of ultrasonic waves—data for silicon and germanium single crystals, and for fused silica, J. Appl. Phys. 24(8), 988–997 (1953) H.J. McSkimin: Notes and references for the measurement of elastic moduli by means of ultrasonic waves, J. Acoust. Soc. Am. 33(5), 606–615 (1961) V. Keryvin, T. Rouxel, M. Huger, L. Charleux: Elastic moduli of a ZrCuAlNi bulk metallic glass from room temperature to complete crystallisation by in situ pulse-echo ultrasonic echography, J. Ceram. Soc. 116(1356), 851–854 (2008) M.J. Bamber, K.E. Cooke, A.B. Mann, B. Derby: Accurate determination of Young’s modulus and Poisson’s ratio of thin films by a combination of acoustic microscopy and nanoindentation, Thin Solid Films 398, 299–305 (2001) X. Xiao, N. Hata, K. Yamada, T. Kikkawa: Mechanical properties of periodic porous silica low-k films determined by the twin-transducer surface acoustic wave technique, Rev. Sci. Instrum. 74(10), 4539– 4541 (2003) ASTM E1875-13: Standard Test Method for Dynamic Young’s Modulus, Shear Modulus, and Poisson’s Ratio by Sonic Resonance (ASTM, West Conshohocken 1875) G. Roebben, B. Bollen, A. Brebels, J. Van Humbeeck, O. der Biest: Impulse excitation apparatus to measure resonant frequencies, elastic moduli, and internal friction at room and high temperature, Rev. Sci. Instrum. 68(12), 4511–4515 (1997) G. Roebben, B. Basu, J. Vleugels, J. Van Humbeeck, O. der Biest: The innovative impulse excitation technique for high-temperature mechanical spectroscopy, J. Alloys Compd. 310(1/2), 284–287 (2000) L. Brillouin: Diffusion de la lumière et des rayons X par un corps transparent homogène. Influence de l’agitation thermique, Ann. Phys. 9(17), 88–122 (1922)
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7.47 7.48
7.49
7.50 7.51
7.52 7.53
7.54
A. Makishima, J.D. Mackenzie: Calculation of bulk modulus, shear modulus and Poisson’s ratio of glass, J. Non-Cryst. Solids 17(2), 147–157 (1975) A.K. Bandyopadhyay, L.C. Ming: Pressure-induced phase transformations in amorphous selenium by x-ray diffraction and Raman spectroscopy, Phys. Rev. B 54(17), 12049 (1996) M.E. Fine: Elasticity and thermal expansion of germanium between 195 and 275 °C, J. Appl. Phys. 24(3), 338–340 (1953) G. Yang, B. Bureau, T. Rouxel, Y. Gueguen, O. Gulbiten, C. Roiland, E. Soignord, J.L. Yarger, J. Troles, J.-C. Sangleboeuf, P. Lucas: Correlation between structure and physical properties of chalcogenide glasses in the Asx Se1-x system, Phys. Rev. B 82(19), 195206 (2010) G. Yang, Y. Gueguen, J.-C. Sangleboeuf, T. Rouxel, C. Boussard-Plédel, J. Troles, P. Lucas, B. Bureau: Physical properties of the Gex Se1-x glasses in the 0 de e , which may be termed p-like conduction [19.261]. Since d and are governed by shallow and deep traps respectively, the latter appears to largely depend upon samples and/or experimental artifacts. In stabilized a-Se films, the carrier ranges tend to become higher than those in pure films [19.86, 110], the reason having been theoretically considered [19.111]. To the author’s knowledge, no transport data have been available for l-Se.
19.5.2 Avalanche Breakdown Juška and Arlauskas discovered that a-Se films in an optical time-of-flight configuration (Fig. 19.17) exhibit photoconductive avalanche breakdown [19.262, 263]. We see in Fig. 19.17 that, at electric fields above 1 MV=cm, hole and electron photocurrents abruptly increase. On the other hand, during invesCurrent density (A/cm 2) 10 –4 Hole photocurrent Electron photocurrent Dark current 10 –5
10 –6 a-Se CeO2 Au (cathode)
Al (anode) Glass substrate
10 –7 A
10 –8
10 –9
0
0.5
1.0 1.5 Electric field (106 V/cm)
Fig. 19.17 Electric field dependence of photo- and dark-
current density at room temperature for a 1 m thick a-Se film under illumination of 400 nm light. The inset illustrates the sample structure, in which the facing electrode area is 1 mm 1 mm and excitation light is incident on the glass substrate (after [19.259])
Amorphous Selenium and Nanostructures
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tin-oxide (ITO) and Al films (no blocking electrodes inserted) at 1 MV=cm, and proposed a different idea for the multiplication mechanism. Park and Tanioka [19.267] analyzed HARP characteristics in a phenomenological way. Tanaka suggests a role for tail states above the valence band for impact ionization of holes [19.279].
19.5.3 Electrical Switching and Crystallization Since the crystallization temperature of a-Se is relatively low at 100 ı C (Fig. 19.3), Joule-heated crystallizations are likely to occur. It may behave as an electrical Ovonic memory effect [19.280, 281], which is an ongoing topic of research in phase-change materials such as Ge2 Sb2 Te5 . Actually, the electrical switching and/or memory phenomena of a-Se had been explored in the 1970s and 1980s [19.282–289], though those results seem to be mostly forgotten. However, further studies of the behavior in the elemental material, which may have some relation to the photocrystallization (Sect. 19.6.3), will shed light upon the electrical phase change. Hence, we briefly take a look on previous studies below. Several pioneering experiments uncovered switching (breakdown) behaviors in g- [19.282] and aSe [19.283–289] samples with symmetric [19.282] or asymmetric [19.283, 284, 289] electrodes. For instance, Matsushita et al. [19.283] investigated a memory effect in Fe point-contacted a-Se=SnO2 structures. Petretis et al. [19.285] observed electrical breakdowns in a-Se films subjected to corona charging. In these phenomena, transformations from a- to t-Se are likely to take place. The threshold fields of these switchings were 0:11 MV=cm [19.282–289], which are similar to that in the avalanche breakdown (Sect. 19.5.2). However, in contrast to the bulky avalanche breakdown, the electrical switching seems to occur with carrier injections from electrodes or surfaces. Mechanisms of the electrical crystallization remain confusing. Taking the photocrystallization phenomenon (Sect. 19.6.3) into account, we may envisage pure electronic mechanisms [19.284, 289]. Alternatively, Bolotov and Komarova [19.286] demonstrate electric field effects on thermal crystal growth in aSe. Otherwise, Joule heating could be responsible. In some memory effects, diffusion of electrode metals such as Pt and Ag has been detected [19.282, 288, 289]. It is therefore plausible that several switching and/or memory processes play roles in each observation. Finally, we mention that optical effects on electrical memory phenomena have been demonstrated using aSe=SeO2 heterojunctions [19.290] and corona-charged
Part B | 19.5
tigations of a-Se vidicon targets, Tanioka et al. noticed dramatic sensitivity enhancements [19.264] arising from carrier multiplications, which have been developed for high-gain avalanche rushing amorphous photoconductor (HARP) vidicons (Sect. 19.7). These two discoveries have then initiated many fundamental studies, which delineate avalanche behaviors as functions of electric field ( 1:6 MV=cm) [19.259], temperature (100300 K) [19.259, 262, 263], a-Se film thickness (0:5200 m) [19.259, 263], and light wavelength (400600 nm) [19.217, 259], and also in several sample-electrode arrangements [19.265–267]. However, scientifically, the avalanche breakdown in a-Se still remains puzzling. The avalanche breakdown in crystalline semiconductors such as Si and InSb has been identified, which appears through successive impact ionizations by field-accelerated hot carriers. But why can the avalanche breakdown occur in an amorphous semiconductor, which probably has a short carrier mean free paths? In addition, the breakdown in a-Se becomes more conspicuous at higher temperatures [19.259, 262, 263], which is opposite to the behavior of conventional and impurity-related [19.268] carrier multiplications in crystalline semiconductors. Also, why does the phenomenon appear clearly only in a-Se, but not in other amorphous semiconductors such as gAs2 Se3 and a-Si:H and in crystalline Se [19.269, 270]? We just know that single crystalline t-Se undergoes piezoelectric oscillations at high fields [19.2], and polycrystalline Se rectifiers exhibit injection-related current increases [19.271, 272]. For such fundamental problems, Canadian groups continue active studies [19.195–197, 273–277]. They have applied a lucky-drift model [19.278] to the amorphous film [19.274–276], under an assumption that carriers undergo elastic collisions with disorder potentials, whereby its energy can successively increase, giving rise to the impact ionization. Nevertheless, estimated lengths of the mean free path between elastic collisions are only 0:5 nm [19.274, 276], and we may cast doubt upon the particle picture [19.279]. Following the model, they have interpreted the temperature dependence with a thermally activated increase in the hole mobility [19.277], which is governed by tail states. Besides, the uniqueness to a-Se has been related to its low vibrational energy ( 30 meV, Fig. 19.7) [19.275], arising from the heavy atomic mass, 79, which is effective at suppressing energy dissipation of accelerated carriers. If this were the case, can we envisage the avalanche multiplication in a-Te (or a-Se-Te alloy) films? Finally, other approaches to the breakdown phenomenon should also be mentioned. Masuzawa et al. [19.266] have demonstrated carrier multiplication in Se/As-Se multilayers sandwiched between indium-
19.5 Electrical Properties
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Part B
Glass Families
a-Se films [19.291], which also seem to involve crystallization.
19.5.4 Electrode, Junction, and Multilayer The choice of metal electrodes is a key issue when examining (photo)electrical properties of semiconductors. For pure a-Se films (Ts D 50 ı C), Mort and Lakatos [19.200] demonstrated using internal photoemission spectroscopy that the barrier height 'h for holes, defined in Fig. 19.18, becomes smaller in the order of Al ('h 1:40 eV and 'M 4:3 eV), Cu ( 1:10 eV, 4:7 eV), and Au ( 0:85 eV, 5:1 eV), which suggests that Au makes a good hole-injecting contact. Au is also known to be less reactive with a-Se than Al [19.292]. Nevertheless, for stabilized a-Se films contacting with metal electrodes of various kinds, Kasap and Rowlands [19.109] found no correlation between dark currents and the metal work functions. Reasons for these seemingly different observations are unknown. Blocking electrodes have also been explored, mainly for photoconductive experiments and applications. In the usage in xerographic photoreceptors, a-Se films deposited on oxidized Al layers are exposed to positive corona discharges, in which the oxide is expected to suppress electron injection [19.15, 86]. For similar purposes, Sb2 S3 [19.93, 265], polyvinylcarbazole [19.256, 293], and cellulose acetate [19.265] films have also been employed. In other cases, we may need blocking electrodes for both polarities. Specifically, since the hole is more mobile, good blocking anodes—even under high voltages—would be required. For such purposes, several layers have been inspected, e. g., nC -type SnO2 (Eg 3:5 eV and 'M 4:8 eV) [19.93, 290], CeO2 (Eg 3:4 eV) [19.93, 265, 267, 294], GeO2 (Eg 5 eV) [19.267], ZnO (Eg 3:2 eV) [19.295], and polyimide (Eg 7 eV) [19.294, 296, 297].
χ ϕM Fermi level
ϕe
Vacuum Conduction band
E gμ
ϕh
Valence band
Metal a-Se
Fig. 19.18 Band diagram of a metal/a-Se junction (af
ter [19.200]). The photoemission threshold Eg C 6 eV and the mobility gap Eg 2:3 eV
Junctions including a-Se films have been prepared mainly for investigating and/or improving photoconductive characteristics. For instance, aSe=polyvinylcarbazole and a-Se=a-Se1x Tex were devised as xerographic photoreceptors [19.200, 298, 299]. More recently, Campbell [19.300] has demonstrated that the heterojunction using a-Se and an organic film, octabutoxy tin naphthalocyanine dichloride, can extend photoconductive responses to wavelengths of 1 m under reverse-bias conditions. Here, it is mentioned that few studies have been performed for a-Se/t-Se junctions [19.254], while the inspections will be valuable for understanding electronic properties of partially crystallized a-Se films. Multilayer structures are expected to extend spectral performance and enhance thermal stability. Maruyama [19.93] examined Se=As2 Se3 films, demonstrating that the 1 nm-periodicity structures can be regarded as an almost uniform material. Masuzawa et al. [19.266] and Yu et al. [19.301] also studied similar systems for improving photoconductive responses. Nesheva et al. uncovered interfacial effects on thermal stability in Se=CdSe [19.302] and Se=Se-Te [19.99] films. In Se=As2 S3 , however, photoinduced diffusion is likely to take place [19.303, 304].
Part B | 19.6
19.6 Light-induced Phenomena Discovery of light-induced structural changes in chalcogenide glasses can be traced back to a short note reporting “the fluidity in g-Se under illumination” by Vonwiller about a century ago [19.305]. Nevertheless, his note attracted little interest. Afterwards, the pioneering work of optical (and also electrical) phase changes by Ovshinsky and Fritzsche [19.280] triggered worldwide studies on light-induced structural changes. We now know several kinds of phenomena in chalcogenide glasses, such as a-Se and As2 S3 ,
which have repeatedly been reviewed [19.5, 6, 223, 306]. What are the outcomes obtained through studying the light-induced phenomena in a-Se? It may be fair to admit that since the glass-transition temperature ( 310 K) of a-Se is just above room temperature, applications of the phenomena will be limited. Or, in some cases, they may cause serious problems in photoconductive applications, e. g., photocrystallization in HARP films [19.307], and accordingly suppression is
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19.6.1 Transitory Effects As mentioned above, g-Se undergoes softening when exposed to light [19.305], and later studies have emphasized respective features; photoinduced relaxation [19.316, 317], aging [19.316, 318], melting [19.319], fluidity [19.320], viscosity [19.321], and so forth [19.322–324]. It is plausible that these transitory changes cause modifications of thermal properties [19.316, 325]. Transitory volume expansion and oscillation have also been discovered [19.326, 327]. Besides, transitory absorption, which has been known for As-S films [19.6], was demonstrated also for aSe at room temperature [19.328, 329]. The origin may be related to the defective absorption (Sect. 19.4.3) and/or the photodarkening (Sect. 19.6.2). Mechanisms of photoinduced changes could be inferred from the excitation spectra. Fig. 19.19 [19.314] compares three kinds of spectra with the absorption spectrum ˛. (1) shows the photoluminescence excitation spectrum (Fig. 19.15), (2) represents the photodarkening magnitude (Sect. 19.6.2), which peaks in the nonphotoconducting spectral region (Fig. 19.13), and (3) includes the photoconduction (Fig. 19.15). The result of Larmagnacs et al. implies that the photoinduced relaxation α (cm –1) 106
α 10
4
3
2
102
1
10 0
E gT 1
2
3
ħω (eV)
Fig. 19.19 Comparison of the absorption-edge spectrum ˛ and the Tauc optical gap EgT with three spectral types of photoinduced phenomena at 80 K (after [19.314]); (1) includes photoluminescence-excitation spectrum (after [19.238]), (2) saturated edge-shift in the photodarkening (after [19.314]), and (3) photoconductivity (after [19.206]), a quantum efficiency of photoetching (after [19.131]), and probably the photocrystallization (after [19.254, 315])
Part B | 19.6
strongly required, for which the understanding of induction processes is a prerequisite. On the other hand, the existence of only the homopolar bond SeSe makes the underlying mechanisms more specific. In other words, it is important to examine whether a phenomenon is unique to the elemental material or universal to compound chalcogenide glasses. In such contexts, studies using S and Te are also tempting, while the glass-transition temperature in a-S is below room temperature ( 260 K [19.308]) and a-Te films appear to crystallize at room temperature ( 285 K) without undergoing a glass transition [19.309]. Incidentally, Sakaguchi and Tamura [19.306] have investigated lightinduced phenomena in thin ( 1 m) l-Se and l-S samples (above the melting temperatures), the results being very valuable to examining the roles of the equilibrium states. Light-induced phenomena in a-Se are of several kinds, so that a classification may be instructive. At the outset, the phenomena can be divided into two. One is the thermal change—heat mode—in which temperature rises induced by light absorption are assumed to govern the structural changes; a known example being the optical phase change [19.280], which has widely been commercialized using Ge2 Sb2 Te5 films [19.281], while studies for a-Se remain to be undertaken. The other is the photoinduced change—photon mode—in which not the temperature rise but electronic excitations directly cause successive atomic transformations. The photon mode can further be divided into two: those appearing only during illumination (as photoconductivity) and those existing after illumination, the two being referred to as transitory and memory effects respectively. Besides, the memory effect may be irreversible (permanent) or reversible (metastable), in the sense of whether annealing treatments can or cannot restore the state before illumination. We may regard the irreversible change as a kind of photoinduced stabilization processes, the known examples being photocrystallization (Sect. 19.6.3) and ring-to-chain transformations [19.70, 310]. The reversible can further be divided into two by required annealing temperatures, which may be Tg =2 (defective) or Tg , the former being already touched on in Sect. 19.4.3. Here, it is plausible that a transitory change at room temperature and a low-temperature defective phenomenon have some common origins, which remains to be studied. Finally, all the photoinduced changes can be divided into scalar or vector, in the sense of whether the polarization of excitation light provides isotropic or anisotropic changes. It should also be mentioned here that not only visible light, but electron [19.5, 311, 312] and highenergy [19.5, 190, 313] beams can exert some structural changes.
19.6 Light-induced Phenomena
664
Part B
Glass Families
efficiency has the type (2) [19.316]. We then straightforwardly assume geminate-pair excitations as the first step of the transitory change. The next problem is whether the excitation induces some atomic changes directly through electron–lattice interaction or indirectly through temperature rises. Inasmuch as the glass-transition temperature of a-Se is just above room temperature, low-temperature experiments are preferred for the distinction. Such studies [19.317] seem to support major roles for the direct mechanism, e. g., excited geminate pairs cut SeSe bonds through some processes, the consequence appearing as the fluidity increase etc. Intra- and interbond mixing may occur in the process, which is consistent with an EXAFS result, demonstrating an increase in the atomic coordination number by 4% in a-Se films at 30 K during illumination (Xe lamp, 100 mW=cm2) [19.330]. With terminations of the exposure, relaxational bond restorations take place. Quantitative formulations connecting induced fluidity with light intensity will be a challenging subject.
19.6.2 Photodarkening and Deformations
Part B | 19.6
There may be some confusion about the usage of photodarkening. In the broadest sense, the word can represent all the photochromic effects, i. e., decreases in optical transmittance induced by illumination, which make the material darker. In the research area of chalcogenide glasses, however, it has restrictively been used to denote photoinduced nearly parallel red-shifts of the optical absorption edge, which can be recovered with annealing at around the glass-transition temperature [19.6, 223, 306]. The word does not include transitory and irreversible photochromic effects. The photodarkening in chalcogenide glasses such as As2 S.Se/3 has been comprehensively studied [19.6, 223, 306]. We may trace its discovery in a-Se back to Chang [19.331], though he seemed to examine optically thick samples. (For quantitative evaluation of photodarkening characteristics, specifically the time variation, inspected samples are preferred to be optically thin, ˛L 1, where L is the sample thickness and ˛ ( 104 cm1 ) is the absorption coefficient to excitation light. Accordingly, most experiments have employed deposited films of L 10 m. Such experiments demonstrate exponential growths, which can be connected with the first-order reaction kinetics [19.332].) Later studies have confirmed its existence, e. g., a redshift of 50 meV at „! 2:3 eV in a- and g-Se at 80 K [19.64, 314, 333, 334], and also under high pressures [19.335–337]. In addition, although no spectral shifts having been presented, photoinduced transmission decreases reported in [19.338–341] seem to arise from the photodarkening. Taking the Kramers–
Kronig relation into account, we straightforwardly envisage that the photodarkening accompanies an increase in refractive index [19.6, 332]. Despite its simple appearances, the mechanism of the photodarkening in chalcogenide glasses has been controversial. For instance, some researchers asserted that the hetero- to homopolar bond change causes the photodarkening [19.306]. Actually, Raman-scattering spectroscopy manifests that in As2 S3 (super)bandgap illumination produces AsAs bonds, which may be oxidized to As2 O3 crystals in some conditions, and also give rise to the photodarkening. Practically, it is very plausible that superbandgap photons induce several structural changes. However, why is the production of AsAs bonds able to cause a red-shift of the optical absorption edge? It should also be noted that subgap illumination can induce the photodarkening in As2 S3 [19.314, 341], producing few AsAs bonds. In addition, the fact that the photodarkening occurs unambiguously in a-Se, and also in a-S [19.336], evinces that such bond alternations cannot have a universal origin. For the photodarkening mechanism, it is valuable to recall the excitation spectra. In a-Se, the red-shift is the highest ( 50 meV at 80 K) upon illumination of light with the photon energy of 2:4 eV [19.314, 333, 336], which is located at the nonphotoconducting gap region, i. e., the type (2) in Fig. 19.19. This fact manifests that the photodarkening is triggered by geminate (excitonic) carriers, which may cause local ( 5 Å) twisted bonds and overall structural disordering [19.223, 234, 306, 330, 336], giving rise to broadening of the lonepair band, and consequently the red-shift of the optical absorption edge. As an example, Fig. 19.20 illustrates a bond-twisting model [19.336] in a trimer structure consisting of two HSeH and a H3SeH, in which the central Se can take electronically transferable bistable positions. An ab initio chemical calculation [19.111] demonstrate that, reflecting stronger intercluster interaction between lone-pair states, the twisted (lower) structure has a higher HOMO (highest occupied molecular orbital) level by 0:3 eV with little change in LUMO (lowest unoccupied molecular orbital) levels (not shown), which is assumed to cause the photodarkening. Incidentally, the number of atoms contributing to the photodarkening is estimated at 1 at:%, the density being consistent with the reversible behavior [19.332]. The structural disordering, with the transitory photoinduced fluidity described in Sect. 19.6.1, may cause quasistable volume expansions. Actually, expansions of 0:3% are detected in a-Se after illumination at room temperature [19.342], despite the photodarkening being short-lived at that temperature, which is just below Tg [19.339, 340]. How can these observations be mediated? We assume that both the phenomena are manifestations of the photoinduced structural disorder-
Amorphous Selenium and Nanostructures
a)
19.6 Light-induced Phenomena
665
Onset time of crystallization (h) 6
5
4
b)
3
2
1 Tg 0
Fig. 19.20a,b Bond-twisting motion in a Se trimer, with
HOMO wavefunctions, which models three Se chains in aSe structures: (a) stable configuration, in which the central atom rotates to the right-hand side under electronic excitation, and relaxes to (b) the quasistable structure upon de-excitation
ing, while because the photodarkening arises from local atomic changes (such as bond twisting) and the expansion appears through successive macroscopic atomic flows [19.342], thermal recovery of the latter needs much longer times. Finally, it should be mentioned that, instead of the structural disordering, some researchers propose Coulombic forces [19.326, 327] and thermal effects [19.343, 344] as expansion stimuli. However, such ideas face difficulties in interpreting the fact that these photoinduced changes become greater at lower temperatures [19.6, 223, 306].
19.6.3 Photocrystallization
280
300
320
340 T (K)
Fig. 19.21 Exposure (incubation) times until photocrystallization is detected as a function of the sample temperature T (after [19.307]). Excitation light is 633 nm in wavelength and 17 W=cm2 in intensity. The inset shows a Se spherulite, the diameter being 0:1 mm, grown with a rate of 0:1 m=min on the free surface of an a-Se(2mthick)/Au/mica sample at 325 K under illumination of 20 mW=cm2 from an Hg lamp (after Tanaka, unpublished work)
by light illumination, or specifically by photogenerated holes [19.254]. In this context, the photocrystallization may be related to the (photo)electric phase change (Sect. 19.5.3). t-Se crystals emerge, depending upon conditions, on the free surface as spherulites and also at the boundary with substrates. On the other hand, suppression of the crystallization by electron beams [19.345] and red light [19.347], the phenomena resembling infrared quenching in photoconductivity [19.215, 253], have been demonstrated. Photocrystallization can also be suppressed by alloying with other atoms such as Ge [19.348], Te [19.97, 99], etc. It is also known that the crystal growth is thermally activated, which exhibits vector behaviors (Sect. 19.6.4). Raman scattering [19.31, 99, 141, 307, 341, 349] seems to have higher sensitivity in crystallite detection. Recently, a Canadian group demonstrated that the photocrystallization occurs at two temperature regions, as shown in Fig. 19.21, lower and higher than Tg ( 310 K), the latter having been known as written above. In contrast, at the lower temperatures, the incubation time of light-induced t-Se growth appears to become longer infinitely, with the variation curve
Part B | 19.6
Photocrystallization, its mechanism being comprehensively studied by Dresner and Stringfellow [19.254], has attracted considerable interest due to its peculiar features. For instance, the crystallization of a-Se to t-Se causes conspicuous morphological and electrical changes. However, it is still difficult to draw a whole picture of the photostructural process, due to its complicated nature involving crystallite nucleation and successive growth [19.5, 6]. Pioneering researchers inspected the phenomenon mainly using optical microscopes, which revealed several unique features [19.254, 315, 345, 346]. A growth rate of crystals in a-Se films just at the crystallization temperature Tc ( 100 ı C) is markedly enhanced
260
666
Part B
Glass Families
Se 480 min
As1Se99 420 min
As8Se92 480 min
As40Se60 480 min
1000 μm
Fig. 19.22 Vector deformations in As-Se films deposited upon silicone grease, induced by linearly (vertically) polarized bandgap light (exposure times given). Note that only a-Se produces a vertical wrinkling pattern, with a transition at As1 Se99 to the horizontal (after [19.113]) (Copyright WILEY-VCH Verlag GmbH & Co. KGaA, reproduced with permission)
resembling that of the viscosity (Fig. 19.8). The group proposes [19.31, 307, 341], following Stephens’s idea [19.350], that the crystallization at 260300 K is driven by local strain. Note that they evaluate the sample temperature from Stokes and anti-Stokes Raman peak intensities, which assures that the sample temperature is accurately determined. Incidentally, several researchers have also reported photocrystallizations at T < Tg using intense or superbandgap laser beams; 676 nm light with intensity of 250 W=cm2 at 100 K [19.141] or 488 nm light with 0:5 W=cm2 at room temperature [19.351], while the crystallization could be enhanced by light-induced temperature rises. These observations show that relations between the optical phase change (heat mode) and the photoenhanced crystallization (photon mode) remain to be studied. For instance, more detailed experiments that separately monitor crystallite nucleation and growth are valuable. The insight will shed light also upon photoeffects in other materials such as amorphous ice [19.352] and proteins [19.353].
19.6.4 Vector Effects Part B | 19.6
Zhdanov and Malinovskii [19.354] discovered optical vector effects (anisotropic changes appearing upon illumination of linearly polarized light or sideward illumination of unpolarized light [19.6]) in As2 S3 , and we naturally envisage similar phenomena in aSe. Actually, optical and structural vector effects have been demonstrated; dichroism [19.355], birefringence ( 0:008) [19.356], transitory optomechanical deformation [19.342], M-shaped deformation [19.342], macroscopic elongation parallel to the light electric filed by 10% (Fig. 19.22) [19.113], and oriented photocrystallization at 350 K [19.357–361], which accompanies birefringence reaching to 0:1.
For the vector effects, we may point out three interesting observations. First, as shown in Fig. 19.22, the vector deformation in the Asx Se100x system exhibits anomalous composition dependence; i. e., the deformation direction abruptly changes at the composition x 1 at:%. Second, different from the photodarkening (Sect. 19.6.2), which becomes greater at lower temperatures, the dichroism and birefringence become maximal at 200 K [19.356], which implies that wider-scale structural changes are involved. Lastly, Kikineshi’s group demonstrated that not single, but twobeam interference patterns can produce clear sinusoidal deformations [19.320], and Trunov et al. reported that the amplitude depends on the polarization directions of the two beams [19.362] and also on plasmonic enhancements [19.363]. These phenomena have been understood through extending Fritzsche’s idea [19.6, 364]. We here assume that anisotropic photoelectronic excitation under illumination of linearly polarized light makes Se segments tend to align normal to the polarization direction, which leads to the optical and shape changes [19.356]. That is, polarized illumination induces rotation and directional flow of atomic units. For oriented photocrystallization, the resultant atomic configurations have actually been detected by structural measurements [19.357, 359–361].
19.6.5 Simulations Photoinduced phenomena have been simulated using empirical [19.149, 150, 365] and ab initio molecular dynamics [19.144, 306, 366, 367] and also analyzed with a quantum-chemical method [19.250]. In a pioneering work by Zhang and Drabold [19.144], initially an Se cluster with 216 atoms is produced by cook and quench procedures, and afterwards an electron is
Amorphous Selenium and Nanostructures
transferred from a HOMO to a LUMO level, which is followed by free structure evolution for a while (400 fs), and then the electron is de-excited and quenched. The process yields valence alternation pairs (C1 , C3 C ), which they assert as an origin of the photodarkening. Hegedüs et al. [19.365] have demonstrated that the volume of Se clusters consisting of 162 atoms expands and shrinks, respectively, during electrons and holes excitation. These results illustrate plausible photostructural changes that may occur under some restrictions, and
19.7 Applications
667
hence further developments are promising. For instance, is it still difficult to trace slow phenomena such as the photocrystallization using molecular-dynamics simulations? For the photodarkening, the reversible behavior by annealing has not been demonstrated, and accordingly we wonder if the simulated photoinduced structures are really quasistable. In addition, to the author’s knowledge, no simulations have been performed for the vector effect so far, which require quantal formulation of polarization-dependent photoelectric structural processes.
19.7 Applications 19.7.1 Vidicon TV cameras employing photoconducting chalcogenide films had been utilized [19.93], which have now been developed to HARP vidicons [19.264]. They operate with phototriggered avalanche breakdown in a-Se films, giving rise to ultrahigh sensitivities, higher by 102 times than that of crystalline Si photodetectors (charge-coupled devices, CCDs). However, because the vacuum-tube structure has an electron gun and beam-scanning assembly it cannot be compact, and is longer than 10 cm, and accordingly challenging work is being devoted to reduce its size by replacing the scanning part to field-emitter arrays (FEAs) with a thickness of 1 cm [19.368], shown in Fig. 19.23.
Otherwise, charge images are scanned by thin-film transistors [19.369]. In addition, intense studies are now focused on suppressing thermal and optical instabilities of a-Se films [19.370] and on enhancing red sensitivity [19.371, 372]. On the other hand, Imura et al. [19.272] have recently demonstrated photomultiplication of electrons injected through metal/c-Se (not a-Se) interfaces, which may promote further developments of vidicons.
19.7.2 X-ray Imager X-ray imaging plates of direct- and indirect-conversion types using a-Se films have been developed for medical [19.261, 373, 374] and scientific [19.375–377] pur-
Light Output signal Glass
HARP target
Holes +
+ Target voltage
Electrons
Fig. 19.23 Schematic cross-sectional
Mesh electrode
Mesh voltage
FEA-gate
Gate voltage
FEA FE tip
view of FEA-HARP vidicons. An image incident upon the top surface excites photoholes, which are avalanche-amplified in the HARP film, and are read by electron beams emitted by a 640 480-pixel fieldemitter array (after [19.368], with permission from American Vacuum Society)
Part B | 19.7
+
668
Part B
Glass Families
X-rays
Top electrode n-like blocking layer
Photoconductor – V
–
+ Electrostatic shield TFT
+
200 μm
FET channel ≈ 1μm Gate G1
SiO2 Pixel electrode
Fig. 19.24 Schematic cross-sectional view of a pixel of a direct-type a-Se x-ray imager (after [19.261])
Storage capacitor C1
p-like blocking layer Bottom electrode Ground
1–2 mm Glass substrate TFT AMA Pixel size ≈ 70–90 μm
Part B | 19.7
poses. The direct type has a simpler structure, an example being shown in Fig. 19.24, which is composed of a wide-area (typically 40 cm 40 cm for medical imaging) thick a-Se film sandwiched in between a positively biased top electrode and back capacitors. The a-Se film converts x-ray photons into electrons and holes, which charge the pixel ( 80 m 80 m) capacitors, from which signals are gated by thin-film transistors (TFTs). X-ray detectors employing avalanche multiplication, with HARP [19.374] or similar structures [19.261, 375] to Fig. 19.23, have also been devised. On the other hand, in the indirect type, an a-Se film works as a photoconductor [19.378], which detects visible images emitted from a stacked x-ray fluorescent screen made from a material such as Tl-CsI. In this system, the a-Se film can be as thin as a few micrometers [19.378], and accordingly it can operate in an avalanche-multiplication mode under moderate applied voltages. Needless to say, there exist other competitive materials such as CdTe in the direct type and Si photodiodes in the indirect type [19.379]. We summarize below some performances of the direct type. The first concern would undoubtedly be x-ray sensitivity [19.109, 261, 380]. It is determined by several successive processes including x-ray absorption, electron-hole generation with recombination, and carrier transport to electrodes. As known, the x-ray absorption coefficient ˛ is proportional to 3 Z3 , where is the density, is the x-ray wavelength, and Z (D 34) is the atomic number of an absorber, which makes Se a potential material for x-ray detectors. However, for pertinent x-ray absorption, the a-Se films must be thicker than 0:2 mm, which requires feasible and economic preparation techniques. An absorbed x-ray
photon then creates a primary electron-hole with energies EX of a few tens of keV (x-ray photon energy), which produces n carriers through impact ionization cascades and instantaneous recombination. The number of resultantly generated carriers can be written as n D EX =Wi , where Wi is an electron-hole pair creation energy, or an ionization threshold, which should be low as possible for obtaining high sensitivity. However, it is still difficult to theoretically predict Wi for a-Se [19.196, 197, 381, 382], and instead, we follow an empirical formula, Wi W 0 C B=F, where W 0 7 eV, which may be related to the energy separation between the DOS peaks of the valence and the conduction band (Fig. 19.12), F is an applied electric field, and B 4:4 106 .eV V/=cm [19.109]. Provided that all generated carriers are transported without recombination [19.383, 384], this relation suggests that a 50 keV x-ray photon is able to charge a capacitor by 104 electrons. In addition to the sensitivity, several specifications should be satisfied. The dark current must be as low ( 10 pA=mm2 [19.217]) as possible under applied high voltages of, e. g., 2 kV ( 10 V=m). However, it is known that the dark current is affected by carrier injection from electrodes [19.297, 383] and bulk thermal generation. The latter increases with decreasing Eg , while we may assume W 0 / Eg , and accordingly it is not straightforward to compromise high sensitivity and low dark current. Other performances concern image resolution [19.385], response times [19.386, 387], device degradation under x-ray exposures [19.388], thermal stability, etc. [19.261, 389]. Smooth amorphous structures, not containing polycrystalline grain boundaries, may be preferred in these measures.
Amorphous Selenium and Nanostructures
19.7.3 Other Devices As known, the usage of a-Se films in xerography and xeroradiography has now been mostly discarded. The xerographic use was replaced by organic photoconductors [19.15], probably because of cost and toxicity problems. The xeroradiographic technique [19.380] has been transferred to the digital x-ray imagers (Sect. 19.7.2), in which x-ray detectability of a-Se remains an inherent advantage [19.109]. In contrast to such established usages, new applications to electrical, photoconductive, and photonic devices of crystalline, amorphous, and liquid
19.8 Nanostructures and Single Molecules
669
Se are now being explored. These include Al=aSe=Au diodes [19.292, 390], ITO=TiO2 =Se=Au solar cells with an efficiency of 5% [19.391], a supercapacitor of porous Se films [19.67], and a radioisotope l-Se battery generating 16 nW [19.392]. Also reported are several photo- and x-ray detectors with lateral configurations [19.393–396], fiber forms [19.397], and diamond cold cathodes [19.266]. Sharma et al. [19.324] have fabricated a-Se photooptical switches having ps response times, which may be based on a defect-absorption principle commonly appearing in other amorphous semiconductors [19.244, 398].
19.8 Nanostructures and Single Molecules The fact that Se forms ring and chain molecules (Fig. 19.1) makes preparations and characterizations of nano- and molecular structures fascinating subjects. Such studies might be thought to start near the end of the 20th century, while it should be noted that the smallest cluster, the Se dimer, has been utilized as a precious dye in ultramarine-type solids over centuries [19.399] and still arouses renewed interest [19.400].
19.8.1 Nanostructured Selenium Nanoscale Se structures with different shapes have been prepared through various procedures, as comprehensively reviewed by Chaudhary et al. [19.401]. Those include spherical [19.402–409] and polygonal [19.410– 412] free nanoparticles of a-, m- and t-Se in gases and solutions. T-Se can also take a variety of shapes; needles [19.405, 408, 412, 414, 415], wires [19.395–412, 414–421], belts [19.422], and tubes [19.413, 419]; the example being shown in Fig. 19.25. Nanoparticles
19.8.2 Isolated Molecules Se can form isolated atomic clusters in vacuum and gases [19.2, 435–438]. Se clusters have also been laid
300 nm
100 nm
Fig. 19.25 Se nanotubes. (Reprinted with permission [19.413]. Copyright 2006 American Chemical Society)
Part B | 19.8
500 nm
have also been produced in transparent insulators such as polymers [19.244, 423], silica [19.424, 425], and opal [19.426]. Se nanocrystals can also be prepared through annealing g-Se [19.427]. These Se nanostructures exhibit several marked features [19.194, 428], such as photoconduction [19.416, 420, 429], irradiation effects [19.418, 430], Li conduction [19.431], and peculiar optical nonlinearities [19.425, 432]. Deng et al. have fabricated filamentous photodetectors using cm-long t-Se wires with diameters of 200 nm [19.433]. In fundamental aspects, scale and confined effects on thermal and mechanical properties have provided interesting subjects such as how the glass-transition temperature varies in smaller and/or thinner flakes [19.194, 428, 434].
670
Part B
Glass Families
b
a)
b)
c)
a
c
Fig. 19.26a–c An illustration of ZSM-5 zeolite with magnified pore arrangements (a), and photographs of the zeolite (b) and an Se-loaded one (c), the dimension being 40 m 40 m 200 m. ZSM-5 is a fairly nonpolar zeolite with
a composition of Si94 Al2 O192 , containing channels with diameters of 0:7 nm (Reprinted from [19.441] with the permission of AIP Publishing)
on graphite surfaces [19.439] and introduced into carbon nanotubes [19.440]. Among these, the gaseous Se behaves as free substances, while only limited properties such as cluster stability have been inspected. After a pioneering work by Bogomolov et al. [19.442], substantial studies have been carried out for Se clusters incorporated into pores in zeolites [19.11] of various kinds [19.245, 246, 400, 441–452]. Terasaki et al. [19.443] evinced, by taking electron microscopy photographs, single Se chains in a zeolite, mordenite (Na8 Al8 Si40 O96 24H2 O). Atomic structures of incorporated Se clusters have also been investigated using x-ray diffraction and Raman scattering [19.246, 400, 447–452]. Such zeolite-Se structures may bestow intrinsic properties to single Se clusters, while we should be careful to note possible guest-host interactions existing between Se clusters
and atoms (such as Na) forming inner walls of pores in zeolites [19.226]. The zeolite-Se system exhibits several characteristic properties, such as blue-shifting absorption edges [19.245, 246, 446, 448, 449, 451], rises of the glass-transition temperature [19.445, 449], and unique photoinduced phenomena [19.245, 246]. Specifically promising may be the optical nonlinearity of Se in ZSM-5 zeolites (Fig. 19.26) [19.441], higher by three orders of magnitude than that of g-Se, which may originate from confined excitons. Since there exist many kinds of zeolites, the zeolite-Se system will exhibit more diverse properties. Or, provided that single Se clusters could be arranged as photonic crystals, optical properties might be resonantly enhanced. It would also be challenging to explore the electrical conduction of single Se chains.
19.9 Summary Part B | 19.9
We have seen that the study of a-Se is promising in two directions: fundamentals and applications, which may be related as shown in Fig. 19.27. The final goal will be to grasp all physical properties as the emergence from atomic structures on the basis of theoretical formulations. If a property would be useful to some purpose, the structure could then be tuned toward the target. In the fundamental, the elemental structure (no chemical disorder) with dualistic atomic bonds (covalent and van der Waals) gives a simple stage for exploring the nature of disordered materials, amorphous semiconductors, and chalcogenide glasses. Currently, we have mostly understood the short-range structure, the band structure, and related properties such as gross optical absorption spectra (Sect. 19.4.1). However, other
atomic structures, including wider-scale conformations and defects, and associated properties cannot yet be correlated. Studies on light-induced phenomena, avalanche breakdown, responses to x-rays, and nanostructures are in progress. Among the chalcogenide glasses, a-Se exhibits common and uncommon features when compared to those in compounds such as As(Ge)-S(Se). The common includes the two-fold coordinated chalcogen atoms with the valence band consisting of lone-pair states (Fig. 19.10), the Urbach edge with a steepness parameter EU greater than 50 meV (Fig. 19.13), no dark ESR signals, and many photoinduced phenomena such as the photodarkening (Sect. 19.6.2). On the other hand, characteristic to a-Se are the power of n D 1 in the Tauc’s
Amorphous Selenium and Nanostructures
Diffraction EXAFS Microscopy Vibrational Simulation ESR
Normal bonding structure Short-range; Z, r, ϑ Medium-range; φ, R, etc. Density fluctuation Heterogeneity, void Defect Spin; D 0 No-spin; Distortions, D+, D –, etc. Impurity, dopant
Band structure Band edge
Gap state
curve (19.3), no clear weak absorption tail (Fig. 19.13), smaller spin density ( 1016 cm1 ) under moderate illumination, high photoconductivity, the highest hole drift mobility (Table 19.1), avalanche breakdown (Fig. 19.17), peculiar vector deformation (Fig. 19.22), and so forth. How can we understand such native facets? The photocrystallization is more-or-less unique to a-Se, probably because of its elemental structure. In applications, the most valuable property of a-Se remains undoubtedly visible and x-ray photoconduction. The HARP vidicon utilizing avalanche breakdown has been commercialized, and is now being reduced in size to more compact devices (Fig. 19.23). Thick aSe layers are employed as direct x-ray imaging plates
Optical absorption Photoconduction Vidicon Avalanche X-ray imager Electrical (transient) Photoluminescence Photoinduced changes TSC
References
671
Fig. 19.27 Relations between structure-analyzing methods (left), atomic structural components, related electronic states, macroscopic properties, and applications (right)
(Fig. 19.24), which are useful for medical inspections and probably for scientific purposes as well. In addition, indirect-type x-ray imagers in combination with the avalanche multiplication are also being developed. Finally, studies on Se nanostructures appear to be promising for future functional devices. Acknowledgments. The author would like to thank Professor K. Nagata in Fukuoka University for showing several kinds of Se single crystals and supplying unpublished data. He is also grateful to A. Odajima and Y. Abe, emeritus professors of Hokkaido University, who introduced him to the physics of polymers and semiconductors.
References 19.1 19.2 19.3 19.4
19.5 19.6
19.8
19.9
19.10
19.11
19.12
19.13
19.14 19.15 19.16
19.17
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Keiji Tanaka Graduate School of Engineering Hokkaido University Sapporo, Japan [email protected]
After graduating in Applied Physics at Hokkaido University in 1972, Keiji Tanaka worked on photoreceptors at Canon Co. Ltd. After his return to the university, he was promoted to Professor in 1991. He received the 1st Ovshinsky Award in 2001 for the excellence in chalcogenide glass research. Since 2011 he is an Emeritus Professor.
Part B | 19
687
Spin and Fer 20. Spin and Ferroic Glasses
John S. McCloy
Spin glasses are a broad class of magnetic materials that exhibit varying degrees of disorder and magnetic frustration, resulting in characteristic glassy relaxation behavior including frequencydependent susceptibility, aging, and memory. Ferroic glasses include spin glasses and also relaxor ferroelectrics and strain glasses, which exhibit glassy dynamics in polarization and strain respectively, in similar ways to spin glasses. This chapter introduces ferroic and spin glasses, their phenomenological classification, and some parallels with structural (amorphous) glasses. A brief theoretical treatment is given, including modeling of the relaxation phenomena in ferroic glasses. Strain glasses and relaxors are discussed, followed by a detailed taxonomy of spin glasses and comparison with collectively behaving particle systems and structurally amorphous magnetic materials. Finally, some characteristic experimental methods are discussed, and an outlook for the future involvement of glass scientists in the study of spin glasses is offered.
20.1
What is a Spin Glass? ........................
688
20.2 Brief Theoretical Introduction............ 20.2.1 Relaxation Models ............................. 20.2.2 Spin Glass Transition as True Phase versus Purely Dynamic Transitions ....... 20.2.3 Site Disorder and Spin Frustration ....... 20.2.4 Model Systems and Theory .................
690 690
20.3 20.3.1 20.3.2 20.3.3 20.3.4
20.4 20.4.1 20.4.2 20.4.3 20.4.4 20.5 20.5.1 20.5.2 20.5.3 20.5.4
703 705 705 706 707 707 709 709 710 711 711
Outlook ............................................
713
References...................................................
713
The perspective offered, then, is from an experimental viewpoint, with hopefully theoretical insights discussed, but in many of our examples we aim to classify and describe material behavior phenomenologically. There are many excellent texts and reviews on spin glasses; three particularly influential ones for ourselves are listed here [20.2–4] and readers are referred to these for more specialized treatments and different viewpoints. Spin glasses are not a recent topic of research, with some of the first references specifically referring to spin glasses in the early 1970s emerging out of discussions on mictomagnetism [20.5–7]. Even in 1993,
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_20
Part B | 20
[we present] this document in the hope that it will be found stimulating, but [we are] conscious that there are in reality complicating factors, other possibilities and differences of opinion. [We] apologize to everyone of whose relevant work [we are] unaware and/or [have] failed to acknowledge.
Other Ferroic Glasses: Materials with Glassy Relaxation ....... Strain Glasses .................................... Relaxor Ferroelectrics ......................... Multiglass Ferroics ............................. Superconductors and Colossal Magnetoresistance..........
696 697 700 701
Measuring Spin Glass Properties ........ AC Susceptibility ................................ ZFC/FC Split........................................ Heat Capacity .................................... Nonequilibrium Dynamics: Aging, Rejuvenation, and Memory ......
20.6
In this chapter, we present an overview of the phenomena of spin glasses and their relationship to broader concepts in the glass science of structural glasses. Our intent is like that stated by Sherrington, pioneer in the early theory of spin glasses, in that [20.1]:
Phenomenological Taxonomy of Spin Glasses.................................. Canonical Spin Glasses ....................... Cluster Glasses .................................. Collectively Behaving Particle Systems . Amorphous Materials: Ferromagnets, Speromagnets, and Antisperomagnets .......................
693 694 695
688
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Mydosh, a pioneer in the early experiments of spin glasses, stated that for spin glasses, “as fame and topicality diminish, the problem remains an interesting, yet passé, research topic” [20.8]. However, particular theory and concepts regarding metastable states, ergodicity, energy landscapes, and others developed during the study of spin glasses have affected such disparate fields of study as economics, complexity theory, fractals and chaos, computer science, neural networks, prebiotic evolution, protein conformational dynamics, and protein folding [20.9–11]. Since topics relating to glass and liquid physics, such as the glass transition and configurational entropy, are still pertinent today [20.10, 12–14], it is our hope that a reminder of the study, development, and insights of spin glasses will cross back over to the field of structural glasses with which the scientific and technical community is more familiar. It is this translation that will perhaps be the most difficult challenge for future scientists of spin and ferroic glass. However, with the increasing number of materials being found that exhibit glassy relaxation in their properties, a deeper understanding of the nature of these relaxations as determined by methods for traditional structural glasses (i. e., viscosity, volume change) as well as methods uniquely available in spin and fer-
roic glasses (i. e., magnetization change, polarization change, elastic relaxation, etc.), will serve in identifying and designing new materials with increasingly tailorable properties. First, a brief theoretical introduction is offered including ways of modeling relaxation in glassy systems. Following this, the two extremes of theory are offered: that of the spin glass transition as a true thermodynamic transition versus the phenomena of a spin glass transition as a purely dynamic phenomenon. Following this, a longer treatise on spin glasses is offered, beginning with a description of the concepts of site disorder and spin frustration. Subsequent to this are examples of the different types of spin glasses depending on the electronic conductivity, size of the relaxing spin, and the presence or absence of crystalline order. Related systems such as spin ices and collectively behaving nanoparticle systems are described as well. Then, some common features and parallels are offered for ferroic glasses including some detail on strain glasses, relaxor ferroelectrics, and related materials. Then, some experimental techniques are described for eliciting the relaxation behavior of spin glass properties. Finally, an outlook for future study of spin glasses is offered.
20.1 What is a Spin Glass? A glass can be seen simply as a frozen disordered state, and this characteristic is evident in many phenomena. Glasses lack long-range order in some order parameter, which differs depending on the class of materials. Structural glasses are disordered in their atomic arrangement, while so-called ferroic (or domain) glasses [20.15, 16] lack long-range order in some other structural parameter: spin glasses in their magnetic moments, relaxor ferroelectrics in their dipole moment, and strain glasses in their lattice strain. Spin glasses have been subject to the greatest number of studies both theoretically and experimentally. This deceptively simple question of what is a spin glass? turns out to have a rather complex answer; as
the materials and behaviors lumped together under the classification scheme of spin glass are very diverse in their phenomenology, as definitions have evolved over time, and as terminology is sometimes inconsistently applied in the literature. However, a working definition is useful, and we rely on Mydosh for that [20.17]: A spin glass is a random mixed-interacting system characterized by a random, yet cooperative, freezing of spins at a well-defined temperature (Tf ), below which a highly irreversible metastable frozen state occurs without the usual long-range spatial magnetic order.
Table 20.1 Comparison of strain glasses, relaxors, and spin glasses; LRO indicates long-range ordered
Part B | 20.1
Spontaneous order parameter
Ferroic
" (strain)
Ferroelastic
p (polarization) m (magnetization)
Ferroelectric Ferromagnetic
Hi-T parent, zero order (disorder) Austenite (Paraelastic) Paraelectric Paramagnetic
Low T, LRO
Low T, glass
Frequency-dependent (complex number with magnitude and phase)
Martensite (Ferroelastic) Ferroelectric Ferromagnetic
Strain glass
Storage modulus (elastic susceptibility)
Relaxor Spin glass
Permittivity (electric susceptibility) Permeability (magnetic susceptibility)
Spin and Ferroic Glasses
20.1 What is a Spin Glass?
689
a) Entropy
Disorder
Na defect
Liquid T* Si O Super cooled liquid
• Liquid • Paramagnetic • Paraelectric • Paraelastic (parent phase)
Structural glass
Thermodynamic transition
Non-thermodynamic transition
Order
Glass
Crystal
TK
Tg
Tm
Temperature
b) Entropy Vacancy defect
Austenite T* Mn Ni/Co In
Conjugate • Crystalline solid • Ferromagnetic • Ferroelectric • Ferroelastic (martensite)
• Structural glass • Spin glass • Relaxor • Strain glass?
Super cooled austenite
Anti-site defect Strain glass
Fig. 20.1 Disorder-order and disorder-glass transitions, af-
Martensite
ter [20.18]
In the following, we extend this definition to describe other types of ferroic behavior that exhibit glassy relaxations, which may or may not involve magnetic spins. The discovery and nomenclature of a new classification of glasses, that of strain glasses, occurred in 2005 [20.19] and recognition of the similarities with spin glasses and relaxor ferroelectrics led to the suggestion of a general term ferroic glasses to describe this class of material behavior [20.15]. In general there are a number of features that can be described analogously for all ferroic glasses [20.20]. First, there is an order
TK
Tg
Ferromagnetic domain
Temperature
Super paramagnetic martensite
Anti-site defect Super cooled paramagnet
Cluster spin glass
Tf
TC
Temperature
Part B | 20.1
TK
T*
Ferromagnetic martensite
Fig. 20.2a–c Comparison of structural, strain, and spin
glasses in terms of entropy versus temperature and the freezing of the supercooled state. Atom key in (b) is the same for (c). Reprinted from [20.21], with permission from Elsevier. For details, see text I
TMs
c) Entropy
690
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Glass Families
parameter that normally results in spontaneous ordering, but which is frustrated in a ferroic glass. For spin glasses, this order parameter is the magnetization (M). There exists a high temperature fully disordered state, which for magnetization is paramagnetic, and a low temperature long-range ordered phase, such as ferromagnetic. When the long-range order is frustrated, it becomes a spin glass. In a spin glass, the frequencydependent observable property is the magnetic susceptibility (or permeability). Analogous quantities exist for the other ferroic glasses (Table 20.1). One interesting aspect of the low temperature disordered phases is that they can become long-range ordered with the application of an appropriate field of significant strength, such as applying a large strain to a strain glass to force it into the ordered martensitic phase [20.20] or applying a strong electric field to a relaxor to force it to an ordered ferroelectric (see Sect. 20.4.2 and Fig. 20.17b). Simply, these transitions can be described as either a thermodynamic disorder-order transition from a high temperature liquid-like state to a low temperature ordered state, or a competing disorder-glass transition to a low temperature disordered state [20.18] (Fig. 20.1). Additionally, the glassy states of these ferroic systems exhibit common features that are analogous to
those observed in structural glasses, such as the following: quenched randomness, field-assisted transitions between low temperature states, temperature-dependent transitions, ergodic and nonergodic states, frequency independence at spontaneous transitions, frequency-dependent susceptibilities at the glassy transition, Vogel– Fulcher law, stretched exponential; and power law descriptions, defect-concentration related effects, as well as aging, rejuvenation, and memory effects [20.22]. A schematic comparing the entropy versus temperature for structural glasses, strain glasses, and spin glasses is shown in Fig. 20.2. In this figure, T indicates the supercooling temperature. In the low temperature ordered state this is Tm , the melting point (for structural glass); TMs , the martensitic start point (for strain glass); or TC , the Curie point (for cluster spin glass). At the end of the supercooling region, the glass transition Tg (structural and strain glasses) or the freezing point Tf (spin glass) marks the frequency-dependent relaxation, which at lower temperatures leads to the glassy state with higher entropy away from the supercooled liquid line. A hypothetical Kauzmann temperature (TK ) exists where the entropy of the supercooled high temperature state is equal to the entropy of the long-range ordered state.
20.2 Brief Theoretical Introduction It is not the intent of this review to offer rigorous mathematical descriptions of spin glasses. Such reviews are found in other publications [20.23, 24]. Rather, it is the intent to offer just enough theory to illustrate the important aspects of spin glasses such that experimental data can be interpreted.
20.2.1 Relaxation Models
Part B | 20.2
An ergodic system is defined as one where the time average and ensemble average in a statistical mechanics analysis are equivalent [20.12]. A different way of phrasing it is: given enough time, an ergodic system can be described as the average of all possible states. Analogous to structural glasses, spin and other ferroic glasses exhibit different transition regions including a liquid-like region where the behavior is ergodic, a glass transition region where there is a continuous breakdown of ergodicity, and a glass region where the system is nonergodic (Fig. 20.3). In nonergodic systems, there is a frequency (time)-dependent change, which is related to the difference between the system internal time scale ( int ) and the external observation time scale ( ext ). The ratio of the internal to exter-
nal time scales has been dubbed the Deborah number (D) [20.25], after the biblical account in Judges 5W5 where “. . . the mountains flowed before the Lord.” In other words, on a geologic (internal) time scale even mountains can be fluid while they seem highly solid to an observer (external) time scale. While this might be taken as evidence to support the myth that stained glass windows are thicker on the bottom due to glass flow, this notion has been repeatedly refuted due to the geologically long timescales required for such flow [20.26]. Recent demonstrations highlighting the apparent solidity of a material with its true fluidity have been conducted on bitumen, for example [20.27], where flow was measured on the timescale of about one year. The glass transition can be seen as the partitioning process from an ergodic liquid to a nonergodic solid, while relaxation is a unifying process from the quenched solid towards the equilibrium ergodic liquid [20.12]. The glass transition (Tg ) or freezing temperature (Tf ) is a measure of the transition between these states. Generally, the breakdown of ergodicity is described in terms of a distribution of relaxation times. This distribution is generally very large below Tf but narrow far above Tf (Fig. 20.3). Generally this relaxation
Spin and Ferroic Glasses
a) Enthalpy, volume τ int D= τ ext
b)
20.2 Brief Theoretical Introduction
P(τ, T)
Liquid
log τ (s) T < Tf
Ergodic (D < 1)
T = Tf
Tg range Glass Nonergodic (D > 1)
691
Continuous breakdown of ergodicity (D ≈ 1)
T > Tf T >> Tf
T (K) Temperature
10
–12
10 –10 10 –8 10 –6 10 –4
10 –2
10 0
102
log τ (s)
Fig. 20.3 (a) Illustration of the breakdown of ergodicity going from a liquid to a glass, in terms of enthalpy or volume as a function of temperature (after [20.14]). (b) Schematic of probability distribution for spin relaxation times as a function of temperature relative to the spin freezing temperature (Tf ) (after [20.8])
time can be modeled in one of three ways: an Arhennian thermal activation, a non-Arhennian model such as the Vogel–Fulcher–Tammann (VFT) relation, or the stretched exponential [20.8]. Thermal Activation The simplest model for spin relaxation is the Néel– Arrhenius (NA) model, where the relaxation ( ) is derived experimentally from the measured temperature peaks of freezing (TP ) (Sect. 20.5) and the interrogation frequency (f ). Fitting parameters are the fundamental relaxation time for a single relaxing unit ( 0NA ) and an activation energy (EANA ) as shown in (20.1), where kB is Boltzmann’s constant NA EA 1 : (20.1) D D 0NA exp f kB TP
Vogel–Fulcher–Tammann (VFT) The most common non-Arhennius fit is the Vogel– Fulcher–Tammann (VFT) model, which has been used to fit viscosity data of structural glasses [20.25, 31, 32], as well as freezing data for spin glasses [20.33–36] and relaxor ferroelectrics [20.34–37] D 0VF exp
EAVF : kB .TP T0 /
(20.2)
The similarity between the Néel–Arrhenius and the Vogel–Fulcher–Tammann expressions are apparent. In the VFT expression, the relaxation of a single spin is still 0VF , which can take various values depending on the type of spin glass. However, here EAVF now describes the activation barrier of a spin cluster and not an individual spin. If we look at the activation energy in a similar way, recalling that EAVF D VK as in the case with the NA model, V now describes the effective spin
Part B | 20.2
The Néel-Arrhenius expression is only valid for noninteracting particles, in which case 0NA is the isolated single spin relaxation time, typically on the order of 1013 s [20.28]. For the case of superparamagnetic (SPM) noninteracting particles, the TP is identical to the blocking temperature (Sect. 20.3.3). SPM particles are single domain magnetic particles, which are sufficiently small that their magnetic moment flips between two stable states depending on the magnetic anisotropy (K), provided that the thermal energy is large enough. This results in zero coercivity for switching, zero moment in the absence of a field, but a large moment in the presence of even a small field (thus superparamagnetic). Below a critical temperature called the blocking temperature, the thermal energy to flip the particle within the measurement time is too small, and a ferromagnetic state is measured during a direct current (DC) experiment or a peak is measured in the
alternating current (AC) susceptibility (see Measuring Spin Glass Properties, Sect. 20.5). The blocking temperature is thus indicative of the competition between the magnetic anisotropy energy and the thermal energy, and can be computed from (20.1) by substituting the anisotropy (K) times the particle volume (V) into the activation energy (EANA ) and solving for temperature; alternatively, a threshold size for SPM can be calculated for each temperature for a given K [20.29]. Typical sizes for SPM of important magnetic materials are 530 nm. If SPM particles are sufficiently concentrated such that they interact, a collective state is created that cannot be described by the NA model and must be described by another model such as the VFT below or the dynamic scaling relationship (critical slowing down) [20.30] (Sect. 20.2.2).
692
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cluster size while K is still the anisotropy. We can then define an equivalent temperature parameter (not to be confused with the Kauzmann temperature which is also indicated by TK ) TK D
EAVF VK D kB kB
(20.3)
so that we can compare TK , a measure of the energy barrier, with the fit parameter T0 , best described as a measure of interparticle or interspin interaction [20.38]. The weak coupling regime is where T0 TK , which gives rise to the VFT relation, whereas in the strong coupling regime T0 TK . Parameters of the VFT are usually obtained by fitting peak temperatures of frequencydependent AC magnetic susceptibility (or electric permittivity) measurements (Fig. 20.4 and Sect. 20.5.1). Stretched Exponential Long timescale relaxation is often described by the Kohlrausch–Williams–Watts (KWW) or stretched exponential [20.40]. An expression describing the relaxation of thermoremanent magnetization (TRM) is, for instance ˇ t MTRM D M0 exp (20.4) ; where M0 is the magnetization at t0 and is the characteristic time scale. Here ˇ varies between 0 and 1 with ˇ D 1 producing an ideal Debye relaxation (exponential is recovered) and ˇ D 0 producing an infinite
relaxation time. Usually, a log-normal distribution of relaxation times is assumed. An expression like the KWW has been used to describe orientational glasses [20.41, 42], strain glasses [20.15], spin glasses [20.43], superspin glasses [20.44, 45], resistance decay in cobaltites under applied field [20.46], and magnetoelectric relaxor multiferroics [20.47]. An example for strain glasses (Sect. 20.4.1) determined by creep measurements is shown in Fig. 20.5. Recently, relaxation of commercial silicate glasses has been described in terms of strain relaxation with time using a KWW form [20.12], where the exponent (1 ˇ here) is equal to 3=5 for stress relaxation containing short- and long-range relaxation pathways, or 3=7 for structural relaxation where only long-range changes occur. Power Law Frequently, relaxation data can be fitted to an entirely different model, the power law or scaling law. The form of this is usually D 0SC
TP 1 TC
zv
;
(20.5)
where the critical temperature TC describes the glass transition temperature (i. e., freezing temperature) for collective behavior, 0SC is the relaxation time of individual particles (Néel–Arrhenius), and zv is an exponent that is determined experimentally or calculated for certain model systems [20.48]. For example, Tholence and coworkers described the correlation length
χ' (emu g–1 Oe –1) 0.48
a)
ln τ (s) 0
10 Hz 100 Hz 500 Hz 1000 Hz 5000 Hz 10 000 Hz
0.40
–2
b) τ (s) TP Scaling law 0.08
–4 75
100
–6
Part B | 20.2
–8 –10
TP Vogel–Fulcher law 72
74
125 T (K)
0.04
0.00 76
78
80 T (K)
72
74
76
78
80 T (K)
Fig. 20.4a,b Illustration of fitting of Fe=-Fe2 O3 core–shell structures with (a) VFT and (b) scaling power law. Reprinted with permission from [20.39]. Copyright (2012) by the American Physical Society
Spin and Ferroic Glasses
a) ε(t)/ε(0)
b) τ (s)
1.12
Strain glass Ti48.5Ni51.5
0.6
143 K 153 K
1.10
158 K
0.5 0.4
104
0.3
1.08
Tg
0.2
103
1.06
140 150 160 170 180 190 200 T (K)
168 K (Tg)
1.04 1.02 1.008 1.004 1.000
693
β
105
1.14
20.2 Brief Theoretical Introduction
102 183 K 193 K 0
1000
2000
3000
4000
5000
6000 t (s)
101 130
Tg 140
150
160
170
180
190
200 T (K)
Fig. 20.5 (a) Normalized strain in Ti48:5 Ni51:5 strain glass as shown by time-dependent creep, and (b) fit of the temperature-dependent relaxation time and exponent fit by KWW with an equation analogous to (20.4) showing both and ˇ (inset) dependencies (after [20.15])
in Cu-Mn and Ag-Mn spin glasses using this equation and a single critical exponent v as D 0 .1 TC =T/v [20.33]. The exponent z is used for the dynamic scaling hypothesis, z [20.49]. Some critical exponents for different typical classes of magnetic spin glasses are shown in Table 20.2, where the classification column refers to the type of model system (Sect. 20.2.4) and the anisotropy column refers to the relative value of magnetic anisotropy. Occasionally, the reduced temperature parameter (TP =TC 1) is denoted "T in the literature [20.50]. A fit to this model is normally taken as evidence that there is a critical slowing down of kinetics in advance of a thermodynamic phase transition [20.50].
20.2.2 Spin Glass Transition as True Phase versus Purely Dynamic Transitions Phase transformations are typically divided into two categories: first-order and second-order [20.58]. During a first-order transition, heat is either absorbed or released, while temperature stays constant, thus mixedphase systems are the normal case as heat cannot be instantaneously removed or added to the system. Boil-
ing of a liquid and melting of a solid are first-order transitions. There has been some theoretical discussion that the structural glass transition can be described as a random first-order phase transition with density fluctuations as the order parameter [20.59], though the argument is far from being universally accepted. During a second-order (or continuous) transition, there is no latent heat added or lost, but second-order transitions are rather characterized by a divergence in susceptibility, an infinite correlation length, and a power law decay of correlations. Examples of second-order transitions include the ferromagnetic and superconductor transitions and the spin glass transition [20.51]. Second-order transitions have been described by various critical exponents, of which only two are independent and related by scaling relations, obtained by fitting data from susceptibility, magnetization, and specific heat as a function of temperature and magnetic field [20.48, 60]. Above the spin glass transition temperature, the spin glass correlation length diverges [20.55]. Oftentimes the ability for data to be fit using the power law is offered as evidence that a spin glass-like transition is a thermodynamic phase transition [20.61].
Table 20.2 Critical exponents of various spin glass types Classification Ising (3-D) XY
Anisotropy Strong Weak
zv 10–12 11
4–5 3
ˇ 0.54 0.5
References [20.51–54] [20.54–56]
Heisenberg
Weak: AgMn, CuMn Strong: AuFe
6–8
2.2–2.3
0.9
[20.52–54, 57]
10
4
1.2
[20.49, 54]
2.5
0.2
[20.54]
SSG SSSG
Part B | 20.2
Material Fe0:5 Mn0:5 TiO3 Eu0:5 Sr1:5 MnO4 Chiral glass superconductor Ag (11 at:% Mn) Cu (6 at:% Mn) Interacting Fe–C nanoparticles (super spin glass) Super-superspin glass
694
Part B
Glass Families
However, as pointed out early on by Tholence [20.40], the VFT and power law “are very difficult to distinguish experimentally, since about the same quality of fits is obtained, and one can be developed as an expansion of the other.” However, the VFT is usually seen as a descriptive model, or as evidence for a collective state in systems that exhibit such. The power law may also be deemed descriptive, but has generally been interpreted as implying the presence of a phase transition [20.61]. A classification of magnetic behavior, much of which has been loosely called spin glass has been offered that differentiates which phenomena actually show evidence of phase transitions (Table 20.3). On the other hand, some researchers have argued that the spin glass transition should be viewed as a purely dynamic effect [20.62], where the observation of a cusp in susceptibility is due to a transition from a relaxational (t > ) to a spin wave (t < ) regime, analogous to the crossover transition between relaxational and elastic regimes in liquids [20.13]. In this view, there is essentially no difference between paramagnetic and spin glass states, only the observation time as opposed to the internal time (see discussion on Deborah number in Sect. 20.2.1). Local relaxation events explain the crossover, and a similar model has been offered for the structural glass transition due to an experimental timescale, explaining heat capacity jump correlations with viscosity and logarithmic increase of Tg with quench rate [20.63].
20.2.3 Site Disorder and Spin Frustration There are two main microscopic factors that combined can classify the magnetic ground state of insulating magnetic materials. Choosing two axes as the degree
of disorder and the degree of frustration, four categories are created [20.64] (Fig. 20.6a). Here the disorder axis refers mainly to crystallographic site location and frustration refers to pairwise interaction between atoms at each site on a lattice. By separating the two phenomena, it allows distinction among a variety of behaviors, and provides insight into obtaining desired interactions. Systems exhibiting both low frustration and low disorder exhibit the spontaneously ordered magnetic states such as ferromagnetism (FM), antiferromagnetism (AFM), and ferrimagnetism (FiM). By increasing the degree of frustration, a class of geometrically frustrated magnets are realized, now commonly called spin ices. It is important to realize that these materials are lattice ordered, but because of the inability to satisfy all the lowest-energy magnetic exchange interactions, there is a spin frustration (Fig. 20.6b,c). In spin ice, the source of frustration is geometric due to the lattice configuration and pairwise magnetic exchange interactions, not due to randomly distributed FM and AFM coupling as in the Sherrington–Kirkpatrick and Edwards–Anderson models [20.65] (Sect. 20.2.4). A number of spin ices have been studied, particularly pyrochlores with the general formula A2 B2 O7 , where A is typically a rare earth metal and B is Pb, Ti, Sn, Ge or Mo [20.66]. The most studied spin ices of this class are Ho2 Ti2 O7 and Dy2 Ti2 O7 . The geometric sources of spin frustration in the pyrochlores is due to nearest neighbor AFM interactions. These AFM interactions cause spin frustration not only on the pyrochlore lattice, but on any equilateral triangular vertex system such as the Kagomé lattice, the honeycomb, and the perovskite [20.67]. Several recent books and reviews give general accounts of frustrated magnetism in various systems [20.68, 69].
Table 20.3 Classification of magnetic glassy systems and similar phenomena (after [20.50]). PM is paramagnet, FM is ferromagnet, AFM is antiferromagnet Type Building block (BB)
Part B | 20.2
0a 0b
Atomic spin Group of spins
1 2 3
Atomic spin Group of spins Group of spins
4
Atomic spin or group of spins Atomic spin or group of spins Atomic spin or group of spins
5 6
Variation in size of BB No Weak or large No Weak Large
High-T Interaction state between BBs PM No PM No
f -dependent Relaxation of 00
Phase transition
Low-T state
No Yes
No No
No No
Paramagnet (PM) Superparamagnet (SPM)
PM PM PM
Yes Yes Yes
Yes Yes Yes
Yes Yes Yes
Yes Yes No
Weak
FM
Yes
Yes
Yes
Yes
Weak
AFM
Yes
Yes
Yes
No?
Spin glass (SG) Superspin glass (SSG) Inhomogeneous disorder magnet; mictomagnet; cluster glass Reentrant ferromagnet (SG or SSG) Reentrant antiferromagnet
Large
FM or AFM
Yes
Yes
Yes
No
Inhomogeneous disordered magnet
Spin and Ferroic Glasses
Frustration
a)
b) Geometrical
c)
frustration Ferromagnetism Anti-ferromagnetism Ferrimagnetism Metamagnetism Disorder
695
Spin glass frustration F
Geometrical frustration
AF
AF AF
• • •
AF Random fields percolation
20.2 Brief Theoretical Introduction
AF AF
Spin glass
Fig. 20.6 (a) Ground states of insulating magnets in terms or relative frustration and disorder; (b) illustration of frustration due to AFM interactions on a triangular lattice; (c) frustration in a spin glass where FM and AFM interactions are present (after [20.64]). In (b,c), the arrows indicate the spin direction at the particular lattice site, and the F indicates ferromagnetic pairwise interaction while AF indicates antiferromagnetic interaction
Random field magnetization and percolation effects are noted in systems exhibiting low frustration and high disorder. In this case, magnetic atom location in the lattice is somewhat disordered, but interactions (FM or AFM) between magnetic atoms can all be satisfied. Spin glasses, on the other hand, require both significant disorder and significant frustration. Here the disorder need not imply that a structural glass is present, only that the probability of a magnetic ion being on a particular lattice site be random, hence the local magnetic fields vary from site to site. The frustration in spin glasses is different than purely geometrical frustration, and results from competition between FM and AFM interactions (Fig. 20.6). It should be noted that frustration need not be in all three dimensions, as two-dimensional topological spin glasses have been reported as well [20.70]. The notion of disorder itself can be further delineated in order to understand the types of lattice site changes. Disorder can proceed from bond disorder (length and angle), topological disorder (connectivity), and chemical disorder (for multiatomic systems) [20.71]. All these types of disorder will affect the magnetic properties. A schematic of this classification is shown in Fig. 20.7, and the similarities with models from structural glasses is notable.
20.2.4 Model Systems and Theory
Part B | 20.2
Two main types of models have been offered for spin glasses. The first is the Edwards–Andersen (EA) model [20.72, 73], where only the nearest neighbor spins interact. This is similar to the Ising model of ferromagnetism where each spin on a d-dimensional lattice can take
only two values, C or . The EA model is the simplest one, which exhibits both disorder and frustration. The second model is the Sherrington–Kirkpatrick (SK) model. In the Sherrington–Kirkpatrick model [20.74], every spin interacts with every other spin regardless of distance. The SK model has an analytical solution whereas the EA one does not. For the SK model, the coupling between any two spins is either FM or AFM, resulting in quenched spatial disorder and frustration [20.75]. The 3-D Ising EA model is solvable numerically, and recent results on supercomputers have determined the critical exponents (see Power Law in Sect. 20.2.1) for this model [20.76]. The spin glass phase in the EA is often interpreted in terms of the droplet model, where fluctuations of the transformed phase exist in compact localizations [20.65]. Note that classical spin models are one of three types: Ising, where spins sit on vertices of a lattice and are twostate (C or ); XY, where spins are planar vectors; and Heisenberg, where spins are vectors in three dimensions [20.77]. Note therefore that the 3-D Ising EA model thus means that the lattice is 3-D, the spins are C or at each vertex, and only nearest neighbor spins interact. Many variations and other mathematical models have been offered, including the Potts model, which is a generalization of the Ising model, but where each spin can interact will all the other spins [20.78]. The manifestation of the frustration depends on lattice geometry, such as square versus triangular [20.79], and has relevance to the discussion of spin ices (Sect. 20.2.3) where the ground state is geometrically frustrated due to unsatisfied antiferromagnetic interactions. For more details on theory, the reader is referred to various books on spin glass theory and included references [20.23].
696
Part B
Glass Families
Bond order
Bond disorder
Topical disorder
Fig. 20.7 Bond,
topological, and chemical disorder (after [20.71])
Monatomic lattice
Chemical order
Binary lattices
Chemical disorder
20.3 Phenomenological Taxonomy of Spin Glasses
Part B | 20.3
This and the following section describe the main classes of ferroic glasses. First, spin glasses are considered in depth. Subsequently, strain glasses, relaxors, and related systems are discussed. In this section, a general summary is offered of the different types of spin glasses, in the strict sense of a disordered magnetic structure. At the most fundamental level, magnetic systems have been defined thermodynamically in three states of matter as paramagnetic (gas), quantum spin liquid (liquid), and magnetically ordered (solid), by reference to the action of the magnetic exchange forces and the resulting quantum critical points [20.80]. It should be noted, however, that real solids can exhibit all of these types of magnetic states. With the tremendous amount of research in magnetic materials in the last 50 years, scientists and engineers have discovered many diverse phenomena of material behavior. Much of this is distinct from the simplistic ferromagnetic (FM), antiferromagnetic (AFM), ferrimagnetic (FiM), and paramagnetic (PM) materials familiar to most nonmagnetic specialists. In fact, there
has been a call for a taxonomy for magnetism as early as 1973 [20.81], to cope with names like mictomagnetism, metamagnetism, asperomagnetism, speromagnetism, sperimagnetism, spin glass, cluster glass, and a dozen others in current use. Clearly, the field presents a bewildering picture to an outsider [20.82].
Hurd, in 1982, attempted such a taxonomy with some success [20.82]. The focus here will be to distinguish between different kinds of spin glasses and their character. Magnetic ordering in solids happens due to the individual magnetic moments on ions and their mutual interaction through dipolar as well as quantum mechanical (QM) forces [20.71, 82]. These QM forces are generally called exchange forces and often represented as J, the exchange parameter or integral. Magnetism can be broadly classified as cooperative or noncooperative.
Spin and Ferroic Glasses
Diamagnetism 1/χ
Ideal ferromagnetism Reduced magnetisation
σs 1/χ
+ 0 –
Antiferromagnetism
Cu, NaCl
Ideal paramagnetism 1/χ
1/χ
H Tc T 0 J>0 |J| >> |D| Crystalline Amorphous
Incipient ferromagnetism
Superparamagnetism
Metamagnetism (field-induced transition) Hi
Reduced magnetisation
77 K
H
0 TORD T 0
Paramagnetism Spin flop
–∆E/(kT)
T
FeCl 2 FeCl 2 ∙2H 2O
1
A B
H
Amorphous: Fe, Co (≈40 Å) in Hg
Mictomagnetism (cluster glass) A H
A 0
CuMn YFe 2 (J > D) (T < TORD) α-Re (D RAN > J)
Ideal spin glass
TF
T
H
B
Exchange dominated
σ B
σ B
T 0 Amorphous
A
T
MnF2, GdAlO3
0
J = ± or – Crystalline Amorphous
∆E V Pd, Pt
Antiferromagnetism
Reduced magnetisation
T TORD
Cr, α–Mn, MnO
σ Paramagnon
Tc
T
Crystalline Amorphous
Crystalline
Fe 80P20, FeF2
D large
1/χ
0 T D=0 Crystalline Amorphous
SiO2 Fe
Ferrimagnetism σs
Curie– Weiss
AF PARA T 0 TN J >> D, J < 0
0
697
Curie
1
T
Crystalline Amorphous
20.3 Phenomenological Taxonomy of Spin Glasses
Anisotropy dominated
|J| > |D| GdAg, YFe3, GdAl 2
|D| > |J| DyNi 3, TbAg
REFe 2, Gd 30Co70
Sperimagnetism (canted ferrimagnetism) D2 > J D1 > J Crystalline Amorphous
FePd1.6Pt1.4 DyCo3, TbFe 2 Fe
Pd, Pt
Dy, Tb Co, Fe
Helimagnetism (crystalline asperomagnetism)
J = ± or – B=0
B
A cooled with no field B cooled in field
T=0
T > TSG
Crystalline Amorphous Crystalline Amorphous Fe3Al, AuFe La 80–xCd xAu 20 (x ≈ 30–50)
CuMn x (x→0)
La 80-xGd xAu 20 (x ≤ 1)
MnAu 2, Dy, Ho, Er
Fig. 20.8 The family tree of magnetism, after [20.82] and [20.83]. In these figures J is the exchange parameter, is the magnetic susceptibility, and D is a parameter related to the crystal field and influences the magnetocrystalline anisotropy. J D ˙ refers to the oscillatory RKKY interaction. s refers to the mass normalized magnetization
ther perturbed by spin-orbit coupling through the socalled Dzyaloshinky–Moriya (DM), or antisymmetric exchange, effect [20.71].
20.3.1 Canonical Spin Glasses An illustration of the consequences of increasing the concentration of magnetic ions randomly distributed throughout a solid can be understood by considering the case of the canonical spin glass (Fig. 20.9). This type of spin glass was the first discovered, and consists of a noble metal (Au, Cu, Ag, Pt) with a dilute impurity
Part B | 20.3
In the latter, the moments are affected by an external magnetic field but they do not affect one another. In cooperative magnetism, the individual magnetic moments on ions interact in some way by exchange forces. These exchange forces can be direct where ions are sufficiently near each other that their QM wave functions overlap. Conversely, indirect exchange happens over larger distances through intermediaries, such as itinerant conduction electrons in metals (RKKY or Ruderman–Kittel–Kasuya–Yosida interaction) or ligands such as in insulators (superexchange) [20.71, 84]. Both of these types of indirect exchange can be fur-
698
Part B
Glass Families
a)
b)
c)
d)
Random freezing of the moments characterized by sharp susceptibility maxima
Kondo regime
Singleimpurities
Spin glass Molecular field scaling interacting single spins
Spin glass non-scaling cluster formation pairs, triplets, etc. for T > T0
Mictomagnetism (cluster glass) Giant clusters in the spin glass matrix at T >> T0
T0 ∝ x
T0 ∝ x2/3
T0 ∝ x
Exp. propertiesuniversal functions of T/C or H/c variables ≈ ½ at.%
≈ 50 ppm
≈ 10 at.%
TK = T0(c) Exchange:
RKKY
RKKY + short range correlation
Inhomogeneous long range order Concentration of magnetic impurity
Ferromagnetic at ≈ 17 at.% Antiferromagnetic at ≈ 45 at.% (for fcc lattices) Magnetic percolation limit Direct
Dipolar interactions
Fig. 20.9a–d Illustration of the effects of increasing magnetic ions in a nonmagnetic metal matrix, after Coey [20.71] and Mydosh [20.8]. In (a) the ion concentration is sufficient for RKKY interaction and spin glass behavior; in (b) shortrange correlations begin to be important, dipolar interaction becomes important, and a cluster glass develops; in (c) the concentration of magnetic ions is sufficient enough that there is magnetic percolation, long-range magnetic order, and direct exchange; and in (d) the concentrated limited shows FM order at 17 at:% Mn in Cu and AFM at 45 at:% Mn in Cu for FCC lattices
consisting of magnetic ions (Mn, Fe, Cr) [20.6]. The noble metal matrix is crystalline and ordered, such as face-centered cubic (fcc) for Cu. Sometimes the matrix is written underlined, such as CuMn:
Part B | 20.3
1. At the dilute limit, e. g., Mn in Cu, each Mn ion is surrounded by spin polarized itinerant conduction s-electrons from Cu, through an interaction with the d-electrons of Mn, in an s–d mixing or s–d exchange. Below a critical temperature called the Kondo temperature (TKondo ) the AFM interactions of the Cu conduction electrons completely cancel the Mn ion magnetic moment. The result is that the material has no magnetic moment. 2. As the Mn ion concentration increases, the Mn ions begin to see each other through the conduction electrons of Cu by the RKKY mechanism. At this point the Mn ions are single spins, which interact over long distances. As the concentration continues to increase, small clusters of two or three Mn ions couple and begin to act as superspins. The inter-
action between these clusters also may not always be purely ferromagnetic. 3. As the concentration increases further, large clusters of Mn ions become correlated and act together, having relaxation times much longer than those of single spins. This phenomenon has been known variously as mictomagnetism [20.85] or as a cluster glass. The term mictomagnetism (mixed magnetism) was coined before the spin glass concept was established, and the behavior was mistakenly assigned to a mixed FM and AFM system [20.82]. Cluster glass behavior has now come to mean any spin glass-like behavior (not just in metals) where multiple spins relax as a unit, slower than a single spin would. 4. The region of cluster glass behavior ends at the percolation limit, where magnetic exchange is no longer indirect via RKKY but rather can be direct exchange of Mn spin to Mn spin through the whole solid. At this limit the solid is inhomogeneous (chemically disordered) but has long-range
Spin and Ferroic Glasses
magnetic order. For Mn in fcc Cu, at 17 at:% Mn the alloy has FM order, whereas at 45 at:% Mn the alloy has AFM order. At the limit where the alloy is 100% Mn, the crystal structure is body-centered cubic (bcc) and the magnetic structure is AFM. Spin glasses that are dilute magnetic systems transition from a high temperature paramagnetic (PM) state to a low temperature spin glass state. However, in systems with concentrated magnetic ions, above the percolation concentration the high temperature paramagnetic (PM) state will proceed through a FM state below the Curie temperature (TC ) before reaching a lower critical temperature (Txy ) known as the re-entrant spin
699
glass temperature, where spins can freeze in an ordered or disordered way depending on the field applied (Fig. 20.10). These systems are often known as reentrant spin glasses [20.87]. In a spin glass, there are regions of short-range ferromagnetic exchange, which below a characteristic temperature show a freezing behavior where longerrange interactions are prevalent. Experimentally, this is observed as a cusp in the magnetic susceptibility (Fig. 20.10); the temperature at which this occurs is a function of the concentration of the magnetic ion, with higher magnetic ion concentrations leading to higher freezing temperatures. The temperature of the cusp is likely frequency dependent, as previously described
b) χ (10 –3 emu cm–3)
a) T
20.3 Phenomenological Taxonomy of Spin Glasses
χ (10 –3 emu cm –3)
2.4 2 at.%
0.2 2.0 TC
8 at.% 1.6
Paramagnet
0.1
Ferromagnet
1 at.%
1.2 Tf
Txy
8
Spin glass
12
16 T (K)
0.8 x
xp
5 at.% 0.4
0
c)
0
20
40
Type-III AFM cluster
T > Tg
T ≈ Tg
60
80 T (K)
T < Tg
Fig. 20.10 (a) Characteristic phase diagram of a magnetic alloy, where x is the concentration of the magnetic ion; above the percolation concentration xp , and below some higher critical x, the system proceeds on cooling from PM to FM then to a low temperature SG state, after [20.71]. (b) The first indication of spin glass behavior, from the AC susceptibility of AuFe alloys, after [20.6]. (c) Schematic of freezing of AFM ordered clusters in a dilute magnetic semiconductor spin glass as a function of temperature relative to the freezing temperature (shown as Tg ), after [20.86]
Part B | 20.3
T >> Tg
2 at.% 1 at.%
700
Part B
Glass Families
(Sect. 20.2.1), whether due to a phase transition or purely a dynamic relaxation. Spin glass behavior is dependent on the strength of the interactions between the magnetic entities. The behavior of transition metal (TM) alloys, such as the aforementioned canonical spin glasses, is somewhat different than those alloys containing instead magnetic rare earth (RE) ions due to the reduced strength of exchange coupling in RE compared to TM. Structurally amorphous metals can be, but are not necessarily, spin glasses, and these are treated in more detail later (Sect. 20.3.4).
comparable to the exchange interaction as the moment of the superspin gets large enough (Fig. 20.11). Some typical examples of spin glasses in these different categories are shown in Table 20.4. There are several well-studied types of semiconducting spin glasses, which are a subset of the magnetic semiconductors or dilute magnetic semiconductors. One is the doped europium chalcogenides, such as Eux Sr1x S, and comparable selenides [20.89, 90], where the nearest neighbors are FM coupled and the next-nearest neighbors are AFM coupled. Another is the Mn-containing II-VI ternary alloys, where Mn is doped into a II(Zn, Cd, Hg)-VI(S, Se, Te) host, of which the most well known is Cd1x Mnx Te [20.86]. Finally, some spinels ranging from semiconductors to insulators have been shown to be spin or cluster glasses. One wellstudied example is CdCr2 S4 spinel, which is a low temperature ferromagnet, but when doped with In or Ga on the Cr site becomes a re-entrant spin glass [20.87, 91]. Similar behavior is obtained with the analogous selenide [20.92], and should be expected in general with doped AB2 X4 spinels, where A and B are metal cations (e. g., A D Mn, Fe, Co, Ni, Cu, Zn, Cd, Ge, Mg, etc.;
20.3.2 Cluster Glasses Spin glass-type behavior has been observed in many material types, not just metals (Fig. 20.11). Therefore, the mechanism of spin exchange cannot be solely due to the RKKY mechanism, which depends on itinerant (free) electrons. In semiconductors and insulators, spin information exchange is short range, and clustering effects lead to superspins, which relax more slowly and interact by dipolar mechanisms [20.88], which become
0
a)
Strong
Medium
Weak
t0
Transition metals Metallic
T < Tf
b)
None
Longrange
Rare earths Amorphous
t1 Spin glass
Semiconductors NonInsulators conductors
Shortrange
Particles Exchange or dipolar coupling
0
Cluster glass
Fig. 20.11 (a) Spin glass types as a function of conductivity and relative strength of spin coupling, after [20.8]. (b) Cartoon showing the difference between a spin glass and a cluster glass Table 20.4 Typical spin glasses by type, after [20.8]. TM—transition metal; RE—rare earth; underlined element indicates the matrix while the other ion is the dilute magnetic ion. Note that some of the amorphous metals could also be classified as speromagnets or asperomagnets
Part B | 20.3
TM (metal) CuMn AuFe PtMn
Dy-Mn-Ge-Fe-Al
RE (metal) LaGd .YGd/Al2 .CeGd/Ru2 ScDy GdAl2 Tb-Ru-Sn
Amorphous (metal) a-.FePd/80 P20 a-FeSn a-GdAl2
Semiconductor (Eu,Sr)S Cd-Mn-Te
Insulator .Mg;Fe/Cl2 ZnFeF2 a-CoO Al2 O3 SiO2
Particulate CoO Fe3 O4 a-Ho2 O3 B2 O3
Spin and Ferroic Glasses
B D Cr, Al, Ga, Fe, Ni, Co, V, Mn, etc.) and X is a chalcogenide (O, S, Se), depending on the relative concentrations of magnetic versus nonmagnetic cations and the details of the spin interaction [20.93, 94]. Many disordered oxides have been shown to be cluster glasses, including perovskites such as .La;Sr/CoO3 [20.95, 96], .Nd;Gd;Ba;Sr/MnO3 [20.97, 98]; double perovskites such as Ca2 FeMoO6 [20.99] and La2 NiMnO6 [20.100]; spinels such as Co-ZnFe-(Rh)-O [20.101, 102], Ni-Fe-(Zn,Ti)-O [20.103], LuFe2 O4 [20.104], and Ni-Co-Cu-Mn-O [20.105]; as well as the occasional hexagonal compound like CaBa.Fe;Li/4 O7 [20.106] and other exotics like .Cr1x Mnx /2 GeC [20.107]. Additionally, some multiferroics and multiglass ferroics have exhibited cluster glass behavior [20.47, 108], as described in Sect. 20.4.3.
20.3.3 Collectively Behaving Particle Systems It has long been observed that collections of magnetic nanoparticles exhibit collective state behavior similar to spin glasses. While Fig. 20.11 suggests that there is no (dipolar) interaction between magnetic particles, this is true only for the very dilute case. SPM particles have shown frequency-dependent susceptibility behavior due to thermal blocking of particle moments, as
20.3 Phenomenological Taxonomy of Spin Glasses
701
well as a split in the field-cooled (FC)/zero field-cooled (ZFC) magnetization curve [20.28, 40] (Sect. 20.5.2). The blocking temperature of the collective particles is defined as the highest temperature where the zero fieldcooled and field-cooled curves coincide (Sect. 20.5.2 and 20.2.1). When the concentration of magnetic particles becomes large enough, the magnetic fields from one particle will influence nearby particles, resulting in a collective behavior due to strong coupling. If SPM particles are sufficiently concentrated such that they interact, a collective state is created and the interacting nanoparticles are classified by their increasing degree of dipole interaction as interacting SPM particles (ISPM), superspin glasses (SSG) and superferromagnets (SFMs) [20.109, 110]. SSG materials exhibit all the usual characteristics of spin glasses, including memory and aging, which are not present in SPM materials [20.109] (Fig. 20.12). SFM materials are distinguished from SSG by the presence of a finite remanent magnetization which remains after the nonexponential decay [20.44, 111]. SSG behavior is known for many types of systems. Nanoparticles are the most well studied, including Fe3 N [20.112] and -Fe2 O3 [20.49, 113]. Ferrofluids show particularly interesting dynamics as a function of temperature [20.110], and magnetic relaxation can
b) Magnetic moment (10 –2 emu)
a) χ'
TS3
TS2
TS1
4
0.8
FC-RCP 3 ZFC-RCP f
0.4
τ (s)
2
10 –2
1
10 –4
0.0
0
20
40
0.2
0.4
60
Reference × 20 Memory effect ×10
0.6 ε
0 80 T (K)
0
50
100
150
200
250 T (K)
Part B | 20.3
Fig. 20.12 (a) Frequency dependence of the real part of AC susceptibility in superspin glass Co-Fe particles separated by Al2 O3 . Frequencies range from 0.1 to 1000 Hz, 0 is given in SI units. Reprinted with permission from [20.109]. Copyright (2005) by the American Physical Society. (b) Randomly close packed (RCP) maghemite nanoparticles showing zero field-cooled (ZFC) and field-cooled (FC) magnetization compared to a magnetically dilute reference; also shown is the memory effect due to four-hour stops at TS1 , TS2 , and TS3 while cooling under zero field, then measured warming under a small field. Reproduced from [20.49], with the permission from AIP Publishing
702
Part B
Glass Families
be altered by the freezing of the carrier medium, removing Brownian motion at a higher temperature and frequency than the Néel relaxation (thermal activation, Sect. 20.2.1) [20.114]. In this system, the frequency dependence of the magnetic relaxation can separate out the Brownian motion ( B 101 s), where the magnetic moment moves due to particle movement, from the simultaneous Néel relaxation ( B 109 s), where the moment moves relative to the particle (Fig. 20.13). Other examples of SSG include: multilayers of Co80 Fe20 /Al2 O3 with close spacing [20.44, 45, 109], glasses of Fe2 O3 -Bi2 O3 -B2 O3 , and Co particles in a Mn matrix [20.115]. Recently, core–shell magnetic particles have gathered increased interest, and many of these have shown collective dynamic behavior as well. It was shown that direct exchange is much more important than superexchange between magnetic particles with a nonmagnetic a) χ" ×103
Solid phase
shell, and that the freezing temperature of the collective SSG transition increased with the volume fraction of the magnetic particle in the core–shell packed spheres [20.116]. Other studies of core–shell systems of magnetic cores and magnetic shells have also shown glassy dynamics [20.39, 117]. It has even been shown to be possible to differentiate between the freezing processes of a ferromagnetic Fe core and a ferrimagnetic maghemite shell in a collective system [20.39] (Fig. 20.14). The core–shell particles exhibit normal ferromagnetic behavior at high temperature, but the magnetization starts increasing as the temperature drops due to the particle cores freezing, with a peak temperature effect at 48 K as indicated by the second derivative of the remanence. As temperature is further cooled, the energy barrier of the blocking temperature distribution shows another peak 21 K, where the shells also freeze, in random directions that depend b) χ' ×102
Mixed phase
χ" ×103 8
16
Tp1( f ) Tp2( f )
8
100 Hz
6
Néel
Néel & Brownian
Heat flow (arb. u.) 0.3 151 K
4
2
0.1 Solid Mixed state state 0 100 150 200
0 50
Liquid state
12
0.01 Hz
5 T = 178 K
250 T (K)
100
6
Brownian
238 K
0.2
7
Néel 14
150
10 250 0.01 T (K)
200
0.1
1
10
100
4 1000 f (Hz)
Fig. 20.13a,b AC susceptibility measurements of a ferrofluid consisting of colloidal 90 Å magnetite particles with surfactant in kerosene. (a) Temperature dependence; (b) frequency dependence; 0 and 00 are the real and imaginary magnetic susceptibility, respectively, and are given in cgs units, after [20.114]
a) MIR (emu/g) 1.4
b) f (T) 10 –1 Isothermal remanence
Random blocking of shell
10 –2
Normal FM behavior
T2 = 21 K Shell freezing
0.7
T1 = 48 K Core freezing
Fig. 20.14a,b
Part B | 20.3
10 –3 Log normal fit 0.0
0
50
100 T (K)
10 –4
10
100 T (K)
Fe--Fe2 O3 core–shell nanoparticle system showing separate freezing of the core and shell, after [20.39]
Spin and Ferroic Glasses
on field strength and history, thus decreasing the overall measured remanence. The descriptors and models for magnetic core–shell systems have also been extended to describe bare magnetic particles with surface spin disorder caused by spin canting and surface ligand effects.
20.3.4 Amorphous Materials: Ferromagnets, Speromagnets, and Antisperomagnets Structurally amorphous materials (glasses) lack longrange crystalline structure. Even though they lack a long-range crystalline structure, magnetic amorphous materials can exhibit a magnetic domain structure. Since they do not have a crystalline structure, amorphous magnetic materials cannot exhibit magnetocrystalline anisotropy, but only shape anisotropy [20.71]. Generally speaking, the absence of magnetocrystalline a)
m Atomic moments P(D)
703
anisotropy decreases the stored energy (coercivity) in the system, making them very useful as soft magnetic materials where low coercivity is desirable. As the fraction of magnetic ions (Fe, Co, Ni) in the material decreases, however, it is not always possible to maintain a ferromagnet by direct exchange. The general case is shown in Fig. 20.15, where a distribution of anisotropy, atomic moments, exchange interactions, and dipole–dipole interactions come together to create the extremes of collinear (ferromagnetic) or random magnetic alignment. A classification scheme can be further delineated based on a probability of angular distribution of the magnetic moment, and the presence or absence of two (or more) magnetic sublattices [20.71, 118] (Fig. 20.15). It can be seen that FM and AFM are special cases where the distribution of moments is only parallel or antiparallel, whereas in the general case one can have a uniform distribution of moments in all directions or some distribution b)
P(J)
P(m)
20.3 Phenomenological Taxonomy of Spin Glasses
Magnetization
J Exchange interaction P(Hd)
Ferromagnet
Hd Dipolar interactions
D Anisotropy
Asperomagnet
Cooperative magnetism Speromagnet Magnetic groung state collinear/random H Excitations
Phase transition
Micromagnetism
c)
Ferromagnet
Antiferromagnet
Speromagnet
Asperomagnet
Ferrimagnet
Sperimagnets
P(θ)/ sin(θ)
–
– SR AFM
– SR FM
–
–
– SR FiM
Fig. 20.15 (a) Ingredients for cooperative magnetism. (b) Magnetization versus field of a ferromagnet, asperomagnet, and speromagnet. (c) Different angular probability distributions of the magnetic moment resulting in long-range ordered
states like FM, AFM, and FIM, and short-range (SR) ordered states of speromagnetism, asperomagnetism, and speromagnetism; after [20.71]
Part B | 20.3
–
704
Part B
Glass Families
that favors a particular direction. The former case is called a speromagnet (SM), which is essentially like a frozen paramagnet, representing only short-range antiferromagnetic interactions. An asperomagnet (ASM), on the other hand, looks like a short-range ferromagnet. SM and ASM are distinguished by the length scale where spin correlations average to zero, which for SM is a few atomic spacings and for ASM is longer [20.71]. In the two-lattice system there is also the sperimagnet (SiM) where the average moment has spontaneous magnetization, essentially a short-range ferrimagnet (which is a special case of the antiferromagnet with unequal cancellation of the moment). Antiferromagnets in the strict sense can only exist in a crystal, since amorphous materials cannot be consistently divided into multiple sublattices. However, different atom types often constitute the sublattices, so in practice it is possible to define SiM systems in analogy to ferrimagnets (FiM). The root of these special names is akin to diaspora (•š’¢ o¡’) K or scattering and dispersion, describing the distribution in angles of the magnetic moments [20.119]. Speromagnet materials are frequently found, though the term is not often used. Technically, CuMn is speromagnetic below its freezing temperature when no field is applied, but with an applied field it becomes an ideal spin glass at low Mn concentration [20.82]. In practice, the canonical spin glasses are usually distinguished from SM, since in SG the exchange (J) dominates the magnetic anisotropy (K), (i. e., J > K), whereas in SM the anisotropy is usually more significant (J < K) [20.120], though this is not universally true [20.82]. SM is most frequently found in structurally amorphous geologic materials, such as natural ferric gels (Fe.OH3 / 0:9H2 O) [20.119, 121] and some ferromanganese concretions [20.122], and in amorphous RETM alloys, such as .Y;Gd;Dy/7 Ni3 random anisotropy systems [20.123], .Tb;Gd/7 Fe3 alloys [20.120], and amorphous pure RE alloys [20.82]. Amorphous ceramics have also been shown to be SM, including heavy ion irradiated Y3 Fe5 O12 (YIG) [20.124], amorphous FeF3 [20.71], MnF2 -BaF2 -NaPO3 glass [20.125], and Fe2 O3 -P2 O5 glasses [20.126]. ASM materials can be either exchange or anisotropy dominated, depending on the relative absolute values [20.82]. Exchange-dominated ASM exhibit magne-
tization that does not saturate even in large fields (i. e., GdAg, YFe3 , GdAl2 , Fe-Sc) [20.127, 128], whereas anisotropy-dominated ASM do saturate due to domination over the anisotropy (i. e., DyNi3 , TbAg). A related phenomenon to ASM is helimagnetism, which can be seen as the crystalline form of ASM, where a spiral or helical spin structure is dominant (e. g., MnAu2 ) [20.82]. Even amorphous Fe has been suggested to be ASM at low densities, transitioning to a SM state at higher densities [20.129]. Only a few examples of SiM systems exist, one example being .Fe;Er/83 B17 metallic glasses [20.130, 131]. Commercial Applications – Amorphous Ferromagnets Perhaps the only commercial application of a spin glass-like material is a class of amorphous soft magnetic metals (i. e., metallic glass). Arguably the most well-known of these is METGLAS, with the example of METGLAS 2826 with composition Fe0:40 Ni0:40 P0:14 B0:06 , an amorphous analogue of Fe0:5 Ni0:5 [20.71]. Its composition can be tuned to have near-zero magnetostriction, higher Curie temperature, higher permeability, or higher saturation induction. Other commercial soft magnets are glass-ceramics. These materials, known as FINEMET, generally have the composition Fe73:5 Si13:5 B9 Nb9 Cu1 and are composed of very small crystallites of Fe3 Si in an amorphous matrix [20.132]. Similar alloys known as NANOPERM are based on Fe88 Zr7 B4 Cu1 and have ˛-Fe nanoparticles as the base magnetic particles. HITPERM is a related system ((Fe,Co)-(Zr,Hf)-B-Cu) where the particles are ˛ 0 -FeCo [20.133]. In general, the concentrations of the various elemental constituents in these systems can be varied to adjust the properties and/or necessary processing. The composition of soft magnetic nanocrystalline alloys can be represented by TL1xyz TEx My NMz with the four constituents including: (1) a nucleation agent noble metal (NM), which is generally Cu, Ag, Au; (2) a metalloid glass former (M), which is B, Al, Ga, C, Ge, or Si; (3) a ferromagnetic late transition metal (TL), where usually 8590 at:% of the total alloy consists of Fe, Co, and/or Ni; and (4) a glass former and growth inhibitor, which is an early transition metal (TE), usually Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, or W [20.132].
Part B | 20.3
Spin and Ferroic Glasses
20.4 Other Ferroic Glasses: Materials with Glassy Relaxation
705
20.4 Other Ferroic Glasses: Materials with Glassy Relaxation 20.4.1 Strain Glasses First discovered for Ni-rich Ti50x Ni50Cx , the ferroelastic, martensitic system where x > 1:5 [20.19], strain glasses are characterized by nanodomains of a martensitic phase where the transformation does not lead to changes in average structure or heat capacity [20.134]. In normal martensitic transitions, which are of first order, a displacive and diffusionless rearrangement takes place spontaneously below the martensitic (Ms ) temperature as the high temperature paraelastic phase converts to a long-range strain-ordered ferroelastic phase [20.19]. In the presence of a significant concentration of defects, either due to composition [20.15] or heat treatment [20.21], a structure with nanodomains of ordered strain is produced, causing this frustrated transition (Fig. 20.16a). Unexpectedly, the strain glass retains some properties of a martensitic phase; shape memory and superplasticity [20.134]. In some references, a domain glass is subtly distinguished from a strain glass in that the former does not require extrinsic defects to form [20.16, 135]. This could be the case with certain Heusler alloys where heat treatment, rather than chemical defects, produce disordered strain fields [20.21]. Similar Heusler alloys to these strain glasses have been shown to have large magnetocaloric effects associated with the shape memory transition [20.136]. Since strain is the order parameter, collective relaxations of a glassy nature can be seen in the complex a) Ms (K)
dynamic modulus E . The real part E0 , known as the storage modulus, represents the elastic portion where stress and strain are in phase with each other. The imaginary E00 is the loss part and represents the outof-phase component where energy is dissipated as heat. The complex dynamic modulus is often used to describe viscoelastic materials, where the internal friction or tan ı D E00 =E0 is similar to the definition for dielectric loss tangent. In both E0 and E00 there is a frequency dependence of the freezing point for strain glasses [20.19], which can be modeled using the VFT relation. Above the freezing point (known as Tg in strain glasses), the strain glass is ergodic as the thermal energy is sufficient to overcome energy barriers created by inhomogeneous local stresses and nanodomains of strain ordering can switch from one state to another, while below Tg the ergodicity is broken as the thermal energy is insufficient [20.15]. Relaxation in strain glasses has also been described by the stretched exponential Kohlrausch–Williams–Watts (KWW) relation [20.15]. Strain glasses are now seen to be distinct from, but related to, tweed structures often observed in martensitic systems. Tweed structures can be seen as intermediate between the parent (austenite, strain liquid) phase and the further cooled low temperature ordered martensite or disordered strain glass dependent on the concentration of defects [20.18, 22] (Fig. 20.16b). Strain glasses, strictly speaking, are distinct from related systems such as orientational glasses [20.79] in that the latter simultaneously freeze other order paramb) T
Ti50 – xNi50 + x Normal parent phase
B2
300
(Strain liquid)
B19' Ms
Unfrozen strain glass (tweed)
20 nm
200 Tg
100
(Sticky strain liquid)
Glassy martensite
0
0
2 x
0 xc Undoped ferroelastic
Tg Strain glass (frozen local strain order) x (defect concentration)
Fig. 20.16a,b Strain glass phase diagrams: (a) Compositional dependence of the strain glass (glassy martensite) in TiNi, where B2 is a high temperature austenite state and B190 is a low temperature martensite phase. SEM images reprinted with permission from [20.19]. Copyright (2005) by the American Physical Society. (b) Illustration of defect-dependent martensite versus strain glass and relation to tweed structure, after [20.18]
Part B | 20.4
Martensite (long-range strain order)
20 nm
xc 1
(Less sticky strain liquid)
Ms
706
Part B
Glass Families
eters, such as the quadrupolar moment [20.134]. Similarly, in relaxor ferroelectrics and certain spin glasses, such as many manganites, strain may be coupled to another order parameter, such as through magnetostriction [20.137].
20.4.2 Relaxor Ferroelectrics
Part B | 20.4
Ferroelectric materials exhibit a spontaneous alignment of polarization (P) below the critical temperature known as the Curie temperature. A distinction between different types of ferroelectrics is made based on the relaxation frequency and mechanism of the dipole polarizability, and the relative magnitude of this effect on the dielectric permittivity, compared to the ionic polarizability [20.138]. A normal ferroelectric, such as BaTiO3 , has dipole polarizability arising from electric field-induced ferroelectric domain wall vibration of the 90ı domain walls between pinning centers, and has a characteristic relaxation frequency 10 MHz [20.139, 140]. A relaxor ferroelectric, on the other hand, exhibits polar nanoregions (PNRs) of various sizes in which the dipole moments fluctuate with a relaxation frequency 100 MHz, as for Ba.Zr;Ti/O3 [20.139]. As the PNR size decreases, the behavior becomes characteristic of a diffuse phase transition (DPT) and relaxation frequencies increase to 10 GHz, such as in .Ba;Sr/TiO3 , and they have behaviors intermediate between a normal ferroelectric and a relaxor. Relaxors are characterized by very large values of the real part of the permittivity "0 , and large drops of "0 as frequency increases over several decades, accompanied by a large loss as shown by the imaginary part of the permittivity "00 . Both "0 and "00 are frequency dependent in relaxors, and the maximum in the permittivity (Tmax ) shifts to higher temperatures with increasing frequency, approaching the ideal glass transition as the frequency goes to zero (Fig. 20.17). Frequency dependence is typically modeled using a VFT relation. Both normal and DPT ferroelectrics also show a Tmax due to phonon relaxation, but this is not frequency dependent [20.141]. A necessary condition for a relaxor is a broad distribution of local fields and dipole relaxation frequencies [20.142]. The interaction of PNRs at low temperatures has been modeled as either a dipole glass or as random fields [20.143, 144]. In the latter case, disorder due to vacancies, substitutions, and antisites results in quenched random electric fields and local nanostresses and nanostrains, which are responsible for the stability of the PNR [20.147]. The so-called Burns temperature, somewhat higher than Tmax , represents the temperature below which PNRs grow as their correlation lengths increase [20.147].
a)
ε'
4500 4000 3500 3000 2500 2000 1500 1000 500 0
200
250
300
350
400
ε" 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0
450 T (K)
20 Hz 1 kHz 50 kHz 1 MHz 10 MHz 68 MHz 225 MHz 1 GHz
200
250
300
350
400
–1
b) E (kV cm )
450 T (K)
(Pb1– zLa z)(ZrxTi1– x)O3 : PLZT 9/65/35 10.0 Ferroelectric 7.5 5.0 Nonergodic relaxor
2.5 0.0
Ergodic relaxor
Tf FC
200
220
240
260
280
300
320 T (K)
Fig. 20.17 (a) Typical temperature and frequency dependence of the real "0 and imaginary "00 parts of the permittivity for a typical relaxor, in this case 0.5PMN–0.5PSN ceramics; symbols in legend correspond to both parts of figure; after [20.145]. (b) Field-dependent transitions in PLZT as the system is field cooled (FC) across the freezing temperature (circles) to the nonergodic relaxor state, after [20.146]
Spin and Ferroic Glasses
Some of the most well-studied relaxors are based on perovskite structures, such as Ba.Zr;Ti/O3 (BZT) Pb.Mg1=3Nb2=3 /O3 (PMN), Pb.Zn1=3Nb2=3 /O3 (PZN), Pb.Sc1=2Nb1=2 /O3 (PSN), and Pb.Sc1=2 Ta1=2 /O3 (PST) [20.148]. Other common systems include the tungsten bronze structures such as .Sr;Pb/Nb2 O6 (SBN) and related materials. Solid solutions of PMN with PbTiO3 (PT) (a ferroelectric) or PbZrO3 (PZ) (an antiferroelectric) are also important; the family PMN-PT [20.35], for example, has shown extremely high dielectric constants, piezoelectric coefficients, and electromechanical coupling coefficients [20.149]. In PMN-PZ materials, increasing PZ content transforms the material from a relaxor FE to a normal FE [20.150]. Alloying La with the normal ferroelectric Pb.Zr;Ti/O3 (PZT) results in the important transparent electro-optic relaxor ferroelectric PLZT [20.148]. Like in strain and spin glasses, the application of a strong field during measurements affects the structure and properties (Fig. 20.17). Starting from the glassy state, application of a strong electric field will convert the relaxor state in PMN to a long-range ordered ferroelectric phase [20.151]. Similarly, if AC permittivity is measured while applying an increasing magnitude of external electric field, the temperature of dielectric maximum and freezing temperature decreases, corresponding to a narrowing of the distribution of relaxation times [20.152].
20.4.3 Multiglass Ferroics Recently, it has been observed that certain materials, notably some Heusler alloys, can simultaneously exhibit multiple glassy phenomena with different ordering temperatures, and as such are both strain glasses and spin glasses [20.21, 108, 156], or multiferroic glasses. Heusler alloys, first discovered in 1903, are ferromagnetic metal alloys based on face-centered-cubic crystal phases of intermetallic composition, and generally have the X2 YZ stoichiometry [20.157, 158]. These materials have generated significant interest for complex magnetic behavior including spin glasses of various types [20.4]. These multiferroic phenomena have been observed in Heusler alloys when defects were intro-
20.4 Other Ferroic Glasses: Materials with Glassy Relaxation
707
duced by varying composition (doping) [20.19], or by changing heat treatments [20.21]. Multiferroic behavior, in general, has been of great interest of late in materials science, with reviews summarizing symmetry requirements and classification [20.159–161]. Multiferroic glassy materials have been shown to possess useful technological properties, such as magnetocaloric and shape memory effects. Other examples have been shown where the same system exhibits relaxor ferroelectricity and spin glass effects [20.47, 154]. A number of these multiglass materials are shown in Table 20.5. The phase diagram of one particularly complex example of a recently reported multiglass Heusler alloy is shown in Fig. 20.18.
20.4.4 Superconductors and Colossal Magnetoresistance A number of important functional material properties have recently been shown to be strongly dependent on correlated electronic structures. Some degree of charge ordering and/or electronic orbital ordering have been reported to be present in some of these systems. For instance, glassy behavior has been observed in superconductors, particularly type-II high temperature superconductors. The vortex glass, which is a collectively behaving state lacking long-range order [20.162, 163], can be described by the critical slowing down model (power law, Sect. 20.2.1). Both thermal and quantum fluctuations contribute to the disorder in vortex glasses [20.164], which can be described as topological defects in superconducting order [20.165]. It is well known that high temperature superconductors defined as type II have an upper magnetic field bound where they exhibit superconducting behavior, not throughout the entire bulk as in type I, but around a series of pinned vortices where magnetic field lines penetrate the sample and are pinned at defects while material around the vortices is superconducting [20.164]. At lower applied magnetic field, the superconductor is in the single phase Meissner state, like in type I superconductors [20.166]. Like spin glasses, type-II superconductors in a magnetic field between the critical fields, Hc1 and Hc2 , display slow dynamics, irreversibil-
Table 20.5 Multiglass multiferroic materials Structural
X X
Strain X X
Magnetic X X X X X X X
Electric
X X X
Reference [20.21] [20.137] [20.47, 153] [20.154] [20.155] [20.125] [20.126]
Part B | 20.4
System Ni45 Co5 Mn36:6 In13:4 .La;Pr/5=8 Ca3=8 MnO3 PbFe1=2 Nb1=2 O3 Fe2 TiO5 Mn:SrTiO3 MnF2 -BaF2 -NaPO3 Fe2 O3 -P2 O5
708
Part B
Glass Families
a)
b)
Magnetization (emu g–1) 30 Ni45Co5Mn 36.6In13.4 H = 0.05 T 25
20
15
TMS
Increasing austenite L21 order
Critical temperature (K)
TC
Paramagnetic austenite
TC 400
TAf Ferromagnetic austenite
Cluster spin glass
Para- 300 magnetic austenite
Superparamagnetic martensite
10
Ferromagnetic austenite
5
TMf
Tf
0
100
200
Ni45Co5Mn 36.6In13.4
Unfro200 zen TM–80MPa S strain glass Tg 100 TK–80MPa
Superparamagnetic martensite
Tf
SA < S M TAS
0
T
TMS
*
300 400 Temperature (K)
Cluster spin glass
0 600
700
800 900 1000 1100 Secondary-HT temperature (K)
Fig. 20.18a,b Example multiglass behavior of Ni45 Co5 Mn36:6 In13:4 , after [20.21]. (a) Temperature-dependent magnetization and thermal hysteresis; (b) phase diagram showing secondary heat treatment (HT) influence on critical temperatures (Curie: TC ; martensite start/finish: TMs ; TMf ; austenite start/finish: TAs ; TAf ; spin glass: Tf ; supercooled austenite: T ; strain glass freezing: Tg and Kauzmann: TK )
ity, and divergent nonlinear susceptibility [20.167]. It has even been suggested that different types of vortex glasses can be distinguished [20.168]. Memory effects suggesting collective states similar to spin glasses have been observed in Bi2 Sr2 CaCu2 Ox (Bi2212) superconductors [20.169]. Superconductivity, particularly high temperature superconductivity (HTSC), is suspected to have origins related to other exotic phenomena observed in functional materials. HTSC has been argued to be related to ferroelectricity, in that a ferroelectric instability is a necessary condition for the possibility of superconductivity [20.170]. Likewise, cuprates such as those of typical HTSC, are chemically related to manganates [20.50]. Manganates have been extensively studied as cluster (spin) glasses and exhibit a complex array of physical phenomena [20.171, 172], partially due to their magnetic double exchange and charge hopping between Mn3C and Mn4C ions [20.71]. The
colossal magnetoresistance (CMR) observed in many manganates has origins in the strong coupling between lattice, orbital, charge, and spin degrees of freedom. Many of the doped manganates show a transition between a ferromagnetic metallic phase and an antiferromagnetic insulating (AFMI) phase, wherein the two phases can coexist and the behavior of the material as a function of temperature and composition is related to the percolation of the disordered collective state. The AFMI state has been described as charge-ordered and orbital-ordered (CO-OO), or charge exchange (CE) spin-ordered [20.173]. Depending on composition, the CO-OO state can lose its long-range order and only have short-range ordered fluctuations, similar to spin glass states [20.50]. Chromates, nickelates, and cobaltates are expected to have similarly complex phase transitions, and many of these have been described to be cluster spin glasses [20.96, 174, 175].
Part B | 20.4
Spin and Ferroic Glasses
20.5 Measuring Spin Glass Properties
709
20.5 Measuring Spin Glass Properties In this final section, a summary of measurements for spin glass properties is offered. As stated in Mydosh [20.4], there are four experimental measurements that distinguish canonical spin glasses. These four will be discussed below: 1. AC susceptibility 2. DC magnetization differences between field-cooled (FC) and zero field-cooled (ZFC) experiments 3. heat capacity, and 4. aging phenomena. It is important to recall that spin glass behavior as measured experimentally relates to a relaxation, thus the time scale or integration time of the measurement is important (Sect. 20.2.1). A typical DC magnetization measurement timescale is 102 s, so any relaxation faster than this will not be noted. AC measurements can be from 0:1 Hz to 10 kHz (10103 s) depending on the instrument. Mössbauer spectroscopy has a time constant of 107 109 s, while a single relaxing isolated spin is generally assumed to have a time constant of 109 1013 s [20.28]. The measured freezing temperature will depend on the internal time scale of the relaxation and the experimental time scale (i. e., the Deborah number). As seen in Fig. 20.19, the longer the time constant of the measurement, the closer to the true freezing temperature after a long relaxation.
20.5.1 AC Susceptibility
ulating a magnetic field to induce a modulation in the magnetization. A small AC magnetic field (Hac ) is applied and a modulated magnetization is measured. The real (0 ) and imaginary (00 ) AC susceptibility are related to the magnitude () and phase ( ) of the susceptibility as shown in Fig. 20.20. If a saturating DC field is superimposed, the slope of M versus H (the susceptibility) is very small, thus an Hac in the presence of large Hdc will produce M 0, thus ac 0. While DC magnetic susceptibility is M=H, AC magnetic susceptibility ac is dM=dH, which can be locally very large, particularly at low total fields (i. e., at zero DC field plus small AC field, such as typical values from 110 Oe). Typically, the ac is measured at different frequencies as a function of temperature. The change of the Tf
Tf0
The hallmark experimental measurement for spin glasses is AC magnetic susceptibility, where a frequency dependence of the real and imaginary components of the AC susceptibility indicate a glassy spin state. Essentially, these measurements work by mod-
10 –9
10 –6
10 –3
10 0
103 Time constant
Fig. 20.19 Measured spin freezing temperature versus time constant of the measurement, after [20.8]
M
M3 M2
M4 χ' = χ cos φ χ = √ χ' 2 + χ" 2 ⇔ χ" = χ sin φ φ = arctan (χ"/χ')
M1
Part B | 20.5
H
Fig. 20.20 Illustration of the AC magnetic susceptibility measurement. Note that if a saturating DC field is superimposed, such that the change in magnetization (M) measured is very small (such as around M4 ) the AC susceptibility will be vanishingly small. Compare this to the large M obtained with a small or zero superimposed DC field and a small oscillating AC field (such as around M2 )
710
Part B
Glass Families
peak temperature (TP ) as a function of frequency is described as TP D TP .log f /
a) tan δ (internal friction) Ti48.5Ni51.5
0.1 Hz (20.6)
and small values of indicate strongly interacting cooperative freezing. Usually the values of TP as a function of frequency (f D 1= , where is the relaxation time) are obtained experimentally, then fit to one of the relaxation models described previously (Sect. 20.2.1). The fit coefficients obtained are then assessed as to whether they are unphysical or not. For example, some fit values assuming Arhennius behavior will be unrealistic if the spins are strongly interacting [20.8]. For different types of materials, the characteristic relaxation time 0 and the will be different. For instance, for dilute superparamagnets, 0 1013 s and 0:1 [20.101]. For a typical spin glass, such as CuMn, 0 1013 s (since spins relax individually) but 0:01 (since they relax collectively) [20.176]. For cluster glasses or superspin glasses, where there are more spins involved in each relaxation, 0 can be much larger, 108 104 s [20.102]. Similar frequency shifts are observed in other properties in ferroic glasses, as described previously (Sect. 20.4). For strain glasses, the frequency dependence is in the internal friction (related to the complex component of the modulus), while for relaxors it is typically the AC electric susceptibility (or "0 ) (Fig. 20.21).
0.02
0.01 10 Hz
0.00 153
b)
233 T (K)
193
ε' 1 MHz 100 MHz 1 GHz 3 GHz
12 000
9000
6000
3000
0 –40
–20
0
20
40
60
80 T (°C)
c) χ (10 –3 emu cm–3)
Part B | 20.5
20.5.2 ZFC/FC Split
0.24
This experiment is usually performed by cooling a sample from room temperature in no field to a low temperature. A small field is then applied and the sample is measured warming, called the zero field-cooled (ZFC) measurement. Note that this measurement can be obtained while cooling, where the remanence will be measured. A new measurement is then obtained from room temperature but this time it is cooled in the presence of a DC field (magnetic, electric, or strain, depending on type of ferroic glass). Generally, there will be a splitting between the path of the ZFC and FC measurements at a point representative of the freezing point. Application of a larger or smaller field in measuring the ZFC/FC (the same field should be applied for both measurements) will result in a shift of the splitting point. Essentially the FC magnetization (or polarization or strain) will be larger below the freezing point, as the spins or clusters are aligned to the field in the FC measurement whereas they are randomly oriented in the ZFC case (Fig. 20.22).
0.22
100 G 200 G 300 G 2 at.%
0.20
0.14 0.12 1 at.% 0.10 4
8
12
16
20
24 T (K)
Fig. 20.21a–c Comparison of AC susceptibility experiments for (a) strain glass, after [20.19]; (b) relaxor, after [20.177]; (c) AuFe spin glass for 1 at 2 at:% Au at zero
field (solid line) and applied magnetic field, after [20.6]
For magnetic systems, the essential difference between a ferromagnet, antiferromagnet, and spin glass is shown in Fig. 20.23. Ferromagnets and antiferromag-
Spin and Ferroic Glasses
20.5 Measuring Spin Glass Properties
Fig. 20.22a–c
ε
a) Frozen
0.0055
Illustration of the ZFC versus FC measurements in the case of (a) strain glass, (b) relaxor ferroelectric, and (c) cluster spin glass, after [20.15]
Unfrozen
Strain glass Ti48.5Ni51.5
0.0054
FC
0.0053 0.0052
Frozen
711
0.0051 ZFC Stress = 40 MPa
0.0050
Tg 120
140
–2
160
180
200
220
240
260
280 T (K)
–1
b) P (C m )
c) M (emu g ) 6
0.3 FC
Relaxor ferroelectrics PLZT 8/65/35
Cluster-spin glass La0.7Ca0.3Mn0.7Co0.3O3
FC
5 4
0.2
3 E = 3 kV cm –1
0.1
2
ZFC
ZFC
H = 0.03 T
1 0.0 –100
0
100
200 T (°C)
0
0
nets have magnetization, which is reversible both above and below their critical points, and does not depend on field cooling since the exchange is spontaneous. For spin glasses, the measured magnetization depends on field history, and the ZFC magnetization at a constant temperature below Tf will slowly climb if left for a long time as the spins are aligned to the field (see aging below, Sect. 20.5.4). The difference between the FC and ZFC branch below Tf is called the thermoremanent magnetization (TRM) (Fig. 20.23).
20.5.3 Heat Capacity
100
150
200
250
300 T (K)
179]. As the area under the curve represents the entropy, there still exists considerable and increasing magnetic entropy above Tf , suggesting short-range magnetic correlations remain to well above Tf , consistent with the general understanding of spin glasses [20.8, 179].
20.5.4 Nonequilibrium Dynamics: Aging, Rejuvenation, and Memory Since the spin glass state is metastable, long waiting times can result in local relaxation and different magnetization. Aging experiments in interacting particle superspin glasses have already been shown (Fig. 20.12). These effects have been clearly demonstrated in CuMn systems as well, showing the effect on ZFC and TRM from waiting times [20.180] (Fig. 20.24). These measurements can be complex to undertake, but many good examples have been shown in the literature, for instance [20.39, 180–182].
Part B | 20.5
Spin glass behavior can be readily distinguished from a ferromagnetic or antiferromagnetic transition by the entropy dependence at the phase transition [20.4]. The molar heat capacity (Cm ) of a spin glass increases from low temperature then undergoes a broad plateau above Tf , while Cm =T is linear below Tf , and shows a peak at Tf for low concentrations of magnetic ions [20.178,
50
712
Part B
Glass Families
a) M
M
Ferromagnet
M
Antiferromagnet
TC
TN
80
Tf
2
8
60
6
θ p = –1
40
1
4
θp = 0
θp = 1 20 0
Fig. 20.23 (a) Magnetization
Spin glass
2 0
1 2 Reduced temperature
0
0
1 2 Reduced temperature
0
0
1 2 Reduced temperature
of a ferromagnet, antiferromagnet, and spin glass, after [20.71]. (b) Definition of thermoremnant magnetization (TRM) for a spin glass, after [20.110]
b) M FC
SPM Tg TRM ZFC
T
a) ∆M/H (arb. u.)
b) M/H (arb. u.) 30
5 tw = 3 s
25
0
ZFC
tw = 3000 s
20
FC
tw = 3000 s
15
FC
ZFC
tw = 3 s tw = 3000 s
TRM
10 TRM
5 tw = 3 s –5 10 –1
10 0
101
102
103
104 t (s)
0 20
30
40
50
60
70 T (K)
Part B | 20.5
Fig. 20.24a,b Aging time experiments for CuMn after different wait times (tw ) at T < Tf , after [20.183]. (a) Timedependent change in magnetization (M) as described by M.tw /M.t D 0:3 s). For ZFC and FC measurements, samples are cooled below Tf in small field (FC) or no field (ZFC), then held for various tw , then measured as a function of time; for TRM, the measuring field is switched off after tw and magnetization measured. (b) Temperature dependence of ZFC, FC, and TRM for normal measurements and for measurements with a stop at 40 K for 3000 s before cooling further and measuring on warming (dip in ZFC and bump in TRM); the system has memory of its previous state at 40 K even after cooling down and warming up again
Spin and Ferroic Glasses
References
713
20.6 Outlook Despite the fact that spin glasses were identified as a class of materials over 40 years ago, their behavior and physics continue to be explored as novel materials exhibiting glassy dynamics in magnetization, polarization, and strain are discovered and studied. This broad class of materials exhibiting glassy behavior is now known collectively as ferroic glasses, and new materials may exhibit multiglass properties. Even within spin glasses proper, which meet the strict experimental criteria involving AC susceptibility, DC magnetization changes with field history, and aging dynamics, there exist subcategories with different degrees of in-
teraction and thus myriad behaviors as a function of temperature and field history. Some efforts have been made over the years to classify these spin glasses, and distinguish them from amorphous magnets and collectively behaving particle systems. It remains intriguing to consider the physical and experimental parallels between the study of structural glasses and that of spin and ferroic glasses. It is hoped that this chapter will spark the interest of some traditional glass scientists in the exotic world of the spin glass menagerie, and result in continued study of these systems for the next generation.
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20.2
20.3
20.4
20.5 20.6
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20.8 20.9
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20.15
20.16
20.17
20.18
20.19
20.20
20.21
20.22
20.23
20.24 20.25
20.26 20.27
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20.84 20.85
20.86 20.87
20.88
20.89 20.90
20.91
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20.98
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>@ >@
Fig. 21.1a,b Comparison of metal organic framework and inorganic network structures. (a) The cubic single-crystal structure of MOF-5, showing the principal axes: zinc (blue) tetrahedrally coordinated to oxygen (red) and then to carbon (black), comprising the linker 1,4-benzenedicarboxylate. (b) The hexagonal crystal structure of ’quartz: silicon (blue) tetrahedrally coordinated to oxygen (red)
721
Part B | 21.1
ture factors of inorganic zeolites where infra-network correlations usually just involve Si, Al, and O [21.14, 19, 35]. In general, atomistic modeling in generating CRNs also sheds light on the network topology that exists beyond nearest neighbor atoms [21.14, 35, 42]. The use of quantum mechanical methods applied to crystalline organic–inorganic structures also enables their mechanical properties to be predicted [21.6], placing them, and indeed their non-crystalline versions, in the category of materials that are both rigid and soft, as Tan and Cheetham have stressed. Transferring the structural concepts of inorganic glasses to model hybrid glasses has been less obvious so far for HOIPs and CPs, as thorough radial distribution function (RDF) analysis often still has to be undertaken. For non-crystalline HOIPs, however, the topology may well align with the inorganic oxygen deficient calcium aluminate glasses and liquids [21.43]. Where CPs glasses are concerned [21.21, 23], an inorganic starting model may not be so useful, and the inherent polymeric morphology probably has more in common with acrylic poly (methyl methacrylate) (PMMA) glasses [21.44] or conjugated polymers [21.45] (Sect. 21.1.2) than the chain and layer structures of inorganic phosphate or chalcogenide glasses [21.35]. We conclude this introduction to hybrid glasses by reviewing the principal methods to fabricate them that have been developed so far. These include: meltquenching [21.1, 2], amorphization [21.23, 34, 35], and solution and gel chemistry [21.3, 22, 23] (Sect. 21.1.3). All of these techniques can result in glasses of different density and also porosity [21.3, 46] compared to the starting organic–inorganic crystal. For MOFs, porosity, in particular, can be very different to that for oxide glasses, for example [21.47, 48], and is an important consideration where applications of low-density hybrid glasses are concerned. At a fundamental level, though, while forming glasses by melt-quenching and the asso-
21.1 Structure and Formation of Hybrid Glasses
722
Part B
Glass Families
Part B | 21.1
tures are networks, their physical bulk densities are quite different (densities of MOF-5 and ’-quartz: 0:621 and 2:648 g cm3 , respectively), which relates to the organic linkers being much longer than bridging oxygens. Furthermore, the porosity measured by the internal surface area (obtained using Brunauer–Emmett–Teller (BET) analysis [21.8]; BET internal surface areas of MOF-5 and ’-quartz: around 1000 and 2 m2 g1 , respectively) is massive for MOF-5 compared to ’-quartz. This gives MOF’s huge potential in applications like heterogeneous catalysis, gas sorption etc., as Yaghi and others have demonstrated [21.6, 9, 11, 13]. As the name suggests, zeolitic imidazolate frameworks or ZIFs [21.4, 12] are nanoporous hybrid frameworks mimicking the better-known inorganic zeolites [21.11], often sharing the same structures [21.13]. This is illustrated in Fig. 21.2 for ZIF-8, which has the same cubic space group P43n as the silicate mineral sodalite. Once again, there are huge differences in density, often expressed in terms of solvent accessible volume or SAV (densities of ZIF-8 and sodalite: 0:95 compared to 2:28 g cm3 ; SAV is 50% for ZIF-8 and 20% for sodalite). Together with the very different internal surface areas between zeolitic organic–inorganic and inorganic structures, these distinctions are once again directly attributable to the greater length of the organic linkages (BET internal surface areas of ZIF8 and sodalite: 1583 and 10 m2 g1 , respectively). Of specific interest here, however, is the fact that inorganic zeolites collapse into viscous phases at modest temperatures TA close to the glass transition Tg . They can also be melted at much higher temperatures Tm and can be solidified by quenching either from TA or from Tm [21.15–19]. The transformation at TA is common to the order–disorder transitions of many network materials and is called amorphization [21.35]. It generally involves more than one liquid phase being in coexistence with another, referred to as polyamorphism [21.36]. Often, these amorphous phases come in a)
pairs, generally low-density and high-density liquids— LDL and HDL, respectively—or their respective lowdensity and high-density amorphous equivalents—LDA and HDA. It is not surprising that ZIFs can also be amorphized [21.1, 39, 40], so low-temperature melting or decelerated melting, the concept developed by Wondraczek et al. [21.14], is an alternative, and as will be described in due course, an equivalent route to the formation of melt-quenched hybrid glasses (Sect. 21.3.2). The only complicating factor, starting with MOFs and other hybrid crystals, is the vulnerability of the organic linkers to decomposition at some temperature TD , which often falls between Tg and Tm . Like polymer systems in general, CPs in particular can adopt structures with different dimensionalities. The 2-D CP ŒZn.H2 PO4 /2 .TzH/2 n is illustrated in Fig. 21.3, where Zn ions are octahedrally coordinated to four bridging 1,2,4-triazoles (TzH) and two orthophosphates .H2 PO4 /. Layers are formed, stacking up along the c-axis, with the source of mobile protons located between the layers. By contrast, a 1-D structure ŒZn.HPO4 /.H2 PO4 /2 2H2 .C3 H3 N2 / can be formed when Zn ions are bridged by phosphates [21.22]. Both 1-D and 2-D CPs are proton conductors. They can also be melted and quenched to form glasses [21.22], but at the risk of linker decomposition. As an alternative, they can be amorphized under pressure as well as thermally [21.23, 24], from which they can also be recrystallized [21.23]. HOIPs have crystalline structures isomorphous with CaTiO3 and are compared in Fig. 21.4. These are illustrated by the methylammonium metal halide ŒCH3 NH3 ŒPbI3 , where CH3 NH3 occupies the A site, Pb the B site, and I the X site [21.26] and by the MOF formate perovskite ŒCH3 NH3 ŒMn.HCOO/3 [21.25] where, in addition to the A site being occupied by 2C CH3 NHC occupies the B site with HCOO the 3 , Mn X site. The densities of HOIPs are much lower than those of their inorganic polymorphs. HOIPs can be
b) Fig. 21.2 (a) Crystal structure of ZIF-8 .Zn.C4 H5 N2 /2 /: zinc (green) tetrahedrally coordinated to the 2methylimidazolate .C4 H5 N 2 / linker made up of nitrogen (cyan) and carbon (black). Central sodalite cage (“-cage) is highlighted in yellow and 6-fold rings in orange. (b) Crystal structure of the mineral sodalite .SiO2 /: silicon (gray) tetrahedrally coordinated to oxygen (red). Sodalite or “-cages are highlighted in gold
Hybrid Glasses
CP proton conductor with Zn ions coordinated to bridging 1,2,4triazoles (TzH) within the layers and orthophosphates .H2 PO4 / between the layers, including mobile protons. Zn (purple), P (yellow), O (red), N (blue), C (gray), H (white). Adapted with permission from [21.21]. Copyright 2012 American Chemical Society
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Fig. 21.4 (a) Classic inorganic perovskite CaTiO3 with corner sharing TiO6 octahedra enclosing Ca cations. (b) HOIP ŒCH3 NH3 ŒPbI3 with corner sharing PbI6 octahedra surrounding methyl ammonium CH3 NH3 cations. (c) Hybrid formate perovskite ŒCH3 NH3 ŒMn.HCOO/3 with manganese formate MnŒHCOO6 octahedra surrounding methyl ammonium CH3 NH3 cations forming a metal organic framework
melted, but TD will often be comparable to Tm [21.29, 30]. Even if decomposition can be avoided, perovskites are poor glass formers precluding the formation of melt-quenched glasses (MQGs) at conventional cooling rates. This currently leaves amorphization induced by pressure as the only practical alternative for forming hybrid amorphous perovskite materials [21.31–34] (Sect. 21.3.1).
21.1.2 Atomic Structure of Hybrid Glasses, Continuous Random Networks, and Charge Compensated Random Networks If MOFs, CPs, or HOIPs can be heated without decomposition until melts are formed, then hybrid glasses can be solidified by employing conventional quenching techniques [21.35] (Fig. 21.5). ZIF glasses are trans-
parent, sometimes yellow, and generally electrically insulating. CP glasses are usually clear dielectrics. So far, HOIP MQGs have not been reported, but like their crystalline counterparts would be semiconducting and black to dark brown. In common with other glasses vitrified in the same way, hybrid glasses can, in principle, be fabricated in any form, shape, or size. They are currently fabricated in mm to cm dimensions, unlike MOF and HOIP crystals whose sizes seldom extend beyond several m. Examples of amorphous hybrids are illustrated in Fig. 21.5 and include MQGs formed from ZIF-4 .Zn.C3 H3 N2 /2 / [21.1] and from ZIF62 .Zn.C3 H3 N2 /1:75 .C7 H5 N2 /0:25 / [21.49], a porous Ti-BPP (semi-rigid derivative of BPA with extra phenol) MOF glass .Ti16 O16 .OEt/32 / prepared following solvent removal [21.3], and a CP MQG formed from ŒZn.H2 PO4 /2 .TzH/2 n [21.22], together with a 4 GPa amorphized pellet of Cd.H2 PO4 /2 (1,2,4-
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Fig. 21.5 (a) MOF MQG ZIF-4 .Zn.C3 H3 N2 /2 / (from [21.1]). (b) Porous MOF solvent evaporated glass Ti16 O16 .OEt/32 . Reprinted with permission from [21.3]. Copyright 2016 American Chemical Society. (c) CP MQG ŒZn.H2 PO4 /2 .TzH/2 n . Reprinted with permission from [21.22]. Copyright 2014 American Chemical Society. (d) MOF MQG ZIF-62 ŒZn.C3 H3 N2 /1:75 .C7 H5 N2 /0:25 from [21.49]. (e) Micrographs in DAC of amorphization of HOIP ŒCH3 NH3 ŒPbI3 , transparency increasing with pressure. Reprinted from [21.34], with the permission of AIP Publishing. (f) CP Cd.H2 PO4 /2 (1,2,4-triazole)2 pellet amorphized at 4 GPa. Reprinted with permission from [21.23]
triazole)2 [21.23]. Also included is the HOIP ŒCH3 NH3 ŒPbI3 at various stages of amorphization [21.34] under pressure within a diamond anvil cell (DAC). Alternatively, crystalline MOFs may also be transformed into hybrid glasses by decelerated melting [21.14] at temperatures close to the glass transition Tg [21.1, 39, 40]. The atomic structures of amorphized and melt-quenched non-crystalline hybrid structures can be obtained by refining the structure factor S.Q/ measured by XRD or neutron diffraction [21.2, 40, 49] and Fourier transforming to obtain the pair distribution function (PDF) D.r/, as shown in Fig. 21.6 for the MOF ZIF-4 (Zn.C3 H3 N2 /2 ) and non-crystalline versions derived from ZIF-4 by amorphization and meltquenching [21.1]. Also included in Fig. 21.6 are Fourier transforms of the extended x-ray absorption fine structure (EXAFS) .k/ from the Cd K-edge and D.r/ for the proton conducting CP CdTz .Cd.H2PO4 /2 (1,2,4triazole)2 ) together with the PDF [21.23]. At first sight, S.Q/ and D.r/ of amorphized and MQGs hybrid glasses appear highly structured, compared to oxide glasses, for example. This apparent high degree of order, reflected in Fig. 21.6, relates to the interatomic correlations within Zn.C3 H3 N2 /2 tetrahedra for the MOF ZIF-4, which are common to crystalline and amorphous structures. Note the first six maxima in D.r/, which can be identified with the Zn-imidazolate-
Zn unit (Fig. 21.2). Likewise, in Fig. 21.6, the pair correlations between Cd and the infra-layer 1,2,4-triazoles (TzH) bridges and inter-layer orthophosphates .H2 PO4 / for the CP CdTz can be seen in the EXFAS Fourier transform, augmented by the infra molecular distances in the XRD PDF, which can be visualized in the isomorphous ZnTz structure shown in Fig. 21.3. For ZIF-4, the retention of the geometry of the organic imidazolate linker through the disordering processes of thermal amorphization and melting has been verified with 13 C nuclear magnetic resonance (NMR) [21.1, 2] and is responsible for the almost identical sharp structure in crystalline and non-crystalline D.r/ up to 0:6 nm, which can be identified with infra-molecular correlations (Fig. 21.6b). The common structure beyond 0:6 nm for the non-crystalline hybrids is due to the dominant inter-molecular Zn-Zn correlations and is simpler and weaker compared to the D.r/ structure in ZIF-4, where cation interatomic distances are defined by crystalline periodicity [21.2, 49]. Conversely, the common tetrahedral geometry in ZIF-4 and the amorphized hybrid and the glass dictates the virtual overlaying of the structure in S.Q/ beyond 0:4 nm1 , with differences in long-range order reflected in divergences in diffraction at shorter wave vector values (Fig. 21.5a). In the same way, for CdTz, the integrity of the triazole ligands through ball-milling amorphization
Hybrid Glasses
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Fig. 21.6 (a) XRD structure factors S.Q/ and (b) corresponding pair distribution functions D.r/ for MOF ZIF-4 .Zn.C3 H3 N2 /2 /, amorphized ZIF-4, and melt-quenched ZIF-4. Overlaying of all three polymorphs in S.Q/ beyond 0:4 nm1 , due to common tetrahedral geometries, and in D.r/ of amorphized and MQGs beyond 0:6 nm, due to dominant Zn-Zn correlations. Imidazolate motif of infra-molecular atomic correlations C-H, C-C, C-N, Zn-N, and Zn-Zn define the sharp structure up to 0:6 nm. Amorphized ZIF-4 (pink dashed), MQG ZIF-4 (green), and ZIF-4 (black dashed). After [21.49]. (c) Fourier transform of Cd K-edge EXFAS and (d) XRD pair distribution functions of crystalline CP [Cd.H2 PO4 /2 (1,2,4-triazole)2 ] and amorphized material after dry ball-milling for 240 min. [Cd.H2 PO4 /2 (1,2,4triazole)2 ] is isomorphous with [Zn.H2 PO4 /2 (1,2,4-triazole)2 ] illustrated in Fig. 21.3. Pair correlations for Cd-O, Cd-N, Cd-C, and Cd-P, and C-C, C-N, P-O are identified: Crystalline CdTz (black) a-CdTz (gray). After [21.23]
(Sect. 21.3.2) is retained, evidenced through 13 C, 113 Cd, and 31 P NMR, albeit with the incorporation of some distortion [21.23]. This is clearer, in the Cd partial PDFs from EXAFS (Fig. 21.6c), where the nearest neighbor Cd–N bonds to triazoles and Cd–O bonds to orthophosphates are present in a-CdTz, but broadened, compared to the crystalline structure. In addition, the PDF reveals the infra-molecular triazole and orthophosphate correlations, together with a Cd-Cd feature, clear in the crystalline CP and just perceptible in a-CdTz (Fig. 21.5d), suggesting that fragments of the 2-D layer CP topology (Fig. 21.3) survive amorphization. X-ray PDF analysis, EXAFS, and NMR all demonstrate the close similarity in short range order (SRO) that exists between the hybrid non-crystalline materials and the corresponding crystalline MOFs and CPs [21.1, 2, 22–24]. While this characterization has been useful in confirming the atomic structure of the bridging linker and/or neighboring ligands and the persistence of SRO,
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21.1 Structure and Formation of Hybrid Glasses
it has been less useful in accessing structure at interpolyhedral distances and beyond. For melt-quenched and amorphous MOFs, modeling diffraction experiments on the CRN introduced by Zachariasen [21.37], widely used in understanding the structure of inorganic tetrahedral glasses [21.35], has been far more informative in deciphering long range order (LRO). Following Zachariasen’s rules [21.37], hybrid CRNs can be developed, comprising cornersharing inorganic tetrahedra, like zinc atoms, connected to organic linkers, such as those from the imidazolate family, bridging pairs of tetrahedra. These, respectively, replace silicon atoms and bridging oxygens in the structure of silica, as is illustrated in Fig. 21.7. As a first step, tolerable agreement has been reported between XRD experiments of MOF hybrid and amorphized glasses and their structures modeled on silica CRNs, such as that due to Ching [21.50]. This initial CRN structure is then used as the starting point, ex-
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Fig. 21.7 (a) Amorphized MOF ZIF-8 CRN .Zn.C4 H5 N2 /2 /, highlighting a 6-fold ring: zinc (gold) tetrahedrally coordinated to the organic linker 2-methylimidazolate–.C4 H5 N 2 /: nitrogen (blue), carbon (green), and hydrogen (light blue). Infra-tetrahedral correlations extend to 6 Å (Courtesy of W. Chen [21.53]). (b) Silica CRN (SiO2 ) containing 4, 5, 6, and 7-fold rings, highlighting a 6-fold ring: silicon (yellow) and bridging oxygens (red). Infra-tetrahedral correlations extend to 3 Å (Courtesy of J. Du [21.54])
panded to accommodate the larger hybrid networks by replacing bridging oxygens with organic linkers like imidazolate .C4 H5 N 2 / bridges [21.38, 39]. A far closer agreement can be achieved from refining the CRN model structure against the experimentally determined S.Q/, as Bennett and Coudert showed recently [21.51] by using reverse Monte Carlo analysis [21.52]. As we have seen, most of the sharp structure in the total pair distribution function D.r/, however, relates to pair correlations between atoms within the metal organic tetrahedron, with structures between the tetrahedra responsible for much weaker features [21.49] (Fig. 21.6). Where infra-tetrahedral pair correlations extend far further out in distance for amorphous ZIF structures compared to silica, because of the larger dimension of the linker compared to the bridging oxygen, it is the structure beyond these limits that determines the LRO and defines the topology of the CRN. This is often expressed in terms of a ring structure pervading the network, as Du and Cormack demonstrated [21.54], and is what differentiates one tetrahedral CRN atomic arrangement from another. Suffice it to say, it is atomistic simulation—molecular dynamics (MD), reverse Monte Carlo (RMC) analysis, and/or ab initio density functional theory (DFT)—that provide the most effective tools for determining the topological characteristics of amorphized zeolites, ZIFs, and their hybrid glasses [21.38, 53, 55]. Care has to be taken, however, if simulations are performed at constant volume (NVT—normal volume and temperature) rather than constant pressure (NPT—normal pressure and temper-
ature). Using a fixed density with rising temperatures can lead to phase transitions like amorphization and recrystallization, which have been observed experimentally [21.1], being masked in simulating the melting of MOFs [21.51] (Sects. 21.1.3 and 21.2.2). Finally, using a silica CRN model as the starting point for RMC [21.39, 51] risks imposing the LRO of the silica model, however impressive the final fit might be. In addition, current DFT codes can provide reliable predictions of the unusual mechanical and dynamical properties of organic–inorganic crystalline materials and glasses [21.6, 56–59]. In particular, these simulations reveal values of Young’s modulus (E < 10 GPa) that are very low [21.6], while those of the shear modulus are lower still, lower than any other group of materials, as Tan and co-workers discovered .G . 2 GPa/ [21.59]. Added to this, the hardness of MOFs is also extremely small < 1 GPa [21.58] but, at the same time, Poisson’s ratio generally falls close to the brittle–tough transition [21.60] at 0:3 (Sect. 21.3.5; Fig. 21.18b). Taken together, MOFs and their hybrid glasses are both rigid, soft, and often brittle. This is in contrast to oxides like ’-quartz and silica, which, while being rigid and brittle, are extremely hard—that is, despite oxide glasses and hybrid glasses sharing archetypal CRN atomic structures (Fig. 21.7). Turning to CPs, MQGs are reported obtained from 1-D and 2-D crystalline phases (Fig. 21.3) [21.21– 23] as well as amorphized phases from 3-D porous crystalline phases [21.24], but a full RDF analysis to establish LRO has yet to be undertaken. For non-
Hybrid Glasses
b)
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Fig. 21.8 (a) A simulated structure of the conjugated polymer poly-2,5-bis(phenylethynyl)-1,3,4-thiadiazole, indicative
of the topology that might be expected for an amorphous 1-D coordinated polymer. Reproduced from [21.45], with permission of The Royal Society of Chemistry. (b) Schematic of the CCRN quasi-network structure for amorphous ŒCH3 NH3 ŒPbI3 proposed for hybrid HOIP ABX3 glasses. This is based on the structure of the calcium aluminate glass .CaO/12 .Al2 O3 /7 , where Ca has been replaced by CH3 NH3 , Al by Pb, and O by I. Pb occupies 4-fold and 5-fold sites, and I 2-fold and 3-fold sites. Hydrogen bonding between A and X-sites is indicated by dashed lines
crystalline phases of lower dimensionality, MD and DFT modeling is possible, as it has already been explored for disordered conjugated polymers [21.45]. In the case of amorphous CPs, where organic monomers are separated by metal cations, melting the crystalline phase and then quenching to form a glass structure could be simulated using standard methods [21.53– 55]. Figure 21.8 illustrates the simulation of disordering a 1-D conjugated polymer poly-2,5-bis(phenylethynyl)1,3,4-thiadiazole [21.45], which mimics the irregular conformation that might be expected if a 1-D CP like ŒZn.HPO4 /.H2 PO4 /1 2H2 .C3 H3 N2 /2 was melt quenched to a glass or amorphized. The polymeric chains will be interspersed by coordinating metal nodes, but hydrogen bonding will dominate intermolecular interactions and topology. Where HOIPs are concerned [21.25], although melt processing and vapor deposition techniques [21.27, 29] are attracting attention for solar cell applications, MQGs have not yet been reported but amorphized phases have [21.31–34]. Full PDF analysis and atomistic modeling remains to be explored. With the higher crystalline packing of HOIPS as compared to MOFs (Fig. 21.2 with Fig. 21.4), however, non-crystalline HOIPs are likely to bear more topological similarity to aluminate oxide glasses than to silicate glasses. As such, they would be better modeled, to a first approximation, on the CCRN model developed by Greaves, Ngai, LeLosq, Neuville, and others [21.41, 42], rather than the Zachariasen CRN [21.35, 37]. In particular, the density of crystalline aluminates, such as corundum .Al2 O3 /, drop on melting, with hexagonally packed AlO6 octahedra being
727
Part B | 21.1
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21.1 Structure and Formation of Hybrid Glasses
replaced by lower coordinated AlO5 and AlO4 polyhedra. Oxygens mainly adopt tricluster O3 geometry and with Al4 and Al5 configurations form a quasi-network structure [21.61, 62]. The same SRO configurations are also found in oxygen deficient liquid and glassy calcium aluminates, like .CaO/12 .Al2 O3 /7 [21.43], whose stoichiometry CaAl1:2 O2:8 is similar to the composition of perovskites like CaTiO3 . A detail from the CCRN structure of .CaO/12 .Al2 O3 /7 glass is shown in Fig. 21.8 [21.43], in which calcium has been replaced by methylammonium, aluminum by lead, and oxygen by iodine, to form a schematic random network for an amorphous HOIP, including suggested hydrogen bonding between A and X-sites.
21.1.3 Hybrid Glass Formation Starting from the liquid state, hybrid glasses can be vitrified if crystallization can be avoided. The conventional approach to explaining glass formation through the supercooled state [21.35], encapsulated in the Adam and Gibbs formalism [21.63], is that, as cooling advances, the excess configurational entropy Sconfig, expressed as the cooperative atomic motion inherited from the thermodynamically stable melt, gradually decreases as the temperature is lowered. In the supercooled region, Sconfig is expressed in terms of cooperatively rearranging regions that reduce in size until the glass transition Tg occurs. This is the point at which relaxation times extend to the scale of minutes, which defines glass formation with cooling rates of 1 K s1 . Experimentally, the glass transition coincides with the
728
Part B
Glass Families
Part B | 21.1
familiar endothermic step in the specific heat Cp , from which the residual Sconfig can be determined [21.35, 49, 64]. The Adams and Gibbs model of kinetic relaxation through atomic cooperativity predicts the well-known Vogel–Fulcher–Tammann (VFT) equation for shear viscosity , as well as the more recent Mauro–Yue– Ellison–Gupta–Douglas viscosity equation (MYEGA) equation [21.65], which hybrid supercooled liquids follow [21.49]. The shear viscosity of most ordinary glasses is approximately Arrhenian around Tm , but, as Tg is approached, it becomes less so. This is characterized by the fragility index m, defined in Angell plots by m D .d.log /=d.Tg=T//TDTg [21.66]. For typical fragile liquids, m falls between 40 and 50, which includes the fragility of many hybrid liquids [21.2, 49], as well as classic glass formers like B2 O3 and GeSe2 [21.35]. In contrast, for liquids of archetypal glass formers like SiO2 , the viscosity is Arrhenian throughout the supercooled region, with m 20, constituting strong behavior. As supercooled temperatures approach 1:2Tg , however, the ergodicity [21.35] or thermodynamic stability of the melt is lost [21.67], slow relaxation processes emerge, and a dynamic cross-over in structural heterogeneity occurs [21.63–71]. This is the region where the supercooled liquid becomes non-ergodic and where polyamorphism can occur [21.35, 36]. Empirically, the sizes of m and Sconfig are proportionately related [21.35], so, fragile liquids exhibit large Sconfig, while for liquids of increasing strength, Sconfig deceases in size. In considering glass formation 70 years ago [21.72], concerns then focused on whether, through progressive protracted cooling and a lowering of Tg , Sconfig might actually undercut the thermal entropy of the (ordered) crystalline state, conflicting with the third law of thermodynamics—the Kauzmann paradox [21.72]. While this thermodynamic anomaly has subsequently been resolved in favor of the supercooled excess entropy continuously decreasing towards zero [21.68], with a baseline glass transition of TK (the K in recognition of Kauzmann), this has since raised the possibility of perfect glasses that might have little or no excess entropy, as Greaves, Sen, Angell, Moynihan, and Hemmati have discussed [21.35, 73]. These glasses would necessarily be super strong with m < 0:2 and ultra stable. If crystallization does not intervene, which is the case for pre-historic ambers [21.74], then very low entropy glasses can be realized, but with cooling rates estimated to be 1014 K s1 . The alternative equivalent laboratory approach is vapor deposition on amorphous substrates held around 0:85 Tg [21.75]. Melt-quenched bulk metallic glasses are generally also of low enthalpy [21.76]. In all cases, these MQGs have passed through the cross-over region of heterogeneity esti-
mated to occur around 1:2Tg [21.69–71] (Sect. 21.3.5; Fig. 21.19b) and are non-affine. It has recently been shown for metallic glasses that enthalpy can be increased by thermal stressing below Tg or, indeed, by mechanical stress [21.76, 77]. In the present context, evidence for perfect glasses has been found through the amorphization of zeolites [21.14–19] and, indeed, when MOFs are amorphized [21.1]. Suffice it to say, as amorphization commences from the nanoporous crystal rather than cooling the molten liquid, the entropy of the amorphous hybrid at Tg will be closest to the low-density crystal. As zeolites and ZIFs are produced using templates and solvents, once these are removed, which usually occurs at temperatures below Tg , their structures will incur distortion and become increasingly unstable as the temperature rises. In particular, careful calorimetry has established that the enthalpy of zeolites exceeds that of equivalent silicate glasses [21.78], and amorphization, therefore, releases heat [21.14–16]. Evidence points to the same scenario applying to lowdensity porous MOFs, amorphization being exothermic (Sects. 21.2.2 and 21.2.3) and supporting the contention that crystalline collapse at TA involves the creation of a low-entropy, low-density amorphous hybrid [21.1] or perfect glass, as has previously been proposed for the thermal collapse of zeolites [21.15, 16]. Amorphization is finally complete when Tg is reached, and the lowdensity MOF phase eventually transforms into a higher density phase that appears almost indistinguishable from a MQG [21.1, 49]. The temperature of amorphization typically occurs at 550600 K for ZIF-4 and its polymorphs [21.1, 2, 49], compared to the melting temperatures Tm of around 700850 K. Thermally-induced amorphization and melt quenching, therefore, appear to be alternative ways of forming very similar hybrid MOF glasses. CPs, similar to the 2-D ŒZn.H2 PO4 /2 .TzH/2 n depicted in Fig. 21.3, can also be melted and quenched to form glasses as Kitagawa’s group has shown [21.23] (Fig. 21.5c). Compared to MOFs like ZIF-4, the temperatures involved are much lower, with Tm around 470 K and Tg around 350 K [21.22, 23]. For these CPs, the Tg =Tm ratio equals 0:74, similar to that for ZIF-4 (0:71), each being comparable to the 2/3 law originally observed for molecular glass formers by Kauzmann [21.72]. These values for Tg =Tm suggest that the glass-forming ability, viz. the ability to avoid crystallization, for these CPs is similar to the majority of conventional glass formers (Sect. 21.5) [21.35, 49]. Nevertheless, CPs like those based on azoles and phosphates adopt different dimensionalities, depending on which of these anions bridge the metal nodes—Zn in this case. Azoles result in 2-D crystals, while phos-
Hybrid Glasses
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phates can form 1-D crystals. In the latter case melting, explored through the increase in the magnitude of thermal vibrations—the Debye–Waller factor obtained from single crystal XRD—as Tm is approached [21.22], seems to be accommodated through changes in coordination bonds, which are restored once the glass is formed at Tg . By the same token, the different crystalline dimensionalities may possibly also transfer to the glassy state. All told, as the organic moieties in this CP system form anion pairs, their balance and ionicity, together with the strength of the coordination bonds with the metal node, appear to be crucial, not just in influencing structural dimensionality, but also in stabilizing the liquid and the GFA of the glass. The melting points of HOIPs, like ŒCH3 NH3 ŒPbI3 reported by Mitzi et al. and illustrated in Fig. 21.4, occur around 520 K, dangerously close to organic decomposition [21.29] (Sect. 21.2.1). To avoid this, melt processing methods operating close to room temperature are currently being pursued [21.30–34], with a view to the spin coating polycrystalline films, for example, of .RNH3 /2 MAn1 Pbn I3nC1 , with its promising stability, photo-voltaic and light-emitting efficiency. Both melting and melt processing routes, but especially the latter, could lead to the formation of MQGs, but rapid quenching techniques would need to be employed to avoid recrystallization, considering the likely poor GFA of perovskites. At the same time, high-pressure amorphization is also being explored in efforts to enhance electronic and photo response, not least through recrystallization [21.31–34]. We will describe this later (Sect. 21.3.1).
Finally, while melt-quenched glasses in general can exhibit considerable porosity, typically around 18% by volume in bulk silica [21.47, 48], porosity can be as low as 5% in melt-quenched MOF glasses, as reported by Thornton et al. [21.46]. By contrast, in crystalline zeolites and ZIFs, pore volumes expressed as SAV amount to 30% in ZIF-4 rise to 50% in ZIF-8 [21.4] with BET values of 1200 and 300 m2 g1 . Moreover, where pores in crystalline zeolitic structures are interconnected, rendering much of the internal volume accessible (e. g., atoms occupy only 26% of the avaiable space in ZIF-4). In hybrid glasses voids in the 3-D structure are virtually isolated, inhibiting the flow of all but the smallest gas molecules. Porosity in liquid MOFs, however, was recently studied by Coudert and colleagues using first principles MD. A substantial internal volume has been predicted, with accessibility reaching 95% for a low-density liquid derived from ZIF-4 [21.51]. Quantifying simulated porosity by volume, though, will be strongly influenced by the density employed if calculations are performed at NVT. This situation contrasts with XRD and neutron S.Q/ and PDFs as MOF glass is heated, for example, which are only modestly affected by density [21.51], as atomic structure is dominated by SRO of metal-linker polyhedra (Fig. 21.6). In a fascinating synthesis reported by Yaghi and Angell, using the solution chemistry methods developed for crystalline MOFs [21.4], porous hybrid glasses with comparable and accessible internal volume have been developed [21.3]. This approach involves mixing the metal node component with the organic linker in
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a solvent moderator, which is then gradually evaporated off as the components connect into a network, and the liquid transforms into a glass. The titanium-oxide clusters and the biphenol linkers (BPA—BiPhenol A) used are illustrated in Fig. 21.9. The progressive removal of the solvent—in this case m-cresol—increases the viscosity of the mixture exponentially following the Adam–Gibbs relation [21.63], together with the associ-
ated reduction in Sconfig [21.3]. This is akin to reducing the temperature of a glass-forming melt from Tm to Tg . Furthermore, the Tg for the porous glass falls with decreasing solvent content and the endothermic step Cp gradually disappears. This is reminiscent of the perfect glass phase associated with the collapse of ZIFs and zeolites [21.1, 14–19]. Porous hybrid glasses are clear and red in transmission (Fig. 21.5b).
21.2 Phenomenology of Amorphization and Melting Where many hybrid glasses can be formed by conventional quenching from the melt, this can often be complex, involving collapse, amorphization, and recrystallization before fusion of the final crystalline phase. Accordingly, hybrid glasses obtained from MOFs can be formed in several ways: customary melting and quenching from Tm or by amorphization at much lower temperatures, either thermally close to the glass transition Tg (Sect. 21.2.2) [21.1, 39] or pressure induced at room temperature (Sect. 21.3.1) [21.79, 80]. For meltquenched hybrid glasses obtained from coordination polymers, fusion does not appear to be anticipated by thermal amorphization (Sect. 21.2.2) [21.22], although pressure-induced amorphization has been demonstrated and is reversible (Sect. 21.3.1, Pressure Amorphization of CPs) [21.81]. To date, fabricating glasses from molten hybrid perovskites has not been reported, pressure-induced amorphization has, but like coordination polymers, this process is reversible (Sect. 21.3.1, Pressure Amorphization of HOIPs) [21.31]. For both groups of organic–inorganic materials, melting and recrystallization influence transport and electronic properties of recrystallized material (Sect. 21.2.3). For MOFs, CPs, and HOIPs amorphization can also be achieved mechanochemically by milling techniques (Sect. 21.3.2) [21.23, 82–84]. One of the main aims of this review of hybrid glasses, then, is to consider all of these varied routes to the amorphous state across the main groups of crystalline organic–inorganic materials and to look at underlying structure, thermodynamic properties, vibrational states, mechanical stability, as well as GFA. Overall, melting per se remains one of the principal phase transitions without a theoretical foundation to date. In the face of this, the recourse has been to fall back on the Lindemann criterion, which compares the amplitude of thermal motion to interatomic separation [21.85–89]. In the present context, this has been used to identify the onset of fusion in MOFs by Coudert, as well as in CP systems by Kitagawa [21.22, 51, 90]. More generally, though, current thinking on melt-
ing relates the crystal–liquid transition to incipient rare events culminating in the occurrence of instantaneous structures at Tm [21.91]. As such, the role of collective long wavelength THz vibrations, with time periods on the scale of the occurrence of rare events, appears an important consideration in cooperatively triggering the melting event [21.92–95] (Sect. 21.2.2). Prior to conventional melting, the phenomenology of framework collapse below Tm is common to both framework MOFs and to inorganic zeolites (Sect. 21.2.4) and derives from the instability of their nanoporous crystalline precursors [21.1, 2, 14–19, 78] (Sect. 21.2.5). Accommodating this structural instability has been crucial in the extensive industrial application of zeolites over many years [21.11, 13] and will be equally important in the roll out of MOFs in due course [21.9, 10]. While this review is focused on hybrid glasses and amorphous hybrids derived from crystalline organic–inorganic materials, the stability of inorganic zeolites and the associated feldspar glasses of shared compositions [21.15, 16, 78] is, therefore, very relevant, as zeolitic frameworks—hybrid or inorganic– undergoing thermobaric stress respond very similarly from a phenomenological standpoint (Sect. 21.2.3). This common behavior of the collapse of nanoporous frameworks will be discussed later in the context of decelerated melting [21.14] (Sect. 21.3.3). Like glass formation at the glass transition, amorphization is a kinetic process that depends on the rate of heating and/or the application of pressure [21.1, 15, 16, 35]. The relaxation time is directly related to the viscosity through the Maxwell equation D G1 , where G1 is the adiabatic shear modulus, usually that of the supercooled liquid [21.35]. For the familiar case of the glass transition, the fragility m can be determined from the rate dependence of fictive temperature using the endothermic step measured in differential scanning calorimetry (DSC) as a metric. This can also be applied to the signature for amorphization in DSC scans, where the fragility is found to be much smaller than for conventional glass formers [21.1, 35]. During amor-
Hybrid Glasses
The initial discovery made in Aalborg was the precursor for the work on MOF glasses that followed [21.1, 2, 49, 51] and which will now be described.
21.2.2 Melting Hybrid Crystals and Collective Vibrations
21.2.1 Discovery of Hybrid Glasses As often happens in the development of new materials, MOF glasses were discovered serendipitously while exploring something else—in this case, the crystallization of fluoro-phosphate glasses using DSC up to 1000 K. Samples were kept under an argon atmosphere, before quenching to room temperature. Yuanzheng Yue, in his laboratory in Aalborg, then dropped a pellet of ZIF-4 .Zn.C3H3 N2 /2 / into the sample crucible and, under the same conditions, obtained the first pellet of a MOF glass (Fig. 21.10). Admittedly, this was foaming and black, because the decomposition temperature had been exceeded, and the glass was discoloured with carbon. Later, by heating to below this temperature, a transparent glass was produced, which was visually similar in appearance to ZIF-4 and ZIF-zni crystals (Fig. 21.5a). a)Cp -J±.±
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The collapse of ZIF-4, followed by crystallization of the stable ZIF-zni and eventual melting at 863 K are detailed in the first DSC upscan in Fig. 21.10. The decomposition temperature TD is identified by the sharp drop in weight in the thermal gravitational analysis (TGA) scan, which occurs close to 900 K. Also included in Fig. 21.10 are DSC and TGA plots for the methylammonium HOIP system .C4 H9 NH3 /2 MI4 , where Tm and TD can be clearly seen and which converge as the metal increases in weight from Ge to Pb [21.29]. The melting temperatures for these dense HOIPs are about half those for less dense MOFs like ZIF-4. For the 2-D CP Cd.H2 PO4 /2 (1,2,4-triazole)2 , whose structure is shown in Fig. 21.3, melting occurs around 470 K [21.22] and also coincides with decomposition (Fig. 21.10c). Quenching from below TD [21.2,
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phization there is also a strong kinetic signature coming from in situ small angle x-ray scattering (SAXS) experiments. Kinetic aspects associated with the formation of amorphous hybrid materials will, therefore, also be considered (Sect. 21.2.6).
21.2 Phenomenology of Amorphization and Melting
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Fig. 21.10 (a) Original DSC and TGA plots on heating ZIF-4, showing solvent release, ZIF-4 collapse, crystallization of ZIFzni, melting, and decomposition with the release of gas. (b) Starting crystalline powder pellet, quenched foaming glass alongside a Danish 5 krone coin (after [21.1]). (c) TGA following decomposition of 2-D CP Cd.H2 PO4 /2 (1,2,4-triazole)2 for increasing amorphization using ball milling. (d) Corresponding DSC scans with arrows marking the rise in Tg and subsequent peak re-
crystallization. Ball-milling (0 min (black), 40 min (brown), 240 min (light blue), 500 min (blue)). Reprinted with permission from [21.23]. (e) DTA and TGA showing Tm and decomposition for the HOIPs .C4 H9 NH3 /2 MI4 , where M D Ge (top), Sn (middle), and Pb (bottom). Reprinted with permission from [21.29]. Copyright 1996 American Chemical Society
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49] or using amorphization [21.23] ensures the production of clear glasses (Fig. 21.5). In all the cases illustrated in Fig. 21.10, the successful melting of hybrid crystals rests in finely balancing the stability of coordination bonds emanating from the metal nodes (Fig. 21.2–21.4), with the stability of the bridging linkers [21.22, 28–30, 51]. As the temperature rises, a measure of the stability of coordination bonds can intuitively be taken from the variance in metal-linker thermal vibrations hui compared to the inter-atomic distance r; hui is the square root of the Debye–Waller factor and can be obtained directly from single crystal XRD [21.22] or simulated using MD methods [21.51]. Generally referred to as the Lindemann ratio, hui=r often reaches a critical value of around 0:1 on melting for elemental systems and also in Leonard–Jones calculations [21.85, 86]. Originally formulated from Lindemann’s concept of molecular vibrations [21.87], included in the Debye model by Gilvarry [21.88] and applied to the melting of metals, it was later extended to alkali halides and perovskites by Poirier, where hui=r increases from 0:08 to 0:13 [21.89]. More broadly, hui=r can take values between 0:05 and 0:20, dependent on structure and bonding, as Chakravarty and Debenedetti discussed [21.85]. Classically for all but the simplest close-packed materials, and this is particularly true for low-density networks like zeolites and ZIFs, the simple Lindemann– Gilvarry model seriously underestimates the vibrational dynamics, and hui=r values at Tm are highly site and material dependent. Notwithstanding, in the absence of anything better, melting in hybrid materials has often been assessed using the Lindemann hui=r ratio. Without a precise numerical value, however, the comparative magnitudes of different coordinative bonds or deviation from the classical linear temperature dependence have been used to estimate or at least corroborate the measured Tm . For example, in a computer simulation of the melting of a MOF framework starting from the ZIF-4 structure [21.51], hui=r values for Zn-N interactions were found to increase linearly with temperature, as would be expected from the retention of SRO (Fig. 21.11). For Zn-Zn interactions, however, which determine the rigidity of the zeolitic framework, hui=r departed from linearity at a point where the heat capacity also rose abruptly. As these were constant volume NVT calculations, however, neither amorphization nor ZIF-zni crystallization event transitions observed when ZIF-4 is heated (Fig. 21.11 and 21.12) were simulated. Instead, the Lindemann hui=r Zn-N and Zn-Zn ratios describe the apparent direct melting of ZIF-4, albeit on computer timescales where the temperature is more than 50% higher than what is actually measured [21.51].
By contrast, for the glassy 1-D CP proton conductor ŒZn.HPO4 /.H2 PO4/2 2H2 Im, the hui=r temperature dependencies of the nearest neighbor tetrahedral ZnO interactions have been directly measured from the XRD Debye–Waller factors. Notably, hui=r for the coordination of Zn to the acid imidazolate H2 Im substantially exceeds the remaining three that coordinate Zn with orthophosphates to create the polymer chains (Fig. 21.11); hui=r for the Zn-H2 Im interactions reaches 0:12 by 413 K where melting occurs [21.22]. It is the H2 Im linkage that binds the 1-D polyphosphate chains together in the solid state. Melting itself is understood to be initiated by rare events [21.91], like the momentary change in coordination of a Zn node in a crystalline zeolitic network [21.51] or the rotation of an imidazolate moiety within the interchain space of a coordination polymer [21.22]. Such transitory local defects and distortions will occasionally compound into multiple competing pathways within the potential energy landscape (Sect. 21.3.4). Collectively they will be driven by vibrational instability to create the delocalized phenomenon of melting. The notion of low-frequency (long wavelength) vibrations destabilizing crystal structures to transform into glass we first proposed could explain the dramatic changes observed in inelastic neutron scattering (INS) THz spectra of zeolite Y (faujasite) during nanoporous amorphization [21.92] (Sect. 21.3.2). In a recent novel study by Tan, Ryder, and co-workers in situ synchrotron radiation infrared spectroscopy was used to follow the equivalent low-temperature melting process of ZIF4 [21.93]. Changes in the frequencies of salient vibrations were reported. Figure 21.11 shows how the imidazolte ring deformation modes and the Zn–N stretching motions both red shift with rising temperature, pointing to anharmonicity in the quasi-delocalized oscillator potential—higher vibrational levels being stacked closer together than those near the ground state. Similar behavior is exhibited by Zn–N vibrations in ultrastable ZIF-8 [21.6, 9] (Fig. 21.2), but the frequency– temperature gradient is lower (Fig. 21.11d). For both MOFs, the temperature dependence of metal node modes follow the Bose–Einstein distribution, as do the low-frequency modes of other organic solids [21.94]. Since the red shift gradient in Zn–N oscillations is a measure of anharmonicity in the metal node environment, which leads to instability, changes through the low-temperature melting of ZIF-4 are to be expected. Indeed, this is what occurs—the amorphized ZIF phase exhibiting less stability compared to either ZIF-4 or ZIF-zni [21.93]. Over the larger territory of the MOF dynamics of ZIF-4 we can expect node stretching at 300 cm1
Hybrid Glasses
21.2 Phenomenology of Amorphization and Melting
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Fig. 21.11 (a) Lindemann ratios hui=r for Zn-N and Zn-Zn correlations shown rising with temperature. Taken from NVT first principles MD calculations starting with the structure of ZIF-4 whose (room temperature (RT) density is 1:625 g cm3 but employing a much lower and constant density of 1:25 g cm3 . After [21.51]. (b) Experimentally determined Zn-O hui=r values determined from the temperature-dependent Debye–Waller for the CP 1-D proton conductor ŒZn.HPO4 /.H2 PO4 /2 2H2 Im. Correlations: Zn-H2 Im (red), Zn-HPO4 (green and purple) and Zn-H2 PO4 (blue). Reprinted with permission from [21.22]. Copyright 2015, American Chemical Society. (c) In situ infrared (IR) spectra with heating of ZIF-4 from RT, through amorphization at TA and crystallization to ZIF-zni at TXX , highlighting red shifts in Zn–N and imidazolate vibrations. (d) Temperature dependence of Zn–N frequencies for ZIF-4 and ZIF-8 fit to the Bose–Einstein relation, including ZIF-4 to TA , amorphized ZIF-4 to ZIF-zni. Reproduced from [21.91] with permission of The Royal Society of Chemistry. (e) Visualization sequence of Zn coordinated to Im groups switching a ligand over a 400 fs period from ab initio MD. (a) and (e) reproduced with permission from [21.51]
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Fig. 21.12a–g Collapse, melting and glass transition of zeolitic frameworks using DSC: ZIF-4 (Zn.C3 H3 N2 /2 ). (a) Upscan 1 showing amorphization at TA with formation of LDA phase, crystallization at TXX to ZIF-zni, and melting at Tm . Initial exotherm in Upscan 2 showing glass transition of MQG at Tg . (b) Similarity of Tg for amorphized ZIF-4 HDA phase and the MQG following melting, suggesting that they both occupy similar minima in the potential energy landscape (PEL). (c) Amorphization at increasing heating rates, showing upward shift in the onset of solvent release and of collapse TA and formation of LDA phase compared to the first upscan. (d) Orthorhombic Pbca structure of ZIF-4 incorporating 2:1 Å diameter nanopores with an overall SAV of 34%. After [21.1, 2]. Collapse, melting and glass transition of zeolitic frameworks using DSC: Zeolite LSX (Na3 KAl4 Si4 O16 ). (e) Similarity of Tg for amorphized zeolite LSX HDA phase and the MQG. Subsequent exotherms TXX1 and TXX2 relate to crystallization Txx1 (carnegieite) and TXX2 (nepheline), respectively. (f) First upscans revealing increase in onset of collapse at TA and the formation of the LDA phase with rising heating rates, followed by crystallization exotherms. (g) Cubic Fd3m structure of zeolite LSX (faujasite) showing 12 Å supercage (’-cage) surrounded by 6 Å sodalite cages (“-cages) with void volume of 48%. Reprinted from [21.19] with permission of AIP Publishing
Hybrid Glasses
21.2.3 Influence of Melting on the Properties of Hybrid Glasses The possibility that liquid MOFs might retain much of the porosity and void connectivity of the crystalline state has already been referred to (Sect. 21.1.3) [21.51]. Based on constant volume simulations the density should physically decrease with temperature, starting with the RT density of ZIF-zni. If calculations of appropriate higher densities, however, confirm liquid porosity, then it raises the possibility of gas capture and/or separation in a liquid medium as opposed to crystalline powders, which has been such an important application in the development of crystalline MOFs to date [21.9–13]. Moreover, as hybrid MOF glasses are known to exhibit limited porosity, with little connectivity in the pore structure [21.46], the prospect of sealing adsorbents introduced above Tm and trapping them in the glassy state would offer an important new and exciting possibility for CO2 capture or drug delivery, for example. Proton conducting CPs, like the orthophosphate triazoles illustrated in Fig. 21.3 [21.21], have molten transitions where the coordinative Zn–O bonds appear to cleave (Fig. 21.11b), reconnecting on glass formation [21.22, 23]. This reversibility via the liquid state has implications for the crystallization of orientated thin films [21.22], and also photo-induced proton conductivity [21.23, 90], which could prove important in future device fabrication. The intrinsic proton conductivity of the 1-D CP, ŒZn.HPO4 /.H2 PO4 /2 .ImH2 /2 , at the glass
transition ( 300 K) exceeds 109 1 cm1 [21.90] and is similar, for instance, to the RT ionic conductivity of traditional alkali silicate glasses [21.41], but reaches 105 1 cm1 by 380 K. The Kyoto CP group have demonstrated how proton conductivity can be enhanced a further decade by doping in the molten state by incorporating triflic acid [21.96], making such CPs attractive as potential protonic devices, mimicking electronic equivalents for rectification, amplification, and photovoltaic power generation [21.90, 97]. Melting around 430 K, the Kyoto group found that the CP orthophosphate triazole liquid is stable up to 470 K, similar to the liquid range of equivalent 2-D CPs (Fig. 21.10c). Furthermore, utilizing their melt-processing approach to introduce the photoacid pyramine [21.96], allowed the pH of the doped molten CP to be radically reduced on UV irradiation and the proton conductivity increased further, decreasing when illumination was removed—reversibility being established over multiple cycles [21.90]. Despite the substantial molecular acid and photoacid doping, the Zn–O SRO in the quenched glass coupled with the integrity of the organic ligands is retained [21.90], leading to the possibility of fabricating of a fascinating prototype proton photovoltaic. Overall, the proton conductivity and efficient reversibility of these orthophosphate azole glasses is attributed to their homogeneous nanostructure, in contrast to their polycrystalline counterparts, where grain boundaries can impede proton transport. Where molten HOIPs are concerned, the current agenda is geared towards creating a stable liquid suitable for spray coating to fabricate efficient solar cell devices [21.29, 30]. As with CPs, crystalline low dimensionality is advantageous to achieve high-quality oriented thin films. There are, however, implications for hybrid glasses if HOIP liquids could be rapidly quenched. Considering that it is likely that HOIPS are poor glass formers, this would preclude conventional cooling rates of 10 s K min1 . The conventional approach to melting HOIPs is to avoid decomposition of the organic components (Fig. 21.10). Two approaches have emerged to realize this. In the first [21.30], judicious choice of metal and organic components enables Tm < TD . Specifically, the phenethylammonium lead iodide .PEA2 PbI4 / system has been developed and, as these are Ruddlesden–Popper phases, 2-D layered structures can be crystallized. Moreover, by choosing Pb rather than Sn [21.29], Tm can be raised by up to 45 to 250 K without incurring decomposition (Fig. 21.10d), while at the same time usefully reducing the viscosity. By increasing Tg to around RT would also assist in accelerating rapid quenching to liquid N2 temperatures, bearing in mind that cooling rates of 104 K min1 would be available. In
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Part B | 21.2
(100 THz) and linker deformation at 660 cm1 (220 THz) in separate minima to be occasionally coupled through long wavelength intermolecular THz vibrations. Evidence for this can be found in the fascinating atomistic simulations of the molten MOF derived from ZIF-4 mentioned earlier [21.51]. Figure 21.11e illustrates a sequence in the local dynamics of vibrational fluctuations in the tetrahedral Zn environment, showing the loss of an imidazolate moiety leading to the momentary under coordination of Zn and, within 0:4 ns, the arrival of another imidazolate group attaching to the Zn node and restoring its tetrahedral environment. On this timescale, such an event could be correlated with a collective frequency of a few THz, exemplifying the rare cooperative dynamics expected on melting [21.91]. This frequency is of the same magnitude as the gateopening mode at 1 THz (33:4 cm1 ) identified in ZIF-4 from earlier INS measurements and DFT calculations by Tan’s group [21.95]. Figure 21.11 demonstrates the attractiveness of bringing MD trajectories and dynamics together with far IR spectroscopy to probe the complex process of melting hybrid materials.
21.2 Phenomenology of Amorphization and Melting
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the second approach [21.98], HOIP liquids have been formed at RT using highly reactive polyiodide melts, which, when placed in contact with metallic Pb, rapidly generate high-quality perovskite films comprising micron-sized crystals. Promoted as a one-step solvent-free process for fabricating opto-electronic devices [21.98], this might also offer routes to thin film HOIP glasses. In this case, the small amount of material could enable sufficiently high cooling rates to be realized. We now turn to the thermodynamics of the low-temperature melting of framework MOFs, comparing this to the equivalent process in zeolites, about which more is known.
21.2.4 Thermodynamic Aspects of Zeolitic Framework Collapse and Glass Formation Before zeolitic framework materials—MOFs or zeolites—melt and form denser liquids, they necessarily first collapse (Fig. 21.10). This usually occurs in the vicinity of the glass transition Tg of the glass that is subsequently formed by melt quenching from Tm . Collapse itself, however, involves amorphization and the creation of an HDA phase Tg that is thermodynamically and, also, structurally very similar to the melt-quenched glass (MQG) [21.1, 2, 14–16, 18, 19, 35]. We illustrate this in Fig. 21.12 for the MOF ZIF-4, setting amorphization properties side by side with the faujasite zeolite low silica X zeolite (LSX—part of the faujasite family). Both of these zeolitic framework materials have very different structures. ZIF-4 is orthorhombic with the Pbca space group and incorporates nanopores (Fig. 21.12d). The space group of the cubic zeolite LSX (faujasite) is Fd3m and, compared to ZIF-4, it has lower atomic density with substantial supercages surrounded by sodalite cages (Fig. 21.12g). Furthermore, ZIF-4, in common with other ZIFs, is mechanically soft and flexible in comparison with the harder more rigid zeolites (Sect. 21.1.2). Despite these huge differences in structure and mechanical properties, ZIFs and zeolites share the same phenomenology of collapse, as judged thermodynamically. For both zeolitic frameworks there are two signatures in the temperature dependence of the specific heat at constant pressure Cp , measured with DSC, that define zeolitic amorphization, the amorphous HDA phase and the MQG: 1. The collapse of the crystalline framework, comprising an exothermic minimum followed by an endothermic maximum encountered on the first DSC upscan at TA (Fig. 21.12a,c,f).
2. The glass transition following melt quenching, identified by the familiar endothermic step that defines Tg for MQGs and appears in the DSC for the second upscan and subsequent upscans (Figs. 21.12b,e). If the upper temperature of the first upscan only extends to just over TA (Fig. 21.12c), therefore avoiding melting or any intermediate crystallization, the HDA phase is captured. When this is reheated, it also exhibits a glass transition Tg at virtually the same temperature as the MQG (Figs. 21.12b,e). Another important observation associated with the thermodynamics of framework collapse concerns the temperatures of amorphization TA and of the glass transition Tg where, if the same conditions (e. g., heating rate) are employed, the former always exceeds the latter, viz. TA > Tg : Fig. 21.12b with Fig. 21.12c for ZIF-4 or Fig. 21.12e,f for zeolite LSX. Notably, the temperature of framework collapse falls approximately in the dynamic cross-over region (1:11:3 Tg ), described earlier (Sect. 21.1.3) [21.63–71], the temperature regime where polyamorphism [21.36] is usually detected. From previous studies of amorphization of nanoporous framework ZIFs and zeolites [21.1, 2, 15, 16] the double upscan feature at TA (1) illustrated in Fig. 21.12c for ZIF-4 or in Fig. 21.12f for zeolite LSX, has been interpreted as the sequential formation of an intermediate low-density polymorph LDA from the low-density crystal, followed by transformation to a high-density liquid polymorph HDL. In the first of these, the exothermic minima, which can be clearly identified for ZIF collapse in Fig. 21.12c and for zeolite collapse in Fig. 21.12f, are associated with the glass transition temperatures of the LDA phases [21.1]. Two phase transitions are, therefore, envisaged in framework collapse at TA . For ZIF-4 these are ZIF–LDA followed by an LDA–HDL transition and for zeolite LSX zeolite–LDA leading to an LDA–HDL transition [21.16]. Furthermore, they are distinguished from one another as being order–order and order–disorder transitions, respectively [21.35]. For each zeolitic framework structure the rate of collapse from Fig. 21.12c,f lead to fragility values of around 12, which is significantly lower than that of silica for which m D 19, classifying the initial polymorph following collapse as super strong in character (Sect. 21.1.3 [21.35, 73]). The second and single feature signature in DSC scans appears in upscan 2, and in further upscans, and identifies Tg , either for the HDA phase, if the temperature has not reached crystallization at Txx or for melting at Tm , of the MQG if Tm has been exceeded. The similarity of Tg for both HDA and MQG
Hybrid Glasses
tributed to the formation of a second amorphous phase, which would be analogous to HDL illustrated for zeolitic collapse in Fig. 21.12, the CP polyamorphic transition not being dissimilar to the order–disorder LDA–HDL transitions in ZIFs and zeolites. The two CP polyamorphs differ in structure, as is envisaged for LDA and HDA phases in zeolitic amorphization. In contrast to thermally-induced amorphization of ZIF-4 and LSX, the first crystal–amorphous transition for .ZnI2 /3 .TPT/2 is reversible on the laboratory timescales, which may reflect the slackening of coordinative bonds on melting observed in other CPs [21.22, 23].
21.2.5 Stability of Porous Crystals in Relation to Topology and Density While the thermodynamics of framework amorphization at TA , melting at Tm , and glass formation at Tg for ZIFs, zeolites, and CPs follow the same pattern with Tg < TA < Tm , the characteristic temperatures that define the DSC signatures are quite different, with those for ZIF-4 (660 K) being approximately half those for zeolite LSX (1200 K), and those for .ZnI2 /3 .TPT/2 [21.24] being lower still around 550 K. Differences in collapse temperatures may be attributed to the often very different coordinative bonding. Tan and Bennett considered that the stability of ZIF networks like ZIF-8 is related to the extra rigidity that might be afforded to ZIF networks by substituted imidazolate linkers such as C4 H5 N 2 [21.51, 58, 93, 95], but topology and density also appear to be relevant. For example, ZIF-8 adopts the sodalite structure (Fig. 21.2) and is closer in atomic density to the faujasite structure of zeolite LSX, which, as we have seen, amorphizes around 1200 K (Fig. 21.12f). In particular, ZIF-8 does not collapse but decomposes first around 910 K [21.1], close to the decomposition temperature of ZIF-4 (Fig. 21.10a) and reflecting the similar chemical resilience of the respective 2-methylimidazolate .C4 H5 N 2 / and imidazolate .C3 H3 N2 / linkers. The exceptional stability of ZIF-8 [21.9, 13] may then reside in its topology and density, rather than in the strength of the bonding between the inorganic metal node and the organic linker. For example, the internal volume of ZIF8 (SAV 50:4%) is very much higher than that of ZIF-4 (SAV 34%) [21.93], and this is reflected in their respective densities of 0:95 and 1:5 g cm3 . Furthermore, their compressibilities ˇ0 are also hugely different: 154 TPa1 for ZIF-8 [21.79] compared to 504 TPa1 for ZIF-4 [21.57]. Isomorphs of ZIF-4 like ZIF-62 and TIF-4 [21.2], which collapse at comparable temperatures, also exhibit significantly higher values of ˇ0 than ZIF-8 [21.57]. The difference in compressibilities is di-
737
Part B | 21.2
phases is clear for ZIF-4 in Fig. 21.12b and for zeolite LSX in Fig. 21.12e, suggesting that these may be equivalent glassy states in each case. This observation, however, is non-intuitive, as the HDA state is reached through amorphization by heating from the nanoporous crystal, while the MQG is formed by cooling from the molten state [21.35]. We will return to how this might be reconciled thermodynamically later [21.1, 19] (Sect. 21.3.3). Incidentally, the differences between the two upscans suggests that the LDA–HDA polyamorphic transition may not be reversible, certainly on the laboratory timescales used. Reversibility for faujasite amorphization has been established, however, but only over extended periods [21.14]. In addition to the amorphization and glass transition signatures in DSC experiments, crystallization exotherms are marked TXX in Figs. 21.12a,f. For the majority of glass-forming systems there is always competition at supercooled temperatures between crystallization and vitrification, depending on the rate of heating or cooling—high rates favoring glass formation and slow rates crystallization. When HDA or MQG phases are heated above Tg at typical DSC heating rates of several K min1 , crystallization is often encountered; Fig. 21.12 provides examples. Once ZIF-4 is amorphized or melt quenched, it crystallizes on heating above the glass transition Tg to the denser MOF ZIF-zni [21.1], as Bennett and Cheetham first reported [21.39], and it is this tetragonal I41 cd crystalline phase that eventually melts at 863 K (Fig. 21.12a). For zeolite LSX, when this is heated above Tg Wondraczek’s Jena group observed that carnegieite is first precipitated and then converts, through a crystalline phase transition, to nepheline [21.14, 19] (Fig. 21.12f) before finally melting at 1600 K. In general, therefore, the HDA phase should be considered in relation to the respective crystalline zeolitic framework—ZIF-4 or zeolite LSX—while the MQG should be associated with the highest temperature devitrified phase—ZIF-zni or nepheline. Lineaments of the ZIF/Zeolite–LDA–HDA–ZIFzni/carnegieite sequence depicted in Fig. 21.12 resemble the thermally-induced polyamorphic crystal– amorphous–amorphous–crystal transition recently reported by Ohtsu and Kawano for a porous CP .ZnI2 /3 .TPT/2 [21.24]. Starting as a low-density zinc iodide triazine, this structure amorphizes endothermally as the pore-containing nitrobenzene is displaced, in a similar way to the desolvation of ZIF-4 (Figs. 21.10a and 21.12c), which is also coupled with the formation of an amorphous (LDA) phase. With further heating of the CP with its 3-D inter-penetrating structure, recrystallization to a 1-D phase takes place. The associated exotherm, however, is structured, with a pre-feature at-
21.2 Phenomenology of Amorphization and Melting
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Part B | 21.2
rectly reflected in the different amorphization pressures PA —1:2 GPa for ZIF-8 [21.79] compared to 0:6 GPa for ZIF-4 [21.80] to be discussed below (Sect. 21.3.4). We have shown for zeolite collapse that the temperature TA and pressure PA of amorphization are linked viz. PA VA Š RTA , where VA is the volume change on collapse [21.15, 16]. This will be discussed later (Sect. 21.3.3), but the relationship projects a doubling of TA [21.1] for ZIF-8, i. e., well above TD , and explains why ZIF-8 is not observed to amorphize thermally. In particular, there appears to be a significant correlation for porous zeolitic frameworks between large internal pore volume, low density and mechanical stability, and thermal stability. We will return to this link between structure and mechanical stability in discussing pressure-induced amorphization of zeolitic frameworks, which can be permanently densified on laboratory timescales, and CPs and HOIPs, which cannot be amorphized thermally, and for which pressure-induced amorphization is reversible (Fig. 21.15; Sect. 21.3.1, Compressibility and Mechanical Stability).
tle consideration was given to the sizable kinetic effects evident in Fig. 21.12. Indeed, the kinetic effects due to different heating rates were seldom explored [21.17, 39], despite substantial effects being reported over a decade earlier [21.15, 16, 35]. Nevertheless, from the most recent studies [21.1, 19], the dynamics of amorphization for both hybrid and inorganic frameworks can now be considered, enabling the thermodynamics and kinetics to be analyzed and quantified (Sect. 21.3.2). Both of the DSC Cp signatures identified in Fig. 21.12—(1) at TA and (2) at Tg —increase in temperature with increasing heating rates, whether for ZIF-4 or for zeolite LSX [21.1, 19]. Crystallization exotherms at TXX behave similarly, predicated on values [21.1, 14, 49]. The dynamics of TXX , together with those of TA and Tg , underscore the kinetic nature of framework collapse, glass formation, and crystallization. By contrast, melting is a thermodynamic first-order phase transition, Tm being fixed for a particular pressure, with the Clapeyron melting curve dT=dP being negative for many materials—not least ZIFs and zeolites [21.1, 16]. The dynamics of the fictive temperature yields the fragility m (Sect. 21.1.1) of the supercooled HDL phase. This is illustrated for ZIF-4 in Fig. 21.13a and yields a value of fragility m of 41 [21.1]. The fragility for the molten equivalent MQG is 39 [21.2] (Sect. 21.1.3), which like the Tg value, is the same within experimental
21.2.6 Kinetics of Framework Collapse and Glass Formation In many earlier studies of zeolitic framework collapse of hybrid, and also of inorganic crystalline systems, lita) Cp -J±.± .PLQ±
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Hybrid Glasses
those of the HDL glass transition Tg (Fig. 21.13a). This results in a far lower fragility value m of 12 (Fig. 21.13c) [21.1]. Fragilities significantly below that of silica (m D 19) are classified as super strong liquids [21.35, 73] (Sect. 21.1.3), which is the case for the LDL phases collapsing from ZIFs [21.1] and also for those collapsing from zeolites [21.14, 15, 35]. On quenching, LDL phases solidify as perfect glasses (Sect. 21.1.3), characterized by extremely low configurational entropy Sconfig [21.1, 15, 19, 35]. The combination of lower m and higher Tg for the LDL phase, compared to polyamorphic HDL phase, accords with its higher viscosity and points to a liquid– liquid LDL–HDL transition at intermediate temperatures taking place during the collapsing process and at temperatures well below the melting temperature Tm for the corresponding hybrid liquid [21.1, 2, 49]. The background to this liquid–liquid transition is the two-state model for polyamorphism [21.36] illustrated for the collapse of zeolitic frameworks in Fig. 21.17c,d for hybrid and inorganic frameworks, respectively (Sect. 21.3.2). Before discussing this, we will review the phenomenology of amorphization induced by pressure, which enables the T–P phase space and the various phases in zeolitic framework collapse to be defined [21.1, 15, 16].
21.3 Pressure-Induced Amorphization and Mechanical Stability With a view to understanding the underlying phase transitions involved in the collapse of porous structures— hybrid or inorganic—the complementary amorphization process induced by pressure, usually at temperatures well below Tg , will now be reviewed [21.31– 34, 79, 80, 99–105]. This has been important in understanding the decelerated melting of inorganic zeolites [21.14–16] and similar processes observed in the amorphization of ZIFs [21.79, 80, 99–105], CPs [21.81, 106], and HOIPS [21.31–34]. In particular, we find that compressibility values of crystalline hybrids [21.29, 30, 32, 57, 79–81, 106] relate to the ease of amorphization (Fig. 21.15; Sect. 21.3.1). Allied to the pressureinduced process of amorphization is the associated process of ball-milling, which has been applied to all categories of hybrid materials [21.23, 82–84, 104, 107, 108] (Sect. 21.3.2). Both temperature and pressure-induced amorphization of zeolitic frameworks substantiates the two-state model [21.109–114] that has become of fundamental importance in describing polyamporphic transitions in general [21.35, 36], as well as the nature of the melting curve dT=dP in T–P phase space, which is often negative [21.36, 109–114]. In the present con-
text, this has been explored by defining the thermodynamic boundaries for a fixed rate of collapse between the starting porous crystal and two coexistent polymorphs LDL and HDL [21.1, 15, 16, 35]. At the lower temperatures, where pressure amorphization is usually explored, these polymorphs become LDA and HDA, respectively (Sect. 21.3.3). The kinetics of zeolitic collapse do not follow the stretched exponential relaxation where a single relaxation process often describes the behavior of numerous disordered systems, for example, from metastable liquids to ionic conduction in melts and glasses [21.41, 114, 115]. Instead, the progress of amorphization, judged from the decline in the area under crystalline diffraction peaks, follows a compressed exponential form. This can be modeled by convoluting two sequential reactions with very different relaxation times, starting with an order–order transition zeolite–LDA and culminating in an order–disorder transition LDA–HDL [21.14]. Taken together, these neatly describe what is effectively decelerated melting (Sect. 21.3.4). In offering an over-arching approach to amorphization, crystallization, melting, and melt quenching, the concepts of the PEL [21.35, 68, 116, 117] will be intro-
739
Part B | 21.3
error. This level of fragility is of intermediate size, similar to the fragility of organic liquids like glycerol and inorganic alumino-silicate melts like anorthite [21.35, 66]. For ZIF-4 this value of m is also very similar to that for molten alumino-silicates like nepheline from which MQGs are formed following the decelerated melting of faujasite zeolites [21.14, 16] such as LSX. Evidence for the initial LDL phases was found in the dynamics of in situ SAXS—first for inorganic zeolites [21.15, 16]—and later for framework MOFs [21.1] (Fig. 21.13). These supercooled polyamorphs can be distinguished from the HDL phases detected from DSC in Figs. 21.12a,e by their fragilities. The dynamics of the collapse (TA ) of ZIF-4 determined from SAXS experiments on ZIFs are illustrated in Fig. 21.13b,c. SAXS measures density contrast [21.35] and, for amorphizing zeolitic frameworks, this derives from the coexistence of the collapsing LDL framework and the initial crystalline zeolite phase, which is of lower density [21.1, 15]. The dramatic rise and then fall in SAXS intensity heralding the amorphization of ZIF-4 (Fig. 21.13b) is the structural equivalent of the thermodynamic DSC exotherm (Fig. 21.12c), and, like this, TA shifts to higher temperatures with increasing heating rate (Fig. 21.13c). In particular, the dynamics of collapse (Fig. 21.8c) are much slower than
21.3 Pressure-Induced Amorphization and Mechanical Stability
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Part B
Glass Families
Part B | 21.3
duced. This usefully facilitates envisaging the different liquid phases, from the classical liquid above Tm through the non-ergodic cross-over region around 1:2 Tg , to the PEL of the solid-state glasses and crystalline states (Fig. 21.19a; Sect. 21.3.5). Glass and crystalline phases generally differ in their elastic moduli, not least Poisson’s ratio [21.60]. This dimensionless elastic constant scales empirically with the mechanical performance of numerous materials beyond the harmonic limit [21.118]. Specifically, for values of around 0:3, fracture toughness changes by upwards of five decades, separating brittle from ductile materials—not least for many glass forming systems. Poisson’s ratio is also related to melt fragility m [21.60, 119, 120], which leads to a useful relationship between fracture toughness and fragility [21.60], enabling brittle and tough glasses, and hybrid glasses in particular, to be distinguished simply by comparing their respective melt fragilities (Fig. 21.19b; Sect. 21.3.6).
21.3.1 Pressure-Induced Amorphization Examples of the amorphization of crystalline materials goes back almost four decades to when Mishima reported the transformation of hexagonal ice into amorphous water at the modest pressure of 10 kbar but at a temperature of 77 K [21.121]. This demonstrated melting taking place well below the ambient pressure Tm following an extension of the negative melting slope or Clapeyron slope dT=dP. Mishima’s pioneering work not only identified an HDA phase for amorphous water, distinct from the LDA phase formed by rapidly freezing water to 77 K at ambient pressure, but also subsequently led to the discovery a reversible polyamorphic HDA– LDA transition in water between these two amorphous phases [21.122]. Shortly afterwards, but by employing the much higher pressures of 18 GPa, the mineral berlinite .AlPO4 / was discovered to form a glass at 300 K, which we would now call HDA. Moreover, the crystalline phase was recovered when the pressure was decreased below 5 GPa, demonstrating the reversibility of this order–disorder transition [21.123]. Examples of pressure-induced amorphous materials proliferated, ranging from semiconductors, such as Si, Ge, and III-Vs [21.84, 124] to minerals, including silica and anorthite [21.125]. Latterly room temperature amorphization under pressure has been extended to zeolites [21.14–16] at pressures of 3 GPa and to ZIFs at the lower pressures of 0:61:2 GPa [21.79, 80, 99– 105]. At lower pressures still, crystalline phase transitions have been reported for single crystal MOFs [21.80,
105] prior to amorphization. For example, tetragonal ZIF-zni (which crystallizes from amorphized ZIF-4 HDA [21.39] or from the MQG [21.2] (Figs. 21.10a and 21.12a), transforms from the ’ phase to a lower symmetry tetragonal “ structure from between 0:6 and 0:8 GPa [21.105]. ZIF-4 itself transforms to a less porous orthorhombic phase between 0:35 and 0:95 GPa [21.80]. As the pressure increases further at ambient temperature, MOFs amorphize. In a similar vein, initial tetragonal–orthorhombic phase transitions occur up to around 1 GPa for methylammonium metal halide HOIPs, like MAPbBr3 [21.31], MASnI3 [21.32], and MAPbI3 [21.34], related to the tilting of the perovskite metal octahedra (Fig. 21.4). These crystalline phase transitions appear to act as precursors for amorphization at higher pressures. Pressure Amorphization of MOFs We start with the example of pressure-induced amorphization of the sodalite MOF ZIF-8 reported by Chapman et al. [21.79]. Figure 21.14a includes highpressure x-ray powder diffraction (HPXRPD) patterns obtained using a DAC with a non-penetrating pressure transmitting medium (PTM). The MOF was also free from internal molecules, just as for thermallyinduced amorphization of ZIF-4 following solvent release (Fig. 21.12c). The decline in the intensity of the XRD powder pattern peaks with increasing hydrostatic pressure can be clearly seen in Fig. 21.14a. The transformation is reported to be reversible up to 0:3 GPa, but, for higher pressures, the crystalline ZIF-8 pattern is gradually replaced by diffuse scattering with progressive irreversible amorphization (Fig. 21.14a), reported to be complete by 1:2 GPa [21.79]. Of particular interest is the considerable nanoporosity that is retained, evident in the N2 uptake sorption isotherms for pelletized powder samples, compressed to the same pressures employed for in situ hydrostatic HRXRPD (Fig. 21.14b). These saturate as P=P0 approaches 1 but, importantly, the porosity of amorphized ZIF-8 remains considerable, so that by 1:2 GPa N2 uptake is reduced by not more than a half that of the staring capacity. By contrast, HDA and MQG phases in fully thermally amorphized or melted MOFs like ZIF-4 have extremely low porosity [21.46, 49, 58]. Accordingly, the considerably porous nature of ZIF-8 amorphized to 1:2 GPa suggests that this may be an LDA phase, sharing similar topology to the crystalline ZIF-8, with the pressureinduced amorphization PA 1:2 GPa. It also underlines the inherent flexibility of low density zeolitic frameworks. Parallel high-pressure measurements of ZIF-8 using Fourier transform infrared (FTIR) spectroscopy were reported by Huang and Song [21.99]. They used de-
Hybrid Glasses
21.3 Pressure-Induced Amorphization and Mechanical Stability
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Fig. 21.14 (a) Synchrotron radiation XRD patterns of ZIF-8 powder as a function of hydrostatic pressure at ambient temperature, showing replacement of ZIF-8 structure by diffuse scattering from amorphized phase above 1:2 GPa. After [21.79]. Diameters of ’-cage and “-cage indicated for 2 values of 2:85ı and 5:4ı , respectively, have been added. (b) N2 sorption isotherms for initially amorphized ZIF-8 using pelletized pre-compressed powders for different pressure treatments P=P0 , with log expansion at lowest partial pressures. (c) FTIR spectra as a function of pressure of ZIF-8 from ambient to 39 GPa, indicating substantive changes in imidazole ring vibrations: Out-of-plane puckering, in-plane bending and stretching, and C–H aliphatic and aromatic stretch. (d) FTIR spectra as a function of pressure of ZIF-8 from ambient to 1:69 GPa [21.99] over a similar pressure range as in (a). Reproduced from [21.99] with permission of The Royal Society of Chemistry. (e) X-ray diffuse scattering patterns for porous MOF glasses Ti-BPA and Ti-BPP, with diameters of equivalent pores from the principal small angle features at 4:8ı and 5:0ı , respectively. Insert shows the pattern for zeolite LDA with the ’-cage and “-cage diameters identified, respectively, with 2 values of 2:7ı and 4:6ı . (f) N2 sorption isotherms for the porous MOFs Ti-BPA and Ti BPP for different pressure treatments P=P0
Part B | 21.3
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solvated crystals and, like Chapman et al. [21.79], scrupulously avoided using penetrating PTM. The FTIR spectrum (Fig. 21.14c) at ambient pressure contains most of the stretching ( ) and bending (ı) modes of neighboring atoms and of the imidazole ring and the aliphatic substitution, the frequency attributions being in close agreement with those identified in the Raman spectrum of ZIF-8 [21.100]. This global signature of the molecular linker reflected in the vibrational density of states, is in many ways richer than the PDFs forthcoming from XRD or EXAFS (Fig. 21.6). As the pressure rises, Huang and Song record substantive FTIR changes occur in the methyl imidazolate .C4 H5 N 2 /, with the C–H.CH3 / (3135 cm1 , 1025 THz) and CDN
modes (1584 cm1 , 525 THz), and the puckering ı modes (760 cm1 , 253 THz) of the imidazole ring splitting and broadening, with the major enhancement of a ring stretching mode (1420 cm1 , 473 THz). All these changes point to the development of inter-linker interactions as the MOF structure convolutes in on itself. Notably, the effects become particularly significant above 1:2 GPa, so that, by 39 GPa, the FTIR peaks are hugely broadened and blue-shifted, indicative of a fully disordered compressed structure. Despite this, considerable reversibility was observed on decompression [21.99], the spectrum resembling the pattern at 4 GPa with all the principal ( ) and bending (ı) modes intact, confirming that the ZIF-8 linker survives amorphization, further compression, and decompression (Fig. 21.14c), just like melt quenching ZIF-4 and the coordination polymer illustrated in Fig. 21.6. In an effort to mirror the HPXRPD Argonne experiments [21.79], the western Ontario group also explored, in greater detail, the ambient to a 1:6 GPa pressure range (Fig. 21.14d), finding subtler changes in the initial stages of compression, most (although not all) of which reversed on decompression. While this was interpreted as signifying structural reversibility [21.99], it is quite clear from HRXRPD [21.79] that when ZIF-8 compresses to 1:2 GPa it remains amorphous when returned to ambient pressure (Fig. 21.14a). If this is the LDA polyamorph of ZIF-8, then, with zeolite–LDA transitions [21.1, 14, 19, 35] being topologically invariant (Sect. 21.2.4), we would not expect major changes in vibrational dynamics. The pressureinduced behavior, however, is in sharp contrast to the considerable spectral evolution that occurs by 4 GPa and above (Fig. 21.14c), which is by no means reversible [21.99]. Accordingly, we propose that the ZIF8 LDA polyamorph formed by 1:2 GPa transforms to an HDA polyamorph by 4 GPa, via an order–disorder transition that is irreversible on laboratory time frames, as we found earlier for the pressure-induced amorphization of zeolites [21.15, 16, 35].
Figure 21.14e includes XRD profiles for the porous MOF glasses introduced earlier (Sect. 21.1.3). The N2 uptake adsorption for Ti-BPP and Ti-BPA glasses are included in Fig. 21.14f, which, interestingly, exhibit comparable porosity to the amorphized ZIF-8 (Fig. 21.14f). Furthermore, despite the very different SRO, there are considerable LRO similarities between partially collapsed ZIF-8 and porous Ti-bisphenol glasses that relate to the porosity. These nanostructural features are evident in the x-ray diffuse scattering profiles reproduced in Fig. 21.14, viz. the presence of one or more peaks at low scattering angles . The locations of these features can be equated with pore diameters 1=.4 sin =/, where is the incident x-ray wavelength. For pressure amorphized ZIF-8, these peaks at well-defined 2 values indicate the retention of the ’cage (11:9 Å) and of the “-cage (6:5 Å) (Fig. 21.2a), in this partially collapsed sodalite structure (Fig. 21.14a). Turning to porous Ti-bisphenol glasses (Fig. 21.9), for comparison, pore diameters for Ti-BPA and Ti-BPP are larger than for pressure-amorphized ZIF-8—viz. 18:5 and 17:6 Å, respectively. Also included in Fig. 21.14e (inset) is the x-ray pattern for zeolite LTA [21.15], where the 2 peaks at correspond with the ’-cage (13:1 Å) in this inorganic zeolitic framework and the “-cage (7:7 Å). For all of these nanoporous amorphous structures, in order for them to accept the appreciable amounts of N2 observed (Fig. 21.14b,e), the pores must also be significantly interconnected. Pressure-induced amorphization of ZIF-4 was reported by Bennett et al. [21.80]. Again, HPXRPD was used in conjunction with a DAC, with amorphization detected by the gradual disappearance of Debye– Scherrer patterns and any reversibility by their return. Pressures at which amorphization occurred, PA , which should have not been unexpected, were highly dependent upon whether or not molecules were present in the MOF framework and also on the type of the PTM employed [21.80]. For example, the PA of solventfree ZIF-4 could increase almost eight times if a small molecule PTM was used rather than a large one. In the latter case, a similar increase in PA occurred, dependent upon whether or not solvent was present in the framework. Zeolitic frameworks have considerable flexibility [21.102, 103], so the obvious conclusion is that small PTM molecules penetrate the framework, resist collapse until higher pressures are reached, and promote reversibility, in a similar fashion to solvent inclusion. Similar conclusions can be drawn from a previous study of pressure-induced amorphization of ZIF-8, where penetrating PTM was used [21.101] and where amorphization at higher pressures was reported, compared to the earlier Argonne studies discussed above, where penetrating PTM was avoided [21.79, 99]. Coupled to
Hybrid Glasses
Pressure Amorphization of CPs While coordination polymers can be melted (Sect. 21.2.2, Fig. 21.11) [21.22] from which glasses could be formed (Fig. 21.5c) [21.23], little work has been reported on the effects of compression leading
to amorphization. By comparison with ZIFs, 3-D CPs have higher atomic densities. The effect of pressure amorphization on the structure and on proton conductivity has been reported for the CP imidazolate phosphate fŒZn.HPO4 /.H2 PO4 /2 2ImH2 gn [21.81] introduced earlier in this chapter in conjunction with the melting of CPs [21.23, 90]. The protonic parts form a hydrogen-bonded network, which proves both flexible and susceptible to compression, amorphizing between 3 and 7 GPa (Fig. 21.15a). The proton conductivity, however, is drastically affected, dropping by three decades under pressure at 370 K (Fig. 21.15b). At the same time, the structure completely reverses on decompression to crystalline fŒZn.HPO4 /.H2 PO4 /2 2ImH2 gn , and the proton conductivity returns close to its original ambient value of 104 1 cm1 at 370 K. This is reminiscent of the reversible melting of ŒZn.HPO4 /.H2 PO4 /2 .ImH2 /2 discussed earlier (Sect. 21.1.3) [21.22]. In that case, however, fusion incurred a loss of some of the Zn coordination, which, however, was then restored when the glass formed. By contrast, though, the glass has a much higher proton conductivity of 105 1 cm1 at 380 K [21.90] compared to the amorphized phase, which is 107 1 cm1 at similar temperatures (Fig. 21.15b) [21.81], suggesting that the hydrogenbonded network is disrupted during compression, breaking up protonic pathways, which, however, are then re-established on recrystallization. Overall, though, unlike the compression of zeolitic frameworks [21.15, 16, 79, 80], where amorphization of desolvated/dehyrdrated structures is irreversible on laboratory timescales, amorphized coordination polymers cannot be recovered because the process is reversible [21.81]. Also, the pressures PA needed to amorphize CPs are many times greater than those required to collapse ZIFs [21.79, 81]. Similar considerations apply to the compression of hybrid perovskites. Pressure Amorphization of HOIPs So far, hybrid perovskite glasses have not been reported, either by melt quenching or by thermal amorphization, leaving pressure-induced amorphization the only practical route. This has started to be addressed by the HOIP community [21.30–34]. The thrust of these developments, needless to say, has been in exploring whether the already attractive electronic and optical response properties of HOIPs might be further improved through compression [21.31]. Nevertheless, these processes may also offer opportunities for extending the field of hybrid glasses. On account of their attractive opto-electronic properties for solar cell applications [21.27], hybrid perovskite methylammonium metal halides like
743
Part B | 21.3
this was the odd observation that the unit cell enlarged as higher pressures were used, which, if the pressure was isotropic, would point to negative compressibility, quite incompatible with the structural stability of ZIF-8 reported. Much of this apparently confusing behavior, resulting from using penetrating PTM, however, is common knowledge in handling porous media under high pressures [21.15, 79]. When thermally-induced amorphization occurs in zeolitic frameworks [21.1, 15], desolvation has already occurred (Figs. 21.10a and 21.12a), so the equivalent conditions for pressureinduced amorphization experiments require the pores to be empty. Happily, this was one of the many options explored in the compression of ZIF-4, where, in this case, amorphization was reported to occur at much lower pressures, viz. between 0:35 and 0:95 GPa [21.80]. Interestingly, the average PA is approximately half that of ZIF-8 at 1:2 GPa [21.79]. This reflects significant differences in mechanical compliance, porosity, flexibility, and structural stability between these two wellstudied MOFs, one of which (ZIF-4) thermally amorphizes before decomposition, while the other (ZIF-8) does not [21.1]. We will show later (Sect. 21.3.3) how PA in conjunction with TA defines the melting curve dT=dP that drives amorphization and the T–P phase space that contains the spinoidal limits of the crystalline zeolitic framework materials and the amorphous phases that they transform into under pressure and temperature (Fig. 21.17c,d). Despite the experimental ambiguities in establishing the fundamental mechanical stability of zeolites and ZIFs, their functionality [21.4–6, 9–11, 13] depends on their capacity to adsorb molecules, which themselves, of course, need to be physically or chemically relevant. In an interesting MD study, when CH4 was progressively introduced into the structure of ZIF-8, it was found that the shear modulus increased dramatically with a small drop in compressibility [21.102]. This will lead to a 50% drop in Poisson’s ratio [21.60], taking empty ZIF-8 from the ductile-tough regime to the rigid-brittle regime when pores are filled (Fig. 21.19b). Moreover, the Born stability limits shift to much higher pressures than for an empty structure, explaining how the presence of non-interacting molecules like CH4 engender increased framework stability. This is in line with a similar observation made earlier for zeolites, where the mechanical strength was enhanced as a result of the adsorption of guest molecules [21.103].
21.3 Pressure-Induced Amorphization and Mechanical Stability
Glass Families
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Part B | 21.3
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Part B
744
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:DYHOHQJWK QP
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Fig. 21.15 (a) Pressure-dependent energy-dispersive XRD patterns of proton conducting CP, fŒZn.HPO4 /.H2 PO4 /2 2H2 Imgn at 25 ı C (after [21.81]) using a MAP with synchrotron radiation. (b) The proton conductivity of fŒZn.HPO4 /.H2 PO4 /2 2H2 Imgn of at 100 ı C at various pressures (red and blue arrows show increasing and decreasing pressure with ambient pressure conductivity shown by a black square) (after [21.81]). (c) XRD patterns of methylammonium metal halide ŒCH3 NH3 ŒPbBr3 using a DAC with 0:4066 Å synchrotron radiation. After initial displacement phase transitions diffuse scattering is established around 8 GPa, but the Pm3m space group returns with recrystallization on decompression. (d) Photoluminescence during compression excited with 0:325 nm laser radiation showing the green– blue switch established around 8 GPa. (e) Photoluminescence band switching back from blue to green on decompression. Reprinted with permission from [21.31]. Copyright 2015 The American Chemical Society
ŒCH3 NH3 ŒPbI3 have been the main focus of attention so far, the CH3 NHC 3 cation occupying the A site with a variety of metals occupying the B site (Fig. 21.4). In all cases, amorphization is preceded by
cubic-orthorhombic symmetry-breaking order–disorder transitions, which occur up to around 2 GPa for ŒCH3 NH3 ŒPbBr3 [21.31] (Fig. 21.15c). These phase transitions replicate the behavior familiar in inorganic
Hybrid Glasses
of HOIPs is generally always found to be reversible, as illustrated in Fig. 21.15c with striking results for CH3 NH3 PbBr3 from Zhao’s Nevada group [21.31]. With A displacement and octahedral BX3 tilting phase transitions up to about 5 GPa, amorphization is not fully apparent until 12 GPa, continuing through to over 20 GPa—in any case, initiated at far higher pressures than for ZIF-8 (Fig. 21.15c) [21.31], higher even than for CPs [21.81]; this is despite MOFs, CPs, and HOIPs all being soft materials, albeit having different atomic densities. Related to this is the return to crystallinity for amorphized hybrid perovskites on decompression, shown in Fig. 21.15c for CH3 NH3 PbBr3 , attributed to the location of the organic A molecules, which are disordered initially under pressure during amorphization, but which ultimately appear to act as a nucleating template on recrystallization [21.31]. Indeed, as Zhao et al. showed, following amorphization and recrystallization the opto-electronic properties of CH3 NH3 SnI3 can be improved significantly [21.32], demonstrating the virtue of nucleating from a monolithic amorphous solid. With evidence for preferred molecular orientation, improved micro-structure with smaller grain sizes, and reduced carrier effective mass m , enhanced electrical conductivity is also expected in hybrid HOIP films recrystallized after being processed through the pressure amorphization cycle. Added to this, the opto-electronic structures of compressed amorphized metal-halide perovskites appears to operate differently from the starting semiconducting crystals. In particular, the energy gap increases, the transmitted color in visible light changing from black to brown for the HOIP ŒCH3 NH3 ŒPbI3 [21.34] (Fig. 21.5e), with photoluminescence that is characteristically green shifting to blue for CH3 NH3 PbBr3 , as shown in Fig. 21.15d [21.31]. Commensurately, the resistivity increases by almost six decades [21.31, 32], which has prompted the suggestion that compressed amorphized hybrid perovskites might act as pressure versus volume (PV) switches [21.31]. DFT calculations indicate that the energy gap of HOIPs like ŒCH3 NH3 ŒPbBr3 is direct and primarily defined by Br 4p states at the top of the valence band and Pb 6p states at the bottom of the conduction band [21.25, 31], largely unaffected by the orbitals of the molecular A cations. This gap should necessarily decrease with increasing pressure as chemical bonds like Pb–Br contract, whereas the opposite is observed, judging by the increase in the optical gap of ŒCH3 NH3 ŒPbI3 (Fig. 21.5e) and the photoluminescence energy of ŒCH3 NH3 ŒPbBr3 (Fig. 21.15d,e). To explain this, Zhao proposed that, as metal-halide bond lengths shorten with pressure, bonds are also broken in the process of amorphization. In the case of ŒCH3 NH3 ŒPbBr3 , because the Pb–Br bonds
745
Part B | 21.3
perovskites, where the octahedral BX3 sites tilt through displacive transitions. In the case of hybrid perovskites, the tilting of metal halide octahedra like PbBr6 is accompanied by the distortion and displacement of A site molecules [21.30–32]. If these molecules are polar, like methyl ammonium (MA) and also dimethylacetamide (DMA), this can lead to ferroic and multiferroic ordering. Above 2 GPa amorphization commences and is usually complete by 12 GPa (Fig. 21.15c) [21.31– 33]. Concepts from the crystallography of displacive transitions have been used by Wang et al. and others to describe the process of amorphization, which they argue results from the increased tilting of metal halide octahedra, where SRO is preserved, but which eventually destroys the LRO and periodicity of the organic cations [21.31]. We proposed earlier that the structure of amorphized hybrid perovskites like ŒCH3 NH3 ŒPbI3 might correspond with the structure of calcium aluminate glasses [21.43] (Fig. 21.8), where Ca is replaced by the molecular cation CH3 NHC 3 , Al by Pb and O by I, with hydrogen bonding being established between molecular A sites .CH3 NHC 3 / and halides on X sites. By analogy with .CaO/12.Al2 O3 /7 , Pb would occupy 4fold and 5-fold sites, and I 2-fold and 3-fold sites. This model aperiodic cluster (Fig. 21.8) gives a guide as to the possible co-operativity between the random rotation of the A site molecules and the reconfiguration of hydrogen bonding in amorphized compared to crystalline MA metal halides (Fig. 21.4). Considering the changes in vibrational dynamics in methylammonium metal halides occurring during compression and decompression some interesting changes have been reported. In particular in crystalline ŒCH3 NH3 ŒSnI3 low-frequency Raman bands occur at 173 cm1 (5:8 THz) and 210 cm1 (7 THz) and have been attributed to librational modes of the ŒCH3 NH3 C1 cation [21.32]. As these disappear after pressure-induced amorphization followed by decompression and recrystallization, this suggests some disordering of the A sites through this cycle, in which case amorphization is not completely structurally reversible. Furthermore, for CH3 NH3 PbI3 , amorphization is accompanied by the appearance of a Raman band around 150 cm1 (5 THz), which is attributed to PbI vibrations [21.34]—presumably octahedral rattling modes—which increases with pressure. There is also evidence in the amorphized structure of CH3 NH3 PbI3 for a feature 25 cm1 (0:8 THz), absent in the crystalline Raman spectrum. This could possibly be the vestiges of a boson peak [21.35] intimating the presence of collective modes (Sect. 21.2.2) in amorphized MA metal halides. In contrast to the amorphization of desolvated ZIFs [21.79, 80], the pressure-induced amorphization
21.3 Pressure-Induced Amorphization and Mechanical Stability
746
Part B
Glass Families
Part B | 21.3
of the BX3 octahedra determine the optical properties, Zhao considers that the two processes competitively balanced in generating an ordered hybrid perovskite glass [21.31]. Certainly, broken bonds will introduce localized states at the band edges, which will effectively increase the optical gap across which recombination occurs and, therefore, the photoluminescence energy. At the same time, mobile carrier resistivity at room temperature will naturally rise hugely. Because band-edge defects will be associated with Br 4p and Pb 6p states, local pairing should readily anneal to complete previously broken Pb–Br bonds. Accordingly, this mechanism might then explain why the pressure-amorphized matrix is capable of templating nucleation and reversing the crystal–amorphous transition on decompression (Fig. 21.15c–e). The success in the considerable improvements in high energy conversion efficiency that have been achieved in thin film perovskite solar cells [21.126] has relied on their structural and, therefore, electronic stability, in which case, synthesis via amorphized or liquid state phases appears beneficial. Compressibility and Mechanical Stability The structural instability of zeolitic frameworks is reflected in the magnitude of the isotropic compressibility
T (Sect. 21.2.5). Where hybrid perovskites are concerned, it has been pointed out that materials like CH3 NH3 SnI3 are amongst the most compressible perovskites known [21.29, 32], with T values at NTP of around 80 compared to 5:8 TPa1 for SrTiO3 . However, in the context of hybrid zeolites 80 TPa1 is much smaller than 154 TPa1 for the extremely stable ZIF-8 [21.79] and smaller still than 504 TPa1 for the less stable ZIF-4 [21.57]. At the same time, for dense non-porous CPs like emin[MnII (btc)] [21.106] T 33 TPa1 , lower still than for CH3 NH3 SnI3 , suggesting that the CP emin[MnII (btc)] may be the more stable MA metal halides. Available compressibility values T for crystalline CPs, HOIPs, and MOFs are collated in Fig. 21.16. Compared to the compressibilities of molecular solids compiled by Klein and Angell [21.127], HOIPs lie close to the RT T of glycerol with cag MOFs like TIF-4 coinciding with o-terphenol (OTP), giving a measure of the softness of organic–inorganic materials. Figure 21.16 also includes the onset pressures of amorphization PA . There is a clear trend of decreasing T and increasing mechanical instability in terms of the difficulty with which these crystalline hybrids pressure-amorphize. Accordingly, CPs [21.16, 81, 127] and metal halide perovskites [21.30–33] only amorphize reversibly with pressure, ZIF-8 with its sodalite zeolite (SOD) structure amorphizes irreversibly with pressure [21.79] but not with temperature [21.1, 93], and ZIF-4 with its cag structure amorphizes both with pressure [21.80]
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Fig. 21.16 T versus PA for metal organic frameworks, hybrid organic–inorganic perovskites, and coordination polymers, to which the molecular crystals OTP and glycerol have been added from [21.127]. The dotted curve is to guide the eye. Closed symbols use T and PA for open symbols PA is not available, and only T is used. The horizontal dashed line separates amorphization that is reported to be irreversible ( T > 100 TPa1 ) from amorphization that is reported to be reversible ( T < 100 TPa1 ). Techniques and references are shown in Table 21.1
and with temperature [21.1, 39]. Coordination polymers and metal halide perovskites then appear the most mechanically stable among crystalline hybrid materials. This is also reflected in their plastic properties, with hybrid perovskites, for example, having hardness H > 1 GPa [21.25] compared to H < 1 GPa for MOFs [21.59]; the softer the material, the more compressible it is. In general, the physical understanding of large values of T at NTP acting as a metric for decreasing mechanical stability lies at the pressure where mechanical stability (in the sense of Born criteria) happens to be located. In particular, since compressibility T necessarily diverges from this stability limit, the larger the value of
T at ambient temperature, the lower the pressure where this limit resides. For comparatively stable crystalline inorganic materials like SrTiO3 with T values around 36 TPa1 mechanical stability is established at positive pressure, but the much larger T values of hybrid materials strongly suggest that the limit of mechanical stability might occur at negative pressures. If this shifts to more negative pressures, cavitation becomes progressively likely, while amorphization is more and more inevitable at ambient pressures or higher, offering a qualitative explanation of the above trend in the degree of amorphization of emin[MnII (btc)] ! ŒCH3 NH3 ŒPbI3 ! ZIF-8 ! ZIF-4. The horizontal dashed line in Fig. 21.16 separates the reversible amorphization of
Hybrid Glasses
21.3 Pressure-Induced Amorphization and Mechanical Stability
Hybrid type CPs HOIPs MOFs
emin[MnII (btc)] fŒZn.HPO4 /.H2 PO4 /2 2H2 Imgn MAPbBr3 MASnI3 ZIF-8 TIF-4 ZIF-62 ZIF-4
T (TPa1 ) 33 – 31 81 154/115 238 521 568
HOIPS and CPs from the permanent amorphization on laboratory timescales for MOFs. This is greatest for ZIF-4 cag structures, with ZIF-8 SOD on the borderline. The implication, then, is that the crystalline mechanical stability limit for hybrid crystals like HOIPs lies at positive pressures for T < 100 TPa1 but at negative pressures for MOFs when T > 100 TPa1 . Later, we will argue that this demarcation may also distinguish ductile from brittle behavior (Sect. 21.3.6, Fig. 21.19b).
21.3.2 Amorphization and Chemical Synthesis by Milling The sophistication of grinding powders has improved considerably with recent developments in ball milling, which offer alternative methods of material synthesis and modification. Through impact and attrition energy is transferred, leading to mechanochemical reactions or physical amorphization under ambient conditions [21.104], with some striking examples involving synthesizing and transforming hybrid materials [21.23, 82–84, 107, 108]. Amorphization of MOFs by Milling Amorphizing hybrid and inorganic zeolitic framework materials by ball milling has produced fascinating insights into the formation of hybrid glasses [21.82, 83]. Cheetham’s group report how XRD patterns of ZIF-4 and ZIF-8 disappear within 20 min of dry ball milling, but how crystallinity survives for up to an hour if these MOFs are solvated, reemphasizing how the resilience of the extensive cavity structure depends on this being internally supported. By contrast, it takes around 200 min for zeolites like Na zeolite Y and ZSM-5 to become x-ray amorphous, requiring a further hour if cavities are filled [21.83], reflecting the higher mechanical stability; zeolites having compressibilities of 8 TPa1 compared to 150500 TPa1 for ZIFs (Sect. 21.3.1, Compressibility and Mechanical Stability). By measuring the density and BET area of ZIF-8 with ball-milling time, collapse is found to extend over more protracted
PA (GPa) > 4:3 4:1 5:2 3:012:5 1:1 – – – 0:350:95
Technique
Reference
DAC MAP DAC DAC DAC/MD DFT DFT DFT DAC
Madsen et al. [21.106] Umeyama et al. [21.81] Lee et al. [21.30] Mitzi [21.29], Lü et al. [21.32] Chapman et al. [21.79], Ortiz et al. [21.102] Xiong et al. [21.57] Xiong et al. [21.57] Xiong et al. [21.57] Bennett et al. [21.80]
timescales than the disappearance of diffraction lines. Interestingly, collapse divides into two zones, starting with a sharp rise in density over the first 20 min accompanied by a marked decrease in N2 sorption, clearly indicating partial collapse of internal cavities (Fig. 21.2). This is then followed over the next 5 h by much slower changes, leaving amorphized ZIF-8 essentially nonporous [21.82]. At the same time, the SRO of ZIF-8 during milling remains intact, analogous to the thermal amorphization of ZIF-4 (Fig. 21.6a,b). Considering the two transitions identified when ZIF-4 collapses [21.1] (Fig. 21.12; Sect. 21.2.4), the two distinct zones that occur when ZIF-8 is ball milled might well be associated with ZIF-8 ! LDA and LDA ! HDA transitions. If this is the case, then the initial partial collapse and disappearance of crystallinity with milling [21.82, 83] could well mirror the initial pressure-induced amorphization of ZIF-8 reported by Chapman et al. [21.79] (Fig. 21.14a), which we have suggested leads to an LDA phase (Sect. 21.3.1). The slower densification of ZIF-8 that follows further ball milling [21.82] might then culminate in the formation of an HDA nonporous phase, which we have associated with FTIR spectra [21.99] at 4 GPa and above (Fig. 21.14c; Sect. 21.3.1, Pressure Amorphization of MOFs). Under the dry mechanophysical conditions used by Cheetham’s group, amorphized ZIF-8 does not recrystallize [21.83] after milling. However, Frišˇci´c and colleagues discovered that when ZIF-8 is ball milled mechanochemically under acid conditions, the amorphized phase formed after 20 min recrystallizes to a dense non-porous MOF phase diaZn.MIm/2 [21.107]. This phase appears equivalent to ZIF-zni, which crystallizes from the amorphous HDA phase when ZIF-4 is thermally amorphized [21.1, 39] (Figs. 21.10 and 21.12). There observations would seem to reveal a similar pattern in the amorphization of ZIF-8, but only when acetic acid is present during milling. Including Si powder apparently also assists in nucleating dia-Zn.MIm/2 from the amorphized ZIF8 [21.107].
Part B | 21.3
Table 21.1 Isotropic Compressibility T and onset of pressure amorphization PA for organic–inorganic crystals
747
748
Part B
Glass Families
Part B | 21.3
Finally, we note an interesting recent application of ball milling porous MOFs, sealing in irreversibly occluded guest species, hugely extended their subsequent release [21.108]. Fairen-Jimenez et al. demonstrated how model anti-cancer drugs, such as the hydrophilic model molecule C46 H46 N2 O23 , when introduced into the UiO-66MOF (Zr6 O4 .OH/4 (1,4-benzenedicarboxylate)6 ), are released rapidly from the crystalline host within 1 or 2 days. After ball milling, however, their release is much slower, continuing for more than a month and making this amorphized MOF host attractive as a potential drug delivery system. Amorphization of CPs by Milling Horike and Kitagawa report synthesizing the amorphous CP proton conductor a-CdTz by ball milling Cd.H2 PO4 /2 (1,2,4-triazole)2 for up to 500 min, resulting in the formation of the transparent flexible pellet illustrated in Fig. 21.5f [21.23]. CdTz is isostructural with the 2-D ZnTz phosphate arrangement shown Fig. 21.3, and a-CdTz retains this layered topology but disordered through the distortion of octahedral Cd sites, as the authors argue from EXAFS and PDF characterization (Fig. 21.6c,d; Sect. 21.1.2). The inherent disorder endows a-CdTz with far superior proton conduction and dielectric properties than its crystalline counterpart [21.23]. The electrical conductivity of amorphous Cd.H2 PO4 /2 (1,2,4-triazole)2 is also about a decade higher than the 1-D amorphous CP conductor ŒZn.HPO4 /.H2 PO4 /2 .ImH2 /2 described earlier (Sect. 21.2.3), reaching 104 1 cm1 before crystallization 350 K, therefore inching towards superionic conductivity values [21.35, 41]. Also of interest are clear Tg endothermic features and exothermic crystallization peaks from DSC scans at fixed heating rate (Fig. 21.10b), both occurring below decomposition TD , which starts around 450 K. Each advances in temperature with increasing milling time and remains similar in size. Progressive ball milling of CPs, therefore, appears to parallel the increase in the fictive temperature of MOF MQGs with heating rate [21.1] or the extent of solvent removal in MOF porous glasses [21.3], each of which is indicative of increasing residual entropy Sconfig (Sect. 21.1.3). It will be fascinating to see how general this novel route for fabricating amorphous CPs will prove to be. Amorphization of HOIPs by Milling In another exciting development, the classic photovoltaic CH3 NH3 PbI3 has been synthesized in a single step, simply by milling CH3 NH3 I and PbI2 together under argon for just 30 min [21.84]. Not only that, Grätzel and Lewi´nski find that the polycrystalline MAPbI3 produced by this short period of milling has supe-
rior PV conversion efficiency compared to solventproduced material. Given the fact that amorphization of HOIPs under pressure is reversible (Fig. 21.15c; Sect. 21.3.1, Pressure Amorphization of HOIPs), ball milling methylammonium metal halides for periods longer than 30 min might enable permanent amorphization to be achieved.
21.3.3 T -P Phase Space for Zeolitic Framework Collapse and Decelerated Melting Turning to the thermodynamics of the collapse of porous crystals, we now explain how the pressure and temperature boundaries for framework collapse can be obtained experimentally from the sigmoidal profile of the decrease in the fraction of crystallinity x measured from the areas of XRD lines as they decline with increasing pressure or temperature. Because amorphization of the model hybrid and inorganic framework systems we have discussed is kinetic (Fig. 21.13), the rates of collapse are necessarily dependent on the rates at which pressure or temperature is increased. These are characterized by collapse times A , defined by the time to reach x D 0:5 from the onset of collapse [21.15]. The dynamics of zeolitic amorphization, for different rates of temperature or pressure increase, fold onto a universal sigmoid, illustrated for zeolite FAU in Fig. 21.17a. The amorphization pressure and temperature limits at x D 0:5, PA and TA , sharing the same A , are shown together with the onset of collapse P1 and T1 and its completion at P2 and T2 . Collapse progresses from zeolite, through the perfect glass LDA to HDA, which, as we have seen, is equivalent to the MQG (Fig. 21.12; Sect. 21.2.4). The precise shape of the sigmoid conforms to ˇ a compressed exponential viz. x / e.t= / , where is the collapse timescale [21.14]. For relaxation in metastable liquids [21.114] or in ionic conduction in melts and glasses and liquids [21.41, 115] ˇ < 1, and the exponential is stretched. For the present case of the kinetics of zeolitic framework collapse, ˇ approximately equals 2. This compressed exponential describes the universal collection of collapse sigmoids shown in Fig. 21.17a, as well as individual ones like Fig. 21.17b, and is indicative of the occurrence of more than one reaction. Wondraczek and co-workers have recently demonstrated that this compressed exponential sigmoid can be accurately modeled as the sequential transitions zeolite-LDA followed by LDA–HDL (Fig. 21.17b), each with a different reaction time 1 and 2 [21.14]. The respective activation energies of these reaction times turn out to be very different, with EzeoliteLDA ELDAHDL , reflecting the respective super strong and
Hybrid Glasses
21.3 Pressure-Induced Amorphization and Mechanical Stability
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Fig. 21.17 (a) Universal sigmoidal fall in crystallinity x of zeolite FAU as a function of reduced time t= A for a variety of rates of pressure and temperature-induced amorphization (after [21.15]). A is the time to reach x D 0:5, defined by TA or PA for common increasing temperature and pressure rates, with the corresponding onset and completion of collapse defined by T1 or P1 and T2 or P2 , respectively. Zeolite, LDA, and HDL show approximately where each phase is dominant. (b) Decelerated melting of zeolite LSX showing the compressed sigmoidal decline of x-ray diffraction peak areas with time and the two-stage transition model of zeolite–LDA followed by LDA–HDL (after [21.14]). (c) T-P phase space for zeolite FAU [21.15, 16] and (d) for ZIF-4 [21.1]. These are determined experimentally from the limiting experimental thermobaric parameters T1 , P1 , T2 , P2 indicated in (a) dT=dP is the negative melting curve taken from 50=50 collapse point: 350 and 208 KGPa1 for ZIF-4 and Zeolite FAU respectively. The critical point C, which is located at negative pressure, is defined in the two-state model for polyamorphism [21.14, 35, 36, 110]
fragile behavior reported for ZIFs [21.1], as well as for zeolites [21.15] (Sect. 21.2.4). From the sequential reactions, the loss of crystallinity g.t/ is modeled as g.t/ D fNT .t/ C f1 .t/ " p # 1 2 1 t exp D exp 2 2 2 2 2 ! 1 1 t erf erf 2 2 2 2 1 t C exp ; 2
where fNT represents the initial solid fraction, decreasing with zeolite ! LDA, while f1 represents the transient LDA phase before transforming into HDL. This simple reaction rate scheme provides an excellent fit to the x-ray experimental data for the collapse of zeolite LSX (Fig. 21.17b) [21.14]. Returning to the thermodynamics of the collapse of zeolitic frameworks, the pressure and temperature limits obtained using the constructions shown in Fig. 21.17a are plotted in Fig. 21.17c for faujasite and Fig. 21.17d for ZIF-4. These have been interconnected—T1 with P1 , T2 with P2 , etc. This depiction reveals the negative slope of Clapeyron curve dT=dP associated with collapse, defined as the stage
Part B | 21.3
b) I
a) x
749
750
Part B
Glass Families
Part B | 21.3
where half the framework has collapsed (x D 0:5). Figure 21.17c,d also identifies the zeolite/LDA boundary defining the locus along which collapse starts and the LDA/HDL boundary where it ends. The two experimentally determined boundaries extrapolate with increasing temperature and decreasing pressure to a critical point C, which is located at negative pressure, beyond which the polyamorphic phases are coexistent and identical [21.1, 15, 111]. The T–P space for ZIF-4 is qualitatively very similar to zeolite FAU, except that the temperature and pressure limits are now much smaller, reflecting the lower mechanical stability of the MOF, increased T , reduced bond strength, and decreased rigidity. Taking on board the fact that dT=dP is negative, together with the well-known Clapeyron relation dT=dP D V=S, as the density increases from LDA to HDL, the entropy change S must be positive, pointing to the LDA phase being the better ordered of the two polyamorphs [21.1, 15, 35]. This appears to be a general description is nearly twice that for the collapse of any zeolitic framework, hybrid or inorganic. The magnitude of dT=dP for ZIF-4 is nearly twice that for zeolite FAU (Fig. 21.17), reflecting the difference between compliant and compressible MOF frameworks and the more rigid and incompressible inorganic zeolite frameworks.
21.3.4 Two-State Model for Zeolitic and MOF Amorphization The T–P phase diagrams, derived from the turning points in the collapse of zeolites and now ZIFs shown in Fig. 21.17c,d, obtained from the time dependence in the decline of the diffraction lines in the Debye–Scherrer XRD patterns (Fig. 21.17a,b), can be shown to be in good agreement with the thermodynamic two-state model for amorphization [21.109–114]. This model has its origins in the prescient work of Rapoport published 50 years ago on the melting point maxima observed in ionic solids like KNO3 [21.109]. It invokes the existence of two coexistent phases at supercooled temperatures of the same composition, but which differ in density and entropy. We now call these polyamorphs. This model has been extended in recent years to describe liquid–liquid phase transitions in polyamorphic systems like water [21.121, 122], Si and Ge and compound semiconductors [21.110, 111], Y2 O3 -Al2 O3 alloys [21.113, 128], and zeolites [21.14, 15, 19, 60]. An important development in applying this model practically to interpret experimental amorphization findings like those illustrated in Fig. 21.17 simplifies the expression for the free energy of G of a metastable mixture of
two polyamorphs to [21.111] G D x.E0 TS0 C PV 0 / C x.1 x/U C RTŒx ln x C .1 x/ ln .1 x/ ; where x is the fraction of HDL and 1 x the fraction of LDA, and E0 , S0 and V 0 are, respectively, the differences on internal energy, entropy, and volume between the two polymorphs. These thermodynamic parameters can be obtained from XRD diffraction line areas .x/ density .V/ measurements and the Clapeyron relation (Sect. 21.3.3) dT=dP D V=S, the usual configurational entropy of mixing RTŒx ln x C .1 x/ ln .1 x/; x.1x/U is the mixing energy of the polyamorphic system and is related to the critical point Tc , Pc [21.35, 111, 112]. The critical point C is identified in the experimentally determined T–P phase space as the point where P1 T1 and P2 T2 converge on extrapolation (Figs. 21.17c and 21.16d for zeolites and ZIFs, respectively). In particular, U D 2RTc [21.111]. The free energy G versus the LDA/HDA composition x is plotted for thermally amorphized zeolite FAU in Fig. 21.18a for the three temperatures shown. The minima in G define the spinodal limits for the LDA and HDA phases. These are transferred for different temperatures in Fig. 21.18b to define the thermodynamic limits for the two polyamorphic phases for faujasite and provide convincing modeling of the experimental data in Fig. 21.17c. Falling inside the experimental boundaries P1 T1 and P2 T2 , the spinodals in Fig. 21.18b offer a guide as to where the LDA and HDA phases are dominant and can be compared directly with the results of kinetic analysis for isothermal amorphization (Fig. 21.17b). It is clear, for instance, that in practical terms isolating polyamorphic phases such as LDA will be more effective through pressure-induced amorphization than temperature-induced amorphization, as we have inferred for the case of the collapse of ZIF-8 (Fig. 21.14a; Sect. 21.3.1, Pressure Amorphization of MOFs). Turning to the critical point C shown for the collapse of faujasite and ZIF-4 in Fig. 21.17, the fact that this occurs at negative pressures is consistent with the mechanical stability limit of porous materials being located at negative pressures with increased values of compressibility T at NTP discussed earlier (Fig. 21.16; Sect. 21.3.1, Compressibility and Mechanical Stability). It also accords with the fact that zeolites are less stable than MQGs of the same composition [21.78], which would include HDA phases too, since they generally appear to be thermodynamically equivalent (Figs. 21.12b,e). The extensive calorimetry measurements conducted on inorganic zeolites and alumino-
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silicate glasses by Navrotsky’s group [21.78] have yet to be applied to ZIFs, but it seems very likely that crystalline nanoporous MOFs will also exhibit higher enthalpies compared to their equivalent hybrid glasses. Finally, a useful intuitive relation coupling the temperature of thermally-induced amorphization TA with pressure of pressure-induced amorphization PA found from the collapse of inorganic zeolites [21.15, 16] is PA VA Š RTA , i. e., the work done to achieve collapse through compression at ambient temperature is equivalent to the thermal energy required at atmospheric pressure. We apply this to ZIF-8, which pressure amorphizes at 1:2 GPa [21.79] but which decomposes before thermal amorphization occurs [21.1]. In particular, equating VA with the respective SAV quoted by Tan et al. [21.58] and coupling these with the amorphization parameters for ZIF-4 and ZIF-8 [21.1, 79, 80] discussed earlier (Sects. 21.2.2 and 21.3.1; Fig. 21.17d) TAZIF-8
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21.3 Pressure-Induced Amorphization and Mechanical Stability
21.3.5 Potential Energy Landscape The equivalence of amorphized and MQG ZIF-4 (Fig. 21.12b) [21.1], which is also displayed by inorganic zeolites (Fig. 21.12e) [21.19], can be rationalized qualitatively in terms of the PEL, as illustrated in Fig. 21.19a. This is a schematic of the potential energy of an entire system of N atoms and shows the PEL fluctuating as a series of minima whose locations are a function of the collective configurational coordinate [21.35, 68]. While PEL systems are theoretically tractable for small numbers of atoms N up to around 30 [21.116] and have been used to explore glass formation [21.117], for MD ensembles, where N might be 10 000, the collective configurational coordinate is non-intuitive. Representations of the various minima at the dynamic cross-over region containing the LDL and HDL liquid–liquid transitions, however, can be envisaged [21.1, 35, 68]. Note that there are always far fewer minima than the 3N C 1 possibilities for a random arrangement of N atoms. This degeneracy derives from the chemical order and packing constraints manifest, for example, in the time-averaged structure of the resulting supercooled liquid and glass (Fig. 21.6). Different thermal energies for the characteristic temperatures Tm , TgLDL , TgHDL , and the solid-state phases ZIF-4, LDA, HDA, and ZIF-zni are also indicated in Fig. 21.19a, including the MQG. When this glass-forming liquid is quenched from the thermodynamically sta-
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Fig. 21.19 (a) Energy levels kB Tm , kB TgLDL , and kB TgHDL represent the ergodic melt (red dash), and the non-ergodic LDL
and HDL phases (green dash) in the dynamic cross-over region. At solid-state temperatures (black dash) the corresponding transitions involving the amorphization phases, LDA and HDA, respectively, are shown alongside the crystalline phases ZIF-4 and the ultra-stable ZIF-zni, together with the exothermic ZIF-4–LDA transition and the endothermic polyamorphic LDA–HDA transition. The most stable crystalline phase is ZIF-zni, separated from the melting point by the enthalpy of fusion Hm . (b) Fracture energy versus fragility m and Poisson’s ratio for a range of glasses and glassforming melts, to which the fragilities of several MQG MOFs and molecular glasses have been added (green circles). This defines a demarcation in fragility between the supercooled ZnIm2 -GIS, TIF-4 and ZIF-62 and ZIF-4 together with ZIF-HDA and ZIF-LDA (blue circles), which all fall on the brittle side of the brittle–ductile threshold, while glycerol and OTP belong on the ductile side, where CPs and HOIPs may be located. ZIF-4 HDA and ZIF-4 LDA are also included, whose liquid fragilities range across the brittle regime. Filled and empty ZIF-8 SOD positions are taken from MD elastic constant calculations (purple squares) and straddle the brittle–ductile transition. After [21.1, 60]
ble (ergodic) liquid at Tm and reaches the temperature of the cross-over (non-ergodic) region (Sect. 21.3.1), it will become trapped in one or the other of the PEL minima, if it does not enter the narrowest and deepest minimum first and crystallize. Figure 21.19a illustrates how the MQG might avoid crystallization by residing in a broader higher energy minimum, exploring different configurations in the process. This MQG minimum is also shown coinciding in the PEL with the amorphized HDA phase, as both are observed from DSC to be very similar (Fig. 21.12b). When the crystalline ZIF-zni precipitates, this occurs at a temperature TXX of 863 K (Fig. 21.12a), retaining its periodic configuration until its melting temperature Tm at 863 K is reached. ZIF-zni is the most stable of the unsubstituted imidazolates [21.12, 13, 56] and is the analog of quartz in the oxide silicalite system. Thermally-induced amorphization operates in the opposite sense to melt quenching [21.35], the zeolitic framework increasing in temperature until it reaches the energies of the saddle points, marked ZIF-4 in the PEL cartoon (Fig. 21.19a). Inorganic zeolites have enthalpies higher than those of the corresponding silicate glass [21.78], so, when amorphization occurs, collapse
is exothermic (Fig. 21.12e,f) [21.14–16], as discussed in Sect. 21.2.2. The similarity in shape of initial DSC upscans for ZIFs (Fig. 21.12a,c) point to the same interpretation, viz. that ZIFs are less stable than equivalent glasses and are, therefore, higher in enthalpy. This is incorporated into Fig. 21.19, where the polyamorph LDA is located at lower energy than ZIF-4. Since the LDA phase has the lowest energy of the amorphous phases, the highest Tg , and the lowest fragility m (Fig. 21.13c), it is associated here with a perfect glass [21.1, 35]— occupying the lowest PEL minimum among the noncrystalline ZIF phases in Fig. 21.19. As the temperature rises further, the low-density LDA state will be lifted out of the LDA minimum into the dynamic nonergodic liquid region, where it is shown transforming into a high-density HDA state via a liquid–liquid LDL– HDL transition, and sharing a similar potential energy to the MQG. This endothermic process replicates the endothermic DSC step that follows the collapse of the zeolitic frameworks illustrated for ZIF-4 and zeolite LSX in Figs. 21.12b,f, respectively. Reversible polyamorphic transitions, such as the solid state HDA–LDA transformations originally discovered in water by Mishima [21.122] or first-order
Hybrid Glasses
21.3.6 Differentiating Brittle MOFs from Ductile Coordination Polymers and Hybrid Perovskites An extraordinary empirical relation exists among a wide variety of glasses between Poisson’s ratio and the fracture energy (FE) (Fig. 21.19b), which is also very relevant here in characterizing the mechanical properties of amorphous and melt-quenched hybrid glasses. Poisson’s ratio measures the ability to distort elastically and Fracture Energy the energy of crack initiation which clearly occurs beyond the harmonic limit. There is no connection between the physics of these two mechanical regimes, which makes the versus FE relationship special. It was originally restricted to comparing bulk metallic glasses with some silicates [21.60, 118]. A dramatic threshold, however, is encountered around 1=3, where FE rises through more than five decades. A monotonic rise in FE with is expected, as materials for which Poisson’s ratio tends towards 0 are brittle (small FE), sacrificing compressibility for distortion in shape, while materials for which Poisson’s ratio approaches 0:5 are tough (large FE), incompressibility giving way to ductility [21.60]. The massive rise in FE as ! 1=3, however, is quite unexpected, but nevertheless offers a unique metric by which to differentiate brittleness ( < 1=3) from ductility ( > 1=3). At the same time, an even less expected experimental relationship was found between Poisson’s ratio for different glasses and the fragility of their associated liquids [21.119, 120]. Originally, Novikov
and Sokolov proposed this as a universal relation for all glasses [21.119]. While this was disputed at the time because of the limited selection of systems chosen [21.35], the gradual increase in m with increasing has subsequently been verified within different glass-forming systems, taking each of these separately [21.60]. Convoluting the m versus relationship with the FE versus relationship for the same types of glass formers leads to the correspondence between FE and m [21.60] included in Fig. 21.19b. This is a useful alternative to FE versus for ascertaining the mechanical properties of glass-forming systems, where melt fragility is often more easily obtained using DSC than measuring Poisson’s ratio. In particular, FE versus m distinguishes brittle glasses like silicates, whose melts have fragility m . 50, from ductile glasses like many metallic glasses whose melts have fragility m & 50. In this regard, the organic glasses glycerol and OTP have been included in Fig. 21.19b, also falling on the ductile side of the brittle-ductile divide. The fragilities of a range of hybrid MQGs a range of hybrid liquids whose crystalline cag ZIF structures are related to ZIF-4—ZnIm2 -GIS, TIF-4, ZIF-62, and liquid ZIF-4 [21.2]—have been added to Fig. 21.19b. These range from m D 17 to 39, and are, therefore, distributed below the brittle-ductile transition at m 50. Crystalline ZnIm2 -GIS is the most porous (57%), while for the other ZIFs, porosity is much less, ranging from 19 to 27%, which may explain why the ZnIm2 GIS glass might be the most brittle if it is also the most compressible. For the remainder of these MQGs, the trend towards toughness approximately follows the melting temperature, with ZIF-62 having the lowest Tm and ZIF-4 the greatest. Also included in Fig. 21.19b are the fragilities of the supercooled polyamorphic phases LDA .m D 11/ and HDA .m D 41/ formed during the thermally-induced amorphization of ZIF-4 (Sect. 21.2.4) [21.1]. Significantly, these straddle across the ZnIm2 -GIS to ZIF-4 series. Accordingly, the lowdensity, low-entropy amorphous hybrid ZIF-4 phase LDA, which we have equated with a perfect glass (Sect. 21.1.3) [21.35], should have the lowest Poisson’s ratio. At D 0:11, LDA approaches the cross-over to auxetic behavior [21.60] and is close to min D 0:06 for ZIF-4, which Ryder et al. obtained from DFT calculations in particular directions [21.93]. These corklike characteristics ( 0) complement earlier work on Na zeolite Y [21.16], where Poisson’s ratio for the polyamorphic LDA phase D 0:07 projected from fragility and 0:02 from in situ inelastic x-ray scattering [21.93]. These porous polyamorphs, which are topologically similar to their crystalline antecedents, are far more compressible and rigid. In contrast, Poisson’s ratio for the high-density high-entropy hybrid
753
Part B | 21.3
HDL–LDL transitions in the molten state detected in supercooled yttria-alumina by the author of this chapter [21.113] were not at first observed on the timescale of thermally-induced ZIF or zeolite amorphization experiments, as these usually only cover a few hours. Reversible HDA–LDA and LDA–FAU transitions, however, have been detected for desolvated zeolites, but over the protracted timescale of several years [21.14]. Clues as to how this might occur lie in the relative stabilities of the HDA, LDA, and FAU phases (Fig. 21.19a), where thermal cycling to dehydrate partially collapsed specimens took place periodically. As both HDA and FAU are non-affine on the nanoscale with their inherent flexibility, periodically-introduced thermal strain well below Tg could well raise the enthalpy until crystallization is restored, as this is the highest enthalpy phase [21.78], mimicking the rejuvenation of ordered glasses to ones with higher enthalpy states (Sect. 21.1.3) [21.76, 77]. Reversibility of liquid– liquid transitions are inherent in the two state-model for polyamorphisms (Sect. 21.3.3) [21.109–111] and are a natural inclusion in the PEL (Fig. 21.19a).
21.3 Pressure-Induced Amorphization and Mechanical Stability
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HDA phase, which as we have seen is almost indistinguishable from the MQG (Sect. 21.2.2, Fig. 21.12b), is much greater ( D 0:28) and less compressible and deformable. Mechanically crystalline hybrid materials, then, are soft and compressible (Sects. 21.1.2 and 21.2.5), but clearly their glasses are brittle and deformable to different degrees. This is the case for MOFs. It would clearly be interesting to see where CP glasses or amorphous hybrid perovskites might be located in Fig. 21.19b, as mechanical toughness is a serious consideration in device fabrication. As they are
less compressible than MOFs (Fig. 21.16) crystalline
values might well lie on the tough side . > 0:33/ of the of the brittle–ductile transition with liquid fragilities m > 50 along with molecular crystals like OTP. This being the case, the brittle–ductile transition (dashed vertical line in Fig. 21.19b) might differentiate between compressible MOFs, and CPs and HOIPs, with less compressible MOFs on the borderline. This would then complement the dashed horizontal line in Fig. 21.16, which distinguishes between high and low compressibilities, and irreversible and permanent amorphization.
21.4 Extending the Range and Application of Hybrid Glasses New glasses are usually developed in response to perceived market forces. So far hybrid glasses have come as a bi-product of MOFs and ZIFs, whose specific applications are directed at CO2 sequestration and catalysis [21.5, 9], co-ordination polymers as prospective materials for protonics and fuel cells [21.90], and hybrid perovskites as solar cells in energy conversion, for instance [21.25, 126]. As glasses in general usually fall short in mimicking the precise physical properties of crystalline materials, the potentially added value comes from homogeneity, fabrication versatility in area and shape, capacity to incorporate benign as well as toxic materials [21.108], etc. Likewise, given that crystals for electronics and lasers, for instance, are often grown from the liquid state, there is also a role for glasses to act as precursors for improving the quality of crystalline applications [21.23, 32]. Most of these advantages have yet to be fully realized in the new field of hybrid glasses, which makes their prospects exciting. Finally, there is the longstanding issue that the physics of glass formation remains elusive [21.129]. Accordingly, new types of glass may provide novel systems to explore the fundamental nature of glass. With these caveats, opportunities for extending the variety of hybrid glasses will now be considered [21.130– 147], not just among MQGs, where thermal decomposition is often an issue [21.2, 23, 30], which can only be circumvented if Tm can be lowered (Sects. 21.4.1 and 21.4.2) in the case of MOFs (Sect. 21.4.2). In addition, though, alternative room temperature amorphization techniques have been utilized, not just for existing MOFs [21.79, 80, 82–84, 107, 108] but also applicable for ones yet to be discovered [21.136–139] (Sect. 21.4.3). Milling and high-pressure routes via the anmorphized state are leading to improved properties of crystalline CPs (Sect. 21.4.4) [21.23, 24, 130– 132] and HOIPs (Sect. 21.4.5) [21.30–34, 133]. We conclude with other room temperature damaging pro-
cesses, which have yet to be applied to hybrid glasses (Sect. 21.4.6) [21.141–147].
21.4.1 Developing Hybrid Glasses with Lower Melting Points A restriction to extending the variety of hybrid glasses by melt quenching clearly relates to the survival of the starting crystalline hybrid materials in reaching the molten state. The frailty of the organic linker is the chief problem in reaching elevated temperatures, as this will often decompose before any melting is possible (Fig. 21.10). However, strategies for lowering Tm are developing deriving from the pallet of linkers and ligands available to alter the solid-state chemistry of the crystalline MOFs [21.2, 10, 138] and CPs [21.21–23], and the variety of metals and molecular cations in the case of HOIPs [21.25, 136]. For MOFs, these have enabled melting points Tm to be lowered significantly below the temperature at which the decomposition of linkers occurs TD (Sect. 21.4.1). For some CPs, Tg can be modified by the ball-milling time [21.23]. For HOIPs, the organic components are strongly linked to functionality, so the recourse to date has been to exploit less damaging pressure techniques [21.31, 34, 84] (Sect. 21.4.2).
21.4.2 MOFs with Lower Melting Points The synthesis of MOFs with lower melting points than ZIF-4 .Zn.C3 H3 N2 /2 / started with its polymorphs [21.2], replacing the imidazolate linker .C3 H3 N 2 / with mixtures of the stiffer 5-methylbenzinimidazolate (mbIm C8 H7 N 2 ) and benzimidazolate (bIm C7 H5 N 2 ) linkers. These have resulted in the crystalline MOFs TIF-4 .Zn.Im/1:5.mbIm/0:5/ and ZIF-62 .Zn.Im/1:75.bIm/0:25/, as illustrated alongside ZIF-4 in Fig. 21.20—all sharing the cag topology. As a con-
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Fig. 21.20 (a) Orthorhombic Pbca structure of ZIF-4 including eight 2:1 Å nanopores per cell and the first DSC upscan revealing an amorphization (TA ) sigmoid, followed by ZIF-zni crystallization exotherm and melting endotherm. The second DSC upscan identifies the MQG glass transition (Tg ) and fragility m D 39. (b) Isomorphous cag structure of TIF4 and first DSC upscan revealing desolvation, followed by HDA melting endotherm, with little evidence for any prior amorphization or crystallization. Second DSC upscan identifies the MQG glass transition (Tg ) and fragility m D 35. (c) Isomorphous cag structure of ZIF-62 and first DSC upscan revealing desolvation followed by melting endotherm, without any apparent amorphization or subsequent crystallization. Second DSC upscan locates the MQG glass transition (Tg ) and fragility m D 23. Adapted and extended from [21.2]
sequence of introducing mixed linker structures, the respective Tm for ZIF-4, TIF-4 and ZIF-62 were lowered to 863, 740 and 710 K—well below the common linker decomposition temperature TD of 875 K. This suggests that increasing the rigidity of the organic component may loosen the constraints that precipitate melting at tetrahedral metal sites; 13 C and 15 N crosspolarization NMR confirm that linkers are randomly mixed in these glasses, and presumably in the liquids too [21.2, 49]. As periodicity is broken on melting, we can envisage flow incorporating nano-sized units, which will encounter increasing steric hindrance the stiffer and bulkier the linkers are, thereby contributing to increased viscosity at Tm —as recently demonstrated in the melting of ZIF-62 (Sect. 21.5) [21.49]. Similar considerations should also apply in decelerated melting [21.14] as TA is approached. For ZIF-62 and TIF-4, however, the initial DSC upscan suggests that amorphization is not abrupt but appears to continue through to melting [21.2] (Fig. 21.20). It is also noteworthy that, unlike ZIF-4, neither of the mixed linker cag
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21.4 Extending the Range and Application of Hybrid Glasses
polymorphs recrystallize after or during amorphization, which is consistent with the supercooled melts having high viscosity (Sect. 21.5.2). Turning to the fragilities of the melts for the cag polymorphs, these are 39 (ZIF4), 35 (TIF-4) and 23 (ZIF-62). The decrease in m actually following increases in linker complexity and decreasing melting temperature Tm (Fig. 21.20), and, as we have seen, these fragilities fall on the brittle side of the brittle–ductile transition (Fig. 21.19b). Despite these significant changes in structural rigidity, PDF, Raman, and NMR characterization [21.2, 49] all point to the survival of the tetrahedral metal node geometry and the integrity of the linkers in the MQGs, and to the CRN structure (Fig. 21.7; Sect. 21.1.2) being adopted.
21.4.3 Increasing the Variety of MOF Glasses by Room-Temperature Amorphization Techniques Transformation of low-density zeolitic frameworks— inorganic and hybrid—into amorphous materials of
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higher density below Tm involves increasing the energy of the crystalline state through thermally-induced decelerated melting at atmospheric pressure [21.14– 20]. As we saw earlier (Sect. 21.3.1), low-temperature melting can also be induced by applying pressure at room temperature [21.14–16, 35, 79, 80, 102]. Moreover, thermally-induced amorphization at TA and pressure-induced amorphization at PA are equivalent routes to the same amorphous state, if they share the same collapse time viz. PA VA Š RTA (Sect. 21.3.3) [21.35]. Clearly, for MOF glasses room-temperature techniques avoid decomposition of the organic linkers. Of these, pressure-induced amorphization has been applied so far mainly to ZIF-4 and ZIF-8 [21.79, 80, 102, 105]. There is, therefore, huge scope to enlarge the variety of amorphous MOFs using low-temperature melting routes. This is aided by the vast range of ZIF structures so far synthesized, many incorporating different linkers and with different potential applications [21.10, 13]. The voluminous catalogue of ZIFs that has so far materialized is much greater than for the inorganic zeolite family, where the number of potential structures far outstrips the diversity of zeolite types that have actually been produced [21.10, 138]. This stark difference in success between generating hybrid zeolitic frameworks compared to inorganic zeolites is attributed to the advantages of solution chemistry, where organic linkers can be cooperatively assembled in conjunction with a versatile combination of solvents and temperatures. By contrast, hydro-thermal chemistry used in the synthesis of inorganic zeolites usually employs organic templates in conjunction with alkaline gel methods, rather than using wholly inorganic reactants [21.139]. Templates then need to be removed in order to prime functionality, but solvent removal is liable to precipitate framework collapse, limiting the number crystalline zeolites that can be realized; the corresponding desolvation process for ZIFs appears more benign. All told, the solution and reticular chemistry processes developed for ZIFs [21.4, 10] has resulted in a rapid realization of hybrid zeolitic networks [21.9] that has been far more successful, both in variety and number, than the equivalent achievement in multiplying zeolite types [21.12, 137]. Furthermore, the ZIFs so far produced have far greater complexity than their zeolite counterparts but, at the same time, conform to geometries that are generally uninodal or vertex-transitive, again reflecting the success in crystallizing low-density frameworks. Basically, this characteristic should also simplify and unify the destruction of crystallinity through any collapsing process, while, at the same time, affording a massive portfolio of compositions and topologies that could potentially be transferred, at least in part, into the amorphous state.
First, here are just a few examples of MOFs that would be very interesting to amorphize under pressure at room temperature. The low-density ZIFs chosen, together with many more, exhibit considerable stability, and as a result, they have been proposed as candidates for industrial applications [21.10]. Accordingly, as is the case for ZIF-8, large pore ZIFs are unlikely to melt before they decompose (Sects. 21.2.5 and 21.3.1, Compressibility and Mechanical Stability), and so pressure-induced amorphization to LDA or HDA phases, or indeed using other mechanochemical processes, would be the choice techniques for creating hybrid amorphous materials. Employing these routes, as we have seen for pressure-induced amorphization of ZIF-8 (Fig. 21.14a,b and Sect. 21.3.1), partial collapse to what may well be a non-crystalline LDA phase should result in substantial porosity being retained [21.79, 82, 83] (Sect. 21.3.2). Other ZIFs sharing the SOD structure, in addition to ZIF-8 .Zn.mIm/2/, are ZIF-67 (Co(mIm)2 ) and ZIF90 .Zn.Ica/2 /. These ZIFs all exhibit maximum pore diameters dp of 11:5 Å as well as adopting the same topology. Accordingly, we would expect them to amorphize in a similar way to ZIF-8, at initial pressures of around 1 GPa, and also to retain considerable porosity in the amorphous state (Fig. 21.14a,b). ZIFs adopting the rhombohedral zeolite (RHO) structure [21.10] include ZIF-11 .Zn.bIm/2/, ZIF-12 .Co.bIm/2/, and ZIF-71 .Zn.dcIm/2 /. Compared to SOD ZIFs, RHO ZIFs have larger dp values of 15 to 16 Å and lower densities, and may amorphize at lower pressures. Here, as elsewhere, the symbols refer to recognized zeolite structures [21.7, 12]. As the largest pores for RHO ZIFs are interconnected by similarly sized openings of around 3 to 4 Å, residual porosity after initial collapse should be similar, but the BET internal surface area could be larger. Then there are the capacious ZIFs with even larger pore sizes, but these are also double skinned [21.10]. For ZIF-95 the internal and external diameters for this poz structure are 24 and 41 Å, respectively, while for the gargantuan moz ZIF-100 the respective diameters are 35:6 and 67:2 Å. By comparison, the super-cage in faujasite measures a mere 18 Å. Openings for ZIF-95 and ZIF-100 are around 3:6 Å, though, similar to the denser ZIFs, restricting the passage of molecules that can enter the major pores without considerable conformational framework flexibility [21.95]. The doubleskin structure will also add rigidity and amorphization pressures for ZIF-95 and ZIF-100 are likely to be higher than for SOD and RHO structures. In expanding the catalogue of 3-D amorphous MOFs the common structure is expected to be the CRN (Fig. 21.7) but different LRO ring topologies are antic-
Hybrid Glasses
21.4.4 Developing CPs with Superior Proton Conductivity Through Mechanochemical Amorphization We have already seen (Sect. 21.3.2) how the protonic CP Cd.H2 PO4 /2 (1,2,4-triazole)2 , whose layered structure is shown in Fig. 21.3, can be amorphized to different degrees of disorder Sconfig with progressive ball milling (Fig. 21.10) and, with subsequent modest pressure (4 GPa), a monolithic clear glass can be formed (Fig. 21.5f) with ambient proton conductivities of around 104 1 cm1 [21.23]. It will be interesting to see how Kitagawa’s Tokyo group extend their wellorganized procedures to synthesize CPs maybe with other functionalities. It will be important, too, to construct models of the atomic structure of CPs by x-ray and neutron methods by extending PDF and EXAFS analysis [21.23] (Fig. 21.6) using small-angle scattering methods, as just indicated. Likewise, by coupling these with MD atomistic simulation the molecular topology could be determined (such as suggested by the example of conjugated polymers in Fig. 21.8), ionic transport predicted, and (with DFT) mechanical properties of glassy CPs ascertained. In the allied area of developing understanding and application of protonic conducting hybrid networks for possible fuel cell applications, the incentive has been in developing acid-containing 1 and 2-D MOFs. Generally falling within the CP categorization [21.12, 20], acids are often located in pores in the crystalline structures [21.130, 131] enhancing the number of mobile protons. Layered metal phosphates, such as those based on the tubular-structured ˇ-PCMOF21 have already demonstrated superior conductivity [21.130]. For example, “-PCMOF2 12 , a trisodium 2,4,6-trihydroxy-1,3,5-trisulfonate benzene (Na3 L1) in which Na3 L1 is isomorphously exchanged with trishydrogen phosphonate (H3 L2) molecules to bolster the number of acidic protons, yields conductivities reaching 102 1 cm1 , several decades greater than the protonic CPs like Cd.H2 PO4 /2 (1,2,4triazole)2 [21.23]. Interestingly, it has been found that isomorphous exchange to synthesize, “-PCMOF2 12 can be facilitated by mechanical mixing, leading to a broadened Debye–Scherrer pattern, suggesting some disordering and that perhaps amorphization has occurred in the process. Even “-PCMOF2 12 , however, falls short of the performance of ionomeric polymers,
such as Nafion, which sustain 1 1 cm1 at temperatures 100 ı C and survive humid conditions. Moreover, ionomeric polymers are amorphous and plastic, which is necessary to meet the physical and mechanical requirements for proton exchange membrane fuels [21.130]. For the fuel cell application of high proton conductivity CPs and MOFs mechanical ductility will be needed (Fig. 21.19b), as well as compatibility with high humidity. Incidentally, crystalline hybrid electrolytes necessarily incorporate grain boundaries, which can impede ionic conduction, which is another reason for developing amorphous hybrid proton conductors. At this stage, though, crystalline versions are attractive for visualizing conduction pathways and mechanisms using crystallographic methods, such as the turnstile-like proton hopping transport promoted by rotation of phosphate ligands envisaged in the CP ŒZn.H2 PO4 /2 .TzH/2 n (Fig. 21.3) by Kitagawa [21.21]. Recently, Schröder’s Manchester group used quasielastic neutron scattering (QENS) to model proton diffusion in a complex phosphonate hexagonal MOF, ŒM3 .H3 L/2 .H2 O/9 .C2 H6 SO/3 (M D Ni, Co; H6 L D benzene-1,3,5-p-phenylphosphonic acid) [21.132]. With a respectable conductivity of 4:5 104 1 cm1 at 98% humidity, they found that the transport mechanism is best described by free diffusion inside a sphere rather than hopping between sites. The size of the sphere from this QENS modeling exercise nicely equates with the hydrogen–acceptor distances obtained from single crystal XRD [21.132]. Although crystalline transport mechanisms do not automatically translate into the amorphous state, these ideas should prove helpful in understanding protonic conduction in hybrid glasses like MQG ŒZn.H2 PO4 /2 .TzH/2 n [21.23] and the protonic MOFs like “-PCMOF2 12 if these can be amorphized. It is likely that high pressures would be needed (Sect. 21.3.1, Pressure Amorphization of CPs) or prolonged milling (Sect. 21.3.2, Amorphization of CPs by Milling).
21.4.5 Processing HOIPs with Improved Optoelectronic, Magnetic, and Dielectric Performance via Amorphization Turning now to HOIPs, as we have seen in describing pressure-induced amorphization (Sect. 21.3.1, Pressure Amorphization of HOIPs), hybrid metal halide perovskites amorphize at higher pressures [21.31–34, 81] than ZIFs [21.79, 80] (Fig. 21.15), reflecting the greater stability of their crystalline structures. However, for the pressure-amorphized HOIPs reported so far, all recrystallize on decompression (Fig. 21.15c–e) [21.31–34]. As previously discussed, if the compressibilities T
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ipated. As these are out of range for determination by standard x-ray and neutron PDF techniques (Fig. 21.6) which are dominated by tetrahedral SRO, SAXS and SANS will be important, and large MD simulations will be required to probe LRO and nanostructures.
21.4 Extending the Range and Application of Hybrid Glasses
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approached 150 TPa1 , corresponding to ZIF-8, for example, then permanent amorphization of metal halide perovskites might be realized (Fig. 21.16). The structural pressure dependence of other HOIPs, such as formate hybrid perovskites, with their attractive magnetic and dielectric properties [21.25], remain to be discovered or simulated, but elastic moduli are known to be an order of magnitude smaller than metal halide perovskites [21.25], in which case T values could be well within those of MOFs (Fig. 21.16), making persistent amorphization at modest pressures a possibility. Another possibility might be to reduce the hydrogen bonding interactions in HOIPs between A-site molecular cations and X-site linkers such as those illustrated in Fig. 21.4 for ŒCH3 NH3 ŒMn.HCOO/3 . In particular, Li and colleagues have shown how for the formate perovskites [AZE]ŒMn.HCOO/3 and [GUA]ŒMn.HCOO/3 the elastic modulus is related to these interactions and can be reduced tenfold [21.133]. There are similar interactions viz. N–H I between A and X sites in metal halide hybrid perovskites (Fig. 21.4), which will also influence mechanical properties and order–disorder transitions. Accordingly, if the strength of hydrogen bonding could be reduced further by tuning organic components with weaker interactions, then higher compressibility might be achievable. The Goldschmidt tolerance factor t may be relevant too in searching for high compressibility hybrid perovskites; t quantifies the efficient packing of cations and anions by ratioing their crystallographic radii, and, for the hybrid perovskite structures discovered so far [21.25], usually lies close to unity. For some formates and azides, however, t < 0:8 pointing to a lowering of rigidity in these structures and, hence, their possible vulnerability to amorphization. t < 0:7 for the simpler ŒNH4 ŒCd.HCOO/3 , where the coordination mode of the formate linker is also anti–syn instead of the customary anti–anti, resulting in polar order at ambient temperatures [21.134]. This, again, may have an amorphous analogue. Finally, the recent synthesis of CH3 NH3 PbI3 by milling organic and inorganic components [21.84] (Sect. 21.3.2), may also offer the opportunity of achieving permanent amorphization of HOIPs, if milling times were to be substantially extended. Our arguments here for developing more compressible and softer HOIPs is to extend the range of hybrid amorphous materials, and is, of course, counterintuitive to that of improving the mechanical stability of crystalline perovskites for current applications, in energy conversion, for example [21.25]. However, if mechanical instability limits can be realized (Fig. 21.16), the door may then open to some exciting possibilities if permanent amorphous HOIPs could then be created.
It is as well to remember that HOIPs themselves are characterized by a wealth of symmetry-breaking phase transitions [21.25, 27, 135, 136], which occur mainly at low temperatures. The dynamic movement of A site displacements promulgate order–disorder transitions, which, as we have described, stem from changes in A–X hydrogen bonding. Moreover, the entropy involved in these switches can be quite small [21.25]. Such subtle changes may play well into kinetics of decelerated melting [21.14] and amorphization of HOIPs into ordered or even perfect glasses (Sects. 21.1.3 and 21.2.6). It is interesting to note that for dimethyl ammonium transition metal perovskites like Œ.CH3 /2 NH2 ŒM.CHOO/3 , which are weakly ferromagnetic, dehydrate first ( 470 K) on heating and then collapse ( 600 K) to form metal oxide powders that are amorphous [21.134], suggesting that thermallyinduced amorphization might actually occur in this case, but entangled with decomposition. Added to this, metal halide hybrid perovskites have very recently been synthesized in the liquid state at RT using reactive polyiodide melts [21.98]. Among methylammonium metal halide perovskites those with Ge or Sn occupying the B site are the most thermally stable with Pb hybrid perovskites being the least, melting almost coinciding with decomposition (Fig. 21.10c; Sect. 21.2.2) [21.29]. These are direct band gap semiconductors, with low carrier–phonon scattering (compared to inorganic perovskites) and high carrier mobility (small m ), all of which contribute to efficient long-range separation of photo-excited electrons and holes after illumination. Likewise, recombination at significant distance from excitation leads to efficient emission, promising good possibilities for (IR) lasing and LEDs. Spontaneous polarization from X site ordering via phase transitions also leads to often impressive ferroelectric properties [21.25, 27, 32]. Crystalline MAPbI3 being the least thermally stable may explain the characteristic low-defect density. How many of these advantageous opto-electronic properties will or even should transfer to the amorphous state has yet to be established. Among the exciting properties of crystalline HOIPs, and formate perovskites in particular, are ferromagnetic, ferroelectric, and ferroic ordering revealed through low-temperature displacive phase transitions [21.25, 134, 135, 137]. For formate perovskites, large molecular cations like dimethylammonium NH2 .CH3 /2 on A sites dilate interactions between transition metal TM formates such as Mn.CHOO/3 on X sites, leading to weak ferromagnetism with critical temperatures Tc 10 K, as Gao and colleagues from Peking have shown [21.134]. Of particular interest, as far as this review is concerned, is the observation that when
Hybrid Glasses
21.4.6 Speculative Amorphization Methods It is well known that MeV neutrons create point defects in silica, and, in large doses of 1020 neutrons cm2 , can amorphize quartz [21.35, 141]. Proportionately less neutron flux may then amorphize hybrid materials but is also likely to adversely affect the hydrogen bonding between linkers and molecule cations. Ion implantation, on the other hand, which effectively amorphizes
Si [21.142, 143], offers more control in terms of ion fluence and energy. Likewise, electron-beam irradiation, which can amorphize berlinite [21.144], also seriously damages MOFs in high-resolution transmission electron microscopy (HRTEM) [21.145], the diffraction pattern of MOF-5 lasting only a few seconds even at 77 K [21.146]. Perhaps for this reason, HRTEM studies have mainly concentrated on imaging nanoparticles included on pores or just metal nodes, linkers generally being unresolvable [21.145]. Accordingly, from the opposite point of view, electron beam irradiation under low magnification might offer another route to amorphizing surface and bulk MOF and HOIP microparticles. Another possibility suitable for damaging larger specimens would be the calibrated use of synchrotron radiation x-rays [21.147]. In either case, this would require a culture shift for electron microscopists and crystallographers, from preserving structural integrity to altering it through dosimetry. A considerable challenge, but worth considering, would be to disorder TM formate perovskites sufficiently by irradiation to create the type of ordered or LDA glasses envisioned in reversibly amorphizing hybrid metal halide perovskites [21.32, 34], but with organic components in the formate perovskites sufficiently intact to sustain ferroic behavior.
21.5 Glass-Forming Ability The glass-forming ability (GFA) is the ability of a liquid to avoid crystallization during cooling. We conclude this review on hybrid glasses by reviewing GFA, not least because of the unusually high stability exhibited by some hybrid MQGs [21.49]. This exceeds the extreme GFA of classic inorganic systems like albite .NaAlSi3 O8 / and B2 O3 [21.148], for which there is a significant crystalline-glass density difference =g , but also of acrylic glasses like PMMA [21.44], where crystallization is blocked by random orientation of side and pendent groups (atacticity). Complex interpolymer interactions may well also play a part in the persistence of ambers in the glassy state over tens of millions of years [21.74]. Another common factor inhibiting crystallization in glass-forming liquids is exceptionally high viscosity .Tm / at the melting point Tm , which reduces the variety of configurations available in the melt for spontaneous nucleation [21.49, 148]. The superior GFA of hybrid glasses can be attributed to all three of these factors—large =g , steric hindrance related to linker complexities that survive melting, and large .Tm /. The GFA metric that is better known is the ratio of the glass transition temperature to the melting point Tg =Tm .
21.5.1 Glass-Forming Ability Expressed as Tg =Tm In his classic paper on the nature of the glassy state, Kauzmann drew attention to the fact that Tg =Tm values were approximately equal to 2=3 for many glass formers [21.72]. Since then, this empirical relation has been ratified for over 50 organic molecular glass formers by Angell, Wolynes, and coworkers [21.149, 150]. It has been extended further by ourselves [21.1] to encompass an additional 20 inorganic oxide glas formers and several hybrid glass formers, as reproduced in Fig. 21.21a. The 2/3 law has also been shown to apply to many metallic glass formers [21.151]. The adherence of the 2/3 slope for Tg versus Tm is impressive, covering so many different glass-forming systems, but there is still significant scatter. When Tg =Tm values are > 2=3, this is taken to signify superior GFA, with poor glass formers exhibiting Tg =Tm < 2=3. Basically, Tg =Tm defines the extent of the supercooled region, so for glass formers for which Tg =Tm > 2=3, this is short and vice versa for liquids where Tg =Tm < 2=3. Although these variations in Tg =Tm are
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Mn.CHOO/3 NH2 .CH3 /2 is decomposed at 520 K, amorphous ferromagnetic Mn3 O4 is formed. As permanent amorphization has yet to be demonstrated in hybrid perovskites; it is unclear whether the necessary local geometries secured in the crystalline state will survive in aperiodic structures. It is fundamentally important, nevertheless, to establish whether weak local interactions can be sufficiently ordered within amorphous network structures, as they are in the close-packed architectures of transition metal metalloid glasses, where amorphous ferromagnetism was first discovered [21.140]. Among the tools for amorphization— compression and/or milling (Sect. 21.3.2; Figs. 21.10c and 21.14)—irradiation and ion implantation can also offer other possibilities, where damage can be proportionately controlled.
21.5 Glass-Forming Ability
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small, they amplify into considerable differences in the context of Angell plots [21.66], as depicted schematically in Fig. 21.2b. Because these log versus Tg =T curves necessarily pivot around .Tg / D 1012 Pa s for conventional cooling rates of 1 K s1 , .Tm / changes through many decades between Tg =Tm D 0:5 and Tg =Tm D 0:8, for instance. It is clear, too, that the fragility m (Sect. 21.1.3) decreases sharply as Tg =Tm rises. Accordingly, strong liquids are good glass formers, and fragile liquids poor glass formers. We note, as others have done [21.77], that GFA rests on the reduced glass transition temperature Tg =Tm and the melt fragility being independent variables. Tg and Tm values are also included in Fig. 21.21a for the melt-quenched MOFs ZIF-zni, which crystallizes from ZIF-4 [21.1], ZIF-62 [21.49], TIF-4 [21.2], and ZIF-8, which decomposes before it can be thermally amorphized, but amorphizes under pressure [21.1, 79]. Melt quenching and temperature-induced amorphization of MOFs were discussed earlier (Figs. 21.10 and 21.12; Sects. 21.2.3, 21.2.4, and 21.4.1). ZIF-62 and TIF-4 all adopt the same orthorhombic Pbca space group as ZIF-4, as does the inorganic mineral variscite CaGa2 O4 with a melting point of 866 K [21.2, 51], which is also included Fig. 21.21a. A similar dft topology is adopted, too, by the cobalt phosphate framework DAF2 melting at 873 K [21.1, 154]. It is striking that all of the MQGs obtained from cag MOFs cluster together with similar albeit distinct Tg and Tm values (Fig. 21.21a). This includes variscite, suggesting that melting relates to the topology of the starting crystalline structure rather than to the metal–metal bonding bridges that can obviously be quite different. ZFI-zni like ZIF4 and ZIF-8 have imidazolate bridges (.C3 H3 N2 /2 and .C4 H5 N2 /2 , respectively) with the primary node-linker bond being Zn–N (Figs. 21.2, 21.6, and 21.7). Exploiting this similarity, we showed earlier (Sect. 21.3.4) how the doubling of PA between the amorphization pressures of ZIF-4 and ZIF-8 leads to a virtual thermal amorphization temperature (Tg ) for ZIF-8 TAZIF-8 of 1100 K. This projects a virtual melting temperature (Tm ) of 1650 K [21.1]. On this basis ZIF-8 has been added to the Tg versus Tm plot (Fig. 21.19a), where it lies close to the Tm value (1557 K) for the isomorphous inorganic zeolite sodalite ([21.1], Fig. 21.2). ZIF-8 and sodalite complement the coincidence of Tg ,Tm values of ZIF-zni and variscite and underline the notion that the retention of topology is dominant in the melting process. Indeed, this is an essential requirement if the porosities of MOFs are, indeed, to transfer from the crystalline to the liquid state, as Coudert et al. argued from atomistic simulations [21.51] (Fig. 21.11e). Melt-quenched MOFs extend across the Tg , Tm values of inorganic glasses [21.1] in Fig. 21.21a. The Tg and Tm values of the coordination polymer
.Cd.H2 PO4 /2 (1,2,4-triazole)) [21.23] have been added. Although Tg are not accessible for amorphized hybrid metal halide perovskites [21.31], the melting points of .C4 H9 NH3 /2 MI4 (M: Ge, Sn, Pb) taken from [21.29, 30] (Fig. 21.10) have been included. CPs and HOIPs group below MOFs in Fig. 21.21a, at the top end of the Tg and Tm values of organic glass formers [21.149, 150]. We note that there is a rough correspondence between Tm and isotropic compressibility T and, as we argued previously (Fig. 21.16; Sect. 21.3.1), ease of amorphization developing from CPs and HOIPs to MOFs. Rates of crystallization growth during congruent freezing were recently compiled by Orava and Greer [21.152, 153], ranging from pure metal liquidcrystalline interfaces surfaces like Ag(100) for which Tg =Tm < 0:4, through phase change materials like supercooled Ge2 Sb2 Te5 (Tg =Tm 0:4), liquid sodium silicates (Tg =Tm 0:6), metallic liquid alloys like Cu0:5 Zr0:5 (Tg =Tm < 0:7), to liquid silica and organic liquids like OTP, for which Tg =Tm > 0:7. To these can be added ultra-quenched liquid Ta (Tg =Tm 0:5), the poorest elemental metal glass former to date in common with other bcc metals [21.155]. By contrast, the supercooled ZIF-62 series for which Tg =Tm D 0:84, clearly sets these liquid MOFs ahead as the melt with ultrahigh GFA to date [21.49]. In particular, the growth rate of congruent freezing U at the crystal–liquid interface rises and falls between Tg and Tm , as illustrated in Fig. 21.21c, reaching a maximum Umax , whose relative temperature Tmax =Tm depends on the melt fragility m [21.152]. Turning now to the tendency to crystallize—or lability—when this is large, which is characteristic of fragile liquids, the U versus T=Tm peak is broad, and Tmax close to Tg . The opposite is true for strong liquids that have much lower lability, where the U versus T=Tm peak is broad, and Tmax is close to Tm (Fig. 21.21c); Umax covers as much as 11 decades between silica and pure metals and quantifies huge variations in GFA [21.152, 153]. Consequently, large lability and fragility are associated with Tg =Tm values below the 2=3 line in Fig. 21.21a and signify liquids with less than average GFA, while if, Tg =Tm values fall above the 2=3 line, the fragility is low, the lability small, and GFA higher than average. For liquid ZIF-62, there is no observable crystallization over periods of a day as Tm is approached [21.49], as Fig. 21.21d makes clear.
21.5.2 Glass-Forming Ability and Viscosity at the Melting Point .Tm / We have already stressed (Sect. 21.2.2) that melting is likely to be triggered by rare events [21.91], which for hybrid liquids might be metal coordination changes
Hybrid Glasses
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2=3), good (Tg =Tm 2=3), and poor (Tg =Tm < 2=3) GFA. (c) Congruent crystal growth versus T=Tm compared for liquid metals, organics, and silicates [21.152, 153]. Upward pointing arrows identify Umax and downward pointing arrows Tg . Reprinted from [21.152] with permission of AIP Publishing. (d) XRD patterns of supercooled ZIF-62 in argon at temperatures approaching Tm (0:88 < T=Tm < 0:92) for 24 h [21.49]. Reproduced from [21.49]
(Fig. 21.10) [21.51] or imidazolate rotations [21.22], initiated by collective THz vibrations [21.92, 93, 95]. The kinetics of melting and freezing, however, are geared to the occurrence of appropriate crystalline micro-configurations [21.14, 152, 153], which, in turn, are governed by the viscosity of the melt at Tm . To suppress crystallization between Tm and Tg the cooling rate must exceed the crystal growth rate Umax . In practical terms, extremely high values of .Tm /, greater than that of molten silica, are needed to block the collective diffusion needed to nucleate crystalline configurations. Log versus reduced reciprocal temperature Tg =T plots for supercooled NaAlSiO8 (albite) and B2 O3 are compared in Fig. 21.22a [21.148] and with supercooled ZIF-62 in Fig. 21.21b [21.49]; (Tm ) for NaAlSiO8 (107:1 Pa s)
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21.5 Glass-Forming Ability
and B2 O3 (104:0 Pa s) straddle that for silica (105:5 Pa s), while (Tm ) for ZIF-62 (107:1 Pa s) approximately coincides; Umax for molten silica, which is close to Tm and is one of the slowest growth rates recorded (Fig. 21.21c), leads to micron size crystallites developing over 24 h. Neither molten NaAlSiO8 nor B2 O3 [21.148] nor, in fact, ZIF-62 [21.49] show any sign of crystallization around Tm , so having (Tm ) close to the value of molten silica is not a sufficient criterion to define ultrahigh GFA. Viscosity and diffusion are coupled in supercooled silica [21.152]. For molten ZIF-62 migration of multiple nanosized imidazolate units and Zn nodes may therefore result in viscosity and diffusion becoming decoupled—this is compared to silica, where Si and O ions are much smaller. In particular, metal nodes
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in liquid ZIF-62 are likely to re-coordinate continually (as liquid ZIF-4 simulations in Fig. 21.11e suggest) but, in addition, altered confirmation related to mixed linkers, as we now explain, leads to a much-expanded liquid network compared to the crystalline ZIF-62 network [21.49].
21.5.3 Glass-Forming Ability, Mixed Linkers, and Density Deficit =g Although ZIF-4 and ZIF-8 are porous MOFs with the network perpetuated by single linkers (Fig. 21.2), we have already stressed that with melting and/or amorphization both structures approximate to CRNs like the one illustrated in Fig. 21.7. Tetrahedra are far larger compared to silica, but two-body Zn–N and three-body Zn–N–Zn constraints are much weaker. In particular, from PDF/Monte Carlo and NMR analysis (Sect. 21.1.2; Fig. 21.6a,b) it is clear that the single linkers survive the melting process [21.1, 39, 40, 51]. Also, if mixed linkers are introduced, the structural integrity of each is retained [21.2, 49]. Moreover, for the ZIF-4 structures TIF-4 and ZIF-62 (Fig. 21.20), the inclusion of mixed linkers leads to MOFs with decreasing melting temperatures Tm and liquids of decreasing fragility compared to ZIF-zni/ZIF-4 [21.2], as Fig. 21.19b illustrates schematically. Figure 21.22 sketches how the imidazolate .C3 H3 N 2 / (Im) and benzimidazolate (bIm) .C5 H7 N 2 / (bIm) linkers might be modeled into a CRN structure for ZIF-62. This has a nominal composition Zn.Im/1:75.bIm/0:25, but the ratio bIm=.bIm C Im/ can be changed, leading to a new range of mixed linker MQGs in which the two different linkers are randomly mixed [21.49]. Interestingly, with increasing bIm Tg and Tm also increase towards those of ZIF-zni/ZIF-4, although the ratio Tg =Tm for ZIF-62 glasses stays fixed at 0:84 [21.49]. We envisage that melting is initiated by a weakening of Zn–N bonds and bridging Zn–N–Zn constraints, which will release nano-sized linkers whose diffusion, because of the substantially different geometries of bIm and Im, will be sterically hindered, resulting in viscous cooperative translational motion [21.49]. The combined effects go towards explaining the large value of (Tm ) for ZIF-62 (Fig. 21.22b). Ultrahigh GFA, however, means that crystallization must also be somehow blocked and that crystalline nucleating sites are not only very rare events but are also incompatible with the surrounding liquid structure. Silica has a similar (Tm ) to liquid ZIF-62. Cristobalite, the crystalline polymorph regarded closest to silica, shares almost the same density and network configuration, contributes to the small but finite Umax observed close to Tm . The densities of ZIF-62 and its glass are also very sim-
ilar, with =g D 0:05. However, unlike silica and its crystalline polymorphs, ZIFs are porous. In particular, the extent of the cavities in ZIF-62 are quite different from ZIF-62 glass, viz. 0:27 and 0:06, respectively, leaving the respective network volumes 0:73 and 0:94 and a crystal–glass network density difference =g network of 0:22. The ZIF-62 glass network density and, therefore, its liquid, is incommensurate with that of the crystal, which lies behind the absence of any measurable crystallization for prolonged periods close to Tm (Fig. 21.20d). This may also be the reason why, when ZIF-62 is heated beyond the Tg of the MQG (Fig. 21.19c), it does not appear to amorphize before it melts. From Fig. 21.22d, it is clear that the enthalpy and entropy of fusion Hm and Sm of ZIF-62 with different mixed linker ratios increases in proportion to the fraction of the bulky bIm linker. The rise in Sm illustrates how bIm ligands enhance the number of configurational states at Tm . Together with Hm , Sm is almost two decades smaller than for quartz, related to its much higher melting point (2003 K) and the more rigid and stronger inorganic tetrahedral bonding. At the same time, Sm is comparable to the configurational entropy Sconfig of silica at its glass transition, reflecting the softer structure of MOFs. The parallel linear rise in Hm with bIm=.bIm C Im/ (Fig. 21.21d) reveals how the bulkier bIm linker requires more energy to initiate the necessary reconfiguration with the large increase in network volume that occurs as ZIF-62 melts.
21.5.4 Holistic Approach to Glass-Forming Ability Not one of the metrics for assessing glass forming ability is sufficient on its own. Rather, all need to be considered holistically, remembering too the relationship between compressibility T and ease of amorphization (Fig. 21.16). Returning to the 2/3 law (Fig. 21.21a), this is re-plotted as Tg =Tm versus Tm in Fig. 21.22d, now comparing ZIF-62 with 50 other glass formers, covering organic, metallic, as well as oxide systems, ranging in melting temperature by more than 1800 K. Of these, ZIF-62 clearly exhibits the highest Tg =Tm [21.49]. By contrast, ZIF-zni/ZIF-4 lies on the line with Tg =Tm D 0:67. As we saw earlier (Sect. 21.3.1, Compressibility and Mechanical Stability), ZIF-4 has the largest compressibility T [21.57] (Fig. 21.16), and of the MOFs examined so far is the one most susceptible to amorphization, whether induced by pressure [21.80] or thermally [21.1, 39], collapsing and crystallizing before melting (Figs. 21.12a,c and 21.19a). ZIF-62 has a similar value of T , but does not appear to crystallize before melting (Fig. 21.21d), no doubt for the
Hybrid Glasses
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Fig. 21.22 (a) log versus Tg =T for albite (blue NaAlSi3 O8 ) and B2 O3 (red) liquids identifying .Tm /, together with Tg =Tm . After [21.148]. (b) log versus Tg =T for ZIF-62 (after [21.49]) identifying .Tm /, together with Tg =Tm . (c) Schematic of the mixed linker ZIF-62 network highlighting possible configurations of imidazolate (Im) and 2-benzene imidazolate (bIm) linkers. (d) Increases in the enthalpy and entropy of fusion Hm and Sm with the increasing bulky bIm linker. (e) The comparison in Tg =Tm ratio between ZIF-62 (0:84) and other types of glass-forming systems, including water, oxide, metallic, and organic liquids–good GFA (> 0:67) typified by CPs, PMMA, B2 O3 , and SiO2 and amber. The poorest Tg =Tm recorded so far for elemental bcc metals like Ta is 0:5 with Tm D 3290 K. Adapted from [21.49]
reasons given above of high melting viscosity (Tm ; Sect. 21.5.2) coupled with high crystal-glass density deficit =g (Sect. 21.5.3). Coordination polymers are also included with Tg =Tm values of 0:71 [21.22, 23].
763
Part B | 21.5
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21.5 Glass-Forming Ability
With a very low (Tm ) and the smallest T (Fig. 21.15), CPs crystallize reversibly (Sect. 21.2.3), and also amorphize reversibly with ball milling [21.23], as well as with pressure [21.90]. Silica with its high (Tm ) and
764
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Glass Families
Part B | 21.6
high Tg =Tm (0:75) but low =g weakly recrystallizes close to Tm (Fig. 21.20c). Both B2 O3 and PMMA glasses also have high Tg =Tm ( 0:77) but show no signs of recrystallization for the following different reasons. B2 O3 , with its boroxol ring structure, is topologically remote from any candidate crystal, suggesting a huge =g [21.148]. For PMMA, atacticity, related to randomly oriented side groups, sterically hinders periodic arrangement [21.44]. Amber, probably the most stable of glasses, is also included in Fig. 21.22d. With a glass transition at 409 K, rejuvenated from pre-historic amber and with Tm coinciding with a decompo-
sition temperature of 570 K [21.74] places Tg =Tm around 0:72 and similar to silica. However, the absence of crystallization from pre-historic times is probably attributable to the steric hindrance locked in between pendent groups on adjacent polymeric units. For ZIF62, ultrahigh GFA, displaying no recrystallization on laboratory timescales (Fig. 21.21d), results not just from the uniquely high Tg =Tm but also the large network density difference =g network , and the randomly distributed bulky linkers such as bIm making (Tm ) comparable to silica [21.156], traditionally the most viscous and strongest of inorganic liquids.
21.6 Synopsis and Outlook The intention of this review has been to introduce hybrid glasses in the broad context of existing inorganic glass formers, rather than in isolation. As we said at the start, their organic–inorganic crystalline counterparts represent one of the most rapidly developing material systems emerging in the last decade [21.4, 5], with exceptional properties ranging from porous MOFs offering excellent gas selection, gas storage, and catalysis opportunities [21.10], to coordination polymers with high proton conduction attractive for protonic devices and fuel cells membranes [21.21], to hybrid perovskites exhibiting striking direct gap semiconducting possibilities for solar cells [21.27], and as model systems in developing ferromagnetic, dielectric, and ferroic phenomena [21.25]. By combing the concepts of solid and liquid physics with those of materials chemistry, hybrid glasses [21.1–3], whose properties so far remain largely undiscovered, will add constructively to the catalogue of novel materials in glass science. In recounting work on hybrid glasses, advantage has been taken of the contrasting structure and properties of non-crystalline MOFs, CPs, and HOIPs, whose mechanical compressibility and rigidity, ionic transport, and opto-electronic characteristics can be very different, and whose amorphization, melting, and decomposition temperatures can differ hugely. We have contrasted the CRN structure useful in modeling amorphous and melt-quenched MOFs [21.37, 38], with polymeric structures that would be appropriate starting points for CP glasses and amorphous phases [21.45], and with charge compensated random networks that we envisage may be appropriate for describing amorphized perovskites [21.42, 43]. While all of these new hybrid MQGs and amorphized organic–inorganic systems represent soft glasses, they can often be rigid and brittle compared to organic glasses and glassy
polymers, which are generally compliant and tough, differences that hinge on the mechanical stability reflected in the very different compressibilities. In particular, compressibility appears to dictate whether amorphization among MOFs, CPs, and HOIPs is reversible or permanent on laboratory timescales (Fig. 21.16). Irreversible amorphization on laboratory timescales, which is characteristic of framework MOFs [21.1] and also zeolites [21.15, 16], involves collapse and the formation of an ordered rigid amorphous intermediate, before a dense disordered and more compliant phase is formed—the final phase being thermodynamically almost indistinguishable from a MQG. On the other hand, the reversible amorphization of CPs and HOIPs does not seem to involve polyamorphic transitions [21.31, 49, 81]. Intuitively, there may be a close link between brittle materials and permanent amorphization, and ductile materials and reversible amorphization, certainly as far as non-crystalline hybrids are concerned. Throughout, the theme of perfect and ordered glasses [21.35, 73] keeps reappearing, either as the initial polyamorph in MOF collapse [21.1] or as persistent metal co-ordination in the melting and crystallization of CPs [21.22], or molecular sites pinning the amorphization of HOIPs and recrystallization [21.31]. There is a swathe of glass-forming ability from multilinker MOFs that show no signs of crystallization close to melting [21.49], to CPs that conform to average GFA [21.23], with HOIPs appearing to be poor glass formers at best. From this wealth of glass-forming and amorphization properties, atomic ordering and structures, and mechanical stabilities, it will be fascinating to watch how hybrid glasses now develop. With the diversity of metals, linkers, and molecules to choose from, alongside different compressibility, rigidity, flexibility, and porosity, the prospects look pretty exciting.
Hybrid Glasses
versity (Research Professorship), University College London (Honorary Professor in Chemistry), University of Cambridge (Distinguished Research Fellow) and Sidney Sussex College, Cambridge (Research Fellowship). The author is also grateful to the oncologist Elin Jones and her dedicated and caring chemotherapy team at Bronglais Hospital, Aberystwyth, UK. He also acknowledges the infinite patience and unstinting support of his wife Jenny.
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Acknowledgments. Stimulating discussions over time with Yuanzheng Yue, Omar M. Yaghi, C. Austen Angell, Alex Navrotsky, A. Lindsey Greer, Lothar Wondraczek, Gopinathan Sankar, Sabiasachi Sen, Tanguy Rouxel, Paul F. McMillan, Daniel R. Neuville, Gregory Chass, Wim Bras, and C. Richard Catlow are all gratefully acknowledged. The following institutions are also thanked for their support: Wuhan University of Technology (Strategic Scientist), Aberystwyth Uni-
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21.82
21.83
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21.85
21.86
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21.90
21.91
21.92
21.93
21.94
21.95
21.96
21.97
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21.122 21.123
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21.127
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21.129 21.130
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G. Neville Greaves (deceased) After his PhD at the Cavendish Laboratory in 1976, Neville Greaves worked in industry, then in the UK’s Synchrotron Radiation Source as Head of the Materials Science Department, before joining the University of Wales, Aberystwyth, as Director of Physics. He was a Distinguished Research Fellow in Materials Science at Cambridge University. His research interests included complex materials, catalysts, ceramics, glasses, and liquids. Sadly, Neville Greaves passed away in June 2019.
771
Natural Glass 22. Natural Glasses
Maria Rita Cicconi, Daniel R. Neuville 22.1 22.1.1 22.1.2
Quenched Glasses ............................. Volcanic Glasses ................................ Lunar Glasses ....................................
781 781 784
22.2 22.2.1 22.2.2 22.2.3 22.2.4 22.2.5
Impact Glasses.................................. Tektites and Microtektites................... K-Pg (KT) Spherules ........................... Younger Dryas Spherules .................... Enigmatic Impact Glasses ................... Fulgurites .........................................
785 786 788 788 788 790
22.3 Obsidian........................................... 22.3.1 Hydrated and Altered Obsidians.......... 22.3.2 Artificial Pumice: Foam Glass ..............
791 793 794
22.4 Other Natural Glasses ........................ 22.4.1 Glasses from Nuclear Explosions: Trinitite ............................................ 22.4.2 Friction Melts: Frictionites/Pseudotachylite................ 22.4.3 Bioglasses: Amorphous Hydrated Silica
795 795 796 796
22.5
Insights into the Structure and Properties of Natural Glasses ............. 22.5.1 Physical Properties of Silicate Glasses/Melts ..................... 22.5.2 Structure of Silicate Glasses ................ 22.5.3 Redox of Natural Glass and Reduction During High-Energy Events .................
802
22.6
Conclusions and Future Directions .....
804
References...................................................
804
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_22
797 797 799
Part B | 22
Natural glasses have been used since prehistoric times and are strongly linked to human evolution. On Earth, glasses are typically produced by rapid cooling of melts, and as in the case of minerals and rocks, natural glasses can provide key information on the evolution of the Earth. However, we are aware that natural glasses are products that are not solely terrestrial and that the formation mechanisms give rise to a variety of natural amorphous materials. On the Earth’s surface, glasses are scarce compared to other terrestrial bodies (i. e., the Moon), since the conditions on the surface give rise to devitrification or weathering. In order to provide an exhaustive overview, we shall classify natural glasses based on the mechanisms by which they were formed: temperature related, temperature– pressure related, temperature–pressure–volatile related, and others. In this chapter, we will review the most common natural glasses and their technological applications and also the scientific and technological advancements achieved from the study of these natural amorphous materials. Finally, we will provide some insights into the structure and properties of natural glasses and melts.
772
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Part B | 22
When talking about natural glasses, the first image is that of an obsidian, a volcanic glass that has accompanied and influenced human evolution. Indeed, the largest volumes (km3 ) of natural glasses (e. g., obsidian, perlite, and pitchstone) are linked to volcanic activity and are associated with cooling close to the surface. Tektites and impact glasses are formed in a completely different way, since their formation is related to the impact of an extraterrestrial body on the surface of the Earth. Therefore, since glasses are formed by different processes, we will provide a subdivision based on the formation mechanisms and divide quenched glasses, impact glasses, obsidian, and others. Several reviews, for the different natural glasses, have been published and the readers are referred to these exhaustive papers: i. e., [22.1–7]. An interesting nomenclature for natural glasses was provided by Heide
and Heide [22.6], which divided natural non-crystalline solids into four main groups, depending on their origin: magmatic, metamorphic, sedimentary and biogenetic. The chemical composition of natural glasses varies from mafic to felsic. Figure 22.1 reports the Total alkali versus silica (TAS) diagram, where the compositions of many natural glasses (Table 22.1) have been recalculated to 100% excluding water and carbon dioxide. The enormous variability of natural glasses composition can be appreciated in the TAS diagram, since they are differentiated as many common types of volcanic rocks [22.8]. Indeed, the diagram shows how widely natural glasses can vary in their composition, with SiO2 contents ranging from 30 to 99 wt%, and total alkali contents ranging from 0 up to 15 wt%. The list presented is, of course, not exhaustive, but represents many different glasses and their average compositions.
Na2O + K 2O (wt %) Obsidian Lunar glasses Basaltic glasses Tektites Fulgurites K-Pg LDG Trinity
15 Phonolite Trachyte
Tephriphonolite
10 Foidite
5
Rhyolite
Phonotephrite
Trachyandesite Basaltic Tephrite trachybasanite andesite Trachybasalt
Picrobasalt
Basalt
Trachydacite
Andesite Basaltic andesite
Dacite
0 30
40
50
60
70
80
90
100 SiO2 (wt %)
Fig. 22.1 Total alkali versus silica (TAS) diagram for several natural glasses (most of the data and references are reported in Table 22.1)
Monte Arci (I) Monte Arci (I) Monte Arci (I) Monte Arci (I) Lipari (I) Palmarola (I) Pantelleria (I) Lipari (I)
Mediterranean
Obsidian Armenian and Caucasian
Sample
76.27 76.7 72.84 75.15 77.37 74.72 73.77 75.05 75.57 74.84 75.96 73.68 74.87 74.51 71.2 75.55 75.36 75.48 75.57 75.62 75.47 75.37 75.45 74.42 75.54
SiO2
0.06 0.1 0.21 0.11 0.08 0.09 0.18 0.13 0.09 0.14 0.13 0.3 0.07 0.08 0.19 0.06 0.06 0.07 0.06 0.08 0.07 0.07 0.08 0.08 0.08
TiO2
13.09 13.5 14.52 13.95 12.64 13.4 13.68 12.97 13.88 14.02 13.44 14.33 13.25 13.45 7.66 12.83 12.83 12.82 12.86 12.63 12.82 12.84 12.82 12.77 12.82
Al2 O3
Cr2 O3
0.52 0.66 1.8 0.94 0.59 1.25 1.31 1.17 1.28 1.48 1.23 1.75 1.63 1.61 8.11
Fe2 O3 or Fe2 O3;tot a
1.6 1.59 1.58 1.6 1.48 1.47 1.57 1.48 1.5 1.47
FeO or FeO tot a 0.07 0.1 0.06 0.07 0.06 0.08 0.11 0.08 0.05 0.04 0.03 0.03 0.06 0.07 0.27 0.06 0.06 0.07 0.06 0.07 0.06 0.07 0.07 0.07 0.06
MnO
0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.05
0.05 0.15 0.48 0.22 0.04 0.08 0.13 0.11
MgO
0.51 0.54 1.67 0.99 0.48 0.59 0.75 0.57 0.57 0.7 0.54 0.85 0.69 0.44 0.25 0.69 0.72 0.7 0.69 0.72 0.72 0.72 0.72 0.72 0.72
CaO
4.07 4.56 4.56 4.29 4.18 3.44 3.34 3.34 3.55 3.49 3.36 3.3 4.16 4.79 6.84 4.13 4.16 4.16 4.16 4.2 4.19 4.19 4.21 4.2 4.17
Na2 O
4.39 4.65 3.76 4.26 4.56 5.26 5.63 5.51 4.71 4.88 4.99 5.31 4.66 4.43 3.72 5.03 5.02 5.04 5.04 5.15 5.16 5.13 5.12 5.18 5.1
K2 O
0.21 0.16 0.16 0.14 0.15 0.14 0.14 0.15 0.14 0.15
0.01 0.01 0 0.02 0.01 0.01 0.01 0.01 0.01 0.01
0 0.02 0.09 0.03 0 0.06 0.04 0.04
H2 O or P2 O5 H2 OC (*)
[22.12]
[22.11]
[22.10]
[22.9]
Reference
Natural Glasses
Part B | 22
Table 22.1 Average composition of major oxides (wt%) in several natural glasses
Natural Glasses 773
Perlites
Turkey
Obsidian Subalkalic
74.26 69.5 72.88 72.78 74.3 73.67 73.7 74.9 71.97 67.59 70.14 70.02 66.68 71.96
73.1 66.8 71.9 76.1 74.3 77.3 76.97 69.47 67.8 77.2 73.16 76.60 75.09 76.26
SiO2
0.13 0.12 0.1 0.1 0.11 0.14 0.14 0.12 0.3 0.19
0.06
0.09
0.31 0.64 0.49 0.13 0.12 0.07 0.14 0.45 0.74 0.10 0.30 0.07 0.16 0.09
TiO2
12.22 13.53 14.22 14.15 12 12.93 12.6 12.5 10.34 12.76 13.49 11.37 15.15 11.89
14.02 16.13 14.33 12.71 13.34 12.66 12.25 13.90 14.98 12.84 13.42 12.69 13.87 13.48
Al2 O3
Cr2 O3
0.76 1.15 0.97 2.34 0.84
0.91 1.86 0.7 0.17 0.77 0.63 2.1 0.8
0.46 0.54 0.13 0.23 0.35 0.37 0.39 0.90 0.97 0.20 0.99 0.35 1.05 0.7
Fe2 O3 or Fe2 O3;tot a
0.41 2.08 0.5 0.09 0.72 0.14
0.36 0.99
0.5
1.30 3.00 2.06 0.93 1.17 0.75 0.81 2.62 3.36 0.35 0.99 0.58
FeO or FeO tot a
0.06 0.03 0.1 0.2 0.01 0.08 0.05 0.01 0.07 0.05
0.09
0.05 0.08 0.06 0.05 0.05 0.05 0.05 0.10 0.20 0.05 0.06 0.06 0.05 0.04
MnO
0 0.31 0.23 0.28 0.5 0.34
0.08 0.12
0.18 1.14
0.39 1.33 0.46 0.15 0.05 0.03 0.15 0.49 0.70 0.07 0.66 0.04 0.1 0.03
MgO
0.73 0.33 1.49 0.82 0.56 1.41 0.7 0.6 0.38 1.33 0.6 2.03 1.66 1.09
1.58 3.57 1.71 1.04 0.84 0.64 0.90 1.89 1.92 0.58 1.61 0.58 0.89 0.85
CaO
3.81 3.06 4.03 4.51 4.04 3.14 3.7 2.9 3.34 3.28 2.86 1.88 3.97 2.35
4.54 4.84 4.88 3.59 4.55 4.34 3.89 5.38 6.87 3.65 3.92 3.80 4.02 4.03
Na2 O
4.66 5.55 2.82 2.48 4.69 4 4.6 5 4.13 4.37 6.62 3.9 5.64 4.45
3.20 2.32 3.13 3.91 4.03 3.65 3.89 3.21 1.82 4.59 4.20 4.73 4.9 4.65
K2 O
3.29* 2.4 3 6 5.3 4.7 6.5 4.9 6.1
3.32* 5.94* 4.52* 4.35*
0.08 0.51 0.49 0.42 0.09 0.09 0.22 0.06 0.12 0.06 0.30 0.09
0.04 0.11 0.09 0.01 0.01 0.01 0.03 0.13 0.09 0.01 0.09 0.01 0.02 0.01
H2 O or P2 O5 H2 OC (*)
Part B | 22
Sample
[22.6] [22.6] [22.6] [22.6] [22.6] [22.6] [22.14] [22.14] [22.15] [22.15] [22.15] [22.15] [22.15] [22.15]
[22.6]
[22.13]
Reference
Part B
Table 22.1 (continued)
774 Glass Families
Mauna Loa glasses
Quenched glasses Kilauea bulk rock Kilauea glasses
Pitchstones
Sample
50.94 51.49 52.14 51.94 52.11 52.06 52.43 52.55 52.55 52.62 52.44 52.84 52.63 52.46 52.61 52.13 52.66 52.78 52.61 52.54 52.52 52.61 52.56 52.16 52.37 52.65 51.9 52.16
71.75 73.37 73.5 67.88 71.9
SiO2
2.41 2.77 2.48 2.46 2.33 2.56 2.10 2.16 2.16 2.71 2.14 2.18 2.17 2.75 2.49 2.34 2.44 2.16 2 2.3 2.12 2.55 2.2 1.97 2.15 2.26 2.15 2.15
0.12 0.16 0.17 0.79 0.23
TiO2
13.49 13.33 13.61 13.63 13.7 13.55 13.75 13.94 13.94 13.11 13.91 13.58 13.76 13.02 13.53 13.32 13.36 13.62 13.94 13.6 14.13 13.68 13.91 13.62 13.85 13.78 13.83 13.81
14.99 10.78 11.59 12.22 11.9
Al2 O3
0.05 0.046 0.03 0.04 0.02
Cr2 O3
0.28 0.96 1.77 5.6 0.8
Fe2 O3 or Fe2 O3;tot a
11.3 11.56 10.95 11.08 10.85 11.34 11.10 10.76 10.76 12.26 10.90 11.11 11.13 12.42 11.56 12.02 12.06 11.32 10.61 11.91 11.06 11.58 10.7 10.79 10.61 10.78 11.18 10.97
1.3
0.53 1.02
FeO or FeO tot a
0.17 0.21 0.16 0.16 0.16 0.16 0.17 0.16 0.16 0.21 0.21 0.15 0.18 0.22 0.21 0.2 0.17 0.19 0.18 0.23 0.15 0.19 0.19 0.18 0.21 0.17 0.17 0.18
0.04 0.37 0.04 0.09 0.06
MnO
7.99 6.3 6.84 6.74 7.04 6.53 6.58 6.61 6.61 5.36 6.28 6.27 6.27 5.46 5.79 5.94 5.9 6.39 6.63 5.92 6.5 5.65 6.81 7.81 6.8 6.48 6.81 6.72
0.26 0.15 0.01 0.65 0.19
MgO
11 11.4 11.05 11.14 11.06 10.9 10.72 10.69 10.69 10.10 10.65 10.68 10.73 10.07 10.3 10.41 10.4 10.61 10.55 10.42 10.73 10.07 10.61 10.47 10.73 10.73 10.97 10.96
0.98 0.77 0.71 2.15 0.89
CaO
2.19 2.32 2.35 2.38 2.35 2.39 2.34 2.36 2.36 2.52 2.41 2.35 2.36 2.49 2.2 2.37 1.99 2.33 2.26 2.26 1.91 2.52 1.98 2.2 2.24 2.3 2.22 2.26
2.97 3.78 3.91 3.59 4.6
Na2 O
0.42 0.41 0.42 0.42 0.38 0.44 0.39 0.48 0.48 0.56 0.41 0.38 0.4 0.6 0.56 0.44 0.43 0.38 0.4 0.39 0.4 0.58 0.43 0.37 0.41 0.45 0.34 0.34
2.83 4.21 3.14 2.7 2.9
K2 O
5.54 4.52 5.23 4.36 5.1
H2 O or H2 OC (*)
Part B | 22
Table 22.1 (continued)
0.24 0.28 0.28 0.29 0.23 0.22 0.27 0.35 0.27 0.26 0.32 0.22 0.25 0.25 0.25 0.34 0.25 0.23 0.28 0.26 0.21 0.23
P2 O5
[22.17]
[22.16]
[22.6]
Reference
Natural Glasses Natural Glasses 775
Phonolitic glasses Erebus (Antarctica)
Basaltic glasses
Hawaiian basalt Kilauea eruption 1959
Quenched glasses Pele’s tears Hawaiian Pele’s hair 1.42 2.77 2.69 3.02 3.08 2.55 2.56 2.61 2.26 2.49 2.54 1.84 2.5 1.04 1.05 1.02 1.03 1.01 1.02 1.02 0.99 1.02 1.01 1.01 1.01 1
55.62 55.75 55.7 55.78 55.78 55.73 55.01 55.74 55.08 55.69 55.02 55.82
TiO2
50.9 48.82 50.26 50.04 50.79 49.61 49.5 49.35 49.41 50.34 49.95 54.08 49.13 54.95
SiO2
19.58 19.67 19.6 19.65 19.61 19.63 19.98 19.64 20.05 19.71 20.07 19.75
13.5 13.42 13.48 14.02 14.1 12.78 12.57 13.2 13.16 12.48 13.77 14.06 13.26 19.87
Al2 O3
Cr2 O3
1.7 1.55 1.72 3.17
Fe2 O3 or Fe2 O3;tot a
5.59 5.38 5.52 5.42 5.41 5.41 5.34 5.49 5.31 5.43 5.37 5.5
13.8 9.9 9.57 9.45 8.33 11.48 11.55 11.74 11.59 16.24 12.8 10.17 12.43 5.45
FeO or FeO tot a
0.28 0.28 0.29 0.27 0.28 0.26 0.26 0.27 0.27 0.28 0.28 0.28
0.16 0.23 0.27
0.25 0.18 0.17 0.17 0.12 0.11 0.18 0.17 0.18 0.29
MnO
0.86 0.83 0.85 0.83 0.8 0.83 0.82 0.84 0.8 0.82 0.84 0.85
4.67 9 7.04 6.93 6.78 8.9 9.32 8.69 8.95 5.03 5.22 5.81 7.14 0.82
MgO
1.85 1.88 1.92 1.84 1.89 1.83 1.89 1.86 1.86 1.84 1.89 1.74
8.81 11.32 11.45 11.44 10.26 11.51 11.34 11.01 10.99 9.47 9.9 9.53 12.35 1.9
CaO
8.82 8.85 8.73 8.86 8.8 8.85 9.09 8.82 9.09 8.8 9.04 8.96
2.83 2.25 2.22 2.42 2.6 2.14 2.11 2.2 2.15 3.05 3.95 3.41 2.2 9.1
Na2 O
5.61 5.64 5.58 5.63 5.7 5.67 5.71 5.61 5.65 5.64 5.57 5.35
1.39 0.58 0.45 0.57 0.48 0.5 0.49 0.52 0.54 0.19 0.25 0.47 0.34 5.65
K2 O
0.02 0.03 0.05 0.09 0.68* 0.33*
0.24 0.26 0.26 0.29 0.25 0.25 0.27 0.27
H2 O or P2 O5 H2 OC (*)
Part B | 22
Sample
[22.20]
[22.6]
[22.18] [22.19]
[22.6] [22.18]
Reference
Part B
Table 22.1 (continued)
776 Glass Families
Tachylyte (Kilauea) Lunar glasses Apollo 15 green C 15 green A 16 green 15 green B 15 green D 15 green E 14 green B 14 VLT 11 green 17 VLT 17 green 14 green A 15 yellow 14 yellow 17 yellow 17 orange
Quenched glasses
Sample
0.99 1.03 0.98 0.98 0.97 1.01 1.03 0.99 1.01 1.02 1.01 1.02 1.03 1.02 1.02 1.02 1.04 1.01 2.86 0.26 0.38 0.39 0.4 0.41 0.43 0.45 0.55 0.57 0.66 0.91 0.97 3.48 4.58 6.9 8.63
48 45.5 43.9 46 45.1 45.2 44.8 46 43.7 45.3 44.3 44.1 42.9 40.8 40.5 39.4
TiO2
55.75 54.93 55.61 55.9 55.63 55.41 54.97 55.12 55.09 54.85 55.17 55.12 55.11 55 54.73 54.94 54.95 55.35 49.99
SiO2
7.74 7.75 7.83 7.92 7.43 7.44 7.14 9.3 7.96 9.6 6.89 6.71 8.3 6.16 8.05 6.21
19.74 20.01 19.71 19.69 19.7 19.74 19.9 19.91 19.83 19.9 19.79 19.91 19.85 19.83 19.93 19.92 19.87 19.8 13.26
Al2 O3
0.57 0.56 0.39 0.55 0.55 0.54 0.54 0.58 0.46 0.4 – 0.56 0.59 0.41 0.63 0.67
Cr2 O3
1.88
Fe2 O3 or Fe2 O3;tot a
16.5 19.7 21.9 19.1 20.3 19.8 19.8 18.2 21.5 19.6 20.2 23.1 22.1 24.7 22.3 22.2
5.52 5.41 5.57 5.4 5.45 5.48 5.45 5.46 5.43 5.5 5.42 5.32 5.34 5.38 5.43 5.39 5.45 5.43 9.76
FeO or FeO tot a
0.19 0.22 0.24 – 0.22 0.22 0.24 0.21 – 0.26 0.23 0.28 0.27 0.3 0.25 0.28
0.29 0.27 0.29 0.28 0.28 0.28 0.28 0.28 0.27 0.28 0.27 0.27 0.27 0.28 0.28 0.28 0.27 0.28 0.16
MnO
18.2 17.2 16.9 17.2 17.6 18.3 19.1 15.9 17 15 19.5 16.6 13.5 14.8 12.6 14.7
0.84 0.82 0.93 0.83 0.92 0.83 0.84 0.83 0.84 0.84 0.82 0.83 0.83 0.83 0.84 0.83 0.82 0.83 8.39
MgO
8.57 8.65 8.44 8.75 8.43 8.15 8.03 9.24 8.44 9.4 7.4 7.94 8.5 7.74 8.64 7.53
1.75 1.89 1.8 1.75 1.81 1.79 1.86 1.88 1.88 1.88 1.88 1.87 1.88 1.86 1.89 1.87 1.9 1.87 10.61
CaO
0.04
0.1
0.04
0.27 0.1 0.45 0.42 0.39 0.41
0.03 0.07
5.41 5.67 5.42 5.43 5.5 5.62 5.65 5.59 5.65 5.65 5.64 5.64 5.65 5.68 5.73 5.67 5.65 5.64 0.54
K2 O
0.06 0.11
8.99 9.14 8.96 8.99 8.93 9.04 9.13 9.02 9.06 9.15 9.06 9.09 9.07 9.13 9.21 9.13 9.1 9.04 2.26
Na2 O
0.16
0.3
H2 O or P2 O5 H2 OC (*)
Part B | 22
Table 22.1 (continued)
[22.2]
[22.21]
[22.20]
Reference
Natural Glasses Natural Glasses 777
Georgiaites Bediasites DSDP 612 Muong Nong-type Georgia
Microtektites Victoria Land (Antarctica)
Lunar glasses 17 orange 74220-type 15 orange 17 orange 11 orange 14 orange 15 red 14 red 12 red Tektite Normal australites Normal indochinites HMg-australites Muong Nong-type indochinites Muong Nong (s.l.) 0.3
0.31 0.25
0.29
17.1 17.3 17.2 17.3 12.3 12.3 12.3 12.2 9.50–11.7 11.2–17.6 14.94 9.19
4.88 4.01 4.44 4 3.16 3.33 2.87 2.6 1.83–3.14 2.29–5.75 5.33 0.07 1.43
0.99 0.97 0.97 1.02 0.71 0.73 0.72 0.76 0.42–0.60 0.59–1.05 0.81 0.34
3.18–4.15
4.67–4.97 4.47–4.49 3.85–8.63 3.75 0.06
22.9 23.7 22.9 23.7 22.2 21.9 23.7 23.9 2.94–3.48 2.17–2.41 1.79–3.73 1.21
7.4 7.41 8.55 7.62 7.04 7.89 6.49 6.27
CaO
1.32–1.56 1.17–1.27 0.62–1.38 0.92
0.38 0.36 0.39 0.31 0.28 0.49 0.5 0.05
Na2 O
2.41–2.62 2.36–2.40 1.34–2.56 2.41
0.12
0.29 0.12
K2 O
4.31 3.47 3.31 3.52 1.99 1.95 2.22 1.89 0.37–0.69 0.37–0.95 1.2 0.59
3.2
3.97 3.66 3.71 3.91 3.14 2.8 2.74 3.44 0.40–0.69 0.49–0.96 0.68 0.44
4.08
0.22 0.21 0.27 0.23 0.25 0.29 0.26 0.26 1.00–1.53 1.20–1.84 0.6 0.72
0.24
0.73 0.81 0.88 0.8 0.93 1.18 1.25 0.89 2.22–2.51 1.60–2.43 3.52 2.53
0.9
1.19–1.65 1.03–1.63 0.77–1.07 2.24–2.55
2.16–2.23 2.00–2.04 1.83–7.95 1.43
14.9 14.9 11.6 14.3 14.5 12.1 13 13
MnO MgO
68.3 68.4 68.5 68.9 77 77 77.2 77.6 79.8–83.6 71.9–80.2 72.93 84.2
12.9–14.3 13.1–13.5 10.7–13.3 10.18
0.84
0.69 0.65 0.66 0.63 0.86 0.77
Cr2 O3 Fe2 O3 or FeO or Fe2 O3;tot a FeO tot a
4.6
0.80–0.83 0.72–0.89 0.66–0.77 0.63
70.4–72.4 72.9–73.3 64.8–77.0 78.3
5.79 5.63 7.62 5.68 5.69 7.15 4.81 4.6
Al2 O3
77.0–81.7 0.53–0.72 8.60– 11.41 67.5 1.02 17.6
9.12 9.12 9.3 10 12.5 13.8 15.3 16.4
TiO2
38.5 37.9 38.8 37.3 37.2 35.6 35.6 33.4
SiO2
H2 O or P2 O5 H2 OC (*)
Part B | 22
Sample
[22.3] [22.3] [22.3] [22.25]
[22.24]
[22.23]
[22.3] [22.3] [22.22] [22.3]
Reference
Part B
Table 22.1 (continued)
778 Glass Families
LDG
Spherules K-Pg
Tektite Moldavites Moldavites Moldavites Moldavite Ivory Coast Ivory Coast High Si-K glass
Sample
98.44 98.27 95.85 98.4 98
62.25 65.07 65.45 62.82 63.53 61.42 63.3
75.5–85.1 74.9–81.4 71.9–81.0 80.3 67.0–69.3 66.17–68.48 86 62.86
SiO2
0.08 0.17 0.18 0.12 0.197
0.71 0.62 0.63 0.69 0.63 0.71 0.68
0.24–0.74 0.31–1.40 0.23–0.50 0.322 0.52–0.6 0.54–0.61 0.47 0.67
TiO2
0.55 1.3 1.48 1.19 1.67
15.06 15.31 15.29 15.05 15.61 15.4 15.31
7.32–11.4 9.44–13.8 8.96–12.7 10.5 15.8–17.1 16.28–17.72 6.93 15.16
Al2 O3
0.01 0.01 0.03
MnO
0.09 0.12 0.98 0.12 0.11
5.4 5.14 5.03 5.34 4.87 5.32 5.44
2.77 2.28 2.35 2.63 2.33 2.75 2.58
1.34–2.74 1.13–2.06 1.52–3.73 1.69 2.64–3.93 2.98–4.39 1.15 2.64
MgO
1 cm), with typical aerodynamic shapes and very characteristic surface features (Figs. 22.8 and 22.9). Microtektites are microscopic tektites (< 0:1 mm) found in deep-sea sediments [22.4]. Based on their shapes it is possible to distinguish three types of tektites: Muong Nong-type (or layered), splash forms, and ablated/flanged tektites. Splash-form tektites (the most common form), include spheres, flattened ellipsoids, tear-shaped bodies (Fig. 22.8), rodshaped bodies (generally thickened at both ends), canoes, and saucer-shaped objects [22.92]. To date, four main groups of tektites, associated with separate impacts and strewn fields (SF), are known (e. g., [22.23, 24, 93, 94]): the North American, the Ivory Coast, the central European, and the Australasian (Fig. 22.10). The source craters have been located for three of the four tektite strewn fields, based on geographic location, geochemical evidences, and composition [22.95–97]. a)
The oldest strewn field is the North American (NA) field of 35:5 Ma age associated with the 40 km wide Chesapeake Bay impact structure [22.98] and includes bediasites, georgianites, Barbados and Cuba tektites, respectively found in Texas, Georgia, Barbados, and Cuba (Fig. 22.10). The central European (CE) or moldavite strewn field of 14:4 Ma age is associated with the Ries crater of about 24 km in diameter (Nördlinger Ries, Bavaria, Germany). There is another impact crater, the Steinheim crater, 3:8 km in diameter, located about 42 km west-southwest from the centre of Ries. These two craters are believed to have formed nearly simultaneously by the impact of a binary asteroid [22.99]. The Ivory Coast (IC) tektite strewn field is associated with the 1:07 Ma old Bosumtwi crater (10:5 km diameter, Ghana, Africa). The youngest SF, of about 0:8 Ma, is the Australasian one, for which no source crater has been identified so far. Tektites of the Australasian strewn field (AA) include australites, thailandites, indochinites, philippinites, and javanites and spread from the southeastern region of Asia down to Australia (Fig. 22.10). Recently, glass spherules (microtektites) were discovered on the Victoria Land transantarctic mountains (Antarctica), and there is clear evidence [22.24, 100, 101] that these microtektites represent a major southeastward extension of the Australasian strewn field. Even if no source crater has been discovered yet, several authors suggest a location for the AA crater in the Indochina region [22.102–105]. Three of the four tektite strewn fields known so far also present microtektites (diameter < 0:1 mm): the North American, the Ivory Coast, and the Australasian SF. These spherules have been found in deep-sea deposits (see, e. g., [22.4, 106–108]) and are very important for defining the extension of the strewn fields (e. g., [22.109]), for constraining the stratigraphic age of tektites, for providing an indication regarding the lo-
b)
Fig. 22.9a,b Photos of tektites, including (a) a moldavite (length 18 mm) and (b) two indochinites (length 25 mm)
Natural Glasses
22.2 Impact Glasses
CE NA IC AA
cation of possible source craters (e. g., [22.102]). Trace element abundances confirm that microtektites are genetically related to tektites in the associated strewn field [22.110], but microtektites usually show a wider compositional range than tektites. Glass [22.4] assigns the different methods of analysis used to explain the compositional differences between microtektites and tektites. A difference between microtektite and tektite samples was recently found by Giuli and coauthors [22.111]. The authors showed that some North American microtektites present a higher Fe3C =Fe2C ratio (up to 0.61), compared to the respective tektites, implying that, probably, different formation mechanisms are involved for the formations of such small objects [22.111]. Muong Nong-type tektites (MN—named after a region in Laos) are a subgroup of tektites that are unusually large (up to several tens of centimeters in size) and with layered structures. MN tektites are enriched in volatile trace elements (e. g., Cl, Br, Zn, Cu, Pb), present chemical heterogeneity (darker and lighter layers), and may contain relict mineral grains (e. g., corundum, quartz, chromite, and cristobalite) and bubbles [22.23]. Muong Nong-type tektites strongly differ from volcanic glasses because of the presence of shocked mineral inclusions, for differences both in major and trace element contents (e. g., REE patterns), very low water content, highly reduced iron, and the presence of 10 Be [22.112]. Koeberl [22.112] observed that Muong Nong-type tektites contain higher abundances of the most volatile elements (the halogens, Cu, Zn, Ga, As, Se, Pb) compared to splash-form tektites (the most common tektites). The presence of relict mineral grain and the relatively higher water amount in Muong Nong-type tektites suggest that MN have experienced the lowest temperatures of all tektites [22.112]. It is assumed that Muong Nong-type tektites were de-
posited closer to the source crater and that they derive from a greater depth in the target deposits than most other tektites [22.105]. The details of tektite and microtektite formation and of their distribution from the source crater are unknown and greatly debated. Numerical modeling indicates that high-velocity impacts (3540 km=s) into a dry target with impact angles of 30°–50° may provide the best conditions for tektite production [22.113, 114]. Indeed, the position of the strewn fields, with respect the inferred parent crater indicates that tektites formed after oblique impacts. However, the tektiteproducing impact processes still have several open questions [22.115] because physical and mathematical models are hampered by the limited information available (e. g., the importance of superheating) and because the impact process is a highly nonequilibrium and heterogeneous process. For instance, the exact target rocks from which tektites were produced are not known yet, because this would require an accurate understanding of the physical-chemical processes, which may alter the chemical composition of the target rocks during impact. Moreover, the extent of volatilization, the state of tektite material after impact melting, or the size distribution of the melt droplets [22.116] are still not understood. Engelhardt and coauthors [22.95] suggested that the tektite material is completely vaporized to a plasma state, and then the condensation from the plasma could form coalescing droplets. The hypothesis of tektite formation from a vapor plume might explain the ejecta homogeneity and also the rapidity of homogenization of large volumes and the long-distance transport. More recently, Johnson and Melosh [22.117] investigated droplet formation in impact-produced vapor plumes and defined a linear correlation between the size of the ejected droplets and the size of the impacting object.
Part B | 22.2
Fig. 22.10 Approximate location and extension of the four strewn fields: NA (North American), IC (Ivory Coast), CE (Central Europe) and AA (Australasian). The location of the known source craters are Chesapeake Bay (NA), Ries (CE) and Bosumtwi crater (IC)
787
788
Part B
Glass Families
22.2.2 K-Pg (KT) Spherules
Part B | 22.2
These small spherules (100500 m) that resemble microtektites were first detected in the CretaceousPaleogene K-Pg (formally known as KT—CretaceousTertiary) layer in Gubbio (Italy) [22.118] and are associated with the most recent major impact event on Earth. Around 6566 Ma ago the collision of an asteroid caused a massive extinction with an impact crater of about 180 km identified on the Yucatan peninsula, and which is known as the Chicxulub crater [22.119]. This large (cataclysmic) event was responsible for the formation of worldwide ejecta horizons and caused the end-Cretaceous mass extinction, around 66 Ma ago. K-Pg distal impact ejecta layers are associated with Ir enrichments, siderophile element anomalies, shock metamorphosed mineral (quartz grains, coesite and stishovite), and rock debris. Because of the poor preservation of the claystone K-Pg boundary, there was an early discussion about the origin of these spherules. Some authors supported the impact hypothesis (e. g., [22.120]), whereas others attributed an authigenic origin for those microspherules (e. g., [22.121]). However, Sigurdsson et al. [22.122], by studying the glasses preserved at the K-Pg layer at Beloc in Haiti, provide clear evidences of an impact event. Moreover, Koeberl [22.123] and Koeberl and Sigurdsson [22.28] also provided exhaustive geochemical data for the impact origin of these Haitian Si-rich glasses and reported the occurrence of rare inhomogeneous glasses with lechatelierite and other mineral inclusions, which are typical for an origin by impact [22.123]. In particular, the identification of planar deformation features (PDF) in quartz in the K-Pg boundary-event bed was the key for the acceptance of this layer as an impact horizon [22.124]. Usually, PDFs occur in silicate minerals, such as quartz and feldspars, which develop PDFs at pressures between 1015 and 35 GPa [22.23]. The study of the K-Pg boundary ejecta provided the most influence on the discussion about the importance of impact events with respect to the evolution of the planet and of life, and the detailed study of a K-Pg distal impact ejecta layers led to the discovery of one of the largest impact structures on Earth—the 180 km Chicxulub crater [22.116].
22.2.3 Younger Dryas Spherules The Younger Dryas (YD) event is the name of a hypothesized impact event that may have occurred at the beginning of the Younger Dryas ( 12:8 ka), and as emphasized by Bunch et al. [22.125], impact de-
notes a collision by a cosmic object either with Earth’s surface, producing a crater, or with its atmosphere, producing an airburst. This hypothetical impact event seems to be supported by several markers, which are listed by Firestone and coauthors [22.126]. The authors describe the occurrence of a 1470 ı C and from 10 to > 30 GPa [22.137]. In 2007, a crater-like feature (Kebira crater, Gilf Kebir region, Egypt) was discovered by using satellite images, and initially it was inferred as the source of LDG, because of its size, geographic location, and topography. However, almost immediately it was disregarded, since it lacked the geologic features associated with impact craters, such as impactites, breccias, and shatter cones. Darwin Glass Darwin Glass is found in a strewn field of about 400 km2 in western Tasmania (Australia). The age of this glass, estimated by Ar-Ar methods, is around 800 ka [22.142]. The glass generally occurs as irregular fragments or masses, but small glasses (spheres and teardrops < 5 mm) can be found across the Darwin SF. The color ranges from white, gray, light or dark green, dark brown, to black, and the glasses are generally vesicular and often exhibit flow structure marked by bands of elliptical vesicles [22.23]. Interestingly, the proportion of white glasses is greatest in the proximity of the crater, and the proportion of darker glasses increases with distance from the crater [22.143, 144]. The Darwin crater, a small ( 1:2 km) simple impact crater formed in sedimentary target rocks, has been proposed as the source of Darwin glasses [22.145]. Howard and Haines [22.146] carried out a detailed petrographic study of the crater-filling samples, but no conclusive evidence of shock metamorphism was found (e. g., shocked quartz grains, PDFs). The chemistry suggests the presence of two main glass groups: the first one richer in SiO2 (average 85 wt%) and depleted in CaO and Na2 O, and a second one with a lower average abundance of SiO2 and a significantly higher content of MgO and FeO [22.147].
789
Part B | 22.2
Libyan Desert Glass—LDG In an area of about 6500 km2 in southwest Egypt, close to the border with Libya, fragments of a natural silica-rich glass, known as Libyan desert glass (or LDG, Fig. 22.11), of an age of 2829 million years, is found [22.133, 134]. Since its discovery, early in the twentieth century [22.135], the origin of the Libyan desert glass still represents an unanswered enigma to all scientists and researchers. However, an origin by impact seems the most plausible mechanism. In fact, LDG fragments are thought to be the remains of a glassy surface layer, resulting from high-temperature melting of sandstones/desert sand, caused either by meteorite impact, or—to explain the absence of an impact crater— by airburst (shock melting caused by a cosmic object exploding in the atmosphere) [22.5, 136]. LDG is very silica rich (about 96:599 wt% SiO2 ; Table 22.1) and shows a limited variation in major and trace element abundances. The remaining few wt% are oxides of iron, titanium, calcium, and magnesium plus a few other oxides. LDG occurs as centimeter to decimeter-sized, irregularly-shaped, and strongly winderoded glass pieces (Fig. 22.11). The age of the LDG was mainly made by fission-track methods. Indeed, due to the low K content of the glass, the age errors from the K-Ar determinations are too high to be meaningful ([22.137] and references therein). The fission track dating from different investigation provides similar ages: 28:5˙2:3 to 29:4˙0:5 Ma [22.138], and 28:5˙0:8 Ma [22.133]. Evidences for an impact origin include the presence of detectable amounts of Ir [22.32] lechatelierite and baddeleyite [22.139] and, more in general, high pressure-temperature phases [22.140]. Moreover, the high concentration of platinum-group elements [22.32],
22.2 Impact Glasses
790
Part B
Glass Families
Part B | 22.2
Moreover, the second group is enriched in Ni, Co, and Cr, with contents higher than the surrounding sedimentary rocks. The enrichment in these elements (likely a meteoritic contamination), and the presence of coesite (high-pressure quartz polymorph) and lechatelierite, seem to confirm the impact origin of these glasses [22.23]. Recently, Gomez-Nubla et al. [22.144] carried out a detailed investigation of Darwin glasses by using Raman spectroscopy, energy dispersive x-ray fluorescence, SEM-EDS, and electron probe microanalysis. The authors reported that the same major elements were found in all the samples analyzed, with compositions ranging from SiO2 D 8090 wt% (excluding the SiO2 pure inclusions), Al2 O3 D 59 wt%, FeO D 24 wt%, MgO D 0:30:8 wt%, K2 O D 1:82:3 wt%, CaO D 0:010:03 wt%, and TiO2 D 0:350:6 wt% [22.144]. Data from Raman spectroscopy identified, in addition to the silica glassy matrix, small inclusions of ’-cristobalite and iron or iron/nickel oxides. In one specimen, the authors also reported the presence of secondary phases (formed or incorporated into the glass matrix after the impact, most likely due to weathering) [22.144].
151]. Some chemical compositions from the literature are reported in Table 22.1, and the studies suggest that fulgurites are typically enriched in SiO2 . During lightning strike in a mafic or ultramafic rock, SiO2 and TiO2 contents increase noticeably, and fulgurites formed in the sand dunes of the Libyan desert glass region have compositions that are similar to LDG. A subdivision of five groups of fulgurites has been proposed by Pasek and coauthors [22.7] based on the different morphology and petrology occurring as a result of target material composition. According to Pasek and coauthors [22.7], it is possible to divide fulgurites into four main types of morphologies (plus a minor type):
22.2.5 Fulgurites Fulgurite is a glass formed as a result of fusion of rock by lightning in many soils, and particularly wellknown fulgurites are the ones formed from desert sands. Usually, fulgurites consist of irregularly shaped tubes (Fig. 22.12) ranging from approximately 1 cm in diameter to 1 mm, but which may extend laterally or vertically for up to 10 m [22.148]. The chemical composition of fulgurites is determined by the extremely high melting temperatures (peak temperatures of lightning up to 39 000 K in the air and to heat target materials to temperatures around 2500 K) and very short heating times (heating rate of the order of 1000 K=s) [22.34, 149–
Fig. 22.12 Some fulgurite specimens with the characteris-
tic irregular tube shapes (square dimension D 5 mm)
Type I fulgurites are formed in quartz sand and usually have thin glassy walls; type I can contain one or two melts consisting prevalently of lechatelierite, and sometimes, also a SiO2 -rich melt with higher concentrations of Al and/or Fe. Also enrichments in Zr oxide- and a Fe-Ti oxide-rich glass has been reported in the groundmass [22.7]. Fulgurites type II has a lower amount of lechatelierite (< 50%) but higher glass thicknesses compared to fulgurites type I. The melt is more compositionally varied, because it has been formed in different environments to quartz sand soils (e. g., soils composed also of clays minerals, quartz, and/or small rocks) [22.7]. Type III consists of lechatelierite and feldspar glasses, and a calcite-rich matrix. Fulgurites type III are mostly found in calcite-rich soils and are the densest (average density 2:1˙0:5 g=cm3 , the density value reported is related to the density of the material as approximated by a whole fulgurite cylinder [22.7]) [22.7]. No zircons were observed in the type III fulgurites. Type IV fulgurites are heterogeneous melts with the outer portion consisting of unmelted (or partially melted) rocks and minerals. Type IV fulgurites usually form in bulk rocks and have densities similar to those of the target rocks. Type V droplet fulgurites are thoroughly mixed and have a homogeneous melt. The two main oxides contained in type V droplets are enriched in SiO2 and K2 O relative to the originating fulgurite, whereas other oxides are depleted [22.7].
Usually, the outer portion of a fulgurite tube is very rough, and this is attributed to fragments of unaltered, or partially melted, minerals and rocks (Fig. 22.13). On the other hand, the inner portion is mainly smooth and glassy (typically lechatelierite) and may also contain spherical inclusions; i. e., Pasek and Block [22.152] re-
Natural Glasses
22.3 Obsidian
791
Fig. 22.13 Photographs of a fulgurite sample. The inner part is more smoothed and has a heterogeneous glassy material, whereas the outer portion is very irregular. Length of the specimen: 5:5 cm
the oxide species with respect to the metals. However, the authors were not able to rule out other mechanisms, such as the presence of carbon, degassing of oxygen, or formation of nitrogen oxide gases. By shock experiments, Rowan and Ahrens [22.155] produced Fe, Si, and Mo-rich metallic microspheres embedded in a shocked glass. Thus, there is the possibility that shockwaves induce reduction. Jones et al. [22.151] artificially (triggered-lightning) produced fulgurite specimens composed of 99:9% pure binary oxides of manganese and nickel in order to study the reduction mechanisms, and while they observed the formation of nickel oxide particles, the manganese oxide fulgurite showed no metallic phase formation. Hence, the mechanism proposed by Essene and Fisher [22.148]—the thermodynamic stability of an oxide—is the most likely.
22.3 Obsidian The most common natural glass deserves a special section. Pliny the Elder, in his famous Natural History, first described obsiana, so named from its similarity to a stone found in Ethiopia. The shape, color, and properties of this volcanic glass (Fig. 22.14) have been key
factors for its use and contribution to human history. Indeed, in prehistoric times, it was widely used for cutting tools or arrowheads (Fig. 22.15), but also for the production of decoration and mirrors. Obsidian occurs in several geological settings [22.13], such as primitive and mature island arcs, active
Fig. 22.14 Obsidian from Lipari (I) (square dimension D
Fig. 22.15 Arrowhead made of obsidian (square dimension
5 mm)
D 5 mm)
Part B | 22.3
port iron phosphide spherules and Ca-P-Si oxide-rich grains in type II fulgurites. Several studies have reported the occurrence of metallic phases [22.148, 153, 154], and several explanations have been proposed to clarify the metallic oxide reduction occurring during fulgurite formation. Essene and Fisher [22.148] explained the occurrence of metallic globules rich in silicon, or spheroids of siliconbearing metals (99:5 at:% of metallic silicon phase with minor amounts of titanium, iron, and phosphorus), via thermodynamic calculations that indicate that extremely high temperatures (> 2000 K) and reducing conditions close to the SiO2 -Si buffer were needed. Thus, the formation of coexisting metallic and silicate liquids was attributed to thermodynamic instability— at high temperature and strong reducing conditions—of
792
Part B
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Part B | 22.3
continental margins, continental interiors, and oceanic extensional zones, and it occurs both as flows of several kilometers in length (e. g., exceptionally large obsidian flows in Oregon, USA) and as domes up to hundreds of meters high. There are a number of different types of obsidian occurring worldwide, with different chemical compositions. The average chemical compositions of some obsidians are reported in Table 22.1. Within each type, there is a restricted range of major-element abundances; however the minor and trace elements can show order-of-magnitude variations [22.13]. Since the composition of this glass varies from place to place, the study of the minor (and trace) elements has been particularly useful for archeologists. The origin of the most common natural glass is not a simple matter of fast cooling. The glass-forming processes of obsidian melt are strongly influenced by the contents of volatile components such as water, fluorine and chlorine, sulphur, and carbon oxides [22.6, 156]. Indeed, small variations in volatile content can cause notable changes in the physical properties, such as rheology, which strongly influences the flow dynamics of obsidian melts. Moreover, depending on various parameters such as temperature, pressure, chemical composition, water content, strain rate, and also microlite (acicular crystals typically less than 10 m in length) preferred orientation [22.157], obsidian may exhibit elastic, viscous, or brittle behavior [22.158]. There are many studies focused on the chemistry and hydration of obsidians, but curiously, there are not many studies on the magnetic, mechanical, and optical properties of these specimens that can provide strong insights on formation mechanisms and the nature of obsidians. Early work by Ericson et al. [22.159] provided an exhaustive study of 28 obsidian specimens and results from many techniques: thermal expansion, density measurements, Vicker’s hardness, chemical durability, electrical properties, and Mössbauer and infrared spectroscopy studies. The mechanical properties of obsidians are characteristic and differ from other glasses such as window glasses. However, the authors also reported that obsidian has high chemical durability, comparable to Pyrex, and high hardness, comparable with SiO2 glass [22.159]. Despite the dominant glassy matrix, obsidian specimens have several crystalline inclusions, such as feldspars, pyroxenes, silica (and polymorphs), Fe and/or Ti, and/or Fe-Ti oxides (e. g., hematite Fe2 O3 , ilmenite FeTiO3 , . . . ). In particular, obsidians have several coexisting paramagnetic, ferrimagnetic, and/or superparamagnetic phases. To explain the complex magnetic behavior of obsidian, recently, Mameli et al. [22.160] studied the magnetic and microstructural properties of 12 obsidian samples from Sardinia (I). By
coupling several techniques, the authors were able to discern that the presence of magnetite nanolites, dispersed into the obsidian glassy matrix, is responsible for the ferrimagnetism and superparamagnetism behaviours. Moreover, the coexistence of two other Feminerals may be responsible for the antiferromagnetic and paramagnetic behaviour [22.160]. Obsidian is a preferred material for provenance studies (to determine from which location an archaeological obsidian came), and in particular, there are several studies on obsidians’ geochemical composition, fission-track dating, and chemical analyses [22.161]. Moreover, Mössbauer, electron-spin resonance, Raman spectroscopies, and magnetization have been largely used in provenance studies [22.11, 162–164]. On the other hand, it is interesting to note that there are not many studies dedicated to the investigation of the redox state of obsidians. Indeed, as pointed out by Heide and Heide [22.6], many analyses have concentrated only on the determination of the total Fe content. Another interesting point of obsidians is their colour. The obsidian colour depends upon the presence of various transition elements along with the formation mechanisms, but obsidian is typically black or gray and sometimes occurs banded or streaky. However, it is possible to find several obsidian specimens with interesting optical properties, such as the so-called rainbow, sheen, or fire obsidian. Rainbow obsidian shows iridescence bands of various colors, ranging from red through purple. Ma et al. [22.165] investigated the optical properties of rainbow obsidians with several techniques, and they observed a correlation of the color bands both with the thickness and with the position of microcrystallites (pyroxenes or feldspars) within the samples. Moreover, they identified a thin-film interference as a possible cause of the rainbow effect. Arrays of crystallites produce interference effects, and the crystallites’ size and spacing control the rainbow effect. Sheen obsidian is usually black to dark brown and displays a single-color sheen, generally characterized by either a silvery or a golden hue. For a long time, the sheen was assumed to be produced by reflections from oriented bubbles. However, Ma et al. [22.165] found that two kinds of vesicles coexist in these obsidians: vesicles filled with a slightly different glass or unfilled. In conclusion, Ma and coauthors [22.165] attributed the sheen to differences in indices of refraction between the glassy obsidian matrix and the lower indices of refraction of either gas-filled or glass-filled vesicles. Fire obsidians have thin layers showing various colors. Indeed, under bright light, these glasses reflect colored bands resembling an iridescent oil slick. Ma et al. [22.166] reported that the iridescent lay-
Natural Glasses
22.3 Obsidian
793
ers were made of nanoparticles of magnetite (Fe3 O4 ) that increased the refractive index, giving rise to thinfilm interference and are the cause of the fire coloration [22.166].
22.3.1 Hydrated and Altered Obsidians
Fig. 22.17 Photograph of a pumice specimen from Glass Mountain (USA). The sample has a typical highly vesicular irregular texture (square dimension D 5 mm)
ter contents similar to that of perlite glasses [22.42]. A beautiful example for a combined obsidian–pumice deposit can be found at the Rocche Rosse on Lipari island (Italy). Usually, pumice samples have pale colors that range from white, gray, or blue, to darker colors of greenbrown or black, depending on the presence/amount of iron. The samples are highly vesiculated with a porosity of up to 90%, with the remaining solid part being mainly amorphous. As a comparison, the volcanic scoria is less vesiculated (denser), and thus it sinks rapidly, whereas pumice samples float on water. Bubbles form a percolating network at porosities between 3080 vol:%, depending on the melt viscosity, crystallinity, magnitude of shear, and bubble expansion rate [22.167–170]. Several studies have been carried out in order to explain the absence of vesicles in obsidian and, thus, to provide insights on the change in eruptive be-
Na2O + K 2O (wt %)
15 Phonolite
Trachyte
Tephriphonolite
10 Foidite
Tephrite basanite
5
Phonotephrite
Rhyolite
Trachyandesite
Trachydacite
Basaltic trachyTrachy- andesite basalt Basaltic andesite
Basalt
Andesite
Dacite
Picrobasalt
0 40
50
60
70
80 SiO2 (wt %)
Fig. 22.16 TAS diagram for obsidians, perlites, and pitchstones. From various references as indicated in Table 22.1. Symbols: Obsidian data from [22.13], from [22.9], from [22.12], from [22.10], from [22.11]. : Perlite/pitchstone
Part B | 22.3
Natural glasses are thermodynamically unstable at ambient temperatures and pressures, and they slowly hydrate through the diffusion of water into the outer surface and along cracks. Natural rhyolitic glasses hydrated at temperatures below the glass transition (Tg ) are volcanic glasses that have lately had a significant economic use in industry (e. g., supports of heterogeneous metal catalysts). The water-rich glasses are pumice, perlite, and pitchstone. Pumices are microvesicular, volcanic foam materials formed by decompression of volatile-rich melts [22.8]. Thus, pumices have compositions close to that of obsidian, while after ejection they release the enclosed gas, forming a porous material. Perlite is a hydrated obsidian, and the perlite deposits mostly occur as lava flows, dykes, and domes. Perlitic glass, which is relatively more altered, fractured, and contains water > 4 wt%, is often called pitchstone [22.15]. Rhyolitic obsidian glasses from different locations are plotted in the TAS diagram (Fig. 22.16), along with data for perlite and pitchstone, and it is possible to observe that the composition of the latter resembles that of obsidians (Fig. 22.16). Obsidian is frequently accompanied by the formation of pumice (Fig. 22.17). Indeed, pumice is usually considered to be foamed obsidian and often has wa-
794
Part B
Glass Families
Part B | 22.3
havior (from explosive to effusive) in silicic volcanic systems (e. g., [22.170]). Experimental works have shown that cooling and heating kinetics strongly control the release of gases of obsidian melts. Indeed, depending on the heating rate, an obsidian glass can transform into pumice or form a melt flow ([22.6] and references therein). By thermal analysis, Bagdassarov and coauthors [22.15] observed that the main factor governing the uniform vesiculation and expansion of perlites is due to the microfracture pattern developed during the dehydration of perlites below the glass transition temperature. Thus, the higher amount of water in perlite glasses is due to diffusion of meteoric water into the glass and not from the original magma. Denton et al. [22.171] report a study on the crystalline and volatile contents in obsidians and perlites. The authors observed that the volatile enrichment in perlites is often accompanied by secondary crystalline phases growth (zeolites). During devitrification the glass slowly crystallizes [22.172]. Figure 22.18 shows spherulites in black obsidians. Spherulites are confocal radial polycrystalline aggregates that commonly occur in glassy felsic materials [22.173]. Usually, there are several polymineralic aggregates, such as intergrowths of quartz, feldspar, and magnetite. The formation conditions of spherulitic textures and the kinetics of spherulite growth in natural silicate are still much debated. For example, Castro et al. [22.174] determined the kinetics of spherulite growth in island obsidians, and the water diffusion modeling yields spherulite growth rates of a few tenths to hundredths of a millimeter per day, depending on the temperature [22.174]. Watkins et al. [22.175] found that spherulites can grow on the order of days to months at temperatures above the glass transition temperature. By using several techniques, Arzilli et al. [22.173] demonstrated that the development of spherulites is dominated by heterogeneous nucleation, and the growth can occur in a short time in water-saturated trachytic melts, reaching 400 m diameter in a few hours [22.173].
22.3.2 Artificial Pumice: Foam Glass In Roman times—and still now—pumice was largely used for construction materials. For instance, Erdogan et al. [22.176] report the production of lightweight concrete with economic and environmental advantages by
Fig. 22.18 Photograph of spherulitic obsidians (length
4 cm; unknown locality). Spherulites are distributed homogeneously all over the samples with sizes ranging from 3.0 to 8:0 mm
using colemanite (a borate mineral) and pumice materials. Furthermore, in the present time, it is also employed both in industry and agriculture, as well as in cosmetics, for polishing, abrasive and exfoliating applications (e. g., exfoliating soaps, dental polishing compounds, filtration of drinking water, purifying oils, and odor removal). Artificial pumice (called different names, such as foam glass, porous glass, or cellular glass) can be produced industrially by decompression of volatilerich melts, where the gas component is ejected in the molten material at an appropriate stage during manufacture [22.177]. Foam glass has several advantages [22.177]:
Light weight Thermal and acoustic insulating properties Resistance to water in both liquid and vapor form Noncorrosive properties Massive reuse of glass wastes.
Nowadays, with the reduction of energy consumptions being one of the main challenges, the reuse of glass wastes for glass foam production enters into the concept of sustainability. For example, Ayadi et al. [22.178] used 99% glass cullet and only 1% CaCO3 (as foaming agent) and obtained a material with excellent thermal, acoustic, and mechanical properties: a 0:5 g=cm3 dense material characterized by low thermal conductivity (0:031 W=.m K/) and good acoustic properties [22.178].
Natural Glasses
22.4 Other Natural Glasses
795
22.4 Other Natural Glasses All glasses that sometimes cannot be classified as volcanic or impact related, and neither purely natural nor of inorganic origin are be grouped under others.
Detonation of nuclear weapons has created glasses, i. e., from the first atomic bomb test in Alamogorgo (Trinity test, 1945) or from the first underground nuclear explosion (Rainier test, 1957). The so-called trinitite glasses (first described by Ross [22.179]) are a record of the first atomic bomb blast on July 16, 1945 (Fig. 22.19). The resulting fireball that burnt the arkosic sand desert formed a crater glazed with green-fused silica sand. Ross [22.179] studied the optical properties of the amorphous layers and reported the occurrence of two different glasses. The first one with higher index of refraction (RI), and the other with a lower index of refraction (close to 1.46), indicating that this material was almost pure silica glass. Ross also recognized the occurrence of gray and red glasses (with dispersed copper). Several years later the early studies of Ross were confirmed and, according to Eby et al. [22.180], the detonation of the 21 kilotons plutonium bomb produced four different type of glass: 1. The top part of the layer mainly consisting of glassy and vesicular green fragments (Fig. 22.19) 2. A Cu-rich glass (red trinitite) containing metallic chondrules 3. Scoriaceous trinitite fragments and 4. Ejecta, which includes aerodynamically-shaped droplets, beads, and dumbbell glasses.
Fig. 22.19 Glass sample from the Trinity site, Tularosa
Basin, Alamogorgo (USA). This green trinitite fragment is glassy and vesiculated and is a product of the first atomic bomb blast on July 16, 1945. (square dimension D 5 mm)
Part B | 22.4
22.4.1 Glasses from Nuclear Explosions: Trinitite
The latter were compared to tektite and microtektites and Glass and coauthors [22.181] described many similarities between tektites and trinitite beads. Moreover, Giuli et al. [22.35] reported the Fe redox ratio (Fe3C =Fe2C ) in a trinitite glass to be close to 0.1, thus similar to tektite values. Many studies have been carried out on the radioactive nuclides present in the materials (e. g., [22.180, 182–184]). Indeed, the migration of actinides at historical test sites has been well studied, since it is closely related to the waste management and to the storage of high-level nuclear waste [22.185–188]. Eby et al. [22.189] recently published a detailed mineralogy and petrology study of the different trinitite glasses. The authors pointed out that to explain the physical processes occurring during the glass formation, two main factors must be considered: the temperature and the duration of high temperatures. Through macroscopic measurements and theoretical calculations, Hermes and Strickfaden [22.190] estimated backward to the yield, fireball temperature, fireball duration, heat in the rising fireball, and the spread of ejecta from the Trinity test. The authors estimate that the yield of the Trinity event was 918 kt, the average fireball temperature was 8430 K, and the crater depth was approximately 4 ft [22.190]. Moreover, Hermes and Strickfaden [22.190] report that the duration of heating was very short ( 3 s), and this could explain why some minerals (zircon and quartz grains) were only partially melted. Interestingly, Eby et al. [22.189] reports the occurrence of quartz with planar deformation features, which is typical evidence of shock metamorphism in impactites. Based on the mineralogy, petrology of the glass samples, and on previous time and temperature estimations, Eby and coauthors concluded that at the instant of detonation, “pressures of at least 8 GPa and temperatures of > 8000 K occurred in the fireball” (c.f., [22.189]). The study of the first nuclear glass, beside applications for waste management and storage of high-level nuclear waste, has nuclear forensic applications, since it provides information on the type of device that was detonated and its origin. Recently, Molgaard and coauthors [22.191] produced synthetic nuclear glasses, comparable with trinitite glasses, as surrogates that could be used to simulate a variety of scenarios (simulated nuclear event parameters such as, fuel type, weapon yield, and emplacement scenario), and could be used as a tool for developing and validating (nuclear) forensic analysis methods.
796
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Glass Families
22.4.2 Friction Melts: Frictionites/Pseudotachylite
Part B | 22.4
The formation of friction melts is associated either with large impact structures, earthquake-generated layers, or very large rock avalanches (e. g., see the reviews [22.192, 193]). A generic definition for pseudotachylite (the generic name for friction melt) is dense rock produced in the compression and shear associated with intense fault movements, involving extreme mylonitization (i. e., the process of formation of a fine-grained rock produced by bending/internal slip of grains, and recrystallization) and/or partial melting. [22.192]
Friction melts (and especially those with a pumice texture) were first associated exclusively to volcanic origin or to impact events. Differences between impactrelated and fault-related pseudotachylites occur in their thickness and their formation history (single-slip event, multiple stick-slip motion) [22.194]. The exclusive volcanic origin or impact-associated origin hypotheses have both been ruled out from the study of pumiceous rocks from Ötz Valley (Köfels landslide, Austria [22.195, 196]). Indeed, in the last decades several studies have focused on fault related friction melts (fault pseudotachylytes) that form by coseismic highvelocity friction (Fig. 22.20). Well studied fault pseudotachylites are from giant rockslides in Himalaya (Nepal) and Köfels (Austria). Masch and Preuß [22.198] report on a detailed study of both events, and they observed that glass matrix is chemically heterogeneous with schlieren (elon-
gate segregations of mafic minerals), bubbles, and rock relicts from the parent material (partial to almost complete melting of host rocks of granitic to granodioritic composition). Moreover they report the occurrence of glasses with pure quartz, plagioclase, and alkali-feldspar compositions. It is worth mentioning that the giant rockslides in the Himalayas (with a dislocation of 170 m) caused the formation of a homogeneous glassy crust of thicknesses between 1 and 3 cm [22.198]. Weidinger et al. [22.199] reviewed 19 basal deposits of giant rockslides, many of which had both micro-breccias and frictionite melts. For the formation of fault pseudotachylite, the estimated melting temperatures derived from the mineral geothermometer of microlites (mineral systems used to estimate the temperatures) or from the chemical compositions of matrices (e. g., [22.200]). Artificial pseudotachylites have been produced by direct high-speed friction experiments (e. g., [22.194, 200, 201]), and the estimated melt temperatures of natural and experimental pseudotachylites are in the range of 7501400 ı C [22.200]. In their review, Heide and Heide [22.6] report melting temperatures of 1700 ı C because of the presence of lechatelierite inclusions in frictionite melts.
22.4.3 Bioglasses: Amorphous Hydrated Silica Biomineralization processes form biogenic materials that are considered eco-friendly, which, thus captured the attention either of organic-/inorganic-chemists or materials scientists. Carbonate and phosphate are the most abundant biominerals in nature. On the other hand, amorphous SiO2 , even if less abundant in biomineralizing organisms, has been widely studied (biomimetic studies—the use of models that partially reproduce the natural conditions of biomineral formation [22.202]). The low-temperature hydrated variety of silica, opal (SiO2 nH2 O), is a biomineral. Opal is composed of differing amounts and arrangements of structural units of amorphous SiO2 , water, and the quartz polymorphs: cristobalite, and tridymite [22.203], and it is possible to distinguish three types:
Fig. 22.20 Microphotography of a pseudotachylite layer
(dark layer) from the Nojima fault, Japan [22.197] (rectangle dimension D 0:5 mm)
Opal-C, with cristobalite Opal-CT, with cristobalite and tridymite Opal-A, x-ray-amorphous opal.
Moreover, the amorphous opal-A can be further divided in opal-AN (e. g., hyalite) and opal-AG with an amorphous silica gel structure. In a maturation process (Ostwald ripening) opals are transformed as follows
Natural Glasses
([22.203] and references therein) opal-AG ! opal-CT ! opal-C ! microcrystalline quartz:
devoted to biogenic silica. In the following, a few examples are provided. Bio-Optical Filters/Fibers Siliceous spicules from siliceous sponges are composed of siliceous layers superposed in a stratified pattern around a central axial filament, c.f., [22.202], and are excellent light transmitters and very good optical bandpass filters. Indeed, exclusively wavelengths between 6151310 nm can pass through these natural spicule fibers [22.207]. Moreover, [22.208, 209] demonstrated that some spicules have compositional variations in the glass/organic composite and a variation in the refractive index profile: with a high refractive index in the spicule core and a low refractive index in the outer portion (cladding), thus presenting optical properties similar to those of commercial telecommunication fibers [22.208, 209]. Metal Oxide Production The enzymes involved in silica formation have attracted increasing attention because of their potential applications in nano-biotechnology and biomedicine [22.206]. Indeed, these enzymes, at low temperature and near neutral pH, are also able to catalyze nanoparticles of metal oxides, such as TiO2 , ZrO2 , nanocrystalline Ga2 O3 , GaOOH, and also nanocrystalline perovskitelike barium oxofluorotitanate (BaTiOF4 ) [22.206, 210, 211].
22.5 Insights into the Structure and Properties of Natural Glasses This section is an attempt to highlight the structure and the physical properties of natural glasses. Natural glasses, being a multicomponent system, require a deep understanding of many factors, thus the understanding of the evolution of natural glasses must be considered an interdisciplinary problem.
22.5.1 Physical Properties of Silicate Glasses/Melts When talking about the physical properties of magma, one of the most important parameters is the viscosity (), i. e., the measure of a fluid’s resistance to flow. It controls magma flow rates, rates of volatiles’ exsolution, rates of diffusion and crystal growth, and volcano morphology. Depending on the bulk chemistry, we have a wide range of viscosities, as reported in Fig. 22.21, which shows the variation of the viscosity against the reciprocal temperature for a pure silica glass (SiO2 ) and some glasses with mineral compositions of three tec-
797
tosilicate and one pyroxene compositions (respectively, Ab D NaAlSi3 O8 , Or D KAlSi3 O8 , An D CaAl2 Si2 O8 , Wo D CaSiO3 ). Nevertheless, for a constant composition, there are rapid variations in viscosity when crystals form and/or gas bubbles exsolve: e. g., the viscosity of basaltic melts varies from < 102 to > 104 Pa s for Hawaiian to Plinian eruptions, respectively ([22.6] and references therein). The rheology of an obsidian flow is a key parameter governing the textural and structural evolution in obsidian flows. Rhyolitic magmas have a greater melt viscosity due to the high silica content, with respect to basaltic melts (Fig. 22.21a). Viscosity of rhyolitic magma ranges from 108 to 1011 Pa s at temperatures of 700750 ı C, although viscosity strongly decreases with increasing volatile content (e. g., H2 O, CO2 ). In tektites, the study of physical properties (e. g., density, viscosity), along with the redox conditions, can provide insights on their thermal history. Figure 22.21b shows the variation of the viscosity () against the
Part B | 22.5
Several siliceous marine organisms exhibit discontinuous, three-dimensional frameworks of short chains of SiO4 tetrahedra, bonded with apical hydroxyls [22.204]. The most studied biomineralized species are fossil diatom frustules and sponge spicules: e. g., [22.205] studied the evolution of biogenic silica produced in marine environments both for fossils and living organisms, and they identify two different networks. The fossils have a highly condensed and wellorganized silica network, whereas the living diatoms are much less condensed, with the silica network suggested to be linked to the bio-organic components of the cell, in agreement with the biosilicification mechanisms [22.205]. Usually, the production of silica requires high temperatures and/or pressures, and/or extreme pH ranges. On the other hand, living organisms are able to form silica under ambient conditions, with low temperatures and pressures and almost neutral pH. Hence, understanding the biosilica formation mechanisms is of high importance for applications [22.206]. Indeed, the structure and the evolution of diatoms have several implications for materials science and palaeoenvironmental research, and in the last years many studies have been
22.5 Insights into the Structure and Properties of Natural Glasses
798
Part B
Glass Families
b) log η (poise)
a) log η (poise) 2300 1950
1600
T (K)
1250
14
2300 1900
T (K)
1100
1500
14 SiO2
SiO2 12
Chi
12
Part B | 22.5
Or
Or
Ab
Bas 10
10
8
8
6
6 Ab
Rhy 4
Mol
4 And
2
2 An
0
4
An
Wo 5
6
7
8
9
10 11 104/T (K –1)
0
4
Wo 5
reciprocal temperature for a moldavite (Mol) and an Australasian tektite (Chi). These tektites are highly polymerized glasses, and the measurements show the very high viscosities of these glasses and their nearly Newtonian behaviour (Fig. 22.21b). It is interesting to note that the Australasian tektite has a viscosity an order of magnitude lower than the moldavite. The compositions and some properties for the unpublished data shown here are given in Table 22.2. To clarify the nature of natural glasses, in addition to physical properties and redox conditions, it would be helpful to understand the evolution of the glass structure upon cooling. The glass properties depend on the process by which it is formed, and close to Tg chemical/physical properties are extremely sensitive to temperature [22.214]. For example, in silica this dependence can be well represented as Arrhenian behaviour (exhibiting approximate linearity), and the liquid is called strong. On the other hand, a liquid is called fragile, where the fragility reflects what degree the temperature dependence of the viscosity deviates from Arrhenian behavior. The glass transitions of the two tektites considered here (taken for log D 12 Pa s) are 1014 and 1070 K, respectively, for chi and mol, and by using the Angell plot [22.215] it is possible to make a Tg -scaled Arrhenius (Tg =T) representation of liquid viscosities (Fig. 22.22).
6
7
8
Fig. 22.21a,b Low and high-temperature measured values of viscosity for SiO2 , tectosilicates (Ab, An and Or), and wollastonite (Wo) melts as a function of reciprocal temperature. (a) Viscosity measurements for a rhyolitic (Rhy), an andesitic (And) and a basaltic (Bas) melt are reported as symbols. (b) The viscosity measurements for a moldavite (Mol) and an Australasian tektite (Chi) are reported as symbols. Lines are only guides for the eyes. Data in Table 22.3 and from [22.212]. Viscosity measurements were obtained following [22.213]
9 10 104/T (K –1)
log η (poise) 12
Chi Mol
10 8 6 4
SiO2
2 Ab 0 0.4
An Or
0.6
Wo
0.8
1.0 Tg/T
Fig. 22.22 Tg -scaled Arrhenius representation of liquid
viscosities showing Angell’s strong–fragile pattern. Both tektites, Mol and Chi exhibit approximate linearity and, thus, a nearly Arrhenian behaviour
Strong liquids, such as SiO2 , exhibit Arrhenius behaviour, which is indicative of a temperatureindependent activation energy [22.214]. Both moldavite (Mol) and Australasian (Chi) tektites show a nearly linear behaviour, and thus they can be considered as strong liquids.
Natural Glasses
22.5 Insights into the Structure and Properties of Natural Glasses
799
Table 22.2 Composition (wt%) and some properties for tektites (Chi and Mol) shown in Figs. 22.21b, 22.22, and 22.23 Moldavite (Mol) 78.12 9.56 0.32 2.73 2.09 0.01 0.06 1.61 0.36 3.49 2.3717 1070 13.4
Indochinite (Chi) 71.85 12.94 0.83 2.48 1.96 0.03 0.14 4.44 1.21 2.43 2.4277 1014 11.9
Table 22.3 Experimental viscosity data (log ) in Pa s measured at each temperature (T) in K for tektite samples and a basaltic glass (Bas) Basalt (Bas) T (K) 936.4 946.7 952.6 956.2 962.5 967.0 976.3 987.7 999.5 1002.2 1011.8 1020.8 1029.8 1473.0 1523.0 1573.0 1623.0 1673.0 1723.0 1773.0
log 12.53 12.16 11.83 11.64 11.37 11.17 10.86 10.53 10.15 10.05 9.80 9.52 9.21 1.43 1.15 0.90 0.67 0.47 0.29 0.13
Moldavite (Mol) T (K) 1059.1 1069.8 1089.7 1101.4 1117.8 1128.2 1135.8 1138.8 1156.2 1157.2 1168.1 1181.7 1192.1 1203.8 1221.7 1223.6 1850.0 1900.0 1950.0
22.5.2 Structure of Silicate Glasses The knowledge of the structure of silicate melt/glass, along with its composition and temperaturedependence is crucial to explain many properties of silicate systems. In the literature, there are several investigations on the structure of silicate glasses, and many studies (e. g., [22.14, 216, 217]) refer to the stuffed tridymite model proposed by Taylor and Brown [22.218]. Based on x-ray radial distribution analysis of glasses in the system SiO2 -Ab-Or, Taylor and Brown [22.218] found several similarities and
log 12.27 12.02 11.53 11.25 10.87 10.64 10.48 10.44 10.06 9.99 9.84 9.58 9.40 9.20 8.98 8.90 3.31 3.08 2.86
Indochinite (Chi) T (K) 1004.9 1020.4 1021.5 1036.7 1038.2 1058.3 1066.2 1080.2 1090.2 1099.8 1107.7 1122.4 1138.2 1144.1 1873.2 1923.2 1973.2 2023.2 2073.1
log 12.24 11.86 11.77 11.44 11.35 10.89 10.67 10.34 10.20 9.92 9.71 9.48 9.20 9.08 3.30 3.10 2.97 2.73 2.53
suggested a stuffed tridymite-like structure for anhydrous Si-rich melts. This model is similar to that proposed by Konnert et al. [22.219], where silica glasses have a tridymite-like bonding topology based on sixmembered rings of SiO4 tetrahedra (c.f., Taylor and Brown [22.218]). Wright et al. [22.220] made distinctions between silica (fulgurite) and silicate glasses (obsidian and tektite) based on neutron diffraction measurements. Okuno et al. [22.221] studied molten and untreated obsidian and also found that the basic structures of samples may be explained by the stuffed tridymite model. Heide and co-workers [22.222] studied obsid-
Part B | 22.5
SiO2 Al2 O3 TiO2 CaO MgO Cr2 O3 MnO FeO Na2 O K2 O Density (g=cm3 ) (˙0.0005) Tg (K) Sconf (Tg ) (J=.mol K/)
Basalt (Bas) 48.37 14.52 2.98 10.28 8.59 – – 10.80 3.11 1.86 2.830 948 7.41
800
Part B
Glass Families
Part B | 22.5
ian with wide angle x-ray scattering and concluded that the structure of obsidian is a superposition of quartz and cristobalite-like structures, in agreement with studies by Wright and Leadbetter [22.223]. A powerful tool to investigate the structure of silicate glasses is Raman spectroscopy, which provides information on the short to medium-range order. Raman spectra have been measured on a collection of obsidians, tektites, and related glasses. These spectra will be presented and discussed in terms of the interpretative framework that has developed from studies on synthetic glasses [22.224]. Raman spectra of silicate glasses consist of three major portions: a high wavenumber region extending from 800 to 1200 cm1 , which provides information on the T–O–T stretching mode (e. g., tetrahedron T D Si, Al), an intermediate-wavenumber region from 400 to 650 cm1 , which gives information on the T–O–T rocking, bending mode, and ring distributions, and a low wavenumber region below 250 cm1 , which provides information on tetrahedral arrangement (see [22.224] for more details). The high wavenumber region, also referred to as the Q-range, contains polarized bands that have been associated with the symmetric stretching motions of silica tetrahedra. Indeed, the short-range order of silicate glasses can be described through the abundance of the Qn species, where n is the number of bridging oxygens atoms (BO) and Q represents the fourfold coordinated cation—e. g., Si, Al (i. e., fully polymerized D Q4 ). A fully-polymerized silica glass (SiO2 —Fig. 22.23) network has only weak high-frequency bands (frequency range 9801350 cm1 ), but may be characterized by its strong asymmetric band in the lowfrequency region (400500 cm1 ) [22.225, 226] and from the well-pronounced D1 ( 490 cm1 ) and D2 ( 600 cm1 ) defect lines, associated with the breathing modes of SiO4 and SiO3 -rings, respectively (see SiO2 in Fig. 22.23). By decreasing glass polymerization (e. g., by adding network modifiers), the main peak in the low-frequency region increases in intensity and shifts to higher wavenumbers, whereas the Q-range increases in intensity because other bands, related to different Q species (Q3 , Q2 ), appear in the 8001200 cm1 region [22.224]. Figure 22.23 shows the unpolarized Raman spectra of some Si-rich natural glasses in comparison with a synthetic pure SiO2 glass. For some spectra, the background was subtracted since there was a strong luminescence both with the excitation lasers at 488 nm and 532 nm. The shape of the Raman spectra for the natural glasses presented here fit well with those reported in the literature (Fig. 22.23) [22.11, 34, 144, 227].
The spectra for fulgurite were collected from the sample reported in Fig. 22.13. A cross-section of the specimen was cut, and the Raman spectra were collected with an excitation laser at 532 nm. The spectra for the inner glassy portion (fulgurite) and for the outer part (fulgurite2) are reported in Fig. 22.23. Both spectra resemble that of the pure SiO2 glass, with the typical doublet 440490 cm1 . Raman spectra for obsidian samples are reported in Fig. 22.23. Bellot-Gurlet et al. [22.11] measured obsidians from the western Mediterranean area by Raman spectroscopy. The authors suggest that the detailed analysis of the Raman spectra in the high-wavenumber region could be used to distinguish between obsidians originating from Pantelleria and Sardinia and/or Lipari and Palmarola, and thus that Raman spectroscopy could be a complementary technique in archaeological obsidian provenance studies. The obsidian samples, from three different locations, shown here have Raman spectra similar to those reported by BellotGurlet et al. [22.11], with the Pantelleria sample showing a strong contribution around 975 cm1 . This feature could be ascribed to the high amount of iron in these glasses [22.228]. The Raman spectra for two different opals (Fig. 22.23) show strong sharp peaks corresponding to the main presence of cristobalite, but also some contributions from a minor presence of tridymite can be observed, in agreement with the observation made by Ilieva et al. [22.229]. Indeed, the two sharp peaks, respectively at 410 and 226 cm1 , are related to a cristobalite-type atomic arrangement, whereas the small broader contributions at 350 and 300 cm1 are related to a tridymite-type arrangement [22.229]. Hyalite (Fig. 22.23) is the opal-AN form (Sect. 22.4.3) and the Raman spectrum highlights the amorphous character, since it presents much broader bands, and no sharp peaks typical of crystalline phases. The trinitite Raman spectrum (Fig. 22.23) was collected on the outer portion of the specimen reported in Fig. 22.19. The trinitite sample is particularly interesting because it seems to consist of the overlap of a highly polymerized glass and of a more depolymerized glass, since it presents both the characteristic features: D lines and Q2 –Q3 peaks. LDG (Fig. 22.23) has the same features of the silica glass Raman spectrum. Galeener et al. [22.230] show how the fractional areas under the lines D1 and D2 vary with fictive temperature in pure SiO2 , and they estimated a fictive temperature for LDG 1000.C50/ ı C and a cooling rate ranging from a few minutes to a few days. However, in this early work, the authors stated that further work on the subject should be done, especially on the effect of radiation, relaxation time, and
Natural Glasses
22.5 Insights into the Structure and Properties of Natural Glasses
801
Intensity (arb. u.) D1
Fulgurite
Fulgurite 2
Moldavite
Indochinite
Tektite AA
Obs Pantelleria
Obs Palmarola
Obs Unknown
D2
300
300
600
600
900
1200
300
600
900
1200
300
600
900 1200 Raman shift (cm –1)
Darwin glass
Hyalite
Opal
Trinitite
LDG
Opal 2
900
1200
300
600
900
1200
300
600
900 1200 Raman shift (cm –1)
Fig. 22.23 Raman spectra for some natural silicate glasses and for a pure SiO2 glass in the range 3001250 cm1 . The shape of the spectra change depends on the polymerization of the glasses and on the presence/amount of other elements (such as Fe)
Part B | 22.5
SiO2
802
Part B
Glass Families
Part B | 22.5
pressure on the D lines. Champagnon et al. [22.227] measured Raman spectra for some natural glasses, and they show a correlation between the position of the Boson peak (at very low frequency: near 4060 cm1 ) and the intensities of the D defect lines. Knowledge of the relationship of the defect lines to the Boson peak can help us understand the fictive temperature, and in turn, the thermal history. The high spatial resolution provided by Raman (micro-)spectroscopy is well suited for the study of heterogeneous samples. Many silicic obsidian specimens contain only very small amounts of crystallized phases, even if it is unusual to find glass samples completely devoid of crystals, and often the crystalline assemblage includes Ti and Fe oxides. We show an example of Raman mapping done on a spherulitic obsidian sample on the boundary between the crystalline portion (spherulite) and the glass portion (map dimension 50 m 30 m in Fig. 22.24). In Fig. 22.24, the photo of an obsidian specimen, along with the microscopy image of the mapped portion and some of the Raman spectra collected (seven discrete points) in the range 2001000 cm1 are reported. All the spectra, and in particular the glass portion, have a strong luminescence (likely caused by the presence of transition elements and REE) at higher wavenumbers (above 1000 cm1 ). Moving from the spherulite to the glass part, we observed the presence of feldspar minerals (blue and violet points), but also the presence of magnetite/ilmenite and hematite (orange, green, and red points). The spectra for the glassy portion (black and cyan points) have the same contributions observed for the other obsidians. The detection and the study of Fe-Ti oxides is very important, because these oxides are particularly susceptible to variations in the redox conditions.
a)
–30
–20
–10
0
10
20
30 Position (μm)
b) Intensity (arb. u.)
22.5.3 Redox of Natural Glass and Reduction During High-Energy Events There are many studies (experimental and theoretical) devoted to the understanding of melt/glass redox equilibria, since the proportion of each species occurring in the melt is controlled by the bulk composition, temperature, oxygen fugacity, concentration, and presence and amount of volatiles and other redox species. Zotov [22.217] reviewed the techniques employed to study the structure of natural glasses and of the elementspecific spectroscopic methods used to investigate redox and coordination of different major, minor, and trace elements in natural volcanic glasses. Most of the studies were carried out on the fourth most abundant element in the Earth (Fe), since it is the only major ele-
200
400
600
800 1000 Raman shift (cm –1)
Fig. 22.24 (a) Photo and light microscopy images of an obsidian specimen and the crystalline portion (spherulite). (b) Raman spectra collected both in the glassy and crystalline parts are reported. In addition to the glass portion it was possible to identify feldspar minerals (blue and pink points), and magnetite/ilmenite, and hematite (orange, green, and red points)
ment with more than one electronic configuration—the oxidation state and the spin state (e. g., [22.231–234]).
Natural Glasses
temperature XAS data at the Fe K-edge (see [22.244] for details on the experimental procedure). Fe redox kinetics were studied in these highly polymerized glasses/melts from room temperature (RT) to 1680 ı C, and the data obtained were compared to the theoretical model of Kress and Carmichael [22.231]. The XAS data analysis and the Fe redox estimation were carried out according to the procedure reported in Cicconi et al. [22.245, 246] for synthetic glasses. At room temperature the indochinite tektite shows, as expected, a Fe3C =†Fe ratio close to 0 ( 0:05˙0:05, Fig. 22.25), in agreement with XAS studies done on several samples by Giuli et al. [22.89–91]. When heated up at temperatures just above Tg (1014 K), the tektite Fe redox ratio increases up to 0.55 (˙0:05) (nonequilibrium conditions), and by further increasing the temperature to 1500 K and maintaining it as long as needed to reach the equilibrium, the redox ratio goes up to Fe3C =Fe tot 0:7.˙0:05/ (Fig. 22.25). By additionally increasing the temperature, the Fe oxidation state starts to decrease, in good agreement with the trend suggested by the theoretical model of Kress and Carmichael [22.231] (K&C) for such compositions at ambient pressure (Fig. 22.25). Of course, being in an oxygen-depleted atmosphere (reducing conditions) will move the Fe buffer to lower temperatures. However, to reach this very high amount of reduced iron, and to preserve it even in the glass, it would be reasonable to consider that the temperatures approached values higher than 2000 K, Fe3+/Fe tot 25 727 1.0
1227
1727
T (°C) 2227 K&C XAS
0.8
0.6
0.4
0.2
0.0 298 1000
1500
2000
2500 T (K)
Fig. 22.25 Fe redox ratio versus T. Circles represent the
theoretical Fe3C =†Fe values calculated for the indochinite tektite composition by using the model of Kress and Carmichael [22.231], K&C. The squares are the Fe3C =†Fe estimated from the XAS data analysis at high temperatures, whereas the empty square represents the value at room temperature ( 0:05˙0:05)
803
Part B | 22.5
The data obtained from collision of cosmic objects, or from an airburst, or from lightning (i. e., tektites, impact melts, trinitite, fulgurites) suggest that these events led to the loss of oxygen and, consequently, to the production of extremely reduced melt phases. Indeed, the high temperatures, speeds, and heating/cooling rates produce exceptional alterations in the rocks involved. Wilding et al. [22.235] determined the quench rate for distal ejecta (tektites) by calorimetric measurements and reported a cooling rate of a few degree/s at temperature around the glass transition temperature. Wasserman and Melosh [22.154] report similar values from simulations of simplified systems and a blocking temperature when the evaporation rate of the liquid becomes so slow that there is no time for the phases to equilibrate. If this blocking temperature happens at a temperature higher than 2800 K, O2 gas will be lost from the liquid, leaving the remaining liquid reduced [22.154]. The knowledge of the fraction of reduced phases (metallic Si or reduced iron and phosphorous) in glasses, created from such high-energy events, could provide constraints for the formation temperatures and thus help to shed some light on the major physical and chemical processes occurring. Many early studies on tektites report Fe3C =Fe2C values between 0.02 and 0.23 (e. g., [22.88, 236–238]). In a study by Schreiber et al. [22.238], with the use of three different methods, the authors estimated the Fe redox ratio values in Australasian tektites and reported iron in those glasses to be almost all Fe2C . Moreover, by remelting the samples at different temperatures and under controlled reducing conditions, they tried to constrain the T–f O2 (oxygen fugacity) regimes for tektite formation. More recent studies on tektites have been carried out by using different techniques: e. g., Mössbauer, ESR (electronspin resonance), XAS (x-ray absorption spectroscopy) (e. g., [22.89–91, 111, 239–241]). As has already been stressed, except for few early studies, all the investigations carried out point to Fe in tektites being highly reduced. Only recently, by studying several microtektites from the three different strewn fields, Giuli et al. [22.111, 242] reported the occurrence of higher Fe3C =Fetot ratios for some North American microtektites. Since alteration of the specimens was ruled out by further analyses (i. e., water content) a different mechanisms was proposed (interaction of melt droplets with a H2 O-rich vapor plume). A slightly different Fe redox state was also reported for MN-type tektites. These glasses have lighter and darker layers, with the lighter ones enriched in Al and Fe with respect the darker ones. Giuli et al. [22.243] report that MN dark layers are slightly more oxidized with respect to the light layers. An attempt to understand the redox ratio variations for tektites has been made by collecting high-
22.5 Insights into the Structure and Properties of Natural Glasses
804
Part B
Glass Families
and the cooling rate must have been in the order of a few K=s. These observations suggest that further studies must be done in order for us to fully understand the mech-
anisms occurring during these high-energetic events. Experimental data on simplified systems along with thermodynamic models could help to understand the main factors involved.
Part B | 22
22.6 Conclusions and Future Directions The study of natural glasses has led to many important discoveries for technological applications, like in the case of nuclear waste management and biomimetic studies. Indeed, since the dawn of humanity, humankind tried to first understand first and then to reproduce natural processes, and sometimes scientists achieved to exceed what nature does. Hence, we hope that this chapter has provided fresh impetus for the understanding/study of natural glasses, not only in the framework of geosciences, but also for many practical uses, or, in general, to provide useful insights into processes involved in the manufacture of glasses. The key information on natural glasses provided here offers a basis for better synergy between disciplines such as Earth sciences and materials science. Indeed, the cooperation between researchers from dif-
ferent sectors could provide the ideas needed for moving forward. Acknowledgments. Some of the data here shown were acquired at the FAME beamline, and we thank the European Synchrotron Radiation Facility (Grenoble, France) for provision of synchrotron radiation facilities. The authors thank D. de Ligny and G. Henderson for the useful discussions, B. Cochain for help during the HT XANES experiments, and J. Stebbins for the Libyan Desert glass sample. MRC thanks E. Guillaud for pictures of natural glasses and S. Wolf for useful discussions on biomimetic materials. DRN thanks J.C. Bouillard, Curator of the Collection de Minéraux University Pierre and Marie Curie, Paris, for providing fulgurite samples.
References 22.1
22.2
22.3
22.4
22.5
22.6
22.7
22.8 22.9
R.A. Weeks, J.R. Underwood, R. Giegengack: Libyan Desert glass: A review, J. Non-Cryst. Solids 67, 593–619 (1984) J.W. Delano: Pristine lunar glasses: Criteria, data, and implications, J. Geophys. Res. Solid Earth 91, 201–213 (1986) C. Koeberl: Geochemistry and tektites and impact glasses, Annu. Rev. Earth Planet. Sci. 14, 323–350 (1986) B.P. Glass: Tektites and microtektites: Key facts and inferences, Tectonophysics 171, 393–404 (1990) T. Aboud: Libyan Desert Glass: Has the enigma of its origin been resolved?, Phys. Procedia 2, 1425– 1432 (2009) K. Heide, G. Heide: Vitreous state in nature—Origin and properties, Chem. Erde 71, 305– 335 (2011) M.A. Pasek, K. Block, V. Pasek: Fulgurite morphology: A classification scheme and clues to formation, Contrib. Mineral. Petrol. 164, 477–492 (2012) R. Gill: Igneous Rocks and Processes—A Practical Guide (Wiley-Blackwell, Chichester 2010) J. Keller, R. Djerbashian, S.G. Karapetian, E. Pernicka, V. Nasedkin: Armenian and Caucasian obsidian occurrences as sources for the Neolithic
22.10
22.11
22.12
22.13
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Maria Rita Cicconi Dept. of Materials Science and Engineering Friedrich-Alexander University Erlangen-Nürnberg Erlangen, Germany [email protected]
Maria Rita Cicconi is a Postdoctoral Research Associate in the Glass group of the Department of Materials Science and Engineering at the FAU Erlangen-Nürnberg, Germany. She obtained her PhD in Experimental Mineralogy in 2010 from the University of Camerino (I). Her research interests include the use of vibrational and synchrotron-based techniques to study structure, redox, optical and physical properties of glasses and melts.
Daniel R. Neuville Institut de Physique du Globe de Paris CNRS-IPGP-USPC Paris, France [email protected]
Daniel Neuville is a Senior Research Director at CNRS-IPGP, where, since 2014, he heads the geomaterials group. In 1992, he obtained his PhD in Geochemistry (University Paris Diderot, IPGP). He studies the thermodynamic and rheological properties of glasses, crystals and melts by linking their high-temperature structure to macroscopic properties relevant for applications in earth and materials sciences.
813
Bioactive Gla 23. Bioactive Glasses
Leena Hupa, Xiaoju Wang, Siamak Eqtesadi
1. Their characterization in vivo and in vitro 2. Clinical experiences and physical properties to be taken into account in the fabrication of the end products 3. In particular, bioactive glass-based scaffolds for tissue engineering. The development of bioactive glasses will be discussed from the materials science point of view. However, one important goal is to explain the various requirements of bioactive glasses due to their special application areas—implantation inside or in contact with the human body.
23.1 23.1.1 23.1.2 23.1.3 23.1.4 23.1.5 23.1.6
Bone Composition and Structure........ Elemental Composition of the Human Body ................................................ Bone Composition ............................. Biological Apatite and Apatite on Bioactive Glasses ............................... Cortical and Cancellous Bone .............. Bone Cells ......................................... Mechanical Properties of Bone............
815 815 815 815 816 816 816
23.2 23.2.1 23.2.2 23.2.3 23.2.4
Bioactivity ........................................ Bioactive Glass—Tissue Interactions ..... Structure of Bioactive Glasses ............. Reactions at Bioactive Glass Implants.. Effect of Ions on Cellular Processes ......
817 817 818 818 819
Composition versus Properties of Silicate Glasses ............................. 23.3.1 Crystallization Tendency ..................... 23.3.2 Hot-Working Properties ..................... 23.3.3 In Vitro Properties.............................. 23.3.4 In Vivo Properties ..............................
821 822 822 822 825
23.3
23.4 23.4.1 23.4.2 23.4.3
Sol–Gel Silicate Bioactive Glasses ....... Sol–Gel Chemistry ............................. Monoliths of Sol–Gel Bioactive Glasses Nanoparticles and Nanofibers of Sol–Gel Bioactive Glasses ............... 23.4.4 Mesoporous Bioactive Glasses .............
826 826 827
23.5
Phosphate-Based Bioactive Glasses ...
830
23.6
Borate-Based Bioactive Glasses .........
831
23.7
Scaffolds for Tissue-Engineering Applications........ Requirements for Bone Tissue Scaffolds .................... Scaffold Fabrication Techniques .......... Postassembly Thermal Treatment ........
23.7.1 23.7.2 23.7.3
Bioactive Glasses in Clinics and Health Care ................................ 23.8.1 Synthetic Bone Graft Granules and Putties ....................................... 23.8.2 Borate Glass Microfibers for Healing Chronic Wounds................ 23.8.3 Bioactive Glass Particulates as Additives in Toothpaste..................
827 828
833 834 834 838
23.8
23.9
839 839 840 841
Summary and Outlook ......................
841
References...................................................
842
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_23
Part B | 23
This chapter summarizes the development of bioactive glasses as implant materials designed to interfacially bond with bone tissue as components of tissue engineering devices that activate and guide the healing and regeneration of damaged or diseased soft and hard tissue. The main ideas and findings of the almost 50 year history of bioactive glasses are discussed, with the main emphasis on the melt-derived silicate-based glasses in clinical use today. In addition, sol–gel glasses and also phosphate and borate glass compositions are introduced. The goal is to cover some fundamental concepts to be taken into account in the development of products consisting of bioactive glasses:
814
Part B
Glass Families
Part B | 23
Bioactive glasses discovered by Prof. Larry Hench et al. in the late 1960s were specifically tailored to chemically bond with bone without a thin fibrous capsule, which typically develops around bioinert metal and polymer implants [23.1, 2]. In general, the word implant refers to any material that is inserted or grafted inside or on the surface of the body. When intended to replace a missing body part, the implant is called a prosthesis. Fibrous tissue formation is a foreign body reaction, which prevents proper integration of a bioinert implant with the host bone and therefore may lead to failure of the bone or the implant with time [23.1, 2]. Bioactive glasses are not inert but capable of forming a mechanically strong bond with the living tissue as a consequence of several reaction steps occurring on the glass surface and in the interfacial solution. Today, we know that inorganic ions released from the glass surface affect cellular processes. Bioactive glasses are thus imperative components of future tissue engineering devices. Bioactive glasses interact with living tissue in a manner that stimulates and aids healing, regeneration and growth of a diseased or injured tissue, especially bone. Fundamentally, bioactive glass is a biomaterial. Williams defines biomaterials as: A substance that has been engineered to take a form which, alone or as part of a complex system, is used to direct, by control of interactions with components of living systems, the course of any therapeutic or diagnostic procedure, in human or veterinary medicine [23.3].
For the desired interactions with the tissue, some properties of the bioactive glasses must considerably differ from the properties of domestic, flat, optical, etc. glasses. The most significant difference is that the bioactive glasses are designed to dissolve in physiological solutions in a controlled manner, while compositions of most other glass families are selected to be practically inert in their target use. a) CaO 9% Na2O 13%
MgO 6%
SiO2 72%
P2O5 6%
b)
The new implant material, bioactive glass, was designed to be accepted primarily by bone. The glass consists mainly of the same oxides as conventional silicate glasses, but the proportions between the oxides Na2 O, CaO and SiO2 markedly differ from the conventional counterparts. Bioactive glasses often also contain phosphorus, which is an essential element in the human body. Figure 23.1 presents an overall comparison of the share of oxides in typical soda-lime and bioactive glasses. After almost 50 years of research and development, certain bioactive glass compositions have found several clinical applications especially in bone grafting [23.4, 5]. Autogenous bone, i. e., bone harvested from the patient, is the gold standard to treat and heal diseases, defects, and trauma in bone reconstruction surgery. Utilization of autogenous bone is limited by morbidity at the donor site, the limited amount of bone available, and the additional procedure needed. Alternatives to autogenous bone are allogenic bone (from same species), xerogenic bone (from another species, usually cow), and synthetic materials. Bioactive glasses are considered as synthetic and safe bone graft substitutes. The implants studied for tissue regeneration typically have a three-dimensional (3-D) biomimetic architecture of interconnecting porosity to enable infiltration, attachment and proliferation of cells, and vascularization of the growing tissue as well [23.1]. These socalled scaffolds provide mechanical and shape stability to controlled tissue growth. Ideally, if fabricated of bioactive glasses, the scaffold degradation kinetics can be tailored not only to provide space for the growing tissue but also to release inorganic ions to stimulate and support the tissue growth. Because of the low content of the glass network former SiO2 and the high amounts of the network modifiers CaO and Na2 O the first melt-derived bioactive silicate glasses easily crystallize during the forming processes. This crystallization challenges their versatile fabrication into various product forms using traditional
SiO2 45%
CaO 24.5%
Na2O 24.5%
Fig. 23.1a,b Typical share of oxides in (a) soda-lime and (b) bioactive glasses (in wt%)
Bioactive Glasses
fast-degrading glasses for especially soft-tissue applications in the borate system [23.12, 13]. For all the compositions studied in the silicate, phosphate and borate glass-forming systems, an essential criterion is the active interaction of the particular glass composition with cellular processes via predetermined ion release and controlled degradation. This chapter reviews the properties and requirements of bioactive glasses. The main emphasis is on melt-derived compositions from the standpoint of glass manufacture and properties but also some commercial applications and research efforts to develop novel products will be introduced. In addition, different techniques for fabrication of porous tissue-engineering scaffolds from bioactive glasses will be covered. Detailed discussion of the various aspects of bioactive glasses can be found in several textbooks: Bioactive Glass: Materials, Properties and Application [23.14], Bio-Glasses: An Introduction [23.15], Introduction to Bioceramics (2nd edn.) [23.16] and Bioactive Glasses: Fundamentals, Technology and Application [23.17].
23.1 Bone Composition and Structure 23.1.1 Elemental Composition of the Human Body The first bioactive glasses were developed to integrate with bone without the formation of scar tissue separating the glass implant from the tissue [23.1, 2]. Why would living bone form a chemical bond with an inorganic silicate glass? Obviously, the glass composition must be chemically compatible with the bone. For this, the glass must consist of elements that are naturally present in high concentrations in the bone and the body. The human body consists of: 1. The basic elements O, C, H and N 2. The physiological elements Ca, P, K, S, Na and Cl 3. The trace elements Si, Mg, Fe, F, Zn, Cu, : : :
23.1.2 Bone Composition Bone is a composite of an inorganic mineral, hydroxyapatite (HAP), and an organic phase, which mainly consists of collagen, noncollagenous proteins, bone cells and water. Simplified, the composition of biological HAP crystals can be described with the formula of geologic HAP, Ca10 .PO4 /6 .OH/2 with the stoichiometric ratio of Ca=P D 1:67. However, the biological apatite is a calcium-deficient and carbonate-substituted
mineral known as hydroxyl-carbonate apatite (HCA), (Ca,Mg,Zn,Na,K)10 (PO4 ,CO3 )6 (OH,F,Cl,CO3 )2 . The formula for HCA shows examples of possible substitutions of metal cations for Ca and anions for carbonate and hydroxide ions.
23.1.3 Biological Apatite and Apatite on Bioactive Glasses The biological HCA crystals in bone have the same composition as the HCA crystals, which form at the surface of the bioactive glasses during incongruent dissolution in the extracellular fluid (body fluid outside the cells) [23.1, 2]. Ultimately, formation of an outer layer of HCA crystal is a result of the poor chemical durability of the glass [23.18]. Thus, the discovery and development of bioactive glasses is the outcome of detailed understanding of the influence of glass composition on its surface reactions in aqueous solutions and how these reactions can be exploited in new types of implant materials for bone surgery. Although the HCA layer may partly retard the dissolution, bioactive glasses degrade with time and provide space for the regenerating tissue. Interestingly, the dissolution products, i. e., ions released from the bioactive glasses, have been found to play an important role in activating the genes that stimulate the regeneration of living tissue [23.19].
815
Part B | 23.1
hot-working techniques. Several other oxides such as K2 O, MgO and B2 O3 have been added into the formulations for easier manufacture of the 3-D devices and fibers [23.6]. The compositions containing the network formers P2 O5 or B2 O3 are known also as bioactive phosphosilicate glasses or bioactive borophosphosilicate glasses. P2 O5 and B2 O3 affect the structure, hotworking properties, and the cellular responses of the glasses as well. However, since silicate compositions are bioactive also without these oxides [23.7], the compositions with SiO2 as the main network-forming oxide will be referred to as bioactive silicate glasses in this chapter. Increasingly detailed knowledge of the role of inorganic ions in both bone and soft-tissue regeneration has led to the development of new glass compositions doped with different elements [23.8, 9]. The rather slow degradation of silicate glasses has encouraged the tailoring of totally resorbable devices based on the phosphate system for soft and hard tissue applications [23.10, 11]. Another trend has been to design
23.1 Bone Composition and Structure
816
Part B
Glass Families
Fig. 23.2 The Dense cortical bone outer layer
structure of bone (reprinted from [23.4], with permission of Elsevier)
Femoral shaft
Exposed porous cancellous bone
Part B | 23.1
Patellar surface
1 mm
Medial condyle
23.1.4 Cortical and Cancellous Bone HCA gives the bone its rigidity and it comprises 6070% of the dry mass of the bone [23.4]. Bone comprises two different types of tissue: the outer shell of bone is dense and is referred to as compact or cortical bone, while the inner core is comprised of a porous cellular structure called cancellous or trabecular bone, as shown in Fig. 23.2 [23.4]. Cortical bone is highly dense, having a porosity of 510% and a wet apparent density of 1:99 g=cm3 . Contrary to cortical bone, cancellous bone is highly porous, typically 7590% with a wet apparent density of 0:051:0 g=cm3 [23.20–23]. Cancellous bone consists of an interconnected network of trabeculae of about 50300 m in diameter. The porosity of cancellous bone is the total volume that is not occupied by bone tissue and is usually filled with marrow. The change from compact to cancellous bone is usually clear and takes place over a small distance in which intermediate porosities are found.
23.1.5 Bone Cells Bone is a living material that is continuously regenerated throughout human life. Every year, approximately 10% of bone mass is renewed in response to the stresses applied to bone itself. The process of bone regeneration involves two types of cells: osteoclasts that resorb bone tissue and osteoblasts that synthesize bone. If osteoclasts are too active, bone demineralizes too quickly, and some diseases such as osteoporosis may occur [23.24]. Demineralization can also occur around
Lateral condyle
1 cm
stiff bioinert implants. The third type of bone cells, osteocytes, originate from osteoblasts, which have become surrounded by the bone matrix. Osteocytes are responsible for the bone maintenance process.
23.1.6 Mechanical Properties of Bone Materials used for orthopaedic prostheses have to bear high cyclic loads and are principally selected for their mechanical resistance. Because of the complexity of bone structure, finding an implant material with a good match to the mechanical properties of the bone is difficult. While polymers exhibit elastic moduli relatively close to bone values, their low strength limits the number of potential applications [23.25]. In contrast, the elastic modulus of inert ceramics and metals used in current orthopaedic implants is higher, at least by an order of magnitude, than that of bone. The mechanical properties of human bone are shown in Table 23.1. Table 23.1 Summary of the mechanical properties and
porosity of human bone [23.26–29] Material property Compressive strength (MPa) Tensile strength (MPa) Compressive modulus (GPa) Young’s modulus (GPa) Fracture toughness p .MPa m/ Porosity (%)
Cancellous bone Cortical bone 212 100230 15 0:121:1
50151 11:517
0:10:5 0:10:8
710 212
5090
510
Bioactive Glasses
23.2 Bioactivity
817
23.2 Bioactivity 23.2.1 Bioactive Glass—Tissue Interactions Understanding the interactions of synthetic implants with tissue was one of the starting points of bioactive glass development. The interactions were divided into four responses according to the interlocking and attachment of the implant to tissue [23.30]:
Bioactive glasses are not only nontoxic, but they form an interfacial bond and dissolve with time as the released ions support and also stimulate tissue growth. For these interactions, the ion release kinetics and the reactions at the surface of glass must take place in a controlled manner. Too rapid dissolution leads to excess concentrations of released ions. This prevents integration of the implants with the tissue because of the ever-retreating material surface. In addition, too high ion concentrations may induce toxic effects [23.31]. Conversely, too slow dissolution does not provide an ionic concentration high enough to stimulate cellular responses. Osteoconduction and Osteoinduction Osteoinductive, or osteoprodutive materials are capable of inducing bone formation in locations outside the skeleton while osteoconductive materials allow growth of adjacent bone along the surface of the material [23.2, 26, 27, 32]. Osteoinduction implies the recruitment of immature cells and the stimulation of these cells to develop into preosteoblasts. The process in which osteoproductive glasses enhance bone formation through a direct control over genes that regulate cell cycle in bone formation is called osteostimulation [23.2]. Classes of Bioactivity Traditionally, bioactive glasses have been divided into two classes according to their capability to guide and stimulate bone growth. Class A refers to glasses which exhibit both osteoinductive and osteoconductive properties. Conversely, in class B bioactivity only osteoconduction occurs, which requires only extracellular responses, due to slower interfacial reaction. Table 23.2 summarizes some characteristics of A and B classes of bioactivity [23.33].
1. They contain less than 60 mol% SiO2 2. They have high Na2 O and high CaO contents 3. They have a high CaO/P2 O5 -ratio. These compositional features made the surface of the glass highly reactive when exposed to aqueous solutions [23.26]. The most rapid rates of tissue bonding were obtained for glasses containing 4552 wt% SiO2 . In this compositional range, a bonding to both soft and hard (connective) tissue occurred within 510 days. Bioactive glasses or glass-ceramics containing 5260% SiO2 required a longer time to form a bond to bone, and did not bond to soft tissues. Compositions with more than 60% SiO2 did not bond either to bone or to soft tissues, and elicited formation of a nonadherent fibrous interfacial capsule. The compositional dependence of bone bonding and soft-tissue bonding for glasses in the system Na2 O-CaO-P2 O5 -SiO2 is presented in the ternary phase diagram with a constant amount of 6 wt% P2 O kept for all the compositions in Fig. 23.3 [23.2]. The composition of Bioglass® 45S5 is also indicated in the figure. As pointed out by Hench and Greenspan [23.1], this diagram is a kinetics compositional phase diagram, not a thermodynamic equilibrium phase diagram. A thermodynamic equilibrium phase diagram gives boundaries for different crystalline phase assemblages present in the system, while the kiTable 23.2 Classification of bioglasses according to bioac-
tivity [23.33] Class A Osteoinductive and osteoconductive Rapid bonding to bone Enhanced bone proliferation Bonding to soft connective tissues
Class B Only osteoconductive Slow bonding to bone No enhancement of bone proliferation No bonding to soft connective tissues
Part B | 23.2
If the material is toxic, the surrounding tissue dies If the material is nontoxic and biologically inactive (nearly inert), a fibrous tissue of variable thickness forms If the material is nontoxic and biologically active (bioactive), an interfacial bond forms If the material is nontoxic and dissolves, the surrounding tissue replaces it.
Compositions of First Bioactive Glasses The first bioactive glass composition developed by Hench in the late 1960s is known as glass 45S5 or Bioglass® [23.2]. The chemical composition of 45S5 is (in wt%): 45SiO2 , 24:5CaO, 24:5Na2 O and 6P2 O5 . The name ‘45S5’ refers to the glass composition: 45S in the code indicates the glass contains 45 wt% silica while the final 5 gives the Ca=P molar ratio of this composition [23.30]. In development of the first bioactive glasses, several compositions in the system SiO2 -CaO-Na2 O-P2 O5 were tested. Three key compositional features of these glasses distinguish them from traditional Na2 O-CaO-SiO2 glasses:
818
Part B
Glass Families
netics compositional diagram of bioactive glasses gives boundaries between mixtures of similar relative reaction rates with tissue. The equilibrium phase diagram was developed for melt-derived bioactive glasses. In general, the composition limits of bioactivity for the sol–gel derived glasses are much wider [23.34].
23.2.2 Structure of Bioactive Glasses
Part B | 23.2
Structural Units, Qn The basic building block in the silicate glass structure is the SiO4 tetrahedron with Si in the middle and oxygen ions in each corner. The tetrahedra are connected to each other via shared oxygen corners, the so-called bridging oxygens. In quartz glass, each corner is shared while in glasses containing network-modifying oxides such as Na2 O and CaO, some of the linkages between the tetrahedra are broken. This leads to nonbridging oxygens (NBOs) and depolymerization of the glass structure. The tetrahedra are commonly referred to as Qn units where n gives the number of bridging oxygens connected to the neighboring tetrahedra. In Q4 units, each tetrahedron shares all four oxygens with its neighbor while a Q0 annotates isolated silicate ions with no shared oxygens. Introducing network modifiers breaks the bridging oxygen bonds thus creating NBOs and increasing concentrations of Q3 , Q2 , etc. The concentration of nonbridging oxygen in the bioactive glasses is high due to its high concentration of the network modifying oxides Na2 O and CaO. As verified with 29 Si magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, the Q2 species dominate among the Q units present [23.35, 36]. In contrast, the network of conventional soda-lime glasses mainly consisting of Q3 and Q4 units is less disrupted. The more disrupted bioactive glass structure shows poor chemical durability and high crystallization tendency. In general, glass structure can be used to describe its properties, but also the size and charge of the ions affect the property values. Recently, molecular dynamics (MD) simulations have been used successfully to describe the structure of bioactive glasses. Also, MD has been employed to predict properties such as ion migration at the glass surface in aqueous solutions [23.37, 38]. The increasing fundamental knowledge of glass structure is becoming an important tool for future predictions of glass properties. Network Connectivity Structure-sensitive properties such as bioactivity, crystallization tendency, and glass transition temperature .Tg / have been correlated with the network connectivity, which gives the number of NBOs per network-forming element. For silicate glasses, the network connectivity,
NCSi , can be calculated according to (23.1) [23.36, 37]. NCSi D
4SiO2 C 6P2 O5 2.M2 O C M0 O/ ; (23.1) SiO2
where M2 O and M0 O are network modifiers and each oxygen refers to its molar amount in the glass. The equation assumes that each Si has four bridging oxygen ions and NBOs decrease the network connectivity. The structural studies using 31 P MAS NMR spectroscopy have verified that phosphorus in the silicatebased bioactive glasses is predominantly present as the orthophosphate ion, PO3 4 . Thus, it increases the number of bridging oxygens as the charge of the ion is balanced by modifier cations [23.36, 39, 40]. Vitreous silica consisting to 100% of Q4 units has NCSi D 4 while for Bioglass® NCSi D 2:11 and Q2 is the dominating structural unit with its share of 89%, with the remaining as Q3 units [23.36]. The network connectivity does not take into account the size and bonding strength of the network modifying ions and is thus suitable for calculating only approximate property values.
23.2.3 Reactions at Bioactive Glass Implants Bioactive glasses dissolve in extracellular fluid according to the same mechanisms as in other aqueous solutions, i. e., ion exchange, hydrolysis and hydration, followed by precipitation. The reactions are controlled by several parameters such as temperature, pH, solution composition, solution flow, etc. In the body environment of constant temperature, the flow of the solution in the implantation site is an important factor, since it directly affects the pH and ion changes in the solution surrounding the implant. The pH of the extracellular fluid is buffered around 7:4 by several simultaneously active systems including proteins, carbonate buffer, phosphate buffer, etc. The reactions of bioactive silicate glasses are usually divided into 12 sequential stages, of which the first five take place at the glass surface, after which biological mechanisms start to affect the reactions and finally lead to bone bonding [23.1, 30]: 1. The glass first reacts incongruently, i. e., shows rapid preferential leaching of alkali .NaC / and alkaline earth .Ca2C / ions from the glass surface through ion exchange reactions with HC or H3 OC from the solution. These diffusion-controlled reactions lead to formation of silanol groups (Si–OH) on the glass surface, i. e., reaction (R1). SiO MC (glass) C HC (aq) ! SiOH(glass) C MC (aq)
(R1)
Bioactive Glasses
2. The pH of the interfacial solution increases in (R1) and leads to attack of the glass network, and to dissolution of silica into the solution according to (R2). Simultaneously, incongruent dissolution continues (R1). In the glass 45S5, the surface group formations according to (R1) and (R2) can be observed within a few minutes after the implantation. SiOSi(glass) C OH (aq) ! SiOH(glass) C SiO (glass)
(R2)
Reaction stages 15 lead to the formation of an inner layer rich in hydrated silica and an outer layer of polycrystalline HCA at the surface of the degrading glass. These reactions take place in vivo (in living organism) but also in vitro (in solutions mimicking the extracellular fluid). The growing HCA layer provides an ideal substrate for the subsequent cellular reaction stages 612, taking place only in biological solutions containing biomolecular growth factors, collagen fibers, etc. [23.1]: 6. 7. 8. 9.
Adsorption of biological moieties in the HCA layer Action of macrophages Attachment of osteoblast stem cells Synchronized proliferation and differentiation of osteoblasts 10. Generation of matrix 11. Matrix crystallization (biomineralization) 12. Bone formation. The nanosized HCA layer on the glass surface allows for attachment of cells and proteins, especially col-
lagen fibers [23.1]. Osteoblasts, the bone-forming cells proliferate, differentiate and secrete collagen within the growing HCA layer. These cellular reactions lead to bonding of the HCA crystals to the collagen fibrils and finally to mineralization of the HCA layer to form new bone tissue. Firm bonding of the glass to the tissue takes place only if the reactions at the glass surface and the cellular reactions leading to new bone formation are synchronized, i. e., take place at the same rate [23.1, 2, 30]. The early experiments also demonstrated that bioactive glasses bond to soft tissues as well through the HCA layer [23.2]. In both cases, formation of the dual silica and HCA-rich layers is the primary requirement for tissue bonding. Both soft-tissue and bone bonding have been reported for compositions with no more than 52 wt% SiO2 while bonding to only bone was achieved with glasses containing up to 60 wt% SiO2 (Fig. 23.3). The glasses that form a strong chemical bond to living tissue are today commonly known as bioactive glasses.
23.2.4 Effect of Ions on Cellular Processes Formation of an HCA layer on the glass surface in vitro is an often-used indicator of bioactivity [23.41]. The composition of Bioglass® was selected to provide a large amount of CaO with some P2 O5 in a Na2 O-SiO2 matrix, which consequently gives rapid formation of HCA owing to the great solubility of the glass [23.2]. This composition would also release ions, which are needed in bone tissue formation. Silicon dioxide, the main component of the formulation, releases Si, a nontoxic element, which would be accepted by the body and be resorbed with time. However, today we know that controlled dissolution of Si species is one key feature of bioactive silicate glasses. Release of both Si and Ca species are important not only in the formation of the HCA layer but also to upregulate and activate seven families of genes in osteoprogenitor cells (mesenchymal precursor cells capable of producing osteoblasts and osteocytes) during the cell cycle [23.19, 42]. For activation of the genes associated with bone regeneration, these ions must be leached within certain limits for a critical period of the cell cycle. For Bioglass® 45S5, osteostimulation was reported for the concentration range of 1330 ppm Si and 6090 ppm Ca [23.19, 43]. Principles of gene activation by bioactive glasses have been reviewed by Hench [23.2, 19] and Jell and Stevens [23.44]. Since the pioneering paper by Xynos et al. [23.42] several research papers have discussed the role of ion dissolution products on gene activation in bone and soft-tissue regeneration. The effect of Si on the cellular
819
Part B | 23.2
3. Polycondensation reaction between neighboring surface silanol groups leads to the formation of an amorphous silica-rich gel on the glass surface. This reaction commences rapidly after the implantation. The high surface area of the silica gel provides a large number of sites for heterogeneous nucleation of the calcium phosphates in the following reaction stages. 4. Glass dissolution continues: Ca2C and PO3 4 ions migrate from the glass through the silica-rich layer, leading to the formation of an amorphous calcium phosphate (ACP) layer on the surface of the silicarich layer. The silica gel provides a large number of sites for heterogeneous nucleation of the ACP. Ions from the solution are also incorporated into the ACP layer. Indications of ACP have already been seen shortly after implantation in rat tibia, and the layer covered the silica-rich layer after 1 h. 5. The ACP layer crystallizes into an HCA layer by incorporation of OH , CO2 3 or F ions from the solution. Glass dissolution continues.
23.2 Bioactivity
820
Part B
Glass Families
SiO2
A = Bone bonding B = Nonbonding (reactivity too low) C = Nonbonding (reactivity too high) D = Nonbonding (no glass forming) S = Soft-tissue bonding E = Bioglass® composition
B A/W glass ceramic (variable P2O5)
A
C S E
Fig. 23.3 A ternary kinetics phase diagram (wt%) showing boundaries between composition regions of different tissue-bonding capabilities. All compositions contain 6% P2 O5 . Region A gives compositions where glasses bond to bone while region S gives compositions of class A bioactivity, bonding to both bone and soft tissue and gene activation. (After [23.2])
D
Part B | 23.2
CaO
6% P2O5
processes has been summarized by Hoppe et al. [23.8]: Si is essential for formation and calcification of bone tissue; the dietary intake of Si increases bone mineral density while aqueous Si induces HAP precipitation. In addition, Si.OH/4 stimulates collagen I formation and osteoblastic differentiation. Similar to Si, P and B also affect bone tissue formation. Phosphorus stimulates the expression of matrix 1a protein in bone formation while boron stimulates bone formation and RNA (ribonucleic acid) synthesis in fibroblast cells [23.8]. Bioactive glasses are capable of activating and stimulating cellular processes without any added chemical supplements; the inorganic ions leaching from the glasses affect not only osteogenesis (bone formation), but are also important for angiogenesis (formation of blood vessels in growing tissue) [23.2, 45, 46]. The degrading glass has also been found to have antibacterial (capable of destroying bacteria) or bacteriostatic (capable of inhibiting bacterial growth) effects on aerobic and anaerobic micro-organisms [23.47–50]. Increasing knowledge of the essential role of certain metallic ions on cellular processes has encouraged incorporation of these metallic ions as therapeutic agents in bioactive glass [23.45]. Ideally, these glasses deliver a controlled dose of metal ions needed for the desired therapeutic effect, without any additional loaded therapeutic drugs or growth factors. Since glasses are homogenous mixtures, several of their properties are additive functions of the constituent oxides and depend on the amount and nature of these oxides. Moreover, glasses are excellent solvents of al-
Na2O
most all elements, thus enabling incorporation of metal ions in the network structure. This enables tailoring of glass composition for controlled degradation and release of ions in a predetermined manner. The challenge is to synchronize the glass degradation rate to meet the local ion release requirements. Incorporation of various metal ions into bioactive glasses has been actively explored over the past years. The release of the ions is thought to locally enhance bone and soft-tissue growth, to induce the antibacterial effect, to cure dental hypersensitivity, etc. The biological effects of metallic ions that are of interest to be incorporated into bioactive glasses have been summarized recently [23.8, 9, 31, 45]. Some effects of the ions are listed below in Table 23.3; for a comprehensive list see Mouriño et al. [23.31]. Several other ions have also been considered as dopants in bioactive glasses. For example, fluoride doping has been studied especially for dental applications [23.51]. Fluoride forms fluorapatite, which is more acid resistant than HCA. Fluoride is also known to prevent caries and tooth demineralization. As discussed above, the release of the ions must exceed a certain minimum level to induce the desired therapeutic effect. Correspondingly, a too high release may induce toxic effects. Locally, the ion concentration leaching from a particular composition depends on the dose of glass, surface area of the sample, surface chemistry and flow rate of the solution along the glass surface. Also the topography of the glass sample has been reported to affect the cellular behavior [23.19, 44].
Bioactive Glasses
23.3 Composition versus Properties of Silicate Glasses
821
Table 23.3 Some biological effects of metallic ions [23.31] Ion Mg2C Ca2C
Sr2C
V4C , VO2C
Mn2C
AgC Zn2C
Ga3C
23.3 Composition versus Properties of Silicate Glasses Commercially available bioactive silicate-based glasses are melt-derived compositions. Despite the almost 50 year history of bioactive glass research, only a few melt-derived compositions are used today in clinical products. Two of the glasses have US Food and Drug Administration (FDA) approval for certain indications: the original bioactive glass Bioglass® 45S5 by Hench and co-workers [23.2] and BonAlive® S53P4 by Andersson et al. [23.52]. Both these compositions crystallize easily during hot-working and are thus available in the amorphous state mainly as particles or powdered fractions. In addition, small amorphous monoliths have been prepared of both compositions. There is, however, a growing trend to fabricate scaffolds with threedimensional interconnecting porosity for various tissue-engineering purposes. The scaffold is a framework that guides the contact and the regeneration of the tissue. Ideally, the scaffolds are designed to allow for tissue ingrowth, nutrient transport and angiogenesis. In addition, the resorption rate must be controlled while providing the required mechanical properties during tissue growth [23.26].
In the first systematic studies to increase the hotworking range of bioactive glasses K2 O, MgO and B2 O3 were added to the four component systems [23.6]. Among these compositions, one glass known as 13-93 turned out to sustain repeated thermal treatments and still provide in vitro bioactivity comparable to that of glass S53P4 [23.53, 54]. Since then, glass 13-93 has been used in several studies to draw continuous fibers or to sinter porous amorphous bodies [23.55–58]. Table 23.4 gives the nominal compositions of the glasses 45S5, S53P4 and 13-93. Table 23.4 Oxide compositions of bioactive glasses 45S5,
S53P4 and 13-93 [23.2, 52, 53] Oxide Na2 O K2 O MgO CaO P 2 O5 SiO2
45S5 S53P4 13-93 (wt%) (mol%) (wt%) (mol%) (wt%) (mol%) 24:5 24:4 23 22:7 6 6 12 7:9 5 7:7 24:5 26:9 20 21:8 20 22:1 6 2:6 4 1:7 4 1:7 45 46:1 53 53:8 53 54:6
Part B | 23.3
Fe3C Co2C Cu2C
Biological effect Stimulates new bone formation and adhesion of osteoblastic cells Cofactor for many enzymes (catalytic action) Stimulates bone cell differentiation, osteoblast proliferation, bone metabolism and mineralization Activates Ca-sensing receptors in osteoblast cells Increases expression of growth factors, e. g., IGF-1 or IGF-II Low doses stimulate bone formation; high doses have deleterious effects on bone mineralization Increases bone formation and reduces bone resorption, leading to a gain in bone mass and improvement of bone mechanical properties Can promote bone and teeth mineralization Stimulates osteoblast proliferation and differentiation; increases mineralization of the matrix and collagen synthesis Cofactor for a very broad number of enzymes Essential in detoxification of superoxide free radicals Participates in redox reactions of metalloproteins and oxygen carrier proteins Upregulation of the expression of proangiogenic growth factors in a variety of cells Stimulates proliferation of human endothelial cells Anti-inflammatory and antibacterial effects Stimulates angiogenesis Antibacterial agent Anti-inflammatory effect Stimulates bone formation by enhancing osteoblast differentiation Facilitates neural growth Inhibits bacterial growth at the surgical site and improves wound healing Antibacterial effects Effective in treatment of hypercalcaemia associated with tumor metastasis in bones
822
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Glass Families
23.3.1 Crystallization Tendency
Part B | 23.3
Glass 45S5 crystallizes shortly above Tg while S53P4 can be thermally treated to some extent before crystallization commences as suggested by the windows between these two temperatures, around 120 ı C for 45S5 and 150 ı C for S53P4 [23.59, 60]. The crystallization of 45S5 is complex and depends on particle size. For small particles, surface crystallization was measured while for larger particles bulk crystallization, possible after liquid-to-liquid phase separation occurred [23.61]. In contrast, S53P4 showed surface crystallization. For 13-93 the temperature window from glass transition to crystallization is around 200 ı C [23.59]. In addition, 13-93 seems to sustain long thermal treatments within this temperature window without crystallization, thus verifying the suitability of this composition e. g., for sintering of porous scaffolds from glass particles [23.62]. The crystallization of 45S5 commences at around 600 ı C. Both Na2 Ca2 Si3 O9 and Na2 CaSi2 O6 have been suggested as the primary phase. A secondary phase, attributed to Na2 Ca4 .PO4 /2 Si2 O4 , forms at higher temperatures [23.61, 63, 64]. The same crystal phases also form, though at slightly higher temperatures in thermal treatment of S53P4 [23.60, 61]. The crystallization retards the hydroxyapatite layer formation in vitro, but the bioactivity is maintained [23.60].
23.3.2 Hot-Working Properties A first estimation of the influence of glass composition on the crystallization behavior of silicate glasses containing Na2 O, K2 O, MgO, CaO, B2 O3 , P2 O5 , F and CaF2 can be calculated using some of the models describing the Tg and crystallization temperatures as a function of the composition [23.59, 65, 66]. The densification also depends on the viscosity of the glass at the sintering temperature. Bioactive silicate glasses also easily crystallize when the liquidus temperature is passed during cooling. Thus, complete viscosity– temperature curves cannot be measured for these composition ranges. However, some values of the viscosity behavior can be measured e. g., by using hot-stage microscopy at low temperatures and rotation viscometer at high temperatures. Alternatively, some temperature– viscosity values can be estimated also with composition models [23.67]. The measured viscosity ./ values for sintering of porous bodies . D 108:4 dPa s/ are around 650 and 710 ı C for S53P4 and 13-93, respectively [23.67]. The composition model gives a 40 ı C lower value for S53P4 and a 10 ı C higher value for 13-93. Glass 45S5 is outside the validity range of the model and also crystallizes easily during the measurement before the desired viscosity is reached [23.67].
In some studies, the impact of other oxides has been mainly tested for compositions derived from 45S5 or S53P4. These include e. g., the influence of substituting SrO for CaO in 45S5 and S53P4 [23.68, 69].
23.3.3 In Vitro Properties The first five reactions at the glass surface after implantation (Sect. 23.2.3) also take place in in vitro conditions, i. e., upon immersion in solutions buffered to the conditions of the extracellular fluid. Most often the reactions are studied in the Tris-buffer (2-amino-2hydroxymethyl-propane-1,3-diol) or the so-called simulated body fluid (SBF) [23.70–72]. The pH of the in vitro solutions is adjusted to pH 7:37:4 at 37 ı C to correspond to the conditions in the extracellular fluid. The effective buffering range of Tris ( pKa D 7:8 at 37 ı C) is pH 6:88:8, which is the dominant buffering system as well in SBF. The inorganic element composition of the blood plasma (extracellular fluid) and the simulated body fluid are given in Table 23.5. The immersion tests are often done in static solutions, with or without agitation, at 37 ı C for various periods of time ranging from a few hours up to 4 weeks [23.41]. At the end of each time period, the sample and the solution are separated and the changes in the glass surface and in the solution composition are analyzed. Several methods have been developed to gain information on the dissolution behavior and reactions of bioactive glasses in vitro. The methods used to characterize the glass surface include Fourier transform infrared (FTIR) spectroscopy, solid-state NMR, Raman spectroscopy, scanning electron microscopy with energydispersive x-ray spectroscopy (SEM-EDS), surface area measurements, x-ray diffraction (XRD) and x-ray microtomography (CT). The changes in the immersion solution are measured by the pH and the ion concentrations using an inductively coupled plasma (ICP) analysis. Technical Committee TC04 of the International Commission of Glass (ICG) has recently suggested a protocol for measuring the apatite-forming ability of bioactive glasses using a static in vitro method [23.41]. Table 23.5 Concentrations of inorganic ions in the immer-
sion solutions in mmol=L Ion NaC KC Mg2C Ca2C Cl HCO 3 HPO2 4 SO2 4
Blood plasma 142 5 1:5 2:5 103 27 1 0:5
SBF 142 5 1:5 2:5 147:8 4:2 1 0:5
Tris
45
Bioactive Glasses
a) Layer thickness (μm)
erties. However, in each particular condition, the trend in bioactivity expressed as ion leaching or layer formation rates, depends on the glass composition. The in vitro tests in static conditions are well suited to comparing different glass compositions. However, using a high SA=V ratio in the test leads to fast supersaturation of the solution. This may give misleading predictions of the dissolution rate or the bioactivity, i. e., HCA formation of the glass [23.75]. Dynamic versus Static Dissolution Tests In vivo, the bioactive glass implant is subjected to an environment that is not static but the dissolution products are resorbed or removed from the surrounding solution by some mechanism. Different experimental arrangements have been used to better simulate conditions in the dynamic body environment. Most often, the solution is regularly replenished either totally or partly to prevent saturation of the solution. In some approaches, a relatively large volume of fluid is continuously circulated in the system. Reactions of bioactive glasses and bioceramics have been compared in static conditions and in a dynamic 1 mL=min flow of SBF [23.76–78]. The pH and ion concentrations of the solution were recorded and the morphology of the samples was characterized during the tests. The structure of the apatite that formed on the glass ceramic samples after the two test systems was different. In static conditions, the apatite layer grew on the material outer surface, while in dynamic conditions the apatite did not cover the sample surface but formed inside the sample with interconnected porosity [23.78]. The reaction layer morphology that formed in dynamic conditions was similar to the bone apatite. These tests suggested that dynamic con-
b) Layer thickness (μm)
20
c)
20
15
15
HAP layer Si + CaP SiO2-rich layer
HAP SiO2 layer
10
10
5
5
S53P4 HAP
SiO2 layer 0
24 h
72 h
168 h
0
24 h
823
72 h
168 h 45S5 10 μm
Fig. 23.4a–c Thickness of the reaction layers on (a) 45S5 and (b) S53P4 glass plates after immersion in SBF for various time points, based on data in [23.73, 74]. (c) SEM micrographs of the cross-sections after 168 h in SBF
Part B | 23.3
In Vitro Formation of Reaction Layers The thickness of the silica-rich and HAP layers on plates of 45S5 and S53P4 after various immersion times in SBF are shown in Fig. 23.4. The thicknesses were measured from SEM micrographs of the cross-sections of the glasses [23.73]. The silica-rich layer grew with time in both glasses while the outer HAP layer rapidly grew to almost a constant thickness of 23 m. In between these two layers, a mixed layer of calcium phosphate (CaP) precipitation and silica was identified. Although the two compositions do not show any marked differences in the HAP layer growth after the first 24 h, the faster silica-rich layer formation on 45S5 means that this composition has a higher ion dissolution rate than S53P4. The SEM micrographs in Fig. 23.4c show the surface layer structures after one week in SBF for these two glasses [23.74]. The images show the intact glass at the bottom, darker silica-rich layer with some calcium phosphate accumulations as light grey structures, the HAP layer covering the surface and various sizes of HAP nodules on the HAP layer. After the one-week immersion, the pH of the SBF had increased from the initial value of 7:4 to 8:4 for a solution containing 45S5 and to 8:0 for S53P4 [23.74]. The sample morphology (as seen in Fig. 23.4) and the changes in the ion composition of the immersion solution followed nicely the trends given by the first five reaction stages suggested by Hench for bioactive glasses [23.74]. The changes also clearly correlated with the oxide composition of the glasses; 45S5 glass with lower SiO2 content gives lower chemical durability and thus more rapid degradation. The experimental conditions such as the surface area to volume (SA/V) ratio affect the numerical values of the observed prop-
23.3 Composition versus Properties of Silicate Glasses
824
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Glass Families
ditions better simulate the in vivo conditions and thus give more precise and reliable results for the bioactivity of the material. A continuous flow-through reactor was developed to measure online the initial dissolution of ions from bioactive silicate glasses [23.79, 80]. In this method, a fresh solution is fed at a desired rate through the sample container after which all the ions released into the solution are simultaneously measured using ICP analysis. When measuring initial dissolution of ions into Tris-buffer with glasses containing from 45 wt% SiO2
(bioactive glass 45S5) to 72:6 wt% SiO2 (float glass), four typical initial dissolution patterns, marked as dissolution profiles A–D, were observed (Fig. 23.5a–d). These dissolution profiles correlated with the bonebonding capabilities of the same glasses in rat femur [23.80]. The oxide compositions of the glasses are given in Table 23.6. Initial Dissolution of Bioactive Glasses All A-dissolution profile glasses had a similar dissolution profile as Bioglass® 45S5 in Fig. 23.5a. The
Part B | 23.3
a) c (mg/L)
b) c (mg/L)
180
180
160
160
140
Ca Na (sat.) i.e. >> 130
120
140 120
100
100
80
80
60
60
Si
40
P
40
20 0
Ca
P 200
300
400
500
600
700
800
900 1000 t (s)
c) c (mg/L)
20 0
200
Mg
K Si Na
300
400
500
600
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800
900 1000 t (s)
Ca Mg 0 Si 200 300
400
500
600
700
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d) c (mg/L)
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80
60
60 Na
40
40
Ca K
20
20 Si
0
P 200
Na
300
400
500
600
700
800
900 1000 t (s)
Fig. 23.5a–d Four initial ion dissolution profiles for silicate glasses: (a) 45S5, typical for A-type bioactive glasses in Table 23.2; (b) 0106; (c) 1106; (d) float glass, almost inert composition. (With data from [23.80]) Table 23.6 Nominal compositions (wt%) of glasses in Fig. 23.5 [23.80] Code 45S5 0106 1106 Floata a
SiO2 45 50 58:3 72:6
Na2 O 24:5 5:9 5 15:2
K2 O – 12 15 –
Contains also minor components (Fe2 O3 , SO3 , etc.)
MgO – 5:3 – 5:3
CaO 24:5 22:6 20:6 4:6
P2 O5 6 4 1:1 –
B2 O3 – 0:2 – –
Al2 O3 – – – 1:7
Bioactive Glasses
Initial Dissolution of Slowly Degrading Glasses The ion dissolution profiles in Fig. 23.5c,d are for slowly degrading (C-profile) and practically inert (Dprofile) compositions. Minor initial dissolution peaks were observed for all compositions but the ion concentration levels rapidly decreased to low (slowly degrading) or negligible (inert) values. Slowly degrading silicate glasses have been tested as reinforcing particles or fibers in bioresorbable polymer composite devices [23.85–87]. The dissolution of the glasses in composites may differ from the behavior measured for the glass as such. For example, when used in composites together with bioresorbable polymers, the dissolution kinetics of the glass is also affected by the polymer degradation. Detailed discussions of bioactive glasses in polymer composites have been summarized in [23.88, 89].
23.3.4 In Vivo Properties The bone- and tissue-bonding capability of the first bioactive glasses were tested in rat femur or tibia, femur in monkey or canine, mandibular and maxillar bone of primates and swine, tibia of rabbit and femur of sheep, etc. [23.2, 52, 90]. Today, the tissue interactions
Fig. 23.6 SEM image of a cross-section of a 13-93 scaffold after 6 weeks in rabbit tibia. The unreacted glass is seen as white particles and the dark layer on the particles represents the silica-rich layer while the uppermost light layer is the HAP layer (Courtesy of Prof. Heimo Ylänen)
of bioactive glasses are studied using cells from animals and humans, and implanting the glasses in bone or soft tissue [23.9]. Figure 23.6 shows an SEM image of a cross-section of a sintered porous scaffold made of 13-93 microspheres (250300 m) after 6 weeks in rabbit tibia. The newly grown bone tissue was seen to infiltrate the 13-93 porous scaffold and the reaction layers on the glass particle can also be clearly observed. The ternary kinetics phase diagram in Fig. 23.3 provides an overview of bonding capabilities of glasses in the system SiO2 -Na2 O-CaO-P2 O5 . The influence of the glass composition on the bone-bonding capability within the systems SiO2 -Na2 O-CaO-P2 O5 -Al2 O3 -B2 O3 and SiO2 -Na2 O-CaOP2 O5 -K2 O-MgO-B2 O3 has been expressed using mathematical models, which give relative values for bone bonding as a function of the glass compositions. The models were based on the analysis of the glass–tissue interfaces and surface layer morphologies at the surface of glass implants after 8 weeks in rabbit tibia [23.7, 53]. These models and the phase diagram can be used to exclude from further in vitro and in vivo testing compositions that do not appear to have promising properties. In vivo studies are together with in vitro studies important steps in developing medical devices into the market. In vivo studies have also been carried out to determine fundamental information about the interactions of bioactive glasses with tissues. In vivo studies always need an approval from the local authorities, and the ethical principles for the welfare of the animals must be observed [23.91].
825
Part B | 23.3
initial dissolution of Na was very high and beyond the calibration limit. Also Ca showed a very high dissolution, 130 ppm after 1000 s, while the Si release was 50 ppm. For all A-dissolution profile glasses, the initial concentrations were higher than the required values of 6090 ppm Ca and 1530 ppm Si for osteostimulation [23.19]. The dissolution profile in Fig. 23.5b was measured for three compositions rich in K2 O (1112 wt%) and MgO (5 wt%), including glass 13-93 (Table 23.4). Also for these glasses, the dissolution profile followed the initial reaction stages of bioactive glasses as suggested by Hench [23.30]. However, the overall ion concentrations were clearly lower than for the A-dissolution profile glasses, 5090 ppm Ca and 2030 ppm Si. Whether these values support osteostimulation should be verified with cell culture tests. However, all these glasses have shown good bone-bonding ability in vivo [23.19, 53, 81]. The lower initial ion release of the B-dissolution profile glasses (Fig. 23.5b), compared to the A-profile glasses, may be due to a mixed alkali or mixed alkaline earth effect. The ion release measurements suggested that MgO might decrease the ion release from bioactive glasses [23.82, 83]. In contrast, gradual substitution of K2 O for Na2 O increased the initial ion dissolution from glasses with low silica contents [23.82, 84].
23.3 Composition versus Properties of Silicate Glasses
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23.4 Sol–Gel Silicate Bioactive Glasses
Part B | 23.4
In the early 1990s, the sol–gel synthesis approach was introduced in the preparation of ternary bioactive glasses of SiO2 -CaO-P2 O5 [23.92–94]. Sol–gel chemistry offers a potential processing method for molecular and textural tailoring of the bioactive glasses. More importantly, the voids present in the gel network between the colloidal particles become pores and pore channels after thermal treatment, which endows the sol–gelderived bioactive glasses with high surface area and porosity. Consequently, sol–gel bioactive glasses exhibit higher rates of apatite phase formation, faster bone bonding, and excellent degradation/resorption properties [23.28].
interparticle forces cause considerable aggregation to form a highly branched cluster of macroparticles until the sol becomes a gel of an interconnected 3-D silica network with Ca2C and PO3 4 groups present, as schematically illustrated in Fig. 23.7 [23.4]. The silica gel is subsequently aged to stabilize the gel network and to develop sufficient strength to resist cracking during drying. During the subsequent thermal treatment .> 400 ı C/, all the organics are removed and Ca2C ions diffuse into the silica network as modifiers. Thus, the gel is transformed into an amorphous glass of the ternary SiO2 -CaO-P2 O5 . In sol–gel glasses, SiO2 forms a covalently bonded network to provide stability to the material. Compared with melting-derived bioactive glasses, the tetrahedral [SiO4 ] units in sol–gel glasses condensate as ramified branches or as 3, 4 or 5 [SiO4 ] rings, depending on the stabilization temperature. This conformation leads to high microporosity and high surface area of the sol–gel glasses. In in vitro SBF immersion, these sol–gel-derived bioactive glasses have shown equivalent to or superior bioactivity than the melt-derived bioactive glasses in terms of HCA precipitation. Notably, when an organic acid— citric acid—was used as the catalyst for the hydrolysis of Si.OC2 H5 /4 in sol–gel synthesis, the 45S5 bioactive glass composition (SiO2 -CaO-Na2 O-P2 O5 ) could be prepared, as demonstrated by Faure et al. [23.95]. The obtained sol–gel 45S5 powder contained more rough and porous grains compared to the smooth grains in commercial Bioglass® in terms of surface morphology. This sol–gel 45S5 also exhibited higher levels of bioactivity in SBF immersion than the commercial
23.4.1 Sol–Gel Chemistry The sol–gel approach is a wet-chemical technique, which employs the sol–gel chemistry of the hydrolysis, water/alcohol condensation and subsequent polymerization of metal hydroxides, alkoxides and inorganic salts. In the preparation of sol–gel-derived bioactive glasses, typical liquid precursors are silicon alkoxide (Si.OR/4 , where R represents an alky group, typically as ethyl of C2 H5 ) as a source of Si, triethyl phosphate (.C2 H5 /3 PO4 , TP) as a source of P, and calcium salt (e. g., Ca.NO3 /2 ) as a source of Ca. These precursors are soluble in a cosolvent of water and alcohol to make a colloidal solution (sol). Under the catalysis of an acid or base, the simultaneous hydrolysis and polycondensation of Si.OR/4 take place. When an acid e. g., HCl, is employed as the catalyst, the hydrolysis of Si.OR/4 occurs fast under acidic conditions. Therefore, the strong H+–
a) TEOS Si(OC2H5) + H 2O + acid or base
O
Hydrolysis
–+
Si
O
–+
O
H+– O
H
H+– O
b) +–
H+–
H
H
–+
H
O
–+H
×4
O
O
Si
Condensation –+
Si
O
H
H+– O
–+
H+– O
O
O Si
O
O Si
H
Si H+– O
H
O
+–
O –+ H +–
H
O
–+
H
O O
–+
H
–+
H
Fig. 23.7 (a) Schematic reactions of the sol–gel chemistry while forming the tetrahedra and nanoparticles of silica at room temperature (hydrolysis of TEOS). (b) A flow-chart of the acidcatalyzed sol–gel synthesis process of a bioactive glass with schematics of the gel and its nanoporosity. (After [23.4])
Bioactive Glasses
23.4.2 Monoliths of Sol–Gel Bioactive Glasses Monoliths of 58S (58SiO2 -33CaO-9P2 O5 ) in forms of crack-free rods and discs were prepared using high relative humidity drying schedules in conjunction with ethanol treatment [23.99]. In in vitro immersion in SBF, 58S showed a higher rate of HCA formation than the melt-derived 45S5. Also, Si leached out from 58S particles completely in 7 days in vitro and within 12 weeks in vivo, which indicated a good resorptive ability of 58S particles. Because of the porous structure and low bulk density, more reactive species on the glass surface are accessible for the surrounding solution. Thus, 58S has a high degradability although it contains higher contents of silica than 45S5. The improved processing of the glass preparation as well as the rapid rate of surface HCA formation make the frits or monoliths of 58S interesting candidates as bone graft materials [23.99].
23.4.3 Nanoparticles and Nanofibers of Sol–Gel Bioactive Glasses Interactions between cells and the biomaterial surface occur firstly in the nanoscale as the components of biological tissues have nanoscale dimensions. The key properties of the biomaterials such as surface area, surface roughness, hydrophilicity and wettability, to a large extent, determine the cell–biomaterial interactions [23.100]. The sol–gel approach provides the accessibility to nanoscale dimensions for the prepared bioactive glasses, e. g., in forms of nanoparticles or nanofibers, to interact with proteins and cells in the tissue regeneration. By precipitating the hydrolyzed sol in ammoniated deionized water containing ammonium dibasic
phosphate, the gel particles were separated by centrifugation, followed by freeze drying, and a calcination procedure to obtain the bioactive glass nanoparticles. By varying the strategies of sol–gel synthesis, including adopting different catalysts for initiating the hydrolysis and condensation of silicate precursors as well as combining sol–gel chemistry with other techniques such as microemulsion or an aerosol technique, both the compositions and the morphological parameters (size, shape, and pore structures) of the bioactive glass nanoparticles can be tuned to meet their utilization purposes in biomedical applications [23.96]. Ag-doped bioactive glass nanoparticles (SiO2 -CaO-Ag2 O) and Cu-doped bioactive glass nanoparticles (SiO2 -CaOCuO) have recently been synthesized by employing the base-catalyzed sol–gel approach [23.101, 102]. These bioactive glass nanoparticles showed excellent bioactivity and relevant physiological effects, and are assumed to be promising filler material in constructing composites for bone tissue engineering and wound healing with improved mechanical strength and controlled dissolution behaviors [23.103, 104]. By combining the sol–gel approach with the electrospinning technique, the precursor sol was successfully spun, followed by thermal treatment to produce nanofibers of bioactive glass. By varying initial sol concentrations, bioactive glass nanofibers of the composition 70SiO2 -25CaO-5P2 O5 were fabricated in different average diameters (630840 nm) [23.105]. Compared with melt-derived or sol–gel bulk glasses, the apatite formation on these nanofibers in vitro appeared to be significantly enhanced by the nanoscale production process. Poorly crystallized apatite was found along the fiber surface after one day of SBF immersion. Meanwhile, the nanofibers also exhibited a more rapid initial drop in the Ca and P concentrations of the immersion solution, compared to the bulk glasses [23.105]. This was due to the fast dissolution of glass and supersaturation of the solution with respect to the HCA crystal nucleation as offered by the large surface area of nanofibers of bioactive glasses. In in vitro cellular assessments, the nanofibers of 70SiO2 -25CaO5P2 O5 showed excellent osteogenic potential; the bone marrow stromal cells (bMSCs) attached and proliferated actively on the nanofiber mesh, and differentiated into osteoblastic cells [23.105]. The nanofibers were aligned and bundled into a microfilament and further molded into a 3-D scaffold using a negative-mold technique [23.105]. The scaffolds had a 3-D open-channeled network with controlled pore size (ca. 500 m) and porosity (ca. 50%) [23.105]. They are of particular interest as tissue-engineering scaffolds since the nanofibrous surface can provide favorable surroundings for initial protein adhesion and cellular responses in vivo,
827
Part B | 23.4
Bioglass® . When a base, e. g., ammonium hydroxide, is employed as the catalyst in the sol–gel synthesis, the hydrolysis of Si.OR/4 is slow under alkaline conditions. Then, the hydrolyzed SiO2 mainly forms a linear or randomly branched polymer and the particles may grow to a sufficient size to become spherical colloid particles. Thus, bioactive glass in forms of nanoparticles (from 50 to several 100 nm depending on the processing parameters used in the sol–gel synthesis) can be yielded after the removal of organic precursors in the thermal calcination [23.96]. Here, two comprehensive and elaborate reviews are referred to in case of further interest in sol–gel synthesis of bioactive glasses [23.97, 98]. In the following, we separately discuss the sol–gel-derived bioactive glasses in terms of the various product forms. In the continued context, the compositions of the sol– gel-derived silicate glasses are given in mol%.
23.4 Sol–Gel Silicate Bioactive Glasses
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as seen in Fig. 23.8 [23.105]. Recently, by fine-tuning the viscoelasticity of inorganic precursor sol solution as well as by using calcium nitrate as the precursor to increase the charge density on the surface of the jet, a flexible, 3-D cotton-wool-like structure of glass 70SiO2 -30CaO was electrospun without using a polymeric binding agent. As an advantage, this approach has avoided the postprocessing of fibers [23.106]. This material showed rapid apatite formation as well as supporting cell attachment and spreading on preosteoblast cells in the material.
23.4.4 Mesoporous Bioactive Glasses Part B | 23.4
The incorporation of sol–gel processes and supermolecular chemistry of surfactants in the wet-method synthesis of bioactive glasses has allowed the porosity of bioactive glasses to be controlled at the nanometric scale. This has advanced a new generation of nanostruca)
tured bioactive glasses: mesoporous bioactive glasses (MBGs) [23.107–109]. This class of bioactive glasses have highly ordered mesoporosity with an average pore diameter of less than 10 nm (as displayed in the TEM image in Fig. 23.9a) and a specific surface area of several 100 m2 =g, both of which are of equivalent orders as the mesoporous silica materials, e. g., MCM-41 and SBA-15 [23.110]. Consequently, MBGs possess superior bioactivities owing to their high surface area and larger pore volume. In vitro, MBGs react much faster and more intensely than the conventional sol–gel glass. MBG 58SiO2 -36CaO-6P2 O5 exhibited a very intense release of Ca when immersed in SBF, resulting in a massive growth of ACP on the surface, which further mineralized to HCA [23.113]. MBGs also showed good biocompatibility when tested in cell cultures with osteoblasts and fibroblasts [23.114]. Apart from the enhanced bioactivity, the unique mesoporous structures
b)
100 nm
c)
10 μm
d)
20 μm
1 μm
1 mm
Fig. 23.8 (a) Transmission electron microscopy (TEM) image of the electrospun bioactive glass nanofiber (70SiO2 25CaO-5P2 O5 ) (average diameter of 84 nm). (b) SEM image of bonemarrow-derived osteoblastic cells on the nanofibrous mesh after 5 days of culturing. (c) SEM image of the fibrous filament made of electrospun nanofibers aligned and bundled into a microfilament. (d) SEM images of the 3-D macroporous scaffold: short filaments were created using a negative-mold technique and then heattreated. (Reprinted with permission from [23.105])
Bioactive Glasses
a)
b)
23.4 Sol–Gel Silicate Bioactive Glasses
829
Ce3+ • Reduces enamel demineralization • Favors osteoblast growth • Neuroprotective Ga 3+ • Antimicrobial • Increase bone calcium content • Blocks bone resorption Zn 2+
Fig. 23.9 (a) TEM image showing the mesoporous texture of MBG of 80SiO2 -15CaO-5P2 O5 (reprinted from [23.111] with permission from Elsevier). (b) Schematic representation of possible biological properties possessed by Ce-, Ga-
and Zn-doped MBGs of .80 x/SiO2 -15CaO-5P2 O5x MO fabricated by 3-D printing (reprinted from [23.112] with permission from Elsevier)
also endow MBGs with a carrier function for delivery of active agents to aid the physiological processes, including antibiotics, anti-inflammatory drugs, antibacterial agents, growth factors, proteins and peptides [23.115]. The mesopores in MBGs provide accommodation to the guest molecules through the physical affinity between the surface functional groups and the molecules to be delivered. In the physiological fluids, the release of the guest molecules from MBGs is governed by both diffusion of the guest molecule itself and the dissolution of the MBGs. From an electrospun fibrous scaffold composed of biopolymers (gelatin/PCL) and MBG nanospheres, the osteogenic drug dexamethasone (DEX) was released in a highly sustained manner over one month [23.116]. This scaffold improved bone formation in vivo, after implantation in rat calvarium [23.116]. MBG nanospheres have also been used as nanocarriers in hollow core–shell fibers of PEO/PLA to deliver the fibroblast growth factor 18 (FGF18) as an osteogenic enhancer [23.117]. The incorporation of MBG nanospheres significantly increased the apatiteforming ability and mechanical properties of the core– shell fiber. The sustainable release of FGF18 in vitro stimulated cell proliferation, alkaline phosphatase activity and cellular mineralization of rat mesenchymal stem cells and in vivo enhanced bone formation in a rat calvarium model [23.117]. Moreover, MBGs of the SiO2 -CaO-P2 O5 system can be substituted with a small amount of extra oxides of some trace elements, including copper, gallium, zinc and strontium [23.118–120]. The cations of these
essential elements can be released from the glass network as therapeutic ions, as previously discussed in Sect. 23.2.4. Cu2C is a promising angiogenic agent and it can upregulate the expression of the proangiogenic growth factors such as vascular endothelial growth factor and fibroblast growth factor to enhance angiogenesis [23.8]. Cu2C also exhibits antimicrobial efficacy in vitro against bacterial strains commonly associated with infection after orthopaedic surgery, including Staphylococcus aureus and Escherichia coli [23.121]. Cu-doped MBG is an intriguing material that has great promise in the construction of a 3-D tissue-engineering scaffold or functional coating on implants [23.122–124]. Ga3C has a dosage-dependent, antiosteoclastic effect by reducing osteoclastic resorption, differentiation and formation, and inhibits bone resorption [23.45]. Zn2C is known to promote bone formation by stimulating the proliferation and differentiation of osteoblasts as well as inhibiting osteoclastic resorption in vitro [23.45]. 3-D printing techniques have been employed to fabricate scaffolds of Ga-doped MBG and Zn-doped MBG, as displayed in Fig. 23.9b [23.112]. These scaffolds possessed a hierarchical porosity consisting of both the mesopores present in MBG and the macropores as constructed in the scaffold via printing, as required by drug delivery and bone regeneration [23.112]. The release of Ga3C from the Ga-doped MBG also gives a broad-spectrum antimicrobial capacity to the material [23.125]. Strontium is a trace element present in bone and it exerts a beneficial effect on osteoblastic activity, i. e., in gaining bone mass and improvement of
Part B | 23.4
• Potent inhibitor of osteoclastic • Resorption in vitro • Stimulates bone formation • Antimicrobial
830
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Glass Families
bone mechanical properties. 3-D scaffolds of Sr-doped MBG have also been fabricated for promising use in regenerating osteoporotic bone defects in several studies [23.126, 127]. Sol–gel bioactive glasses are attractive candidates to be applied as thin bioactive coatings with nanoscale roughness to biomedical devices or constructing com-
ponents of tissue-engineering scaffolds, owing to their large specific surface area, encapsulation properties, physiochemical and biological advantages. To date, understanding of how these nanosized biomaterials interact with biological systems and any risk of possible adverse systemic reactions caused by the nanoscale dimension and surface roughness is still limited.
23.5 Phosphate-Based Bioactive Glasses Part B | 23.5
In bone repair applications or scaffolds for bone tissue engineering, ideally, a controlled degradation rate is desirable to match the growth rate of bone in vivo. Silicate bioactive glasses, including 45S5 and S53P4, are absorbed slowly or undergo incomplete conversion into HCA after in vivo implantation. As alternative initiatives to construct biomaterials with controlled biodegradability, phosphate-based bioactive glasses have been developed to meet the clinical needs of biodegradable implants in orthopaedic and dental applications. Phosphate-based bioactive glasses were first proposed in the ternary system 45P2 O5 -.55 x/CaOxNa2 O (19 < x < 43) with P2 O5 as a network former and CaO and Na2 O as modifiers by Knowles et al. [23.10]. These glasses consist of a polymer-like, regular tetrahedral structure based on [PO4 ] with network-modifying ions interrupting the physical structure of the glass. As all their constituent atoms are found in the inorganic mineral phase of bone, they show excellent biocompatibility and have also a chemical affinity to natural bone. Bioactivity of these glasses was indicated by the formation of brushite precipitate (CaHPO4 2H2 O) on the glass surface, which further matured to apatite. Compared with Bioglass® , these phosphate-based bioactive glasses are water soluble and display a wide spectrum of solubility ranging from highly soluble (23 h) to relatively stable glasses (several months up to one year), mainly depending on the content of CaO in the composition. As the CaO content increases, the solubility of the glass decreases and becomes less linear-dependent with immersion time [23.10]. Although the more soluble compositions were found to adversely affect the proliferation of human osteoblast cells in in vitro culture, glass 45P2 O5 40CaO-15Na2 O with the lowest dissolution rate was able to enhance bone cell growth and bone-associated protein expression [23.128]. These features define the application disciplines of phosphate-based bioactive glasses mainly as biodegradable tissue implants in orthopaedic and periodontal surgeries, where a fast release of active ions is sought. Knowles et al. conducted
a systematic study on the process and characterization of the ternary system P2 O5 -CaO-Na2 O; they varied the levels of the P2 O5 content at 45, 50 or 55 mol% while keeping the CaO content constant at 30, 35 or 40 mol% [23.129]. Both Tg values and solubility of the glasses firstly increased from 45 to 50 mol% P2 O5 and then decreased from 50 to 55 mol% P2 O5 , as displayed in Table 23.6 [23.129]. Glass 50P2 O5 -30CaO-20Na2 O gave the highest solubility rate among the nine experimental glass compositions. A correlation between the glass solubility and the release of NaC suggested the preferential release of Na from the glass. In general, these phosphate-based bioactive glasses showed low Tg and melting temperatures (seen in Table 23.7). Meanwhile, higher content of CaO resulted in increased Tg and crystallization temperatures. These thermal properties enabled production of the glass at relatively low temperatures compared to Bioglass® as well as facilitating easy fabrication of the glass into desired shapes. Glass fibers with varied diameters were drawn from both 50 and 55% P2 O5 compositions [23.130]. But no fibers could be obtained from 45% P2 O5 compositions, which was attributed to the short chain length and the low network connectivity and crosslink density of the glass network [23.130]. The fast dissolution rates of phosphate-based bioactive glasses restrict their biomedical applications. Metal oxides (MO), such as MgO, SrO, Al2 O3 , ZrO2 or TiO2 have been introduced into the quaternary system P2 O5 -Na2 O-CaO-MO to improve their physiochemical properties as well to actively enhance bioactivity. In the system 45P2 O5 -23Na2 O-.32 x/CaO-xMgO .0 < x < 22/, the substitution of MgO for CaO decreased the glass solubility. These glasses containing 7 mol% MgO or more increased the proliferation of human osteoblast-like cells in in vitro culture with the glass extracts [23.131]. Strontium ions have positive effects on bone metabolism by inhibiting osteoclast activity, while promoting osteoblast activity [23.132]. In the system 50P2 O5 -10Na2 O-.40 x/CaO-xSrO (0 < x < 40), the substituting of SrO for CaO led to a less rigidly crosslinked glass network as well as lower Tg and
Bioactive Glasses
23.6 Borate-Based Bioactive Glasses
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Table 23.7 Properties of phosphate-based bioactive glasses of the ternary system of P2 O5 -CaO-Na2 O (data from [23.129]) Glass 45P2 O5 -30CaO-25Na2 O 45P2 O5 -35CaO-20Na2 O 45P2 O5 -40CaO-15Na2 O 50P2 O5 -30CaO-20Na2 O 50P2 O5 -35CaO-15Na2 O 50P2 O5 -40CaO-10Na2 O 55P2 O5 -30CaO-15Na2 O 55P2 O5 -35CaO-10Na2 O 50P2 O5 -40CaO-5Na2 O
Solubility (mg=.cm2 h/) 12:68 104 2:038 104 1:557 104 2:883 103 1:260 103 0:5883 103 3:455 104 2:940 104 3:125 104
Tm (ı C) 734 731 727 and 761 731 and 760 774 769 and 870 674 634 and 761 775
and Tg increased [23.135]. The presence of TiO2 in glass also induced calcium phosphate surface nucleation. In SBF immersion, more rapid formation of HAP in the glass was confirmed as the content of TiO2 increased. Glass 45P2 O5 -30CaO-24Na2 O-1TiO2 showed increased glass stability, controlled solubility, as well as an enhanced bone-binding ability [23.135]. The biodegradability of phosphate-based bioactive glasses makes them ideal delivery vehicles of inorganic therapeutic ions in the implantation sites [23.45]. The degradation rate of the glasses is controllable over several magnitudes by altering the glass composition. In contrast to silicate bioactive glasses, the concurrent release of phosphate-based bioactive glasses is highly linear with time [23.136]. This is favorable in the biomedical applications where a long-term and sustainable release of therapeutic ions into physiological fluids is desired to promote biological functions, such as osteogenesis, angiogenesis or antibacterial capacity. Various therapeutic ion species, including AgC , Ca2C , Mg2C , Sr2C , Cu2C , Zn2C , Fe3C as well as different forms of phosphate, e. g., orthophosphate and pyrophosphate, can be released from glasses doped with different metal oxides [23.131, 137–140]. For more comprehensive discussion on such perspectives of phosphate-based bioactive glasses, readers are referred to two extensive reviews [23.31, 136].
23.6 Borate-Based Bioactive Glasses Borate-based bioactive glasses have also been developed to address sufficient bioactivity and controllable degradability to meet clinical applications. The first borate-based bioactive glasses were produced by replacing the SiO2 in silicate bioactive glasses with varying amounts of B2 O3 [23.141, 142]. The glass is called borosilicate bioactive glass when SiO2 is substituted partially and borate bioactive glass when all the SiO2 is
substituted. Unlike 3-D network Si–O, B has a threefold coordination number, which forms trihedrals or chains of [BO3 ] triangles in the glass network. Consequently, borate-based glasses exhibit lower chemical durability as well as faster dissolution rates [23.141, 143]. The compositions of 45S5B and 13-93B series were mainly derived from 45S5 and 13-93 by gradually replacing B2 O3 for SiO2 , as shown in Table 23.8.
Part B | 23.6
crystallization temperatures [23.133]. The substitution of SrO for CaO up to 20 mol% gave the largest hotworking window .T D 164 K/ in terms of the glass resistance towards crystallization. In in vitro SBF immersion, an apatite-like layer with increasing thickness as a function of the immersion time formed on all SrOcontaining phosphate glasses. Meanwhile, the concentration of SrO in the reaction layer at the glass surface increased with the SrO content in the glass, which was assumed to limit phosphate leaching in the solution and thus increase the durability of phosphate glasses. Glass 50P2 O5 -10Na2 O-20CaO-20SrO with Sr=Ca D 1 presented the slowest dissolution as indicated by the decrease in the pH and the P concentration released into SBF [23.133]. Moreover, the apatite-like layer on the SrO-containing phosphate glass was confirmed to facilitate the proliferation and growth of human gingival fibroblast in in vitro culture on the glass discs [23.134]. TiO2 and ZrO2 are bioinert implant biomaterials and they do not develop any inflammatory reaction while in contact with tissue. In the system 45P2 O5 -30CaO.25 x/Na2 O-xTiO2 (0 < x < 1), the addition of TiO2 up to 0:25 mol% decreased glass density and Tg . This was attributed to a loose packing of the glass network due to the breaking of P–O–P bonds by addition of Ti4C . However, above 0:25 mol% crosslinkage through NBOs led to structural compactness and both density
Tg (ı C) 374:88 407:36 432:96 385:26 420:6 450:39 367:77 399:71 440:64
832
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Table 23.8 Nominal composition (mol%) of the borate-based bioactive glasses Glass 45S5B1 45S5B3 13-93B1 13-93B3
Na2 O 24:4 24:4 6:0 6:0
K2 O 0 0 7:9 7:9
a)
MgO 0 0 7:7 7:7
CaO 26:9 26:9 22:1 0
SiO2 30:7 0 36:4 0
b)
B2 O3 15:4 46:1 18:2 54:6
P2 O5 2:6 2:6 1:7 1:7
c)
200 nm
Part B | 23.6 2 μm
d)
Day 0
Day 5
Day 10
200 nm Day 14
Control
13-93B3
Cu-doped 13-93B3
Fig. 23.10 (a) Cotton wool-like appearance of Cu-doped borate bioactive glass microfibers (13-93B3); (b) SEM image of the Cu-doped 13-93B3 microfibers; (c) SEM image of the surface of Cu-doped 13-93B3 microfibers after immersion in SBF for 7 days. (d) Representative images of full-thickness skin defects in rodent, left untreated (control) or treated with 13-93B3 or Cu-doped 13-93B3 microfibers, at 0, 5, 10 and 14 days postsurgery (scale bar D 10 mm). (Reprinted from [23.144] with permission from Elsevier)
Bioactive Glasses
scaffold was toxic to osteogenic cells in the cellular culture due to a high content of B2 O3 , histological evaluation of the scaffolds at 6 weeks postimplantation showed that the scaffold supported soft-tissue infiltration and extracellular matrix formation [23.145]. This is most likely due to the more dynamic microenvironment in the body, which presumably facilitated rapid metabolism of boron ions and reduced the steep local boron concentration gradient. More recently, microfibers of borate bioactive glasses have attracted growing interest for the healing of soft-tissue wounds [23.146, 147]. The microfibers are fabricated by blowing a high-pressure jet of gas at the molten 13-93B3 glass and then quenching the fibrous material [23.146]. Borate 13-93B3 microfibers converted to HAP quickly in SBF and released high concentrations of Ca and B ions into the solution [23.146]. Cu, Zn, Sr, Ce and Ga in small amounts have been doped into borate 13-93B3 microfibers and then released from the glass network as therapeutic ions, which are beneficial for healing soft-tissue wounds [23.144, 148, 149]. These metal ion dopants had little effect on the degradation of the parent 1393B3 glass fiber but they inhibited the crystallization of ACP to HAP. In vitro, the ion dissolution products from Cu-doped 13-93B3 microfibers were not toxic to human umbilical vein endothelial cells (HUVEC) and fibroblasts; it also stimulated HUVEC migration, tubule formation and VEGF (vascular endothelial growth factor) secretion [23.144]. In a rodent model in vivo, Cudoped 13-93B3 microfibers demonstrated a promising capability to stimulate angiogenesis and heal full-thickness skin defects [23.144], as shown in Fig. 23.10.
23.7 Scaffolds for Tissue-Engineering Applications Most commercial products of bioactive glasses on the market are either glass particles or glass monoliths (Sect. 23.8). These products are either melt-casted into water to give granules or cast and annealed to give cones or thin plates of certain dimensions. The granules are sieved into different particle size fractions and used as such or as components in different products. The major trend within biomaterial research is to develop tissue-engineering scaffolds with interconnecting porosity. These scaffolds act as frameworks for infiltration, attachment and proliferation of cells throughout the scaffold to regenerate new vascularized tissue. For bone tissue engineering, different methods are employed to manufacture the desired 3-D porous structure mimicking the HCA architecture of cancellous bone (Fig. 23.2). In general, a porous product can
be manufactured from melt-derived glasses through sintering of particles, fibers and rods. As discussed in Sect. 23.3, the strong crystallization tendency of glasses 45S5 and S53P4 during thermal treatments within the temperature window from glass transition to liquidus temperature challenges the manufacture of any complicated products through hot-working. The glasses crystallize before the melt viscosity is low enough to promote viscous flow, and fiber drawing cannot be realized as the melt crystallizes at much lower viscosities than typically used in fiber drawing [23.59, 61]. However, the problems with hot-working can be overcome through composition tailoring, and the bioactive glasses are promising materials for tissue-engineering scaffolds capable of releasing therapeutic ions into the surroundings.
833
Part B | 23.7
These glasses possessed controllable conversion rates to HAP upon immersion in phosphate-containing solutions [23.141, 142]. The conversion rate to HAP was dependent on the ratio of B2 O3 =SiO2 . Higher B2 O3 content produced a more rapid conversion of the glass. HAP also formed on the silicate-free borate glass, which suggested that the presence of SiO2 or B2 O3 did not affect the ability to form HAP [23.141]. Because of the presence of K2 O and MgO in 1393B glass, it is easier to fabricate the B2 O3 -containing porous body by hot-working with the glass particulates. Porous 3-D scaffolds of 13-93B1 and 13-93B3 with a trabecular microstructure were prepared with a polymer foam replication technique [23.12]. When immersed in SBF, these scaffolds showed a marked decrease in mechanical strength with time as the conversion of glass into HAP increased [23.12]. The increase in conversion rate of the scaffolds with an increase in B2 O3 content was accompanied by an increase in the pH of the SBF. In the cell biocompatibility tests, the higher content of B2 O3 in the glass severely reduced the proliferation and cell functions of osteogenic cells in the scaffold [23.145]. Above a certain concentration, boron is known to be toxic to cells. The dissolution products of a borate glass in cell media were found to markedly inhibit the proliferation of bMSCs after 24 h of incubation when the boron concentration was above 1 mM [23.145]. When 13-93B1 and 1393B3 scaffolds were implanted in the dorsum of rats, faster degradation of the glasses was observed, compared with in vitro tests in SBF. Both glasses degraded completely and converted into HAP relics in the implantation sites in vivo [23.145]. Although the 13-93B3
23.7 Scaffolds for Tissue-Engineering Applications
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23.7.1 Requirements for Bone Tissue Scaffolds
Part B | 23.7
Bone tissue scaffolds must fulfil several criteria: They should have desired porosity, bioactivity, biocompatibility and adequate mechanical properties. In addition, the material should be capable of being economically processed into the desired shapes and dimensions [23.150]. The physicochemical and biological requirements for a tissue-engineering scaffold are schematically shown in Fig. 23.11. The different criteria for the bone tissue scaffolds are partly overlapping but also opposite in respect to e. g., biological and structural applications [23.151– 155]:
cells and excretion of waste products resulting from cell activity and scaffold degradation. 5. Mechanical integrity: The scaffold should have the mechanical performance needed to ensure its mechanical integrity during surgical implantation and to replace bone function during the healing process. Higher scaffold porosity results in diminished mechanical properties, thereby setting an upper functional limit for pore size and porosity. Also, the degradation rate of the scaffold material must match the rate of remodeling of bone to ensure mechanical integrity. 6. Manufacturability: The manufacture of the scaffold should by easy, flexible and cost effective.
23.7.2 Scaffold Fabrication Techniques 1. Biocompatibility: The elementary feature of any scaffold used for tissue engineering is that it must be biocompatible. After implantation, the scaffold must elicit a negligible immune reaction in order to prevent it from causing a severe inflammatory response that might impede healing or cause rejection by the body. 2. Osteoconductivity: The scaffold material should be able to serve as a template for bone formation by encouraging cells to colonize on its surface, to proliferate and to produce new bone. 3. Biodegradability: The scaffold material should be able to degrade over time in vivo to allow cells to produce their own extracellular matrix. The degradation rate should match the rate of tissue growth. 4. Scaffold architecture: The porosity of the scaffold must be high .> 80%/ and the pore size must be > 100 m to support tissue ingrowth, vascularization and cell penetration. An interconnected porous structure also ensures diffusion of nutrients to the
Scaffold fabrication techniques can be divided into different techniques according to the control capability of the size, geometry, interconnectivity and spatial distribution of the pores. Below these techniques are reviewed as (1) conventional techniques enabling lower control of the porosity parameters and (2) additive techniques giving more precise control of the porosity parameters. Conventional Techniques Sintering of Particles. Porous scaffolds of bioactive glasses have been manufactured through sintering of particles in a mold. The scaffolds manufactured through sintering of glass microspheres or particles have interconnected porosity but their porosity is lower than the optimal value reported for scaffolds [23.60, 156]. The porosity depends on the particle size and the sintering temperature [23.157]. The scaffolds sintered of glass microspheres of bioactive glass 13-93
Biodegradability
Architecture (pore size and porosity)
Bioactivity
Mechanical integrity
Nontoxicity and biocompatibility
Ease of fabrication
Scaffold
Angiogenic response possible
Osteoconductivity, Osteogenicity, Osteoinductivity
Fig. 23.11 Physicochemical and biological requirements of bone tissue-engineering scaffolds
Bioactive Glasses
showed good bone ingrowth in rabbit tibia [23.81] (Fig. 23.6).
Freeze Casting. In freeze casting, a colloidally stable aqueous suspension of bioactive glass particles is
100 μm
Fig. 23.12 SEM micrograph of a typical pore network within a foam scaffold of bioactive glass 58S (Reprinted from [23.159])
rapidly frozen in a nonporous mold after which the frozen solvent is sublimed at low temperatures in a vacuum. The mechanical strength of the scaffolds is fixed in a sintering process during which the fine pores in the walls of the macropores are eliminated. The growth direction of the ice crystals and thus the orientation of the microstructure of the scaffold can be controlled by directional freezing. A benefit of this oriented microstructure is the high scaffold strength, up to four times higher in the case of hydroxyapatite scaffolds, in the direction of orientation, compared to the strength of a scaffold with a randomly oriented microstructure [23.166, 167]. These strengths allow their consideration for load-bearing applications. However, most oriented scaffolds prepared from aqueous suspensions typically have a lamellar microstructure with a pore width in the range of 1040 m, which is considered to be too small to support tissue ingrowth. Scaffolds based on 45S5 and 13-93 glasses have been prepared using the freeze drying technique [23.168]. The oriented columnar structure of the porosity provided the scaffolds with high strength [23.169, 170]. These scaffolds supported cell proliferation and differentiation in vitro as well as tissue infiltration in vivo [23.58]. However, while the textured microstructure enhances the strength along determined orientations, it simultaneously weakens the material in other directions, which seriously limits their application in regions subjected to multiaxial loading. Foam Replica Technique. The foam or sponge replication technique is a process that was originally developed for the manufacture of ceramic foams in 1963 [23.171] and it has been extensively used to fabricate scaffolds. In this technique, a green body is prepared by immersing a synthetic or natural foam template into a slurry containing fine-grained bioactive glass particles. The slurry infiltrates the structure thus producing a homogeneous coating of particles on the foam struts. After drying, the polymer template and any organic binders used to prepare the slurry are burned out through controlled heat treatment between 300 and 600 ı C. In the end, the ceramic or glass struts are densified through sintering at an appropriate temperature. For most bioactive glasses the sintering temperature is 6001000 ı C, depending on the composition and particle size of the glass [23.63, 151]. The scaffolds have highly porous (4095%) open and interconnected porosity resembling the structure of cancellous bone. The external shape and microstructure of the scaffold replicate those of the porous polymer, generally polyurethane foams, serving as templates. Therefore, different pore sizes and geometries can be achieved by using appropriate polyurethane foams [23.172]. How-
835
Part B | 23.7
Foam Scaffolds. The gas-foaming technique originally developed for fabrication of polymeric scaffolds has been used to manufacture bioactive glass scaffolds from sols. First, the sol is foamed with the aid of a surfactant, followed by condensation and gelation steps. After aging and drying to remove the liquid byproduct, the gel is sintered to form a porous, three-dimensional scaffold, as described for the sol–gel bioactive glasses designated 58S and 70S30C [23.158, 159]. These scaffolds consist of both interconnected macropores (10500 m) resulting from the foaming process and mesopores (250 nm) that are inherent to the sol–gel process [23.160–163]. This technique has the advantage of being an organic solvent-free process. Its main weakness is that the process may yield a structure with largely unconnected pores and a nonporous external surface. The porous structure is considered to be beneficial for stimulating cell response in the scaffold. The macroporous bioactive glass foams have shown favorable results in both in vitro and in vivo tests for bone regeneration [23.164, 165]. However, although the scaffolds show appropriate biological properties, they had low strength (0:32:3 MPa) due to their large volumetric porosities. Consequently, they are suitable for substituting defects in low-load sites only [23.161]. Figure 23.12 shows a typical pore structure of a foam glass scaffold.
23.7 Scaffolds for Tissue-Engineering Applications
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Part B
Glass Families
ever, the strength of the final scaffold is typically in the range reported for cancellous bone, which limits its use to the repair of nonload-bearing bones. The foam replication method has been used for fabricating scaffolds from silicate, borosilicate, and borate bioactive glasses [23.145, 173, 174], including 45S5 [23.63, 175] and 13-93 bioactive glasses [23.56]. Figure 23.13 shows the microstructures of polyurethane foam, a sample of dry human trabecular bone and a scaffold of 13-93 manufactured using the foam replication method.
Part B | 23.7
Additive Techniques Additive manufacturing (AM), also referred to as rapid prototyping (RP), solid freeform fabrication (SFF) or 3-D printing (3-DP), has received significant attention in the field of tissue engineering [23.176, 177]. Additive manufacturing is a common name for a number of advanced fabrication techniques that can be used to produce objects layer-by-layer from a computer-aided design (CAD) model without using traditional tools such as dies or molds [23.178]. AM can also be used to build scaffolds whose porous structure follows a predesigned architecture modeled on a computer. In that way, the scaffold architecture can be controlled and optimized to achieve the desired mechanical response, and to accelerate the bone regeneration process. Moreover, by using data from medical scans (magnetic resonance a)
imaging, tomography techniques, etc.) to create the CAD model, it is possible to produce customized scaffolds that fit the patient’s lesion [23.166, 179, 180]. Additive manufacturing was used for the first time in the early 1980s to fabricate automotive engine parts and small telecommunication industry components. However, it took until the 1990s before rapid prototyping techniques were adapted into the medical and biomedical fields [23.181]. Over the past two decades more than 20 additive manufacturing techniques have been developed and commercialized. Basically, these methods can be classified into three basic types [23.182]: 1. Liquid-based 2. Solid-based 3. Powder-based rapid prototyping systems. The additive manufacturing techniques, which have been used in the preparation of tissue-engineering scaffolds from bioactive glasses, are described below. Stereolithography. In stereolithography (SLA), the scaffold is produced by curing a photoreactive resin with an ultraviolet (UV) laser or another similar power source. The SLA also utilizes a CAD file that describes the geometry and size of the parts to be built. The CAD file lists the coordination triangles that together
b)
Fig. 23.13a–d 250 μm
c)
500 μm
d)
250 μm
100 μm
Microstructures of (a) polyurethane foam (b) dry human trabecular bone, and (c,d) 13-93 glass scaffolds fabricated by polymer foam replication. (Reprinted from [23.56] with permission from Elsevier)
Bioactive Glasses
Selective Laser Sintering. Selective laser sintering (SLS) is an AM process that allows generation of complex 3-D parts by consolidating successive layers of powder material by sintering selected areas using the thermal energy supplied by a focused laser beam [23.186, 187]. Consolidation mechanisms involved in SLS can be solid-state sintering, liquid-phase sintering, partial melting, full melting or chemically induced binding [23.188]. After one layer of powder is a)
selectively sintered, a new layer of powder is spread on top to repeat the process. The preprocessing of the part model is similar in all other aspects to that described for SLA. The SLS technique has frequently been used to manufacture scaffolds of the bioactive glass 13-93. The compressive strength of cylindrical 13-93 scaffolds varied from 41 MPa for a structure with 60% porosity to 157 MPa for a structure with no designed porosity [23.189]. 13-93 scaffolds with cubic pores of the size range 300800 m and 50% apparent porosity exhibited an average compressive strength of 20:4 MPa, which is appropriate for nonload-bearing applications [23.190]. Figure 23.15 shows the structure of 13-93 scaffolds and the CAD model for the cubic repeatable unit used in the SLS fabrication of the structures. Direct Ink Writing. Direct ink writing or direct-write assembly techniques use a computer-controlled translation stage, which moves a pattern-generating device to create materials with controlled architecture and composition through the deposition of colloidal or organicbased inks. In these techniques, the ink is extruded utilizing standard syringes and needles to create structures layer-by-layer [23.191, 192]. The inks are formulated to create a stable, homogeneous suspension with a desired and reproducible rheological behavior. The critical rheological parameters for a given ink formulation include its apparent viscosity, yield stress under shear and compression, and viscoelastic properties. 3-D ink-writing techniques can be divided into two approaches: 1. Droplet-based techniques such as ink-jet printing [23.193] and hot-melt printing [23.194] 2. Filament-based techniques such as robocasting [23.195, 196], fused deposition [23.197], and freeze extrusion [23.198].
b)
1 mm
20 mm
Fig. 23.14a,b 45S5 bioglass parts fabricated by lithography-based DLP after sintering: (a) cylindrical cellular structure and (b) customized bone implant. (Reprinted from [23.185], with permission from Elsevier)
837
Part B | 23.7
make up the surface of the designed 3-D structure. This structure is virtually sliced into layers of the thickness that is used in the layer-by-layer (layer thickness 25100 m) fabrication process [23.183]. After the first layer has been photopolymerized by the UV laser, the built layer is recoated with the liquid resin and the procedure is repeated to give a structure of desired size and shape. The green structure is obtained after draining and removing the excess resin. In order to improve the mechanical properties of the structures, a postcuring with UV-light is often done. When printing ceramics or glasses, the photocurable resin is eliminated in the sintering treatment needed to consolidate the part. The main advantages of the SLA technique are its high reproducibility and high resolution (down to 200 nm), which enable the fabrication of objects with very small features [23.184]. Scaffolds of 45S5 have been manufactured with a lithography-based AM technique called digital light processing (DLP). Figure 23.14 shows cellular structures fabricated with the DLP technique from a slurry containing 45S5 particles, an acrylate-based monomer, an organic solvent (polypropylene glycol), a light absorber, and a photo initiator [23.185]. The porosity of the structures was 50%. The compressive strength of structures (0:33 MPa) was lower than the strength of porous 45S5 structures made by the foam replica method with much higher volumetric porosities [23.63].
23.7 Scaffolds for Tissue-Engineering Applications
838
Part B
Glass Families
b)
a)
1 mm
2 mm 10 mm
Part B | 23.7
Fig. 23.15 (a) SLS-fabricated 13-93 cubic porous parts with different pore size. (b) Repeatable cubic unit in the CAD model. [23.190], © IOP publishing. Reproduced with permission. All rights reserved
Regardless of whether the ink is deposited as a continuous filament or as individual drops, a careful control of ink composition, rheological behavior and printing parameters, enables the fabrication of 3-D structures layer-by-layer. All direct ink-writing techniques follow the same principals. Yet, robocasting has been used more than the rest of this family for fabrication of scaffolds from bioactive glasses. In robocasting, the desired structure is deposited layer-wise from a filament-based ink consisting of a highly loaded colloidal slurry. The ink is virtually binderless since less than 1 vol:% of organic additives are needed. Parts can be fabricated, dried and sintered in less than 24 h [23.199]. Robocasting requires careful characterization and control of the ink being deposited. The ink must be viscoelastic so that it yields upon extrusion but sets upon deposition [23.200]. In addition, it must contain a high solid volume fraction to minimize drying-induced shrinkage after assembly is complete [23.201]. The ink is extruded through a nozzle to construct the three-dimensional part in a layerby-layer sequence to achieve the desired CAD-designed scaffold. After deposition, the structure is dried and sintered to get the final scaffold. The compressive strength of bioactive glass 13-93 and 6P53B scaffolds fabricated by robocasting is comparable to the strength of human cortical bone (100150 MPa) [23.191, 202]. Similar to the other direct ink techniques, robocasting provides precise control of pore size, shape and alignment. In addition, highly uniform macroporosity can be obtained by varying rod spacing and size [23.202, 203]. Scaffolds with pore widths and strut diameters covering a wide range, from 10 to 1000 m, have been created by robocasting [23.204]. Robocasting allows the fabrication of scaffolds with homogeneous struts of high mechanical strength. Robocasting has been used to fabricate scaffolds of bioactive glasses 45S5 and 1393 [23.64, 205–207]. The strength of the robocasted
structures with uniform strut dimensions was significantly higher than the strength of the scaffolds of the same porosity but fabricated by conventional additive techniques. Figure 23.16 shows optical and SEM images of 45S5 glass-ceramic scaffolds fabricated by robocasting.
23.7.3 Postassembly Thermal Treatment In most of the additional manufacturing fabrication methods discussed in Sect. 23.7.2, the slurries and inks used to build the green bodies consist of glass particles and additives, usually polymeric materials. The polymeric components in the green scaffold are removed in thermal treatment, usually referred to as debinding treatment. The temperatures for debinding vary between 150 and 600 ı C, depending on the polymer decomposition temperature. The heating rate in the debinding step is also an important variable: the heating rate must be optimized to prevent void formation in the struts, and thus a decrease of the mechanical strength of the scaffold [23.189]. Since each polymer has its own decomposition temperature, it is sometimes necessary to develop a binder burnout schedule with several isothermal holding stages or very slow heating rates. This may result in lengthy debinding treatments that may last even several days [23.177, 208]. Final densification and mechanical strengthening of the scaffold are achieved in the sintering step. Sintering of glasses takes place through viscous flow between Tg and crystallization peak temperature while at higher temperatures the sintering mechanisms change. As discussed in Sect. 23.3, the temperature window for viscous flow sintering is narrow for bioactive glasses 45S5 and S53P4, thus preventing the manufacture of amorphous scaffolds with adequate mechanical strength. The additives in the slurry or the ink may affect the sin-
Bioactive Glasses
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23.8 Bioactive Glasses in Clinics and Health Care
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Fig. 23.16a–c Optical images (a) and SEM micrographs (b,c) of as-cut robocasted glass-ceramic 45S5 scaffold sintered at 1000 ı C. (Reprinted from [23.64, 205], with permission from Elsevier)
scaffolds are comparable to the strength of cancellous bone [23.64]. The wide sintering window for bioactive glass 13-93 (around 200 ı C) enables full densification at relatively low temperatures .< 700 ı C/ [23.62, 209]. Since the porosity is eliminated, the amorphous scaffolds have significantly improved mechanical properties compared to 45S5 scaffolds [23.205, 210]. The bioactive glass 13-93, despite its somewhat lower bioactivity, has been used by several research groups to manufacture porous tissue-engineering scaffolds. Also new compositions, which have better hot-working properties, are developed and tested. These compositions are often doped with a certain therapeutic ion to enhance tissue integration.
23.8 Bioactive Glasses in Clinics and Health Care The invention of Bioglass® initiated a totally new approach to development of biomedical implants; the implant should form a direct bond with the bone, rather than be encapsulated by fibrous tissues, as seen for inert implants. The later finding of the capability of Bioglass® to stimulate bone regeneration as well as to provide antimicrobial effects against many pathogens at the implant sites made bioactive glasses attractive materials for fabricating tissue-engineering devices. To date, granules of Bioglass® 45S5 have been used as a graft in bone defects and reconstruction in more than 1:5 million patients. One additional advantage of this synthetic graft is that besides stimulating bone growth it reduces the need of harvesting autograft bone from one part of the patient to be transplanted into the defect site. Today, extensive research efforts are underway to utilize the degradation of bioactive glasses with tuned compositions to deliver inorganic dissolution products for the stimulation of genes to regenerate tissue. The
discovery of gene-activating glasses [23.19] has opened up new horizons for applications ranging from additive ingredients in personal health care products to the healing of chronic wounds. The most representative medical devices and products developed from bioactive glasses either already on the market or showing success in clinical trials are discussed below. Clinical trials and applications have recently been reviewed more comprehensively [23.4, 5].
23.8.1 Synthetic Bone Graft Granules and Putties Most commercial bioactive glass products on the market are based on the compositions 45S5 and S53P4. Since both compositions easily crystallize during processing, the majority of products are based on glass granules or different powdered fractions. During the past years, products and packages that can be easily used by clinicians have been launched.
Part B | 23.8
tering window. For 45S5, Tg for the as-received glass powder was 560 ı C and the crystallization peak temperature 685 ı C. However, these temperatures were 60 and 30 ı C lower, respectively, for the dried ink [23.64]. The robocasted 45S5 scaffolds shown in Fig. 23.16 have crystallized during the sintering step and are thus partly crystalline. The residual liquid phase in the system aids in densification although some porosity will remain in the struts depending on the sintering temperature. In general, the phase composition and the residual porosity of the bioactive glass-ceramic scaffolds depend on the heating rate, particle size and upper sintering temperature used for each composition. The compressive strength of 45S5 glass-ceramic
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Particulates of 45S5 are marketed under the names PerioGlas® (NovaBone Products LLC, FL), NovaBone® (NovaBone Products LLC, FL) and Biogran® (Biomet 3i, FL). The two first products consist of 90710 m particles while Biogran® particles are of a narrow size fraction, 300350 m. These products are used in the repair of nonload-bearing bone defects in orthopaedics and in maxillofacial reconstruction [23.5]. In preclinical and clinical studies, all these products have effectively filled bone defects. NovaBone® has had FDA approval for orthopaedic use since 2005 and for using the term osteostimulation to describe its cellular activity since 2015 [23.5]. Glass S53P4 is commercially available as BonAlive® particles of three different size fractions: 500800, 10002000 and 20003150 m (BonAlive Biomaterials Ltd, Finland). The indications of all size fractions are in orthopaedics for cavity filling and treating of chronic osteomyelitis, while the smallest fraction also has applications in craniomaxillofacial surgery and ear, nose and throat surgery. BonAlive® granules received the FDA’s 510 (k) clearance for orthopaedic use in 2008. The documented data is extensive on clinical trials concerning application of S53P4 in the removal of benign bone tumors [23.211], treating bone defects from trauma [23.212], aiding bone repair in maxillary sinus floor lifting treatment [23.213], as well as treating chronic osteomyelitis in the spine owing to the antimicrobial properties of the products [23.214]. Table 23.9 summarizes the results of using glass S53P4 for the reconstruction of cranial defects in 271 patients in the Department of Otorhinolaryngology—Head and Neck Surgery of Turku University Hospital (Turku, Finland) over the period 1991–2010. In the 14 year follow-up to the implantations of S53P4 granules (14 mm, 14 patients) into bone defects left by benign bone tumor surgery in hands, tibia and humerus, the cortical bone regenerated with S53P4 treatment was twice as thick as that when autograft was used [23.211, 215]. However, some of the glass remained in the bone, even after 14 years. The clinical follow-up studies also verified the curing effect
of S53P4 on chronic osteomyelitis in the spine, which was treated with S53P4 by filling the cavity bone defects, with metallic stabilization of the vertebrae. In the 1038 month follow-up, nine patients healed without complications, while the other two had unrelated complications [23.214]. S53P4 granules have also successfully been used in trials of 7 patients for filling cavities in the middle ear created by surgeons removing mastoid air cells and mucous membranes that were damaged by chronic infection [23.216]. Novabone® and BonAlive® are today available also in the form of putties, in which bioactive glass granules are mixed with water-soluble synthetic binders. The binding agent temporarily binds the glass granules together in the putties, which allows the surgeon to mold the material directly to the bone defects without further mixing and preparation. After implantation, the binder is absorbed and leaves more space for new bone to grow between the granules.
23.8.2 Borate Glass Microfibers for Healing Chronic Wounds Bioactive glass has also demonstrated great potential in soft-tissue repair. Excellent clinical results have been reported in veterinary practices as well as in human trials using a cotton candy-like scaffold made of borate glass microfibers for treating chronic wounds [23.217]. The product is available as the commercial product RediHeal, for healing skin wounds in animals. MoSci Corporation (Missouri, US) has also endeavored to commercialize the borate glass 13-93B microfibers under the name of DermaFuse for clinical use in the healing of chronic wounds in patients. In a clinic trial with 12 venous stasis volunteers conducted at the Phelps County Regional Medical Center in Rolla, Missouri, DermaFuse was applied as pads to the wounds of the patients and was proven to speed up the healing process of their long-term wounds [23.218, 219]. Currently, more human trials of DermaFuse are progressing towards FDA approval [23.219]. Borate glass microfibers are advantageous as wound care dressing materials due to their outstanding properties, e. g., high
Table 23.9 Number of patients and success rate in clinical studies of using bioactive glass S53P4 for the reconstruction
of fronto-orbital defects in 271 patients (table courtesy of Prof. Kalle Aitasalo) Operative treatment Frontal sinus obliteration (granules) Fronto-orbital trauma reconstruction (plates/granules) Fronto-orbital tumor reconstruction (plates and/or granules): Benign tumor Malignant tumor
Number of patients Success Total 88 91 116 124 27 20
28 28
Success rate (%) 72 94 96 71
Bioactive Glasses
surface area, rapid degradation and conversion to HCA, ease of handling and shape flexibility. Still, the main hurdles on the commercialization path of borate-based bioactive glasses are the public’s perception of the systemic effect of boron in higher dosages as well as the lack of large-scale clinical trial data featuring more diverse patient complexity criteria.
23.8.3 Bioactive Glass Particulates as Additives in Toothpaste
or thermal stimuli, also termed dentine hypersensitivity. The dissolution products of bioactive glass fine particles added in toothpastes can stimulate natural HCA formation over and in the tubule ends and thus can prevent dentine hypersensitivity. The most successful commercialization of 45S5 fine particulates (average size around 18 m) is NovaMin® in the Sensodyne Repair and Protect® formulation (GlaxoSmithKline, UK). Another bioactive glass-containing toothpaste with improved functions is the newly launched BioMinF® toothpaste by BioMin Technologies Ltd (London, UK). BioMinF® is based on the patented fluoride-containing glass compositions of SiO2 -CaO-Na2 O-P2 O5 -CaF2 . BioMinF® has a high phosphate content, which significantly increases apatite formation [23.220]. BioMinF® slowly releases calcium, phosphate and fluoride ions over a timeframe of 812 h to form fluorapatite mineral on the dentine for longlasting protection, which is even more resistant to acid attack than HCA.
23.9 Summary and Outlook The discovery of the first bioactive glass in 1969 gave birth to a new era in the development of synthetic, nontoxic and safe materials to be implanted inside the human body. Using a brittle material, glass, in implants may appear not an ideal choice. However, the special composition of bioactive glasses favors their rapid integration and bonding with living tissue, especially bone. Moreover, the bioactive glasses degrade while providing space for growth of new tissue. The finding that the inorganic ion dissolution products stimulated cellular processes at the genetic level opened up the possibility to develop bioactive glass scaffolds for novel bone and soft-tissue engineering applications. Among the solid materials, glasses are unique; their amorphous structure enables the incorporation of almost any element. Further, their properties can be tailored to smoothly vary with the overall composition and content of the individual components. Glasses are thus ideal materials for controlled delivery of any particular inorganic therapeutic ion into the interfacial solution over the critical period needed for tissue regeneration. The bioactive glass products on the market today are mainly particles used as bone grafts capable of stimulating tissue growth and/or cure infections in certain indications. The future challenge is, however, to utilize the possibility of fabricating bioactive glasses into any desired 3-D form supporting and stimulating ideal tissue growth. This requires a better understanding of the
concentrations of therapeutic ions needed to stimulate tissue regeneration and a detailed knowledge of the release rate of the ions from the glasses in the conditions of the target application. Needless to say, the composition choice must also fulfil the requirements of the scaffold fabrication. The inherent brittleness of glasses prevents their use in load-bearing applications. However, if used as components in composite devices, the gene stimulating or bacteriostatic and antibacterial effects can be exploited. Coating the bioactive glass scaffolds with polymers is being explored as a means of increasing the mechanical performance. The interactions and degradation rates of different composite components in the body environment are not fully understood. Future medical devices will be customized structures with a specified external geometry and an optimal internal structure and morphology. For these, new glass compositions and new manufacturing techniques are being developed. Accordingly, the field of bioactive glasses continues to be a topical issue. The increasingly detailed understanding of the atomic scale structure and its influence on glass properties will provide a means for future design of bioactive glasses for medical devices. However, although the bioactive glass-based devices appear promising after the preclinical and clinical tests, their full potential will not be revealed until after several years of clinical follow-up studies.
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Bioactive glasses also find application in personal health care products. Currently, the largest commercial use of bioactive glass is in toothpaste. HCA is the main inorganic material in teeth, i. e., in enamel, dentine and cementum. The tooth surface is covered by dense enamel while the dentine below the enamel consists of narrow tubules that lead to the pulp and sensitive nerve endings. The decay of enamel exposes the dentine tubules, which causes the pain associated with chemical
23.9 Summary and Outlook
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K.C.R. Kolan, M.C. Leu, G.E. Hilmas, M. Velez: Effect of material, process parameters, and simulated body fluids on mechanical properties of 13-93 bioactive glass porous constructs made by selective laser sintering, J. Mech. Behav. Biomed. Mater. 13, 14–24 (2012) K.C.R. Kolan, M.C. Leu, G.E. Hilmas, R.F. Brown, M. Velez: Fabrication of 13-93 bioactive glass scaffolds for bone tissue engineering using indirect selective laser sintering, Biofabrication 3, 025004 (2011) J.A. Lewis, G.M. Gratson: Direct writing in three dimensions, Mater. Today 7, 32–39 (2004) C. Chang, E.D. Boland, S.K. Williams, J.B. Hoying: Direct-write bioprinting three-dimensional biohybrid systems for future regenerative therapies, J. Biomed. Mater. Res. B 98, 160–170 (2011) X. Zhao, J.R.G. Evans, M.J. Edirisinghe, J.H. Song: Ink-jet printing of ceramic pillar arrays, J. Mater. Sci. 37, 1987–1992 (2002) V. Chovancova, A. Pekarovicova, P.D.I. Fleming: Hot melt inks for 3-D printing. In: Proc. Digit. Fabr. Conf. 2005 (2005) pp. 143–147 D. Therriault, S.R. White, J.A. Lewis: Chaotic mixing in three-dimensional microvascular networks fabricated by direct-write assembly, Nat. Mater. 2, 265–271 (2003) G.M. Gratson, M. Xu, J.A. Lewis: Microperiodic structures: Direct writing of three-dimensional webs, Nature 428, 386 (2004) M. Allahverdi, S.C. Danforth, M. Jafari, A. Safari: Processing of advanced electroceramic components by fused deposition technique, J. Eur. Ceram. Soc. 21, 485–1490 (2001) T.S. Huang, M.N. Rahaman, N.D. Doiphode, M.C. Leu, B.S. Bal, D.E. Day, X. Liu: Freeze extrusion fabrication of 13-93 bioactive glass scaffolds for repair and regeneration of load–bearing bones, Ceram. Trans. 228, 45–55 (2011) J. Cesarano III: A review of robocasting technology, Solid Free. Addit. Fabr. Mater. 542, 133–139 (1999) J. Dellinger, J. Cesarano, R.D. Jamison: Robotic deposition of model hydroxyapatite scaffolds with multiple architectures and multiscale porosity for bone tissue engineering, J. Biomed. Mater. Res. A 82, 383–394 (2007) J.E. Smay, J. Cesarano, J.A. Lewis: Colloidal inks for directed assembly of 3-D periodic structures, Langmuir 18, 5429–5437 (2002) A.M. Deliormanli, M.N. Rahaman: Direct-write assembly of silicate and borate bioactive glass scaffolds for bone repair, J. Eur. Ceram. Soc. 32, 3637–3646 (2012) J.G. Dellinger, A.M. Wojtowicz, R.D. Jamison: Effects of degradation and porosity on the load bearing properties of model hydroxyapatite bone scaffolds, J. Biomed. Mater. Res. A 77, 563–571 (2006) C. Gao, M.N. Rahaman, Q. Gao, A. Teramoto, K. Abe: Robotic deposition and in vitro characterization of 3-D gelatin-bioactive glass hybrid
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K. Pernaa, I. Koski, K. Mattila, E. Gullichsen, J. Heikkilä, A.J. Aho, N.C. Lindfors: Bioactive glass S53P4 and autograft bone in treatment of depressed tibial plateau fractures: A prospective randomized 11-year follow-up, J. Long Term Eff. Med. Implants 21, 139–148 (2011) T. Turunen, J. Peltola, A. Yli-Urpo, R.-P. Happonen: Bioactive glass granules as a bone adjunctive material in maxillary sinus floor augmentation, Clin. Oral Implant Res. 15, 135–141 (2004) N.C. Lindfors, P. Hyvönen, M. Nyyssönen, M. Kirjavainen, J. Kankare, E. Gullichsen, J. Salo: Bioactive glass S53P4 as bone graft substitute in treatment of osteomyelitis, Bone 47, 212–218 (2010) N.C. Lindfors, J.T. Heikkilä, I. Koski, K. Mattila, A.J. Aho: Bioactive glass and autogenous bone as bone graft substitutes in benign bone tumors, J. Biomed. Mater. Res. B 90, 131–136 (2009) P. Stoor, J. Pulkkinen, R. Grenman: Bioactive glass S53P4 in the filling of cavities in the mastoid cell area in surgery for chronic otitis media, Ann. Otol. Rhinol. Laryngol. 119, 377–382 (2010) S. June: Treatment of chronic wounds with bioactive borate glass fibers. In: An Introduction to Bioceramics, 2nd edn., ed. by L.L. Hench (Imperial College Press, London 2013) P. Wray: Cotton candy’ that heals?, Am. Ceram. Soc. Bull. 90, 25–29 (2011) P. Wray: Wound healing: An update on Mo-Sci’s novel borate glass fibers, Am. Ceram. Soc. Bull. 92, 30–35 (2013) M. Mneimne, R.G. Hill, A.J. Bushby, D.S. Brauer: High phosphate content significantly increases apatite formation of fluoride-containing bioactive glasses, Acta Biomater. 7, 1827–1834 (2011)
Leena Hupa Faculty of Science and Engineering Åbo Akademi University Turku, Finland [email protected]
Leena Hupa is Professor of Inorganic Chemistry and leader of the Combustion and Materials Chemistry group at Åbo Akademi University, Finland. Her research deals with high-temperature processes and properties of high-temperature materials for biomedicine, bioenergy, and circular economy applications.
Xiaoju Wang Faculty of Science and Engineering Åbo Akademi University Turku, Finland [email protected]
Xiaoju Wang is a Postdoctoral Researcher at the Johan Gadolin Process Chemistry Centre of Åbo Akademi University, Finland. Her research has focused on sol-gel derived bioactive glasses and their composite materials with biodegradable polymers in various tissue engineering applications.
Siamak Eqtesadi Abalonyx AS Oslo, Norway [email protected]
Siamak Eqtesadi was a Postdoctoral Researcher in the Laboratory of Inorganic Chemistry at Åbo Akademi University (Finland). He has worked on glass synthesis, rheology and chemistry of high concentrated inks, direct write printing of 3-D scaffolds for biomedical applications and sintering.
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scaffolds for biomedical applications, J. Biomed. Mater. Res. A 101, 2027–2037 (2013) S. Eqtesadi, A. Motealleh, P. Miranda, A. Lemos, A. Rebelo, J.M.F. Ferreira: A simple recipe for direct writing complex 45S5 Bioglass® 3-D scaffolds, Mater. Lett. 93, 68–71 (2013) Q. Fu, E. Saiz, A.P. Tomsia: Direct ink writing of highly porous and strong glass scaffolds for loadbearing bone defects repair and regeneration, Acta Biomater. 7, 3547–3554 (2011) S. Eqtesadi, A. Motealleh, A. Pajares, P. Miranda: Effect of milling media on processing and performance of 13-93 bioactive glass scaffolds fabricated by robocasting, Ceram. Int. 41, 1379–1389 (2015) N.D. Doiphode, T.S. Huang, M.C. Leu, M.N. Rahaman, D.E. Day: Freeze extrusion fabrication of 13-93 bioactive glass scaffolds for bone repair, J. Mater. Sci. Mater. Med. 22, 15–523 (2011) L. Lefebvre, J. Chevalier, L. Gremillard, R. Zenati, G. Thollet, D. Bernache-Assolant, A. Govin: Structural transformations of bioactive glass 45S5 with thermal treatments, Acta Mater. 55, 3305–3313 (2007) S. Eqtesadi, A. Motealleh, A. Pajares, F. Guiberteau, P. Miranda: Improving mechanical properties of 13-93 bioactive glass robocast scaffold by poly (lactic acid) and poly ("-caprolactone) melt infiltration, J. Non-Cryst. Solids 432, 111–119 (2016) N. Lindfors, I. Koski, J.T. Heikkilä, K. Mattila, A.J. Aho: A prospective randomized 14-year follow-up study of bioactive glass and autogenous bone as bone graft substitutes in benign bone tumors, J. Biomed. Mater. Res. B 94B, 157–164 (2010)
References
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Part C
Character Part C Characterization of Glasses
24 Thermal Analysis of Glass Erick Koontz, Tucson, AZ, USA 25 Optical Spectroscopy of Glass Barrett G. Potter Jr., Tucson, AZ, USA 26 Terahertz Time-Domain Spectroscopy of Glasses S. K. Sundaram, Alfred, NY, USA
29 Refractive Index of Optical Materials Jean-Louis Meyzonnette, Palaiseau, France Jacques Mangin, Dijon, France Michel Cathelinaud, Rennes, France 30 Neutron and X-Ray Diffraction of Glass Laurent Cormier, Paris, France
27 Electron and Ion Beam Characterization of Glass Jennifer McKinley, Orlando, FL, USA 28 Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass Josef W. Zwanziger, Halifax, Canada Ulrike Werner-Zwanziger, Halifax, Canada Courtney Calahoo, Halifax, Canada Alexander L. Paterson, Halifax, Canada
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_23
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Erick Koontz
This chapter explores the use of thermal analysis in the characterization of glassy materials. Common characterization methods are described as well as a basic overview of the techniques mentioned. Differential scanning calorimetry, thermomechanical analysis, and measurement of glass viscosity are among the primary topics covered. The inner workings of each of the instruments in question is touched upon, along with general calibration procedures and best practices for measurement. Where appropriate, basic material science principles are used to improve the readers’ understanding of the reason for a measurement or particular method. While outlining the most important instruments in the thermal analysis of glasses, key glass properties such as glass transition temperature, crystallization temperature, melting temperature, and softening point are explained. Finally, a discussion of glass viscosity necessary for an understanding of the most common viscosity measurement instruments and methods is included.
Thermal analysis is a major part of scientific discovery. Scientists use the thermal radiation of distant objects to interpret the history of gas expansion in the far reaches of the known universe on a scale of 10’s of Giga-lightyears. On the other end of the spectrum, thermal analysis can be used in material science to probe the bonding of molecules on a scale of 10’s of nanometers. The field of material science relies heavily on thermal analysis, while in the study of glass, it is absolutely essential. Thermal analysis in this case is testing that analyzes the properties of a material with thermal energy. In materials, the study of thermal properties is most often carried out with either the stimulus or the measurement of temperature. The measurement of temperature is the easiest and most common way to characterize the thermal properties of a material. Thermocouples and thermistors are well characterized, well understood, and relatively inexpensive technologies used to measure the temperature of a given target. Thermocouples in partic-
24.1 24.1.1
Differential Scanning Calorimetry (DSC)............................... DSC Techniques..................................
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24.3 Thermomechanical Analysis............... 24.3.1 TMA Property Measurement ................ 24.3.2 Structural Relaxation .........................
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Thermogravimetric Analysis (TGA).......
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24.5 Viscometry........................................ 24.5.1 Measuring Viscosity............................ 24.5.2 Quantifying Viscosity..........................
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ular are in widespread use and capable of very accurate temperature measurement over a wide range of temperatures. Different types of thermocouples are used to characterize different temperatures, and the most common types are capable of measuring temperatures from well below freezing to nearly 1500 ı C. This ability to measure temperature over such a large range makes characterization of many glass properties possible. Temperature in itself is often not sufficient to reveal details about a material’s thermodynamic response to nonthermodynamic stimuli or its nonthermodynamic response to thermodynamic stimuli. When temperature measurement is combined with the measurement of heat flow, which is also dependent on temperature measurement over a physical distance, a large amount of material property information can be gained. Heat capacity, thermal conductivity, phase change temperatures, and other parameters can be measured and analyzed using thermal analysis.
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_24
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Thermal Ana 24. Thermal Analysis of Glass
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The broader field of material science, into which glass science falls, often utilizes nonthermal testing methods to determine material properties. Mechanical characterization methods are useful for determining material properties like hardness, Young’s Modulus, fracture toughness, and related values. However, mechanical testing of glasses can be difficult. This difficulty is because of the fracture mechanisms in glasses. Crystalline materials fracture along crystal planes; the fracture can be aided by defects in the material. Because of this, crystalline materials made by similar processes and having a similar concentration of defects exhibit consistent mechanical properties. Glasses are more difficult to analyze mechanically because flaws and imperfections in the material’s surface are usually the dominant modes of fracture. This means that slight cracks, chips, or irregularities in the glass surface can cause the mechanical properties, measured by mechanical means, to vary greatly. Mechanical testing of glasses requires extensive sample preparation, aided by the testing of a large volume of samples in order to statistically determine the validity of measured results. This is one of the main reasons that glass scientists rely heavily on thermal analysis. Another reason that mechanical testing of glasses is not as common as thermal analysis, is that glasses are typically used in nonstructural applications. There are exceptions to this, of course, but a lack of load-bearing applications and the difficulty of mechanical property measurements makes thermal analysis a more attractive tool for characterizing glasses. The thermal analysis methods discussed in this chapter generally fit into one of two main categories. The first is what we will call thermodynamic properties; this includes material properties such as phase transitions, glass transition temperatures, decomposition temperatures, etc. These are thermal properties that are uncovered by modulating the temperature of the sample and measuring the thermal response. Thermal properties are responses of the material to thermal
changes that have thermodynamic form. When a material is heated past melting, the additional heat energy input is not the only occurrence. The material must go through a transition from one thermodynamic state to another in order to go from solid to liquid. The second general type of measurement that falls under the umbrella of thermal analysis is the observable mechanical response of a material to an increase or decrease in temperature. Thermal expansion properties and viscosity fall under this type. The actual change in average bond lengths that lead to an apparent thermal expansion are a thermodynamic change. This change in bond lengths with temperature is observed as thermal expansion in both solids and liquids. Similarly, a change in viscosity is observable when a glassy material is heated. The fundamental change behind this is a thermodynamic one, however that change can be measured mechanically. It is possible to measure bond lengths in glasses and in doing so learn how a material’s expansion and viscosity behavior scales with temperature, but oftentimes in thermal analysis of glasses a material’s macroscopic properties are of more interest. Additionally, x-ray diffraction is used to measure bond lengths in solids and the scientific know-how to carry out this technique precludes its use in many cases [24.1]. Glass scientists in industry and academia often rely on macroscopic thermomechanical testing to obtain the data needed in relation to the expansion and viscosity versus temperature behavior of glasses. Thermal analysis of glass is a highly empirical part of glass science. As more computing power enables advanced modeling, more experimentation is required to serve as the basis of assumptions and validation of theoretical calculations. Without concrete measurement techniques, models and calculations hover as educated deduction between theory and fact. From simple industrial qualification of the most basic properties, to the pursuit of a detailed understanding of the glass transition, thermal analysis is an indispensable tool for the manufacture and study of glass.
24.1 Differential Scanning Calorimetry (DSC) Differential Scanning Calorimetry (DSC) is a technique used to detect phase transitions and other thermodynamic events occurring within a material. DSC can detect phase changes such as melting, crystallization, and solidification (or fusion). Additionally, DSC is a powerful tool for measuring percent crystallinity, heat of reaction, and heat capacity in glasses. Not only are DSCs capable of identifying temperatures of reactions as well as the magnitude of energies involved in those reactions,
but they are also capable of identifying the kinetics of a given reaction. Reaction kinetics can help glass scientists identify the way in which reactions take place. This is particularly useful when studying the way in which reaction kinetics differ when heating through a reaction as opposed to cooling through a reaction. On the most basic level, a DSC allows a scientist or engineer to determine where in terms of temperature these transition events occur. However, a DSC involves not just the
Thermal Analysis of Glass
temperature of the material. This increase or decrease in energy without an increase or decrease in temperature or pressure causes an observable peak or valley in a DSC measurement. The practical effect of this can be seen when boiling water. The 1st-order phase transition from liquid to gas creates a mixture of the two phases which are both at 100 ı C; the liquid water which is boiling can never be at a temperature higher than 100 ı C at standard atmospheric pressure and the latent heat (of vaporization) is being absorbed to complete the transition to steam. Mathematically, the definition of a 1st-order transition is a transition over which the Gibbs free energy as a function of temperature and pressure is continuous, while the partial derivative of the Gibbs free energy with respect to temperature and with respect to pressure are discontinuous. The Gibbs free energy is essentially the amount of thermodynamic potential energy in a material at constant temperature and pressure. The expressions in (24.1) are discontinuous for a 1st-order transition. @G @G SD and V D ; (24.1) @T p @p T where G is the Gibbs free energy, T is temperature, p is pressure, V is volume, and S is entropy. Glassy materials exhibit what is known as a glass transition. This transition occurs at the glass transition temperature (Tg ). This transition falls into the category of what is known as a 2nd-order phase transition [24.2]. A 2nd-order phase transition has a continuous Gibbs free energy with respect to temperature and pressure. The first derivatives of Gibbs free energy (24.1) are continuous, but the second derivatives are discontinuous. This is true for all partial 2nd derivatives of Gibbs free energy as functions of temperature and pressure. Equation (24.2) shows the 2nd derivative which has greater relevance when making DSC measurements. 2 @G Cp D T ; (24.2) @T 2 p where Cp is the heat capacity, and all other values are the same as those defined in (24.1). Heat capacity is a property that defines how much heat must be input into a specific mass of a material in order to increase its temperature. The SI unit for heat capacity is J=K. There are two ways of measuring the flow of heat into a material. The first is called power compensation DSC. Power compensation DSC operates by ensuring that the temperatures of both the sample and the reference are kept identical (as far as possible). In order to keep the temperature equal between two different materials, different magnitudes of power (heat flow) are
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measurement of temperature with respect to transitions but also the magnitude of thermal energy absorbed or evolved by those transitions. If the mass of the sample is accurately known it is possible to determine properties like the heat of fusion, heat capacity of the material in different phases, and other critical material properties. Before discussing the physical operating principles of DSC, a few basic points related to thermal analysis and reactions within materials should be discussed. The first basic principle to understand when measuring or interpreting the heat flow data output by a DSC is the difference between exothermic and endothermic reactions. An exothermic reaction is one in which heat is one of the byproducts of the reaction. This type of reaction is easily demonstrated when a strong base like potassium hydroxide (KOH) is added to liquid water (H2 O). The chemical result of this mixture is a KOH solution that is produced through a very exothermic reaction. The vessel used for such a reaction becomes too hot to touch. This same principle is seen in reactions such as the solidification of liquids, i. e., when a liquid is cooled to its melting point, it must get rid of a significant amount of heat as its structure changes from a disordered liquid to a much lower energy solid. The difference in internal energy between the two states must be output as heat. That is the essence of an exothermic reaction. An endothermic reaction is a reaction that requires energy to be absorbed into the system. This is evident in an everyday task such as boiling water. In order to move from the liquid phase to a higher energy gaseous phase a large amount of energy must be absorbed into the system. Each DSC readout has a positive and negative heat flow direction. It is necessary to carefully observe whether the DSC readout uses the sign convention of exothermic up or exothermic down. This will affect the appearance of the graph and could lead to confusion if not clearly understood. All graphs in this chapter follow the sign convention exothermic up. DSC measurements produce heat flow versus temperature diagrams as seen in Fig. 24.3; the features of interest in these heat flow diagrams are phase transitions. A phase transition is a thermodynamic transition from one material phase to another (i. e., liquid to gas, solid to liquid, gas to plasma, and the reverse). More specifically, those types of transitions are called 1st-order phase transitions. First-order transitions are defined as phase transitions that show a discontinuity in entropy and volume. Within a particular phase, materials exhibit a continuous entropy versus temperature and volume versus pressure behavior. However, when undergoing a 1st-order phase transition, a latent heat is involved. Latent heat is the energy increase or decrease needed to facilitate a transition, however, this absorption or release of heat does not apparently change the
24.1 Differential Scanning Calorimetry (DSC)
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necessary for each of the different samples. It is this difference in heat flow that provides the essential information on a DSC readout. If the sample is going through a phase transition such as melting which requires an instantaneous, large input of energy to the sample, the heat flow from the DSC will need to be increased to keep the sample and reference at the same temperature. This spike in heat flow will appear on the DSC readout and can be interpreted as the melting point of the sample material. The other method is called the heat flux method. The heat flux method works by keeping the heat flux to the samples constant and measuring the resultant temperature change. The standard relation between heat flow, ramp rate, and heat capacity for DSC is shown in (24.3). dH D Cp dt
dT dt
C f .T; t/ ;
(24.3)
where H is enthalpy in Joules, t is time in seconds, Cp is heat capacity in J=K, T is temperature in Kelvin, and f .T; t/ is a temperature- and time-dependent function of the system. The principles that guide how a DSC measures material properties are quite straightforward. The essential makeup of what is called the DSC cell can be seen in Fig. 24.1. DSC is a comparative technique, meaning one reference material is measured alongside the sample material of interest, and the difference between the two is the recorded information. Materials measured in a DSC are placed in pans; these pans can be made of different materials. Most commonly, the pans (Fig. 24.2) are made of aluminum, platinum, or for high tempera-
tures, alumina. The pans can be hermetically sealed or left open to the environment within the DSC cell which is typically flushed with a dry inert gas. Within the DSC cell, two smooth flat spots mark the placement locations for the sample and reference materials. The pans containing these materials are placed on each of these spots. The skin of the DSC cell is made of a very heat-conductive material, often Inconel. When considering homogenous crystalline materials, the transitions that can be seen are often clearly defined. As the temperature is increased, transitions from one crystalline phase to another can be observed, and finally melting can be seen. If the temperature is then lowered, solidification and any reversible crystalline phase changes will be seen during cooling. The heights of these peaks or valleys (depending on the direction of the heat flow) combined with the mass of the sample undergoing transition, will allow the various energies associated with those transitions to be calculated. In the case of glass, the major transitions are the same with some notable exceptions. Glass is amorphous, therefore it has no long range order even when it is in its solid state. Figure 24.3 shows the DSC trace of a glass ceramic material. A glass ceramic is a glass that has been crystallized to some extent; the amount of crystal versus glass in a glass ceramic is typically discussed as vol:% crystallinity. In Fig. 24.3, the key transitions have been noted. Low to high temperature, the first transition that can a)
b)
c)
Fig. 24.2a–c Aluminum DSC pans: top (a) and bottom (b) half and assembled pan (c) Measuring cell Reference Heat-flux sensor
Heat flow (W/g)
Sample
2.9 Protective gas
2.7 2.5 2.3
Furnace block with heating
Tg
2.1 1.9 90 Purge gas
Fig. 24.1 Schematic representation of a Netzsch DSC cell
140
190
Tx1
240
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340 390 440 Temperature (°C)
Fig. 24.3 DSC curve of an example glass ceramic
Thermal Analysis of Glass
24.1.1 DSC Techniques Standard DSC The most common type of DSC measurement used in both industry and academia is a simple ramp rate method. This method involves a sample of known mass (typically a few mg) in a pan, opposite a reference pan that contains either a reference material or sometimes no material at all. DSC samples are most commonly powder, crushed to a fine particle size by mortar and pestle. If very detailed, mass-dependent properties are
to be measured, monosized particles are desired. Conduction is the main method of heat transfer in a DSC cell, so good conductive contact between the pan and sample material is necessary for accurate results. The smaller the particle size, the faster each particle will absorb and expel heat energy and the faster the temperature change response will be. In the case of surface crystallization measurements, powder size can strongly affect the measured crystallization response. Bulk samples are sometimes used in DSC measurements, but the samples must be flat and sometimes polished to make the interface between the bottom of the sample and the sample pan as seamless as possible. In glass science, low-temperature glasses can be synthesized in the DSC pan from raw elements; this creates a sample that has an exceptional interface with the bottom of the pan. A typical DSC is capable of reaching temperatures of 800 ı C and heating rates from 0:1 to 100 ı C=min. Cooling rates vary based on the equipment and accessories purchased for a DSC. Ambient cooling could be used for cooling rates of 10 ı C=min, forced gas cooling (nitrogen, argon, etc.) could be used for higher cooling rates of 2050 ı C=min. Very high cooling rates can be achieved with liquid nitrogen DSC accessories up to 100 ı C=min [24.8]. This same liquid nitrogen option can be used to do DSC scans on materials well below room temperature. Most inorganic glasses do not require very low temperature DSC scans because Tg for these types of glasses is typically well above room temperature. However, many polymers, plastics, and rubbers have sub-room temperature Tg and may require liquid nitrogen cooling accessories. Calibration is crucial when doing thermal analysis of glasses. There are three main types of calibration for a DSC: baseline, temperature, and heat capacity. Establishing the baseline of the DSC involves running the instrument through a temperature window using a ramp rate similar or identical to the intended experimental ramp rate that is planned. This run is usually done without any sample pans; this ensures no influence from differences in the two sample pans. The instrument measures what are typically subtle heat flow differences between the two nodes of the sample and reference nodes of the DSC cell. In theory an empty DSC cell should have a flat heat flow versus temperature signal. In reality that is never exactly the case. So the DSC software takes the slope of the empty cell heat flow signal and removes it by rotating the signal. The result is a software correction that should yield a flat DSC heat flow versus temperature signal. This calibration file is usually present in the background during DSC runs allowing the software to constantly remove the difference in heat flow rate and show data which is free of that bias.
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be seen is a 2nd-order transition known as the glass transition. Tg is the temperature at which a solid glass transitions to a viscous material with a liquid-like structure. The glass transition is a topic of much study in glass science [24.2–7]. The next transition, labeled Tx1 , is the first observable crystallization peak. This 1storder transition from a disordered liquid-like structure occurs in different material phases at different temperatures. This exothermic event involves the release of an amount of energy specific to the mass of the sample and the percentage of the sample made up by the phase that is crystallizing. That energy value, known as the heat of reaction, is calculated in J or kJ as the area under the crystallization peak. The integral of the heat flow during that event produces the enthalpy of the reaction. In Fig. 24.3, the enthalpy of reaction of the 1st crystallization peak is graphically demonstrated. It is important to note that in a glass or glass ceramic with more than one phase present, there will be a crystallization event for each phase. If those crystallization events are separated in temperature, then it is possible to discern them. In Fig. 24.3, there is more than one crystallization peak. The heat of reaction associated with the first crystalline peak appears higher than the energy associated with the second at Tx2 . It is also possible that there is a third crystallization peak overlapping with the second, but that is not important for this example. The final feature is a melting valley, indicated by Tm . This valley shows the melting of at least one phase and, similar to crystallization, the heat of reaction can be measured by calculating the area under the curve. In a multiphase system there could be multiple melting peaks. Now that the principle behind how a DSC measures heat flow has been explained, as well as the key 1st- and 2nd-order transitions most important to DSC of glasses, we will go on to explain that there are a few variations in measurement technique which are best suited for different measurements within a material. Different techniques are driven by different fundamental questions that the experimenter wants to ask of the material. These techniques are explored below.
24.1 Differential Scanning Calorimetry (DSC)
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Temperature calibration employs a metal with a well-defined melting temperature that is heated in the DSC until it melts. The melting temperature as determined by the DSC is compared to the known melting temperature of the pure material. The difference is used to calibrate the DSC temperature readings. Several metals (In, Sn, Zn) with various melting temperatures are used in separate runs to calibrate the DSC over the temperature range of interest. The calibration consists of a simple temperature shift to force the DSC temperature readout to match the known melting temperature. The final type of calibration is the calibration of the DSC’s heat capacity measurement. This test involves a bulk sample, usually made of a well-known crystalline material such as sapphire. The heat capacity of the sample is measured and compared to the known heat capacity, this allows a calibration adjustment to be applied. A value known as a DSC cell constant is used to correct for errors in heat capacity measurement [24.9]. The general form of the cell constant calculation can be seen below in (24.4), it is simply the ratio of the known and measured heat capacity of the sample. Cp Heating Rate KD ; Heat Flow
(24.4)
where K is the dimensionless DSC cell constant, Cp is the known heat capacity of the standard samples in J=.g ı C/, Heating Rate is the programmed heating rate of the DSC for the calibration run in ı C=min, and Heat Flow is the measured heat flow into the sample in W=g. This calibration takes into account the heat capacity of the DSC cell, hence the same cell constant. When an old DSC cell has been exchanged for a new one a calibration must be done to determine the correct cell constant to use during measurement. It is also advisable to calibrate a DSC when beginning a suite of measurements or greatly changing the temperature range at which samples are being measured. As with any form of analysis, asking the right question is critical to obtaining a useful answer. Programming a DSC run that “asks the right questions” of the glass is dependent on understanding some basic properties of glasses. A typical DSC run involves, at a minimum, a commanded temperature ramp from room temperature up to the final desired temperature, at a constant ramp rate (ı C=min). The end temperature of the ramp depends on what knowledge is desired. For instance, if an operator only wants to measure the glass transition temperature (Tg ), then a ramp to 50ı above the anticipated Tg is all that is needed. An investigation of crystallization in glasses requires a higher final temperature. It is important not to forget the sample and reference pan material in this calculation. When study-
ing the crystallization behavior of As40 Se60 glass, an aluminum pan is easily able to withstand the necessary temperatures as well as chemical interactions with the glass. However, a platinum pan used with the same glass, even though it has a much higher melting point than aluminum, would be quickly corroded even at relatively low temperatures. On a similar note, reaching the crystallization temperature of a common oxide glass like Schott’s N-BK7 would turn an aluminum pan into a puddle and likely ruin an expensive DSC cell. The other thing to keep in mind is to stay below the temperature at which the material under test outgasses. In the best case it is an unnecessary result that can dirty or even corrode the DSC cell, and in the worst it can be a health hazard if the glass under test off-gases toxic constituents. One of the unique things about glassy materials is that they have what is known as a glass transition. As discussed in Sect. 24.1 above, the glass transition is a 2nd-order transition. This is the region of temperature in which the kinetics of the material begin to allow rearrangement of the glass network, upon heating, to achieve thermodynamic equilibrium. Because of this interaction between thermodynamics and kinetics, glasses retain information based on their thermal history. Thermal history is a general term used to describe the unique network structure of a glass based on prior exposures to specific temperatures over specific times and based on heating and cooling rates that the glass was subjected to. In order to talk about thermal history in a more precise way, it is necessary to define something called the fictive temperature Tf . Since glass is an amorphous material, its structure is nonperiodic and disorganized compared to the crystalline state for the same material. The structure of a solid glass resembles that of a liquid at a specific temperature, that temperature is known as the fictive temperature [24.10]. Figure 24.4 demonstrates the idea of thermal history and where it comes from. The x-axis is temperature and the y-axis is some intrinsic property P.T/ which is a function of temperature. The blue line represents a generic glass material. The dashed green line is known as the liquidus or liquid equilibrium line of the glass. At high temperatures such as T1 , where the glass is liquid, the network structure of the glass and therefore the intrinsic properties of the glass will remain on the liquid equilibrium (liquidus) line. As the glass is cooled towards T2 however, the viscosity of the glass continually increases until the glass structure is unable to relax faster than the rate at which it is being cooled. The region in which the material behavior diverges from the liquidus line is the glass transition region. At lower temperatures, the glass behaves like an elastic solid and the property versus temperature relationship becomes essentially linear. The straight, dashed
Thermal Analysis of Glass
P (T1) ∆P L ∆Pg
P (T2) Liquidus line
T2
Tf
T1
Fig. 24.4 Intrinsic material property P (e. g., volume) versus temperature graph for a generic glass material (after [24.11])
red line is extended backwards from the linear region of the blue curve until it intersects with the liquid equilibrium line. The point at which those lines intersect defines the fictive temperature. The rate at which the glass is cooled has an effect on the fictive temperature, and the fictive temperature defines what we call the thermal history. The blue curve in Fig. 24.4 represents a glass that was cooled at a slower rate than the glass represented by the brown curve. This demonstrates the effect of cooling rate on the properties and structure of the glass. Faster cooling results in a higher temperature departure from the liquid equilibrium line and therefore a higher fictive temperature. So, a glass with a higher fictive temperature was cooled at a higher rate than the same glass with a lower fictive temperature, thus yielding different thermal histories and different final results when measuring them side by side. The thermal history can affect the results of almost any thermal analysis of glass. Take for instance the example in Fig. 24.4. The expression PL which in this case is the change in property P while the glass is in the liquid region, is greater for the blue curve than it is for the brown curve. Because the blue curve was cooled or quenched at a slower rate, there was more time for the property to relax than for the brown curve which was cooled at a higher rate. What that means for the glass structure, is that the more slowly cooled glass is closer to liquid equilibrium at room temperature than the glass represented by the brown curve which represents a faster cooling rate. The farther from equilibrium the property P is, the higher the thermodynamic driving force is for the glass to reach the equilibrium line. If a scientist was to heat both glasses up from room temperature at the same rate, the glass farthest from equilibrium would move towards equilibrium at a lower temperature and more energetically than the glass that
was cooled more slowly. That is the effect that differing thermal histories can have on, for instance, the measurement of Tg by DSC. For that reason, a common DSC method involves ramping the temperature above the Tg of the glass in order to reset the thermal history of the material. In this way, even glasses with differing fictive temperatures and thermal histories are heated to a temperature that is high enough to allow them to relax to the equilibrium line. Cycling all glasses within a set of experiments in this manner ensures that they have identical thermal histories and removes that potential difference from the experimental results. Then the DSC temperature is dropped to near room temperature and then ramped up through Tg once again. This same method is used on all measured samples ensuring that the measured properties of the glass are not affected by variations in the sample’s thermal history. The results of the first run to above Tg and the second run are different. The magnitude of the difference is dependent on how different the glass structures were before and after the annealing step. Figure 24.5 demonstrates how the apparent glass transition is different from the initial ramp to the final ramp. The first ramp in Fig. 24.5 has a significantly lower dip than the 2nd ramp. In this graph, exothermic is defined as positive on the y-axis. Therefore, the Tg feature seen on the 1st ramp absorbed a greater amount of energy to allow it to go through the glass transition from a super cooled liquid state to an equilibrium liquid state. Because the Tg feature on the 1st ramp is more energetic it shows that the glass was further from equilibrium prior to the 1st ramp above Tg . The 2nd ramp, which contains a smaller Tg feature shows the difference in apparent thermal history between the two conditions. One of the most important and commonly measured thermal properties of glasses is the glass transition temHeat flow (W/g) 0.2
0.1 Cooling 0.0 2nd ramp –0.1 Heating –0.2
0
50
100
1st ramp 150
200 250 Temperature (°C)
Fig. 24.5 DSC example: 1st ramp for annealing and 2nd ramp for Tg measurement
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P
24.1 Differential Scanning Calorimetry (DSC)
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perature (Tg ). It often appears as a dip in the heat flow graph as the glass absorbs energy to transition from a solid-like state to a liquid-like state. However, not all Tg features appear the same when measured. Both Tg features shown in Fig. 24.5 are comprised of a dip followed by what looks like a recovery or peak directly afterwards; not all Tg features are like this. Some measurements of Tg reveal a dip in the curve that never recovers and simply remains at a lower heat flow baseline. This difference is due to the difference between the temperature at which Tg occurs and the fictive temperature of the glass. If Tf for a given glass is far above Tg , that is to say far from equilibrium, the rapidity and energy involved in the glass transition can actually overshoot the equilibrium liquid structure represented by Tf . As the glass network relaxes toward equilibrium during Tg , the momentum gathered during that transition can sometimes carry the glass structure past equilibrium. At some point the glass has to adjust for that overshoot, this adjustment can be seen when the heat flow during Tg dips and then rises after the minimum is achieved. In cases where Tf is not too high above Tg , the glass structure relaxes directly to the equilibrium structure with no overshoot, causing the Tg feature to dip to a minimum and remain at that baseline until the next phase transition. The glass transition is a 2nd-order phase transition unlike melting or vaporization which are 1st-order transitions. It is generally described as a range of temperature/viscosity below which a glass behaves most like a solid and above which it behaves more like a liquid. There are three accepted ways to indicate Tg ; Fig. 24.6 gives a graphic example. Each of these three methods are used by various academic and industry professionals, however very rarely is the method of Tg determination noted on datasheets and academic publications. Therefore, for the same glass, different entities often report different Tg values. This can lead to Heat flow (W/g) –0.06 –0.08 –0.10 –0.12
Tg inflection
–0.14 –0.16 –0.18 160
Tg peak
Tg onset
170
180
190
200 210 Temperature (°C)
Fig. 24.6 Example of the three most common ways to cal-
culate Tg , Tg onset, Tg inflection, Tg peak
confusion because it causes people to use different temperatures for what they assume to be the same material property. The first method is called the onset method, which involves drawing a line tangent to the curve just before the transition begins and another line tangent to the curve during the first down slope after Tg begins. This method effectively assigns a temperature to the knee of the glass transition and when used as the reported Tg of a glass, is the value that best describes the beginning or onset of the glass transition region. The second common way of indicating Tg is the inflection point method. This method is the only one of the three that relies on a mathematical approach for the determination and designation of Tg . Directly following the onset knee in the graph, the heat flow curve decreases faster and faster until it hits an inflection point. This is the point where the decrease begins to slow as the heat flow curve heads towards its local transition minimum. The most reliable way of determining this point is by taking the derivative of the heat flow curve and finding the minimum in that region. A local extreme in the derivative indicates an inflection or change in the direction of acceleration. The temperature at which this inflection occurs is called the inflection point Tg . This representation of Tg is preferred by some because it is a well-defined mathematical point rather than the intersection of arbitrarily chosen tangents. However, as we discuss below the experimental parameters used during a DSC run have an even greater effect, so in some sense the method of Tg measurement is not the most important factor. The inflection point Tg is the best representation of the center of the glass transition region. The third method for determining Tg is the peak method. Near the end of the glass transition bump or dip in the heat flow curve, there is another knee which is the opposite of the onset knee. Using the same method of drawing lines tangential to the rising curve before the knee and the approximately flat curve after the knee, the peak Tg is determined. This value gives a temperature for the end of the glass transition region. It is the least commonly used of the three methods. It is important to stress that the width of Tg and the values themselves are just as dependent on the experimental conditions of the DSC run as they are to the method of designating Tg . When measuring the Tg of a glass via DSC, it is important to understand the ramp rate dependence of the observed Tg . The basic understanding for this concept is based on the difference between the rate of temperature change induced in the material and the rate of kinetic change in the glass from a solid-like to a liquid-like structure. Take for instance a heating rate of 1 ı C=min versus a heating rate of 10 ı C=min for two identical samples with the same thermal history. At the slow
Thermal Analysis of Glass
those two lines define the crystallization onset temperature. Crystallization can also be defined as the peak maximum, however, that is not commonly done because in many applications, once crystallization begins the material becomes unusable as a glass. The other piece of information that can be gleaned from the crystallization peak is the area under the curve (Fig. 24.3 shows an example). This area under the curve combined with the mass of the sample being measured, allows the energy per unit mass of crystallization to be calculated. This value is useful when researching crystallization of glasses and the forces that govern that crystallization [24.13, 14]. When observing the generic DSC curve of a generic glass as shown in Fig. 24.3, the final feature that can be detected is the melting feature. In the case of exothermic heat flow being positive, melting is clearly an endothermic process. This means that in order for the now-crystalline material to melt, it must absorb energy. As defined in this section, the melting temperature (Tm ) can be defined by its onset or its minimum, however as before, once you have begun to melt you are already in trouble from a practical standpoint. Once again the area under the curve of the melting valley will allow you to define the amount of energy needed for melting. If you know the mass of the sample that is being measured, then you can calculate the heat of fusion for that material as in (24.5). R q dT Hx D ; (24.5) Heating Rate where Hx is the intrinsic heat of crystallization in J=g, q is the heat flow measured by DSC in W=g, Heating Rate is the heating rate in ı C=s, and T is the temperature in ı C. It is also possible to calculate the total heat of crystallization by multiplying Hx by the mass of the measured sample. These crystallization and melting features are of interest to glass scientists, but from an industrial standpoint it is wise to stay far below either Tx or Tm when processing glass material. Aside from the signature temperature measurements of the DSC, the intrinsic heats for crystallization and melting can be determined along with the heat capacity of the material in various phases. Calculations of mass-dependent properties require precise measurement of sample mass. There is a subset of glassy materials known as glass ceramics which, as the name implies, are a mixture of some volume fraction of crystallized material and some volume fraction of glassy or amorphous material. These materials are most commonly created by first forming and then heat treating a base glass to nucleate and grow crystals within the material. Precise control
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heating rate, the speed at which the glass structure can relax towards equilibrium upon passing through Tg is closer to the actual heating rate of the DSC. This means that structural relaxation is taking place along with the temperature increase. Given a higher DSC ramp rate, the structural relaxation will occur at a rate relatively slower compared to the heating rate. The result of this is to push the apparent Tg feature to higher temperatures. Because the heating rate is higher, the relaxation of the glass structure actually lags and does not become apparent in the heat flow until a higher temperature. This is one effect of heating rate. The second is in the energy of the transition or the depth of the Tg feature. A lower heating rate allows the glass to relax along with the heating rate so that the glass gradually comes to equilibrium and remains at equilibrium as the temperature of the DSC increases. A higher heating rate, in addition to pushing the apparent Tg to higher temperatures, has the effect of increasing the difference between the glass structure and the equilibrium liquid state. This causes the resulting 2nd-order transition to be more energetic and therefore results in a Tg feature with a deeper dip and typically a more severe recovery after the structural overshoot past equilibrium [24.12]. Glass is defined by its lack of a crystalline structure in the form of periodic order. There is a temperature or temperature range at which a glass will begin to crystallize (Tx ). Upon reheating of the glass this typically occurs above Tg when the kinetics of the glass speed up enough to allow crystallization to take place on a laboratory time scale. This is accomplished by thermodynamically driving the material system to seek the lowest energy state, which is an ordered or crystalline state. When experimenting with glass in the lab, when making raw glass in industry, and when processing glass into products using heat, staying away from this crystallization temperature or region is imperative. DSC heat flow curves are setup in one of two ways, either heat flow into the sample (endothermic) is positive on the graph or heat flow out of the sample (exothermic) is positive. The examples in this chapter are referenced by exothermic up which means that heat flow out of the sample will be shown as a peak on the graph. Crystallization is an exothermic process, when the glass moves from a relatively high-energy thermodynamic state of disorder to a relatively low-energy thermodynamic state of crystalline order it releases the amount of energy difference between those two states. The crystallization temperature (Tx ) is defined as the onset of the crystallization peak, and the temperature is determined the same way as the onset of Tg . A line tangent to the curve just before the crystallization peak is drawn and a line tangent to the curve just after the beginning of the event is drawn, and the intersection of
24.1 Differential Scanning Calorimetry (DSC)
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of the volume fraction of crystal versus glass requires an understanding of the nucleation and crystallization temperatures of the glass as well as the nucleation and crystallization rate at those temperatures. A standard DSC run is not the best way to obtain accurate nucleation and crystallization information, and is discussed in the next section. When considering DSC measurements of glasses, it is crucial to remember that the phenomena being measured are thermodynamic in nature but are subject to the kinetics of the glass structure. This is why all of the important temperature and material properties above are dependent on the ramp rate of the DSC run. A graphic example of measured material property variation as a function of temperature ramp rate can be seen in Fig. 24.7. Take Tg as an example; for As40 Se60 chalcogenide, infrared glass the onset Tg for a 10 ı C=min ramp rate is approximately 185 ı C. If you were to adjust the ramp rate on such a DSC run to 100 ı C=min the Tg feature observed on the heat flow curve could easily exceed 200 ı C [24.11]. The specific form of this temperature dependence was derived by Moynihan et al. and can be seen below in (24.6). d ln jqj h D ; R d T1g
(24.6)
where jqj is the heating or cooling rate, h is the activation enthalpy for the relaxation time controlling structural enthalpy or volume relaxation, and R is the ideal gas constant. This illustrates the difficulty in thermal analysis of glasses, the material properties reported in so many places are dependent on very specific measurement conditions. In many cases there are no real standard measurements aside from generally accepted industry practices. Researchers must use and report the experimental parameters used for precise DSC measurements. Industrial applications using glass, whether in plate form like windows, or in optics require detailed material properties. It is important that the engineers and scientists using these data understand the parameters and assumptions used to make those measurements and use the data accordingly.
measurement artifacts as possible, to minimize the effect until it is negligible, or characterize the effect well enough to adjust the measured data and essentially remove the effect in postprocessing. Measurements such as those that seek to characterize the crystallization thermodynamics of glasses are particularly sensitive to the effects of ramp rate [24.15]. DSC crystallization measurements are a two-part question. Prior to crystal growth in a glass, seed crystals must be nucleated. Nucleation involves the probabilistic appearance and disappearance of very small crystals, and whether a nucleus survives to become a fully fledged crystal is dependent on whether it achieves some critical size as determined by the thermodynamic state of the material. Glasses have one thermodynamic range in which crystals are nucleated and once those nuclei exist there is another thermodynamic range in which those crystals grow. Determining the nucleation and growth behavior for a glass can be done by constructing nucleation-like and growth-like curves for a specific glass. This technique can also be used to compare varying glass compositions in the same family [24.15]. The nucleation-like curve is constructed using the following expression (24.7) defined by Marotta et al. [24.16] ! Ec 1 1 ln .I0 / D (24.7) C Const ; R Tp Tp0 where I0 is the steady state nucleation rate, Ec is the activation energy for crystallization, Tp is the temperature Heat flow (mW) 0.8 q = 5 W/g 0.7 q = 10 W/g q = 15 W/g 0.6 q = 20 W/g 0.5 0.4 0.3 0.2 0.1 0.0 –0.1 –0.2
Isothermal DSC Isothermal DSC measurements are a variation of standard DSC. The main drawback of standard DSC measurements is that all of the measured material responses are heating rate dependent and therefore there exists an influence on the measured properties that is an artifact of the measurement [24.11]. In experimentation of all kinds it is important to remove as many of these
–0.3 –0.4 325 350 375 400 425 450 475 500 525 550 Temperature (°C)
Fig. 24.7 Heat flow versus temperature curves measured
at different heating rates by DTA (differential thermal analysis) for a 70TeO2 -10Bi2 O3 -20ZnO glass. Reprinted from [24.15] with permission from Elsevier
Thermal Analysis of Glass
(1/Tp)–(1/T 0p) (°C –1) 0.00005
A typical crystallization experiment like the one discussed above is particularly sensitive to ramp rate. For instance, if you are heating a sample in a DSC or DTA to the peak crystal growth temperature at 10 ı C=min, you likely have to pass through the nucleation region of the glass as well. If the nucleation region is 40 ı C in width, it will take 4 minutes to pass through it. During that 4 minutes, significant nucleation could take place, additional nuclei significantly change the nucleation condition of the glass, and the actual glass material will then vary from the condition that was assumed when designing the measurement. This is an example of how a finite heating or cooling rate can make characterizing crystallization behavior in a glass difficult, ambiguous, or even impossible. Isothermal DSC seeks to make the heating/cooling rate as high as possible, so high in fact that the movement from one temperature to another is practically instantaneous. One of the factors related to getting heat into a material, which cannot be as easily controlled, is the thermal conductivity of the sample material itself. Isothermal DSC allows the experimenter to eliminate the measurement instrument as the choke point for getting heat into a material but does not change the ability of the material to absorb heat. In order to reduce the time it takes for all of the material in the sample pan to reach the commanded temperature, two main options are available. First, the amount of sample mass tested can be reduced and this will generally allow faster heating, however, it has the drawback of reducing the strength of the crystallization signal that will be detected by the DSC therefore reducing the sensitiv∆A (mW) 50
0.00004
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10 Nucleation and growth x = 15 x = 17.5 x = 20 x = 25
0.00000
–0.00001 325
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0
–10 475 500 525 Temperature (°C)
Fig. 24.8 Nucleation (open cir-
cles) and growth-like curves (full circles) for glasses investigated in the .90 x/TeO2 -10Bi2 O3 -xZnO system. Reprinted from [24.15] with permission from Elsevier
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at the maximum of the exothermic crystallization peak for a glass measured using a specific heating rate and an isothermal hold for a specific amount of time at a temperature T which is a suspected nucleation temperature. Tp0 is the temperature at the maximum of the exothermic crystallization peak for a glass measured using the same heating rate as Tp but without the isothermal hold. The results of these measurements can then be plotted as (1=Tp 1=Tp0 ) versus temperature to obtain nucleationlike curves resembling those seen in Fig. 24.8. Likewise, the growth-like curves can be constructed using a technique pioneered by Ray et al. [24.17]. The specific techniques for reaching the results shown in Fig. 24.8 are detailed by Massera et al. [24.15]. The essence of the construction of growth-like curves is the heating of a glass sample to a potential growth temperature where an isothermal hold occurs. The sample is then cooled below Tg and ramped up through crystallization. The area of the crystallization peak for the glass subjected to the growth step (AT ) is subtracted from the area of the crystallization peak from a sample not subjected to a specific growth step (A). The resulting difference in area under the curve, called A, is plotted versus temperature as shown in Fig. 24.8. These curves create a picture of the nucleation and growth rates of a given glass. Since all nucleation and growth experiments were subjected to the same conditions (with the exception of temperature), the higher the nucleation-like and growth-like curves, the higher the rate of nucleation and growth at that temperature. This gives glass scientists a picture of the maximum nucleation and growth temperatures for a specific glass.
24.1 Differential Scanning Calorimetry (DSC)
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ity of the measurement. The second and more effective way of forcing the actual temperature in the material to follow the commanded temperature more closely is to use a smaller particle size in the powder sample. Even materials with low thermal conductivities will heat up quickly with small-enough particle sizes. The downside to this is that the crystallization behavior will likely be dominated by surface crystallization and not volume crystallization. The purpose of the measurement must be taken into account when determining whether to use this approach or not. Adjusting for all of these factors, the advantages of isothermal DSC become clear. In order to measure the energy associated with crystallization, the DSC would be brought to a temperature just below the nucleation range and held until isothermal equilibrium was reached. Then a high ramp rate such as 100 ı C=min would be used to go quickly through the nucleation region, and directly to the target temperature in the crystallization region. The resulting measurement would be much less affected by ramp rate and time spent in the nucleation region. This is one of the main advantages of using an isothermal DSC technique for glass property measurements. The study of the time-dependent properties at a given temperature rely on isothermal DSC [24.18]. The rapid temperature ramp of an isothermal DSC has applications in other areas of glass science. In the study of structural relaxation, which is the time- and temperature-dependent process of the glass network relaxing from its current network configuration towards equilibrium, it is preferable to move as quickly as possible to the relaxation temperature of interest. Structural relaxation measurements using isothermal DSC are carried out by ramping the temperature of a glass sample from a temperature at which relaxation is not occurring (typically 40 ı C below Tg or more), to the test temperature [24.19]. The test temperature is typically somewhere above 40 ı C below Tg . If the relaxation temperature was above Tg , for instance, then a slow ramp through Tg to reach that temperature would cause a certain amount of relaxation thus affecting the measured result. Using an isothermal DSC ensures the fastest ramp possible through temperature to the target. The effective heating rate is still limited by the sample’s thermal conductivity, but isothermal DSC removes the measurement as the limiting factor. This is yet another example of the advantages of an isothermal DSC measurement.
out of a material is comprised of heat flow related to thermodynamic events. For instance, a 2nd-order phase transition like the glass transition temperature which involves a change in heat capacity, demonstrates reversing heat flow. Heating through the glass transition and then cooling back down, the change in heat capacity, excluding any kinetics such as relaxation, will be the same in both directions. The nonreversing portion, which can be determined by taking the total heat flow (measured like a traditional DSC) and subtracting the reversing component, will reveal kinetic events in the glass. These events can include things like any relaxation or viscous flow that occur as the experiment passes through Tg . It is important not to confuse reversing and nonreversing heat flow with the reversibility or irreversibility of transitions within the glass. Modulated DSC (MDSC) is a technique involving a modulated temperature ramp, which produces an average ramp rate but applies a periodic modulation of the commanded temperature, keeping the system in a slight state of perturbation. The resultant heating curve appears often as a sinusoid or stochastic modulation whose average temperature is changing the same way a traditional DSC heats or cools [24.21]. An example of a sinusoid modulation can be seen in Fig. 24.9. This allows the dependent and independent components of the heat flow to be analyzed separately. The component of the temperature that is ramping linearly provides information similar to a standard DSC while the sinusoidal component is simultaneously measuring the heat capacity of the material. This allows kinetic events, such as crystallization, to be deconvolved from changes in heat capacity, such as Tg . Temperature (°C) 60
Modulated temperature (°C) 60
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Fig. 24.9 Example of the temperature change during
Modulated DSC Standard DSC heat flow measurements of materials, including glasses, are comprised of a summation of two different types of heat flow. These are reversing and nonreversing. The reversing portion of heat flow in and
a modulated DSC experiment (after [24.20]). The average temperature change (solid line, left axis) is programmed to 4 ı C=min, while the modulated temperature change (dashed line, right axis) is programmed with a sinusoidal oscillation of ˙0:42 ı C every 40 s
This method of DSC has several advantages. First, it allows overlapping transitions to be discerned within a single material. Testing materials that are comprised of different chemical components is something that is more commonly done in pharmaceuticals than glass, however when studying the properties of a glass ceramic or glass composite, there may be instances where one or more of the components are going through different phase changes or transitions at the same time. If those instances overlap in temperature, a standard DSC would miss that information and depict the average heat flow response of the components. The average heat flow would likely not show a Tg event if a phase change was taking place at the same time and would report an erroneous value for the phase change energy. With MDSC, the standard heat flow information coupled with the change in heat capacity information can reveal the crystallization characteristics of the first material while indicating the Tg of the other simultaneously. A further advantage of MDSC is the capability of detecting events that are very faint or weak. Sampling both the kinetics and heat capacity based changes gives this technique increased sensitivity [24.22, 23]. Figure 24.10 shows an example of how MDSC can be used to separate the heat flow behavior of different materials that are mixed together; the same capability can be used when measuring a glass material. Figure 24.10 shows an MDSC scan of a composite polyethylene terephthalate (PET) and polycarbonate (PC). The blue line in the figure is the reversing heat flow, the red is the nonreversing, and the green is the total heat flow signal. The key thing to note is that the total heat flow (green curve) would be the result of a standard DSC measurement. In such a measurement, the PC
Heat flow (mW) 2
24.2 Differential Thermal Analyzer (DTA)
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Thermal Analysis of Glass
2 0
Nonreversing Total
–2 –4
Reversing
53.6 J/g –53.5 J/g
0 –2
Polycarbonate Tg –4
–6 50
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150
200
–6 250 300 Temperature (°C)
Fig. 24.10 MDSC scan of total, reversing, and nonrevers-
ing heat flow in a PET and PC composite. After [24.20]
Tg which can be seen in the reversing heat flow curve would be totally obscured by the PET crystallization seen in the nonreversing and total heat flow curves. That is information that is only discovered due to the ability of MDSC to separate the reversing and nonreversing heat flows through combination of a linear temperature ramp overlaid with a sinusoidal or stochastic modulated temperature profile. As MDSC is a relatively new technique there has not been extensive study done to reveal all that it is capable of and where its main limitations lie. It is certainly useful for thermal analysis of composite materials and materials with weak thermodynamic and kinetic events. Future applications of MDSC could include greater study of the nature of the glass transition as well as the complex relationship between multiple phases within a phase-separated glass.
24.2 Differential Thermal Analyzer (DTA) Differential thermal analysis (DTA), is analogous to DSC. The end material information gained using this technique is essentially the same as DSC, however the method used to gain that information is different. DTA uses a comparative method, with a sample and reference material that are ramped through various temperature ranges to gain the information desired. Whereas a DSC holds the temperature of the sample and reference equivalent and measures the heat flow difference, a DTA, maintains an equivalent heat flow while monitoring temperature difference. In this way, a DTA is capable of measuring the same signature temperatures (Tg , Tx , Tm ) as a DSC. The area under a DTA curve is the enthalpy of the system, but because the heat flow is held constant, the
heat capacity of the sample material cannot be determined. Because DSC and DTA conduct very similar analysis and the DSC can be used to calculate heat capacities, the use of DTAs has dwindled compared to that of DSCs in more recent years. The physical structure of the DTA makes it suited to measuring at very high temperatures (as high as 1400 ı C). Since DSC cells are typically made of Inconel and can only reach a max temperature of 800 ı C, a DTA may be more suitable for higher temperature experiments. There are hightemperature DSCs that can reach nearly the temperature of a DTA, but they are currently very expensive. As always, the instrument most suitable for each inquiry must be chosen.
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24.3 Thermomechanical Analysis Thermomechanical analysis involves the measurement of mechanical material properties in response to thermodynamic changes. Thermodynamic changes within a material are most commonly effected using changes in temperature. A thermomechanical analyzer (TMA) is the most common instrument used for this type of analysis for inorganic glasses. As in most measurements, sample geometry can be optimized to provide the best measurement response and sensitivity. There are three major considerations when choosing or fabricating a sample for TMA measurement. First, it is best to have a sample that is taller than it is wide. The taller the sample, the greater the change in length of that sample per degree change in temperature, and as seen in (24.8), the more sensitive the length change is to temperature change, the more sensitive the system is in detecting temperature-related phenomena in the material. ˛ D T
L ; Li
(24.8)
where ˛ is the linear thermal expansion coefficient, T is the difference between the final and initial temperature over the range considered, L is the change in sample length over that same range, and Li is the original length of the sample. A longer sample will effectively increase the sensitivity of the measurement. Second, the width of the sample effects the TMA measurement because it directly impacts the effective heat transfer rate into or out of the sample. A sample with a larger cross section will respond more slowly to commanded temperature changes when all other factors are equal. It is also best to have a TMA sample with a consistent cross section throughout its length; when a material expands or contract in one axis, it also contracts a)
or expands in the two other dimensions. This relation is described by Poisson’s ratio. Having an inconsistent sample cross section means that the internal resistance of the material to shape change in the two dimensions not being measured will have a different effect on the dimension being measured at different heights on the sample. This is alright if you are always measuring samples with the exact same cross-sectional distribution, but for fundamental material property measurements it is better to maintain a consistent cross section. The final and most important sample-geometry-related necessity is that of having a column of material unbroken by bubbles, cracks, or other macro flaws from the base of the sample to the measurement head. This is necessary because the thermal expansion calculations are done assuming a continuous column of material. Inside a TMA, the sample sits on a fused silica stage, which is used for its very low thermal expansion properties. The height change of the sample is measured at its top by a shepherd’s hook, this piece of fused silica rod rests on the top of the sample, and then curves 180ı from vertical facing upward to vertical facing downward and extends down into the instrument. The rod attached to the shepherd’s hook probe is fused to a metal rod. This metal rod is used to measure the height change of the entire probe using a linear variable differential transformer (LVDT). The LVDT very accurately tracks the increase or decrease in height of the metal part of the rod and hence can measure the changing height of the sample. An LVDT is an absolute position sensor. As seen in Fig. 24.11 it is comprised of two main parts. The first is the outer cylinder which serves as the sensor. This outer cylinder has three electrically conductive rings embedded in it, an upper, lower, and middle ring. These three rings work in concert with a ferromagnetic cylindrical AC voltage
b) P Core
Arm S1
P
Arm
S2
Core Displacement
Soft iron core
+ S1
Vs1
Displacement +
Fig. 24.11 (a) Construction and (b) circuit connection of LVDT. After [24.24]
Difference output voltage Vd = (Vs1 – Vs2)
+ S2
Vs2
Thermal Analysis of Glass
Silica probe
Pt foil Glass Thermocouple
Silica stage
using a wide probe head and the measurement of viscosity as described in a following section, using a ball penetration probe. An alternative instrument to the TMA is a dilatometer. A dilatometer is very similar to a TMA, the main difference being that a dilatometer does not allow the operator to control the force exerted on the sample by the measurement probe, but instead uses a passive spring system to hold the measuring head in contact with the sample. Dilatometers often orient the sample in a horizontal, rather than vertical, position. The discussion of property measurement below pertains to both instruments but the TMA is more versatile. The most important calibrations for a standard TMA are temperature and expansion calibrations. Temperature calibration can be done by testing a sample of a pure metal with a well-known melting point (aluminum for example). When the metal reaches its melting point, the sample rapidly begins to loose height. Choosing at least two different calibration materials over the anticipated test range will ensure accurate temperature measurements, although at least three calibration points are needed to ensure the temperature measurement behavior of the instrument is linear. It is also important to pay attention to the temperature distribution within the TMA furnace. A TMA furnace will often have a radial and vertical temperature gradient within the furnace even at “isothermal equilibrium.” This can become a significant factor when testing rather tall samples, as the temperature at the top of the sample will be different from the bottom. This difference can be made even worse while ramping the system up to temperature. If the experiment being done is a high-precision experiment it may be necessary to use a shorter sample or track the temperature distribution within the furnace using additional thermocouples. The downside of using a shorter sample is decreased measurement sensitivity. Calibration of the system’s deflection can be done using any material with a linear and well-characterized expansion rate. Preferred sample geometries for an expansion calibration standard are either a cube or right cylinder with both ends polished parallel to one another. It is best to calibrate with a reference material that has an expansion within the same order of magnitude as the expected expansion behavior of the sample that will be tested on the instrument.
24.3.1 TMA Property Measurement LVDT
Fig. 24.12 TMA
schematic. After [24.25]
The coefficient of thermal expansion (CTE) is the property most often measured using a TMA. Standard TMA chambers can be heated, and some can be cooled to cryogenic temperatures for testing of materials whose
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core which is attached to the object whose position is being measured. The center ring of the outer cylinder works like the primary coil of a transformer, the inner core acts as the core of the transformer, and the power from the center conducting ring is transformed to the upper and lower secondary rings. The voltage differential between the upper and lower ring (the two secondary transformer coils) is measured. When the magnetic cylinder is perfectly positioned amongst all three coils, the voltage differential is zero. As the core is moved up or down that voltage differential changes either positively or negatively (which is determined by whether the voltage difference is in-phase or outof-phase with the primary coil voltage). LVDTs are designed so that the voltage differential between the upper and lower secondary coils is linear over a long displacement. This linearity ensures that measurement over a given displacement can be accurate and repeatable without any nonlinear effects. A furnace is placed over the entire assembly and used to control the sample temperature as needed. The sketch in Fig. 24.12 depicts the inner workings of a TMA. Most TMAs can be flushed with air for cooling and inert gas for materials that are sensitive to oxidation. When it is necessary, the TMA has a place onto which small masses can be placed to increase the static force of the TMA probe on the top of the sample. Although the most common TMA samples are tall thin bulk pieces of glass, changing the probe type allows for the measurement of thermal expansion of powders
24.3 Thermomechanical Analysis
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glassy state is below ambient temperature. Standard CTE measurement for glasses involves a tall and thin sample with a constant cross section, and it is optimal if both the top and bottom of the sample are polished, flat, and parallel to one another. The measurement of CTE differs for different materials and even for different glass families. The heating rate must be tuned depending on the thermal conductivity and sample thickness of each glass. It is important to note that the exact same sample measured at two different heating or cooling rates will produce a different expansion result. This behavior is analogues to the heating and cooling rate dependence described in the previous DSC section. Great care must be taken to only compare data that has been measured using either (a) the same heating/cooling rate setting on the instrument, or (b) the same effective heating rate calculated using the thermal conductivities and thicknesses of each different material. The heating rate for a CTE measurement depends on the glass type. There is no well-defined standard, the important thing is to choose a heating rate that will allow the desired behaviors to be investigated. Factors such as the sensitivity of your sample material to thermal shock, the thermal conductivity of your sample, and the ramp rate sensitivity of any features you intend to measure should be taken into account. The key is to keep the heating rate, or the effective heating rate consistent when comparing results. A typical CTE run begins with the sample at ambient temperature ramping to the final test temperature at the desired rate. Figure 24.13 shows the resultant curve for a typical TMA run. The initial part of the curve in Fig. 24.13 is the glassy behavior of the material, this is when the glass behaves more or less like a solid. The change in sample height versus temperature is relatively linear. The linear CTE of any region can be calculated using (24.8) above. The liner CTE is the expansion coefficient measured in only one axis. This number is different from the volumetric CTE. In materials that Dimension change (μm) 150
CTE = 90.44 ×10 –6 °C
100 CTE = 8.841×10 –6 °C 50 Td = 570 °C 0
0
100
200
300
400
500 600 Temperature (°C)
Fig. 24.13 Example of a TMA expansion curve of L-
BAL35 glass
are considered isotropic (meaning there are no measurable differences in material properties based on the axis in which the measurement is taken) the volumetric CTE is assumed to be three times that of the linear CTE. This assumption holds true for most wellannealed glasses. Glasses are disordered systems with negligible long-range order, and by nature that disorder creates an average response to stimuli making glasses respond isotropically to measurements. The only exception to these assumptions would likely be cases where there is an extreme difference between the length and the cross section of the sample. Glass fibers, for instance, have different properties along their long axis than their transverse axis due to the stress involved in their fabrication. At some point in temperature the linear behavior of the glass expansion begins to undergo a transition. This departure from linear behavior marks the beginning of the glass transition as measured by thermomechanical means. A TMA can also be used to identify the Tg of a glass, although as stated before, the value for Tg depends on how it is measured. Precise identification of Tg will be dealt with a little later on. After the transition, a brief period of linear behavior can be seen in the sample deflection rate versus temperature. The glass has transitioned from a material exhibiting a solid-like behavior to a material exhibiting a more liquid-like behavior. This is evidenced by the dramatic increase of the deflection rate and therefore the effective CTE of the glass in that region. The CTE measured in the liquid-like region is many times higher than the CTE measured in the glassy region as Fig. 24.13 demonstrates. This is due to the changing of the glass structure to a liquid-like bonding state where attraction between structural units is weaker and therefore expansion and contraction are much more sensitive to temperature change. Measurement of Tg by TMA can be done using the linear portions of the glassy and liquid regions. If the linear region of expansion in the glassy section of the measurement is extended beyond the transition region, and likewise the linear region of the liquid section is extended back towards room temperature, the point at which they cross can be used to define Tg . This value is different to the Tg values determined by DSC. A TMA measures the kinetics of a glass while a DSC measures the thermodynamics, causing the Tg values to differ. The final information that a standard TMA run reveals is a temperature known as the dilatometric softening point (Td ). This temperature is defined as the temperature at which the glass begins to deform under its own weight. In Fig. 24.13 this is seen as the expansion in the liquid-like region slowing, and stopping, and if the test continues the curve will begin deflect-
Thermal Analysis of Glass
24.3.2 Structural Relaxation Thermal expansion measurements makeup the vast majority of TMA runs. However, there are more advanced measurements that can be made using thermomechanical analysis. One such measurement is the characterization of structural relaxation [24.26]. Structural relaxation is the rearrangement of the glass structural network in response to a thermodynamic change. In the temperature region just below, at, and above Tg the kinetics of the glass are sufficiently fast to allow the glass structure to rearrange on a timescale of seconds to days. If a glass is held at a specific temperature and pressure near Tg , then the temperature of the glass is changed, the volume, specific heat and enthalpy relax toward equilibrium. This effect is called structural relaxation. Figure 24.14 shows a TMA representation of structural relaxation. In that plot, the temperature of the sample in the TMA is equilibrated at T0 and then rapidly changes to T1 . The time-dependent response of the sample height change is represented by the brown curve after ti . Structural relaxation can be measured by tracking how the intrinsic properties of the glass change with temperature or pressure. DSC measurements are often used to measure enthalpy relaxation, and in a similar Dimension change (μm)
Temperature (°C)
way TMA measurements can be used to measure volume relaxation of a glass. These measurements are carried out by placing a glass sample in a TMA, ramping to a temperature near the transition region, and holding the glass at this temperature until the glass has reached structural equilibrium. When the glass has finished relaxing at the specific temperature, the temperature is either raised or lowered and held isothermally at the new temperature. The volume of the glass as measured by height change in the TMA is slower to change than the temperature. Since the structural rearrangement of atoms typically follows an Arrhenius-like trend, the change of volume appears exponential or nearly exponential. Figure 24.15 shows the normalized change in height for various structural relaxation steps between various temperatures for Schott N-BK7 optical glass. Structural relaxation is a topic of academic study, but is also important when manufacturing glass through thermoforming. The most common type of thermoforming of glasses is precision glass molding. When molding, a piece of glass is deformed at high temperature which corresponds to a specific viscosity. The molded optic is then cooled. While cooling, the glass structurally relaxes which can change the shape of the optic. Structural relaxation can also affect the shape of the optic during postprocess annealing. Significant work has been done to better understand the role of structural relaxation as it pertains to precision glass molding [24.27, 28]. Using the TMA for a purpose other than its common application allows glass scientists to measure the Normalized change in height 1.0
0.8
0.6
Tg,d +10 °C T0 T1
0.4 587–577 °C
552–542 °C
0.2
0.0 0.0 0.5
ti
0
100
200
300
400
500
600 700 Time (min)
Fig. 24.14 Graphical representation of structural relax-
ation, temperature and dimension change versus time
1.0
1.5
2.0 2.5
3.0
3.5
4.0 4.5 5.0 Time (log(s))
Fig. 24.15 Normalized change in height versus time for structural relaxation data from Schott N-BK7 measured by TMA. Relaxation for temperature ranges between 552 and 587 ı C. After [24.25]
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ing negatively. Td is defined as the global maximum on a TMA curve. Once Td has been reached, the sample will rapidly loose height, and if heating is continued past this point it could result in a puddle of glass stuck to the inside of the TMA cell. Depending on the test sample, this could ruin the cell, and cost significant money to repair or replace. A TMA can also be used to measure the viscosity of a glass sample. Ball penetration viscometry using TMA is described below in Sect. 24.5.1.
24.3 Thermomechanical Analysis
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viscoelastic nature of glass and demonstrate the temperature dependence of that behavior. Figure 24.15 clearly displays the temperature sensitivity of viscoelastic glass behavior. The high-temperature experiment carried out between 587 and 577 ı C shows that the structural change that occurs from one thermodynamic state to the other is fully completed in 103 seconds and reaches its halfway point at approximately 101:5 seconds. In contrast, the lowest temperature step, which takes place 35 ı C below the previous test and 15 ı C below Tg , takes nearly 104:5 seconds to complete. This is approximately 30 longer than the highest temperature test. Additionally, the nature of the structural relaxation can be seen in the shapes of normalized change in height curves. All of the curves are more similar at the beginning of each test, suggesting that the short-time relaxations of each are similar. The largest difference in behavior is seen as the volume relaxation nears the end. It is also possible to view the curves in Fig. 24.15 in relation to the Tg of the material. N-BK7 has a reported Tg at 557 ı C. The blue dashed curve in the center is a clear divider between the higher and lower temperature behaviors. At temperatures above the blue dashed curve, the high temperature curves have the same shape as one another with the only difference being an increasing decay time as the temperature of the test decreases. However, below the blue dashed curve, which was a test carried out at Tg , the nature of the curves changes and they become shallower. The lower temperature curves seem to reach a limit in time after which further relaxation appears difficult. This suggests a lack of structural modes for rearrangement at decreasing temperatures. Figure 24.16 shows a graphical representation of the reduction of possible structural relaxation modes
Decreasing temperature
Fig. 24.16 Graphical representation of decreasing relaxation modes with decreasing temperature. After [24.29]
with the decrease of temperature in a generic glassy system. In the left-most picture, individual atoms or groups of atoms are free to move along any of the available lines shown on the diagram. However, as the temperature decreases and begins to pass through Tg , the center schematic shows some formerly free relaxation modes being closed off. Finally, after reaching a low-enough temperature, the right-most sketch describes a system in which relaxation is only possible when done within those specified regions. Structural relaxation which must take place cooperatively within regions is relatively much slower than relaxation which occurs at or above Tg [24.29]. These structural relaxation data can be fit with various exponential functions such as the Kohlrausch– Williams–Watts function, or a Prony series in order to characterize the specific parameters related to the materials’ structural relaxation behavior [24.30–32]. This ongoing research seeks to study the structure and modes of kinetics within the glass to better understand the glass structure and how it changes with the thermodynamics of the material. Studies such as this demonstrate the power of thermal analysis to advance glass science.
24.4 Thermogravimetric Analysis (TGA) Thermogravimetric analysis (TGA) is a technique whereby the mass of a sample is measured relative to a known mass as the system is increased in temperature at a specific rate. TGA is a technique used widely in the pharmaceutical and polymer fields, however it has several uses within glass science and industry. The mass measurement capabilities of a TGA allow researchers to measure a sample’s weight loss or gain. For instance, some glasses absorb constituents from their environment upon heating. This can often be seen in the mass change of a sample. Likewise, other glasses lose constituents and mass at the same time. In glasses that contain toxic elements, it is important to know the upper use temperature in order to avoid burning off
dangerous elements during DSC or DTA experiments; a TGA can be used to determine this temperature. There are no clear universal standards for measuring the upper use temperature of glasses. However, it is convenient to define a percent loss that is characterized as the target of the test and end the test once that percentage of mass is lost. The value set for this cutoff will vary depending on the material that you are measuring and the expected chemical components that will burn off. If you are analyzing the decomposition temperature of an oxide glass, you may set the cutoff at 5% or 3% weight loss as long as none of the byproducts of decomposition are harmful or toxic. If you are measuring the upper use temperature of a chalcogenide glass that is
Thermal Analysis of Glass
mass of a sample to transitions like vaporization or sublimation. One example is a study by Schiavon et al. in which the decomposition of polycyclic silazane and then subsequent cross-linking to form silicon carbonitride glass is measured by a TGA/DTA [24.33]. TGA alone could only characterize the decomposition component of the transformation of polycyclic silazane, but running DTA in combination allows the second crucial part of the transformation to be characterized. Not only do the two tools give a more complete picture of the reaction, but they also help identify the relative position in temperature-space of the two events.
24.5 Viscometry Glass formers in general exhibit unique properties at elevated temperatures. Whereas crystalline materials heat up until melting at a specific temperature, glasses undergo a second-order transition from a solid-like state to a liquid-like state prior to going through the melting phase change. Once the temperature of the glass increases past Tg it becomes quite evident that glasses behave in some ways like liquids, and the temperature of the glass determines how thick or thin this liquid-like material is. At temperatures just above Tg glass flow under pressure or the weight of gravity might resemble caramel that has just come out of the freezer, while glasses at temperatures double their Tg would likely resemble water. This property is called viscosity. The measurement of viscosity in glasses is generally known as viscometry or rheology. The methods and instruments for measuring viscosity are various. Measuring the same property in a liquid that has a high viscosity (a liquid which is thick) and a liquid that has a low viscosity is not trivial. Real viscosity data is valuable to glass researchers and scientists alike. The effects of glass viscosity on macroscopic glass properties is present above, at, and even slightly below Tg . Viscosity is an influential factor for many material properties. If a glass remains at sufficient temperature for a length of time similar to the magnitude of the timescale for viscous flow, then there will often be observable viscosity effects. Understanding how viscosity changes with temperature and effects other properties is one of the main goals of fundamental glass science research. Figure 24.17 shows a typical glass viscosity curve as well as signature temperatures associated with glass study and manufacturing. The two most common viscosity measurement techniques for inorganic glasses are noted on the graph.
24.5.1 Measuring Viscosity Viscosity is most commonly described by two different but interchangeable units, poise and pascal-seconds (Pa s). The units of viscosity are most often referred to in log scale, with a viscosity of 5 poise being really a viscosity of 105 poise. The following equation relates poise and Pa s 10 poise D 1 Pa s ) log .poise/ D log.Pa s/ C 1 : (24.9)
The range of viscosities that are of interest in glass science and manufacturing is quite wide. Academic η (Pa s) 15 Beam-bending viscometer Annealing point Tg 10 Td Softening point
5
Working point Parallel plate viscometer
0 500
750
1000
Melting temperature
1250 1500 Temperature (°C)
Fig. 24.17 Example glass viscosity graph with approxima-
tions for key temperatures and regions
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comprised most often of chemicals like arsenic and selenium, then a 1% cutoff might be wisest, coupled with adequate safety precautions such as placing the instrument in a fume hood or providing suction at the TGA gas outlet port. Often the data produced by a TGA measurement is more valuable when coupled with other thermal analysis data, so TGA/DSC or TGA/DTA combination instruments are more common than simple TGAs. A TGA/DSC combo can record the mass of the sample while also measuring heat flow during heating or cooling; this allows researchers to tie changes in the
24.5 Viscometry
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experiments or industrial handling of glasses near Tg involve glasses with viscosities in the 1013109 Pa s range, while fiber drawing is done in the 103 101 Pa s range. Because of the wide range of temperatures at which glass is processed and used, it is necessary to measure glass viscosity at a wide range of temperatures. The following techniques are the most common for measurement of inorganic glass viscosity. Parallel Plate Viscometer Measurement of glass viscosities in the 104 108 Pa s range is typically done using a parallel plate viscometer (PPV). The theory behind the measurement is based on simple mechanics. The sample for a PPV measurements should be a flat disk, preferably with polished faces, with a height-to-diameter ratio of greater than 1 for maximum sensitivity. This sample is placed between two parallel plates inside of a furnace. The top plate is attached to a linear variable differential transformer (LVDT) which accurately measures the change in vertical position of the parallel plate. The plates are commonly made of Inconel which is chosen for its rigidity even at high temperature, high melting point, and high heat transfer coefficient. Once the sample has been placed between the two plates (Fig. 24.18a), a mass is sometimes added to the top plate, the entire system is enclosed and the temperature is increased. Accurate and repeatable temperature control and vertical height measurement are essential to a)
a
b) a ∙ 0.2
c) a ∙ 0.2
Fig. 24.18a–c Different conditions in a PPV measurement: (a) Initial condition, (b) no stick and (c) no slip PPV condition
achieve a true measurement of the glass viscosity versus temperature behavior. As the sample heats and passes Tg and the dilatometric softening point (Td ), the glass begins to deform under its own weight, the weight of the upper plate above it, and any mass added to the upper plate. During this deformation one of two boundary conditions is assumed for the plates and the glass disc. Either a no stick condition is assumed (Fig. 24.18b), where the disc becomes thinner and wider while the edges stay parallel to one another, or a no slip condition is assumed (Fig. 24.18c) where the glass disc retains its initial diameter where it contacts the upper and lower plates but barrels in the middle. Depending on the boundary condition, the rate of height change can be used, along with the other experimental parameters to calculate viscosity as a function of temperature. The equation for doing this in the most common case, no slip, is seen in (24.10). D 2
30V
dh dt
Mgh5 ; .2 h3 C V/ .1 C ˛/
(24.10)
where is the glass viscosity in Pa s, M is the applied load in g, g is the acceleration due to gravity in cm=s2 , t is time, V is specimen volume in cm3 , h is specimen thickness at time t in cm, dh=dt is compression rate in cm=s, and ˛ is the glass mean coefficient of thermal expansion from 25 ı C to the measuring temperature T in m=.m=ıC/ [24.34]. The “no slip” condition is most commonly assumed because it is the general nature of materials to have increased frictional forces at higher loads. This leads to the result that an experimental setup can come much closer to a perfect full sticking or no slip scenario than it could to a perfect no stick scenario. In real life experimentation there is no achievable no slip condition. This measurement relies on the accuracy of the dh=dt measurement which is a function of the internal resistance of the glass to volume change. If the viscosity of the glass is calculated using a no slip assumption, then any amount of slipping which might occur will essentially increase the observed rate at which the height of the sample is changed leading to an error skewing the calculated viscosity downward. PPV measurements are done at viscosities at which it is assumed the glass material’s internal resistance to volumetric change is much lower than the resistance of the material’s surface to sliding along the top and bottom plates [24.35]. All of the material and sample parameters in the above equation can be measured or found in the literature; the experimental aspect of this test is the relationship between dh=dt versus T for each specific sample. Figure 24.19 is an example of a PPV measurement curve for Schott N-FK5 oxide glass.
Thermal Analysis of Glass
6 5 4 3 2 1 0 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240
T (K)
Fig. 24.19 Viscosity versus temperature curve measured
by PPV for Schott N-FK5 glass
Several tests should be done with identical samples of each glass to ensure the repeatability of the experimental setup and the consistency of glass behavior. A variety of sample sizes can be used for this test, provided they are adequately tall compared to their diameter. Another consideration is that at high temperature the Inconel plates and sample material will likely interact chemically. To prevent any sticking to or corroding of the PPV plates, a very thin foil of an appropriate material must be chosen. The chemical interaction of many oxide glasses at high temperature can be reduced using a platinum foil on both top and bottom between the parallel plate and glass. For other glasses such as chalcogenides which will corrode platinum, an aluminum foil can be used assuming the test temperature does not exceed the melting temperature of aluminum. It is important to use a foil or very thin piece of buffer material so that the thermal expansion behavior of that material does not affect the measurement of the glass viscosity. The use of the PPV as a viscosity measurement tool is rarely complete by itself. To gain a thorough understanding of the entire viscosity region, viscosity must also be measured at lower temperatures, in the temperature region near Tg . The beam-bending viscometer (BBV) is the instrument of choice to complete the measurement of glass viscosity versus temperature. Beam-Bending Viscometer A beam-bending viscometer (BBV), works on a principle similar to a PPV. Instead of deforming a thick and narrow disk into a thin and wide disk, a BBV works by bending a thin and long beam of glass at temperatures significantly lower than a PPV. Both methods rely on a change in height measurement which is a result of the volumetric deformation of a well-defined glass cross section. In order to test glass at higher viscosities (1013 108 Pa s) without dedicating days or weeks to
the test, a small cross section glass sample is used. The BBV setup consists of a fused silica tube approximately 50 mm in diameter with two notches at the top located 180ı from one another. The notches are typically 55 mm. The prepared BBV sample is typically 33 mm, and slightly longer than the tube is wide. The beam is set into the notches. A fused silica shepherd’s hook, hangs on the sample like a hangar. The shepherd’s hook is attached to a long piece of fused silica that is connected to another length of metal rod. A furnace lowers down over the entire fixture and the metal rod, attached to the shepherd’s hook hangs through a hole in the bottom of the furnace. This rod is passed through an LVDT to measure sample deflection. Attached to the bottom of the metal rod is a cage or basket that holds calibrated weights. The weights are added to the basket depending on the temperature of the test. For a viscosity test at or even slightly below Tg , for instance, a larger mass is needed to affect a deformation on the sample. An example of a BBV sample setup can be seen in Fig. 24.20. The BBV test consists of first placing the sample on the slots in the tube, then lowering the furnace and ramping the temperature. The placement of the shepherd’s hook on the sample is dependent on the temperature and viscosity condition being measured. During PPV testing, the temperature is ramped without pausing from room temperature until the sample has reached the max deformation target. However, in BBV testing, the temperature is ramped to the test temperature and held until the sample has reached the max deformation commanded by the program. Tests that target relatively low temperatures (around Tg ), allow the shepherd’s hook to be placed on the sample before closing the furnace and beginning the temperature ramp at the beginning of the test. Tests at temperatures near the upper edge of feasibility for the BBV may require the technician to keep the weight of the hook and attached mass off of the sample until the test temperature is reached. Deformation of the beam adheres to common mechanical principles and is described by an equation Shepherd´s hook Glass sample
Fig. 24.20 BBV initial condition
Silica tube
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η (Pa s)
24.5 Viscometry
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Part C | 24.5
similar to that of the PPV. # " AL .1 C ˛s T/3 gL3 MC D 4 ; 1:6 1440Ic dh 1 C ˛g T dt (24.11)
where is viscosity in Pa s, M is the mass of the shepherd’s hook and fixturing plus any applied load in g, dh=dt is the midpoint deflection rate of the test beam in cm=s, g is the acceleration due to gravity in cm=s, Ic is the cross-sectional moment of inertia of the test sample in cm4 , is the density of the glass in g=cm3 , A is the cross-sectional area of the beam in cm2 , L is the support span, and ˛s and ˛g are the coefficients of expansion of the stand and sample glass respectively from 25 ı C to the measurement temperature [24.36]. Common BBVs are intended to measure viscosity over a temperature ramp; this allows a range of viscosity to be sampled on a single run. However, measurement over a temperature ramp adds a heating rate element to the measurement. During a temperature ramp test the ramp rate of the system as well as the thickness and heat transfer coefficient of the sample material come in to play. In order to obtain more precise viscosity data without the uncertainty added due to an effective ramp rate, it is possible to carry out a BBV measurement at a single temperature. A result of the BBV measuring viscosity at a single temperature is that it becomes necessary to sample several different temperatures in the range of interest. A single BBV test produces only a single data point, while a single PPV test produces several hundred or more. Figure 24.21 shows BBV test results for a sample glass, it is made up of three separate measurement runs. As seen in the figure below, the viscosity versus temperature behavior of many glasses is more or less linear over the typical test range of a BBV. This is not representative of viscosity behavior over the entire temperature range above Tg , η (log(Pa s)) 13.0 12.8 12.6 12.4 12.2 12.0 11.8 720
725
730
735
740
745 T (K)
Fig. 24.21 Viscosity versus temperature curve comprised
of three separate runs, measured by BBV for Schott N-FK5 glass
however it does allow practical viscosities within that region of temperature to be assumed as linear, making the need for measurement at the exact use temperature within that range unnecessary in many cases. This is just a generalization and each glass must be evaluated to test whether or not such assumptions can be made. Fiber Elongation Test (Littleton Softening Point) The fiber elongation test is a unique way of measuring glass viscosity. In principle it is similar to the first two methods discussed. A glass sample of known dimensions is heated and deflected and the deflection rate is measured and used to calculate glass viscosity using simple mechanics. A fiber of test glass is drawn to a diameter of 0:550:57 mm, one end of the fiber is heated into a ball large enough to suspend the fiber, and the fiber is cut to a length of 23:5 mm. The ball end of the fiber is used to hang the sample vertically in a furnace. The furnace is heated to a starting temperature, the sample is inserted, then the furnace is ramped through a range of temperatures while the deflection rate of the end is measured using a laser. The laser tracks the end of the fiber sample and calculates the deflection rate. Testing at temperatures near Tg may require a load to be applied to the sample in order to force deflection of the sample at an experimentally observable rate. The fiber elongation test is unique, in that it is used to define a standard glass viscosity and temperature known as the Littleton softening point. When the fiber elongation test is carried out, the temperature at which the fiber elongates at 1 mm=min is designated the Littleton Softening point, and this corresponds to a viscosity of 106 Pa s for most glasses. Certain glasses do not conform to criteria of the Littleton Softening Point, meaning that when the above condition is met, the viscosity of the glass is not precisely 106 Pa s. This does not mean that the fiber elongation test cannot be used to measure the viscosity of those glasses, only that the Littleton Softening point as a viscosity benchmark does not hold up for certain glass families. The drawback to this fiber elongation test is that a fiber must be drawn to make the sample, which is a fairly laborious process, involves expensive equipment, and is not practical for many companies and researchers. Additionally, some glasses cannot be drawn into fibers due to crystallization or thermal shock problems [24.37, 38]. Ball Penetration Viscometry Ball penetration viscosity testing operates on a different principle than the macroscopic sample deformation methods discussed above. In this test, a hemispherical
Thermal Analysis of Glass
24.5 Viscometry
.T/ D A C
Fig. 24.22 Penetration probe for measuring viscosity be-
havior by TMA. After [24.41]. Copyright TA Instruments. Used with permission
probe is forced into the surface of a glass sample. This is usually done using a special probe on a TMA. An example of a penetration probe viscosity setup can be seen in Fig. 24.22. The deflection rate of the probe into the glass is used to calculate the viscosity using (24.12). D
3V
dh dt
2 Mgh5 ; .2 h3 C V/.1 C ˛T/
(24.12)
where is the glass viscosity, M is the applied load in grams, g is the acceleration due to gravity, h is the sample height in cm, V is the sample volume, dh=dt is the sample deformation rate, ˛ is the linear coefficient of thermal expansion, and T is the temperature difference between the test temperature and ambient temperature [24.39, 40]. All length dimensions should match.
24.5.2 Quantifying Viscosity Beam bending and parallel plate viscometry are the primary ways of characterizing glass viscosity over a large range of temperature. However, they are only physically capable of measuring viscosity in certain temperature windows. Therefore, there must be a way to infer or predict viscosities at intermediate temperatures.
B T T0
;
(24.13)
where is the glass viscosity in log.Pa s/, A and B are fitting parameters, T0 is the temperature at which the model supposes the configurational entropy of the system to be zero and must be in either ı C or K, and T is the temperature whose units must correspond to T0 . When the parameters of the glass are known, the viscosity versus temperature curve can be reconstructed using this equation. However, if the properties are not known, they must be determined through experimentation. In Fig. 24.23, the set of PPV data for Schott N-FK5 seen in Fig. 24.19 and the set of BBV data seen in Fig. 24.21 are shown combined and fitted with a VFT curve. Assuming the experiments were carefully conducted, this fit can reveal the VFT parameters thereby allowing an approximation of the viscosity at any temperature between the two testing temperatures to be calculated. The VFT parameters for this glass, based on these experiments are as follows: A D 2:528, B D 475:96, and T0 D 139:45 ı C. Interpolation of viscosity for the majority of the range from Tg to Tm is fairly well described by the VFT equation; it is sufficient in a production environment and even in many research settings. η (log(Pa s)) 16 14 12
BBV data
10
VFT fit
8 6
PPV data
4 2 0 700
800
900
1000
1100
1200 T (K)
Fig. 24.23 Temperature versus viscosity measured data for Schott N-FK5, overlaid with a VFT fit of the viscosity data
Part C | 24.5
There are several fitting equations that have been developed to take PPV and BBV data, fit them, and then extract certain parameters which will allow anyone with those parameters to reconstruct the viscosity curve for a given material. The most common model is the Vogel, Fulcher, Tammann (VFT) model which was developed in the 1920s and uses a three-parameter equation to describe the viscosity of glass-forming melts [24.42, 43]. The VFT equation can be seen below in (24.13).
875
876
Part C
Characterization of Glasses
Part C | 24
a) η (log(Pa s))
b) Fragility parameter 37
14
36 12
35 34
10
33 8
32 31
6
30 4 As10Se90 2 300
350
As40Se60 400
450
500
550
600
650 T (K)
29 28
10
15
20
25
30
35 40 As content (at.%)
Fig. 24.24 (a) Viscosity versus temperature curves for glasses in the Asx Se100x system. (b) Fragility versus arsenic content for the same glass system. Reprinted from [24.44] with the permission of AIP Publishing
Viscosity is important for glass makers and fabricators, but the viscosity of glasses is a heavily researched topic because the way in which material properties change with temperature is very closely linked to the type of bonding and molecular interactions that occur as a material is heated or cooled. Another important viscosity linked parameter is what is known as the fragility of a glass. The fragility is the rate at which the viscosity changes with respect to temperature when measured at a viscosity of 1012 Pa s. For instance, certain glasses (known as strong glasses) have a viscosity that is relatively insensitive to temperature, while other glasses (known as fragile glasses) have viscosities that change very quickly with respect to temperature [24.45]. Studying the fragility can give researchers a window into the structure and bonding within a glass. A paper by Musgraves et al. explores the viscosity curves and fragility values for various compositions in the Asx Se100x glass system [24.44]. This study, demonstrated in Fig. 24.24, shows how viscosities of glasses with different concentrations of arsenic change with respect to temperature. Further analysis of the fragility parameter derived from each composi-
tion shows a definite difference in the type of bonding present in the various glasses of the Asx Se100x system. At high selenium compositions, Se–Se chains sliding and rotating are believed to be the primary method of rearrangement of the glass structure, while at higher As concentrations, chemical bonds must be completely broken and reformed to allow rearrangement. Several other fitting methods have been developed to either improve on or extend the prediction capability of the VFT. Methods developed by Mauro et al., and Avramov and Milchev are designed to fit viscosity data using a single equation, while others, including those developed by Wang and Fecht use a two-branch method to fit high and low viscosity data assuming cooperative rearrangement at temperatures nearer to Tg and truly Arrhenius behavior at high temperatures approaching Tm [24.46–48]. While more recent efforts have attempted to link an expression of glass viscosity versus temperature data to physical phenomena within the material, for the majority of industrial uses and many academic uses the VFT equation represents glass behavior sufficiently.
References 24.1
24.2
C. Meade, R. Hemley, H. Mao: High-pressure x-ray diffraction of SiO2 glass, Phys. Rev. Lett. 69(9), 1387– 1390 (1992) J.H. Gibbs, E.A. DiMarzio: Nature of the glass transition and the glassy state, J. Chem. Phys. 28, 373–383 (1958)
24.3 24.4
C.A. Angell: The glass transition, Solid State Mater. Sci. 1, 578–585 (1996) U. Fotheringham, R. Muller, K. Erb, A. Baltes, F. Siebers, E. Weiss, R. Dudek: Evaluation of the calorimetric glass transition of glasses and glass ceramics with respect to structural relaxation and
Thermal Analysis of Glass
24.6
24.7 24.8
24.9
24.10
24.11
24.12
24.13
24.14
24.15
24.16
24.17
24.18
24.19
24.20
24.21
24.22
24.23
24.24
24.25
24.26
24.27
24.28
24.29
24.30
24.31
24.32
24.33
24.34
24.35
24.36
24.37
lated differential scanning calorimetry (MDSC), Jpn. Soc. Appl. Phys. 35, 1116–1120 (1996) S. Kasap, D. Tonchev, T. Wagner: Heat capacity and the structure of chalcogenide glasses studied by temperature-modulated differential scanning calorimetry, J. Mater. Sci. Lett. 17, 1809–1811 (1998) Instrumentation Today: Linear Voltage Differential Transformer, Instrumentation Today, 19 July 2011. http://www.instrumentationtoday.com/ linear-voltage-differential-transformer-lvdt/2011/ 07/ E. Koontz, V. Blouin, P. Wachtel, J.D. Musgraves, K. Richardson: Prony series spectra of structural relaxation in N-BK7 for finite element modeling, J. Phys. Chem. A 116(50), 12198–12205 (2012) J. Malek: Structural relaxation of As2 S3 glass by length dilatometry, J. Non-Cryst. Solids 235, 527– 533 (1998) A.Y. Yi, A. Jain: Compression Molding of Aspherical Glass Lenses – A Combined Experimental and Numerical Analysis, J. Am. Ceram. Soc. 88, 579–586 (2005) T. Zhou, J. Yan, T. Kuriyagawa: Evaluating the visoelastic properties of glass above transition temperature for numerical modeling of lens molding process, Proc. SPIE 6624, 662403 (2008) S. Carmi, S. Havlin, C. Song, K. Wang, H.A. Makse: Energy-landscape network approach to the glass transition, J. Phys. A: Math. Theor. 42, 105101 (2009) R. Gy, L. Duffrene, M. Labrot: New insights into the viscoelasticity of glass, J. Non-Cryst. Solids 175, 103–117 (1994) K.L. Ngai, A.K. Rajaggopal, R. Rendell: Models of Kohlrausch relaxations, IEEE Trans. Electr. Insulation 21, 313–318 (1986) M. Potuzak, R.C. Welch, J.C. Mauro: Topological origin of stretched exponential relaxation in glass, J. Chem. Phys. 135, 214502 (2011) M.A. Schiavon, G.D. Soraru, V.P. Yoshida: Synthesis of polycyclic silazane network and it’s evolution to silicon carbonitride glass, J. Non-Cryst. Solids 304, 76–83 (2002) ASTM Standard C1351M-96: Standard Test Method for Measurement of Viscosity of Glass Between 104 Pas and 108 Pas by Viscous Compression of a Solid Right Cylinder (ASTM International, West Conshohocken 2012) E. Fontana: A versatile parallel-plate viscometer for glass viscosity measurements to 1000 °C, Bull. Am. Ceram. Soc. 49(6), 594–597 (1970) ASTM Standard C1350M-96: Standard Test Method for Measurement of Viscosity of Glass Between Softening Point and Annealing Range (Approximately 108 Pas to Approximately 1013 Pas) by Beam Bending (ASTM International, West Conshohocken 2013) ISO 7884-3: Glass Viscosity and Viscometric Fixed Points, Part 3: Determination of Viscosity by Fibre Elongation Viscometer (International Organization for Standardization, Geneva 1998)
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24.5
dimensional stability, Thermochim. Acta 461, 72–81 (2007) A. Bestul, S. Chang: Excess entropy at glass transformation, J. Chem. Phys. 40, 3731–3733 (1964) M. Goldstein: Viscous liquids and the glass transition: A potential energy barrier picture, J. Chem. Phys. 51(9), 3728–3739 (1969) R.J. Speedy: Kauzmann’s paradox and the glass transition, Biophys. Chem. 105, 411–420 (2003) R.B. Cassel: High Heating Rate DSC (TA Instruments, New Castle 2002), http://www.tainstruments.com/ pdf/literature/TA297.pdf L.C. Thomas: Making Accurate DSC and MDSC Specific Heat Capacity Measurements with the Q1000 Tzero DSC (TA Instruments, New Castle 2002) J. Mauro, R. Loucks, P. Gupta: Fictive temperature and the glassy state, J. Am. Ceram. Soc. 92, 75–86 (2009) E. Koontz: Characterization of Structural Relaxation in Inorganic Glasses Using Length Dilatometry, Ph.D. Thesis (Clemson Univ., Clemson 2015) C. Moynihan, A.J. Easteal, J.T.J. Wilder: Dependence of the glass transition temperature on heating and cooling rate, J. Phys. Chem. 78(26), 2673–2677 (1974) E. Marseglia, E. Davis: Crystallization of amorphous selenium and As0.005 Se0.995 , J. Non-Cryst. Solids 50, 13–21 (1982) N.P. Bansal, R.H. Doremus, A.J. Bruce, C. Moynihan: Kinetics of crystallization of ZrF4 -BaF2 -LaF3 glass by differential scanning calorimetry, J. Am. Ceram. Soc. 66(4), 233–238 (1983) J. Massera, J. Remond, J.D. Musgraves, M.J. Davis, S. Misture, L. Petit, K. Richardson: Nucleation and growth behavior of glasses in the TeO2 –Bi2 O3 –ZnO glass system, J. Non-Cryst. Solids 356, 2947–2955 (2010) A. Marotta, A. Buri, F. Branda: Nucleation in glass and differential thermal analysis, J. Mater. Sci. 16, 341 (1981) C. Ray, K. Ransinghe, D. Day: Determining crystal growth TRAte-type of curves in glasses by differential thermal analysis, Solid State Sci. 3, 727 (2001) H. Yinnon, D. Uhlmann: Applications of thermoanalytical techniques to the study of crystallization kinetics in glass-forming liquids, Part I: Theory, J. Non-Cryst. Solids 54, 253–275 (1983) J. Holubova, Z. Černošek, E. Cernoskova, M. Liska: Isothermal structural relaxation: temperature and time dependencies of relaxation parameters, J. Non-Cryst. Solids 326, 135–140 (2003) L.C. Thomas: Why Modulated DSC?; An Overview and Summary of Advantages and Disadvantages Relative to Traditional DSC (TA Instruments, New Castle 2005) J. Schawe, T. Heutter, C. Heitz, I. Alig, D. Lellinger: Stochastic temperature modulation: A new technique in temperature-modulated DSC, Thermochim. Acta 446, 147–155 (2006) S.O. Kasap, T. Wagner, K. Maeda: Heat capacity and structure of chalcogenide glasses by modu-
References
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Part C
Characterization of Glasses
Part C | 24
24.38
24.39
24.40
24.41
24.42
24.43
ASTM Standard C338-93: Standard Test Method for Softening Point of Glass (ASTM International, West Conshohocken 2003) R. Douglas, W.L. Armstrong, J.P. Edward, D. Hall: A Penetration Viscometer, Glass Technol. 6, 52–55 (1965) R. Brueckner, G. Demharter: Systematic investigation of the use of penetration viscometers, Glass Technol. 48(1), 12–18 (1975) TA Instruments: TA Thermomechanical Anaysis, http://www.tainstruments.com/wp-content/ uploads/BROCH-TMA-2014-EN.pdf (2006) G.W. Scherer: Editorial comments on a paper by Gordon S. Fulcher, J. Am. Ceram. Soc. 75, 1060–1062 (1992) G.S. Fulcher: Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8, 1043 (1925)
24.44
24.45
24.46
24.47
24.48
J.D. Musgraves, P. Wachtel, S. Novak, J. Wilkinson, K. Richardson: Composition dependence of the viscosity and other physical properties in the arsenic selenide glass system, J. Appl. Phys. 110, 06503 (2011) C. Angell: Relaxation in liquids, polymers and plastic crystals – Strong fragile patterns and problems, J. Non-Cryst. Solids 131-133, 13–31 (1991) J.C. Mauro, Y. Yue, A.J. Ellison, P.K. Gupta, D.C. Allan: Viscosity of glass-forming liquids, Proc. Natl. Acad. Sci. USA 106, 19780–19784 (2009) I. Avramov, A. Milchev: Effect of disorder on diffusion and viscosity of condensed systems, J. NonCryst. Solids 104, 253–260 (1988) L.W. Wang, H.-J. Fecht: A kinetic model for liquids: Relaxation in liquids, origin of the VogelTammann-Fulcher equation, and the essence of fragility, J. Appl. Phys. 104, 113538–113538-10 (2008)
Erick Koontz Fisba LLC. Tucson, AZ, USA [email protected]
Erick Koontz received his Bachelors in Mechanical Engineering from The Pennsylvania State University in 2010. He received his PhD in Materials Science and Engineering from Clemson University where he studied with Dr. Kathleen Richardson and specialized in glass science. Erick has been Engineering Manager in the precision molded lens department of FISBA LLC in Tucson, Arizona since January 2015.
879
Optical Spect 25. Optical Spectroscopy of Glass
Barrett G. Potter Jr.
Optical spectroscopy refers to a class of measurement techniques that involve the collection and interpretation of material spectral response to an incident optical field. These methods probe phenomena arising from light interaction with multilength-scale material structure that includes excitations involving electronic and nuclear constituents and their coupled states. In this context, optical spectroscopy plays a critical role in establishing structural attributes and performance characteristics of glassy materials and their composites—impacting the study of mechanical, thermal, electronic, and optical behavior. Effective optical spectroscopic analysis of materials is dependent upon an appreciation of the interrelationships between the mechanisms contributing to frequency-dependent material optical response, the measurement instrumentation and its performance, and the analysis of the resulting spectra. This chapter will address these primary aspects of successful optical spectroscopic examination of glass (and materials in general):
25.1 Light–Matter Interactions.................. 25.1.1 Classical Development........................ 25.1.2 Quantum-Mechanical Development ....
880 880 882
25.2 25.2.1 25.2.2 25.2.3 25.2.4
Instrumentation ............................... The Grating Spectrometer ................... The Interferometer ............................ Spectrophotometers........................... General Measurement Concerns ..........
891 891 895 898 898
25.3 Spectral Analysis and Interpretation .. 25.3.1 Preprocessing .................................... 25.3.2 Deconvolution, Derivatives, and Curve Fitting ............................... 25.3.3 Chemometric Analysis ........................
902 902 904 905
25.4
Conclusions ......................................
906
References...................................................
906
1. Light–matter interactions that form the basis for commonly used spectroscopic techniques and that underlie our ability to probe different structural units in the material. 2. Instrumentation concerns common to standard spectroscopic techniques and their contributions to spectrum appearance and interpretation. 3. Spectral analysis and interpretation associated with electronic and vibrational spectroscopies. A complete assessment of all potential phenomena and associated techniques that could be brought to bear, however, is beyond the scope of the present work. Here, we will attempt to highlight some key concepts of interest to the study of solid-state material atomic and electronic structure. Several important spectroscopic techniques and their theory of operation, relevant to this pursuit, will also be highlighted. Our discussion will be limited to linear optical phenomena (i. e., associated with the linear polarizability or first-order dielectric susceptibility of the material) and their measurement.
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_25
Part C | 25
Optical spectroscopic methods offer an important means to investigate glass structure and its associated dynamics. Moreover, they provide a set of powerful tools to evaluate material optical performance for a broad range of applications. Successful use of optical spectroscopy requires an understanding of intrinsic phenomena associated with the interaction of light with matter, of concerns surrounding measurement tools and techniques, and of data analysis and interpretation. While not intended to be an exhaustive examination of all techniques and phenomena, the present work seeks to highlight concepts of significant interest to the study of solid-state material atomic and electronic structure, and associated optical spectroscopic properties, in the context of the study and application of glass.
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25.1 Light–Matter Interactions 25.1.1 Classical Development
Part C | 25.1
The primary mechanism of interaction between an oscillating electromagnetic field (light) and a material arises from a coupling between charged components of the material structure and the incident field. The resulting charge displacement creates an induced dipole moment that contributes to an overall field-induced polarization in the material. It is the frequency, orientation, and phase dependence of this induced polarization that forms the basis for the observed material dielectric function and, hence, the complex refractive index that dictates the characteristics of light propagation in the medium. A common means to illustrate the coupling between an oscillating field and the material structure at a classical level is to model the material as a collection of simple harmonic oscillators (SHO). While this is a simplified approach, it is sufficient to establish key characteristics of free and driven oscillators that can provide early insight into the use of frequencydependent (spectral) behavior to elucidate the nature of different structural elements in materials. In the present context, such processes can include the redistribution of electron charge density (associated with atoms/ions and their bonds) and the displacement of nuclear positions (associated with atomic configuration and bond characteristics). Beginning with a free (undriven) oscillator, described in the SHO approximation by a mass of m, a restoring force constant of k, a damping factor of , and a characteristic angular frequency of !0 , the solution of a force balance equation (in one-dimension (1-D), x) describes the time-dependent displacement of the mass after an initial displacement of x0 at t D 0 x.t/ D x0 e t cos !0 t ;
(25.1)
In the context of frequency-based spectroscopic analysis, this time-dependent behavior can be alternatively represented in terms of the frequency dependence of the damped oscillation. A Fourier transformation of (25.1) results in a complex amplitude function A.!/ that can be multiplied by its complex conjugate A .!/ to produce the intensity spectrum for the oscillator I.!/ x0 1 ; A.!/ D p (25.2) 2 i.! !0 / C x2 1 I.!/ D A.!/A .!/ D 0 : (25.3) 2 .! !0 /2 C 2 The result in (25.3) is the well-known Lorentz function. The maximum Fourier coefficient is found at the natural resonance frequency for the SHO (i. e., !0 ). The full-width-at-half-maximum (FWHM) of this resonance feature is often termed the natural or homogeneous linewidth for the oscillator resonance; it is proportional to the damping factor for the oscillator in this treatment .FWHM D 2 /. With the behavior of the free oscillator established, we can move to a driven system to further establish some basic characteristics of interaction between an applied, oscillating field of frequency !, (analogous to an incident electromagnetic (EM) wave in a spectroscopic experiment), and the oscillator (modeling the material structural unit that is coupling to the EM wave). In this case, we assume a charge, q, on the oscillator and an incident E-field to provide a physical mechanism for the interaction that is analogous to that in the material. Under these conditions, the resulting displacement of the charged oscillator represents an induced dipole moment, . With N oscillators per unit volume, the induced polarization, P, for the ensemble of oscillators under an applied field, E D E0 "i!t is given by
where k !02 D : m The damping factor, , for the SHO is associated with the rate at which the amplitude of the oscillation decreases with time from the initial displacement .x0 /. This can be seen in (25.1) which contains an exponentially decaying amplitude factor characterized by a relaxation time constant or lifetime, , that is inversely related to the damping factor, i. e., D 1= . This can also be shown to be associated with the decay in energy stored in the oscillator in which the exponential decay time constant D 1=2 .
2
P D N D Nq x.t/ D
N qm E0 ei!t !02 ! 2 2i !
:
(25.4)
Note that the induced polarization term is maximized when the driving field frequency .!/ is near (or resonant with) the characteristic oscillator frequency .!0 /. It is also proportional to the amplitude of the applied field. Increased coupling between the field and the oscillator as a resonance condition is approached is observed in the enhanced amplitude of the polarization function. While the discussion thus far has addressed only a single SHO type, it is straightforward to extend the
Optical Spectroscopy of Glass
P D "0 ." 1/E.t/ ; " D "1 C i"2 ;
a) ε1
macroscopic material polarization (25.5), 2
P D "0 ." 1/E.t/ D
N qm E0 ei!t !02 ! 2 2i !
;
(25.7)
we find that the complex dielectric function, an intrinsic property of the material, can be expressed in terms of the characteristic response of the N-oscillator ensemble 2
" D 1 C
q N m" 0
!02 ! 2 2i !
D "1 C i "2 :
(25.8)
At optical frequencies, the complex dielectric function is more directly represented in terms of the complex refractive index, n , for the material, " D n 2 D .n C i /2 D n2 2 C 2i n ;
(25.9)
with n D refractive index and D extinction coefficient. The real and imaginary components for the complex dielectric function can then be expressed both in terms of the complex refractive index components and the induced polarization of the oscillator ensemble "1 D n2 .!/ 2 .!/ Nq2 2 !0 ! 2 m"0 ; D 1C 2 !02 ! 2 C 4 2 ! 2
(25.5)
"2 D 2n.!/ .!/ D
(25.6)
where "0 D electric permittivity of free space, "1 D real portion of the complex dielectric function, "2 D imaginary portion of the complex dielectric function. The polarization, P, and applied field, E.t/ are vectors with the complex dielectric function, " , expressed as a second-rank tensor in the general case. Equating the induced polarization derived for the one-dimensional, classical SHO model (25.4) to the
2 ! 2 Nq m"0 2 2 2 .!0 ! / C 4 2 ! 2
Similarly, it can be shown that, vq u u "2 C "2 C " t 1 1 2 ; nD 2 vq u u "2 C "2 " t 1 1 2 :
D 2
(25.10)
: (25.11)
(25.12)
(25.13)
b) ε2
2Γ
ω0
881
ω0
Fig. 25.1a,b The real (a) and imaginary components (b) of the complex
dielectric function for a classical SHO with resonance frequency, !0 , and damping factor,
Part C | 25.1
treatment to include a system of multiple oscillator types with different characteristics (i. e., force constants, damping factors, masses). The total induced polarization, then, will include contributions (and associated frequency and decay-rate characteristics) from each oscillator type weighted by the corresponding oscillator population. The collection of dissimilar oscillators will thus produce an induced polarization spectrum (via a transform like that used to obtain (25.3)) exhibiting enhanced polarization around frequencies that are resonant with the characteristic frequencies of the different oscillators. Even under this classical model, the ability to differentiate the mass and spring constant characteristics between different oscillators using the frequency dependence (i. e., resonance peaks) of the polarization response can be readily recognized. Thinking of the masses and springs of the classical model as atoms and bonds thus provides some initial insight into the utility of spectral measurement of material response as a means to examine the nature of the underlying resonance processes and their associated structural origins. The microscopic oscillator model above can be directly related to a macroscopic material response characteristic through the induced polarization. From electrodynamics, the induced polarization can be defined in terms of the complex relative dielectric permittivity of the material, " , often referred to as the complex dielectric function.
25.1 Light–Matter Interactions
882
Part C
Characterization of Glasses
Part C | 25.1
Figure 25.1 depicts the dispersion (frequency dependence) of the real and imaginary components of the complex dielectric function assuming the SHO oscillator model. The similarity between the curves in Fig. 25.1 and those observed experimentally confirm the underlying consistency of an oscillator model for material response. The material optical characteristics that are the focus for spectroscopic measurement (e. g., absorption spectroscopy) are based on the dispersion (frequency dependence) of the complex refractive index function in real materials. For example, (25.14) and (25.16) show how the absorption coefficient, ˛.!/ and reflectance, R.!/ for the material can be derived from the terms of the complex refractive index. Beer’s law (25.15), describes how the absorption coefficient contributes to the exponential decay of the incident optical beam, I0 , with propagation distance in the material. Equation (25.16) defines an intensity-based reflection coefficient for an optical beam in air at normal incidence to the material surface. This can be derived from the Fresnel equations [25.1] 2! .!/ ; c I D I0 expŒ˛.!/x ;
˛.!/ D
R.!/ D
(25.14) (25.15)
Œn.!/ 1 C .!/ Ireflect .!/ D : I0 .!/ Œn.!/ C 12 C .!/2 2
2
(25.16)
Referring to the above relationships, frequency-dependent absorption and reflectivity behavior arise directly from the dispersion in the complex refractive index that, itself, is associated with the underlying structural behavior (oscillator response) of the material. This is the foundation for the use of optical spectroscopic measurement of such phenomena to establish insight into the structural characteristics of materials.
25.1.2 Quantum-Mechanical Development Energy Structure We have found that a structural interpretation of optical spectroscopic measurement requires that the contribution of intrinsic oscillator characteristics to the complex dielectric function and, in turn, to the measured material response to an incident optical field, be firmly established. An analysis of optical spectroscopy data from real materials, therefore, must move beyond the classical oscillator model toward a description consistent with the quantum-mechanical nature of the light–matter interaction. At a fundamental level, we can again establish the basic energetics and spatial characteristics of
structural unit behavior, in this case, through the solution of the Schrödinger wave equation (SWE) that incorporates the appropriate physics of the structural element and its environment. See for example [25.2–4] for further detail. Eigenenergies for the stationary (i. e., time-independent) quantized states of a given structural element (comprised of i masses) that will interact with an incident field are the solutions of the time-independent form of the SWE ((25.17), shown in Cartesian coordinates) "
# X h 2 r C V.x; y; z/ n .x; y; z/ 2 mi i i D n n .x; y; z/ ; (25.17)
where h D Planck’s constant and remaining terms are defined below. The operator expressions within the square brackets of (25.17) are called the Hamiltonian for the system of interest (abbreviated, H). The first term of the Hamiltonian in (25.17) describes the kinetic energy operators for the masses, mi , comprising the structural assembly, the second term, V, is the potential energy operator defining the interactions between the masses and with their environment. Solution to the SWE for systems of interest for optical spectroscopy will result in a collection of quantized, orthogonal solutions or wavefunctions, n , and associated eigenenergies, n , each denoted by unique sets of indices called quantum numbers, n. The specifics of the system, including its dimensionality, geometry, and the nature of the potential energy operator influence the number and physical significance of the quantum numbers used to identify the set of wavefunctions obtained. In the context of optical spectroscopy, the eigenenergies obtained by solution of the SWE define an allowed energy level structure for the system under study that can be used to understand the resonance characteristics of its optical response. In contrast to the classical model, a specific oscillating structural unit (e. g., an isolated structural moiety in a glassy material) is now associated with a spectrum of optically mediated transitions between quantized states .n / upon interaction with light. Again, the specifics of the structural unit and associated interaction potentials and masses involved (i. e., the specifics of the Hamiltonian in (25.17)) can influence the nature of the SWE solutions and the associated energy level structure. The use of the SWE thus provides a platform from which to capture the salient characteristics of material atomic and electronic structure and its interaction
Optical Spectroscopy of Glass
s !0 D
k I red
1 1 1 D C ; red m1 m2
(25.18)
where k is again the force constant for the oscillator and red is the reduced mass of the molecule. In contrast to the classical solution, however, a quantum-mechanical treatment of the diatomic molecule returns a collection of quantized energy levels associated with allowed molecular vibrational states (identified by their quantum numbers) whose energy separation is directly related to the oscillator resonance frequency. A more complete analysis of this system, in which rotational degrees of freedom for the molecular motion are included, produces a set of wavefunctions defined by rotational and vibrational quantum numbers with modifications to the eigenenergies associated with these mixed states [25.3]. Moving to more complex, multiatom systems in the solid state (where rotational motion can be neglected), a mass-weighted normal coordinate transformation allows separation of the problem into a series of simple harmonic oscillator-type solutions to describe system motion along these normal coordinates. Each normal coordinate, Qk , represents a specific, in-phase motion of a collection of atoms in Cartesian space and it is associated with its own characteristic frequency, !k . The approach enables the decomposition of more complex vibrational motion in multiatom systems into linear combinations of orthogonal or normal modes of vibration. Optically excited transitions within the energy level structures for these normal modes provide the basis for the interpretation of vibrational spectroscopy
883
and related, coupled electronic and vibrational state transitions. Optical Transitions–Resonant Excitation The interaction between an applied electromagnetic (EM) field and the quantum-mechanical system is described in terms of the time-dependent evolution of the occupation of higher energy allowed states; energy transfer to the material is associated with the promotion of the oscillator system from one state to another. Using a first-order perturbation approach for the solution of the time-dependent SWE for simplified two-state system in which a weak incident electric field .E D E0 exp.i!t// is the basis of the perturbation, the probability, P2 , that the system will be promoted to the upper state of a two-state system (Fig. 25.2) can be developed. (While beyond the scope of the present chapter, a number of references provide a detailed development of this approach [25.2–4]). h i sin2 . 2 12„!/t 2 (25.19) P2 / E02 M12 . 2 1 „!/2 In (25.19), the probability that the system will be found in the upper state, 2, is time dependent and is proportional to three primary factors: 1. The intensity of the incident field, E02 . 2. The energy of the incident photon relative to the energy separation between the states of the system . 2 1 / (i. e., a resonance condition). 3. The transition moment, M12 . While the classical description of the SHO described earlier also includes contributions from points 1 and 2 above in terms of coupling to an oscillating applied field (25.4), the transition moment (point 3 above) is a fundamental outgrowth of the quantum-mechanical nature of the interaction and the system involved. The transition moment is central to a determination of the viability of a transition between states. Specifically, with M12 D 0, a given transition will not contribute to the induced polarization in the material even if the apΨ2
ξ2
Fig. 25.2 2-level Ψ1
ξ2
system with no state degeneracy
Part C | 25.1
with light. Challenges in the development of analytical solutions for the wavefunctions and associated eigenenergies for real materials arise from structural complexity and the potential interactions involved. Thus, various strategies, including coordinate space transformations, point and translational symmetry-based simplifications, interaction potential, correlation and coupling estimates, and the use of computational methods and tools are used to make these problems more tractable. As an example, the classical solutions for the internal, one-dimensional vibrational motion of a diatomic molecule can be readily found, assuming a harmonic oscillator (linear spring constant) interaction potential. The fundamental characteristic frequency for this simple harmonic oscillator system, in which the atoms vibrate in-phase about their common center of mass, is analogous to the expression developed earlier for the classical case of a single mass. In this case, the resonance frequency is expressed as
25.1 Light–Matter Interactions
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plied field frequency (or photon energy) is resonant with the energy separation of the states involved. This requirement was not present in the classical model. Equation (25.20) provides a generalized definition for the transition moment. The integral over indicates over all spatial coordinates
Part C | 25.1
Z1 M12
2 O 1 d :
(25.20)
1
As shown, the transition moment is defined in terms of the wavefunctions of the initial and final states involved in the field-induced transition connected through an operator, O, defining the primary nature of the perturbation that couples the incident field with the system. The nature of the perturbation spans a range of electronic and magnetic interactions, including electric dipole (ED), magnetic dipole, and electric quadrupole. Each of these interactions can be represented by an appropriate operator within the transition moment expression. An examination of the relative magnitudes of these different contributions to the transition moment reveals that the electric dipole-mediated interaction is on the order of 105 times greater than magnetic dipole and 106 times greater than the electric quadrupole interactions [25.4]. In this context, the electric dipole transition moment is routinely used to evaluate the probability for a given optical transition. For example, the electric dipole operator for an electron in one-dimension, ED D ex, produces an electric dipole transition moment expressed as Z1 M12 D
2 ex 1 dx ;
(25.21)
1
where e is the electronic charge and x is the charge position. It is important to note that, while the magnitude of the transition moment is dependent on the value of the integral, an analysis of the transition moment in terms of conditions leading to its nonzero value, i. e., corresponding to a nonzero transition probability, is a very useful application of the transition moment in the context of spectroscopic analysis. An optical transition associated with a nonzero electric dipole transition moment is termed a dipole-allowed transition. We will take up the characteristics of the wavefunctions for the initial and final states as a contributor to a nonzero electric dipole transition moment presently. However, the form of the ED transition moment provides some immediate insight into the general nature of dipole-allowed optical transitions. Using the earlier
discussion of normal vibrational modes for a more complex atomic assembly as an example, for a given vibrational mode, k, the problem is again one-dimensional (associated with the single, normal coordinate Qk replacing x in (25.21)). It can be shown that a finite value of the electric dipole transition moment .MED / for a vibrational state transition involving the k-th normal mode can be found only when there is a change in the dipole moment of the atom assembly through its vibrational motion, i. e., d ED =dQk ¤ 0 [25.2]. In other words, an incident optical field can only induce a transition from one state to another of a normal vibration mode if that vibrational motion itself results in a change in dipole moment for the structural assembly involved. In the context of vibrational spectroscopy, this is termed an infrared (IR)-allowed transition, and addresses the probability of observing such a transition in, for example, an infrared absorption measurement. The requirement of a changing dipole moment along a given normal coordinate in a vibrating system, however, is a necessary but not a sufficient condition for a dipole-allowed vibrational transition. Indeed, a complete assessment of the ED transition moment for either electronic or vibrational transitions must include the specific characteristics of the initial and final wavefunction states involved ((25.20) and (25.21)). This relies on an analysis of the inherent symmetry characteristics of the wavefunctions and their product with the electric dipole moment operator. Group theory principles and associated tools (e. g., character tables) provide a means to perform this assessment [25.2, 4]. Initial and final state combinations that result in nonzero MED values can be used to generate a set of quantum number changes (selection rules) that will define those optical transitions that are electric dipole-allowed. Deviations from the symmetry properties of the states involved in an optical transition, e. g., associated with the variability in local structural and electrostatic environment, can result in a relaxation of selection rules developed under ideal symmetry conditions. Common examples central to glass spectroscopy include deviations from the simple harmonic interaction potential in real vibrational systems (e. g., involving more realistic, Morse-type potential functions for example). This can result in the lifting of selection rules to allow changes in vibrational quantum number jnj > 1 that correspond to vibrational overtones and mixedmode transitions. A second example is the breaking of spherical symmetry in trivalent lanthanide or transitionmetal ionic dopant environment in glass and crystalline hosts to allow electronic transitions in which a change in angular momentum quantum number, l, is equal to zero .l D 0/ (i. e., enabling technologically important 4f–4f or 3d–3d optical transitions).
Optical Spectroscopy of Glass
S12 D
g2 g1 X X
j M1 i 2 k j 2 ;
(25.22)
iD1 kD1
where gx indicates the degeneracy of level x (i. e., the number of states having the same energy). Key absorption strength metrics that are often extracted from spectroscopic measurements can be devel-
885
oped from the line strength [25.5], for example, absorption cross-section: 1 !12 S12 ; 12 D ! 6"0 chg1 absorption coefficient: g1 ˛12 .!/ D N1 N2 12 .!/ ; g2 oscillator strength: 1 4 me !12 S12 ; f12 D g1 3e2 h
(25.23)
(25.24)
(25.25)
where ! D transition linewidth (angular frequency), !xy D angular frequency difference between levels x and y, "0 D free space permittivity, h D Planck’s constant, c D speed of light, Nx D occupation of energy level x, gx D state degeneracy of energy level x, me D electron mass, and e D electron charge. In a similar manner, the line strength can also provide insight into the dynamics of energy decay from the system, i. e., the spontaneous emission rate, A21 , from the excited state to the ground state A21 D
3 1 2!21 dP2 D S12 : dt g2 3"0 hc3
(25.26)
In the context of the Einstein treatment of energy transfer between an EM field and a two-level system [25.4, 5], the A21 rate in (25.25) is the spontaneous emission rate while the corresponding induced absorption coefficient, B12 and induced emission coefficient, B21 , are also accessible from the line strength of the transition. The reciprocal of A21 is the natural radiative decay time constant for the excited state. This is a focus of luminescence spectroscopy that monitors relaxation of the system from its excited condition back to its ground state accompanied by the emission of a photon. The spectral characteristics and time scale of this decay thus provides insight into the lifetimes of allowed states and their underlying structural origins. Excited-state relaxation dynamics, however, often involve more than just a single radiative process and may also include contributions from nonradiative energy loss mechanisms. The measured decay rate for the upper state can be thus described in terms of all processes contributing to the observed de-excitation rate Aobs D Arad C WNR C Wtransfer D
1 ; obs
(25.27)
where Aobs D the observed luminescence intensity decay rate, Arad D radiative (spontaneous) relaxation rate, WNR D nonradiative relaxation rate, Wtransfer D energy transfer rate to another luminescent center or defect
Part C | 25.1
Finally, structural disorder in glass produces bond angle distributions, local coordination deviations, and point defects that distort local electrostatic and vibrational environments, resulting in a range of optical transition probabilities. The above discussion focuses on excitation conditions in which the incident field must be resonant with a vibrational or electronic transition within the allowed energy level structure of the material. The corresponding transitions contribute to an induced total polarization for the material representative of enhanced coupling between the incident field and the material as the field frequency approaches the resonance condition. Thus, as described earlier, the induced polarization contributes to the dielectric function that, in turn, dictates the frequency-dependent optical properties of the material (i. e., n.!/ and .!/). The induced polarization thus influences light propagation characteristics within a material via absorption, reflection, scattering, and luminescence behaviors that would be probed in a spectroscopic measurement. While the above results provide insight into the frequency positions for spectral features in spectroscopic measurements, the magnitude of such a response is also of interest and is often used to more completely assess the nature of underlying material structure. In an absorption measurement, for example, the absorption coefficient would provide an indication of the degree of coupling and energy transfer efficiency between the material and the incident light, providing insight into the characteristics of the states involved as well as the relative population (concentration) of structural elements participating in the response. On the basis of the above theoretical outline, the rate of energy transfer to the material from the field in an allowed transition (state 12), i. e., the transition rate, may be expressed as dP21 =dt which is related to the square of the transition moment (and, under broad-band incident light, is found to be time independent [25.4]). Of interest in the context of an experimental observable, the transition rate is found to be proportional to the observed magnitude of spectral features associated with this transition. In the case of an absorption measurement, an expression describing the strength of a transition, called the line strength .S/, can be developed based on the corresponding transition moment
25.1 Light–Matter Interactions
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Part C | 25.1
state and obs D the observed luminescence decay time constant. It is important to note that, depending upon the material system and states involved, each of the above terms may encompass multiple processes (e. g., radiative decay to multiple lower stationary states) contributing to the de-excitation of the excited state. Moreover, depending upon the relative timescales for different processes, multiexponential decay of the luminescence intensity may be observed and fitted to provide insight into the different time constants and associated de-excitation processes involved. Absorption and luminescence spectra find great utility in establishing the nature of intrinsic point defects and impurity or dopant species within glass. Point defect species associated with, for example, anion or cation vacancies, coordination deviations, and charge transfer, are often examined in concert with electron spin or nuclear magnetic resonance techniques [25.6– 15]. Absorption spectroscopy also is used to examine photoinduced modification in defect structure in the context of photosensitive modification of optical constants for photonic device development [25.8, 10, 16– 21]. In the case of the optical behavior of transition metal and lanthanide dopants, theoretical treatments that adress the intrinsic electronic structure of these dopants and the influence of bonding conditions provide a means to use absorption spectra to assess the contribution of local electrostatic environment to the optical behaviour of the ions. Analyses involving Tanabe–Sugano diagrams, for example, are often used to provide information useful in an analysis of d-level optical transition behavior in transition metal ions [25.2, 4, 22] while Judd–Ofelt parameterization is routinely employed to estimate 4f–4f radiative transition probabilities from the ground-state absorption spectra of trivalent lanthanide ions in glass and other host materials [25.23–26]. These approaches find direct use in a wide variety of studies focusing on glass host optimization for use in such applications as optical filtering, frequency conversion, optical amplification, and phosphor emission [25.27–35]. Inelastic Scattering Finally, we will take up another type of light–matter interaction within materials spectroscopy that also plays an important role in the evaluation of glass structure. This interaction contrasts those based on resonant photon excitation of allowed transitions within the allowed energy level structure (either electronic or vibrational). In this case, inelastic scattering of nonresonant incident optical excitation with structural perturbations that are associated with thermal phonons (optical or acoustic) is the focus.
Raman Spectroscopy. The Raman effect forms the basis for a family of vibrational spectroscopies. It is associated with inelastic scattering of the incident optical radiation with the optical phonon modes of the material. Extending the approach used for direct optical transitions, Raman scattering can be described using second-order perturbation theory applied to the solution of the time-dependent SWE. In this case, the corresponding transition moment is now found to be derived using the electric polarizability operator, i. e., coupling between the applied field and the polarizability of the structural unit under study is now the issue. The polarizability, ˛ij , is a second-rank tensor that describes the intrinsic response of the structure to an applied field, Ej , to produce an induced dipole moment, i ; it is associated with the electron density redistribution accompanying the vibrational motion of the nuclei i D ˛ij Ej :
(25.28)
Or, in explicit terms 2 3 2 ˛11 1 4 2 5 D 4˛21 3 ˛31
˛12 ˛22 ˛32
32 3 ˛13 E1 ˛23 5 4E2 5 : ˛33 E3
(25.29)
Clearly, the polarization condition of the incident field, and its propagation direction relative to the primary coordinates associated with the structural element and its vibration, have a significant impact on the components of the polarizability tensor accessed and the magnitude of the induced dipole moment observed. In what is termed normal Raman (i. e., nonresonant excitation conditions), the polarizability tensor is symmetric, i. e., ˛12 D ˛21 ; ˛13 D ˛31 ; ˛32 D ˛23 [25.36]. While a full quantum-mechanical description of the Raman process is beyond the current scope (references that provide additional detail include [25.37, 38]), a classical description of the scattering process is often used to motivate an understanding of the Raman process. Again, we examine the effect of an applied field to induce a dipole moment (or polarization) in the structure. As above, the induced dipole moment is described using the polarizability and an applied oscillating field induced D ˛.!/ E0 cos.!0 t/ :
(25.30)
By assuming a linear field response and a corresponding functional form of ˛ based on a Taylor expansion about the normal coordinate corresponding to the k-th vibration, Qk , with resonance frequency, !k , the induced dipole moment under an applied field with frequency
Optical Spectroscopy of Glass
!0 can be found [25.36, 37]
(25.31)
The induced dipole moment (and thus the induced polarization and scattered EM field) has three primary components that are associated with different scattering processes. Rayleigh scattering, an elastic scattering process in which there is no change in the frequency of the incident light, is represented by the first term within the square brackets of (25.31). The frequency-shifted components of the induced dipole moment correspond to the inelastic, Raman processes. Raman scattering results in new electric field components, associated with the applied field-induced oscillation of the vibrational mode involved. Both an increase in frequency over that of the incident field (anti-Stokes, second term in (25.31)) and a decrease in field frequency (Stokes, third term in (25.31)) is found. The frequency shift (Stokes or antiStokes) is associated with the resonance frequency of the normal mode involved, !k . In this context, Raman spectra are most often presented in terms of the Raman shift frequency rather than the absolute frequency (or wavelength) of the scattered light as the shift value corresponds to the vibrational frequency of the mode in question. Examination of (25.31) also shows that an inelastic response is only finite if the derivative of the polarizability with respect to the normal coordinate is nonzero, consistent with a quantum-mechanical treatment. In this case, Raman-allowed vibrational transitions must exhibit a change in polarizability of the structural assembly along the normal coordinate .Qk / representing the vibrational mode. As with the electric dipole-allowed transitions described earlier, the symmetry of the vibrational modes and that of the polarizability operator will finally dictate whether the transition moment for Raman is nonzero. Raman is often described as a complimentary technique to that of infrared absorption (IR) due to the coupling between the incident field and different aspects of the vibrational state motion, i. e., Raman couples to polarizability while IR couples to the dipole moment (see earlier discussion). Since Raman spectroscopy is based on a scattering phenomenon, it does not rely on the incident light to be resonant with the vibrational state transitions involved (although this condition can be used to enhance Raman response—see resonant Ra-
man scattering [25.36, 37]), enabling greater versatility in experimental conditions and equipment when the need to produce an infrared photon to probe the material is removed. Figure 25.3 depicts another way to view the Raman effect in terms of transitions between energy states. Three different processes are shown, accompanying optical excitation at energies much greater than the vibrational transitions. Excitation from one of the lower vibrational states is pictured as involving an upper, virtual state for the system. This can be thought of as a rapid, transient perturbation of the material in response to the incident field. The system relaxes to one of the vibrational states, emitting a scattered photon whose frequency is either lower (Stokes), higher (antiStokes), or the same (Rayleigh) as that of the incident photon. Thus, Stokes scattering results in the excitation of a phonon while anti-Stokes involves the de-excitation of an existing phonon in the upper, excited state. Under thermal equilibrium conditions, the occupation of the higher energy vibrational state will be lower than that of the ground state (Maxwell–Boltzman distribution). This effect is readily observed in the higher scattering intensity of the Stokes Raman peak as compared to the corresponding anti-Stokes peak in Raman spectrum (Fig. 25.4) and can, itself, form the basis for noncontact temperature measurement through a comparison of Stoke and anti-Stokes scattered peaks from the same vibrational mode. In the context of Fig. 25.3, the resonant Raman scattering method (another form of the Raman spectroscopy) mentioned above involves the replacement of the virtual state level with an allowed, stationary electronic state for the system. In a classical treatment of Raman scattering, the inelastic scattered intensity, In!m , associated with a vibrational transition .n ! m/ in an harmonic oscillator, is often described in terms of a scattering cross-section .n!m /. The cross-section is dependent upon the freVirtual states
Vibrational states Infrared Rayleigh absorption
Stokes Anti-Stokes Raman Raman
Fig. 25.3 Energy level schematic illustrating Raman scat-
tering effects (inelastic) in the context of Rayleigh scattering (elastic) and direct infrared absorption
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Part C | 25.1
induced @˛ D E0 ˛0 cos.!0 t/ C Qk cosŒ.!0 C !k /t @Qk 0 @˛ C Qk cos Œ.!0 !k /t : @Qk 0
25.1 Light–Matter Interactions
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Characterization of Glasses
Fig. 25.4 Schematic Raman spectrum showing Stokes and anti-Stokes scattered line positions and relative peak heights. A vibrational transition energy .h vib / is illustrated
Rayleigh Anti-Stokes
Stokes hνvib
Part C | 25.1
Frequency decreasing Wavelength increasing
Excitation frequency
quency of the scattered light and the polarizability tensor components .˛pq /. In!m D I0 n!m ;
X ˇ ˇ2 ˇ˛pq ˇ ; n!m / .!0 ˙ !k / 4
(25.32) (25.33)
p;q
where I0 D incident light intensity at frequency !0 , !k D resonant frequency of vibrational mode k [25.37]. Thus, the Raman intensity scales with the fourth power of frequency of the scattered light, i. e., !0 ˙ !k . Since Raman is typically performed using visible light excitation (!0 near 1015 s1 versus vibrational frequencies, !k near 1012 s1 ) the anticipated scattered intensity is then most dependent upon the excitation frequency chosen. That said, the overall Raman intensity is orders of magnitude smaller than that of Rayleigh scattered light (at the excitation frequency) leading to more rigorous performance requirements for the spectrometer system used in the measurement (see next section). The potential to increase Raman scattering intensity by increasing the excitation photon energy is also limited by the increased probability for spectral interference from photoluminescence. Here, resonant excitation of higher energy electronic states of the material and their subsequent radiative decay can produce emitted light with much higher intensity than that of the Raman scattered light. A quantum-mechanical treatment of the Raman effect is required to fully describe the anticipated Raman intensity [25.37, 38]. The tensoral nature of the material polarizability that contributes to the Raman scattering cross-section and the scattered intensity is associated with the symmetry properties of the structures and resulting normal vibrations involved. It can produce significant variation in the magnitude of the induced polarization with experimental configuration. An analysis of the underlying symmetry properties of the structures/vibrations, thus, can be pursued by accessing different polarizability tensor components through control of measurement ge-
ometry and excitation and scattering polarization conditions. Isolation of specific polarizability terms is not directly possible in amorphous systems as the structural elements under study are typically randomly oriented with respect to the laboratory frame. In this case, we must deal with average values for the components of the polarizability. Insight into the relative asymmetry of a particular vibrational mode can be obtained by polarization-selective scattered light measurement. In this case, the Raman peak intensity is obtained for a given vibrational mode under two different polarization conditions with respect to the plane-polarization direction of the incident beam i. e., scattered light polarized perpendicular to the excitation light polarization and scattered light polarized parallel to the excitation polarization. Further, the scattered light is collected normal to the propagation direction of the incident beam. The depolarization ratio (, (25.34)) obtained from these measurements can be related to the underlying polarizability tensor components, ˛pq , contributing to Raman scattering intensity under these excitation/collection conditions. For a normal (nonresonant) Raman measurement I? 3 2 D ; Ik 45˛2 C 4 2 1 ˛ D .˛xx C ˛yy C ˛zz / ; 3 1
.˛xx ˛yy /2 C .˛yy ˛zz /2 2 D 2 2 2 2 : C.˛zz ˛xx /2 C 6 ˛xy C ˛yz C ˛zx D
(25.34)
For a totally symmetric vibration, ˛ ¤ 0, the depolarization ratio ranges from 0 0:75. In this case, the vibrational mode is described as polarized. For nontotally symmetric vibrations (asymmetric modes) ˛ D 0 and D 0:75. In this case, the mode is called depolarized [25.36]. While subject to assumptions re-
Optical Spectroscopy of Glass
Brillouin Spectroscopy. Another inelastic scattering process involves interaction with propagating acoustic phonons in the material. These lower energy vibrations (GHz frequencies) are characterized by longer wavelengths and thus interrogate longer length-scale structural assembly and behavior. A brief description of the nature of Brillouin scattering and its application to structural characterization is provided here. The reader is referred to an excellent treatment of the phenomena and associated techniques in the context of amorphous material systems [25.47]. As in Raman, the fundamental nature of the interaction involves an induced oscillation in material dipoles and the resulting generation of scattered optical fields. Variation in the density of these dipoles, associated with propagating acoustic phonons, result in spatially and temporally varying material density fluctuations, that, in turn, are associated with variations in the local dielectric function for the material (and its response to an applied field). It is the presence of this inhomogeneity in the material density (and associated induced polarization via the dielectric function) that provides the opportunity for off-axis propagation of frequencyshifted, scattered light and that forms the basis for Brillouin scattering spectroscopy. Given the commensurate wavelength of typical excitations used in Brillouin scattering (visible) and the longer wavelengths characteristic of acoustic vibrational modes, the scattering phenomena associated with these propagating density fluctuations can be formulated in terms of diffraction theory that employs phasematching conditions involving the incident, phonon,
and scattered field wavevectors. A dynamic structure factor is also used to describe the characteristics of the periodically varying material perturbation involved in the incident field–matter interaction. In this case, the dynamic structure factor can be shown to incorporate material heat capacities, thermal diffusivity, and kinematic viscosities to develop a total scattered field intensity that is a function of both excitation and scattering geometry (dictating the phonon wavevectors, q, probed by the experiment) and scattered field frequency. As with the Raman discussion above, terms in the resulting scattering intensity describe components associated with Rayleigh (elastic), Stokes-shifted, and anti-Stokes frequency shifted fields. In this case, the frequency shifts .˙!s / are associated with the frequencies of the acoustic phonons involved in the scattering process, described in terms of their wavevector, q, and the velocity of sound in the medium, cs ˙ !s D ˙cs q :
(25.35)
The corresponding frequency shifts observed in Brillouin scattering (associated with the acoustic phonon energies) typically fall in the range 0:15 cm1 , two or more orders of magnitude smaller than those observed in Raman scattering involving higher energy optical phonons. The extremely small energy separation between the excitation and the Brillouin-scattered light frequencies requires unique spectroscopic instrumentation to recover these spectra as will be discussed in a subsequent section below. Figure 25.5 illustrates the position of Brillouin and Raman scattered light relative to Rayleigh scattered light of the excitation radiation. Rayleigh Stokes
Anti-Stokes 0.1 – 5 cm–1 100 – 1500 cm–1
Brillouin Raman
Brillouin Raman
Frequency
Fig. 25.5 A schematic depicting the relative frequency po-
sitions of Stokes and anti-Stokes Brillouin peak locations relative to the Rayleigh and Raman scattered light
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Part C | 25.1
garding the random orientation of the ensemble of vibrating elements sampled by the measurement (leading to potential deviations from the depolarization ratio values and their interpretation), the use of polarizationselective techniques in Raman is of significant value in the development of vibrational mode assignments in glass. The approach provides insight into the degree of asymmetry characteristic of the vibrations involved and, hence, the nature of the corresponding structural elements present in the material. Raman spectroscopic investigation of glass structure typically has been pursued as a characterization technique within a suite of complementary x-ray, neutron, and electron scattering and resonance methods. This inherently noncontact technique has been applied over varied temperatures, in the melt, and after exposure to a broad range of ionizing and nonionizing radiation. Recent reviews of Raman applied to glass systems and its role in glass structural studies are available [25.39, 40]. Some specific studies employing Raman spectroscopy are provided in [25.41–46].
25.1 Light–Matter Interactions
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Part C | 25.1
With suitable correction for instrumental broadening contributions, fitting of the resulting Brillouin scattering spectrum is used to extract the sound velocity (Brillouin Stokes or anti-Stokes shifted peak position) and attenuation coefficient for the propagating phonon mode (associated with Brillouin scattering peak widths). Contributions to the sound attention coefficient associated with thermal relaxation processes (thermal diffusivity, structural relaxation) can be further extracted from widths of the Rayleigh peak and an underlying thermal relaxation peak, respectively. Thus, a rich collection of viscoelastic properties (including the complex elastic modulus and the dynamic viscosity) can be obtained from an analysis of these key characteristics, providing a noncontact, spatially localized approach for the assessment of glass elastic, transport, and structural relaxation behavior. Manipulation of specimen temperature and/or scattering geometry (accessing different phonon mode frequencies that are, themselves, the probing frequencies for dynamic behavior) can be used to provide insight into the frequency dispersion of the elastic storage and loss moduli leading to an assessment of relaxation processes and glass transition behavior [25.48–53]. Control of incident light polarization conditions and polarizationselective detection of scattered light also provides an opportunity to isolate tensor components of material elastic modulus. The above discussion addresses the relationship between the absorption and scattering behaviors observed in a spectroscopic measurement and the underlying multilength-scale structural elements and light–matter interaction processes within a material. In a general sense, we can see that spectroscopies probing electronic transitions in glasses (e. g., UV-Vis (Ultraviolet-visible) absorption, photoluminescence) can be used to provide insight into local discontinuities in network connectivity and electron density distribution (e. g., point defects, dopant ions). Vibrational behavior, examined using IR absorption and spectroscopic techniques based on Raman and Brillouin scattering, addresses medium to longer range structural features (up to hundreds of nanometers) depending upon the frequencies examined and the corresponding spatial wavelengths for the vibrational modes involved. Spectral Lineshape Considerations In the case of an absorption measurement, the intrinsic, or homogeneous, linewidth of a resonance peak corresponding to a single oscillator transition between allowed energy states is related to the natural energy decay rate of that excited state. This transform-limited linewidth was described earlier in the context of a classical oscillator. In a real material, often modeled as
a collection of oscillating structural units, the potential for local modifications in structural environment (e. g., bond angles, coordination, electrostatic field) can result in spatial variation in the conditions dictating the oscillator behavior and the corresponding spectroscopic resonance characteristics (resonance energy, linewidth, excited-state decay time). Classically, this could be depicted as local changes in force constant, damping factor, or bond geometry. In the quantum-mechanical framework, these local variations in environment would impact the Hamiltonian for the SWE, likely via the potential energy operator or the geometry of the system under study, directly modifying the wavefunctions and eigenenergies obtained. Combined transitions, involving the coupling of electronic and vibrational states and their transitions, while not a focus of our earlier discussion, can also play a key role in homogeneous lineshape determination and the spectral distribution of oscillator strength. These resonances can be dramatically influenced by specimen temperature as well as local structural and vibrational environment. Of particular interest are optically active dopants in glass and crystals, including transition metal ions and trivalent lanthanide systems. Additional depth into these areas can be found in several texts, e. g., [25.4, 54]. When an ensemble of oscillators (a material specimen) is interrogated using optical spectroscopy, the resulting spectrum will reflect this structural heterogeneity. Local environment-mediated modification in the resonance characteristics of an optical transition (electronic, vibrational or mixed states) will result in an increase in the observed linewidth for the homogenous resonance feature, reflecting the contributions from the same structural unit oscillating and interacting within different environments. The resulting inhomogeneously broadened linewidth can be determined through a convolution of the homogeneous, transformlimited lineshape (Lorentzian) with the distribution of resonance frequencies representing the site-to-site variation in local environment (often described by a Gaussian distribution). In an amorphous material, structural variation produces an inhomogeneous broadening that is often much larger than that associated with the homogeneous linewidth of a particular vibrational or electronic transition. Under these conditions, the relative width of the resonance frequency distribution produced by the local environment is much larger than that of the transform-limited Lorentzian, resulting in an observed lineshape that can be well described by a Gaussian lineshape (in frequency). Under more generalized conditions the convolved lineshape is described by the Voigt function [25.5]. Thus, the linewidth returned by
Optical Spectroscopy of Glass
a spectroscopic measurement can be used to extract information important both to the intrinsic characteristics of the resonances (and structures) involved as well as the diversity of local structural and/or electrostatic environments present within a material, a significant consideration in the evaluation of glasses and their composites.
25.2 Instrumentation
In addition to knowledge of the physical foundations for optical phenomena in materials introduced above and its intrinsic impact on spectral behavior, it is important to note that an accurate assessment of optical spectra is intimately linked to the measurement conditions and instrument characteristics used to collect the data. This is the topic of the next section.
25.2.1 The Grating Spectrometer A primary issue in the measurement of spectral behavior is the isolation of individual spectral bands for analysis. Most optical spectroscopy within the UV-Vis and near infrared (near-IR) range (this covers most electronic resonances and, via Raman spectroscopy, vibrational response) is performed using a grating-based a)
Entrance slit
spectrometer system. Two variants of the standard grating spectrometer are typically used, differentiated by their detection approach. A spectrograph is associated with the simultaneous collection of a full spectrum using an array-type detector (e. g., photodiode array or charge-coupled device (CCD)), while a monochromator refers to a single-element detector which is exposed to a limited spectral band width using a slit to spatially restrict the grating-dispersed beam that is incident on the detector (Fig. 25.6). (A spectrophotometer is a term often used to describe a standalone measurement system that also includes a light source to probe the sample and an integrated specimen chamber). The spectral range and feature characteristics (e. g., lineshape, width, intensity) of interest will dictate the specific grating characteristics, detector type, and overall design of the optical system to be used. The observed lineshape for a spectral feature being measured is the result of a convolution between the spectral feature being measured after interaction with the material and an instrument function that describes the spectral performance of the spectrometer. In this context, (25.36) defines the convolution (i. e., the observed lineshape) of the actual spectral feature, f , and that of the instrument function, g. (Linear frequency, , is now used for
b) Mirror
Mirror
Grating
Grating
Exit slit Single detector
Fig. 25.6a,b Schematics of the monochromator (a) and spectrograph (b). The internal optical design Entrance slit
Detector array
depicted is known as a Czerny–Turner arrangement
Part C | 25.2
25.2 Instrumentation The light–matter interactions introduced above dictate the frequency characteristics of the material optical response in a spectroscopy measurement and thus provide a means to examine the structure and structure-based properties of the material. However, accurate analysis and interpretation of the spectroscopic data is necessarily dependent on the instrumentation and methods used to obtain the data and their contribution to the resulting spectrum. The potential for distortion of key spectral feature characteristics (e. g., peak width, frequency position, spectral strength) by the instrument used to make the measurement must be addressed. In this section, we will examine some performance characteristics of conventional spectroscopic instrumentation that play a key role in the representation of material spectral response.
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increased consistency with instrumentation-relevant notation. & is the dummy frequency variable used in the convolution defined Z1 .f g/. / D
f .& /g. & /d& :
(25.36)
1
Part C | 25.2
The impact of convolution is of particular interest in terms of the accurate recovery of the peak (or line) width observed for an optical resonance within the material under study. For example, a perfect spectrometer system would be characterized by a g that is a delta function. Such a system would produce no significant distortion in the incoming spectrum and the output from the spectrometer would be f , the true spectral response of the material. The instrument function can be determined by measurement of a known spectral feature whose linewidth is known to be much narrower than the anticipated instrument spectral resolution (e. g., this could include scattered laser radiation or a gas emission line from a calibration lamp). The resulting spectral width in this case can be assumed to be associated with the instrument. In a measurement context, the linewidth of the material resonance, then, can be recovered (or deconvolved) by first performing a Fourier transform of the measured spectrum .f g/ and the instrument function .g/. Division of the measured spectrum transform by the instrument function transform followed by an inverse Fourier transform of the quotient will return the deconvolved f , the resonance lineshape of the material, free from instrument broadening effects. In glassy materials, and other systems exhibiting inhomogeneously broadened spectral features (e. g., vibrational resonances associated with network or network modifying structures, transition metal ion dopants), the linewidth of the material resonances are often much broader than most instrumental spectral broadening making a transform-based deconvolution unnecessary. However, in some cases (e. g., trivalent lanthanide dopant spectroscopy in which electronic transitions can be more insensitive to local structural environment), care must be taken to insure such an assumption is valid. Without a full analysis of instrument function and the associated convolution assessment, however, insight into the contributions to the measured spectral response from spectrometer performance characteristics can be obtained from the following expression. q dobserved d2intrinsic C d2grating C d2bandpass ; (25.37)
where dobserved D the spectral linewidth (in wavelength); dintrinsic D the actual spectral linewidth produced by the material; dgrating D a linewidth contribution from finite grating dispersion performance; dbandpass D a linewidth contribution associated with the spectral bandpass incident on the detector element. (A similar expression can also be developed in frequency space). The relationship of (25.37) describes contributions to the observed spectral linewidth returned by a spectroscopic system analyzing an input optical beam with an intrinsic linewidth given by dintrinsic . The two primary contributors to the observed spectral width (second two terms on the right-hand side of (25.37)) are associated with different aspects of the spectrometer optical system performance. Their origins are described below. Grating Performance The primary dispersive component of most UV-VisNIR spectrometer systems is the reflection grating. The grating element is an array of periodically varying physical grooves with a metallic coating. Broad-band light is diffracted along different directions according to wavelength, incidence angle, and grating period according to the requirements for constructive interference— Bragg’s law. m D a.sin m sin i / ;
(25.38)
where m D the order of the diffracted beam; i D angle of incidence; a D grating groove separation distance (pitch); m D diffraction angle for order m. Note that m D 0 denotes no wavelength dependence (i. e., specular reflection from the grating surface). Most spectrometers are designed to analyze the m D 1 diffracted order but overlap between adjacent orders can be observed (see additional discussion below). Bragg’s law establishes the relationship between angle and wavelength that provides a means to spatially isolate or disperse the broad-band light to be analyzed according to its wavelength (frequency). In this regard, two measures of grating performance are often used to quantify the dispersing capability of a grating [25.55], i. e., the angular dispersion and the linear dispersion. Angular dispersion (in rad=nm) d 106 mN D ; d cos m
(25.39)
linear dispersion (in nm=mm) d 106 cos m D ; dx mNLB
(25.40)
where N D the groove density (grooves/unit length normal to groove orientation); LB D spectrometer length.
Optical Spectroscopy of Glass
a)
length of the spectral segment entering the slit changes with the incident and diffracted angles (Bragg condition). The intensity of light leaving the slit is plotted versus the center wavelength to produce the measured spectrum. If we again consider the accurate reproduction of an input spectral feature, the frequency convolution of the target resonance peak (e. g., an absorption peak) with the spectral bandpass function (resulting from the grating linear dispersion and slit width) will be returned by the spectrometer system. The convolution can produce distortions in the measured spectral characteristics. The approximation of (25.37) provides an estimate of the contribution to measured linewidth due to spectrometer bandpass .bandpass/. While the Bragg condition defines conditions leading to constructive interference and a maximum in an observed diffracted beam, a full analysis of multiple beam interference in the far-field (Fraunhofer diffraction) is required to anticipate the variation in diffracted beam intensity with incidence/diffracted angle conditions when angular conditions are near but not identical to the Bragg conditions for a given wavelength. This treatment [25.1], shows that the number of grooves (i. e., scattered beams) combining to produce the observed diffracted beam contributes directly to the development of destructive interference at off-Bragg angle conditions. More participating beams produce a greater reduction in intensity at off-Bragg conditions due to the addition of incremental destructive phase shifts. The result can be illustrated in Fig. 25.7 where the phase width b)
I/I0 25 V=5
I/I0
400
V = 20
20 300 15 200 10 100
5 0
0 –2π
0
2π δ = 2π (d/λ) sinθ
–2π
0
2π δ = 2π (d/λ) sinθ
Fig. 25.7a,b Relative diffracted intensity (I=I0 , where I0 is the incident beam intensity) of a monochromatic beam from a grating. The phase shift in scattered light from adjacent grooves of the grating is dependent upon the angle of observation ./ for a given groove separation .d/ and light wavelength ./. As anticipated, diffraction maxima are observed when the phase shift is ˙2m (where m is an integer, defined as the order of the diffracted maximum). The effect of the number of illuminated grooves, V, on the widths of the diffraction maxima is shown. (a) V D 5; (b) V D 20
893
Part C | 25.2
In these expressions, the primary grating design parameter is the groove density (number of grooves/unit length across the grating). From (25.39), it is clear that a higher groove density will provide increased angular separation of adjacent spectral bands. At a given distance from the grating .LB /, this will also result in a greater linear separation between adjacent spectral bands, or an increased linear dispersion (smaller wavelength band within a given unit length at the spectrometer exit port (25.40)). In terms of spectrometer design, then, increased spectral dispersion of incoming broad-band light can be anticipated for higher groovedensity gratings and longer lengths between the grating and the detector element or array (Fig. 25.6). The linear dispersion of the grating coupled with the slit/detection system characteristics dictate the spectral bandpass for the spectrograph or monochromator. In the case of a monochromator, for example, the spectral bandpass incident on the detector is dependent upon the slit widths used. While to first order, we can consider the linear dispersion multiplied by the slit width .x/ to be the spectral bandpass incident on the detector, i. e., bandpass D d=dx x, a more thorough analysis of the spectrometer as an imaging system shows that it is the spatial convolution of the entrance and exit slit widths that should be multiplied by the linear dispersion to provide a measure of spectral bandpass [25.55]. As the grating incidence angle is scanned (via grating rotation) in a monochromator, the dispersed spectrum is moved across the exit slit. The center wave-
25.2 Instrumentation
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(associated with spectral width) in a given monochromatic diffracted order is observed to decrease with an increased number of grooves illuminated by the incident beam. It can be shown that the angular width of the monochromatic diffracted beam is given by
Part C | 25.2
D
2 ; Va cos m
(25.41)
where V D number of illuminated grooves on the grating. The product, Va, in the denominator of (25.41) is just the physical width of the grating (if the grating is fully illuminated). In this case, (and the corresponding grating linewidth) will be decreased as the number of grooves illuminated is increased, usually accomplished by increasing the groove density for a given illuminated area. grating is thus the other contribution to measured linewidth as described in (25.37). With a typical grating-based spectrometer system, the bandpass associated with grating linear dispersion and slit width is larger than that associated with the diffracted linewidth, thus making the selection of grating groove density, spectrometer length and slit settings of primary concern in establishing minimum spectrometer performance criteria for a given measurement. Instrumental concerns regarding the inherent distortion of an isolated lineshape also impact the ability to resolve or differentiate adjacent spectral lines within a spectrum. In the context of grating performance, two additional metrics provide some insight into this issue. The resolving power of a grating [25.1] describes its ability to separate or distinguish two adjacent spectral features. Multiple criteria can be used to define what separate means. In terms of the Rayleigh criterion [25.1], two features are resolved when the diffracted peak position of the first corresponds to the first minimum of the diffracted peak for the second. Under these conditions, resolving power, R, in terms of the minimum resolvable wavelength difference, min is defined as RD
Va.sin m sin i / : (25.42) D mV D min
Of additional interest in terms of spectral measurement free from interference from other spectral features is the grating free spectral range fsr D : m
(25.43)
The free spectral range is defined as the maximum wavelength range available within a given diffracted
order that is free from diffracted beams arising from an adjacent order. For example, it is possible for the second diffracted order .m D 2/ for D 300 nm to be at the same angular position .m / as the first-order diffracted beam for D 600 nm, i. e., mD1 . D 600 nm/ D mD2 . D 300 nm/. In measurements of strong photoluminescence peaks, for example, this can be a significant source of incorrect analysis. Moreover, when a monochromator is used to select a wavelength from a broad-band source (e. g., typical for commercial UV-Vis-NIR spectrophotometer systems) order-sorting (long wavelength pass) filters are used to preferentially block the higher order diffracted beams (shorter wavelengths). A comparison of instrumentation factors contributing to resolving power and to free spectral range show that independent optimization of these metrics is not possible, thus illustrating at least one point of compromise associated with the selection or design of spectrometer systems. Finally, another grating parameter associated with performance in the context of spectroscopic measurement is the grating blaze—a measure of the spectral range associated with the highest diffraction efficiency. Taking a physical relief reflection grating as an example, in a flat-profile grating surface, most of the incident intensity is directed into the n D 0 (i. e., specular reflection) order, thus limiting the resulting intensity available for the higher order diffracted beams that will provide spectral dispersion. By modifying the surface profile of the grating grooves, the surface normal of the profile (corresponding to reflection) can be shifted relative to the grating normal (i. e., normal to the grating wavevector defining the direction of the grating periodicity) to move more of the incident intensity along an angle range consistent with the n D 1 diffracted order. The blaze angle corresponds to the difference between the grating and surface normal as defined in (25.44) and shown in Fig. 25.8 blaze D
˛ ˇ : 2
(25.44)
Gratings are specified in terms of a center wavelength corresponding to the spectral range of enhanced diffraction efficiency and should be selected based on the anticipated spectral range to be examined. Housing Design Although a complete discussion of the spectrometer optical design is beyond the scope of the present work, a common design used in commercial instruments is the Czerny–Turner arrangement (Fig. 25.6). Given the above description of key factors influencing grating
Optical Spectroscopy of Glass
Groove surface normal α
θblaze β
Grating normal
performance, it should be evident that the use of appropriate mirror elements and their arrangement is necessary to insure, for example, collimated light incident onto the grating and efficient collection of diffracted light to the detector element. This should be accomplished with a minimum of off-axis light entering the system or extraneous scattered (and hence undispersed) light escaping to the detector (stray light rejection). We have seen that spectrometer length directly impacts the linear dispersion of the system. Longer spectrometers typically also have more effective stray light rejection. Commercial systems provide a fixed optical system for the spectrometer with the potential to change gratings using a rotating turret. Optimized alignment of external optics to collect light from the specimen and to provide it to the spectrometer requires that the etendue, or optical throughput, of the external collection and internal (spectrometer) optical systems be matched. The reader is referred to [25.55] for more detailed discussion. Detector After spectral dispersion of the incoming light, the intensity of the spectral band exiting the spectrometer is measured by the detector. A collection of characteristics is used to define detector performance. These include spectral response, quantum efficiency, linearity, dynamic range, and noise. For a full analysis, the reader is referred to [25.56]. In measurements focusing on time-dependent signal characteristics, the response time of the detector is also of significance. Low-intensity applications may require detectors providing low noise levels (low noise equivalent power (NEP)). For UVVis-NIR applications (addressing electronic and some vibrational processes), typical photodetectors include solid-state options (photoconductive devices and photodiodes including Si, Ge, and InGaAs) as well as
nonsolid-state detectors (photoemissive devices, including photomultiplier tubes with varied photocathode materials). Mid- to far-infrared applications (vibrational spectroscopy) typically employ mercury cadmium telluride (MCT) photoconductive detectors or a deuterated triglycine sulfate (DTGS) pyroelectric bolometer-type detector. As mentioned above, two primary formats for detector integration within the spectrometer system are common. The monochromator involves a single element with a slit to define the bandpass incident on the detector, a spectrum is collected by scanning the grating incidence angle and recording the resulting light intensity as a function of grating position (wavelength). In contrast, a one- or two-dimensional (2-D) array of solid-state detector elements or pixels (e. g., Si photodiodes, Si charge-coupled devices (CCD)) can also be used. In this case, no slit is required, the grating is static, and the entire spectrum is collected simultaneously (Fig. 25.6). The spectrum is thus discretized according to the pixel array characteristics. Under these conditions, the linear dispersion at the plane of the detector array, in conjunction with the pixel spacing (pitch) and the pixel width, determines the effective bandpass that is incident on each pixel and the spectral density of data obtained. The spectral window of observation is thus also related to the total width of the detector array. The appearance of the measured spectrum is related to the pixel size and pixel linear density; this dictates the number of pixels available to define a given spectral feature.
25.2.2 The Interferometer In contrast to grating-based spectral dispersion, frequency analysis in infrared-based spectroscopy is often performed using interferometric methods. In Fourier transform infrared spectroscopy (FTIR), broad-band infrared light is passed through a scanning Michelson interferometer in which the length of one of the legs of the interferometer is periodically varied. The light intensity is recorded with interferometer mirror travel after it is transmitted or reflected from the specimen (Fig. 25.9). Different mirror positions change the relative optical path length and an associated phase difference between the beams traveling along each interferometer leg. The intensity of the resulting recombined beam with mirror position, the interferogram, thus reflects the spectral make-up of the broad-band light. A Fourier transform of the interferogram can be used to recover the spectrum (Fig. 25.10). Similar to our description of diffraction grating behavior, the spectral performance of an FTIR spec-
895
Part C | 25.2
Fig. 25.8 Schematic of a physical relief grating structure defining the grating blaze angle, blaze
25.2 Instrumentation
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Characterization of Glasses
Fig. 25.9
Schematic optical diagram for FTIR spectrophotometer system. The Michelson interferometer is shown in the upper right of the figure, adjacent to the source assembly
Beamsplitter
Interferometer
Part C | 25.2
Source assembly Sample compartment
Detector
Reference or sample cell holders
External beam
Collimated beam for visual alignment
a) Intensity
b) Intensity 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Optical path difference
0.0
1000
2000
3000
4000
5000 6000 Frequency (cm –1)
Fig. 25.10a,b Representative interferogram (a) and resulting spectrum (b) obtained using an FTIR system
trometer can also be described based on contributions to multiple beam constructive and destructive interference associated with spectrometer design. Moreover, arising from issues unique to the Fourier transform nature of the measurement, the finite mirror travel during the scan naturally limits the frequency space being sampled, thus also limiting the frequency components that can contribute to the transform-limited spectral width of a given feature. The longer the mirror travel, the narrower the corresponding instrument function that would be convolved with the spectral response being measured.
Finally, there are also limitations in spectral resolution associated with the discretized nature of the interferogram itself. In this case, the sampling frequency of the intensity output from the scanning interferometer will produce a frequency-pass limitation that can impact the observed lineshape upon transformation. However, Michelson interferometer-based FTIR systems offer advantages over grating spectrometers, including: 1. A significant signal-to-noise (S=N) ratio since all spectral components of the beam are incident on
Optical Spectroscopy of Glass
The lower vibrational energies associated with acoustic phonon modes probed by Brillouin scattering make separation of the Rayleigh scattered light from the inelastic scattering peaks impractical using standard grating-based dispersion approaches. In this case, another interferometer geometry called the Fabry–Pérot (FP), is used (Fig. 25.11). The round-trip phase shift of light reflecting from mirror surfaces within the FP cavity define conditions of constructive interference for light of a specific wavelength [25.1]. Spectral scanning in an FP is accomplished by scanning the FP mirror gap via a piezoelectric transducer thus sampling a range of cumulative phase shifts for a given wavelength in a similar manner to the Michelson system above. It can be shown that the interference-limited spectral band pass, min , is given by min D
2 p ; Fd
(25.45)
where d D the mirror gap for the Fabry–Pérot and F, given by FD
is the finesse coefficient and R is the mirror reflectance [25.1]. The finesse coefficient scales with the reflectivity of the mirrors and thus influences the number of reflected beams surviving within the cavity that are available to contribute to destructive interference when the mirror position is displaced from a constructive interference condition. Figure 25.12 shows how the transmission of a FP varies with accumulated phase shift for monochromatic light propagating within the cavity (proportional to mirror separation). The width of the resonances decreases with increasing mirror reflectance. Also in Fig. 25.12, it can be seen that the interferometer will exhibit multiple orders of constructive interference corresponding to phase differences at intervals of 2 , thus defining an effective free spectral range .fsr / analogous to that described above in the context of grating performance. The ratio of the free spectral range to the spectral bandpass for the FP describes the finesse for the cavity. For R > 0:5, the finesse can be approximated in terms of the finesse coefficient p fsr F : ID min 2
(25.47)
The high finesse values of typical FP interferometers used for Brillouin, coupled with the development of tandem FP systems, provide the required light rejection and the suppression of adjacent interfering orders necessary for Brillouin measurements [25.47, 58]. The design of a temperature-dependent Brillouin set-up can also be found in [25.59]. It (normalized)
4R ; .1 R/2
(25.46) 1.0
R = 0.2 R = 0.4 R = 0.6 R = 0.8
d I0 θ
0.5 It
Fig. 25.11 Schematic of a Fabry–Pérot interferometer con-
structed from two semitransparent mirrors to form an optical cavity. The interferometer is typically used under normal incidence conditions . D 0/. In the schematic, d D mirror separation distance or gap, I0 D incident light intensity, It D transmitted light intensity
0.0 0
2π
4π Accumulated phase shift
Fig. 25.12 Transmission for monochromatic light within a Fabry–Pérot cavity as a function of accumulated phase shift and with varied mirror reflectance
897
Part C | 25.2
the detector simultaneously (the multiplex or Fellgett advantage [25.57]) 2. A single detector with no slit resulting in higher optical throughput (the throughput or Jacquinot advantage [25.57]) 3. Precise wavelength calibration provided by an embedded monochromatic laser source whose intensity after passing through the interferometer is used to calibrate mirror position and interferogram sampling.
25.2 Instrumentation
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25.2.3 Spectrophotometers
Part C | 25.2
The term spectrophotometer is typically associated with a complete spectroscopic measurement system that integrates an optical source, specimen compartment, spectral dispersion and detection. Ultraviolet-visiblenear infrared (UV-Vis-NIR) spectrophotometers can perform transmission and reflection-type measurements over a typical wavelength range from 190 nm to 3:2 m. Computer control of multiple lamps (halogen, deuterium), order-sorting optics, multiple gratings (varied blaze, groove density), and detectors (e. g., photomultiplier tube (PMT) and lead-sulfide (PbS)) is used to achieve an automated broad-band spectrum measurement. A double-beam spectrophotometer is shown in Fig. 25.13. Here, the source output is split to provide two beam lines, a reference beam (measuring I0 ) and a specimen beam (measuring I). The optical chopper allows alternating measurement of these beam intensities with wavelength at the detector. The ratio of these intensities enables the determination of transmission coefficient (25.48). This approach allows the simultaneous removal of contributions to the observed intensity from the spectral responses of the source, detector, grating, and other optical elements in the system, leaving only the transmission (or reflection) response associated with the specimen. A similar effect can be obtained by performing two sequential, single-beam measurements (one with and one without the specimen). However, this approach does not also allow the removal of time-dependent changes in source output or detector drift. This sequential, single-beam method is routinely used in interferometer-based FTIR and Brillouin measurements. Note that spectral separation via a monochromator is often achieved before the specimen in these instruments. Spectrofluorimeters used for photoluminescence
Monochromator
Optical chopper
measurement are also based on similar source and detector types with an additional monochromator stage after the specimen to allow spectral analysis of the luminescence. In the case of FTIR, the detector must be sensitive to the mid- to long-infrared range (Sect. 25.3.1, Thermal Reduction–Raman). Moreover, an optical source capable of delivering these photon energies is also required. The typical source used in commercial FTIR instruments is the glo-bar, a resistively heated filament whose emitted black-body radiation provides the incident beam for the measurement.
25.2.4 General Measurement Concerns The above discussion has provided an introduction to the operational theory and primary components involved in the spectroscopic assessment of materials. Effective implementation of these components, however, is needed to insure as accurate a measurement (and associated interpretation) as possible. In this regard, several spectroscopic measurements, differentiated in terms of the optical phenomena being probed, will be examined. Absorption and Reflection Optical absorption, corresponding to optically allowed transitions between stationary states, can be obtained from a transmission measurement in which the intensity of an incident optical beam is measured after traversing a specimen to obtain the transmittance .T/ It TD ; (25.48) I0 and absorbance .A/, or optical density, which is defined as 1 : A D log10 (25.49) T
Sample
Source White light
Sample beam Analytical wavelength
Detector
Reference beam Reference (blank)
Wavelength
Display
A or % T
Phase-sensitive amplifier
Fig. 25.13 Functional block diagram of a double-beam spectrophotometer system (A D absorbance and %T D percent transmission)
Optical Spectroscopy of Glass
In the absence of competing contributions (e. g., reflection, scattering) to intensity loss as a beam traverses the specimen of thickness, d, in a transmission measurement, the observed transmitted intensity can be described in terms of an exponential involving the absorption coefficient, ˛ (25.50)
Combining (25.49) and (25.50), a relationship between absorbance and absorption coefficient can be obtained (again, assuming no other contribution to the intensity loss in the specimen) AD
˛d : 2:303
(25.51)
Finally, as mentioned earlier, a connection back to the imaginary portion of the complex refractive index, i. e., the extinction coefficient, , can be made ˛D
4
:
(25.52)
On the basis of the above set of equations, the extinction coefficient function (imaginary portion of the complex refractive index) can be directly extracted from a transmission spectrum. In practice, however, this can be difficult. It is important to remember that the transmission measurement is an extrinsic measure of sample optical throughput and that any process that can reduce the measured intensity of light arriving at the detector can contribute to the transmission value, e. g., scattering, reflection, diffraction, refraction etc. Thus, care must be taken even in this relatively straightforward measurement as these effects can produce distortions in the underlying absorption coefficient dispersion involving both the determination of resonance frequency (e. g., absorption peak position) and strength (absorption peak height). Reflection measurements, typically associated with highly absorbing or scattering specimens involve a similar monochromator and source arrangement with suitable modifications made to select an incident angle and polarization conditions and to insure collection of the reflected light. In a specular reflection measurement, the intensity of the reflected beam is compared to that of the incident beam and the resulting reflectance, R D Iref =I0 , can be related to the intrinsic, complex refractive index as described in (25.16). In light of (25.16), a direct relationship between R and either n or k is not possible, requiring the use of such tools as dispersion or Kramers–Kronig analyses to extract the underlying contributions to the reflectivity from the individual components of the material dielectric function. In this regard, the use of reflectivity
peak position to directly identify the transition energy of a corresponding transition is not possible, as significant changes in reflectivity peak frequency can be associated with minor changes in absorption peak width or height, for example. In a related concern, the measurement of thinfilm specimens in transmission present some interesting challenges and opportunities. Despite the short coherence length typical of incoherent, broad-band light sources typically used in UV-Vis-NIR transmission measurements, thin-film glass and ceramic specimens (100s of nanometers to micrometers in thickness) can be sufficiently optically thin to observe interference behavior in the transmitted (or reflected) spectrum associated with partial transmission and reflection at the air–film and film–substrate interfaces. Figure 25.14 shows the measurement geometry. If the analysis is restricted to normal incidence, then the amplitude coefficients at the air–film interface (labeled 0 in Fig. 25.14) and the film–air interface (labeled 1 in Fig. 25.14) are independent of polarization and given by .n1 D 1/ nf 1 I nf C 1 2 t0 D I nf C 1 r0 D
n2 nf ; n2 C nf 2nf t1 D ; nf C n2 r1 D
(25.53)
n2 nf n1 I0
d Ai
Ait0t1eiδ/2 Ait0t1t0t1ei3δ/2 Ait0t1r02r12ei5δ/2
0
1
Fig. 25.14 Thin-film measurement geometry and contributions to multibeam interference at wavelength D . ı D round-trip accumulated optical phase shift within the film of thickness, d, and complex refractive index D n C i . Ai D the incident beam amplitude
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Part C | 25.2
I D exp.˛d/ : I0
25.2 Instrumentation
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Characterization of Glasses
where nf D film index, n2 D substrate index, and the index for air D 1:0. The transmitted intensity coefficient (transmittance) can then be determined in terms of the complex refractive index characteristics of the film (the substrate is assumed to have D 0 in this treatment)
Part C | 25.2
TD T./ D
At A t ; Ai A i t02 t12 eb ; 1 2r0 r1 .cos a/eb C r02 r12 e2b
(25.54)
where 4 f d 4 nf d Ci ; 0 0 ı D a C ib :
ıD
(25.55)
Thus, a and b are the real and imaginary components of the accumulated phase shift, respectively, as defined in (25.55). Under general incidence angle conditions, a Fresnel equation analysis can be used to derive the anticipated transmission coefficient [25.1] under arbitrary incidence angle and polarization conditions with amplitude coefficients developed for p- and s-type incident polarization. The transmittance in (25.54) is often termed the Airy function for the asymmetry cavity. This general treatment is also used to describe the Fabry–Pérot interferometer resonance behavior discussed in Sect. 25.2.2. The dispersion behavior of the real and imaginary components of the film complex refractive index (i. e.,
nf ./ and f ./) implies that the transmission behavior will be strongly wavelength-dependent, particularly near optical resonances. This is, of course, the underlying motivation for the transmission measurement in the first place, i. e., the isolation of absorption resonances associated with the extinction coefficient of the material. Under conditions favoring multibeam interference, however, the added influence of the real portion of the refractive index is now important. The effect is typically observed as oscillations or Fabry–Pérot fringes within the spectra collected with the contrast of the fringes (i. e., the peak to valley depth) and periodicity dependent upon film thickness and index mismatch with the substrate. The common approach adopted by many UVVis-NIR instrument manufacturers to plot spectra with wavelength, results in a wavelength-dependent variation in fringe periodicity. Figure 25.15 shows a representative thin-film optical absorbance spectrum in which FP fringes can be readily observed. As shown in Fig. 25.15, Fabry–Pérot fringes are typically observed overlaid on the spectral resonances of interest in the data. It is often difficult to isolate the material absorption spectrum from the fringes given that both incorporate the same material extinction coefficient dispersion function. However, iterative fitting using the Airy function above and the anticipated n and dispersion for the material can be effective in extracting the material optical constants [25.60]. Conversely, the fringe spacing and contrast, as mentioned above, can be used to develop insight into the dispersion in the material complex refractive index components. A commonly used method, based on the collection of
A 0.25
0.20
0.15
0.10
0.05
200
300
400
500
600 λ (nm)
Fig. 25.15 Representative thin-film absorbance spectrum showing the effects of FP interference. The light brown line models the underlying FP effect of a nonabsorbing film with the same refractive index and thickness as the sample
Optical Spectroscopy of Glass
Photoluminescence and Inelastic Scattering In an absorption or reflection measurement, we are concerned with an examination of light at the excitation frequency (wavelength) after its interaction with the material. In contrast, luminescence or inelastic scattering measurements analyze frequency-shifted light that is emitted from the specimen after excitation. In photoluminescence, optical absorption results in a redistribution of occupied electronic states with both radiative and nonradiative processes contributing to the relaxation of the material back to the ground state. The observed optical emission spectrum corresponds to radiative relaxation processes. As previously discussed, inelastic scattering is associated with incident photon interaction with vibrational modes in the material, resulting in scattered radiation at frequencies shifted from the excitation according to the phonon energies involved. In the case of photoluminescence spectroscopy, the incident light is assumed to be resonant with an absorption transition within the allowed energy structure of the material. Such excitation involves a tuned laser or monochromator/broad-band lamp source. The luminescence is then analyzed using a spectrometer or monochromator arrangement. As mentioned earlier, commercial spectrofluorimeters utilize two monochromators, one for excitation wavelength selection and one for emission analysis. If the analyzing spectrometer is held at a specific emission peak wavelength and a pulsed optical excitation is used in conjunction with appropriate transient detection instrumentation and methods [25.5], the time dependent decay of emission associated with a particular transition event can be monitored. Such timedependent emission measurements provide insight not only into the nature of the transitions involved but also offer a complementary view of competing, nonradiative
901
processes leading to the observed upper state depopulation rate (Sect. 25.1.2, Optical Transitions–Resonant Excitation). Aobs D Arad C WNR C Wtransfer D
1 ; obs
(25.56)
where Arad D radiative (spontaneous) relaxation rate, WNR D nonradiative relaxation rate, Wtransfer D energy transfer rate to another luminescent center or defect state. The low scattering efficiencies associated with Raman and Brillouin require the use of high-intensity laser sources (typically in the visible) to achieve significant scattered light intensity. In addition to the need for a Fabry–Pérot interferometry to isolate nearfundamental (excitation) frequency, inelastically scattered light (Sect. 25.2.2), the low-energy shift associated with acoustic phonon scattering in Brillouin spectroscopy typically requires a single-longitudinal-mode laser excitation to limit the corresponding breadth of the Rayleigh line. In multimode gas lasers (e. g., Ar-ion), selection of a single longitudinal optical (LO) mode can be accomplished using an intracavity etalon. In grating-based technique measurements, i. e., Raman and photoluminescence spectroscopies, the removal of incident excitation frequencies (present via Rayleigh scattering) is also required to insure the effective measurement and analysis of spectral response (either Stokes/anti-Stokes Raman or luminescence peaks). For example, a typical Raman shift (corresponding to the vibrational transition energy) is on the order of 1501400 cm1 . With a commonly used 514:5 nm excitation line this corresponds to a separation between the excitation light and the scattered spectrum of only 4 nm (corresponding to a vibrational mode frequency of 150 cm1 ). Combined with a Raman scattering intensity that is typically 34 orders of magnitude weaker than the excitation light, the need to remove unwanted elastically scattered excitation (or fundamental) intensity is paramount. Excitation light rejection from the detector must be optimized in this case. Because of the inherent limitations of grating groove density, grating size and spectrometer length (contributing to linear dispersion and diffraction limited linewidth) as well as the potential for inadvertent, off-axis light introduction into the spectrometer, increased light rejection is often achieved using grating-based prefilters, holographic notch (narrow band rejection) filters, and/or by the use of long or multiple stage (double or triple) spectrometer systems. As mentioned earlier, there is also the potential for intrinsic radiative emission processes (associated with resonant excitation of electronic states in the material) to occlude the low intensity of the Raman scattered light. With typical Raman excitation occurring in the
Part C | 25.2
multiple transmission measurements at different incidence angles, can be used as a means to extract this information [25.61]. Rough surfaces and composite materials (e. g., glass-ceramics) containing inclusions with varied refractive index, with length scales commensurate or larger than the incident wavelength, exhibit increased diffuse scattering. Here, portions of the incident light intensity propagate in different directions requiring the use of integrating sphere detection to capture this offaxis light. In this case, depending upon the relative size scale and shape of the scattering centers involved, the scattering intensity, frequency, and angular dependence can be used to recover the dielectric (refractive index) functions of the material using Mie scattering theory or direct analysis of Maxwell’s equations.
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visible, the potential to be resonant with such states is likely. Despite an anticipated reduction in Raman scattering intensity (25.30), the excitation frequency used in a Raman measurement can often be reduced so as to minimize resonant excitation of the material and to remove unwanted luminescence contributions to the measured spectrum.
Part C | 25.3
Photoluminescence Excitation Spectroscopy (PLE) A related approach to examine resonant excitation and decay processes is through the use of photoluminescence excitation spectroscopy (PLE). The technique involves monitoring a single emission band while scanning the excitation frequency. The intensity of the emission is plotted as a function of the excitation wavelength or frequency. The commercial spectrofluorimeter described above can be used to readily collect these data.
In this case, only absorption processes that decay through relaxation paths resulting in emission within the monitored spectral band are recorded. Multiple measurements made at different emission spectral bands can be used to extract information useful in mapping key excitation and relaxation pathways within the allowed energy states of the material. The technique is useful in establishing energy transfer characteristics between luminescent dopants in glass, for example. When the excitation process involves a phonon-assisted transition to the upper stationary electronic state of a luminescent center, the resulting phonon-sideband (PSB) spectrum provides insight into the phonon modes that are directly coupled to the electronic state, a subset of the more generalized phonon spectrum obtained via Raman or FTIR. The technique finds significant use in establishing local environments surrounding rare-earth ions in glass [25.62–65].
25.3 Spectral Analysis and Interpretation An accurate assessment of spectroscopic data relies on an appreciation for the underlying physical processes contributing to the material optical response as well as the limitations imposed by the measurement apparatus and methodologies used in the collection of these spectra. The above sections have provided a brief description of some key issues contributing to both these general areas. Under optimal conditions, even a spectrum that is free from distortions associated with instrumental limitations or interfering physical phenomena will present challenges in interpretation. In this section, we take up some remaining concerns that impact both the initial processing of spectral data and its reduction and interpretation.
25.3.1 Preprocessing Before more elaborate methods are used to extract metrics associated with resonance features in optical spectra (e. g., peak height, width, position etc.), it is often necessary to remove contributions to the collected data that are not associated with the targeted spectral characteristics of the material under investigation. As described earlier, there are multiple contributors to spectral background associated with different measurements that result in either broad-band (limited frequency-dependent) effects or strongly frequencydependent phenomena that are associated with known physical behavior of the material specimen or artifacts of the measurement itself.
Effective use of experimental methodology and instrumentation are important to provide the clearest spectrum possible before any subsequent processing of the data is pursued. For example, different detector noise contributions can adversely affect the signal-tonoise ratio observed in a spectrum (see earlier discussion and [25.56]). Effective detector selection and design of support electronics can significantly reduce such noise sources. In addition, as mentioned earlier, Rayleigh scattering of the excitation beam in a Raman or photoluminescence measurement can detrimentally affect the observation of nearby Raman scattering or radiative relaxation. Design of a spectroscopic system with high scattered light rejection (long length, high groove density, prefiltering (Sect. 25.2.4, Photoluminescence and Inelastic Scattering) can help to eliminate this effect. Addressing the presence of Fabry–Pérot interference in thin-film specimens through sample design can moderate this frequency-dependent effect (Sect. 25.2.4, Absorption and Reflection). Finally, the use of single beam, reference measurements or doublebeam instrumentation can effectively remove significant (and often wavelength-dependent) contributions to the observed spectrum from the optical elements, grating components, and detectors used in the measurement (Sect. 25.2.4, Absorption and Reflection). Despite good methodology and instrumentation, however, complete removal of background signal from a raw spectrum is typically not possible. An exhaustive listing of contributing phenomena and approaches
Optical Spectroscopy of Glass
Subtraction In many cases, raw spectral data exhibits material resonances (e. g., absorption or emission peaks) that are superimposed on a flat or minimally inclined baseline signal. When such a frequency or wavelength-independent (or nearly independent) contribution is observed in the spectrum, it often can be removed by modeling it as either a linear or weakly nonlinear (polynomial) function of wavelength and subtracting it from the raw data. Such backgrounds are often associated with incoherent scattering effects within the material, detector noise contribution, or broad-band reflection at the specimen surface. In some cases, a weak tail extending into the observation window from the laser excitation line in a Raman or photoluminescence spectrum can be removed in this way. A functional form for the background consistent with the anticipated Lorentzian nature of the excitation laser can be used if deemed necessary. The approach can also be applied to remove broad luminescence tails extending into the frequency range of interest for Raman. Smoothing Noise associated with detection electronics is typically observed in raw spectra. All detectors exhibit a minimum output current even in the absence of photon flux due to thermally activated carriers. Detector noise signal is dependent upon such conditions as detector temperature (Johnson) noise and incident intensity and gain (generation-recombination (G–R) noise) [25.56]. Noise in the spectrum is often exhibited as a highfrequency fluctuation in intensity superimposed on the spectral resonance of interest. Intensity variation associated with noise is often at a much higher frequency than that characteristic of the signal associated with the spectral feature. The noise amplitude is also smaller than the targeted spectral resonances under conditions
of high signal-to-noise ratio. In this case, selective removal of this noise component can be accomplished via smoothing or filtering of the data set. A moving average (MA) smoothing approach typically involves a linear fit to a restricted multipoint (often 3-point) data window that is moved along the data set. Each datapoint is then replaced by the average of itself and its adjacent datapoints. This can be extended to use polynomial fitting within the moving window. Savitzky–Golay filtering or smoothing reduces the computational overhead of the conventional application of a polynomial moving average approach [25.66] and is often found in most data processing and manipulation software packages. An increase in the number of points in the data window used will have an increased effect on lower frequency noise components of the raw spectrum. Hence, care must be taken to avoid significant distortion of the underlying spectral features of interest when pursuing a smoothing operation on narrow spectral features. In some measurements, e. g., time-dependent luminescence decay, electrical line interference signal components, or other noise signal components with known frequency and bandwidth can be removed using Fourier transform-based filtering. Here, the noise frequency band can be selectively suppressed by zeroing the corresponding Fourier components of the signal. An inverse transform is then used to recover the filtered signal. Thermal Reduction–Raman Given the widespread use of Raman spectroscopy for the investigation of the structure of amorphous materials, particularly over varied specimen temperatures, it is appropriate to mention another preprocessing approach associated with this measurement. As described in Sect. 25.1.2, Inelastic Scattering, in addition to contributions from excitation frequency and the transition moment associated with the vibrational mode under investigation, Raman scattering intensity is also dependent upon the thermally equilibrated phonon population. To account for this contribution, the phonon population factor (based on the Boltzmann distribution) can be used to correct the Raman spectrum for this effect [25.67]. The thermally corrected Raman intensity can be approximated via (25.57). The effect on the spectrum is most pronounced for lower vibrational frequencies. h Icorr D Iobs 1 exp ; kB T
(25.57)
where Icorr D thermally corrected intensity, Iobs D observed intensity, D frequency, T D temperature, and kB D Boltzmann constant.
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for preprocessing and manipulation of data is outside the scope of the present work but more complete discussions are available [25.66]. Several spectrum processing concerns that are often used in electronic and vibrational spectroscopic measurement and analysis are addressed below. It is very important to recognize the inherent potential to inadvertently distort key spectroscopic characteristics while using such data processing approaches. Care should be exercised whenever such methods are adopted to employ them consistently and only when appropriate. It should be obvious that success will be greatly enhanced when spectra exhibiting high signal-to-noise (S=N) characteristics are available. Enhancement of spectra exhibiting low S=N using such techniques, while attractive as a means to promote increased interpretation options, is typically ill-advised.
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25.3.2 Deconvolution, Derivatives, and Curve Fitting
Part C | 25.3
Appropriate preprocessing is intended to provide a spectral data set that will serve as a focus for subsequent analysis and interpretation. Spectral features corresponding to different vibrational or electronic transitions, however, often overlap, obscuring a clear examination of the spectral characteristics of interest. Given the tendency for significant inhomogeneous broadening in glasses, the potential for spectral overlap is that much more at issue. The concepts associated with the convolution of either frequency-, time- or spatially dependent response characteristics of measurement apparatus have been discussed previously (Sect. 25.2.1, (25.32)). Deconvolution, by dividing the Fourier transform of the measured spectrum or time-dependent data set, by that of the instrument response and performing the inverse transform of that quotient, can be accomplished. In a glass, the broadening effects associated with a typical grating-based spectrometer is often small compared with other contributions to spectral broadening associated with, for example, thermal effects (phononmediated transitions, broadening) and inhomogeneous broadening due to site-to-site variations in structure. In this case, a means of assessing the dominant contributions to a spectral envelope anticipated to contain multiple resonances associated with different transitions is needed. One straightforward method to gain some initial insight is the use of derivatives. Often used to improve the resolution of electron spin resonance (ESR) spectroscopy, derivatives of overlapping resonance peaks can often provide useful information regarding the likely number of peaks present and their approximate positions [25.66]. Through the examination of zero crossings and maxima and minima in first, second, and higher order derivative spectra, peak positions and relative widths can be estimated. Figure 25.16 illustrates the utility of derivative techniques in defining the presence and characteristics of peak components in a spectrum. In this case, a spectrum synthesized from three overlapping Lorentzian peaks is shown (top curve) with successive first- and second-order derivative spectra provided below (D1 D first derivative, D2 D second derivative). The center positions of each of the Lorentzian peaks are indicated by the vertical dashed lines. The anticipated zero crossings in the D1 spectrum and minima in the D2 spectrum associated with the dominant peaks in the original spectrum (at 4:7 and 5:0) can be clearly observed. While the third Lorentzian (centered at 5:1) appears only as a subtle high-frequency shoulder on the main central peak (centered at 5:0), its presence is confirmed in the derivative
D1
0
D2
0
4.4
4.6
4.8
5.0
5.2
5.4
Fig. 25.16 A synthesized spectrum (top curve) composed
of three Lorentzian peaks with varied height and width centered at 4:7, 5:0, and 5:1. Peak centers are indicated with vertical dashed lines. First and second derivatives of the original spectrum are located below. D1–first derivative, D2–second derivative
spectra. Here, the additional, weaker peak produces deviations in the derivative spectral functions from that anticipated from a single, symmetric resonance peak. Thus, derivative results can provide insight into the number of resonance peaks contributing to the spectral envelope, informing the development of a fitting function that would describe the collection of lines present in the overall spectrum. This curve-fitting technique is ubiquitous in x-ray photoelectron spectroscopy (XPS) analysis and vibrational analysis and requires some knowledge of the form of the underlying peak functions describing the resonances. In most cases involving glass and other disordered systems, where significant inhomogeneous broadening is anticipated, a Gaussian lineshape function is typically employed. For each
Optical Spectroscopy of Glass
25.3.3 Chemometric Analysis In some cases, manual analysis via visual assessment of primary spectral peaks or the use of derivatives or curve-fitting approaches are insufficient due to the degree of spectral complexity, lack of clearly defined features in the measured data set, or limited access to corroborating data for related specimens that could be used to aid in analysis. In this case, the use of chemometric techniques can often provide additional insight useful in the evaluation and interpretation of the spectral data. Chemometrics refers to a rich collection of mathematical, statistical, and computational methods and tools that can be used to extract correlations between different measurements made on a material or chemical system and the nature or state of the system. The chemometrics field and its application within spectroscopy and other measurement and analysis fields has been the focus of intense activity for decades with many reviews and texts available on the topic [25.66, 68]. Chemometrics includes a host of multivariate analysis techniques that focus on the development of mathematical models that can help to describe and predict system properties based on measurements. A significant focus of common chemometric analysis techniques (e. g., principal component analysis (PCA), multivariate curve resolution (MCR)) is the identification of primary factors (or principal components (PC)) that describe the largest variance in the data, i. e., the measurement results obtained are found to be most sensitive to these factors. The number of PCs is often found to be much smaller than the number of measurement variables, thus providing a simplified means to describe the data. The new PCs can be thought of as defining a new coordinate space to which the original measurement variables are mapped and within which the measurement data themselves can
be plotted and visualized. In the case of only two sets of measurement data (2-D space), the identification of the new PCs is analogous to an axis rotation (Fig. 25.17). The projection of the PC basis vectors onto the original measurement variables is referred to as the loading. Scores are then used to map the measurements onto the PCs. Total score values for each PC can then be used to establish insight into primary correlations between measurement data and system state. Higher score magnitudes for a particular PC indicate that it is more effective in representing a greater percentage of the original data behavior. Formally, the maximum number of PCs for a given set of measurements will be equal to the number of measurement variables involved. In practice, however, when examining many measurements of the same sample (many dimensions), only a small number of PCs will exhibit significant scoring magnitudes (resulting in a higher eigenvalue for the PC vector). These PCs can then be used to model the data set, resulting in an effective reduction in the number of variables needed to describe the behavior observed [25.66]. In this context, and given the inherent multivariate nature of spectroscopic measurements (i. e., optical spectra are essentially a collection of many material measurements at different wavelengths—the variables), chemometric techniques are often applied to optical spectroscopy, typically using PCA and MCR techniques. While PCA provides the above-described PCs that identify maximum variance in the data set, the PCs themselves are often abstract and not in a form that is physically interpretable or is consistent with that anticipated from the experimental context. Of interest in Measurement 2 700 First principal component
600
Second principal component 500 400 300 Measurement data 200 0
10
20
30
40 50 Measurement 1
Fig. 25.17 Graphical representation of principal components and their relationship to original measurement variable space and the data set. The first principal component represents the greatest variance in the data. This example involves only two measurements
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Gaussian, then, three different adjustable parameters (center frequency, width, and height) must be defined. Nonlinear least-squares methods are typically used to work from some initial set of parameter values to obtain a fit to the data. For broad spectral envelopes containing multiple resonances, the number of adjustable parameters available can grow large and the relative ease with which a mathematically consistent fit can be produced that lacks physical significance is increased. The need to temper fitting results with informed input regarding anticipated peak characteristics and the number of peaks to be included (i. e., supervision of the fitting process) cannot be overstressed. Typically, information regarding the known characteristics of the material resonances involved and/or corroborating measurement results from other techniques are needed to increase confidence in the fitting results.
25.3 Spectral Analysis and Interpretation
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the present discussion, MCR techniques begin with an initial estimate of PC loadings and scores that can be guided by PCA or obtained via other means but that are restricted to non-negative values. Iterative nonlinear least-squares methods are used to optimize these PCs and their description of the data. The result is a collection of PCs characterized by loadings that resemble chemical spectra and scores that describe the contributions of these chemical components to the spectrum obtained from the chemical mixture under study. If a glass or related composite system is thought of as a collection of vibrational or electronic structural components with characteristic spectral responses, the application of MCR can be readily appreciated. When successful, the MCR approach can provide a description of the observed optical spectrum in terms of the
relative contributions and underlying spectral behavior of the resonances involved. This could be done even in cases where there was significant spectral overlap. While MCR is generally more readily interpreted in a chemical context, there is a potential to miss factors of interest that may correspond to minor constituents contributing to the measured spectra. This is associated with the need for the user to identify an initial set of non-negative loading estimates to begin the nonlinear least-squares optimization process. It is also important to note that the successful application of MCR and PCA-type factor analysis methods is very sensitive to artifacts associated with preprocessing of the initial spectrum. The use of chemometric techniques has seen increasing use in the analysis of optical spectra of glass [25.41, 69].
25.4 Conclusions Optical spectroscopy offers the opportunity to probe a broad range of material properties and phenomena, including multilength-scale structure and structural dynamics, mechanical, thermal and electronic properties, and optical performance. Successful application of this family of characterization tools requires an appreciation of fundamental light–matter interactions, the instrumentation and methodologies used to recover the optical response of the material, and the principles contributing to an effective
analysis and interpretation of the resulting spectral data. An overview of these three interrelated areas has been presented above. While not an exhaustive survey of the rich range of phenomena and measurement approaches contributing to an understanding of glass structure and properties, it is hoped that this introduction offers the reader a starting point from which to identify opportunities for the application of optical spectroscopy and to explore its use in greater depth.
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25.4 25.5
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E. Hecht: Optics, 5th edn. (Pearson, London 2016) D.C. Harris, M.D. Berolucci: Symmetry and Spectroscopy: An Introduction to Vibrational and Electronic Spectroscopy (Oxford Univ. Press, Oxford 1978) P.W. Atkins, R.S. Friedman: Molecular Quantum Mechanics, 3rd edn. (Oxford Univ. Press, New York 1997) B. Henderson, G.F. Imbusch: Optical Spectroscopy of Inorganic Solids (Oxford Univ. Press, Oxford 1985) W. Demtröder: Laser Spectroscopy: Basic Concepts and Instrumentation, 3rd edn. (Springer, Berlin 2003) A. Alessi, D. Di Francesca, S. Agnello, S. Girard, M. Cannas, N. Richard, A. Boukenter, Y. Ouerdane: Evidence of different red emissions in irradiated germanosilicate materials, J. Lumin. 177, 127–132 (2016) L. Giacomazzi, L. Martin-Samos, A. Boukenter, Y. Ouerdane, S. Girard, N. Richard: Ge(2), Ge(1) and Ge-E’ centers in irradiated Ge-doped silica: A firstprinciples EPR study, Opt. Mater. Express 5(5), 1054– 1064 (2015)
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A. Trukhin, B. Poumellec: Photosensitivity of silica glass with germanium studied by photoinduced of thermally stimulated luminescence with vacuum ultraviolet radiation q, J. Non-Cryst. Solids 324, 21– 28 (2003) S. Girard, S. Member, J. Kuhnhenn, A. Gusarov, B. Brichard, M. Van Uffelen, S. Member, Y. Ouerdane, A. Boukenter, C. Marcandella: Radiation effects on silica-based optical fibers: Recent advances and future challenges, IEEE Trans. Nucl. Sci. 60(3), 2015–2036 (2015) R. Naik, S.S. Chinnaiyah, R. Ganesan: Structural and optical modification in Bi doped As40 S60 thin films structural and optical modification in Bi doped As40 S60 thin films, AIP Conference Proceedings 1665, 070011 (2015) A.N. Trukhin: Luminescence of localized states in silicon dioxide glass. A short review, J. Non-Cryst. Solids 357(8/9), 1931–1940 (2011) D.L. Griscom: Trapped-electron centers in pure and doped glassy silica: A review and synthesis, J. NonCryst. Solids 357(8/9), 1945–1962 (2011)
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25.16
R.A. Weeks, R.H. Magruder III, A. Stesmans: Review of some experiments in the 50 year saga of the E’ center and suggestions for future research, J. NonCryst. Solids 354, 208–216 (2008) G. Pacchioni, L. Skuja, D.L. Griscom (Eds.): Defects in SiO2 and Related Dielectrics: Science and Technology, NATO Science Series (Springer, Dordrecht 2000) K. Tanaka, K. Shimakawa: Amorphous Chalcogenide Semiconductors and Related Materials (Springer, New York 2011) A. Alessi, S. Girard, M. Cannas, S. Agnello, A. Boukenter, Y. Ouerdane: Evolution of photoinduced defects in Ge-doped fiber/preform: Influence of the drawing, Opt. Express 19(12), 11680– 11690 (2011) B.G. Potter Jr., K. Simmons-Potter: Photosensitive point defects in optical glasses: Science and applications, Nucl. Instrum. Methods Phys. Res. Sect. B 166(167), 771–781 (2000) M. Olivier, P. Němec, G. Boudebs, R. Boidin, C. Focsa, V. Nazabal: Photosensitivity of pulsed laser deposited Ge-Sb-Se thin films, Opt. Mater. Express 5(4), 1450–1453 (2015) X. Su, R. Wang, B. Luther-Davies, L. Wang: The dependence of photosensitivity on composition for thin films of Gex Asy Se1-x-y chalcogenide glasses, Appl. Phys. A 113, 575–581 (2013) I. Voynarovych, J. Buzek, K. Palka, M. Vlcek: Spectral dependence of photoinduced optical effects in As40 S60-x Sex thin films, Thin Solid Films 608, 8–15 (2016) K. Tanaka: Photo-induced phenomena in chalcogenide glasses. In: Chalcogenide Glasses: Preparation, Properties and Applications, ed. by J.-L. Adam, X. Zhang (Woodhead, Cambridge 2014) pp. 139–168 S.L. Reddy, T. Endo, G.S. Reddy: Electronic (absorption) spectra of 3d transition metal complexes. In: Advanced Aspects of Spectroscopy, ed. by M.A. Farrukh (InTech, London 2012) pp. 3–48 M.P. Hehlen, M.G. Brik, K.W. Kramer: 50th anniversary of the Judd–Ofelt theory: An experimentalist’s view of the formalism and its application, J. Lumin. 136, 221–239 (2013) R. Reisfeld: Spectroscopy of rare earth ion. In: Nanostructured and Advanced Materials for Applications in Sensor, Optoelectronic and Photovoltaic Technology, ed. by A. Vaseashta, D. Dimova-Malinovska, J.M. Marshall (Springer, Dordrecht 2005) pp. 77–100 V. Ter-Mikirtychev: Optical properties and optical spectroscopy of rare earth ions in solids. In: Fundamentals of Fiber Lasers and Fiber Amplifiers, ed. by V. Ter-Mikirtychev (Springer, Cham 2014) J.G. Buenzli, S.V. Eliseeva: Basics of lanthanide photophysics. In: Lanthanide Luminescence: Photophysical, Analytical and Biological Aspects, ed. by P. Hänninen, H. Härmä (Springer, Heidelberg 2010) J. Heo, W.J. Chung: Rare-earth-doped chalcogenide glass for lasers and amplifiers. In: Chalcogenide Glasses: Preparation, Properties and Ap-
References
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25.45
Part C | 25
25.46
25.47
25.48
25.49
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25.55 25.56
C. Mendoza, S. Peuget, O. Bouty, R. Caraballo, C. Jegou: Simplified nuclear glasses structure behaviour under various irradiation conditions: A Raman spectroscopy study, Procedia Chem. 7, 581– 586 (2012) G.S. Henderson, D.R. Neuville, B. Cochain, L. Cormier: The structure of GeO2 –SiO2 glasses and melts: A Raman spectroscopy study, J. NonCryst. Solids 355, 468–474 (2009) H. Aguiar, J. Serra, P. González, B. León: Structural study of sol–gel silicate glasses by IR and Raman spectroscopies, J. Non-Cryst. Solids 355(8), 475– 480 (2009) J. Kieffer: Brillouin light scattering. In: Modern Glass Characterization, ed. by M. Affatigato (Wiley, Hoboken 2015) pp. 107–157 C. Sonneville, D. De Ligny, A. Mermet, B. Champagnon, C. Martinet, G.H. Henderson, T. Deschamps, E. Barthel: In situ Brillouin study of sodium alumino silicate glasses under pressure, J. Chem. Phys. 139, 074501 (2013) S. Chakraborty, A.K. Arora, V. Sivasubramanian, P.S.R. Krishna: Anomalous Brillouin shift in leadtellurite glass above glass transition. In: AIP Conference Proceedings, Vol. 1512 (2013) pp. 574–576 P. Voudouris, N. Gomopoulos, A. Le Grand, N. Hadjichristidis, G. Floudas, M.D. Ediger, G. Fytas: Does Brillouin light scattering probe the primary glass transition process at temperatures well above glass transition? Does Brillouin light scattering probe the primary glass transition process at temperatures well above glass transition?, J. Chem. Phys. 132, 074906 (2013) M. Naji, F. Piazza, G. Guimbretière: Heating rate effect on the activation of viscoelastic relaxation in silicate glasses, Phys. Procedia 48, 125–131 (2013) M.M. Smedskjaer, L. Huang, G. Scannell, J.C. Mauro: Elastic interpretation of the glass transition in aluminosilicate liquids, Phys. Rev. B 85, 144203 (2012) M. Guerette, C.R. Kurkjian, S. Semjonov, L. Huang: Nonlinear elasticity of silica glass, J. Am. Ceram. Soc. 99(3), 841–848 (2016) J. Sole, L. Bausa, D. Jaque: An Introduction to the Optical Spectroscopy of Inorganic Solids (Wiley, Hoboken 2005) J.M. Lerner, A. Thevenon: Optics of Spectroscopy: A Tutorial (Horiba Scientific, Kyoto 2002) G. Rieke: Detection of Light: From the Ultraviolet to the Submillimeter, 2nd edn. (Cambridge Univ. Press, Cambridge 2003)
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P.R. Griffiths, J.A. De Haseth, J.D. Winefordner: Fourier Transform Infrared Spectrometry, 2nd edn. (Wiley, Hoboken 2007) J.R. Sandercock: Brillouin scattering study of SbSI using a double passed stabilised scanning interferometer, Opt. Commun. 2, 73–76 (1970) M. Guerette, L. Huang: A simple and convenient set-up for high-temperature Brillouin light, J. Phys. D. Appl. Phys. 45, 275302 (2012) K. Simmons-Potter, J.H. Simmons: Modeling of absorption data complicated by Fabry-Pérot interference in germanosilicate thin-film waveguides, J. Opt. Soc. Am. B 13(2), 268–272 (1996) R. Swanepoel: Determining refractive index and thickness of thin films from wavelength measurements only, J. Opt. Soc. Am. A 2(8), 1339–1343 (1985) W.C. Wang, J. Yuan, X.Y. Liu, D.D. Chen, Q.Y. Zhang: Spectroscopic properties and energy transfer parameters of Yb3+ /Tm3+ co-doped fluorogermanate glasses, J. Non-Cryst. Solids 431, 154–158 (2016) D. Ramachari, L.R. Moorthy, C.K. Jayasankar: Phonon sideband spectrum and vibrational analysis of Eu3+ -doped niobium oxyfluorosilicate glass, J. Lumin. 143, 674–679 (2013) D.L. Sidebottom, M.A. Hruschka, B.G. Potter, R.K. Brow: Increased radiative lifetime of rare earth-doped zinc oxyhalide tellurite glasses, J. Appl. Phys. 84, 509 (1998) M. de Oliveira Jr, T. Uesbeck, T.S. Gonçalves, C.J. Magon, P.S. Pizani, A.S.S. de Camargo, H. Eckert: Network structure and rare-earth ion local environments in fluoride phosphate photonic glasses studied by solid-state NMR and electron paramagnetic resonance spectroscopies, J. Phys. Chem. C 119, 24574–24587 (2015) R.G. Brereton: Chemometrics: Data Analysis for the Laboratory and Chemical Plant, Vol. 8 (Wiley, Chichester 2003) M.H. Brooker, O. Faurskov Nielsen, E. Praestgaard: Assessment of correction procedures for reduction of Raman spectra, J. Raman Spectrosc. 19, 71–78 (1988) R. Tauler, A. de Juan: Multivariate curve resolution. In: Practical Guide to Chemometrics, 2nd edn., ed. by G. Paul (CRC, Boca Raton 2006) E. Černoškova, J. Holubová, B. Bureau, C. Roiland, V. Nazabal, R. Todorov, Z. Černošek: Thermoanalytical properties and structure of (As2 Se3 )100-x (Sb2 Se3 )x glasses by Raman and 77 Se MAS NMR using a multivariate curve resolution approach, J. Non-Cryst. Solids 432, 426–431 (2016)
Barrett G. Potter Jr. Dept. of Materials Science & Engineering University of Arizona Tucson, AZ, USA [email protected]
B.G. Potter, Jr. is a Professor of Materials Science and Engineering and Optical Sciences at the University of Arizona in Tucson. Prior to joining the University, he was a Principal Member of the Technical Staff and served as the Technical Manager for the Chemical Synthesis and Nanomaterials Department at Sandia National Laboratories, Albuquerque NM. His research involves glass, ceramic, and molecular-hybrid optical and electronic materials focusing on photoactivated phenomena, optoelectronic nanocomposites, energy applications, and materials aging and reliability.
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Terahertz Tim
26. Terahertz Time-Domain Spectroscopy of Glasses
S. K. Sundaram
The terahertz (THz) regime (0:110 THz) shows promise for applications in sensing, imaging, and communications [26.1, 2]. THz waves [26.3, 4] cover a large portion of the electromagnetic spectrum between the infrared and microwave bands. With a timescale of about 1 ps, THz radiation is important in studying and controlling many fundamental systems, processes, and transitions relevant to physics, chemistry, biology, and materials science. For example, electrons in highly-excited atomic Rydberg states orbit, and small molecules rotate, at THz frequencies. Electrons resonate at THz frequencies in semiconductors and nanoscale semiconductor structures. Matter emits black-body radiation above 10 K at THz frequencies. Correlated electron materials (CEMs) defy the Landau theory of Fermi liquids (FL) and challenge our understanding of these systems. Some examples of CEMs are d- and f-shell metals, semiconductors doped
26.1
THz Spectrometers ............................
910
26.2
Modeling and Experimental Validation .............
915
26.3 26.3.1 26.3.2 26.3.3 26.3.4 26.3.5 26.3.6
Glass Systems ................................... Silica ................................................ Borate Glasses ................................... Silicate Glasses .................................. Tellurite Glasses................................. Chalcogenide Glasses ......................... Glass Composites ...............................
917 918 919 920 921 923 923
26.4
Summary..........................................
924
References...................................................
925
Our results in hydroxyapatite (Ca10 .PO4 /6 .OH/2 ; HA)-glass (0.05CaO-0:12TiO2 -0:17Na2 O-0.28ZnO0:38SiO2 ) composites demonstrate that the THzTDS can be a promising non-destructive tool for evaluating these composites and tracking their degradation in simulated body fluids in biological applications.
near the metal-insulator transition, and the low-dimensional systems known as quantum dots. The theory of quantum transition and criticality can be used to understand the non-FL behavior of these systems. A quantum phase transition is a disorder–order transition taking place at zero temperature as a parameter of the Hamiltonian is varied. Figure 26.1 shows a schematic phase diagram. The quantum critical regime coves a large inverted triangle-shaped region in Fig. 26.1. Within the quantum critical regime (large inverted triangular region in Fig. 26.1), the Fermi liquid state is disrupted by strong fluctuations between the competing ordered and disordered phases. Detailed characterization of excited states or elementary excitations is needed for understanding the nature of these phases and the transitions among them. As the most important excitations are those with an energy of order kB T (kB D Boltzmann constant and T D temperature) above the ground state,
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_26
Part C | 26
Terahertz-time domain spectroscopy (THz-TDS) uses the real and imaginary parts of the dielectric and optical constants for glass characterization over a wide frequency range in the electromagnetic spectrum. This chapter provides an overview and analysis of various THz spectrometers and typical data sets over 0:110 THz. Phonon modes in THz region and Lunkenheimer–Loidl plots for disordered materials along with density-functional based tight-binding (DFTB) modeling results for As2 S3 are described. THz optical and dielectric properties of selected model glass systems, e. g., silica, alkali borate, and silicates, based on works reported in the literature, are discussed. Mixedalkali effects and thermal stability in terms of THz properties of simple tellurite glass composition, 80TeO2 -10WO3 -(10x)Li2 O-xNa2 O with x D 0, 2, 4, and 6, are reported. Chalcogenide (As-S) glasses show that the refractive indices in THz, infrared, and visible frequencies decrease with arsenic composition up to a point of optimal constrained structure with average coordination number, hri, beyond which the refractive index increases.
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Temperature Quantum critical regime (non-FL)
Ordered
Disordered
Tuning parameter: pressure, carrier density, magnetic field, etc.
Part C | 26.1
Fig. 26.1 Schematic phase diagram of a system with a critical point. Quantum critical point refers to a phase transition at T D 0 (after [26.5])
these fall in the THz region. These excitations can be studied using the THz spectroscopy on single particles or collective modes. For example, single modes include energy gap in semiconductors, internal transition of excitons and intersubband transitions in low-dimensional materials. Examples of collective modes are phonons, antiferromagnetic resonance and soft mode in ferroelectrics. Readers are referred to an expert workshop report [26.5] published by the Department of Energy (DOE)-National Science Foundation (NSF), and National Institute of Health (NIH) in 2004 on various transitions that can be probed using THz spectroscopy and the latest road map published in 2017 [26.6]. THz spectroscopy [26.6, 7] describes molecular rotational and vibrational spectra from 10 GHz to 10 THz. In the time domain, it uses the real and imaginary parts of the dielectric function for material studies over a wide frequency range. It allows access to the complex refractive indices of a variety of materials, such as dielectrics [26.8], semiconductors [26.9, 10], liquids [26.11], superconductors [26.12], ceramics [26.13], environmental pollutants [26.14], chemical
mixtures [26.15], and gases [26.16]. THz spectroscopy is a versatile tool for characterizing glasses. Theoretical models have been used to describe absorption of low-frequency radiation by phonon modes in glasses. The density of vibrational states g. / in a THz region are critical to understanding the vibrational properties of glasses across the electromagnetic spectrum. Vibrational modes in glasses and their structures have been investigated using far-infrared (FIR) and Raman scattering. It is difficult to analyze low-energy excitations related to the vibrational states in glasses, as the quality of spectra decreases significantly in the case of IR spectroscopy below 3 THz. Since boson peaks are generally very broad, it is challenging to interpret and validate various physical models using spectroscopic data. THz spectroscopy in the time domain, as well as in the frequency domain, provides a unique window on the temporal evolution of optical response functions on time scales over 100 fs–500 ps. This region is sensitive to thermally accessible excitations that determine the properties of correlated electron systems. THz methods are compatible with the study of materials under extreme conditions of temperature, electric, and magnetic fields. Non-contact measurements are plausible, as good ohmic contacts are difficult to make with some materials. Pump–probe experiments can be used to study the response of correlated systems to high electric fields, e. g., of the order of MV=cm, without the risk of excessive heating or electrical breakdown. In addition, heterogeneous materials and structures and detailed information on interface quality or the presence of buried defects or structures can be studied. Various THz spectrometers cover a wide range of frequencies, resolutions, and data qualities. This chapter summarizes recent advances in modeling and THz time-domain spectroscopy (THz-TDS) of major glass families and composites. The chapter also presents the glass structure-optical properties relationship that is evolving and extending well into the THz regime.
26.1 THz Spectrometers Free space propagation of radiated pulses from a generator to a detector reported in the late 1980s [26.17, 18], led to development and applications of THz spectroscopy [26.19]. THz waves can be generated and detected using many different technologies [26.20]. The photoconductive antenna (PCA) is the most commonly used technology. In this case, ultrafast laser pulses induce transient photocarriers, which can be used to generate and detect THz pulses. Figure 26.2 shows
a schematic of the concept. A GaAs semiconductor substrate supports two metal electrodes with a gap (e. g., 5 m) between them. A bias voltage is applied across the electrodes. As the substrate is more insulating than the electrodes, the electrical energy is stored across the gap. The laser pulses (e. g., < 90 fs) generate photoinduced free carriers and act like a gate, releasing the energy as THz pulses (e. g., < 500 fs). The bias field drives these free carriers across the gap producing pho-
Terahertz Time-Domain Spectroscopy of Glasses
26.1 THz Spectrometers
911
Fig. 26.2 Schematic of laser-gated Vbias < 90 fs NIR pulse < 500 fs THz pulse
PC antenna technology for THz generation and detection; near-IR D Near infrared. (Courtesy of Phil Taday, Teraview, UK)
– +
Part C | 26.1
5 μm
GaAs substrate
tocurrent. The current density can be described as J.t/ D N.t/e Eb ;
(26.1)
where N is density of the photocarriers, e is the elementary charge, is the electron mobility, and Eb is the bias electric field. The contribution of holes is ignored, as the electrons have higher mobility. The laser pulse shape and the carrier lifetime determine the time dependence of N and the photocurrent. The electric field generated can be described as follows ETHz D
Ae @N.t/ 1 A @J.t/ D Eb ; 4 "0 c2 z @t 4 "0 c2 z @t (26.2)
where A is the area in the gap illuminated by the laser light, "0 is the vacuum permittivity, c is the speed of light in vacuum, and z is the distance between the field point and the THz source. The field point is assumed to be normal to the PCA and z is assumed to be larger than the PCA dimension. The PCA can also be used as a THz detector. In detector mode, the two electrodes are connected to a current sensor. By controlling the time delay between the THz pulse and the laser pulse, the electric field can be probed by the laser pulses, generating transient photocarriers in the substrate and inducing current between the two electrodes. The THz field induced current can be described as J D Ne E. / ;
(26.3)
where N is the average electron density and is the temporal delay between the probe pulse and the THz pulse. One can scan the temporal delay and record the THz
pulse waveform as a function of . Readers are referred to [26.21, 22] for more details on THz generation and detection and PCAs. Generally, THz spectroscopy is used for identification of different materials using their THz spectral signatures or measurement of the optical and dielectric constants in THz frequencies. The THz-TDS directly measures the THz wave’s temporal electric field. Fourier transformations of this time-domain data give the amplitude .E/ and phase . / of the THz wave pulse, thereby providing the real and imaginary parts of the dielectric constant directly without using the Kramers–Kronig relations [26.23, 24]. The THz-TDS is capable of a frequency resolution of a few GHz, a dynamic range of 108 in power, and a bandwidth of 0:16 THz. The spectrometer is typically powered by laser pulses, each of several tens of femtoseconds duration. A beam splitter splits the laser beam into two parts, pump and probe beams. The pump beam hits an emitter, typically low-temperature (LT)-GaAs or GaBiAs PCA material, that releases a short pulse of electromagnetic radiation of a few picoseconds duration. The radiation then reaches a detector gated by a probe pulse, as shown in Fig. 26.3. The output signal of the detector is proportional to the magnitude and the sign of the field of the THz pulse at every moment of time. One can trace the entire time profile of the THz pulse by the variation of the delay between pump and probe optical pulses. The subpicosecond pulse of the radiation passes through a sample, which changes its time profile compared to a reference pulse. One can obtain the spectrum of the refractive index .n/ of the sample by analyzing the changes in the complex Fourier spectrum introduced by the sample. The spectrum also contains responses from
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Characterization of Glasses
Fig. 26.3 Schematic of THz-TDS
Parabolic mirror
Sample Optical delay stage
THz detector
THz ermitter Parabolic mirror
Part C | 26.1
Pump beam Femtosecond Ti:sapphire modelocked laser
Beam splitter
Probe beam
both the absorption coefficient ˛ and the dielectric constant of the material. The n. / and ˛. / as a function of THz frequency are related as follows
1 C c sample . / reference . / n. / D ; (26.4) .2 d/ h i T. /Esample . / Ereference . /
; d Œn. / 12 T. / D 1 R D ; Œ. / C 12 ˛. / D ln
(26.5) (26.6)
where d is the sample thickness, T is the fraction of power transmitted through the air-sample interface, and R is the Fresnel loss at the air-sample interface. A backward oscillator (BWO)-based frequency-domain THz spectrometer [26.25] is more versatile. It can be used for solid, liquid or gaseous samples. Measurements are typically made at frequencies covering a broad range of 0:031:5 THz at 21000 K with linear or circular polarization. It combines the advantages of microwave and infrared domains. It exploits free space propagation and flexible quasi-optical measurement schemes, thus allowing direct determination of the polarized spectra of any optical quantity of a sample, e. g., real and imaginary parts of the refractive index, dielectric constant, dynamical conductivity, and magnetic permeability. In the case of non-magnetic materials (permeabilities 0 D 1 and 00 D 0), the spectrometers measure two quantities: transmission coefficient .Texp . // of a plane-parallel sample and the phase shift . exp. // of the radiation passing through a sample. Fresnel expressions (26.7) and (26.8) for complex transmissivity of a plane-parallel slab [26.26] can be used to
calculate the unknown "0 and "00 by solving equations (26.9) and (26.10) 2n1 cos i Ak and n2 cos i C n1 cos t 2n1 cos i A? ; (26.7) T? D n1 cos i C n2 cos t n2 cos i n1 cos t Rk D Ak and n2 cos i C n1 cos t n1 cos i n2 cos t A? ; (26.8) R? D n1 cos i C n2 cos t T."0 ; "00 ; / D Texp . / ; (26.9) ."0 ; "00 ; / D exp . / ; (26.10) Tk D
where T is the transmission coefficient, R is the reflection coefficient, A is the phase coefficient, n1 and n2 are refractive indices of media 1 and 2, respectively, i is the angle of incidence, and t is the angle of refraction. The subscript k denotes parallel to the plane of incidence. The subscript ? denotes perpendicular to the plane of incidence. Eisele et al. [26.27] have recently designed and developed a simple and compact far-infrared Fouriertransform spectrometer that works as a Michelson interferometer without a beam splitter and uses a Golay cell and a pyroelectric detector for operation over 0:13 THz with a frequency resolution of 6 GHz. In this setup, a pair of flat lamellar mirrors is used to introduce a precisely defined phase difference between two parallel beams of nearly equal radiated power, as shown Fig. 26.4. The THz source is positioned at the focus of the input parabolic mirror, which produces a diffraction-limited parallel beam directed onto the
Terahertz Time-Domain Spectroscopy of Glasses
a)
b)
Movable split mirror
Lamellar mirror
26.1 THz Spectrometers
Translation stage
Water cooling
Movable split mirror Phase delayed THz signals θ Golay cell
THz signal
Motorized translation stage
Beam chopper
Side view with 7 of 12 lamellae shown
Photoconductive switch Laser beam
90° parabolic mirrors
Golay cell
Entrance pupil
Parabolic mirrors
Focusing lens
Fig. 26.4 (a) Schematic of the Fourier-transform THz interferometer; (b) Photograph of the setup showing the lamellar mirror, the translation stage, and the Golay cell. From [26.27] © IOP publishing. Reproduced with permission. All rights reserved
split lamellar mirror. One half of the lamellar mirror is fixed, while the other half is mounted on a computercontrolled translation stage that can be moved to cause differential delay. The THz beam illuminates each half of the mirror equally. The reflected beam containing both these components is collected by the parabolic mirrors and focused on the detector. The difference between the two parts of the lamellar mirror produces an interferogram in the detector. A Fourier transform of the signal from the detector as a function of time delay produces the frequency spectrum. This spectrometer is easy to align and it can be used with both continuouswave (CW) and pulsed sources. a) Electric field (arb. u.)
Readers are referred to an excellent book on THz metrology by Naftaly [26.29] for detailed descriptions of various aspects of THz measurements and a paper by Gorshunov et al. [26.30] for a comparison of different spectrometers. Only the THz-TDS exploits the time-resolved nature of spectroscopy. This chapter is focused on the principle and applications of THz-TDS to study of glass systems. Figures 26.5 and 26.6 show typical data collected and analyzed for various ZnS samples [26.28] using THz-TDS at Terahertz and Millimeter Waves Laboratory (T-Lab) of Alfred University. We used a Teraview TPS 3000 (Teraview, UK) to measure the spectra b) Spectral amplitude (arb. u.)
7500
Reference (air) Elemental ZnS Multispectral ZnS Standard ZnS
5000
108 107 10
Reference (air) Elemental ZnS Multispectral ZnS Standard ZnS
0.78 THz
6
105 2500
104 103
0
2.20 THz
102 0
10
20
30
40
50 60 Time (ps)
101 0.0
0.5
1.0
1.5
2.0
2.5 3.0 Frequency (THz)
Fig. 26.5 (a) Time-domain pulse of the samples and the reference and (b) Comparison of frequency-domain pulse of the samples and the reference. Reprinted from [26.28], with permission from Elsevier
Part C | 26.1
THz source Horizontal exit slit
913
914
Part C
Characterization of Glasses
a) ε'
b) n
9.0
3.00 Elemental ZnS Multispectral ZnS Standard ZnS
Elemental ZnS Multispectral ZnS Standard ZnS 8.8 2.95 8.6 2.90 8.4
Part C | 26.1
8.2 0.0
0.5
1.0
1.5
2.0 2.5 Frequency (THz)
2.85 0.0
0.5
1.0
1.5
2.0 2.5 Frequency (THz)
d) α (cm–1)
c) ε'' 0.15
10 Elemental ZnS Multispectral ZnS Standard ZnS
Elemental ZnS Multispectral ZnS Standard ZnS
8
0.10 2.20 THz
6
4 0.05
0.78 THz
0.78 THz
2.20 THz 2
0.00 0.0
0.5
1.0
1.5
2.0 2.5 Frequency (THz)
0 0.0
0.5
1.0
1.5
2.0 2.5 Frequency (THz)
Fig. 26.6a–d Data analyzed: (a) Real part of the dielectric function, (b) refractive index, (c) imaginary part of the dielectric function, and (d) absorption coefficient of ZnS samples. Reprinted from [26.28], with permission from Elsevier
of the samples from 0:11:2 THz at room temperature in transmission mode. A reference measurement was made in pure nitrogen prior to the sample measurements. A pulse of THz radiation is generated by a mode-locked Ti:sapphire laser with a center wavelength at approximately 800 nm, a repetition rate of 80 MHz, and a pulse width of 100 fs. The THz pulse is separated into pump and probe beams. The pump
beam generates the THz radiation and the probe beam is used to detect the THz beam using LT-GaAs as PCAs. The optical and dielectric properties were calculated by comparing the reference and sample time delays of the THz pulse using the thickness of the sample. These data showed fingerprint vibrational modes for ZnS at 0:78 and 2:20 THz, which are observed as kinks in the frequency plot.
Terahertz Time-Domain Spectroscopy of Glasses
26.2 Modeling and Experimental Validation
915
26.2 Modeling and Experimental Validation
˛. / D C. /g. / :
(26.11)
The linear absorption coefficient is generally measured by IR spectroscopy [26.33, 34]. In the FIR region, the relationship is found to be ˛. / D 2 . The coefficient C. / indicates the degree of coupling between IR photons and atomic vibrations, which depends on the vibrational eigenmodes and the distribution of atomic charges in these materials. But, the coefficient C. / cannot be measured directly. Therefore, two independent experiments for measuring ˛. / and g. / are necessary. Currently, no detailed rigorous model of these processes in amorphous materials exists. Reported theoretical models focus mainly on the origin of the BP modes [26.35] within a soft-potential model or on the role of charge disorder in simple lattice models without positional disorder [26.36–38]. Taraskin et al. [26.39] have demonstrated that the C. / indeed exhibits a universal frequency dependence of the following form in the FIR region C. / A C B 2 ;
(26.12)
where A and B are material-dependent constants. This relationship is valid for frequencies below the Ioffe– Regel crossover, IR , separating well-propagating plane waves from the strongly damped ones due to disorder-induced scattering [26.40]. The Ioffe–Regel frequency . IR / is generally close to the BP for many materials [26.41]. The coupling coefficient below the Ioffe–Regel crossover has two components: 1. A frequency-independent component due to uncorrelated static charge fluctuations caused by medium and long-range structural irregularities, resulting in
the quadratic frequency dependence of the absorption coefficient frequently observed in disordered crystals and glasses. 2. A quadratic frequency-dependent component caused by structural disorder on the short-range (interatomic) scale, leading to static correlated charge fluctuations obeying local charge neutrality within structural units. Taraskin et al. [26.39] have provided analytical arguments, confirming molecular-dynamics (MD) models, and experimental THz-TDS measurements of ˛. / for oxide .SiO2 / and non-oxide .As2 S3 / glass systems. The authors have also used experimental VDOS data generated by others for SiO2 and As2 S3 [26.42, 43] glass systems to determine C. /. The general expression for the coefficient of absorption of FIR photons by harmonic atomic vibrations obtained within the rigidion model [26.44] is as follows ˇ2 ˇ ˇ ˇX q ˇ i ˇ C. / C0 ˇ p ei . /ˇ ; ˇ ˇ mi
(26.13)
i
1=2
where C0 D 2 2 n=c"˛ , with mi and qi being the atomic masses and fixed atomic charges, ei . / the component of the eigenvector of frequency corresponding to atom i, "˛ stands for the high-frequency dielectric constant, n is the atomic concentration, and c is the speed of light in vacuum. The rigid-ion model uses an anharmonic ionic crystal for which only cubic anharmonic terms are retained in the lattice Hamiltonian. The authors suggest that a more general model with the fixed charges replaced by charge tensors [26.33, 45] should be used for higher frequencies to properly describe the absorption peak positions and their relative intensities across the IR vibrational band. In the FIR range, the rigid-ion model is adequate, as the model is validated by the density-functional based tight-binding (DFTB) [26.46, 47] molecular dynamics (MD) model of As2 S3 glass [26.48]. In SiO2 glass, uncorrelated charge fluctuations dominate the whole frequency range below the Ioffe–Regel crossover (or BP) and result in a frequency-independent absorption coupling coefficient. In contrast, in As2 S3 the uncorrelated charge fluctuations are less pronounced, and correlated charge fluctuations preserving local charge neutrality become appreciable, even below the BP. Therefore, the absorption coupling coefficient exhibits an onset to 2 dependence in this frequency range. The universality extends over a broader range of the electromagnetic field’s GHz to THz region [26.49]
Part C | 26.2
The THz region exhibits many phonon modes. An inherent inhomogeneous broadening of the THz modes is observed in disordered solids, such as glasses. Glasses respond to the THz field the same way they respond to a thermal field, e. g., with low-temperature anomalies in thermodynamic properties of glasses and the vibrational modes in excess of the Debye vibrational density of states (VDOS), g. / / 2 , at typical frequencies 30 cm1 , called the boson peak (BP) [26.31]. In the far infrared (FIR) region, the atomic vibrations are material-independent. Therefore, interaction of photons with atomic vibrations in disordered materials is also postulated to exhibit a universal behavior [26.32]. This interaction can be described as a simple first-order perturbation process that is characterized by a linear absorption coefficient
916
Part C
Characterization of Glasses
Change distribution function (e–1) 10
a) log σ' FIR peak
S
As
8 SLPL
6 4
DC
UDR
2 1
Relaxation
Part C | 26.2
b) log ε''
Relaxation
UDR kHz
0.5
1 q (e)
model of As2 S3 . After [26.51] © IOP publishing. Reproduced with permission. All rights reserved FIR peak
Hz
0
Fig. 26.8 Atomic charge distribution from the DFTB
DC
T
–0.5
MHz
SLPL GHz
THz log v
Fig. 26.7a,b Lunkenheimer–Loidl plot for disordered materials for two temperatures: (a) logarithmic DC conductivity as a function of frequency and (b) logarithmic imaginary dielectric constant as a function of frequency. Reprinted with permission from [26.49]. Copyright 2003 by the American Physical Society
for various disordered materials, including glasses. Figure 26.7 shows a Lunkenheimer–Loidl plot for two different temperatures, which captures the universality of frequency-dependent conductivity, 0 . /, and frequency-dependent dielectric loss or imaginary dielectric constant, "00 . /, for the disordered materials. An universal dielectric response (UDR) represents Jonscher’s universal dielectric response [26.50]. A superlinear power law (SLPL) bridges the classical dielectric and the infrared regions. Dashed lines at low frequencies show relaxation behavior corresponding to
nonconducting dipolar systems. Dash-dotted lines show transitioning to dielectric current (DC) conductivity for the conducting systems. Solid lines show the region of universality. Phonon resonances (BP) show up in the FIR region, indicated as dotted lines. Readers are referred to the paper by Lunkenheimer and Loidl [26.49] for more detail. THz-TDS can be used to obtain experimental data on the scale of charge fluctuations and possible charge ordering in inorganic glasses [26.33, 39, 52–55]. Taraskin et al. [26.51] have demonstrated that the frequency dependence of the coupling coefficient for FIR absorption can be used to extract the characteristics of the atomic charge distribution in glasses. A theoretical law, A C B 2 , can be used to fit the experimental data and to extract the constants A and B. The value of A is proportional to the variance of the uncorrelated charge distribution, 1 2 . Estimated 1 value for As2 S3 glass is ' 0:12. First principle tight-binding MD model’s estimate of ' 0:054 supports the theoretical law and experimental data. Figure 26.8 shows the DFTB modeling results. The dashed curves show the Gaussian fits for these distributions with the mean values qAs ' 0:56 and qS ' 0:36. The standard deviations are 1As ' 0:06 and 1S ' 0:05, confirming how close the experimental data fit the theoretical law.
Terahertz Time-Domain Spectroscopy of Glasses
26.3 Glass Systems
917
26.3 Glass Systems
Z cos i Z0 cos t ; Z cos i C Z0 cos t Z cos t Z0 cos i and RTM D ; Z cos t C Z0 cos i RTE D
(26.14)
0 ; ˛c 2 0 n2 4 i 2n˛c 4
1. Amorphous silica 2. Pyrex (81% SiO2 , 13% B2 O3 , 4% Na2 O, 2% Al2 O3 ) borosilicate 3. High silica low alkalis 4. BK7 borosilicate (70% SiO2 , 11:5% B2 O3 , 9:5% Na2 O, 7:5% K2 O, 1:5% BaO) 5. Low silica high alkalis.
(26.15)
where i is the angle of incidence and reflection, t D arcsin.sin.i / .Z=Z0 // the angle of refraction, Z0 D 377 the free space wave impedance, and Z is the wave impedance of the reflecting material, which can be computed using the following equation v u ZDu t
where 0 and "0 are free space permeability and permittivity, c is the velocity, and is the frequency of the incident wave. The authors have found a good agreement between simulated and measured reflection coefficients with reflectivity for TE polarization greater than that for TM polarization. Window glass has been found to be the best reflecting material, followed by plastic and wood. This is important for inexpensive construction of integrated THz photonics. FIR and Raman scattering have been used to investigate low-frequency vibrational modes structure [26.60, 61] in glasses. Theoretical models describe absorption of low-frequency radiation by phonon modes in the glass [26.34]. The density of vibrational states g. / in the THz region, especially in excess of the Debye squared-frequency law [26.62, 63], are of interest in vibrational properties of glasses. It is difficult to analyze low-energy excitations related to the g. /= 2 of glasses as the quality of spectra decreases significantly in the case of IR spectroscopy below 3 THz. The lowfrequency Raman scattering spectra show the broad peaks g. /= 2 (BP), which are challenging to interpret and validate various physical models. The THz-TDS data gives new insights into the understanding of boson peaks in glassy materials [26.9, 64–66], including complex dielectric constants in the THz region [26.66– 68]. Kojima et al. [26.69] have studied the low-energy excitations of organic and inorganic glasses using THzTDS. These excitations are closely related to the density of vibrational states and the intermediate local order or structural units in glasses. Naftaly et al. [26.70] have used THz-TDS to study:
(26.16)
These latter glasses have more weak-alkali-nonbridging-oxygen (NBO) silicon bonds, less long range order, smaller structural units, and more NBOs than Pyrex and quartz (polycrystalline silica) over 0:32:4 THz. Pyrex and BK7 have stronger THz absorption than the silicas. BK7 has stronger absorption than Pyrex. Therefore, the THz absorption increases with the proportion of alkali oxides, indicating a structural correlation. The authors have proposed a model that is like multi-photon infrared absorption in solids. Per this model, the absorption coefficient can be de-
Part C | 26.3
Lamb [26.56] has summarized several parameters of various materials, including solid and foam dielectrics, absorbers, and metals, collected for use in optical design in the millimeter and submillimeter range. Simonis [26.57] has prepared an index to the literature of the near-millimeter wave (941000 GHz) properties of solid and liquid materials listed alphabetically with detailed sources of references. Wilke et al. [26.58] have reported the optical constants of selected commercial glasses (Robax, blue membrane, borosilicate silicate, quartz) and glass ceramics (Macor) by THz-TDS. The authors used experimental complex transmission data to calculate the frequency dependence of the complex index of refraction n0 D n C ik and the frequency-dependent conductivity 0 . / D 2 "0 "00 D 2 "0 2nk of these materials, where "0 is the high-frequency dielectric constant and "00 is the imaginary dielectric constant. Except for quartz, these materials exhibit a power law behavior, 0 . / / b with 1 < b < 2. Piesiewicz et al. [26.59] have measured the angle-dependent reflection coefficients using THz-TDS for common building materials, window glass, plaster and pine wood, in transmission geometry over 70350 GHz. The authors have measured the samples at 20ı , 30ı , 40ı , 50ı , 60ı , 70ı , and 75ı with transverse-electric (TE) and transverse-magnetic (TM) polarized waves and determined the frequency dependent reflection coefficients as the ratio of the Fourier transforms of consecutive reference and sample measurements. The reference measurements are obtained by placing a polished copper mirror in place of the sample so that the reflection coincides with the surface reflection of the sample. The authors have used Fresnel’s equations to calculate the reflection coefficients RTE and RTM from the experimental measurements of absorption coefficient ˛ and refractive index n as follows
918
Part C
Characterization of Glasses
Part C | 26.3
scribed by ˛ D A exp. = o /, where is the frequency of the incident radiation. The frequency parameter, !0 , is related to vibrational modes and glass structure, and therefore glass transition temperature; it is determined by the energy of the phonon mode predominantly responsible for the absorption process and is expected to reflect the lowest energy phonon mode present in the material. The pre-exponential coefficient A is related to the electron-phonon coupling interaction and strength (i. e., bond strength and expansion coefficient.)The refractive index reflects electronic bonding, which is also related to the expansion coefficient. The authors have used the data to determine the real and the imaginary parts of complex dielectric constants. The THz-TDS signals with and without a sample are recorded and converted into the frequency-domain transmission power T. / and phase shift f . /. Then, the transmission power is normalized by the reference signal without a sample to be measured. Since a complex dielectric constant is related to a complex refractive index n. / C ik. / by the relation from Kojima et al. [26.69] ". / D "0 . / C i"00 . / D Œn. / C ik. /2 ; (26.17) p "sample . / D T. /expŒi . / ; (26.18) "reference . / "sample . / D "reference . / 4.n C ik/ exp.ikı/ Œ.n C ik/ C 12 expŒi.n C ik/kı 1 Œ.n C ik/ 12 expŒi.n C ik/kı ; (26.19) where ı is a thickness of a sample, and Esample . / and Ereference . / are the transmitted electric field measured with and without a sample, respectively. k D 2 = is the magnitude of the wave vector. Therefore, one can calculate the real and imaginary parts of a complex dielectric constant "0 . / and "00 . / from observed transmission power T. / and phase delay ı. / spectra normalized by the reference signal. The complex dielectric spectra of glasses clearly show the existence of the BP, broad low-energy excitations. The readers are referred to paper by Koijima et al. [26.69] for more detail. THz refractive indices and absorption coefficients are related to the glass’s structure and properties. The Clausius–Mossotti equation [26.71] relates the dielectric constant " (D n2 ) to the microscopic polarizability P as follows 4 "1 D NA P ; "C2 3 M
(26.20)
where NA is Avogadro’s number, is the mass density, and M is the molecular weight. The frequency dependent absorption coefficient ˛. / can be described by the power-law relation n. /˛. / D K.h /ˇ g. / ;
(26.21)
where n. / is the frequency-dependent refractive index and the exponent ˇ for glassy materials is approximately 2 [26.70]. The coefficient K is determined by material properties, and is given by [26.34] KD
je j2 Ne k2 ; .4 "0 /¯2 cvD3
(26.22)
where "0 is the vacuum permittivity, Ne is the density of charge fluctuations of amplitude je j, c is the speed of light, k D .n2 C 2/=3 is the local field correction factor, ¯ is reduced Planck’s constant .D h=.2 //, and vD is the Debye velocity of sound. Strongly absorbing glasses have a narrower data range [26.72] with little dispersion in the refractive indices. The absorption coefficients for silicate glasses are very high in the THz region [26.73]. Readers are referred to a paper by Naftaly and Miles [26.73] for more detail. In this section, THz properties of selected model glasses (silica, alkali borate and silicates) from the works of Kojima et al. [26.69] and Naftaly and Miles [26.73] are summarized. In addition, recent results on tellurite and chalcogenide glasses as well as glass composites from the author’s works in collaboration with other researchers are also summarized.
26.3.1 Silica Several workers [26.74–77] have measured the BP and FIR spectrum in silica using a variety of techniques, including THz-TDS. The refractive index of silica is 1:96 at 0:5 THz, corresponding to a dielectric constant of 3:84, which is significantly higher than that in the visible range (1:45 at 589 nm) due to the contribution of ionic polarizability to the dielectric constant at THz frequencies. The dielectric constant of silica is 3:91 at 1 kHz and 3:82 at 1 MHz [26.78], and remains approximately constant up to 5 THz [26.76]. It is possible to calculate the polarizabilities at THz and optical frequencies using (26.15) [26.79]. Figure 26.9 from Naftaly and Miles [26.73] shows the product of the THz absorption coefficient and refractive index .n˛/ as a function of frequency on a log–log scale. The solid line is a fit to (26.21) and (26.22). The fitting parameters are ˇ D 2, Kh2 D 5:5 1024 cm1 s2 , and l D 2:1 nm. The Kh2 is used instead of K for easy comparison of various glass compositions.
Terahertz Time-Domain Spectroscopy of Glasses
nα (cm –1) 10
26.3 Glass Systems
919
ε'' (ν) ×10 –3 50
ε' (ν) 4.0 Data Model ε' (ν)
40
3.9 1 30 3.8
ε'' (ν)
0.1
20 3.7 10 1 Frequency (THz)
Fig. 26.9 Frequency dependence of the product of the THz refractive index .n/ and absorption coefficient .˛/ of silica. Reprinted from [26.73], with permission from AIP publishing
The results for ˇ and l agree with those obtained by Strom and Taylor [26.32] and are consistent with the values reported in the literature [26.9, 74–77]. Figure 26.10 shows the real and imaginary parts of the dielectric constant of a silica glass calculated from transmission power and phase shift from Kojima et al. [26.69]. The BP is known to be inactive both in infrared and Raman [26.80]. THz-TDS shows only a gradual change of the real part "0 . / around the BP frequency, indicating very weak infrared activity. This is probably due to the slight distortion of SiO4 tetrahedra. However, the imaginary part "00 . / clearly shows the broad absorption around the BP frequency, demonstrating the detection of the BPs. In the damped harmonic oscillator model, the quantity "00 . /= indicates the peak at the mode frequency. The frequency dependence of "00 . /= shows the BP at 30 cm1 , in good agreement with the boson peak frequency observed by inelastic neutron scattering and hyper-Raman scattering [26.9, 79–81] constant in Raman scattering.
26.3.2 Borate Glasses Alkalies in borate glasses change the network structure, in terms of a decrease in the fraction of B3 O6 boroxol rings and appearance of pentaborate, triborate, diborate, and metaborate groups. These changes of various structural units are reflected in the composition dependence of the BP frequency [26.82, 83]. Figure 26.11 shows the real and imaginary parts of dielectric constants in 0:5Li2 O 0:5B2 O3 glass from Kojima et al. [26.69], where the BP appears at about b D 30 cm1 in the
0
3.6
20
40
60 80 Frequency (cm –1)
Fig. 26.10 Real and imaginary part of complex dielectric
constants of silica glass. Reprinted from [26.69], with permission from Elsevier ε' (ν) 8
ε'' (ν) 5
ε' (ν)
4
6 3 4
ε'' (ν) 2
2
1
0
0 10
20
30
40
50 60 Frequency (cm –1)
Fig. 26.11 Real and imaginary parts of complex dielectric constants of lithium borate glass. Reprinted from [26.69], with permission from Elsevier
imaginary part "00 . / spectrum, with corresponding step-like changes in the real part "0 . / spectrum. This strongly indicates that the dominant vibrational contribution to the BP is closely related to infrared-active motions in these glasses. The line shape of the imaginary part is very similar to the material independent
Part C | 26.3
0.01 0.1
920
Part C
Characterization of Glasses
line shape of the BPs predicted recently [26.84]. The line shapes of the BP show marked variations among glasses, suggesting that the origin of the BPs depends on the chemistry of the glasses [26.85].
(ε – 1)/(ε + 2) SF6
0.8 SK10
0.7
26.3.3 Silicate Glasses
0.6
Part C | 26.3
Table 26.1 shows the properties of silica and selected Schott glasses studied by Naftaly and Miles [26.73]. THz refractive indices of glasses are generally higher than those in the visible range, due to ionic polarization. Consequently, the glasses with ionic components will have a larger difference between their THz and optical refractive indices than silica. The Clausius–Mossotti equation (shown in (26.15)) can be used to calculate and analyze the refractive indices of the glasses. Figure 26.12 shows the ratio ." 1/=." C 2/ at 0:5 THz and at 589 nm .nD / against the glass density. The value at 0:5 THz has been chosen because in all glasses it is close to the average over the measurement bandwidth. At optical frequencies, the relationship is linear, while at THz frequencies, it is linear for all glasses except silica and Pyrex. A linear relationship implies that P=M (polarizability/molecular weight) is a constant: the value of the P=M ratio is 2:01026 g1 cm3 at 589 nm and 2:61026 g1 cm3 at 0:5 THz. Therefore, for all glasses studied except silica and Pyrex, a linear relationship between the refractive index at THz and in the visible regions is expected, as demonstrated in Fig. 26.13, where the slope is 3:3. The ionic polarizability of silica and Pyrex is lower than it is in the Schott glasses because silica contains no ionic components and Pyrex relatively few; therefore, their
SF15
SF10
BK7 B270 N-Zk7 Pyrex
0.5 SF6
Silica
SF15 SF10
0.4 0.3
SK10 Pyrex
BK7 B270
Silica
0.2
2.0
N-Zk7
2.5
Visible, 0.17 + 0.05 3.0
3.5
4.0
4.5 5.0 5.5 Density (g/cm 3)
Fig. 26.12 ." 1/=." C 2/ at 0:5 THz (brown circles) and at 589 nm .nD / (grey circles) vs. glass density of the glasses. Pyrex (81% SiO2 , 13% B2 O3 , 4% Na2 O, 2% Al2 O3 ); BK7 (70% SiO2 , 11:5% B2 O3 , 9:5% Na2 O, 7:5% K2 O, 1:5%BaO); B270 (a high-transmission crown glass—modified soda-lime glass); N-ZK7 (zinc crown glass); SF series (dense flint glasses); SK10 (dense barium crown glass). Reprinted from [26.73], with the permission of AIP publishing
dielectric constant at THz deviates from the behavior of other glasses studied. At optical frequencies, numerous studies have correlated the refractive indices and other glass properties. Duffy [26.86] has highlighted the effect of alkali network modifiers on the refractive index. Glass refractivity increases with its optical ba-
Table 26.1 Properties of glasses [26.73] Glass
Refractive Refractive Kh2 1024 ˇ (cm1 s2 ) index index at 589 nm at 0:5 THz
Silica Pyrex BK7 B270 N-ZK7 SF6 SF10 SF15 SK10
1:458 1:474 1:517 1:523 1:508 1:805 1:728 1:6999 1:623
1:962 2:105 2:514 2:570 2:508 3:558 3:214 3:080 2:911
5:5 ˙ 0:5 62 ˙ 1 180 ˙ 5 200 ˙ 5 175 ˙ 5 700 ˙ 20 430 ˙ 10 390 ˙ 10 240 ˙ 5
2:00 ˙ 0:05 1:97 ˙ 0:03 2:28 ˙ 0:05 2:07 ˙ 0:03 2:21 ˙ 0:03 2:23 ˙ 0:03 2:38 ˙ 0:03 2:42 ˙ 0:04 2:80 ˙ 0:20
Density Glass transition Glass melting Expansion coefficient (g=cm3 ) temperature, Tg temperature, Tm (measured between 20 (ı C) (ı C) and 300 ı C) (106 K1 ) 2:20 1100 1720 0:55 2:23 565 820 3:25 2:51 557 719 8:3 2:55 533 724 9:4 2:49 539 721 5:2 5:18 423 538 9:0 4:28 454 595 8:4 4:06 455 595 8:9 3:66 632 744 8:0
Pyrex (81% SiO2 , 13% B2 O3 , 4% Na2 O, 2% Al2 O3 ); BK7 (70% SiO2 , 11:5% B2 O3 , 9:5% Na2 O, 7:5% K2 O, 1:5%BaO); B270 (a high-transmission crown glass—modified soda-lime glass); N-ZK7 (zinc crown glass); SF series (dense flint glasses); SK10 (dense barium crown glass)
Terahertz Time-Domain Spectroscopy of Glasses
Refractive index at 0.5 THz 3.6
SF6
3.4
1000
3.0
SK10
SF10 SF15
2.8 2.4
B270 N-Zk7 BK7
2.2
Pyrex
SF6
SF15
SF15 BK7
SF10 BK7 B270 SK10 N-ZK7
B270
N-ZK7
100
921
Refractive index at 0.5 THz
SF6
Pyrex
Pyrex
10 Silica
2.0 1.8
3
SF10
3.2
2.6
Kh2 ×10 –24 2 (cm –1 s2)
26.3 Glass Systems
Silica
Silica
800
1000
1200
1400 1600 1800 2000 Tm (K)
Fig. 26.13 Relationship between the refractive indices at
0:5 THz and at 589 nm of the glasses. Pyrex (81% SiO2 , 13% B2 O3 , 4% Na2 O, 2% Al2 O3 ); BK7 (70% SiO2 , 11:5% B2 O3 , 9:5% Na2 O, 7:5% K2 O, 1:5%BaO); B270 (a hightransmission crown glass—modified soda-lime glass); NZK7 (zinc crown glass); SF series (dense flint glasses); SK10 (dense barium crown glass). Reprinted from [26.73], with the permission of AIP publishing
sicity and the relationship is linear for some families of glasses. Polarizability and the refractive index are closely related to bond strength and configuration. Bond configuration also affects the thermal expansion coefficient. Jewell [26.87] has studied the effect of network modifiers on glass structure and the consequent changes in the optical refractive index and thermal expansion coefficient, focusing on the relationship between the expansion coefficient and electronic polarizability. The THz refractive index has a much stronger relationship with the expansion coefficient than does the optical refractive index, as the ionic polarizability is more strongly affected by bond variation than the electronic processes. Figure 26.14 shows the absorption parameter Kh2 versus the refractive index at 0:5 THz on a log–log scale; the dashed line is a linear fit to the data. All glasses except silica conform to the expected relationship. Silica does not fit the trend in Fig. 26.14 due to lack of ionic components in the glass, which influence the ionic polarizability of the glass. For the same reason, Pyrex deviates from the linear fits in Figs. 26.12 and 26.13 from Naftaly and Miles [26.73]. Figure 26.13 shows Kh2 against Tm , where the Tm melting point values for the glasses are obtained from published data sheets. The dashed line is a linear fit to the data, which illustrates a strong relationship between THz absorption and the melting point in the silicate glasses studied. As-
Fig. 26.14 Absorption parameter Kh2 vs. refractive index
at 0:5 THz (brown circles) and melting point (grey circles) of the glasses. Pyrex (81% SiO2 , 13% B2 O3 , 4% Na2 O, 2% Al2 O3 ); BK7 (70% SiO2 , 11:5% B2 O3 , 9:5% Na2 O, 7:5% K2 O, 1:5%BaO); B270 (a high-transmission crown glass—modified soda-lime glass); N-ZK7 (zinc crown glass); SF series (dense flint glasses); SK10 (dense barium crown glass). Reprinted from [26.73], with the permission of AIP publishing
suming Arrhenius behavior of glass viscosity ./, the slope of ln with 1=T indicates the bond strength, which is roughly proportional to Tm , the melting temperature of glass [26.88, 89].
26.3.4 Tellurite Glasses Tellurite glasses [26.90] have been studied over several decades for various optical applications. Structural aspects of tellurite glasses have been characterized using x-ray [26.91–93] and neutron [26.94] diffraction, extended x-ray absorption fine structure [26.95, 96], and several spectroscopic techniques, Fourier transform infrared (FTIR) [26.93, 97] Raman [26.98–105] nuclear magnetic resonance (125 Te NMR) [26.106–109] and Mössbauer [26.110]. Effects of alkali [26.111–114] and alkaline earth [26.113] on tellurite structural units of these glasses have been reported in the literature. Recent work [26.115] shows that WO3 acts as a network former and Li2 O acts as a network modifier by breaking the network structure. With the equimolar substitution of TeO2 by WO3 C Li2 O, the glass network becomes more connected and the number of bridging oxygen atoms increases. This increases the average cross-link density. The mixed alkali effect reported in this system [26.116] shows that the structural units of TeO4 and
Part C | 26.3
1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 Refractive index at 589 nm
922
Part C
Characterization of Glasses
b) Absorption coefficient (cm–1)
a) Refractive index 5.50
34 33
5.40
32 5.30
31 30
5.20
29 5.10
28 27
5.00
26 4.90
Part C | 26.3
4.80
25 0
5
10
15
20
25 x (mol%)
24
0
5
10
15
20
25 x (mol%)
Fig. 26.15a,b THz properties as a function of glass composition: (a) Refractive index at 0.5 THz vs. tungsten content and (b) Absorption coefficient at 0.5 THz vs. tungsten content
b) Absorption coefficient (cm–1)
a) Refractive index
50
5.20
48 5.15
46 44
5.10
42 5.05
40 38
5.00
36
4.95
34
4.90
30
32 0
2
4
6
8 x (mol%)
c) Crystallization peak (°C)
0
2
4
6
8 x (mol%)
2
4
6
8 x (mol%)
d) Tg (°C)
490
310 308
485
306
480
304
475
302
470
300 298
465
296
460
294
455
292
450
290
0
2
4
6
8 x (mol%)
0
Fig. 26.16a–d Mixed alkali effect, thermal stability, and THz properties in 80TeO2 -10WO3 -(10 x)Li2 O-xNa2 O glass system with x D 0, 2, 4, and 6: (a) Refractive index at 0.5 THz, (b) Absorption coefficient at 0.5 THz, (c) Crystallization peak, and (d) Tg as a function of Na2 O content (mol%)
Terahertz Time-Domain Spectroscopy of Glasses
Refractive index n 30 2.9
32
As (at.%) 34 36 38
0.63280 μm 1.5473 μm 3.3910 μm
2.8
40
Vm (cm 3/mol) 42 16.0
5.4380 μm 10.591 μm 220 GHz
15.9
2.7 2.6
15.8
2.5 15.7
2.4 2.3
15.6 2.2
26.3.5 Chalcogenide Glasses 2.1
THz properties of selected chalcogenide glasses are briefly summarized in this section. Kang et al. [26.118] have used THz-TDS to measure optical and dielectric properties of Ge30 As8 Ga2 Se60 , Ge35 Ga5 Se60 , and Ge10 As20 S70 glasses. The data fit the Sellmeier equation well, demonstrating compositional dependence of phonon modes in chalcogenide glasses. The ˇ value of these glasses is 2 [26.112]. Parrott et al. [26.119] have developed a new approach that used two samples of different thicknesses instead of a reference waveform to extract absorption coefficients at low frequencies and validated the approach with THz-TDS measurements of As2 S3 . We have recently studied optical properties and structural aspects of Asx S1x glasses beyond visible and infrared regions up to terahertz frequencies. A series of annealed bulk Asx S1x glasses .x D 0:30:42/ have been processed and their refractive index determined at THz, IR, and visible frequencies using a combination of a quasi-optical BWO spectrometer for THz measurements and a prism coupler for visible and IR measurements [26.120]. The results show that the refractive index, at all frequencies, increases with arsenic composition up to 40 at:% and then decreases with more arsenic, as shown in Fig. 26.17 [26.121]. The vertical dashed line in the figure shows the optimally constrained coordination composition for As-S. For all compositions, the refractive index at 0:2 THz is larger than the visible and infrared values. A simple model based on atomic refractivity and molar volume cannot account for the reduction in refractive index above the percolation threshold. Additional datasets extending well into THz frequencies over a range of compositions and hri and analysis are needed to develop an improved model to explain this
923
2.30
2.32
2.34
2.36
2.38
2.24
2.42 r
15.5
Fig. 26.17 Variation of refractive indices with arsenic con-
tent and average coordination number hri. Brown triangles connected by a line for guidance show the molar volume as quantified on the right axis. The vertical line shows the optimally constrained As-S composition with a hri value of 2:24, beyond which the trend of the curves reverses. Adapted from [26.121], with permission from Elsevier
behavior. The arsenic level produces a minimum in the molar volume, as supported by density and x-ray diffraction (XRD) measurements. Index dispersion (described by Ed ) increases linearly as a function of arsenic content and of the average covalent coordination number, hri. The experimental optical gap decreases with increasing arsenic content as reported in the literature. These glasses are transparent out to at least 0:5 THz. Our results suggest the structural models can be extended to explain optical properties in the THz region.
26.3.6 Glass Composites We used THz-TDS at T-Lab in Alfred University to characterize hydroxyapatite .Ca10 .PO4 /6 .OH/2 ; HA)glass composites to assess their bioactivity in vitro. We summarize our THz-TDS data of different morphological aspects of the HA-glass composites on exposure to simulated body fluids (SBF) in this chapter. We synthesized the HA powder with a Ca W P ratio of 1:667, produced at a synthesis temperature of 25 ı C, based on a chemical precipitation method. The solutions were then filtered under vacuum. The filter cake was then dried in a fan-assisted oven at 85 ı C for 20 h. We prepared our target glass formulation, 0:05CaO-
Part C | 26.3
TeO3 are connected weakly with each other. Therefore, the rearrangement kinetics of these units affect the alkali mixing during heating. Dynamic and calorimetric measurements [26.117] have shown that the fragility of the melts in this system exhibit a minimum in the middle of the mixed-alkali range. We present our preliminary results collected with a selected tellurite glass system at T-Lab in Alfred University. We used the glass composition, 80TeO2 -(20x)Li2 O-xWO3 with x D 5, 10, 15, and 20 mol%, to generate results shown in Fig. 26.15. We used the glass composition, 80TeO2 10WO3 (10x)Li2 O-xNa2 O with x D 0, 2, 4, and 6, to generate the results shown in Fig. 26.16. Our results show that the mixed alkali effect extends to THz frequencies, suggesting that the structural effects scale with frequency of the THz waves.
26.3 Glass Systems
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Part C
Characterization of Glasses
a) Refractive index n
b) Refractive index n
c) Refractive index n
12.5
12.5
12.0
12.0
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0
10 20 30 Glass content (vol.%)
10.5
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0
10 20 30 Glass content (vol.%)
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0
10 20 30 Glass content (vol.%)
Part C | 26.4
Fig. 26.18a–c Average measured refractive index for HA and HA-glass composites at: (a) 0:6 THz, (b) 1:0 THz, and (c) 1:4 THz (after [26.122])
0:12TiO2 -0:17Na2 O-0:28ZnO-0:38SiO2 , by mixing appropriate amounts of analytical-grade reagents, melting at 1450 ı C for 1 h in a platinum crucible, and shockquenching into water. The resulting frit was dried, ground, and sieved to retrieve a glass powder with a maximum particle size of 45 m. Green bodies were obtained by mixing the HA powder with incremental glass additions of 10 to 30 wt%. The dry mixtures were uniaxially pressed into pellets using a 15 mm diameter stainless steel die at 200 MPa. The discs were sintered at a heating rate of 5 ı C min1 to a maximum temperature of 560 ı C with a hold time of 2 h, and then allowed to cool in the furnace. Figures 26.18 and 26.19 show some of our results. The oscillations in Fig. 26.19 are due to artifacts for frequencies less than 0:2 THz and minor changes in the surface conditions of the samples during soaking in SBF. Refractive index and dielectric constant values in THz frequencies provide a reliable determination of glass content of these composites [26.122]. In addition, THz-TDS was used to track morphological changes in HA during simulated body fluid (SBF) incubation. Our
Refractive index n 12.0 11.6 11.2
Before soaking
10.8 10.4 10.0 1 day in SBF 1.95 7 days in SBF 1.90
0.2
0.4
0.6
0.8
1.0
1.2 1.4 Frequency (THz)
Fig. 26.19 Refractive index vs. frequency for different soaking periods of time in SBF (after [26.122])
results demonstrate that the THz-TDS can be a promising non-destructive tool for evaluating these composites and tracking their degradation in service.
26.4 Summary THz-TDS has proven to be a versatile as well as a useful tool for studying structure and properties of glasses. The THz refractive index generally increases with the thermal expansion coefficient of the glasses, which depends on both the bond strength and configuration. A linear relationship observed between the Clausius–Mossotti ratio and the glass density and between the THz and optical refractive indices in glasses is valuable for prediction of the THz properties of glasses. Glass structure-THz property relationships
show promise for designing and processing of passive and active optical glass components with desired tolerance and performance, leading to integrated THz photonics. Acknowledgments. The author thanks the support from the Energy Conversion Initiative, Pacific Northwest National Laboratory (PNNL). The author acknowledges THz measurements performed by Mr. Rob Koch (Alfred University), peer review by Dr. John
Terahertz Time-Domain Spectroscopy of Glasses
S. McCloy (Washington State University, Pullman, WA), some of the illustrations by Mr. Mike Perkins (PNNL), and suggestions from Professor Robert E. Miles (University of Leeds, UK). The author also
References
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acknowledges support from Inamori Foundation and Kazuo Inamori School of Engineering at Alfred University. PNNL is operated for the U.S. Department of Energy by Battelle under Contract DE-AC05-76RL01830.
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T. Nishida, M. Yamada, H. Ide, Y. Takashima: Correlation between the structure and glass transition temperature of potassium, magnesium and barium tellurite glasses, J. Mater. Sci. 25, 3546– 3550 (1990) K.J. Rao, M.H. Bhat: Investigation of lithium chloride–lithium borate–tellurium dioxide glasses: An example of complex anionic speciation, Phys. Chem. Glasses 42, 255–264 (2001) M.H. Bhat, M. Kandavel, M. Ganguli, K.J. Rao: Li+ ion conductivities in borotellurite glasses, Bull. Mater. Sci. 27, 189–198 (2004) M. Arnaudov, V. Dimitrov, Y. Dimitriev, L. Markova: Infrared spectral investigation of tellurites, Mater. Res. Bull. 17, 1121–1129 (1982) R. Akagi, K. Handa, N. Ohtori, A.C. Hannon, M. Tatsumisago, N. Umesaki: High-temperature structure of K2 O–TeO2 glasses, J. Non-Cryst. Solids 256/257, 111–118 (1999) M. Çelikbilek, A.E. Ersundu, S. Aydin: Preparation and characterization of TeO2 –WO3 –Li2 O glasses, J. Non-Cryst. Solids 378, 247–253 (2015) T. Komatsu, T. Moguchi, Y. Benino: Heat capacity changes and structural relaxation at glass transition in mixed-alkali tellurite glasses, J. NonCryst. Solids 222, 206–211 (1997) K. Putz, P.F. Green: Fragility of mixed alkali tellurites, J. Non-Cryst. Solids 337, 254–260 (2004) S.B. Kang, M.H. Kwak, B.J. Park, S. Kim, H.-C. Ryu, D.C. Chung, S.Y. Jeong, D.W. Kang, S.K. Choi, M.C. Paek, E.-J. Cha, K.Y. Kang: Optical and dielectric properties of chalcogenide glasses at terahertz frequencies, ETRI Journal 31(6), 667–674 (2009) E.P.J. Parrott, J.A. Zeitler, L.F. Gladden, S.N. Taraskin, S.R. Elliott: Extracting accurate optical parameters from glasses using terahertz time-domain spectroscopy, J. Non-Cryst. Solids 355, 1824–1827 (2009) S.K. Sundaram, B.J. Riley, J.V. Crum: Terahertz transmission spectroscopy of chalcogenide glasses. In: Proc. IEEE IRMMW-THz, Pasadena (2008) J.S. McCloy, B.J. Riley, S.K. Sundaram, H.A. Qiao, J.V. Crum, B.R. Johnson: Structure-optical property correlations of arsenic sulfide glasses in visible, infrared, and sub-millimeter regions, J. NonCryst. Solids 356, 1288–1293 (2010) C. Yatongchai, A.W. Wren, S.K. Sundaram: Characterization of hydroxyapatite-glass composites using terahertz time-domain spectroscopy, J. Infrared Millim. Terahertz Waves 36, 81–93 (2015)
S. K. Sundaram Inamori School of Engineering Alfred University Alfred, NY, USA [email protected]
Dr. S. K. Sundaram is the Inamori Professor of Materials Science and Engineering at Alfred University. He is also the Chair of the Mechanical and Renewable Energy Engineering Programs. Before joining Alfred University in 2011, he was a Chief Materials Scientist at Pacific Northwest National Laboratory (PNNL). He joined PNNL after earning his PhD from School of Materials Science and Engineering, Georgia Institute of Technology in 1994. In the past 25 years, he has made major contributions in the areas of millimeter/terahertz (THz) wave science and technology, ultrafast materials science and engineering, and extreme/additive materials processing.
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27. Electron and Ion Beam Characterization of Glass
Jennifer McKinley 27.1.3 27.1.4 27.1.5 27.1.6 27.1.7 27.1.8
27.1.9
27.1.10 27.1.11 27.2 27.2.1 27.2.2
Electron Beam Techniques................ Electron Beam–Matter Interactions .... Scanning Transmission Microscopy (SEM) and Transmission Electron Microscopy (TEM): Imaging and Quantitative Analysis ....
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Glass is a material that is studied in a broad range of disciplines and is used in both high-tech products and artistic endeavors. Depending on the industry, glass materials may be produced by melting, sol–gel, thermally grown methods, or vapor deposition [27.1]. The imaging and characterization of these insulating glass materials for elemental composition or atomic structure often requires expertise that is highly specific to the field of study. For example, a geologist may use analysis tricks that are unknown to an integrated circuit device physicist, or potential errors that are known to arise with sample preparation or particular analysis conditions may not be easily discovered by an analyst in another discipline. Understanding some basic principles about
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Conclusions .....................................
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References...................................................
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27.2.5 27.3
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Ion Beam Techniques....................... Ion Beam–Material Interactions ........ Secondary Ion Mass Spectrometry ................................... SIMS Applications ............................. Rutherford Backscattering Spectrometry ................................... Complementary and Combination Ion Beam Techniques .............................
27.2.3 27.2.4 27.1 27.1.1 27.1.2
Scanning Electron Microscopy ............ Transmission Electron Microscopy ...... Scanning Transmission Electron Microscopy (STEM)............................. Environmental SEM/TEM (ESEM/ETEM) .. Electron Beam Instrument Imaging Examples......................................... Quantitative and Qualitative Analytical Techniques Using Electron Beams ....................... Electron Probe Microanalysis (EPMA): Energy-Dispersive Spectroscopy (EDS/EDX) and Wavelength-Dispersive Spectroscopy (WDS)........................... Electron Energy Loss Spectroscopy ...... Electron Beam Quantification Applications ....................................
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the beam–matter interactions, strengths and weaknesses of the analytical method, signal-to-noise ratios, matrix effects, charge buildup, and how to obtain accurate results within the limitations of the analytical technique is crucial to the investigation of these materials [27.2]. The fundamentals of the analytical instrumentation are similar for all the techniques to be described in this chapter. A primary beam of ionic particles or electrons is directed onto a sample, interacts with the materials, and causes backscattering of the incident beam or the emission of secondary particles. Often, several processes occur at once, and a given analytical technique focuses on one (or more) of these to provide information about the materials. The information gained
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_27
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Scientists and engineers have available to them powerful qualitative and quantitative analytical techniques for the analysis of materials. Specifically, ion and electron beam instrumentation can deliver a wealth of information about a material like glass, provided that the limitations of the measurements for insulators and materials without long-range atomic order are well understood. This chapter brings together expertise from the fields of geology and mineralogy, semiconductors, and glass science to provide an overview of how ion and electron beams interact with glass materials. All these disciplines require accurate analytical techniques, and an incomplete understanding of interactions, interferences, and calibration can lead to inaccurate conclusions. The aim is to encourage the reader to be aware of the scientific principles and constraints of the instrumentation in the analysis of glass materials, and to be vigilant in interpreting the results.
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is typically elemental composition as well as identification of how that element concentration varies as a function of depth into the material or across the material within a given region. Sometimes matrix analysis (determination of the major components of the material with atomic or mass percentages > 1%) is required, and often trace analysis of concentrations down to parts per trillion is possible. In general, qualitative techniques utilize the term spectroscopy, while quantitative methods incorporate spectrometry in the method name, but this is not a strict definition across different fields of study. Most techniques described here allow for tight focus of the primary beam such that electron or ion imaging and element mapping is possible. Selection of the appropriate technique for a particular analysis will depend upon the required sensitivity, spatial resolution, and whether elemental or molecular information
is needed. The speed, cost, and destructive nature of the method is also important. To assist the selection of ion and electron beam elemental analysis techniques, Table 27.1 compares the analytical techniques discussed in this chapter [27.3–5]. Investigations of glass with charged beam techniques certainly have challenges, but the analysis community has continued to be inventive, with everything from practical suggestions to in-depth studies of the underlying physics and chemistry principles in order to further understand how these materials behave when impacted by charged particles. This chapter includes discussions of selected analysis techniques, and specific material applications are included to assist in the determination of analysis parameters and sample preparation for similar investigative studies of insulating glass materials.
Table 27.1 Comparison of selected electron and ion beam analysis techniques (includes information from [27.3–5])
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Electron beam techniques Energy-dispersive spectroscopy (EDS) Also known as Energy-dispersive x-ray spectroscopy (EDX) Wavelengthdispersive x-ray spectroscopy (WDS) Electron energy loss spectroscopy (EELS)
Secondary ion mass spectrometry (SIMS)
Detectable elements B to U
Detection limits 0:11 at:%
Lateral resolution 0:3 m
Depth resolution 0:53 m
Comments
Elements with atomic mass greater than or equal to Na Elements with atomic mass greater than or equal to B H to U, all isotopes
100 ppm
0:3 m
0:53 m
Characteristic x-rays detected for elemental analysis. Lower detection limits than EDS/EDX but slower and not available on common instruments. Typically part of electron probe microanalysis (EPMA). Not destructive.
12 at:% with standards, up to 20 at:% without standards
0:1 nm (on probecorrected systems)
Thickness of specimen
Characteristic change in energy of electron beam measured to determine electronic and atomic structure and local chemical concentration. Typically a technique available on imaging microscopes (SEM/TEM/STEM). Non-destructive.
ppm–ppb
1000 nm (imaging mode)
0:5 nm
110 at:% for low atomic number (Z) elements, up to 100 ppm for high Z elements 0:1100 ppm, depending on whether surface or bulk analysis is performed
14 mm (1 m in specialized equipment)
230 nm
Detection of secondary ions removed during sputtering of the sample to determine composition of trace-level impurities. Sample material removed during a sputtering process, although low-impact energy surface measurements may sustain little measurable damage to the point of being considered non-destructive. Detection of backscattered high-energy particles, typically He, to determine crystalline structure and concentration of dopants and impurities at specific depths within the upper 12 m of the sample. Radiation and He implantation damage the sample, but is considered non-destructive.
5 m to 2 mm
10 m
Rutherford Li to U backscattering spectrometry (RBS)
Particle-induced x-ray emission (PIXE)
Li to U
Characteristic x-rays detected for elemental analysis. Typically a technique available on imaging microscopes (SEM/TEM/STEM). Light element analysis (even to Be) improved with advances in hardware and software. Not destructive.
Detection of characteristic x-rays during irradiation with high-energy particles. Fast analysis for many elements. Background x-ray radiation lower than electron-induced emission techniques like EDS, WDS, or x-ray fluorescence (XRF). Non-destructive.
Electron and Ion Beam Characterization of Glass
27.1 Electron Beam Techniques
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27.1 Electron Beam Techniques an electric potential difference of 1 V. Elastic scattering, due to interactions of the electrons with nuclei, changes the direction of the original electrons, with minimal energy loss. Inelastic scattering, due to interactions with valence and core electrons, results in energy loss with minimal change in direction. The combined result of these interactions is a broadened interaction volume within the material. Figure 27.2 summarizes the types of particles that result from the
Primary electrons
1 nm Auger electrons Secondary electrons
5–50 nm
Backscattered electrons (BSE)
27.1.1 Electron Beam–Matter Interactions Re
The interaction of an electron beam with a material, and its subsequent detectable signals with related characterization techniques, is shown in Fig. 27.1. An incident electron beam (with energy Ei ) interacts with a sample and the electrons are reflected, absorbed, transmitted, or emitted. X-rays and other radiation may also be emitted as a result of electronic transitions. These electrons and photons are then detected and provide information about the sample topography, crystallography, chemical composition, or other physical structure details. When electrons interact with a material, they lose energy along the way by inelastic and elastic scattering. This energy is measured in electron volts, defined as the energy change of an electron moving across Emission • Auger electron spectroscopy (AES) • Cathodoluminescence (CL) • Electron microprobe analysis (EMPA)
Absorption • Electron beam induced current (EBIC)
Ei
Characteristic x-rays
Continuum x-rays BSE resolution X-ray resolution
Fig. 27.2 Range and spatial resolution of electrons and x-rays for an electron beam impacting a material (after [27.4])
Reflection • Scanning electron microscopy (SEM) • Low energy electron diffraction (LEED) • High energy electron diffraction (HEED) • Surface potential, voltage contrast
Transmission • Transmission electron microscopy (TEM) • Electron energy loss spectroscopy (EELS)
Fig. 27.1 Electron beam
characterization techniques (after [27.4])
Part C | 27.1
The following techniques use an electron beam to interact with the sample and either image the surface or perform elemental analysis. The ability to view the sample morphology and gain elemental information simultaneously leads to powerfully informative analyses that make these instruments essential to materials research labs and commercial manufacturing. Specific advances and insights in the areas of insulator analyses are highlighted in this section. The descriptions below are divided into imaging instrumentation in Sects. 27.1.2–27.1.6, followed by the complementary elemental analysis techniques in Sects. 27.1.8– 27.1.10. Both scanning electron microscopy (SEM) and transmission electron microscopy (TEM) are covered, with additional information about instrument configurations that combine these techniques (scanning transmission electron microscopy—STEM) or add capability to them (environmental scanning electron microscopy/environmental transmission electron microscopy—ESEM/ETEM).
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Fig. 27.3 Scanning electron mi-
croscopy schematic (after [27.4]) Electron gun Condenser aperture Condenser lens Scanning coils Objective lens Objective aperture
X-ray photons
Backscattered electrons
Detector
Display
Secondary electrons
Absorbed electrons
Part C | 27.1
To turbomolecular pump
interaction volume of the electron beam with range Re with the sample, each of which can be utilized in a characterization technique, and are specifically described in more detail in the electron instrumentation sections to follow. The shape of this volume depends upon the atomic number Z of the sample. For lowZ samples .Z 15/ it is more teardrop-shaped, for 15 < Z < 40 the shape becomes more spherical, and for Z 40 the shape approaches hemispherical. These shapes of the interaction volume of electron trajectories have been confirmed by observing the physical destruction of polymer materials impinged with an electron beam and with Monte Carlo methods, which utilize computational techniques to obtain probability distributions [27.4].
27.1.2 Scanning Transmission Microscopy (SEM) and Transmission Electron Microscopy (TEM): Imaging and Quantitative Analysis Transmission and scanning electron microscopes provide imaging over a wide magnification range. Qualitative and quantitative analysis is available with x-ray spectrometry on both instruments and electron spectrometry on TEM. Spatial resolution down to the nanometer scale and quantitative analysis capabilities covering nearly the entire periodic table make these techniques exceptionally versatile [27.6].
27.1.3 Scanning Electron Microscopy Scanning electron microscopy (SEM) provides the user with a magnified view of the surface of the sample. Figure 27.3 shows a schematic of an SEM instrument [27.4]. The electron source may emit electrons by a thermionic emission filament (tungsten or lanthanum hexaboride, LaB6 ) or by a field emission atomically sharp tip (hot or cold). The beam is defocused and focused through a series of magnetic lenses within a vacuum. The focused electron beam is scanned over the surface of the sample, interacts with the sample, and allows images or composition data to be generated by detecting reflected or scattered electrons: secondary electron images (SEI), backscattered electron images (BEI), or elemental x-ray maps. The resolution of the instrument is close to a few nanometers, with magnifications of several 100 000 [27.3]. SEM Imaging Secondary electron imaging is the principle of the detection of electrons that have energies below 50 eV. These secondary electrons have lost their original energy by undergoing inelastic scattering with atomic electrons and are emitted from the first few nanometers from the surface of the sample. Contrast for these images is realized because secondary electron yield is highest (i. e., brightest) when the beam is at normal incidence to the sample; therefore, sample topography
Electron and Ion Beam Characterization of Glass
Artifacts and Charging for SEM Very little sample preparation is required for the analysis of electrically conductive and vacuum-compatible samples using a SEM. For insulating materials like glass, static charging will occur at the surface when the electron beam interacts with the sample, and dynamic charging can occur within the sample itself through the creation of electron–hole pairs. The process of charging changes the surface potential of the sample, creating high electric fields that cause the primary beam to drift or secondary electrons to deflect from the detector. The result of charge buildup of the sample is an inability to image the sample or observation of image drift, degradation, or areas of contrast change. This is a simplistic explanation for complicated electrostatic-electrokinetic mechanisms, and further treatment of the intricacies of the charging phenomena is available in the literature [27.7]. There are a few well-known methods to mitigate charging to allow insulating samples to be imaged. These include coating with a thin (220 nm) conductive layer (typically gold, palladium, silver, chromium, iridium, or carbon) or using low primary beam voltages [27.8]. Other techniques like sample-biasing (applying a voltage to the sample holder to dissipate accumulated charge buildup) and mounting the sample with carbon tape or silver paint may be used [27.4].
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27.1.4 Transmission Electron Microscopy Transmission electron microscopy (TEM) provides higher spatial resolution than SEM: 106 magnification can be achieved with high-voltage instruments. In order to transmit electrons through the sample, the area to be imaged must be less than 100-nm thick. Figure 27.4 illustrates the interaction of the electron beam with a TEM specimen, highlighting the comparison with the typical SEM interaction volume. These specimens are typically prepared by ion milling, microtome, or a focused ion beam (FIB) [27.4]. Although the process of sample preparation and locating the area of interest is extensive and can require several hours, TEM has the ability to provide immense information at the atomic level, and additionally offers compositional analysis techniques available during imaging, described in Sects. 27.1.9 and 27.1.10. Figure 27.5 shows a schematic of the TEM instrument. The electrons that are transmitted and forward-scattered form either a magnified image in the image plane or a diffraction pattern, providing additional chemical information, on the back focal plane. Figure 27.6 details the electron ray paths for scattered and unscattered electrons. TEM Imaging Modes The three types of imaging modes available are brightfield, dark-field and high-resolution microscopy. Detecting only the transmitted electrons, by blocking all Electron beam SE and BSE
Characteristic x-rays
TEM interaction volume
Equivalent SEM interaction volume
Elastically scattered electrons
Transmitted beam (unscattered)
Inelastically scattered electrons
Fig. 27.4 Electron beam–sample interaction in the TEM (after [27.9])
Part C | 27.1
with features that are at different angles relative to the incident beam will have an altered yield of secondary electrons, showing areas that are darker in comparison with the higher-yield areas. Higher-energy electrons, which have retained a great deal of their original energy by undergoing elastic scattering with the atomic nucleus, exit the sample at energies of greater than 50 eV and are the basis of backscattered electron imaging. Since these backscattered electrons come from a greater depth within the sample, the lateral resolution of these images is not as good as those of the secondary electron images. Contrast here is dependent on the chemical composition (known as the Z-contrast) of the sample: the higher the atomic number, Z, the more likely that the electrons will be able to be emitted from the sample. Areas of the sample with a higher atomic number will appear brighter than lower Z regions. When the primary electron beam interacts with the sample atom and a core electron is ejected, the excited atom will emit an x-ray with an energy (or wavelength) that is characteristic of the element. This signal can be separated to allow for chemical mapping images. Additional information on compositional analysis based upon these electron-imaging techniques is described in more detail in Sects. 27.1.2–27.1.6 [27.1, 3, 4].
27.1 Electron Beam Techniques
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Electron source
Incident electron beam Pre-field of the objective lens
Condenser I
Specimen
Reflecting planes
θ
Condenser II 2θ
Secondary electron detector
Objective aperture
Backscattered electron detector X-ray detector
Transmitted beam
Post-field of the objective lens Diffracted beam Back-focal plane of the objective lens
Specimen
Back focal plane
Part C | 27.1
Projector lens to control detector collection angle
Selected area aperture
Transmitted electron detector (bright field) Annular detector for scattered electrons (dark field)
Screen Electron energy loss spectrometer
Fig. 27.5 TEM schematic (after [27.4])
diffracted beams by an objective aperture, results in the formation of bright-field images. Dark-field images are obtained with one or more specific diffracted beams that have interacted with the sample, providing useful information about the sample’s crystal structure or precipitates. High-resolution TEM (HRTEM or HREM) is made possible by allowing both the transmitted beam and a diffracted beam to combine to form an interference image, and individual columns of atoms can be visualized. Image contrast in bright-field and dark-field is mostly due to diffraction-contrast, where crystalline materials show variations in diffraction intensity, and is a result of coherent elastic scattering of the periodic atomic arrangement. In amorphous materials, where the scattering centers are not periodic, masscontrast is observed, and locations of high atomic number will scatter electrons more efficiently than areas of low Z. Consequently, the material will appear darker in high-Z phases. At high magnifications, the periodic fringes from the difference in phase of the transmitted and diffracted electrons give rise to phase contrast.
Image plane of the objective lens
Fig. 27.6 Schematic representation for the ray paths be-
neath the TEM samples (after [27.4])
TEM Diffraction Mode In addition to the imaging modes, the TEM can be operated in diffraction mode, providing selected area diffraction (SAD) of specified areas at nanometer scale by inserting an aperture into the image plane of the objective lens. The diffraction image patterns produced by this mode provide crystallographic information about the sample. In crystal materials, the images are made up of a regular array of reflections, called spot patterns. In amorphous materials with no long-range order, the electron diffraction pattern will appear as diffuse concentric rings [27.3]. Artifacts and Charging for TEM The mechanisms for charging that occur in TEM samples are similar to those in SEM samples, and in addition to severe image degradation, distortion of the electron diffraction pattern in crystalline materials or even rupture of the thin sample may be experienced. Techniques that are effective in mitigating charging in SEM samples, such as coating, may not always be useful in TEM analysis, due to interference of the coating material with diffraction patterns or high-resolution images. Other methods for analysis improvement include supporting thin samples by carbon support film medium, removing ion-milled or focused ion beam
Electron and Ion Beam Characterization of Glass
27.1 Electron Beam Techniques
ample of what image distortion looks like and some creative methods to overcome charging.
27.1.5 Scanning Transmission Electron Microscopy (STEM)
Application: Observation of the Structure of Mesoporous Silica with FE-SEM Mesoporous silica is a synthesized amorphous material that has a highly ordered structure that contains sub-nanometer pores with a large internal surface area. Because of these attributes, this material has attracted interest for applications such as drug delivery and biosensors [27.15]. Due to the high porosity and insulating nature of the material, it can experience significant charging in an electron microscope plus collapse and damage from the electron beam. Coating these samples does not work, since the original nano-structure would be obscured by the deposited particles. Combining low-voltage imaging with beam deceleration that lowers the electron impact energy on the sample by applying a voltage bias to the holder, these materials have been successfully imaged at high resolution in a field emission SEM (FE-SEM), providing direct observation of the intricate nano-pores. Figure 27.7 highlights the differences in image quality with and without beam deceleration [27.15].
The principles of scanning and transmission electron microscopy can be combined in a technique called scanning transmission electron microscopy (STEM), which results in improved spatial resolution over SEM instruments and the ability to resolve secondary and backscattered electron signals for chemical analysis, which cannot typically be correlated in TEM instruments. Simultaneous high-spatial-resolution images with detailed compositional analysis make this type of instrument a highly versatile and powerful tool for the analytical lab. There are different ways a STEM instrument can be configured, and recent developments continue to advance this technique to highlight strengths such as speed or additional resolution [27.3, 11].
27.1.6 Environmental SEM/TEM (ESEM/ETEM) Researchers in instrument design persist in efforts to mitigate time-consuming sample preparation, improve charge buildup artifacts, and conduct experiments that allow for observation of material changes under realistic conditions. First, in order to maintain a focused electron beam, high-vacuum conditions are required for both SEM and TEM, and substantial sample preparation is typically required for samples that would outgas and cause contamination of the chamber or electron beam source. Next, insulating materials may not be able to dissipate electron charge, as described above, which can degrade imaging quality. The technique known as environmental scanning (or transmission) electron microscopy (ESEM or ETEM) uses differential pumping to maintain higher-vacuum conditions in the area of the electron source, while allowing lower-vacuum conditions near the sample. Near the sample, water vapor (or other gas) is introduced and, through interactions with the primary electron beam and secondary electrons, forms positive ions, which assist in charge neutralization of the sample surface. Glass samples that would typically require extensive sample preparation in order to eliminate charging can be examined without the need for coating [27.12–14].
27.1.8 Quantitative and Qualitative Analytical Techniques Using Electron Beams Some of the most important material analysis techniques rely on the characterization of x-rays emitted after a surface is impacted with electrons. As was described in Sect. 27.1.1, when materials are impacted with a primary electron beam, electrons and x-rays are produced. The electrons that are known as secondary and backscattered electrons are differentiated by their energies, shown in Fig. 27.1. Characteristic x-rays, the unique transition energies released after the return of an ionized atom to its ground state following impact by this primary electron beam, may be used to obtain chemical information. Elemental identification on a microscale has been a vital tool in characterization techniques since the 1950s [27.16]. Descriptions of energy-dispersive spectrometry (EDS), wavelength-dispersive spectrometry (WDS), and electron energy loss spectroscopy (EELS) follow.
27.1.7 Electron Beam Instrument Imaging Examples
27.1.9 Electron Probe Microanalysis (EPMA): Energy-Dispersive Spectroscopy (EDS/EDX) and Wavelength-Dispersive Spectroscopy (WDS)
The main problem arising with sample charging is distortion of the electron image. This can manifest as no image, blurry images, or distortion. Below is one ex-
When an electron bombards a sample, characteristic x-rays, with energies (or wavelengths) that correspond to the originating element, are emitted. This principle is
Part C | 27.1
amorphous damage layers by plasma cleaning, or lowering the electron gun bias level [27.10].
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a)
b)
150 nm
150 nm
Part C | 27.1
the basis for the technique called electron probe microanalysis (EPMA). An EPMA is typically a dedicated instrument capable of performing chemical analysis using either energy-dispersive spectrometry (EDS) or wavelength-dispersive spectrometry (WDS), depending upon the detector used. The detector in an EDS (also known as EDX, see Table 27.1) system is able to register all the x-rays (0:120 keV) generated from the sample, and the analysis can be completed in minutes. Note that in addition to the characteristic x-rays generated, there are background x-rays known as continuum x-rays (Fig. 27.2) or Bremsstrahlung, that are produced as the beam electrons lose energy within the Coulombic field of the sample material’s atoms. This background radiation overlaps the energies of the characteristic x-rays, and will limit the sensitivity of the measurement. The detection system in WDS analyzes each element’s characteristic x-ray wavelength individually (each peak that is resolved to the full width at half maximum, or FWHM, may be on the order of 10 eV), allowing for high-resolution analysis, although with a factor of 10 greater acquisition time than EDS (WDS analyses may require several hours) [27.8]. A spectrum with peaks corresponding to the intensities of characteristic x-ray energies is the output of the analysis, as shown in Fig. 27.8. Quantification Methodology Comparing the unknown sample constituent to a known standard measured under similar conditions of beam energy, dose, and detector efficiency allows the analyst to perform quantitative analysis. The methodology of the k-ratio protocol, developed by Castaing in 1951 [27.16], compares the intensity of the emitted x-ray signal I of the element of interest in an unknown sample to the intensity in a known-composition sample (usually a pure metal) to arrive at a k-value kD
Iunknown : Istandard
(27.1)
Fig. 27.7a,b FE-SEM image of SBA-15 (Santa Barbara amorphous-type material-15) powder: improvement in image quality with beam deceleration technique: (a) without beam deceleration and (b) with beam deceleration. Reprinted from [27.15]. Copyright 2010, with permission from Elsevier
Intensity (cps) 10 000 Si Kα 9000 8000 7000 6000 Bi Mα
5000 4000
Fe Kα Dy L α
3000 Bi L α Ga Kα Bi Lß
2000 1000 0
0
2
4
6
8
10
12
14
16 18 20 Energy (keV)
Fig. 27.8 EDS spectrum showing x-ray peak identification
(after [27.4])
Every sample will have additional matrix interactions that affect the intensity of the detected x-rays, and these must be taken into account when converting these intensities into concentrations. A mixture of empirical and theoretical methodology, known as ZAF correction, allows the well-understood physics of these interactions within a material after electron beam bombardment to be factored into the concentration calculation. This correction factor is applied as Cunknown D kZAFc Cstandard ;
(27.2)
where C is the concentration in the unknown and standard, k is the k-value, and ZAFc are the correction factor variables. The electron scattering and associated energy loss is a function of atomic number Z, the loss due to x-ray absorption within the sample is A, the generation of low-energy x-rays or fluorescence is F, and the continuum x-rays are accounted for by c. Concentrations can be determined for both major and minor constituent elements in this manner.
Electron and Ion Beam Characterization of Glass
Artifacts and Data Analysis Issues with EDS While EDS can be a powerful tool for elemental analysis, there are a number of limitations of which to be aware. Interference can occur during data collection as a result of overlapping spectral peaks from elements within sample coatings or contamination from other areas of the sample or even the holder. During data analysis, numerous artifacts can be encountered: escape peaks (detector artifact) and sum peaks (x-rays arriving at detector simultaneously), peak overlaps (poor spectral resolution), excessive dead time (higher beam currents can lead to a situation where the electronics cannot keep up with the x-ray detection, known as pulse pile-up), and the disappearance of alkali signal (electron beam impact and charging artifact). Typically, automatic software accounts for some
of these issues, but misidentification of peaks does occur—the analyst should not count on the software to do the job of matching spectral peaks to specific elements. The informed and careful analyst will take these artifacts into account and manually check peak identification [27.18–22]. The strategies for acquiring accurate EDS spectra (including appropriate sample surface preparation, coating non-conducting specimens, attention to standards, consistent and appropriate operating conditions—time constant, detector-to-specimen distance, beam current, dead time, energy calibration, and sufficient count level—for known and unknown samples, and manual verification of vendor-software quantitative calculations) are provided in the literature [27.22, 23], and tables for commonly misidentified peaks are also listed. Special considerations for analysis of glass include migration of alkali ions under electron beam irradiation (which can be accounted for in the data collection algorithm by analyzing for alkali elements first), temperature increase in the sample (cold stages may be available on some instruments), beam damage, and ensuring that a coated sample for quantitative x-ray analysis is metallographically polished (elimination of surface relief above 50 nm rms for high-accuracy measurements) [27.16] with sub-micrometer mechanical abrasives to avoid systematic errors from surface variations that would affect x-ray intensity [27.1, 24].
27.1.10 Electron Energy Loss Spectroscopy In TEM and STEM, the analysis of the distribution of energies for the transmitted electrons through the sample, due to the energy loss from inelastic collisions, is known as electron energy loss spectroscopy (EELS). The scattering from inelastic events with tightly bound inner shell electrons or loosely bound valence electrons leads to the excitation of these atomic electrons to higher energy states (Fig. 27.9a,b), and this energy transfer of the incident beam electrons is recorded as an energy spectrum, called the edge profile (Fig. 27.10). The technique is more sensitive to low-Z elements .Z 10/ than EDS .Z > 10/ and is able to acquire elemental mapping of species at the resolution of the electron beam. Note, however, that hydrogen and helium have absorption edges that may be hidden by the more intense inelastic valence band scattering. Quantitative results are more straightforward than other electron beam techniques, because EELS measures the primary interaction event as opposed to secondary emission processes measured in other methods. The thickness of the sample relates directly to the characteristic energy edge signal intensity, as well as the background signal, since additional scattering
937
Part C | 27.1
When using standards of pure metal, stoichiometric compounds, or National Institute of Standards and Technology (NIST) standard reference materials (which exist for glass samples and are described in the EDS application discussions that follow), detection limits for EDS are 0:1 wt%, with an accuracy of 57%, and for WDS 0:01 wt%, with 12% accuracy. Higher beam currents (10100 times higher than EDS) are necessary for WDS to achieve an adequate signal-tonoise ratio, since the detector has a larger collection area and is farther from the sample, which can damage some amorphous materials [27.1, 3, 4, 16]. Sometimes EDS is colloquially known as semi-quantitative due to its higher relative errors compared to WDS and the pervasiveness of the reliance on standard-less measurements using database values for x-ray parameters. With recent advances in both detector materials (for example, silicon drift detectors, SDD, versus silicon-lithium, Si(Li), detectors) that provide higher resolution and higher count rates, and careful adherence to the quantitative analysis protocols described above, the accuracy of EDS can rival that of WDS [27.16]. Both EDS and WDS can be employed on SEM instruments. On TEM instruments, WDS detectors typically have not been implemented, due to limitations of analysis speed and physical constraints of the detector positioning [27.17]. Additionally, EDS analysis with a TEM can achieve high spatial resolution, since there is far less electron scattering due to electron beam material interactions and beam spreading in a thin sample. EDS systems are therefore the most common x-ray spectroscopic technique found in electron beam microanalysis [27.9]. EDS is capable of identification and quantification of all elements except H, He, and Li, since the protective window in front of the detector absorbs the low-energy x-rays emitted by these elements [27.3].
27.1 Electron Beam Techniques
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Characterization of Glasses
a)
b)
Incident electrons
EVac CB Ejected inner shell electron
Fig. 27.9 (a) Inner shell Coulombic interaction excitation and (b) the corresponding energy level diagram. (After [27.3])
EF VB
M Inelastically scattered electron: ∆E > 0
Elastically scattered electron: ∆E = 0
L
K
Intensity (arb. u.)
Be K-edge
Zero-loss peak
Part C | 27.1
×100 Plasmon loss 0
50
100
150 200 Energy loss (eV)
to those achievable on EPMA/WDS instrumentation. By close attention to sample surface preparation, instrument conditions that minimize beam damage to the glass samples, and adherence to the use of the k-ratio protocol, major constituents (mass concentration > 0:1) were measured with ˙5% relative error, minor constituents (between 0:01 and 0:1 mass concentration) with ˙10% relative error, and trace constituents from 0:001 to 0:01 mass fraction were measured with ˙25% relative error. This study also examined various discrepancies in data that can arise from failure to adhere to careful analytical protocols, and these are described below.
Fig. 27.10 Example of an energy loss spectrum (af-
ter [27.3])
will occur within the sample. An appropriate edge-tobackground ratio must be found to minimize multiple scattering events [27.3].
27.1.11 Electron Beam Quantification Applications With advances in instrumentation design to improve detection, image resolution, and the ability to image biological and environmental samples, the analyst has the ability to image a wide variety of samples—including insulating glass samples. By paying close attention to available standards, instrument parameters, and sensitivity of samples to beam damage, accurate quantitative analysis can be achieved. Application: High-Accuracy, High-Precision SEM/SDD-EDS Analysis of NIST Glass Standards In a study by Newbury and Ritchie [27.16], advances in EDS instrumentation, utilizing a silicon-drift detector (SDD), demonstrate accuracy and precision measurements of trace and bulk constituents that are comparable
Specimen Geometry Effects: NIST SRM 470 (K411). The geometry of the analyzed specimen impacts the scattering of electrons and the path length of the x-rays en route to the silicon-drift detector (EDS), so that the measured intensities may not correspond at all to the actual composition of the sample. The results from the measurements of the analysis of a NIST SRM 470 (K411 glass) sample that was highly polished using 0:11 m alumina final polish showed relative errors (when compared to the standard reference materials, SRM, certificate) of the average of 20 analyses for iron, magnesium, oxygen, silicon, and chromium ranging from 1:1 to 1:8% (Table 27.2). When the 20 analyses of Fe and Mg were plotted to inspect the range of the data (Fig. 27.11), the values were tightly clustered with the exception of one point in the data—which could easily be assumed to be an actual compositional variance in most samples [27.16]. Upon further inspection of the analysis surface, it appeared that the outlier arose from the analysis of a scratched area, with the recorded composition varying several tenths of a percent from the SRM value—highlighting the need to consider surface geometries and roughness when performing microanalysis.
Electron and Ion Beam Characterization of Glass
27.1 Electron Beam Techniques
939
Table 27.2 SEM/SDD-EDS analysis of NIST SRM K411 glass (after [27.16]) Element
SRM certificate
EDS analysis
SDa
O Mg Si Ca Fe
0:424 0:0885 0:254 0:111 0:112
0:428 (stoich) 0:0876 0:258 0:111 0:114
0:022 0:045 0:053 0:026 0:031
Relative error (%) 0:9 1:1 1:6 0 1:8
Conditions: polished specimen; E0 D 20 keV; analysis following the k-ratio protocol with standards using the NIST DTSA-II software; standards included the pure elements Mg, Si, and Fe; Ca from SRM 470 (glass K412), with oxygen calculated on the basis of assumed stoichiometry of the cations a 20 analyses
b) Fe (wt%)
a) Fe (norm. wt%) 11.5
1 μm diamond polish
11.5 Relative errors for average concentrations compared to SRM values Fe +1.8% rel Mg –1.0% rel
11.4 Outlier
*Av
1% relative
11.3 SRM certificate values
11.2 Outlier 11.1 1% relative 11.3 8.6
8.65
8.7
8.75
8.8
8.85 8.9 Mg (norm. wt%)
11 7.8
8
8.2
8.4
8.6
8.8 Mg (wt%)
Fig. 27.11a,b Quantitative analysis of Fe and Mg SEM/SDD-EDS analysis of NIST SRM K411 glass (after [27.16]): (a) as a flat polished bulk sample and (b) slightly scratched bulk samples
Dead Time and Pulse Coincidence Problem: NIST SRM 470 (K412). Analysis conditions should be chosen to minimize problems that arise from known artifacts— specifically how beam current choice (and therefore detector dead time) results in the formation of sum peaks. Results from repeated analyses of NIST SRM 470 (K412 glass) with varying beam current show how coincidence peaks (combinations of elements in the glass) at the detector could be misidentified as entirely different elements. Selecting a beam current that reduces the formation of coincidence peaks (and results in a dead time of 10%) on a standard, and then using those same analysis conditions for the unknown, showed that coincidence peaks cannot be entirely eliminated, but strict analysis protocols can reduce these peaks to close to baseline.
Trace and Minor Constituent Quantification with Interferences: NIST Microanalysis Glass K873. Using modern software to process spectra (e. g., NIST DTSA-II EDS), and again, with adherence to strict measurement protocols, even challenging analytical cases with issues of peak overlap can be shown to have low relative errors, rivaling WDS measurements. Relative accuracy ˙5% was shown for major constituents, ˙10% relative for minor constituents, and ˙25% for trace constituents (from 0:001 to 0:01 mass fraction). In the reported case of the analysis of NIST microanalysis glass K873, major constituents interfered with the trace constituents, yet relative errors of some elements were low. Although some trace constituents showed up to 20% relative error, subsequent analyses (to obtain higher counts) could reduce this error. These results
Part C | 27.1
11.4
0.1 μm alumina polish
940
Part C
Characterization of Glasses
a)
b)
90 nm
d)
c)
90 nm
90 nm
f) Intensity (arb. u.)
e)
(111)
Part C | 27.1
(200) (220) (311) (222) 300 nm
10 μm
30 35 40 45 50 55 60 65 70 75 80 2θ (°)
Fig. 27.12 (a–d) TEM, (e) SEM images of Cu2 O precipitate, and (f) XRD pattern of annealed Cu-NBS-A glass. Reprinted with permission from [27.25]
demonstrate that detailed analysis of unknown samples should be performed in an iterative manner: major constituents and resolved minor (even trace) elements first; then after examination of the spectrum, identified peaks may be stripped off to reveal minor and trace peaks that were hidden under the interference peaks. Application: HRTEM and EELS Studies of Nanocrystal Formation in Cu-Borosilicate Glass Modifications of glass structure and composition under impact of an electron beam are well studied, and typically cause issues in analysis and imaging. These changes include phase separation, bubble formation, alkali migration, and precipitation [27.25]. In particular, the formation of metal nanoparticles under electron beam impact has garnered much interest due to potential optical applications for this process, since the particles can exhibit very different properties from those of the bulk glass. A recent study achieved in situ formation of copper nanoparticles in glass using HRTEM, confirming the metallic particles with EELS. Samples
were carefully prepared to eliminate other metallic interferences (a gold grid was used instead of the typical copper grid), and specimens were coated with carbon to alleviate charging. Intensity and dose-dependent results showed that electron beams with nanometer-scale control can be used to precipitate Cu nanoparticles from a glass matrix, similar to laser irradiation studies that aim to tune optical and mechanical properties [27.25]. Figure 27.12 shows the TEM and SEM micrographs of the Cu2 O particles. Application: Non-Destructive ESEM-EDX Characterization of Ancient Objects While many glass fragments may be easily analyzed for bulk composition with x-ray fluorescence (XRF) [27.26], archaeological glass pieces with trace components that must be preserved are excellent candidates for analysis with EDS. In one study, several small fragments of highly decorated, colored glass from fifth- and fourth-century BC Greece were available only for nondestructive analysis with ESEM-EDX (no micro-sam-
Electron and Ion Beam Characterization of Glass
Area A
Area B
Area C
Fig. 27.13 Fiber-optic microscope image of glass fragment analyzed by ESEM-EDX to reveal cobalt as the colorant used. Reprinted with permission from [27.27]
ancient glasses, fingerprinting artifacts to the specific cobalt-containing alum mineral that has been found in the mines of the Dakhleh region [27.27, 28].
27.2 Ion Beam Techniques The following techniques are based upon characterization instruments that utilize incident ion beams, which subsequently scatter or emit secondary particles from the sample surface. The methods discussed in the following Sects. 27.2.2–27.2.5 include ion beam characterization techniques that describe examples of glass analysis with secondary ion mass spectrometry (SIMS), Rutherford backscattering spectrometry (RBS), and particle-induced x-ray emission (PIXE). The extreme versatility of these techniques for qualitative and quantitative elemental and isotope analysis allows for widespread use in the fields of materials science, archaeological sciences, and art and architectural conservation efforts—all of which require analysis of glass samples.
If the primary ion beam interacts with the sample such that removal of material and generation of ions and neutral species from the sample material occurs, this physical process is known as sputtering [27.3]. The secondary ions that are generated can be collected and measured, and this is the basis for SIMS. After the ion beam impact, the primary ions that penetrate the sample can be scattered away from the Emission • Particle induced x-ray emission (PIXE) • Electron emission Ei
Reflection • Sputtering/scattering • Secondary ion mass spectrometry (SIMS) • Rutherford backscattering (RBS)
27.2.1 Ion Beam–Material Interactions Just as electrons can interact with a sample and be emitted, reflected, or absorbed, ions will interact with a material and cause reflection (scattering or sputtering) of ions or emission of light, electrons, or x-rays. Figure 27.14 summarizes ion–material interactions with selected examples of related analytical methods or material processing [27.4].
941
Absorption • Ion implantation (II)
Fig. 27.14 Ion beam material interactions and associated characterization techniques (after [27.4])
Part C | 27.2
pling or coating could be done due to the age and value of the samples) [27.27]. Compositional data provided by these analysis techniques can provide extensive insight into the glass technology of the time, showing which colorants were used in manufacturing materials during a specific historic period. The resulting qualitative and semi-quantitative results of this study, which was the first attempt to study the composition of these fragments, suggested core-forming was the main glassforming manufacturing technique, along with some samples of mold-pressing and casting. Elemental analysis also identified the specific colorants used in these samples, providing insight into the raw materials used during manufacture and where those materials were likely to have been mined. One example of a colorant detected in one of the objects in this study (see area B in Fig. 27.13), cobalt, is known to impart blue color even at ppm levels. Many of the objects showed blue to bluegreen coloration, and the analyses were able to differentiate which blue color came from cobalt and which from reduced iron or oxidized copper. Cobalt-blue glass was unique to the late Bronze Age in Egypt, and the trace levels of elements such as lead, antimony, nickel, manganese, zinc, iron, and bismuth distinguish these
27.2 Ion Beam Techniques
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Characterization of Glasses
sample by interactions with the nuclei of the material’s atoms, and the energy of those backscattered ions can be measured. Rutherford scattering, which is the process that describes the decrease in energy during the ion–atom nucleus interaction and the loss during transmission into the sample, models the energy loss that occurs [27.3]. This is the physical basis for RBS measurements. Irradiation by a primary ion beam will also give rise to x-ray emission, just as the x-rays in the techniques described in Sect. 27.1 are emitted after electron beam irradiation. These x-rays are produced by the inner-shell ionization of atoms in the specimen, and the measurement of these characteristic x-rays is the basis for PIXE. There are additional subsets and combinations of ion beam analysis (IBA) techniques used for analysis of glass samples. The instruments described in the following sections have been chosen as some of the most common techniques encountered in the analysis of amorphous samples.
Ion source
Energy analyzer
Mass spectrometer Mass spectrum
Primary ions
Secondary ions
Detector Depth profile
Sample Image
Fig. 27.15 Secondary ion mass spectrometry diagram (af-
ter [27.29]) Secondary ions to mass spectrometer Primary ion beam
Part C | 27.2
27.2.2 Secondary Ion Mass Spectrometry Secondary ion mass spectrometry (SIMS) is a technique based on the destructive removal of material by a primary ion beam and detection of secondary ions generated by this process. Figure 27.15 shows a diagram of the components of a SIMS instrument. A primary ion C beam source (commonly used species OC 2 , O , Cs , C C C Ar , Xe , or Ga ) at energies from several hundred electron volts to 20 keV is focused onto a sample material surface. As the focused primary beam is rastered over an area of the sample, material is removed by the sputtering process (Fig. 27.16), which involves implantation of the primary ions into the material, displacing atoms from the sample in a collision cascade of direct and indirect collisions. Within this mixing zone, secondary particles are generated, ejected from the surface, analyzed for mass and energy, and counted by the detector. Information about how the selected species for detection is distributed within the depth of the sample can be obtained in the form of a mass spectrum, a depth profile (Fig. 27.17a,b), or an image [27.3, 29]. These instruments can be operated in the modes of static SIMS for surface analysis/mass scans or dynamic SIMS for depth profiling/bulk analysis. Imaging modes can also be used to determine lateral distribution of selected species and can combine these modes. How the secondary ions are resolved by mass depends on the design of the mass analyzers, which include electrostatic/magnetic sector, time-of-flight, and quadrupole instruments. Magnetic sector instruments physically separate the secondary ions within a magnetic field, with ions traveling tighter or broader arcs through the
Solid sample material
Fig. 27.16 Secondary ion mass spectrometry sputtering
process (after [27.3, 29])
magnet depending on the mass/charge ratios. High mass resolution is an advantage of this instrument design, which can analyze the surface up to 100 m into the bulk of the sample. Time-of-flight SIMS (TOF-SIMS) instruments use short pulses of the ion beam to analyze the top monolayers of the surface for molecular information, identifying the secondary ion species by the time they take to reach the detector. Quadrupole instruments use the application of quickly changing AC (alternating current) and DC (direct current) potentials to a structure with four rods, separating ions by mass as they pass through the quadrupole. The mass resolution of quadrupole instruments is not as high as
Electron and Ion Beam Characterization of Glass
106
1019
104
1018
103
1017
102
1016
101
1015
0
200
400
600 Time (s)
1014
0
magnetic sector instruments, but the instruments can switch rapidly between selected masses to allow a particular mass range to be scanned in a short period of time. SIMS is used to measure elemental (nearly the entire periodic table) and isotopic impurities at partsper-million (ppm) and parts-per-billion (ppb) detection limits. Lateral and depth resolution is on the order of nanometers (nm), depending on instrument type and set-up. Quantification is accomplished through the use of standards that have matrix composition and known elemental concentration similar to those of the unknown sample. The generation of secondary ion yield may be improved by the use of particular reactive ion beams (like oxygen or cesium), and the beam and analysis conditions will be chosen to enhance the secondary ion counts of a particular species [27.29]. Analysis of the reference material must be done under the same analysis conditions to calculate an appropriate relative sensitivity factor (RSF) that can, in turn, be used to quantify the unknown selected species in a subsequent analysis [27.1, 3, 4]. This conversion factor allows the analyst to calculate atom density from the secondary ion intensity i D
Ii RSF ; Im
(27.3)
where i is the atom density of the impurity isotope in atom=cm3, Ii is the secondary ion intensity of the impu-
0.2
0.4
0.6
0.8 1.0 Depth (μm)
rity isotope in counts/s, Im is the secondary ion intensity of the matrix isotope in counts/s, and the RSF has units of atom=cm3. Instrument Artifacts SIMS has a number of instrument artifacts that the operator must be knowledgeable about, and the following examples of glass analysis applications highlight various issues that can affect the quality and accuracy of a result. These artifacts can include charging, mass interferences, instrumental mass fractionation, and preferential sputtering. The next section takes a closer look at charging artifacts specifically. Primary ion beams striking the surface of an insulting sample can accumulate charge and lead to beam defocus. This charging phenomenon can interfere with the ability to raster the beam within a defined area or alter the energy of the secondary ions, changing the transmission and detection of the secondary species. Charge neutralization can be accomplished in a number of ways. An electron flood gun can be directed at normal incidence to the sample in order to neutralize the buildup of charge on the sample surface [27.30– 32]. Computer-controlled biasing of the secondary ion accelerating voltage [27.33] can compensate for the charge buildup by assessing ion energy changes with respect to the matrix during an analysis. Applying a conductive coating or grid to the sample [27.29] provides a conductive leakage pathway for the accumulated charge to dissipate. The requirements for the
Part C | 27.2
10 0
Secondary ion mass spectrometry depth profile. (a) Raw secondary ion signal as a function of sputtering time or (b) density of implanted ions in a surface (after [27.3, 4])
1020
105
943
Fig. 27.17a,b
b) Density (ions/cm 3)
a) Ion counts (cps)
27.2 Ion Beam Techniques
944
Part C
Characterization of Glasses
analysis will determine the best charge neutralization method: the sample may not withstand electron gun bombardment, or coatings may introduce contamination that would mask detection of the unknown species. A constant and stable matrix signal is an indicator of appropriate charge neutralization. While charging is a significant issue with magnetic sector SIMS instruments (insulators can be more easily analyzed in quadrupole or ToF-SIMS), the above-mentioned methods have been shown to produce excellent and reproducible results for all types of instrumentation.
27.2.3 SIMS Applications
Part C | 27.2
The following examples provide insight into the analysis of insulating samples. These applications highlight how charging can change the outcome of an analysis— leading to a completely incorrect assumption about the location and detection of chemical species. The examples show how careful attention to standards and statistical methods of data collection can lead to more accurate and trustworthy conclusions. Application: Magnetic Sector Dynamic SIMS Analysis of Insulators in the Semiconductor Industry Amorphous glass layers are used in every process step to build structures in integrated circuits. They may be dielectric layers, doping masks, or annealing/diffusion barriers. These amorphous layers may be thermally grown or deposited by chemical vapor deposition or plasma-enhanced chemical vapor deposition (CVD or PECVD), and may include various doped silicon dioxide glass layers or carbon/fluorine-doped low-k oxides [27.33–35]. During electron beam usage for charge neutralization of semiconductor insulating materials, two main issues can arise: mobility of species within the layer, or damage to the layer from the electron beam. Alkali contamination (sodium, potassium, and lithium) is a major problem within integrated circuits— the mobility of these species causes the insulating layers to conduct electricity, significantly altering the electrical properties of the layer from those intended in the design. Analysis conditions for diffusion of other typical metallic contamination elements used in integrated circuits have also been examined [27.36]. SIMS depth profiling can provide information about the location of contamination and can target specific process steps where the contamination occurred [27.37]. Even when charge neutralization appears to be good, certain ions such as alkalis can show significant mobility within glass layers during analysis, distorting the depth profile and showing inaccurate mobile species location. Figure 27.18a shows successive depth profiles
of a sodium ion-implanted sample of a 0:3 m SiO2 layer on Si. In these analyses, charge neutralization was adequate, as evidenced by the stable matrix signal, but repeated analyses gave different results, with analysis #1 detecting some alkali migration from the original ion-implanted sample to the SiO2 =Si interface, analysis #2 showing migration to the surface and interface, and analysis #3 detecting no alkali species at all [27.32]. Selecting appropriate analysis conditions so as to match the penetration depth of the electron beam with the film thickness allows the film to become conductive during analysis similar to electron-beam-induced current (EBIC) analysis, where in order to measure electrically active defect distribution within a semiconductor device, changes to the beam energy translate to changes in the penetration depth of the electron beam, and differences measured in the current indicate the presence of defects [27.30]. This conductive pathway through the sample film allows the dissipation of ion mobility to be minimized. Figure 27.18b shows successive analyses for sodium with an electron beam impact energy specifically chosen for the film thickness being analyzed. Analysis #2 is similar to analysis #1, although some mobility of the sodium is noted at the SiO2 =Si interface [27.32]. In addition to silicon dioxide materials deposited by CVD, research into the use of new low-k dielectric materials, produced through plasma-enhanced chemical vapor deposition (PECVD), was undertaken to investigate improved device performance. Low-k dielectric materials, which include fluorine-doped oxides (FSiO2 ), carbon-doped oxides (SiCOH), and porous carbon-doped oxides (p-SiCOH), have presented a number of integration challenges for semiconductor manufacturing, including mechanical stability and process-induced damage, although many of these have been successfully overcome [27.34]. These materials provide an interesting example of how new materials may be attractive because of their electrical properties, yet possess features that complicate analysis. In investigations of low-k dielectric materials by SIMS, film collapse during analysis with an electron beam used for charge neutralization has been shown [27.38]. Figure 27.19a shows a profilometer trace of the surface of a low-k material after SIMS analysis with OC 2 beam and electron gun bombardment, and Fig. 27.19b shows a top-down schematic of damage regions on the sample surface. Figure 27.20 shows loss of dielectric material as a function of electron beam dwell time. While it may not be possible to completely mitigate damage for these types of samples, it is important to be aware that analysis conditions can have a significant effect on the sample and may alter the results.
Electron and Ion Beam Characterization of Glass
a) Ion counts (cps)
945
b) Ion counts (cps)
109
109 SiO2
10
27.2 Ion Beam Techniques
Si
SiO2
8
10
Si
8
107
107
106
106
105
105
#1 #2 104
104 #1
103
103 #2
102
#2
102
101
#1
101
0 0.0
0.1
0.2
0.3
0 0.0
0.4 0.5 Depth (μm)
Part C | 27.2
#3
0.1
0.2
0.3
0.4 0.5 Depth (μm)
Fig. 27.18 (a) Successive depth profiles for sodium in silicon dioxide. (b) Optimized SIMS profile for sodium showing
little alkali migration in successive profiles. (After [27.32]) a)
b) Step height (nm) Exposed in sample holder
Covered by sample holder Rastered area
Secondary electrons/neutrals Electrons 108 135 162
e-beam impact area Exposed in sample holder
e –/neutrals
769
Ions
Fig. 27.19 (a) Profilometer trace of the surface of a low-k material after SIMS analysis with OC 2 beam and electron gun bombardment. (b) A top-down schematic of damage regions on the sample surface. (After [27.39])
Application: ToF-SIMS Analysis of Ancient Glass Archaeometry of glasses can provide important information about manufacturing techniques, provenance, and dating. Quantitative and qualitative ToF-SIMS analysis of ancient archaeological glass samples for specific isotopic fingerprints within inclusions and phases has been shown in an exciting work that com-
pares quantitative chemical imaging analysis of major, minor, and trace components of sample matrix and inclusions at ppm levels—which cannot be performed with other analytical techniques—of a number of glass samples [27.40]. Other techniques such as SEM/EDX or EPMA/WDS systems may provide some quantitative compositional information, but they do not have the
946
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Characterization of Glasses
Decrease in film thickness (nm) 2500
Peak intensity ratios 100 Inclusions Matrix 10
2000
1
1500
0.1 1000
B O Mg Al Si S Ca 47Ti Cr Mn Fe Ni Cu Rb Sr Sb 136Ba Pb
Fig. 27.21 Relative ToF-SIMS intensity differences for an-
cient glass samples with normalization of Ca for inclusions, Si for matrix (after [27.40])
500
0
0
100
1000 10 000 Elecron irradiation time (s)
Part C | 27.2
Fig. 27.20 Loss of dielectric material as a function of electron beam dwell time (after [27.38])
sensitivity or lateral and depth resolution of ToF-SIMS. Chemical analysis techniques such as inductively coupled atomic emission spectrometry (ICP-AES) or laser ablation inductively coupled mass spectrometry (LAICP-MS) have the ability to measure ppm and ppb concentration levels, but the samples must be dissolved, and spatial resolution is lost. The glass samples from the study are fragments of 14th century BC opaque turquoise glass found at Pella, Jordan and Tel el-Amarna, Egypt. Without directly quantifying the matrix or the particles, the relative compositions of each glass specimen can be normalized to the ToF-SIMS dominant intensity peaks and the ratio of the elemental intensities (Amarna=Pella) plotted, as shown in Fig. 27.21. Higher levels of Sr, Ca, S and Rb within the Amarna glass provide the ability to distinguish the compositions between these two samples. Careful attention to mass interferences, matrix effects, and quantification techniques enabled these authors to demonstrate that differences between samples could provide information about mineral content as well as soil impurities at the time of fabrication. This ultimately provides a non-destructive ppm-detectionlevel chemical diagnostic analysis able to pinpoint markers from a particular glass-making era. Application: ToF-SIMS in Forensic Analysis Glass samples from burglaries are often examined as forensic evidence, since broken glass pieces can be deposited on the intruder upon breaking a window or door.
Analysis of these samples often focuses on determining the origin of the glass fragment, and pieces containing < 200 ng may be encountered [27.41]. ToF-SIMS is one particular technique that has the advantages of elemental ppm detection limits of small particles (tens of micrometers across) and the ability to depth profile into the bulk beyond the surface, showing potential for this technique to be used in the analysis and comparison of forensic glass samples, provided evidence can be shown that the small pieces encountered may be representative of the bulk glass. One such study on the use of ToF-SIMS in forensic analysis [27.41] provides an exploration into the various complications that can arise in the SIMS elemental analysis of these types of samples, and highlights the characteristics of these samples that can lead to errors, e. g., float and nonfloat glass surface versus bulk differences, diffusion of elements, and variation across repeated analyses. In general, surface techniques such as ToF-SIMS may be used in forensic analysis as long as statistical sampling methods are adhered to and the examined area is taken from the bulk of the glass, not the surface.
27.2.4 Rutherford Backscattering Spectrometry Rutherford backscattering spectrometry (RBS) is based upon the technique of impacting a sample with MeV helium ions and measuring the reduced energy of the backscattered helium ions [27.3, 4]. The technique can determine the mass and areal density of the sample’s elements as well as the distribution of the depths of those elements from 10 nm to several micrometers [27.4]. The interaction of the incident beam and the sample ions are modeled by classical elastic collisions, where the energy of the backscattered species is a result of energy
Electron and Ion Beam Characterization of Glass
loss due to (1) interaction with the sample material and (2) the scattering collision event. The method is shown in Fig. 27.22, where incident ions of mass M1 , atomic number Z1 , energy E0 , and velocity v0 impact the sample target that is made up of atoms with mass M2 and atomic number Z2 . Sample atoms M2 have an energy E2 and velocity v2 after the scattering event, and the scattered ions M1 have an energy E1 and velocity v1 . The amount of energy a projectile loses as it travels into and out of the sample depends on the incident ion velocity and mass as well as the sample matrix elements. The conservation of energy and momentum between the incident ion and the scattering atom determines the energy of the backscattered He ions. Equation (27.4) gives the conservation of energy relationship for these variables M1 v02 M1 v12 M2 v22 D E1 C E2 D C : 2 2 2
E0 D
(27.4)
M1 v0 D M1 v1 cos. / C M2 v2 cos. / ; 0 D M1 v1 sin. / M2 v2 sin. / :
(27.5) (27.6)
The relationship of these variables describes the loss of energy during the collision of the projectile and the target atoms. The ratio of the energy of the particle after
Primary ion beam
ΔEin ΔEout
Sample
Detector ϕ M2 , E 2 , v 2
M1, E0, v0 M1, E1, v1
θ
Fig. 27.22 Rutherford backscattering spectrometry (af-
ter [27.4])
947
.E1 / and before the scattering event .E0 / is known as the kinematic factor k E1 D kE0 ; E1 kD E0 0r B DB @
1
(27.7)
h
M1 M2
i2
sin C 1 1C M M2
M1 M2
12 cos C C : A (27.8)
These equations inform the understanding of the kinematics of these interactions but do not provide information about how many ions will be backscattered. Energy is lost in collisions with the nuclei and electrons within the sample, and the angles of the scattered particles will vary. These variables impact the yield of backscattered particles and contribute to the differential scattering cross section, proportional to the square of the atomic number Z of the target element. The differential stopping cross section of the matrix, proportional to the atom density of the matrix, will impact the energy loss as the target ion travels through the material and back out. Therefore, RBS can be used to determine layer thickness and elemental concentrations to achieve a depth profile of the sample’s elements. Quantification is achieved by accounting for the scattering cross section of the element of interest and the stopping cross section of the matrix of the sample. Although the model of Rutherford backscattering can be used to calculate the scattering cross sections of elements and stopping power of the matrix, the reality of an ion beam impacting a multi-elemental sample is far too complicated to be completely captured by the models. Therefore, semi-empirical methods, using experimental values determined for each element in combination with models, are used in order to quantify elements at specific concentrations within a matrix. With the knowledge of these basic principles of ion–atom interactions, RBS can be used to quantitatively determine elemental concentrations as a function of depth without the use of standards. Detection limits for heavy elements are on the order of ppm and a few percent for light elements. The technique is especially suited to the determination of trace element concentrations that are heavier than the matrix elements. RBS is considered a non-destructive technique, although primary ion beams are implanted into the sample and implantation damage will occur, and this method has typically been used within the semiconductor industry in the analysis of crystalline and amorphous materials, both metallic and non-metallic, for depth-
Part C | 27.2
Equations (27.5) and (27.6) show the conservation of momentum in the parallel and perpendicular to incidence directions
27.2 Ion Beam Techniques
948
Part C
Characterization of Glasses
profiling, implant dose measurements, and crystal lattice imperfections, layer thicknesses, and impurity and stoichiometric determination [27.3, 4].
Part C | 27.2
Artifacts—RBS The most complicated detail about an RBS spectrum plot (Fig. 27.23) of backscattering energy versus yield of backscattered ions is that the energy axis is a combined mass and depth scale. This leads to frequent spectral interferences between a signal from a lightermass species at the surface and a heavier species within the sample. Procedures to reduce these interferences include channeling (i. e., aligning the atoms in the lattice so that they are parallel to the incident ion beam) crystalline samples to reduce the signal from the matrix, adjusting the detector or incident angle of the beam, or changing the energy of the incident ion. Additional issues that cause inaccuracies may be unaccounted-for channeling, misinterpretation of the statistical energy distribution of the backscattered energy loss (known as straggling, which may limit mass and depth resolution), Counts 5×104
230 nm TaSi1.2 590 nm TaSi 2.3
4 ×104
Ta
Si × 5
3×104 2×104
sample roughness, or damage to the sample by the ion beam. While sample charging of insulator samples has been verified [27.43] and needs to be taken into account, RBS is used extensively for glass samples.
27.2.5 Complementary and Combination Ion Beam Techniques The RBS instrumentation set-up of a particle accelerator and detector can allow simultaneous detection of other particles generated from the impact of the incident particle beam. These suites of techniques are collectively referred to as ion beam analysis (IBA), and Table 27.3 provides a summary of the techniques, their associated detection capabilities, and main fields of application. In particle-induced x-ray emission (PIXE), characteristic x-rays are detected instead of backscattered ions, allowing for simultaneous trace-element quantitative detection of species in multi-element samples on the ppm level. The non-destructive nature of this analysis extends the application of this ion beam technique to many different fields including archaeology, art, biology, and forensic science. Other techniques such as particle-induced gamma-ray emission (PIGE) and nuclear reaction analysis (NRA) enable the detection of lighter elements, while elastic recoil detection analysis (ERDA) detects knocked-out target atoms. Advances such as nano-beam imaging, accelerator and detector innovations, and software and automation procedures will continue to push ion beam techniques into increasingly complex applications [27.42].
1×104 0 0.200
0.600
1.000
1.400
1.800
2.200
Backscattering energy (MeV)
Fig. 27.23 RBS spectrum of TaSix films with differing Si=Ta ratios and film thickness. Si signals were multiplied by a factor of 5 (after [27.3])
Application: Vitrified Nuclear Waste Corrosion Studies with RBS-NRA High-level radioactive waste materials, whether from weapons and propulsions, industrial processes, or spent fuel from commercial and research operations, may be vitrified into solid form for long-term storage. Borosilicate glass, due to decades of study on analogous
Table 27.3 Summary of IBA techniques (after [27.42]) Relevant technique Rutherford backscattering spectrometry (RBS) Elastic recoil detection (ERD) Particle-induced x-ray emission (PIXE) Particle-induced gamma-ray emission (PIGE) Nuclear reaction analysis (NRA) Scanning transmission ion microscopy (STIM) Ionoluminescence (IL)
Detection capability Z>1
Main applications Materials science
Z < 17 (typically including H) Z > 11 Z < 17 (Li, B, F, Na, Mg, Al, Si) Z < 17 (often for C, N, O and isotope detection) Sample density
Archaeometry and cultural heritage
Defects and sample structure
Forensic
Earth and environmental sciences Biological sciences Nuclear safety and radioprotection Fundamental nuclear and atomic physics
Electron and Ion Beam Characterization of Glass
glasses have been created to mitigate the migration and dissolution of glass in aqueous environments. Application: MicroPIXE-RBS of Bioactive Glass While corrosion of glass that is intended to contain nuclear waste is a process to avoid, the ion leaching of bioactive glasses, used in vivo to replace bone loss, enables the proliferation of osteogenic cells, which are responsible for new bone formation. The combination of the porous structure of the glass, composition, and the change in localized pH due to the mobility of the ions at the glass surface promotes osteoblast activity and mimics the bone repair mineralization mechanism. The first bioactive glass, 45S5 Bioglass® , was first described by Larry Hench in 1971, in which evidence of bone growing into the implanted Bioglass® material was shown [27.53, 54]. The decades since have seen this material, as well as numerous compositional variations, used in medical applications including periodontal and orthopedic surgery, engineered tissues, and drug delivery. Applications beyond dental use are emerging, and many exciting research endeavors are ongoing in the areas of wound healing and bone restoration [27.55]. The most biologically active part of these glass materials is the time-dependent kinetic creation of a hydroxycarbonate apatite (HCA) mineral layer at the interface between the material and the surrounding tissue, and a glass can be intentionally designed to control and enhance the rate of material degradation and interfacial bonding. In one study of a strontium-containing bioactive glass scaffold created using a sol–gel process, quantitative elemental microPIXE-RBS imaging was performed on bioactive amorphous foams immersed in simulated body fluids (SBF) to monitor the in vitro movement of strontium, a naturally occurring trace el-
r ≈ 0.4 μm/day
r < 0.4 μm/day
Forward rate, Si, Al, ... surface detachment
Protective layer: Si transport limited
Si saturation of solution
r< ~ 0.000 04 μm/day Precipitation rate of secondary phases r (t = 0) 0.4 μm/day r (t = stationary state with forward rate) ≈ 0.4 μm/day r (at Si saturation) decreasing with time Alkali ion detachment from surface, ion exchange
Water diffusion in glass, creation of hydrated glass
949
Ion exchange alkali/H+ at depth within hydrated glass
Selective B, Na, ... diffusion in hydrated glass, dealkalization
Fig. 27.24 Glass corrosion mechanisms, a coupling of surface reaction, affinity, and transport (after [27.46])
Part C | 27.2
archaeological and geological amorphous materials, is considered stable from diffusion loss of radionuclides and is thought to be resistant to long-term water corrosion [27.44–49]. In the case of long-term underground waste repositories, water corrosion becomes an issue if a waste canister were to be breached. The corrosion of glass when in contact with humidity or groundwater has been studied extensively, and the stability of glass under these conditions is thought to extend hundreds of thousands to millions of years. Because corrosion can significantly increase the release of the vitrified radionuclides, research continues in this area in order to validate these models, with various corrosion mechanisms the focus of improved understanding. The proposed mechanisms of glass corrosion, shown in Fig. 27.24, take place in parallel, with dissolution of the glass network attributed to the mobility of alkali ions within the glass network. Investigation of the hydrated glass layers provides insight into the ion exchange reactions within the glass material, and ion beam analysis techniques are well suited to these investigations. The surface analytical techniques of RBS and NRA have been used to probe the alkali concentration and depletion in the hydrated glass layer of modified glass coupons exposed to a solution of isotopically labeled water, D2 18 O, in order to monitor uptake of hydrogen and oxygen [27.50–52]. Because of the limitations inherent in monitoring a light element signal in a heavy element matrix with RBS, and in order to take advantage of isotope-specific nuclear reactions, the complementary technique of nuclear reaction analysis (NRA) was employed to investigate how the elements were incorporated in the hydrated layer and to provide insight into the corrosion mechanisms. Results from these studies show that composition of the glass is an important factor in limiting ion exchange processes, and new
27.2 Ion Beam Techniques
950
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Characterization of Glasses
ement in bone that has anti-osteoporotic properties. The results show rapid movement of strontium into a surface-deposited calcium-phosphate apatite during the 10-day simulated bone generation, indicating that this porous material can enhance bone generation in vivo [27.56]. These in vivo investigations were carried out with a novel analysis combination of microPIXE and scanning electron microscopy—backscattered electron (SEM—BSE), since both ppm elemental detection and excellent spatial resolution were required to monitor trace mineral concentration at the interface between bone and the bioactive glass scaffold. After just weeks, these analysis techniques showed that the glass scaffold was replaced with a mineralized structure and the glass dissolution products were eliminated from the implant location. These stunning results show the power of combination techniques and the evolution of ion beam imaging to a point suitable for advancement of these technologies to in situ applications [27.57].
Part C | 27
Application: External Beam Simultaneous RBA-NRA-PIXE/PIGE Studies of Cultural Heritage Materials Analysis of materials with significant historical importance is helpful for determining authenticity and identifying fabrication procedures, as was described in the prior SIMS section (Sect. 27.2.2). While typical ion beam analysis is conducted in vacuum, studies using combined RBS-PIXE/PIGE are performed in air at the AGLAE (accélérateur Grand Louvre d’analyses elémentaires/accelerator Grand Louvre elemental analysis) facility of the C2RMF (Centre de Recherche et de
Fig. 27.25
A PIXE measurement in AGLAE on the seated scribe (© C2RMF)
Restauration des Musées de France/Center for Research and Restoration of the Museums of France), located in the basement of the Louvre in Paris (Fig. 27.25). This external helium beam analysis allows for the non-invasive investigation of large, movable art pieces. PIXE/PIGE techniques are used for bulk elemental composition, and RBS is used to provide information on multi-layered structures such as glazed ceramics. While this unique set-up has a diminished, yet useful, elemental sensitivity in the PIXE measurements, the resulting RBS data are comparable to those obtained in vacuum [27.1, 58, 59].
27.3 Conclusions This chapter provides a summary of typical electron and ion beam analysis techniques for glass materials and highlights instrument artifacts and analysis methods that may not be common knowledge outside the analysis community for a particular application. While the number of errors that can be introduced during the analysis of insulating materials may be daunting,
these pitfalls can typically be minimized or eliminated with careful attention, and specialists in the fields will normally possess the technical skills necessary to overcome these artifacts. Knowledge of the potential problems that can arise will help chart a clearer path toward the end goal—achieving accurate and credible results.
References 27.1
27.2
K. Janssens (Ed.): Modern Methods for Anayzing Archaeological and Historical Glass, Vol. 1 (Wiley, Chichester 2013) D.A. Leary, J.J. Skoog (Eds.): Principles of Instrumental Analysis, 5th edn. (Saunders College Publishing, Fort Worth 1998)
27.3
27.4
C.R. Brundle, J. Evans, S. Wilson (Eds.): Encyclopedia of Materials Characterization (ButterworthHeinemann, Boston 1992) D.K. Schroder (Ed.): Semiconductor Material and Device Characterization (Wiley, New York 1998)
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27.5
27.6
27.7
27.8
27.9
27.10
27.11
27.13
27.14
27.15
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27.26
27.27
27.28
27.29
27.30
27.31
27.32
27.33
27.34
27.35 27.36
D. Newbury: Misidentification of major constituents by automatic qualitative energy dispersive x-ray microanalysis: A problem that threatens the credibility of the analytical community, Microsc. Microanal. 11(6), 545–561 (2005) D.E. Newbury, N.W.M. Ritchie: Is scanning electron microscopy/energy dispersive x-ray spectrometry (SEM/EDS) quantitative?, Scanning 35, 141–168 (2013) D.E. Newbury: Mistakes encountered during automatic peak identification of minor and trace constituents in electron-excited energy dispersive x-ray microanalysis, Scanning 31, 1–11 (2009) H. Bach, D. Krause (Eds.): Analysis of the Composition and Structure of Glass and Glass Ceramics (Springer, Berlin 1999) M.M. Sabri, G. Möbus: Electron irradiation induced nanocrystal formation in Cu-borosilicate glass, J. Nanopart. Res. 18, 1–9 (2016) C.A. Hope, P. Kucera, J. Smith: Alum exploitation at Qasr el-Dakhleh in the Dakhleh Oasis. In: Beyond the Horizon: Studies in Egyptian Art, Archaeology and History in Honour of Barry J. Kemp, ed. by A.S. Ikram (Am. Univ. Cairo Press, Cairo 2010) M.S. Tite, A.J. Shortland: Production technology for copper-and cobalt-blue vitreous materials from the new kingdom site of Amarna—A reappraisal, Archaeometry 45(2), 285–312 (2003) E. Cheilakou, N. Liarokapi, M. Koui: Non destructive characterization by FOM and ESEM-EDX of ancient glass objects from the Aegean with an approach of the manufacturing technique, Mater. Struct. 45, 235–250 (2012) R.G. Wilson, F.A. Stevie, C.W. Magee (Eds.): Secondary Ion Mass Spectrometry: A Practical Handbook for Depth Profiling and Bulk Impurity Analysis (Wiley, New York 1989) A.L. Pivovarov, F.A. Stevie, D.P. Griffis: Improved charge neutralization method for depth profiling of bulk insulators using O2 + primary beam on a magnetic sector SIMS instrument, Appl. Surf. Sci. 231/232, 786–790 (2004) Z. Zhu, F.A. Stevie, D.P. Griffis: Model study of electron beam charge compensation for positive secondary ion mass spectrometry using a positive primary ion beam, Appl. Surf. Sci. 254, 2708–2711 (2008) J.M. McKinley, F.A. Stevie, C.N. Granger, D. Renard: Analysis of alkali elements in insulators using a CAMECA IMS-6f, J. Vac. Sci. Technol. A 18, 273–277 (2000) G. Stingeder: Quantitative distribution analysis of B, As and Sb in the layer system SiO2 /Si with SIMS: Elimination of matrix and charging effects, Fresenius Z. Anal. Chem. 327(2), 225–232 (1987) G. Dubois, W. Volksen: Low-k materials: Recent advances. In: Advanced Interconnects for ULSI Technology, 1st edn., ed. by M.R. Baklanov, P.S. Ho, E. Zschech (Wiley, Chichester 2012) H.W. Werner: SIMS: From research to production control, Surf. Interface Anal. 35, 859–879 (2003) H.G. Francois-Saint-Cyr, F.A. Stevie, J.M. McKinley, K. Eishot, L. Chow, K.A. Richardson: Diffusion of
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Evans Analytical Group: Analytical resolution versus detection limit, http://www.eag.com/documents/ analytical-resolution-versus-detection-limitBR004.pdf (2014) D.E. Newbury, D.B. Williams: The electron microscope: The materials characterization tool of the millennium, Acta Mater. 48(1), 323–346 (2000) J. Cazaux: About the mechanisms of charging in EPMA, SEM, and ESEM with their time evolution, Microsc. Microanal. 10, 670–684 (2004) D.C. Bell, N. Erdman (Eds.): Low Voltage Electron Microscopy: Principles and Applications (Wiley, Chichester 2013) Oxford Instruments: Application note: EDS in the TEM explained, https://www.oxford-instruments. com/OxfordInstruments/media/nanoanalysis/ brochures%20and%20thumbs/TEM-Explained.pdf (2013) Y.-M. Kim, H.Y. Jeong, S.-H. Hong, S.-Y. Chung, J. Lee, Y.-J. Kim: Practical approaches to mitigation of specimen charging in high-resolution transmission electron microscopy, J. Anal. Sci. Technol. 1(2), 134–140 (2010) S.J. Pennycook, A.R. Lupini, M. Varela, A.Y. Borisevich, Y. Peng, M.P. Oxley, M.F. Chisholm: Scanning transmission electron microscopy for nanostructure characterization. In: Scanning Microscopy for Nanotechnology: Techniques and Applications, ed. by W. Zhou, Z.L. Wang (Springer, New York 2006) pp. 152–191 D.J. Stokes: Environmental scanning electron microscopy for biology and polymer science, Microsc. Anal. 26, 67–71 (2012) J.B. Wagner, F. Cavalca, C.D. Damsgaard, L.D.L. Duchstein, T.W. Hansen: Exploring the environmental transmission electron microscope, Micron 43, 1169–1175 (2012) A.N. Bright, K. Yoshida, N. Tanaka: Influence of total beam current on HRTEM image resolution in differentially pumped ETEM with nitrogen gas, Ultramicroscopy 124, 46–51 (2013) A. Endo, M. Yamada, S. Kataoka, T. Sano, Y. Inagi, A. Miyaki: Direct observation of surface structure of mesoporous silica with low acceleration voltage FE-SEM, Colloids Surf. A 357, 11–16 (2010) D.E. Newbury, N.W.M. Ritchie: Performing elemental microanalysis with high accuracy and high precision by scanning electron microscopy/silicon drift detector energy-dispersive x-ray spectrometry (SEM/SDD-EDS), J. Mater. Sci. 50, 493–518 (2015) D.B. Williams, C.B. Carter: Transmission Electron Microscopy: A Textbook for Materials Science, Vol. 2 (Springer, New York 2009) D.E. Newbury, N.W.M. Ritchie: Trace analysis is worthless if the peaks are misidentified!, Microsc. Microanal. 18(52), 1010–1011 (2012) D.E. Newbury, N.W. Ritchie: How to do really bad SEM/EDS quantitative analysis, and never even notice!, Microsc. Microanal. 18(52), 1004–1005 (2012) N.W. Ritchie, D.E. Newbury, S. Leigh: Breaking the 1% accuracy barrier in EPMA, Microsc. Microanal. 18, 1006–1007 (2012)
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27.46 27.47 27.48
18 elements implanted into thermally grown SiO2 , J. Appl. Phys. 94(12), 7433–7439 (2003) Evans Analytical Group: Alkali contamination in thin dielectric films—Application note, http:// www.eag.com/documents/alkali-contaminationin-thin-dielectric-films.pdf (2003) K. Yamada, N. Fujiyama, J. Sameshima, R. Kamoto, A. Karen: SIMS depth profile of copper in lowk dielectrics under electron irradiation for charge compensation, Appl. Surf. Sci. 203/204, 512–515 (2003) J.M. McKinley, F.A. Stevie, C.N. Granger: Analysis of low-k dielectrics using a magnetic sector SIMS instrument. In: Proc. 12th Int. Conf. Second. Ion Mass Spectrom., Amsterdam (2000) pp. 607–610 F.J.M. Rutten, D. Briggs, J. Henderson, M.J. Roe: The application of time-of-flight secondary ion mass spectrometry (ToF-SIMS) to the characterization of opaque ancient glasses, Archaeometry 51(6), 966– 986 (2009) J. Coumbaros, J. Denman, K.P. Kirkbride, G.S. Walker, W.S. Skinner: An investigation into the spatial elemental distribution within a pane of glass by time of flight secondary ion mass spectrometry, J. Forensic Sci. 53(2), 312–320 (2008) A. Zucchiatti: A.R.- Cubero: Ion beam analysis: New trends and challenges, Nucl. Instrum. Methods Phys. Res. B 331, 48–54 (2014) J. Kim, W. Hong, H.J. Woo, C.H. Eum: Chargebuildup effect during ion-beam irradiation of an insulator and its suppression by deposition of a thin metal film, J. Korean Phys. Soc. 43(4), 582– 584 (2003) R.C. Ewing, W.J. Webert, J. Clinard: Radiation effects in nuclear waste forms for high-level radioactive waste, Prog. Nucl. Energ. 29(2), 63–121 (1995) World Nuclear Association: Treatment and conditioning of nuclear wastes, http://www.worldnuclear.org/information-library/nuclear-fuelcycle/nuclear-wastes/appendices/radioactivewaste-management-appendix-1-treatment.aspx (2015) B. Grambow: Nuclear waste glasses—How durable?, Elements 2, 357–364 (2006) S. Gin: Open scientific questions about nuclear glass corrosion, Procedia Mater. Sci. 7, 163–171 (2014) M.I. Ojovan, A. Pankov, W.E. Lee: The ion exchange phase in corrosion of nuclear waste glasses, J. Nucl. Mater. 358, 57–68 (2006)
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M. Fournier, S. Gin, P. Frugier: Review: Resumption of nuclear glass alteration: State of the art, J. Nucl. Mater. 448(1–3), 348–363 (2014) S. Thevuthasan, V. Shutthanandan, Y. Zhang: Applications of high energy ion beam techniques in environmental science: Investigation associated with glass and ceramic waste forms, J. Electron. Spectrosc. Relat. Phenom. 150, 195–207 (2006) V. Shutthanandan, D.R. Baer, S. Thevuthasan, E.M. Adams, M.H. Engelhard, J.P. Icenhower, B.P. McGrail: High energy ion beam studies of ion exchange in a Na2 O–Al2 O3 –SiO2 glass, J. Appl. Phys. 91(4), 1910–1920 (2002) A.A. Salem, G. Stingeder, M. Grasserbauer, A.M. Shreiner, K.H. Giessler, F. Rauch: SIMS and RBS analysis of leached glass: Reliability of RSF method for SIMS quantification, J. Mater. Sci.: Mater. Electron. 7, 373–379 (1996) S.K. Nandi, B. Kundu, S. Datta: Development and applications of varieties of bioactive glass compositions in dental surgery, third generation tissue engineering, orthopaedic surgery and as drug delivery system. In: Biomaterials Applications for Nanomedicine, ed. by R. Pignatello (In Tech, London 2011) pp. 69–116 L. Hench: Bioglass: 10 milestones from concept to commerce, J. Non-Cryst. Solids 432, 2–8 (2016) V. Miguez-Pacheco, L.L. Hench, A.R. Boccaccini: Bioactive glasses beyond bone and teeth: Emerging applications in contact with soft tissues, Acta Biomater. 13, 1–15 (2015) J. Lacroix, J. Lao, J.-M. Nedelec, E. Jallot: Micro PIXE-RBS for the study of Sr release at bioactive glass scaffolds/biological medium interface, Nucl. Instrum. Methods Phys. Res. B 306, 153–157 (2013) J. Lao, J. Lacroix, J. Nohra, N. Naaman, J.-M. Sautier, E. Jallota: Chemical imaging of the reconstruction of new bone and trace elements inside bioactive glass scaffolds in vivo: A multimodal and quantitative micro-ion beam analysis, Surf. Int. Anal. 46(10/11), 702–706 (2014) J. Salomon, J.-C. Dran, T. Guillou, B. Moignard, L. Pichon, P. Walter, F. Mathis: Present and future role of ion beam analysis in the study of cultural heritage materials: The example of the AGLAE facility, Nucl. Instrum. Methods Phys. Res. B 266, 2273–2278 (2008) H. Fajfar, Ž. Šmit, M. Kos: PIXE–PIGE analysis of coloured historic glass, Glass Technol. Eur. J. Glass Sci. Technol. A 54(6), 218–225 (2013)
Jennifer McKinley Office of Research University of Central Florida Orlando, FL, USA [email protected]
Jennifer McKinley holds degrees in Chemistry and Materials Science and Engineering from the University of Central Florida. She began her professional work with academic research in optics, continued in materials characterization at Lucent Technologies, and then started two companies: NanoSpective, Inc. and IRradiance Glass, Inc. She currently works in the Technology Transfer group in the Office of Research at the University of Central Florida.
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Nuclear Magn
28. Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass Josef W. Zwanziger, Ulrike Werner-Zwanziger, Courtney Calahoo, Alexander L. Paterson
Nuclear magnetic resonance and electron paramagnetic resonance (NMR and EPR respectively) are powerful experimental probes of the atomic-scale structure of glass. This chapter provides a practical introduction to the current state of the art of these methods in glass research, and is intended to provide researchers with the basic knowledge needed to apply and interpret the results of these methods. Topics covered include the basic physics of spin resonance experiments, necessary instrumentation and sample considerations, representative experimental results, and methods of interpretation.
28.1
953 954 954
Local Interactions: NMR ...................... Local Interactions: EPR ....................... Relaxation Phenomena ...................... The Basic Experiment .........................
954 956 956 956
28.3 Experimental Details ......................... 28.3.1 Magnetic Resonance Techniques and Experiments ............................... 28.3.2 NMR Methodology ............................. 28.3.3 Relating NMR Information to Material Structure .......................... 28.3.4 EPR Methodology...............................
958 958 958 966 966
28.4
Magnetic Resonance Studies of Glass ............................................ 28.4.1 NMR Studies of Spin-1/2 Nuclei ........... 28.4.2 NMR Studies of Quadrupolar Nuclei ..... 28.4.3 EPR Studies of Glass ...........................
967 967 974 982
28.5
Summary..........................................
984
References...................................................
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28.1 Magnetic Resonance Probes of Glass Spin resonance experiments comprise a large family of related spectroscopic methods that probe the quantum spin levels in a material. The spins can arise from both electrons and atomic nuclei. In the former case the experiments are termed electron paramagnetic resonance, or EPR (sometimes also electron spin resonance, ESR). In the nuclear spin case the experiments are called nuclear magnetic resonance, or NMR. In both NMR and EPR, the sample is placed in an external magnetic field so that the spin levels are split; this splitting is then probed in a spectroscopic experiment. The splitting value is also perturbed by the local structure of the material, and can be measured very precisely. Because the interactions governing the splitting perturbations are very short-ranged, typically 15 Å, these methods provide complementary information on structure to diffraction-based techniques [28.1]. The short-ranged nature of the interactions probed makes these experi-
ments highly suited to the study of glass and amorphous material structures. Furthermore, NMR in particular is quite element-specific, in that the spectrometer can be tuned to detect the resonance of a single isotope only (say, 29 Si). Thus the local structure of a sample may be mapped out element-by-element. Of course the methods also have limitations. Only glasses with unpaired electrons are suitable for EPR experiments. For NMR, some nuclei possess no spin and so are invisible in the experiment (such as 12 C and 16 O), while others have intrinsic properties that render the experiment too insensitive to be useful (for example, 183 W and 103 Rh). Nevertheless, both EPR and NMR have had and will continue to have major impact in the study of glass and amorphous material structure and dynamics. This chapter outlines the theoretical foundations of the methods, the equipment necessary, and typical examples of how the experiments are used.
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_28
Part C | 28.1
Magnetic Resonance Probes of Glass ............................................ 28.2 Theoretical Background..................... 28.2.1 The Zeeman Interaction .....................
28.2.2 28.2.3 28.2.4 28.2.5
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28.2 Theoretical Background In this section we outline the basic theory of the spin resonance experiment. More detailed discussion can be found in various standard texts [28.2–5].
the other hand, as „!0 kB T, that is, the frequency is small compared to thermal energies, the NMR experiment requires relatively large samples and often long acquisition times.
28.2.1 The Zeeman Interaction 28.2.2 Local Interactions: NMR Electrons and most atomic nuclei have nonzero spin angular momentum, a vector operator described by a quantum number I (nuclei) or S (electrons). The value for electrons is S D 1=2, while for nuclei it might be I D 1=2, as in 29 Si and 31 P, or larger, such as I D 1 for 14 N, I D 3=2 for 11 B, and I D 5=2 for 17 O. In any case whenever the spin is greater than zero, the particle also possesses a magnetic dipole moment . Because the spin is quantized, the magnetic moment is similarly quantized, with 2S C1 or 2I C1 values for its projection along an axis. Such a moment interacts with a magnetic field B via the Hamiltonian B, producing discrete energy levels. This interaction is termed the Zeeman interaction. For the simple and common spin-1/2 case, two levels are produced, separated in energy by „!0 , where !0 D B ;
(28.1)
Part C | 28.2
with B the magnetic field strength and the proportionality between the spin and the magnetic dipole moment, D I. In the EPR case, the Larmor frequency is typically written as !0 D g B B ;
(28.2)
where B is the Bohr magneton (the fundamental unit of magnetic moment) and g is the so-called g-factor (scaling B for the specific case of electron spin). The important outcome here is that application of an external magnetic field produces an energy splitting (termed the Larmor frequency !0 ), which can then be probed in a spectroscopic experiment. External magnetic fields in modern NMR spectrometers are on the order of 1020 T, while in EPR spectrometers they are typically an order of magnitude smaller. In such fields, the Larmor frequency of typically observed nuclei are in the 50400 MHz range, while electron Larmor frequencies are 10100 GHz. Because of the Pauli exclusion principle, in diamagnetic solids all the electrons are spin-paired and no EPR experiment is possible. EPR is only possible for unpaired spin density, for example electronic defects, or paramagnetic ions such as Cr(III) or Nd(III). NMR-active nuclei are readily available in almost all glasses, making the experiment in principle feasible. On
In addition to the external magnetic field, the nuclear magnetic dipole interacts with local fields due to the distribution of electron density and ions in its vicinity. These interactions are typically short-ranged, and are the primary source of structural information in the NMR experiment. Furthermore, because the interactions are of short range, the lack of order in a glass does not complicate interpretation of the spectra to the extent that it does in a diffraction-based experiment. The chemical shielding arises from the interaction between the electron density in the glass and the external magnetic field. In the presence of a magnetic field, a torque is induced on moving charged particles, which then circulate about the field. Thus, the external magnetic field generates small orbital currents in the electron density, which then generate a small additional magnetic field. This additional field typically opposes the external field, reducing the effective Larmor frequency, and hence the name shielding. The effect is small and linear in the external field strength, giving Larmor frequency changes on the order of 11000 ppm (parts per million). The resonance shift of a given nucleus is usually determined by the electron density within one to two coordination shells. This local nature allows separation in the spectrum of, for example, the resonances arising from silicon bonded to four bridging oxygen, three bridging and one nonbridging, two and two, and so forth. The shielding is directional in that its value depends on the spatial relationship between the external magnetic field and local bonding structure; therefore, in a powdered sample there will be a range of observed shifts and a broadened resonance. The shape of the resonance, if resolvable, can yield additional information about the local bonding geometry. For example, in a tetrahedral unit such as SiO4=2 in quartz, all directions around Si are equivalent, leading to no shifting or powder pattern. However, if the Si atom has three bridging oxygen ligands and one nonbridging ligand, its local symmetry is reduced. One direction (the threefold axis) is distinct from the other two, leading to an axially symmetrical powder pattern and a broadened resonance. Such spatial anisotropy, whether in glass or crystal samples, can be reduced by magic angle spinning (MAS, Sect. 28.3.2). Examples of of shielding powder patterns are given in Fig. 28.1.
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
a)
b)
Cubic symmetry
ω/ω 0
R
Si
δ
–δ/2 0
ω/ω 0
O
O O
Si
955
Chemical shift (η ≠ 0)
–δ/2(1 + η) –δ/2(1 – η) δ
O–
O O O
c)
Chemical shift (η = 0)
28.2 Theoretical Background
ω/ω 0
O– O O
O
Si
O–
Fig. 28.1a–c Typical chemical shielding anisotropy (CSA) powder patterns and the structures giving rise to them. In (a), the silicon has nearly tetrahedral symmetry (locally), thus all directions are equivalent, and all powder orientations give the same NMR frequency response and there is no line broadening. In (b) and (c) the symmetry is reduced as the number of nonbridging oxygens increases, and the powder patterns become more complex. In (b), with locally trigonal symmetry, two directions are equivalent, leading to two identical shielding values and one unique value, while in (c), no directions are equivalent and hence no shielding values are degenerate. Powder patterns from [28.6] with permission
ml = –3/2 ST ω 0
ω 0 – 2ω Q
ST
ω0
CT
ω 0 + 2ω Q
ST
ml = –1/2 CT ω 0 ml = +1/2 ST ω 0 ml = +3/2 Zeeman
First-order quadrupolar
Second-order quadrupolar
Fig. 28.2 Splitting pattern of the energy levels of a spin-
3/2 nucleus in a magnetic field and an increasingly strong electric field gradient. In an external magnetic field, the levels are split according to m, the projection quantum number. In a weak electric field gradient, an additional shift proportional to m2 is induced, leading to spread satellite transitions (ST) but an unshifted central transition (CT). In a strong gradient even the CT is spread. Adapted from [28.7] with permission from the PCCP owner societies
The magnetic nuclear dipole moments of different nuclei may also interact with each other, both directly and indirectly. Direct interaction is termed throughspace or nuclear dipole coupling, and is due simply to the fact that a magnetic dipole moment has a magnetic field associated with it, which can interact with neighboring dipoles. These fields fall off with distance as r3 and hence can be an important source of interatomic distance information in glass. However, the shift they produce in spectra is typically small, so in
Part C | 28.2
The nuclear quadrupole interaction results from the coupling between the nuclear electric quadrupole moment and the electric field gradient at the nuclear position. In nuclei with spin quantum number I > 1=2, the nucleus itself has a nonspherical charge distribution, described by the nuclear electric quadrupole moment. There is therefore an interaction in such cases with the electric field gradient arising from the local distribution of electric and ionic charge, which adds to the splitting due to the Zeeman interaction. The coupling between the quadrupole moment and the electric field gradient is denoted CQ , and is measured in MHz, like the Larmor frequency. For nuclei with large quadrupole moments and/or in highly asymmetric environments, CQ might be significantly larger than the Larmor frequency, making the NMR experiment impossible. This is so because the principal direction of the nuclear quadrupole interaction is dictated by the crystal structure, not the direction of the external magnetic field; therefore, in powdered samples, a strong quadrupole interaction leads to very broad NMR resonances. This broadening is somewhat mitigated for nuclei with halfodd-integer spin (I D 3=2; 5=2; : : : ) because in these cases, the allowed 1=2 $ 1=2 transition remains narrow to first order (Fig. 28.2). As in chemical shielding, MAS mitigates the broadening due to quadrupole interactions, but only partially. As noted in Fig. 28.2, to first order in the quadrupole coupling the central transition remains sharp and MAS is unnecessary. For stronger coupling, as is usually encountered, even the central transition is broadened but by more spatial terms than in chemical shielding. The result is that MAS in such cases removes some but not all of the broadening, and more sophisticated experiments must be used (Sect. 28.3.2).
956
Part C
Characterization of Glasses
order to extract this information relatively complex experiments are typically required. The second type of nuclear dipole interaction is termed through-bond or J-coupling and arises from dipole interaction mediated by the bonding electrons. This interaction is a rich source of information in liquids, but its very small magnitude makes its observation in disordered solids quite difficult. These interactions are depicted schematically in Fig. 28.3.
28.2.3 Local Interactions: EPR
Part C | 28.2
Similarly to the NMR chemical shielding interaction discussed above in Sect. 28.2.2, in EPR the orbital current generated by the external magnetic field is an important source of interactions, called the g-shift. In the EPR context the interaction is typically viewed as arising from the net orbital angular momentum of the electron charge density, which is proportional to the applied magnetic field, interacting with the electron spin through the usual spin-orbit coupling mechanism. Because of the proportionality of the induced orbital angular momentum to the external magnetic field, the resulting resonance shift can be expressed as an apparent change in the electron magnetic moment, g B , through shift of the g-factor (28.2). For a bare electron the value is about g D 2:002, but this is shifted by the interaction with the field-induced currents. Because of the delocalized nature of the electron spin density, interaction with neighboring nuclear spins is also important. This hyperfine interaction arises both from direct overlap of the unpaired spin density with the nuclear spin, which is termed a contact interaction, and a through-space dipole interaction similar to that a)
b) Si
Si Si
Si O
O
Fig. 28.3a,b Schematic depiction of nuclear dipole interactions. (a) Magnetic dipole moments of active nuclear species (29 Si in this example) interact through space, with a r3 distance dependence. The magnetic field lines are indicated for each silicon nucleus. (b) Bonding electron pairs, shown here as paired arrows in each bond, also mediate the spin-spin interactions, leading to a through-bond interaction. This second mechanism is typically much weaker than the first
described above for nuclear spin pairs. The interaction tensor representing the hyperfine interaction is typically denoted by A.
28.2.4 Relaxation Phenomena As probing the spin system in the magnetic resonance experiment necessarily requires perturbing it, and the detection is carried out in the time domain, the relaxation of the spin system to equilibrium is central to the magnetic resonance experiment. There are two primary time scales, conventionally denoted T1 , the spin-lattice relaxation, and T2 , the spin-spin relaxation times. Because the total magnetization is a vector quantity, when it is perturbed there will typically be both a component parallel to the external magnetic field and a component in the perpendicular plane. More precisely, the parallel component describes population differences between spin-up and spin-down states, that is, the net magnetization. The perpendicular component describes spinspin coherences, that is, phase relationships between spin states. Relaxation of the parallel component happens on the T1 time scale, while relaxation of the perpendicular component happens on the T2 scale. The scales differ because the T1 scale reflects relaxation of the populations of the spin components back to their equilibrium values as given by the Boltzmann factor exp.„!0 =.kB T//, and generally requires energy exchange with other lattice degrees of freedom. On the other hand, the T2 scale reflects relaxation of the spin coherences between levels, which can typically happen much faster. Both processes yield information about the dynamics of the atomic or electron spin relative to its environment, though interpreting this information in detail is complicated by the fact that the environment dynamics typically represent a stochastic bath of coupled degrees of freedom, and also can be probed over only a limited range of frequency scales, as set by the external magnetic field strength and the temperature range available for the experiment. In solids, including glass, the two time scales differ typically by several orders of magnitude. In NMR, T1 ’s of 1100 s or even longer are common, while T2 is often on the s to ms scale. In EPR, relaxation times are often much shorter than in NMR, such that frequently EPR experiments must be done at low temperatures to increase the relaxation times.
28.2.5 The Basic Experiment The basic solid-state NMR experiment for a glass sample consists of enclosing the sample, usually ground into a powder, in a container and placing it in the ex-
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
ternal magnetic field by way of a probe. The container is typically a ceramic cylinder capped with a ceramic or polymer disk. The probe holds the sample suspended inside a wire coil, which will act both as emitter and receiver. The coil is part of a tuned circuit. Thus for 29 Si at 16:4 T, the circuit is tuned to 138:98 MHz, the Larmor frequency for this spin at this field. The entire probe assembly is inserted into the magnet and connected by way of cables to both the transmitting amplifier and the receiver. A very simplified schematic of the apparatus is shown in Fig. 28.4. A short burst of radiofrequency (RF) energy is supplied to the probe, which, through the tuned probe coil, is resonantly coupled to the spins. The spin magnetization is thus driven out of equilibrium such that it develops a component in the plane perpendicular to the field direction. As it relaxes back to equilibrium on the T1 time scale, it precesses about
28.2 Theoretical Background
957
the external field, because a magnetic moment in the presence of a magnetic field is acted on by a torque that causes it to precess around the field direction. The precessing magnetization thus generates a time-varying magnetic field in the tuned coil, which by induction generates a detectable electromotive force across the coil. It is the associated time-varying voltage that is actually detected in the experiment. The detection can continue during the T2 duration (Fig. 28.5), and is digitized relative to a reference signal so that its sense of precession may be recorded as well. Finally, the spectrum is obtained by Fourier transformation of the timedomain signal. A number of factors limit the sensitivity of the experiment. First, as noted above, available magnetic fields are relatively small in the sense that „!0 kB T, so the equilibrium signal available is small (the spin
Probe coil Magnet coil Signal processing
Gate
Digitiser
Transmitter
Receiver
Part C | 28.2
Pulse programmer
RF source
Fig. 28.4 Highly simplified schematic of an NMR spectrometer. The central feature is the magnet, typically consisting of multiple cryogen jackets (not shown) to keep the magnet coils cold enough to maintain the superconducting phase. The probe holds the sample (only the sample coil is shown, inclined at the magic angle), and is used both to supply radiation to the sample and detect it after excitation. The overall transmission chain is shown on the left, consisting of a radiofrequency source, a pulse programmer, a gate, and the final transmitter, which sends the excitation pulses into the probe. During detection, signals are amplified in the receiver, then digitized, and finally processed by at least Fourier transformation to a spectrum and typically various other steps of filtering, referencing, and so forth
a)
b)
c) T2
d)
e) T1
Fig. 28.5a–e Schematic of the magnetization during the NMR experiment. (a) Spins are in thermal equilibrium with their environment, leading to a net magnetization in the external magnetic field direction. (b) Following an excitation pulse, the net magnetization and hence spins are rotated into the plane perpendicular to the field. During the relaxation time T2 , the spins lose phase coherence (c). Also during this time, an oscillating signal is detected as each spin precesses around the external field. Simultaneously, but generally much more slowly, the spins relax back to equilibrium (d) on a time scale T1 , returning finally to the original equilibrium state (e)
958
Part C
Characterization of Glasses
levels are almost equally populated at thermal equilibrium). Second, the signal size is affected by an additional factor of !0 through Faraday’s law of induction – this is the rate of change (precessing frequency) of the magnetization. Third, the natural abundance of the spin species of interest might be small, further limiting the amount of signal possible. Because of all these factors, NMR is typically a low-sensitivity method, requiring relatively large sample volumes and very lownoise amplification techniques. On the other hand, as both T2 and T1 are relatively long, there is ample time to perform complex series of pulses and by so doing to carry out sophisticated experiments. Furthermore, the signal can often be detected for many cycles, allowing for very accurate frequency determinations.
Whereas in NMR almost all current spectrometers operate in the time domain, in EPR there is a mix of frequency-domain and time-domain systems available. Frequency-domain experiments involve sweeping the magnetic field through resonance; in EPR this is quite a practical approach, due to the relatively low magnetic field used to generate the Zeeman splitting, the short relaxation times of electron spins, and the fact that only one resonant species (the electron) needs be considered. The multiplex advantage of time-domain spectroscopy is lost, of course, in which many frequencies are effectively sampled simultaneously, and so currently timedomain EPR is becoming more widespread as the ability to implement the necessary microwave electronics improves.
28.3 Experimental Details 28.3.1 Magnetic Resonance Techniques and Experiments
Part C | 28.3
This section introduces standard and important experiments for magnetic resonance studies on solids, in particular amorphous samples, and gives practical tips. In-depth discussion of each experiment is beyond the scope of this chapter, and we direct the reader to many excellent references [28.1, 2, 4, 8–10].
28.3.2 NMR Methodology Intensities and Frequencies Solid-state NMR spectra correlate frequency and signal intensity information (see for example Figs. 28.1, 28.6, etc.). The frequency distribution provides information about the materials via the NMR interactions (Sect. 28.3.3). The signal intensities are influenced by the experimental conditions much more so than in liquid-state NMR. Their effects must be carefully considered before relating the spectral intensities to distribution of chemical species and structure. However, once these experimental impacts are understood, intensities provide valuable information about site distributions, dynamics, and coordination environments. Magic Angle Spinning Probably the single most widely used technique in solid-state NMR of glass or indeed of any material is magic angle spinning (MAS). In MAS the sample is rotated rapidly about an axis inclined at the so-called magic angle of M D 54:74ı with respect to the external magnetic field direction. This spinning averages the local interaction anisotropies, which typically have spatial
variance of P2 .cos /, where P2 is the second Legendre polynomial [28.4]. Because P2 .cos M / D 0, the associated anisotropies, including chemical shift and dipoledipole interactions, are averaged to zero, thereby collapsing the signal into a centerband at the isotropic shift position. However, if the spinning frequency is slower than the width of the anisotropic interactions, the NMR signals will additionally form so-called spinning sidebands. These sidebands are harmonics of their associated isotropic shift peaks and can be identified by acquiring spectra at different MAS frequencies. The intensity profiles of the spinning sidebands can be analyzed with the Herzfeld–Berger relationship [28.11] (Fig. 28.6) to extract anisotropic interaction parameters, which is available in programs such as D MFIT and others (Sect. 28.3.3). On the other hand, some pulse sequences, such as total supression of spinning sidebands (TOSS) and phase-adjusted spinning sidebands (PASSs) [28.12, 13], remove spinning sidebands by introducing cleverly chosen phase shifts. The MAS speeds need to be carefully chosen to avoid overlap between isotropic shift peaks and spinning sidebands of different sites. Moreover, spinning faster comes at the cost of smaller rotors holding less sample material, and correspondingly, giving less signal. For example, samples in 7 mm (outer diameter) rotors typically can be rotated up to 7 kHz, while 2:5 mm rotors are usually quoted to spin up to 35 kHz. Currently the fastest spinning speeds available are on the order of 110 kHz in 1:3 mm rotors, spinning fast enough to remove proton-proton dipole couplings, but also holding so little sample material that only highly abundant nuclei with large gyromagnetic ratios ( ), such as 1 H and 19 F, are amenable for its use. For some samples, espe-
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
a)
c)
b)
d)
300
200
100
0
–100 δ (ppm)
300
200
100
0
28.3 Experimental Details
959
–100 δ (ppm)
C MAS NMR spectra of Zn.13 C15 N/2 highlighting Herzfeld–Berger fits ((a) and (c)) to experimental spectra spinning at 6:0 kHz (b) and 8:0 kHz (d) using the simulation program D MFIT [28.14, 15]. The isotropic shift position is marked by the arrow. Both fits give isotropic chemical shift values ıiso D 141:0 ppm and chemical shift anisotropies ıaniso D 223 ˙ 1 ppm Fig. 28.6a–d
13
One-Dimensional (1-D) Experiments Single-Pulse Excitation Experiments. The simplest NMR experiment consists of excitation by a single pulse followed by detection (Fig. 28.5). Even for this experiment, peculiarities of solid-state NMR require careful consideration of the experimental parameters, such as pulse lengths and powers, instrument dead time, and experiment repetition times. For nuclei with spin I D 1=2, an on-resonance pulse (that is, at the center of the spectrum) with pulse lengths p , and excitation field strength characterized by 1 (where
1 D
B1 ; 2
(28.3)
depends on the strength of the exciting magnetic field, B1 , and the spin-field coupling through ), rotates the magnetization by an angle D 2 1 p ;
(28.4)
orthogonal to the pulse direction. However, the effective pulse angle and phase differ with frequency offset [28.4, 18, 19]. Shorter pulses cover a wider excitation range but high RF powers are needed to achieve
significant pulse tip angles. For quadrupolar nuclei, the relationship of the pulse field strength, 1 , compared to the quadrupole frequency, Q ,
Q D
3CQ ; Œ2I.2I 1/
(28.5)
where CQ is the coupling strength, influences the pulse response. Only when the RF power is strong enough that the pulse excites the satellite transitions, that is,
1 q (hard pulses), or so weak that it selects only the central transition, 1 Q , does the signal intensity oscillate sinusoidally with pulse lengths. The 90ı pulse duration in the weak RF limit scales to that for the hard RF limit by 1=.I C 1=2/ [28.19]. For intermediate RF field strength . 1 Q /, the pulse duration-tip angle relationship is complex, allowing the evaluation of the quadrupole couplings via nutation spectroscopy, during which the intensity response to the pulse duration is recorded and analyzed [28.20, 21]. This dependence of the pulse angle on the size of the quadrupole coupling causes inequivalent excitation of nuclei in different environments, such as, for example, boron nuclei in threefold and fourfold coordinations even when present in the same borate glass sample. Quantification under such conditions is difficult if not impossible. Fortunately, equal excitation (less than 5% error in intensity) of different sites and therefore quantification can be achieved with small pulse tip angles 2 .I C 1=2/ 1 p =6, i. e., for I D 3=2 a 15ı pulse, for I D 5=2 a 10ı pulse angle, relative to a cubic site or liquid [28.19, 22]. Shaped pulses, such as WURST (wideband uni-
Part C | 28.3
cially those containing heavy quadrupolar nuclei with wide central transitions, (for example 93 Nb in phosphate glasses [28.16]), MAS with sufficient speeds to resolve isotropic peaks are not available. In such cases NMR experiments on static samples are the choice. Finally, an issue to be aware of with MAS is heating of the sample through the mechanical friction of the rotation [28.17].
960
Part C
Characterization of Glasses
form rate smooth truncation, Fig. 28.7) pulses can help with a wider excitation bandwidth [28.23]. Even then for wide signals, when the pulse and probe electronics responses are incapable of even excitation, variable-offset cumulative spectroscopy (VOCS) [28.24, 25] is the method of choice. In VOCS, consecutive experiments offset by excitation frequency are recorded and eventually added. Finally, attention must be paid to the experimental repetition times, which depend on the spin-lattice relaxation times, T1 . Deceivingly, even though the timedomain signal decays quickly in broad spectra (the effective T2 , denoted T2 , is short), the spin-lattice relaxation times of nuclei with I D 1=2 can be on the order of 10103 s. On the other hand, large quadrupole interactions or large chemical shift anisotropies aid with relaxation, sometimes allowing experiment repetition times on the order of milliseconds. For long T1 relaxation times small angle excitations on the order of 10°–20° allow for faster acquisition (Ernst angle relationship [28.26]), but one has to avoid selectively exciting species with different relaxation times within one sample. a) Pulse amplitude
Part C | 28.3
1.0
Spin Echoes. The acquisition of echoes can help to overcome dead time problems, such as signal loss during the dead time, rolling baselines, and breakthrough of pulse ring-down, as well as being important components of experiments designed to measure spin interactions selectively. Echo sequences consist of 90- -180 pulses for Hahn/Solomon echo types [28.27] (Fig. 28.8) and 90- -90 pulses sequences for solid echo experiments. After the initial excitation by the first pulse (1!2), the free evolution (3) of the (refocusable) coherences during the first period are reversed (evolution (5)) by the second pulse (4), and they combine again in phase with each other after the second time period (6). The Hahn/Solomon echoes refocus interactions, which are linear in the spin quantum number of the observed nucleus, such as the chemical shift anisotropy and heteronuclear dipole coupling in I D 1=2 and the central transition of I > 1=2 systems. The solid echoes refocus interactions bilinear in spins, such as homonuclear dipole-dipole and quadrupolar interactions. Under MAS, the centers of the pulses must be rotor synchronized. Also, proper phase cycling to avoid interference between free induction decays (FIDs) created by the b) MZ 1.0
80 20
0.5 5 0.0
80
20
5
0.5 –0.5
0.0
Time
c)
–1.0 –120
–80
–40
0
40
80
120 kHz
d)
Time
Time
Fig. 28.7 (a) Amplitude profiles for WURST-5, WURST-20, and WURST-80 shaped pulses, respectively, and (b) their corresponding spin-inversion profiles .Mz /. (c) Real (solid curve) and imaginary (dashed curve) components of a WURST-20 pulse and the (d) equivalent hyperbolic secant pulse. For details, please see original paper. Reprinted from [28.23] with permission from Elsevier
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
1
1
2
3 τ
4
2
5 τ
3
28.3 Experimental Details
961
6
4
5
6
Fig. 28.8 The basic spin-echo pulse sequence (90- -180-detection) and its effect on quickly and slowly evolving spins
(relative to the excitation frequency, silver and black arrows) showing the formation of an echo
last pulse and the forming echo is extremely important [28.28]. Multiple Echo Experiments. The refocusing of multiple whole echoes was first introduced by Carr and Purcell [28.29] and modified by Meiboom and Gill [28.30] for nuclei with I D 1=2, and has recently found increased application for quadrupolar nuclei (then called quadrupolar Carr–Purcell–Meiboom– Gill (QCPMG)) [28.31, 32]. The combination of the
(Q)CPMG technique with broadband excitation pulses, especially WURST pulses [28.23, 33], called WURSTQCPMG or WCPMG [28.34], opened up the study of many quadrupolar nuclei with large quadrupoles and wide central transition spectra, which suffered from low sensitivity especially in glasses. Fast Fourier transformation (FT) of the multiecho FIDs leads to spikelets in the spectra (Fig. 28.9). Their positions and separation is solely governed by the excitation frequency and pulse separation, and in contrast to the MAS spinning
Part C | 28.3
b) a)
c)
FFT 0.0002
0.0004
1000
0.001
0.002
0.003
0
–1000
–2000
–3000
ppm
0.004 Time (s)
Fig. 28.9a–c FID (a) acquired with a WCPMG pulse sequence and the resulting spectrum (c) after Fourier transformation (FFT) in magnitude presentation. The insert (b) reveals multiple echoes by focusing on the beginning of the FID
962
Part C
Characterization of Glasses
sidebands, chemical species are not separated. The envelope of the spikelet maxima is then compared to simulated powder patterns. As an alternative to Fouriertransforming the whole echo manifold, the individual echoes can be added, and Fourier transformation of these patterns provides a spectrum with visually much lower resolution but in fact identical information to the spikelet envelope. In practical applications, the detection of multiple echoes requires very finely optimized pulse timings to avoid spikelet intensity oscillations [28.35]. Also, since the excitation width of the spectra is not only limited by the calculated frequency profile of the WURST pulses, but also by the probe head and spectrometer responses, these experiments are often used in conjunction with VOCS [28.36].
Part C | 28.3
Correlations Using Heteronuclear Dipolar Coupling. Because the heteronuclear dipole coupling strength can be related directly to the local coordination environment of an atomic species in the sample, its measurement is of continuing interest. This measurement can be accomplished based on the Hahn echo pulse experiment, which refocuses heteronuclear dipole-dipole couplings, using a variety of so-called double resonance experiments, including spin-echo double resonance (SEDOR) [28.27, 37, 38], rotational-echo double resonance (REDOR) [28.39], transferred-echo double resonance (TEDOR) [28.40], transfer of populations with double resonance (TRAPDOR) [28.41], and rotationalecho adiabatic passage double resonance (REAPDOR) [28.42]. All of these experiments introduce a dependence of the echo intensities on the heteronuclear dipolar coupling thereby providing qualitative spin–spin correlations and, in some cases, distances and distributions [28.43]. These experiments analyze the difference, S, of the signal intensities from the echo spectra without .S0 / and with dipolar recoupling. The dependence of the normalized difference signal, S=S0, on the echo delay or position of the dephasing pulse is then simulated (Fig. 28.10). The distance between isolated heteronuclear spin pairs can then be calculated, but in multiple spin systems, especially in glasses with ill-defined and wide local distributions, the analysis is more complicated. Even more detailed information about glass structures can be obtained by comparing experimentally the initial REDOR curves of glasses and related crystals [28.44]. Cross-Polarization. Cross-polarization (CP) is a standard experiment in the study of organic solids, for example polymers, where the dipole-dipole mediated magnetization transfer from abundant protons to 13 C or other heteronuclei enhances the sensitivity and takes advantage of the usually faster proton spin-
a) ∆S/S 0 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 nTR (s) b) ∆S/S 0 1.0 0.8 0.6 0.4 0.2
8
6
4
2
0 –2 –4 –6 –8 δ (ppm)
0.0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 nTR (s) c) ∆S/S 0 1.0 0.8 0.6 25
20
15
10
5
0
–5
0.4 0.2 0.0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 nTR (s)
Bf33 Pg-REDOR S=S0 results for three silver phosphate borate glasses, 50Ag2 O-50Œ.B2 O3 /x .P2 O5 /1x with (a) x D 0:2, (b) x D 0:4 and (c) x D 0:6. The solid curves correspond to the fits of the initial data ranges of the normalized difference intensities .0 < S=S0 < 0:2/ allowing for the determination of site selective (indicated in (b) and (c)) second moments, M2BP . Reprinted from [28.45] with permission from Elsevier Fig. 28.10a–c
11
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
lattice relaxation time. Following a 90ı excitation pulse on protons, their magnetization is transferred to other nuclei by spin-locking both nuclear spin species in radiofrequency fields [28.46]. In typical inorganic amorphous systems, protons are absent but experiments can be done between other nuclei as well. Cross-polarization involving quadrupolar nuclei, in particular under MAS, is subject to complicated spinlocking behavior due to level crossing between various quadrupole transitions [28.19]. The selectivity of CP to dipole-dipole coupled heteronuclei makes it useful as an experiment to select for spatial correlations, and CP type transfers are often incorporated into twodimensional (2-D) experiments. Multidimensional Experiments Overview. Multidimensional Experiments correlate two or more frequencies with each other through crosspeaks (Figs. 28.11–28.15). The frequency pairs can be homonuclear, based on one spin, (for example multiple quantum magic angle spinning (MQMAS), or two-dimensional exchange spectroscopy), or between different spins of the same type, such as different 11 B nuclei or 31 P-Qn species (Figs. 28.12, 28.14), or heteronuclear, for example characterizing 31 P27 Al vicinities (Fig. 28.15). The correlation can be accomplished by various mecha-
28.3 Experimental Details
nisms, such as J-coupling, dipole–dipole coupling (for example via recoupling under MAS, spin locking, or multiple quantum excitation), through dynamics or mechanically by switching spinning axes. The experiments can be as simple as a single-pulse excitation whose pulse length is varied [28.20, 21], or complex pulse sequences with sophisticated recoupling schemes. Typically, two-dimensional experiments consist of four segments (Fig. 28.11), termed preparation, evolution (in the first time period, t1 ), conversion, and detection (in the second time period, t2 ). The evolution time, t1 (indirect dimension), is incremented in a series of one-dimensional experiments. The processing of these experiments may simply be Fourier transformation in both dimensions or may include more sophisticated treatments such as shearing or symmetrizing. Phase cycling and the acquisition of hypercomplex datasets using the time-proportional phase incrementation (TPPI) [28.50] and States [28.51] methods or their combination is necessary to obtain pure absorptive cross-peaks in both dimensions. Multiple Quantum MAS. Of all two-dimensional experiments, the development of multiple quantum magic angle spinning (MQMAS) by Lucio Frydman [28.52, 53] was one of the major breakthroughs in solid-state
Preparation
Evolution
τeff = 0 ms
ppm
Conversion
two-dimensional experiment with time periods preparation, evolution, conversion, and detection during the second time period, t2 . The evolution time, t1 (indirect dimension), is incremented in a series of onedimensional experiments
Detection
τeff = 3.4 ms
ppm
20
20
20
10
10
10
0
0
0
–10
–10
–10
–20
–20
–20
–20
–10
0
10
Fig. 28.12 Two-dimensional
20 ppm 11
–20
–10
0
10
τeff = 15 ms
ppm
20 ppm
–20
–10
0
10
20 ppm
B NMR spectra of B2 O3 glass, correlating the anisotropic frequencies of the boron nuclei through spin diffusion with increasing effective magnetization transfer times . eff /. These data allowed the assignment of the fraction of 11 B nuclei to boroxal ring and nonring sites. Reprinted from [28.47] with permission from Elsevier
Part C | 28.3
Fig. 28.11 Schematics of a typical t2
t1
963
964
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Characterization of Glasses
O
Isotropic dimension
O
Fig. 28.13 11 B MQMAS spectrum of B2 O3 glass and cross-sections acquired in a 16:5 T magnet. The isotropic dimension separates the signals from trigonal ring and nonring boron nuclei. The cross-sections reveal the second-order quadrupolar broadened, anisotropic MAS spectra of each site
O
B
B
O
O
O
B
O
B
O
30 25 20
O
15
10
5
0
–5 –10 ppm
Anisotropic dimension
a) Double quantum axis (connectivities)
b) ω1
ω1
ωa ωb
Q3.334
Q 4.3,klm
ωa + ωb
Part C | 28.3
ωa 2ωa
Q3.334
ωa
Q3.333 ωa
ωb ω2 Chemical structure
ω2
Fig. 28.14a,b Schematic examples of DQ NMR spectra. (a) Coupled Q units (frequency !a ) to Q units (frequency !b ) cause cross-peaks at (!a , !a C !b ) and (!b , !a C !b ), while Q3 –Q3 coupling produces a peak along the SQ-DQ diagonal, at (!a , 2!a ). (b) Similar schematic, but showing how the couplings between differing nearest-neighbor Qn species (indicated by superscripts) can be resolved. Reprinted from [28.48] with permission from Elsevier 3
NMR in the past 25 years, and has had a major impact on the study of glasses. For half-integer nuclei, the quadrupolar central transition has symmetries of the second rank Legendre polynomial, P2 .cos /, which is removed by MAS, and the fourth rank Legendre polynomial, P4 .cos /, which is not. Hence, the central transition has characteristic, anisotropic quadrupolar broadening even under MAS. The MQMAS experiment exploits the fact that single and multiple quantum coherences evolve under both Legendre polynomials, but their ratios depend on the coherence order and the spin quantum number, I. Consecutive evolution under different coherence orders can then be used to refocus the P4 .cos / dependence, while spinning at MAS removes the P2 .cos / dependence. Both effects together create echoes, which shift in time. Fourier transforma-
4
tion and accounting for the shifting echoes, for example by shearing of the the spectra, provides high-resolution spectra in the indirect dimension and site-separated MAS data in the directly detected slices [28.54] (Figs. 28.13, 28.22–28.24). Immediately after the introduction of MQMAS, many improvements to the original two- and three-pulse sequences were developed to address efficient MQ excitation and reconversion, symmetric excitation of positive and negative pathways, split-time-domain sequences to alleviate the need for shearing transformations, etc. Especially for solidstate NMR of glasses, MQMAS spectroscopy has become a standard NMR experiment on 27 Al, 23 Na, 17 O and other nuclei, where the central transition is narrow enough for efficient multiple quantum excitation and sufficient signal intensity is available, possibly after
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
a)
δ (ppm) (31P)
10
0
–10 –20 –30
–20
40
–30 –20
0 20
965
b)
δ (ppm) (27Al) –40
28.3 Experimental Details
–10 10
0
–10 –20 –30 0
60
10
80 10
Fig. 28.15a,b
31
parallel to the
31
0
–10 –20 –30 δ (ppm) (31P)
10
0
–10 –20 –30 δ (ppm) (31P)
80 60 40 20 0 –20 –40 δ (ppm) (27Al)
Pf27 Alg NMR spectra of 50K2 O-10Al2 O3 -40P2 O5 glass: (a) CP-HETCOR NMR spectrum and slices P shift axis. (b) HMQC NMR spectrum. Reprinted from [28.49] with permission from Elsevier
isotopic enrichment. The recent realization of the importance of Czjzek distributions on the NMR spectra of disordered quadrupolar nuclei [28.55, 56] and their incorporation in fitting software (Sect. 28.3.3) has made MQMAS even more useful in glasses.
Variable Spinning Angle Experiments. While the above examples use RF pulses to generate and manipulate spin coherences, another (technically more difficult) strategy is to manipulate the sample spinning angle in order to modulate the spin interactions. Dynamic angle spinning (DAS) [28.66–68] and other variable angle
Heteronuclear Correlations. In contrast to the experiments mentioned above, heteronuclear correlation (HETCOR), wideline separation (WISE), heteronuclear single quantum coherence (HSQC), and heteronuclear multiple quantum coherence (HMQC) experiments correlate resonances of two different types of nuclei, such as 27 Al and 31 P [28.74] (Fig. 28.15). In solid-state NMR, the coherence transfer can be done by dipoledipole coupling (through space), using spin-locking (CP-type, see above) or TEDOR-type transfers (HETCOR, WISE) or via J-couplings (through bond, HSQC, HMQC). These types of experiments require high-sensitivity nuclei, but can provide interesting information about spatial proximity of different chemical species or their direct bonding in glasses.
Part C | 28.3
Spin–Spin Correlations. While MQMAS correlates coherences that arise from the spin levels of a single nucleus, other two-dimensional experiments correlate coherences between pairs of spins. Double quantum (DQ) experiments correlate the single quantum frequencies of each site with the sum of frequencies of coupled I D 1=2 nuclei [28.57–62], either through space, via dipole-dipole coupling, or through bonds, via J-coupling. DQ experiments have revealed fine distinctions within otherwise unresolved 31 P-Qn -species in glasses (Figs. 28.14, 28.18, and 28.19). The J-coupling experiment displays the chemical shift information on one axis, while the second contains only the homonuclear J-coupling patterns such as singlets, doublets, etc., which are well known from liquid-state NMR (Fig. 28.20). This experiment allows for the determination of through-bond connectivities, in contrast to sequences that rely on the dipole-dipole couplings. In the exchange spectroscopy experiment, two single quantum frequencies are connected either by motion of each spin, for example in polymer chains [28.4, 63], or by spin diffusion between different spins [28.47, 64, 65].
correlation spectroscopy (VACSY) [28.69] experiments between different rotation axes require specially designed probe heads, which allow fast and controlled changes of the sample rotation axes. This type of probe head was developed for DAS on quadrupolar nuclei to simultaneously remove second- and fourthorder Legendre polynomial broadening of the central transition [28.66–68]. While not a two-dimensional experiment, the problem of canceling both second- and fourth-order polynomials was also accomplished in double rotation (DOR) NMR, where the sample is spun in two nested rotors, which is mechanically challenging and leads to slow speeds of the outer rotor [28.70– 72]. The introduction of MQMAS rendered DAS and DOR experiments largely obsolete, but the flexibility of the DAS probe heads leads to other interesting experiments. Frydman et al. introduced VACSY [28.69] and Grandinetti has recently used such a probe head to measure precise Qn distributions in a silicate glass [28.73].
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28.3.3 Relating NMR Information to Material Structure
Part C | 28.3
Obtaining structural information from NMR data requires two steps, first, determining the NMR interactions, such as chemical shift anisotropy (CSA), quadrupole parameters, their relative orientations, parameter distributions (Czjzek) [28.55, 56] etc., and second, relating these parameters to structure. Several excellent tools are available to help with both aspects. Some examples of programs that allow the extraction of spin interaction parameters from solidstate NMR spectra include D MFIT [28.14], WS OLIDS [28.75], Q UEST [28.76], Q UADFIT [28.77], and S IMP SON [28.78]. The programs differ in the problems they help to solve. The program D MFIT [28.14] can fit oneand two-dimensional spectra to obtain chemical shift interactions (static and MAS), and center bands of quadrupole interactions, including Gaussian and Czjzek distributions, which is especially useful for glasses. WS OLIDS [28.75] is particularly strong in simulating quadrupolar spectra including central and satellite transitions on crystals. Q UEST [28.76] permits simulating full quadrupolar spectra when the high-field approximation breaks down, and interactions with chemical shift tensors at specifiable relative angles. Q UADFIT [28.77] allows Czjzek distributions to be simulated. Finally, S IMPSON [28.78] takes a different approach to the other programs mentioned here: the user specifies the NMR interactions (such as CSA, quadrupole, dipoledipole, J-coupling, and relative angles) and defines the pulses and delays of the executed experiment. Applying the density matrix formalism, the program then calculates the time evolution, and its Fourier transform. This program gives the user the utmost control over the calculations, but consequently is more complex to use. While the above programs are useful for fitting complex spectra and extracting NMR parameters, they do not relate the parameters back to the underlying atomic-scale structure. These relations can be discovered empirically by comparing the parameters to those of crystals with known structures and NMR parameters, or by computing the NMR parameters of structural models based on first principles. Such computations have become reasonably accurate in recent years, at least for lighter nuclei, with the advent of advances in both theory and computational power. A variety of software packages are available for such computations, specifically designed for solids [28.79– 81].
28.3.4 EPR Methodology The collection of EPR methods available for glass studies is considerably smaller than in NMR, for several reasons. First, the relaxation times of electron spin densities are usually many orders of magnitude shorter than for nuclear spins, so that applying multiple pulses in the time domain becomes impossible. Secondly, the linewidths of the signals are typically so large that mechanical sample manipulation, as done in MAS for example, is also not feasible. As noted above, still the most common experiment for EPR in glass is a simple field-swept absorption measurement, which is effectively the frequency-domain analog of the single-pulse experiment on a static sample in NMR. Field sweeping in EPR remains in use because it vastly simplifies the experimental apparatus: an electromagnet with variable current is employed, which is sufficient because the very high gyromagnetic ratio of electron spins means that relatively small magnetic fields are sufficient. The standard X-band EPR spectrometer operates at about 0:35 T and a Larmor frequency of 9:8 GHz; contrast this to a modern NMR spectrometer with a 16:4 T magnet and a proton Larmor frequency of 700 MHz. Furthermore, sweeping the field by means of the current is simpler than generating variable frequencies in the 10 GHz region. Even in field-swept EPR, more sophisticated experiments can be performed. For example, electron-nuclear double resonance (ENDOR) measurements involve simultaneous irradiation of both the electron resonance and nuclear spin resonances in the common field, which alters the line shape and relaxation properties [28.5]. In this way, the nuclei close to the unpaired spin density may be determined, thus localizing the origin of the EPR signal in the glass network. As pulsed EPR spectrometers become more common, a wider array of experiments is becoming available, similar to what can be done in NMR [28.5]. Once pulses are at hand, a range of experiments using electron spin echoes is achievable. For instance, electron spin echo envelop modulation (ESEEM) as an alternative to CW ENDOR, to measure nuclear site proximities, and hyperfine sublevel correlation spectroscopy (HYSCORE), a two-dimensional generalization of ESEEM [28.5]. Finally, we note that dynamic nuclear polarization (DNP), in which electron spin polarization is transferred to nuclear spin degrees of freedom for direct detection, is becoming widespread for the study of complex materials [28.82], and is certain in the near future to have a major impact on glass surface studies.
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
28.4 Magnetic Resonance Studies of Glass
967
28.4 Magnetic Resonance Studies of Glass 28.4.1 NMR Studies of Spin-1/2 Nuclei
Si peaks in glasses are broadened by the range of Si environments found within the structure (termed heterogeneous broadening) and have peak widths of 1020 ppm [28.90]. This can lead to substantial overQ1
a) Na2O (mol%)
Q2
Q3
Q4
55.6 50.0 44.4 42.9 40.0 36.4 33.3 28.6 25.0 20.0
b)
–40
–60
–80
–100
–120 ppm
Q0 Q1
Q1 (SiOSi = 180°) Q2 Q3 Q4
–60
–70
–80 29
–90
–100
–110 –120 ppm (TMS)
Si MAS NMR spectra of a series of sodium silicate glasses. The locations of various Qn species are indicated with dotted lines. Note that the chemical shift of each Qn unit becomes more positive with increasing modifier content. Adapted from [28.85] with permission from Elsevier. (b) 29 Si chemical shift ranges of crystalline silicates with a different degree of condensation of SiO4 tetrahedra (Q0 , neso/orthosilicates; Q1 , soro/pyrosilicates; Q2 , ino/metasilicates; Q3 , phyllo/disilicates; Q4 , SiO2 polymorphs). Adapted with permission from [28.89]. Copyright 1984 American Chemical Society Fig. 28.16 (a)
Part C | 28.4
Silicon Si MAS NMR is commonly used in the oxide glass field: it can quantify the degree of condensation of the Si–O tetrahedra (denoted as Qn -units, where n is the number of bridging oxygen atoms) and is sensitive to the identity and chemical environment of its second neighbor. Additionally, 29 Si NMR is capable of detecting changes in Si–O bond length, Si–O–Si bond angle and the degree of disorder within the glass structure [28.83]. The majority of 29 Si MAS NMR studies use single-pulse experiments because they are quantitative, reliable and relatively simple to execute. Nonetheless, due to the overlap of signals from Qn sites, complex multipulse sequences are often required to confidently separate 29 Si Qn sites and learn more about the connectivity of the glass structure. 29 Si has relatively low natural abundance, only 4:7%, and a low-magnitude gyromagnetic ratio, leading to low sensitivity (similar to unenriched 13 C). As a consequence, many researchers choose to use isotopically enriched 29 SiO2 as a starting reagent [28.73, 84]. Since 29 Si is an I D 1=2 nucleus, it lacks quadrupolar interactions and has relatively long spin–lattice relaxation times, anywhere from a few minutes to an hour in a silicate glass [28.85]. Spin lattice relaxation times can be shortened by adding a small amount of a paramagnetic ion, such as 0:1 wt% of Fe2 O3 or CoO [28.73, 85], however, care must be taken to ensure that the addition does not affect spectral lineshapes. Like liquid-state NMR, solid-state 29 Si NMR uses tetramethylsilane (TMS) as the primary reference compound, although in practice a secondary standard is commonly referenced. Almost all Si found in glass is tetrahedrally coordinated, the exceptions being high pressures ( 8 GPa [28.86]) and binary phosphosilicates [28.87, 88], where five- and sixfold coordinated Si atoms are observed between 120200 ppm. Figure 28.16a shows typical 29 Si MAS NMR spectra of a potassium silicate glass series; the addition of modifier breaks up the silica network and converts bridging oxygens (BOs) into nonbridging oxygens (NBOs). It is worth noting here that the total amount of modifier affects the entire glass network, shifting all Qn species to more positive chemical shifts. When attempting to identify 29 Si structural units, silicate crystals are used for comparison; if glassy and crystalline silicates have similar compositions, they will also have similar chemical shift ranges as shown in Fig. 28.16b. However, unlike crystals, which possess sharply defined peaks of roughly 1 ppm width, 29
29
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Characterization of Glasses
Part C | 28.4
lap between sites; thus, care must be taken to fit spectra using as few Gaussian lineshapes as is necessary and physically justifiable from crystal data. Qn distributions should be similar to those expected from compositional analysis (notable exceptions include more-covalent modifiers, such as Li2 O [28.85]); large discrepancies from fitting a one-pulse experiment typically indicate a large relaxation time difference between Qn units or a real lineshape that is nonGaussian [28.90]. The 29 Si chemical shift ranges shown in Fig. 28.16b are large because the identity and proximity of the second-nearest neighbor has a significant effect on the local electron density. Higher cationic potential (charge/radius) modifiers usually result in both wider Qn distributions and individual 29 Si Qn peaks, indicative of more disorder [28.85, 91, 92]. Weaker cations shift the signal to a lower (more negative) ppm for the same Qn -species; likely due to wider average †Si– O–Si and shorter average Si–O bond distances, which cause increased shielding on the silicon atom [28.91– 94]. Nonetheless, the †Si–O–Si distribution is difficult to measure with 29 Si NMR, thus 29 Si NMR parameters are used in models along with other data [28.83, 95, 96]. Thus far only the influence of modifiers has been discussed, but many glass compositions have additional formers as well. Aluminosilicates are unique due to a phenomenon called aluminum avoidance [28.97], where it is energetically preferable for Si–O–Al linkages to form over homonuclear ones such as Si–O–Si or Al–O–Al, so they contain almost entirely Q4 -units bonded to varying amounts of Al neighbors. Nonetheless, the 29 Si peak position becomes deshielded (less negative) with increasing Al content, approximately 5 ppm for each additional Al neighbor in alkali and alkaline-earth aluminosilicates [28.91, 97]. On the other hand, Si–O–B bonds in borosilicates do not form preferentially and additional B2 O3 increases the chemical shift negligibly, a few ppm at most [28.98, 99]. Upon initial addition of P2 O5 , Si remains tetrahedrally coordinated and 29 Si peaks move to lower frequencies, however, at higher P2 O5 concentrations, six-coordinated Si forms and Si–O–P linkages become sterically unfavorable [28.87, 88]. Unfortunately, there are silicate compositions, such as Cs- and Rb-, aluminosilicates and some alkaline earth silicates, which have such narrow Qn distributions that only a single broad peak is observed in the one-dimensional MAS spectrum [28.91]. Identification and quantification of Si structural units is possible by 29 Si MAS, however additional information for fitting is often required from other NMR experiments, such as 29 Si double resonance, as discussed later (Sect. 28.4.1). Other 1-D experiments, such as static or off-magic-
angle-spinning experiments can offer more qualitative information about the glass structure and can aid in separation of overlapping sites. For example, Q4 units are known to have almost no CSA due to their high symmetry, making them easily identifiable in static spectra [28.73, 90, 95, 100, 101]. Additionally, the intensities of spinning sidebands can be fit to obtain the magnitude of the anisotropy .33 11 /, however the asymmetry factor is more difficult to ascertain with certainty [28.90]. NMR also offers unique insights into dynamic aspects of glass, such as the glass transition point and viscosity at high temperatures; it can probe lower frequency motions, which many spectroscopic techniques are unable to detect, and has the ability to tune its timescale from a few Hz to hundreds of MHz. Several 29 Si studies have obtained activation energies at Tg ; by plotting T1 as a function of inverse temperature, the T1 minimum is correlated with the rate of motion (assuming Arrhenius-like behavior) [28.102]. However, it can still be difficult to assign the activation energies to specific motions, e. g., whether contorted transition-state 29 Si tetrahedra or longer range motions are present. Nonetheless, Q3 and Q4 units in K2 O-4SiO2 have been shown to exchange on the order of seconds just above the glass transition, before eventually combining into a single peak at higher temperatures (in the molten state) [28.102]. Additionally, high-temperature states of silicon, namely fivefold coordinated silicon .SiO5 /, have been investigated and proven to exist using 29 Si NMR [28.103]. Phosphorus P is a receptive nucleus ( 400 times more than 13 C), having 100% natural abundance and a relatively high gyromagnetic ratio. 31 P NMR can measure the extent of depolymerization of the phosphate network and is sensitive to the identity and proximity of the second-nearest neighbor (assuming oxygen is first-nearest neighbor). Like 29 Si, 31 P is spin-1=2 and also suffers from long relaxation times. 31 P MAS NMR spectra can be deconvoluted and used to quantify PO4 tetrahedra types (denoted again as Qn species, where n is number of P–O–P bonds). An example of a glass series with Q0 , Q1 , and Q2 units is shown in Fig. 28.17a. Q3 units would be visible at more negative shifts, but are not observed in Fig. 28.17a. Q4 species are rarely observed in glasses with high modifier concentrations, due to their formal positive charge; when present, they are observed at chemical shifts more negative than those of Q3 units [28.104]. In favorable cases, the Qn species do not overlap (Fig. 28.17b) in which case the corresponding Qn peaks are discernible in amorphous solids. For many 31
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
a) Intensity (arb. u.)
Q 0 Q1
Q2
0.71 ZnO
0.65 ZnO
0.60 ZnO
0.55 ZnO
0.50 ZnO
50
25
0
–25
–50 –75 –100 P chemical shift (ppm)
31
b) Q0
Q1
Q2
Q3
[Na]/[P] Glass
53/47 50/50 40/60 25/75 +20
0
–20
–40 –60 31 P chemical shift (ppm)
31
P MAS NMR (141:1 MHz) spectra for several xZnO.1 x/P2 O5 glasses. Isotropic peaks are labeled using the Qn notation and the remaining peaks are spinning sidebands. Reproduced from [28.106], with permission from Elsevier. (b) 31 P chemical shift ranges reported in the literature for crystalline sodium phosphates with different tetrahedral arrangements. Also plotted are the chemical shifts obtained from the spectra of sodium silicate glasses. Reproduced from [28.107], with permission from Elsevier Fig. 28.17 (a)
modifiers, however, the Qn species overlap even in simple binary glasses. 31 P spectra are referenced to 85% aqueous phosphoric acid (H3 PO4 (aq)) [28.105]. Phosphate glasses are particularly vulnerable to water attack; in the ultraphosphate region, water is likely present as –OH groups and it can be important to consider when
comparing expected Qn distributions from composition to experiments. Figure 28.17a displays spinning sidebands (SSBs), which are common in 31 P spectra. The 31 P CSA is very large in glasses, often hundreds of ppm [28.58]; thus, fairly high spinning speeds are required to separate SSBs, however, they can be used to calculate the principal components of the chemical shift tensor (from which the magnitude of anisotropy and asymmetry factor can be obtained) [28.11, 108]. Figure 28.17a also demonstrates how an additional modifier shifts all Qn peaks to higher ppm (less negative), indicating that the effect is averaged over the entire glass system. Additionally, the type of cation also affects the isotropic shift; for higher cationic potential (charge=radius), the 31 P peaks become more shielded (more negative) and have wider lineshapes (evidence of tetrahedral distortion). However, dissimilarly, analysis of the SSBs showed the asymmetry of the electron distribution to be independent of cation type [28.108]. The large ppm difference between each Qn species has mainly been attributed to variations in -character of P-NBO bonds; a decrease in cationic potential increases -bonding and shortens the average P–O bond-length [28.108]. Furthermore, O–P–O bond angles, which also vary with the degree of bonding, have been empirically correlated with chemical shift [28.109]. The presence of a second glass former also affects the chemical shift. In aluminophosphates, each additional P–O–Al bond decreases the ıiso by 57 ppm [28.110]. Conversely, each additional P–O–B bond in borophosphates increases the 31 P ıiso by 810 ppm. The relatively narrow chemical shift range of 31 P leads to poor resolution in the case of glasses with multiple glass formers, as P–O–X substitution can cause substantial peak overlap between distinct Qn units. For example, the chemical shift of Q1 with one P–O–B bond is very similar to Q3 with three P–O–B bonds [28.104]. Heteronuclear experiments are of significant value in deconvoluting poorly resolved 31 P spectra with multiple network formers present [28.104, 110]. Finally, in phosphosilicates modifiers preferentially bind to the phosphate backbone and an Si–O–P bond shifts 31 P peaks to higher frequencies, as expected for the less electronegative silicon [28.87]. Generally, for identification of the different Qn .mA/ environments, where mA is the number of former or modifier bonds, a multiresonance experiment is required as discussed in Sect. 28.4.1. Multiresonance NMR Experiments for Spin-1/2 Nuclei Multiresonance experiments offer more and different information about glass structure compared to single-
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coherence experiments. However, as the interactions mediating the magnetization transfer may have different efficiencies for different structural units, a multiresonance experiment may not necessarily have quantitative intensities for a given glass system [28.111]. Nonetheless, multiresonance experiments can provide the needed separation of sites for confident identification as well as give intermediate structural insight by observing correlation between neighboring or bonded sites. In the case of 29 Si, isotopic enrichment is usually required to observe signal from the weaker double quantum coherences. DQ experiments take advantage of the interactions between nuclei, namely dipole-dipole and J-coupling for I D 1=2 nuclei. Generally, MAS and large chemical shift interactions average out dipolar coupling leaving only the smaller J-interaction; thus experimental conditions, i. e., pulse sequence, spinning speed, and sample relaxation times, must be considered carefully to ensure only the desired interactions remain at detection. As a result, many 2-D experiments are selective by including dephasing of unwanted coherences, giving the technique the term double quantum filter. The combination of MAS and multiresonance experiments is a powerful tool for the determination of glass structure.
Part C | 28.4
Homonuclear Dipole-Dipole Coupling. Many DQ experiments use the relatively strong and distance-sensitive .d 1=r3 / dipole–dipole coupling to examine the intermediate glass structure; namely, the connectivity between Qn units. Through-distance dipolar coupling experiments generally offer greater signal-to-noise ratios than comparable through-bond J-coupling experiments (see below), but are not as selective. As the dipolar interaction is mediated through space, and not through bonds, nearby but nonbonded Qn species can lead to spurious peaks [28.111, 112]. In DQ experiments, the horizontal single quantum (SQ) !2 axis contains the chemical shift information, analogous to the MAS spectra, while the vertical !1 axis contains the connectivity information. Structural units connected to like species (e. g., Q3 connected to Q3 ) will produce peaks along the SQ-DQ diagonal. These diagonal peaks are also known as autocorrelation peaks. If two different species are connected (e. g., Q4 connected to Q3 ), they will produce a matched pair of cross-peaks, one to the left and one to the right of the diagonal (Fig. 28.14). DQ experiments are capable not only of observing connections between various Qn species, but can distinguish the bonding environment of their nearest neighbors as well. Qn correlations are denoted as Qn;jklm , where jklm represent other possible Qn species attached to the central unit (for example, Q3;334 is
a Q3 unit attached to two other Q3 and one Q4 units) [28.113]. Dipolar DQ experiments have been applied with great success to phosphate crystals and glasses [28.111, 113–116], as well as to silicate systems [28.48, 117]. Figure 28.18 is an example of dipolar DQ spectra of two sodium phosphate glasses [28.114]. Q1 –Q2 connectivities can be identified from the twin cross-peaks in Fig. 28.18a), where Q2 –Q3 connectivities are identified in Fig. 28.18b). However, it is ambiguous whether the Q1 –Q1 autocorrelation peak is due to isolated diphosphate units or from nearby but nonbonding Q1 units [28.112, 114]. Qn;jklm distributions measured from DQ experiments are often compared to computational simulations [28.48, 118]. Beyond Qn connectivity, Witter et al. [28.113] were able to estimate the mean chain length in calcium phosphate, Jäger et al. [28.116] observed phosphate chains of alternating Q2 and Q3 species, and Tischendorf et al. [28.115] found the phosphate backbone evolves from cross-linked rings to long chains to dimers and isolated phosphate units as phosphate content decreased using DQ NMR. Heteronuclear Dipole-Dipole Coupling. Pulse sequences similar to those used in the previous section can also be used to obtain intermediate bonding information between heterogeneous nuclei. This is not limited to systems where both nuclei are spin-1/2; interactions between spin-1/2 and quadrupolar nuclei can be probed with the appropriate choice of pulse sequence. For example, in a sodium-phosphate glass 31 Pf23 Nag REDOR has demonstrated both Q2 and Q3 units have a significant dipole interaction, indicating that sodium associates nonpreferentially and that in the presence of more sodium, 31 Pf23 Nag dipolar coupling increases [28.119]. Additionally, 31 Pf27 Alg and 31 Pf23 Nag TRAPDOR provided intermediate structural information, such as how added modifiers (Al2 O3 and Na2 O) were distributed in the phosphate backbone [28.110]. Homonuclear J-Coupling. Despite being of small magnitude, scalar or J-coupling can also reveal connectivities between Qn -species, which are connected through an oxide bond. Due to their small magnitude, large J-couplings relative to the linewidth of the Qn peak (samples with narrow resonances or long T2 are desirable) and very high spinning speeds at a precise angle are required for glass samples. Although 2 29 J( SiO29 Si) couplings have been shown to be sensitive to Si–O–Si angles in crystalline [28.120] and glassy [28.121] compounds, J-couplings are complex and are best used along with other NMR parameters to perform structure refinement.
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
Q1
a)
Q2
Q2
b)
Doublequantumdimension ω1 (ppm)
Intensity (arb. u.)
28.4 Magnetic Resonance Studies of Glass
971
Q3
Doublequantumdimension ω1 (ppm)
Intensity (arb. u.)
–120 –60 3-3
2-2
–100
–40 –80
1-2
2-3 2-1
–20
3-2
–60
2-2 1-1
10
Intensity (arb. u.)
–40
0
0 –10 –20 –30 Single-quantum-dimension ω2 (ppm)
–20 –20 –30 –40 –50 –60 Single-quantum-dimension ω2 (ppm)
Intensity –10 (arb. u.)
31
P double quantum NMR spectra of two phosphate glasses, (a) 58Na2 O-42P2 O5 and (b) 35Na2 O-65P2 O5 . The small peak at approx. 14 in the !1 dimension is a spinning sideband. Reproduced from [28.114], with permission from Elsevier Fig. 28.18a,b
Q1
a)
Q2
Q1
b)
Part C | 28.4
ω1/2 (ppm)
ω1/2 (ppm) –70
–70
–60
–60
–50
–50
–40
–40
–30
–30
–20
–20
–10
–10
0
Q2
–8
–16
–24
–32 ω2/2 (ppm)
0
–8
–16
–24
–32 ω2/2 (ppm)
Fig. 28.19 (a) Through-bond double quantum MAS correlation spectra of a crystalline Pb3 P4 O13 sample and (b) a glass Pb3 P4 O13 sample. Reproduced from [28.112] with permission from The Royal Society of Chemistry
Figure 28.19 compares through-bond J-coupling DQ spectra for a crystalline and glassy lead phos-
phate [28.112]. The glassy DQ spectra has cross-peaks between Q1 and Q2 peaks indicating Q1;2 and Q2;1k
972
Part C
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Part C | 28.4
species are present, k being any Qn unit. As the correlation in J-coupling experiments is through-bond, the Q1 –Q1 autocorrelation peak can be unambiguously attributed to P2 O7 units, which are absent from the crystalline sample. However, unexpected cross-peaks have been known to result from residual homonuclear dipolar interaction and dipolar/CSA cross-terms [28.122]. As with all NMR experiments, one must be aware of the possibility of artifacts. NMR parameters can be determined from 31 P 2-D through-bond correlations and used to more reliably fit 1-D spectra. In the case of PbOx .P2 O5 /1x glasses precise quantities of each type of Q0 , Q1;j and Q2;jk were obtained [28.123]. Additionally, 2 J(29 SiO29 Si) coupling has been exploited to identify and quantify 0 0 additional peaks (unique Q2 and Q3 units) in K2 OSiO2 , Rb2 O-SiO2 and Cs2 O-SiO2 1-D spectra, as well as producing further evidence for the existence of threemembered rings in silicates [28.92]. Beyond DQ, Fayon et al. [28.124] recorded through-bond triple quantum–single quantum correlation spectra to observe spin-triplets of three connected PO4 tetrahedra, such as Q1 –Q2 –Q1 trimers or Q2 –Q2 –Q1 /Q2 –Q2 –Q2 in longer chains. This allowed for clarification of the chain length distribution, but also highlights the sensitivity of the chemical shift to the bonding environment of neighboring Qn -species. Furthermore, Hiet et al. [28.125] have used up to quintuplequantum-filtered experiments to precisely quantify the small amount (roughly 4:2%) of Q3 (3Al) units in a calcium aluminosilicate glass. J-resolved experiments also depend on throughbond coupling, with the major difference lying in the
resulting spectrum. Figure 28.20 shows a J-resolved dimension, which separates the Qn -species into their J-interactions, such as a doublet or doublet of doublets, and can rigorously quantify the Qn units despite the overlap in the 1-D spectrum. This allows for correlation of isotropic chemical shifts with J-coupling values; for example, in lead phosphates Q1 peaks located between 6 to 11 ppm were observed to have J-coupling constants, which increased continuously between 1720:5 Hz [28.121, 123]. Furthermore, Florian et al. [28.121] have been able to strongly correlate 2 29 J( SiO29 Si) coupling to Si–O–Si angle in CaSiO3 glass. Other Interactions. A different strategy for improving deconvolution of overlapping lineshapes has been correlation of isotropic and anisotropic nuclear shielding contributions, most recently by use of magic angle flipping (MAF) [28.73, 126]. These specialized pulse sequences and/or probe heads measure the magnitude of the shielding anisotropy and asymmetry factor, which often can more clearly identify Qn species. Furthermore, correlations between local symmetry and structure can be determined, such as between nuclear anisotropic shielding and Si–NBO bond length [28.126]. Finally, MAF has been shown to be an order of magnitude more quantitative for Qn -species than typical 1-D 29 Si MAS experiments [28.73, 126]. NMR Studies of Other Spin-1/2 Nuclei of Interest Fluorine. 19 F is the most sensitive nucleus after 1 H, thus even small amounts of fluorine can provide struc-
MAS dimension (ppm) –100
Q3
×8
–90
–80 Q2 –70 Q1 –60 30
20 29
10
0
–10 –20 –30 J-resolved dimension (Hz)
30
20
10
0 –10 –20 –30 J-resolved dimension (Hz)
Si J-resolved experiment for a glass of wollastonite composition, with slices showing the J-resolved spectra taken at 94:2 (Q3 , vertically expanded), 81:7 (Q2 ) and 71:8 ppm (Q1 ) in the MAS dimension. Reprinted with permission from [28.121]. Copyright (2009) American Chemical Society Fig. 28.20
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
tural information and it can be used in double resonance experiments [28.127, 128]. It has 100% natural abundance, a high gyromagnetic ratio, and a large chemical shift range (C500 to 500 ppm), however, it also has large CSA and even with high spinning speeds many SSBs are present [28.129]. Additionally, care should be taken to subtract the background signal that often arises from machinable ceramic parts in the probe or the fluorinated polymer rotor cap. In transition metal fluoride glasses, 19 F MAS NMR can distinguish between different bond environments of fluorine (free, unshared and shared) and deduce the connectivity of the MF6 octahedra [28.130, 131]. The 19 F chemical shift is dependent on CN and the modifier radius, although the variation is system dependent and tends to be much stronger where F is the only anion [28.132]. Generally, fluorine prefers to bond to higher field strength cations, such as Al over Si or Ca2C over Ba2C and partial ordering has been found around higher field strength cations [28.133–135]. There have been multiple studies using 19 F NMR to examine the dynamics of fluorinecontaining glasses as well, namely conductivity and crystallization processes [28.127, 136–138].
973
will behave both as modifier and former, and tend to behave much differently than ternary SnO-containing systems [28.149–153]. Impurities of Sn(IV) can sometimes also be present, especially in the presence of an alkali, but have much smaller CSA and linewidth compared to Sn(II) [28.149, 151, 152]. Selenium and Tellurium. Although 77 Se has a low receptivity, similar to 29 Si, and a broad signal . 1200 ppm/, the main issue is the long recycling times required between scans, at least 30 s and possibly even up to 1200 s in undoped samples [28.154, 155]. 77 Se NMR has been used to identify Se sites and quantify connectivity in many chalcogenide glasses [28.156–158]. Peak assignment and structure of Gex Se1x is an active area of research [28.154, 155, 159–161]. Some high-temperature 77 Se dynamic studies have also been performed on Px Se1x glasses [28.162, 163]. 125 Te suffers from the same problems as 77 Se in that it has low natural abundance and long relaxation times, therefore paramagnetic doping is advised. Even with MAS, 125 Te glass spectra are wide and difficult to interpret due to the wide distribution of Te sites found in the glass structure, with at least five distinct sites being present [28.164]. In tellurite glasses, 125 Te NMR is able to quantify TeO3 trigonal pyramid and TeO4 trigonal bipyramid units, and in some cases distinguish the number of NBOs per structural unit [28.165, 166]. However, in telluride glasses, Te is twofold coordinated, and strong correlations between ıiso and important structural parameters have been found [28.167]. Silver, Yttrium. 109 Ag has relatively high natural abundance, but a low gyromagnetic ratio, giving it poor sensitivity. Nonetheless, 109 Ag NMR has attracted significant attention for ionic conductivity studies; NMR parameters such as line narrowing and spin-lattice relaxation times can provide information about the mechanisms of ion transport [28.168] and more recent experiments reveal a wide range of ion hop correlation times [28.169, 170]. Finally, 109 Ag is also able to discriminate between different silver environments due to a large chemical shift range, which has indicated that AgC is randomly distributed within many glass networks [28.171, 172]. Paramagnetic doping along with the signal enhancement provided by the CPMG sequence have made 89 Y NMR possible in a vitreous system. The Y3C chemical shift is sensitive to its surrounding environment, but there is some disagreement about whether the identity of the next-nearest neighbor or CN is responsible for variations in ıiso [28.173–175].
Part C | 28.4
Lead and Tin. 207 Pb has medium sensitivity (about 12 times that of 13 C) and is 22:6% naturally abundant; however, it suffers from a broad signal . 5000 ppm/ and large CSA, partly due to its electron lone pair [28.139]. As a result, typical excitation bandwidths are unable to fully excite the very broad resonance and requires the use of VOC. Furthermore, even at high spinning speeds, poor resolution is achieved and 207 Pb NMR of glasses is almost always collected under static conditions [28.140]. Several studies indicate that the concentration of lead is a more significant parameter than that of the glass former [28.140–144]: at low PbO concentrations (< 30 mol%), the chemical shift is largely negative and distorted PbO6 octahedra are present, while at high concentrations (> 60 mol%) covalent Pb–O–Pb bonds form and and a mixture of distorted PbOn pyramids from with n of 3 or 4, with Pb at the apex. Other experiments have taken advantage of 19 F sensitivity [28.145, 146] or made use of the large CSA tensor [28.147] to gain insight into the Pb environment. The 207 Pb CSA can also be quite sensitive to temperature, making it useful as a probe of temperature conditions within a MAS rotor [28.148]. Like 207 Pb, 119 Sn is also of medium receptivity and suffers from large CSA, resulting in static spectra typically being collected, however, here the signal width is only approximately 1500 ppm. The lone pair of Sn(II) dominates many of the spectral characteristics and binary SnO-containing glasses, where SnO
28.4 Magnetic Resonance Studies of Glass
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Characterization of Glasses
a)
b)
7.04 T
11.74 T
40
20
0
–20
–40 30 δ (ppm)
20
10
0
–10
–20 δ (ppm)
Fig. 28.21a,b 11 B MAS spectra of a sodium aluminoborate glass. Simulated spectra are overlaid on the experimental data. (a) Spectrum acquired at 7:05 T; (b) the same sample acquired at 11:74 T. Note the increased resolution of the three-
and four-coordinate peaks at the higher field. Resolution is further improved at higher fields. Adapted with permission from [28.176]. Copyright 1998 American Chemical Society
28.4.2 NMR Studies of Quadrupolar Nuclei Boron NMR B NMR spectroscopy is a straightforward method for probing the local coordination of boron in oxide glasses. Boron has two NMR-active isotopes: 10 B (natural abundance 20%) and 11 B (natural abundance 80%). Both isotopes are quadrupolar, with nuclear spin of I D 3 and 3=2 respectively, and small nuclear quadrupole moments. However, due to the half-integer nature of 11 B, as well as its greater gyromagnetic ratio, 11 B is by far the preferred choice for the study of boroncontaining glasses. Boron chemical shifts are generally referenced with respect to boron trifluoride etherate at 0:0 ppm [28.105]. Two commonly used secondary chemical shift references are 0:1 M aqueous boric acid (19:6 ppm) and NaBH4 ( 42:16 ppm). The primary use of 11 B NMR spectroscopy is the quantification of the relative proportions of Œ3 B and Œ4 B structural units. Œ3 B units are trigonal BO3 clusters, with the number of nonbridging oxygens ranging from three to zero. Three-coordinate boron typically has a moderate CQ ranging from 2:3 to 2:9 MHz, while the isotropic chemical shift ranges from 12 to 23 ppm in oxide materials. This is in contrast to the tetrahedral BO4 structural unit, which typically has small CQ values .< 0:75 MHz/ and more negative isotropic chemical shifts (24 ppm). These general properties typically require high magnetic fields .> 11:7 T/ and moderate MAS speeds .> 5 kHz/ to provide sufficient resolution of the two environments, and their spinning sidebands, in borate glasses (Fig. 28.21). In the event of multiple BO4 environments, higher fields will likely be required for adequate resolution. 11 B MAS NMR experiments are typically straightforward in their execution. Quantification of the two 11
Part C | 28.4
coordinations requires short pulse lengths (0:20:6 s), corresponding to tip angles between approximately 10ı and 30ı (Sect. 28.3.2). Due to the short tip angle, recycle delays are typically on the order of 530 s. As 11 B is a quite receptive nucleus, experiments typically can be completed with a modest number of coadded transients and small sample mass; the latter property lends itself well to very fast MAS speeds. Care must be taken with regards to background signal from boron within the probe. This signal is typically eliminated by collecting a spectrum with an empty rotor and subtracting this background spectrum from the spectrum of interest. Another means of preventing this signal is by use of probes constructed of boron-free, or boron-depleted (i. e., containing mainly 10 B) materials, though this can be prohibitively expensive for the casual user. One-dimensional 11 B NMR has been used for many investigations into boron coordination in borate glasses. It was first applied by Silver and Bray in 1958 to identify four-coordinate boron in sodium borate glass [28.177]. The temperature dependence of boron speciation in borate glasses has been probed using highresolution 11 B MAS NMR by Sen et al. [28.178]. The relative composition of ring-forming, nonring-forming, and nonbridging BO3 units was found to vary with fictive temperature in borate and borosilicate glasses, but the latter was not sensitive to fictive temperature in boroaluminate glasses. Martens and Müller-Warmuth investigated a broad set of binary and ternary sodium borosilicate glasses [28.179]. The mean isotropic chemical shift of the BO3 peak was found to decrease with increasing silica content, while the mean isotropic chemical shift of the BO4 peak varied with both Na2 O and SiO2 content. Recent work in the field has benefited from the increasing availability of high field strengths and fast MAS speeds. Bajaj et al. found that
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
a)
[3]
[4]
B
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B
R = 0.75
R = 0.50
R = 0.25
R = 0.05 30
20
10
0 –10 –20 Relative frequency (ppm)
b) MAS dimension (ppm) Ring –10
Non-ring [4]
B
0
10 [3]
B
20 50
40
30 20 10 0 –10 Isotropic dimension (ppm)
11
B (a) MAS and (b) MQMAS spectra of a sodium borosilicate glass. Note the increase in Œ4 B as the NaC concentration increases. The MQMAS spectrum corresponds to the R D 0:25 1-D spectrum on the left. Both ring and nonring Œ3 B peaks are visible in the isotropic dimension of the MQMAS spectrum, while only one Œ4 B peak is apparent. Reprinted from [28.183] with permission from Elsevier Fig. 28.22a,b
vestigations. Of particular use is the rotational echo double resonance (REDOR) experiment (Sect. 28.3.2 and Fig. 28.10). REDOR is applicable in both crys-
Part C | 28.4
the concentration of BO4 units in binary bismuth borate glasses was incongruous with crystalline samples of similar composition [28.180]. Šubˇcík et al. use 11 B MAS NMR to track the evolution of multiple boron sites in a pseudobinary glass with changing molybdenum content [28.181]. The effects of varying modifier cation field strength on the structure of the glass network was studied by Wu and Stebbins, who found that high field strength network modifiers lead to significant network depolymerization, i. e., formation of nonbridging oxygen [28.182]. 11 B MQMAS is a valuable tool for the study of borate glasses. While Œ3 B and Œ4 B units can be resolved through the use of 1-D techniques, one glass can contain multiple environments of either type. Œ3 B units can consist of ring-forming units (where the trigonal BO3 units are part of a larger B3 O6 ring), symmetric nonring-forming units (where all oxygens are bridging oxygens), and asymmetric nonring-forming units (where one or more of the oxygens are nonbridging oxygens) (Figs. 28.12 and 28.13). While Œ4 B units do not tend to include nonbridging oxygen, changes in the second coordination sphere can cause small changes in the isotropic chemical shift. These differences cannot be resolved using 1-D techniques, but are straightforward to distinguish using MQMAS. Du and Stebbins use 11 B 3QMAS to resolve multiple boron environments in alkali borosilicate glasses (Fig. 28.22) [28.183]. The isotropic projection of the spectra reveal (three or four) independent peaks, which they attribute to Œ3 B(ring), Œ3 B(nonring), and Œ4 B(1B,3Si), which are assigned isotropic chemical shifts of 17:3 ˙ 0:1 ppm, 12:9 ˙ 0:1 ppm, and 0:05 ˙ 0:1 ppm, respectively. The Œ3 B shifts are consistent with those measured by Youngman and Zwanziger and by Hung et al., who examined the bond distribution in vitreous B2 O3 using respectively dynamic angle spinning and double rotation NMR [28.67, 72]. While MQMAS is not itself quantitative, it can aid in the quantification of the relative proportions of ring and nonring Œ3 B units. The Œ4 B environments can be similarly differentiated, with changes in the second coordination sphere of Œ4 B resulting in small changes in the isotropic chemical shift. Multiple coexisting Œ4 B environments have been observed in both borosilicate and borophosphate glasses, but are not typically observed in boroaluminate glasses [28.183– 185]. When using MQMAS, care must be taken with regards to the precise sequence (e. g., split-T1 , Z-filter, etc.), as well as with the chemical shift convention in use. The reader is directed toward the article on the topic by Millot and Man for further details [28.54]. MAS and MQMAS are the most versatile tools for the NMR study of 11 B, but there are additional pulse sequences worth mentioning for specialized in-
28.4 Magnetic Resonance Studies of Glass
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talline and amorphous systems, and can be used to probe both I D 1=2 and quadrupolar nuclei. However, careful handling is required to obtain quantitative results related to network connectivity. Naito et al. show that REDOR behavior is quite dependent on the geometry of the system when more than two spins are considered, as is likely to be the case in a glassy system [28.186]. However, if the dipolar evolution time is kept short, the difference in behavior due to local geometry is negligible [28.187]. Bertmer et al. applied short dipolar evolution REDOR to probe the intermediate-range order of sodium aluminoborate glasses. They found that both BO 4 and AlO4 units prefer to bond to neutral BO3 units, and that NaC ions are homogeneously distributed through the glass network [28.185]. Quantification is further complicated by the size of the quadrupole interaction, which can preclude complete recoupling of the dipolar interaction [28.188].
Part C | 28.4
Oxygen NMR Despite the ubiquity of oxygen in most inorganic glasses, oxygen NMR is not a common tool in the study of materials. Oxygen has only one NMR-active nucleus, 17 O, which has nuclear spin .I D 5=2/, a small nuclear quadrupole moment, and moderate gyromagnetic ratio. The primary limiting factor in the use of 17 O NMR spectroscopy is the extremely low natural abundance of the nucleus (0:037%). Timely acquisition of 17 O NMR spectra typically requires isotropic enrichment to the order of 20%. The two most common means of isotropic enrichment are hydrolysis of an appropriate reagent with H2 17 O, or exchange with gaseous 17 O2 , both of which are commercially available at a variety of concentrations of 17 O [28.189]. The potential for background signal originating from the sample rotor (typically made of ZrO2 ) is minimized if the sample is enriched in 17 O; however, if natural abundance spectra are collected, or if signal enhancement techniques are utilized, the background signal must be considered. This is exacerbated by natural abundance studies at high spinning speeds, where the mass of the rotor is comparable to that of the sample. The isotropic chemical shift of the oxygen site in ZrO2 is approximately 378 ppm [28.190]. 17 O has a significant chemical shift range, spanning more than 1000 ppm in inorganic crystalline oxides. However, in glasses the chemical shift range is significantly smaller, typically on the order of tens of ppm. The relatively narrow effective isotropic chemical shift range, combined with the inherent spectral broadening due to structural disorder, leads to significant peak overlap that is difficult to remove. 17 O CQ values are typically significant (on the order of 5 MHz), further worsening peak resolution. None of this precludes
the use of 17 O NMR in the structural characterization of glassy materials, but studies involving 17 O benefit significantly from methods that increase spectral resolution; MQMAS is particularly relevant for this purpose. 17 O spectra can provide a wealth of information regarding the structure of oxide glasses, as there are many relevant observable NMR interactions. In order to maximize the recovery of structural information, many experimental approaches must be considered. Collection of 17 O NMR spectra under static conditions can assist in peak separation when CQ differences between multiple sites are large. The use of MAS conditions is recommended when variance in ıiso is the dominant convolution factor. MQMAS can assist in the separation and identification of overlapping sites, but is formally nonquantitative with respect to site populations. DOR and DAS have allowed for significant increases in resolution, but due to the specialized hardware required these techniques are not widely used [28.66, 68, 71] 17 O peaks in NMR of glassy materials can broadly be separated into two groups: bridging oxygen (BO), where oxygen atoms link network forming atoms (e. g., Si, Al, P); and nonbridging oxygen (NBO), where oxygen atoms are bonded to a local network modifier cation (e. g., NaC , Ca2C , La3C ). Bridging oxygens typically have larger CQ values than nonbridging oxygens in the same system. The relative values of ıiso of NBOs versus BOs depend strongly on the properties of the modifier, with the shift becoming more positive as the difference in electronegativity increases [28.191]. Silicate glasses have been the subject of much study using 17 O NMR, due to both the abundance of silicate minerals to use as structural models, as well as the simplicity of the systems involved. Both electric field gradient (EFG) parameters CQ (coupling strength) and (asymmetry parameter), and consequently the quadrupole product s 2 PQ D CQ 1 C (28.6) 3 of BOs are primarily determined by the Si–O–Si bond angle in alkali silicate glasses [28.192]. While the various bridging oxygen environments (e. g., Si–O–Si, Si–O–Al, Al–O–Al) are difficult to resolve using static or MAS NMR experiments, MQMAS is capable of separating the peaks in the isotropic, or high-resolution, dimension. This information is extremely valuable for the study of intermediate-range order in network glasses, and has been widely applied. Lee and Stebbins used 17 O MQMAS to quantify the deviation of an aluminosilicate glass from Lowenstein’s rule, identifying Al–O–Al environments [28.193]. Similarly, MQMAS can be used to identify network link-
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
a)
Experiment Simulation
MAS 7.02 T
b)
used 17 Of31 Pg REDOR to probe the bond length of the P-NBO bond in binary sodium phosphate glasses [28.197]. Aguiar et al. used 17 Of11 Bg REDOR to assist in the assignment of bridging oxygen peaks in 17 O MQMAS spectra [28.198]. Aluminum NMR Aluminum is a very accessible target for NMR studies of glassy materials. The NMR-active isotope of aluminum, 27 Al, is 100% naturally abundant. 27 Al is a quadrupolar nucleus, with nuclear spin I D 5=2 and a significant nuclear quadrupole moment. These factors contribute to fast relaxation times, on the order of seconds. The high natural abundance of 27 Al, combined with its high gyromagnetic ratio, makes acquisition of 27 Al spectra quite accessible, despite significant broadening factors. 27 Al NMR benefits from both high field strengths .> 14:1 T/ and high magic angle spinning speeds .> 20 kHz/: the former increases the resolution by minimizing quadrupolar broadening, while the latter both narrows central transitions and prevents the overlap of spinning sidebands with the central transitions of other sites. The primary chemical shift reference for 27 Al NMR is a 1:1 molal solution of Al.NO3 /3 in D2 O at 0:0 ppm [28.105]. Commonly used secondary shift references include the octahedral site of Y3 Al5 O12 (0:7 ppm) and KAl.SO4 /2 12H2 O ( 0:03 ppm). Aluminum in oxides glasses can take on three coordinations: tetrahedral AlO4 ; octahedral AlO6 ; and the less-common pentacoordinate AlO5 . The four- and
Experiment Simulation
MAS 11.72 T
c)
Si– O – Si
MAS dimension (ppm)
Si– O –B B – O –B
–50 0 Si–O–Na
50 NBO Si–O–(Na, La) Si–O–(Na, La)
Si–O–Na
Si–O–Si
100
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150 200
100
17
0 –100 –200 O chemical shift (ppm)
200
100
17
977
0 –100 –200 O chemical shift (ppm)
–20 –30 –40 –50 –60 –70 Isotropic dimension (ppm)
Fig. 28.23a–c 17 O MAS NMR spectra of a lanthanum sodium silicate glass. (a) Collected at 7:02 T. (b) Collected at 11:72 T. Note the significant change in profile with the change in field strength. Reproduced with permission from [28.196]. (c) 17 O MQMAS spectrum of a sodium borosilicate glass. The projection of the MAS dimension on the right is featureless and indistinguishable. The isotropic projection clearly separates the three bridging oxygen environments. Reprinted with permission from [28.195]. Copyright (2003) American Chemical Society
Part C | 28.4
ages between many common glass formers. Wang and Stebbins used MQMAS to distinguish the spectral behavior of Si–O–Si, B–O–B, Si–O–B, and Al–O–B environments [28.194]. Youngman et al. used DOR to resolve distinct B–O–B environments in vitreous B2 O3 ; through the use of a 11 Bf11 Bg NMR correlation study, Joo et al. have confirmed ring structures in the same system [28.47, 65]. For an example of the resolution of multiple network forming units, see Fig. 28.23c. Du and Stebbins used the high-resolution dimension (horizontal axis) of 17 O MQMAS to identify contributions from Si–O–Si, B–O–B, and Si–O–B environments [28.195]. The MAS dimension (vertical axis) shows only a broad featureless resonance. Small contributions from NBO can be seen to the left of the spectrum. MQMAS can also distinguish between multiple NBO environments. Angeli et al. examined the effects of lanthanum on a mixed modifier borosilicate glass structure, and were able to separate Si–O–Na, Si–O– (Na,Ca), and Si–O–(Na,Ca,La) resonances, concluding that the modifier cations were grouped into clusters (see left of Fig. 28.23). Note the sharp environment at 41 ppm, identified as Si–O–Na, and its contrast with the broad resonance at 120 ppm, identified as oxygen adjacent to a (Na, La) cluster [28.196]. Heteronuclear correlation experiments involving 17 O have not been extensively reported, largely due to the requirement for isotopic enrichment. However, aside from this consideration 17 O REDOR poses no special technical difficulty. Zeyer et al. have
28.4 Magnetic Resonance Studies of Glass
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Part C
Characterization of Glasses
Part C | 28.4
six-coordinate peaks are typically well resolved, with approximately 60 ppm separating their isotropic chemical shifts. The five-coordinate AlO5 peak is located between the four- and six-coordinate peak, and is often seen as a shoulder on the AlO4 peak when the experimental conditions do not provide for adequate resolution. Due to its spectroscopic accessibility and mineralogical importance, many pulse sequences have been developed to aid in the investigation of aluminum-bearing compounds. The two most commonly used for glassy aluminate materials are the single-pulse experiment and MQMAS (Fig. 28.24). The behavior of 27 Al isotropic chemical shift is broadly similar to that of 29 Si and 31 P; that is to say that the isotropic chemical shift depends on both the Al–O–X bond angle and the average Al–O bond length. However, two factors make these subtle changes difficult to resolve in the 27 Al NMR spectra of aluminate glasses. The structural disorder inherent to glasses tends to produce distributions of NMR parameters; these distributions typically obscure any slight changes to ıiso . Additionally, quadrupolar broadening must be considered. These factors generally obscure fine structural details, limiting the conclusions available from 27 Al NMR of glass to coordination number, Al–X substitution, and Al–O–X substitution. The 27 Al isotropic chemical shift decreases with an increase in coordination number, with typical values of 5, 35, and 65 ppm for AlO4 , AlO5 , and AlO6 respectively [28.200]. The chemical shift generally decreases by approximately 30 ppm per increase in coordination, assuming like compositions. Substitutions from the AlOx composition can also lead to significant changes in the 27 Al isotropic chemical shift. The two most relevant substitutions to the first coordination sphere are N replacing O, leading to an increase in ıiso , and F replacing O, decreasing ıiso by a few ppm per substitution [28.201, 202]. Second coordination sphere substitutions are more likely to be encountered in most common glass compositions. As with first coordination sphere substitutions, an increase in electronegativity in the second coordination sphere tends to decrease the 27 Al isotropic chemical shift. The chemical shifts of AlO4 units in aluminophosphate or aluminoborate glasses is hence lower than those in aluminosilicate glasses, which in turn is lower than those of binary aluminate glasses [28.10]. These trends can assist in the assignment of coordination and speciation in 27 Al spectra of glass. Beyond the distribution of chemical shift parameters inherent to disordered materials, the distribution of quadrupolar parameters must also be considered. The variations in the local environment of aluminum (e. g.,
bond angle, bond length, and composition distributions) can cause significant changes in the distribution of the EFG parameters CQ and . While both can usually be determined separately in ordered materials, separating their influence in disordered materials is nontrivial. Typically only the product PQ (28.6) is reported. There are several approaches for accounting for the distribution of quadrupolar parameters in disordered materials. Estimates of the mean CQ of the disordered peak can be made by approximation of the full-width at halfmaximum and comparing this breadth to an ordered peak, but this fails to account for the potential effect of distributed chemical shift parameters. MQMAS can be used to estimate the quadrupole product by means of comparing the centers of gravity of a peak in both dimensions [28.54]. While it is tempting (and straightforward) to assume that a Gaussian distribution can be applied to the quadrupolar parameters, as it is applied to chemical shift parameters, this does not account for the asymmetry observed in the lineshapes of disordered quadrupolar materials. While there has been some success in fitting disordered quadrupolar environments with a bivariate independent Gaussian distribution of CQ and , there is no physical justification for CQ and to be independently distributed [28.55]. The Czjzek model, first developed by Czjzek in the context of Mössbauer spectroscopy, has been adapted for use in NMR spectroscopy [28.199, 203, 204]. It has a more rigorous physical justification for the distribution of EFG tensor elements than a Gaussian distribution CQ and , and additionally has only a single breadth parameter, reducing the number of free parameters in the fitting process [28.55]. This allows for the quantitative decomposition of poorly resolved spectra, as well as for the determination of the root mean square of the quadrupole product of various species. Several assumptions are made in the derivation of the Czjzek distribution, which restrict the situations in which it may be used. While a full derivation of the distribution is beyond the scope of this chapter, the authors strongly encourage reading the overview by d’Espinose de Lacaillerie et al. [28.55] for a proper understanding of the theoretical underpinnings. The two most pertinent restrictions to the experimentalist, however, are the following: 1. The material under investigation must be disordered on length scales significantly greater than those of the quadrupole interaction. 2. There must be a sufficiently large number of structural contributions to the EFG. The first condition is easily satisfied by glasses, which are by definition disordered. It is the second
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
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CA 50.25
28.4 Magnetic Resonance Studies of Glass
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Experiment Model
Experiment Model
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300 200 100
0 –100 –200 ppm
} AlO4
} AlO4
AlO5
} AlO5 AlO6
120 100 80
60
40
20
0
b) Isotropic dimension (ppm) 20 40
Experiment 400 MHz 750 MHz
CA 50.25
–20 –40 –60 ppm
120 100 80
Isotropic dimension (ppm) 20 40 60
80
80
100
100
120
120
CA 50.25
40
20
0
–20 –40 –60 ppm
Isotropic dimension (ppm) 20 750 MHz CA 50.25 Experiment Model
40
Part C | 28.4
60
400 MHz Experiment Model
60
60 80 100
20 40
Experiment 400 MHz 750 MHz
CA 50.30
20 40
60
60
80
80
100
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120
400 MHz Experiment Model
CA 50.30
20
CA 50.30
40
750 MHz Experiment Model
60 80 120 100
120
80
40 0 –40 MAS dimension (ppm)
120
80
40 0 –40 MAS dimension (ppm)
80
40 0 –40 MAS dimension (ppm)
Fig. 28.24 (a) 27 Al MAS; and (b) 27 Al MQMAS spectra of two calcium aluminosilicate glasses. (a) Deconvolution of the AlO4 , AlO5 , and AlO6 environments through the use of the Czjzek distribution. In (b), MQMAS resolves the AlO4 and
AlO5 environments in both samples, but does not detect the AlO6 environment in the CA50.30 glass. Improved spectral resolution is observed with higher magnetic field strength. Reprinted from [28.199] with permission from Elsevier
condition that is of the most practical significance. d’Espinose de Lacaillerie et al. report that the de facto lower limit of sufficient is a coordination number of
4 for the nucleus under investigation [28.55]. This restriction therefore precludes the use of the Czjzek distribution for the analysis of 11 B and 17 O MAS spectra.
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As the coordination number of aluminum in glass is at least 4, the Czjzek model can be applied to 27 Al spectra. As the multiple sites that can be observed in these spectra are typically poorly resolved, this makes the Czjzek distribution a valuable tool in understanding the glass environment under observation. Like 11 B and 17 O, double-resonance experiments have been applied to 27 Al NMR spectroscopy. Chan et al. apply both REDOR and CP/MAS to aluminoborate glasses with varying network modifiers [28.205]. The 27 Alf11 Bg and 11 Bf27 Alg REDOR presented show that the 27 Al is homogeneously distributed through the glass network, but shows a preference for three-coordinate boron over four-coordinate boron, but that this is dependent on the modifier identity. CP/MAS experiments on the same systems were used to probe the intermediate-range connectivity between borate and aluminate structural units. Bertmer et al. use 27 Alf11 Bg REDOR to investigate preferential connectivity in sodium aluminoborate glasses [28.185]. van Wüllen et al. have recently conducted a thorough spectroscopic investigation of a potassium aluminophosphate glass, in part using 27 Alf31 Pg REDOR and HMQC [28.49]. The AlOx units were found to be fully bound to phosphate units, and the various second-order coordinations of the phosphate units were identified.
Part C | 28.4
NMR Studies of Other Quadrupolar Nuclei While many elements have been incorporated into useful and interesting glass compositions, others are less attractive targets for study through NMR spectroscopy. A selection of particularly relevant elements are discussed below. Alkali Metal Ions. Sodium is a commonly used glass network modifier, being abundant, inexpensive, and versatile. However, like most network modifiers, the structural information that can be obtained through NMR is limited. The NMR active isotope of sodium, 23 Na, is spin I D 3=2 and has several attractive nuclear properties. It is 100% abundant, has gyromagnetic ratio comparable to 27 Al, and has a moderate nuclear quadrupole moment. The isotropic chemical shift of 23 Na is referenced to a 0:1 molar solution of NaCl (0 ppm), though solid NaCl can also be used (7:2 ppm). The chemical shift range of 23 Na is narrow, covering approximately 40 ppm in most oxide materials. As such, 23 Na NMR spectroscopy benefits significantly from fast MAS speeds and high magnetic field strengths to maximize resolution. This is most relevant in species with multiple sodium environments, including glass ceramic composites. The 23 Na resonance of sodiumcontaining glasses is broad and featureless, indicating
a distribution of parameters. The most accessible and reliable NMR parameter that can be obtained in this context is the chemical shift of the center of gravity of the resonance, which will necessarily deviate from the isotropic chemical shift. This apparent chemical shift has been found to trend to more positive values with increasing NaC concentration in a number of glass compositions, but little structural information could be obtained [28.107, 179, 206]. 23 Na MQMAS has been used in conjunction with 17 O MQMAS to deconvolute the environments present in sodium aluminosilicate glasses [28.207], and has been used independently to probe mean Na–O bond lengths through the use of a modified Czjzek distribution [28.208]. Heteronuclear 23 Na experiments have provided significant information in silicate glasses. Gee et al. used REDOR to conclude that NaC and LiC are homogeneously distributed throughout the glass network [28.209]. Alam et al. come to a similar conclusion regarding the NaC distribution in a sodium phosphate glass using 23 Na23 Na homonuclear coupling [28.210]. Behrends and Eckert used 23 Naf31 Pg to establish the preference of sodium to modify the phosphate network over the germanate network in a mixed-network-former glass [28.211]. Due to its favorable spectroscopic properties, 23 Na is an extremely accessible nucleus for study by NMR in glasses and glass-ceramic composites. However, the information that can be obtained is less explicit than that from similar studies of common network-forming elements, a trait shared by most network-modifier cations. Lithium has two NMR-active nuclei, 6 Li and 7 Li. Both are used in NMR spectroscopy, though 7 Li is generally the more frequent target. 7 Li has a high gyromagnetic ratio, small quadrupole moment, and high abundance (92:6%), leading to high sensitivity. Whereas 7 Li is a half-integer spin nucleus (I D 3=2), 6 Li is an integer spin nucleus (I D 1), complicating the observed lineshape. Despite the moderate gyromagnetic ratio and lower natural abundance (7:4%) leading to lower sensitivity than 7 Li, 6 Li NMR spectroscopy is valuable due to the extremely small quadrupole moment, which can lead to higher resolution in systems where the quadrupole interaction dominates. Due to its use in the battery industry, many lithium NMR studies of glasses focus on glasses with ionic conductivity. For example, 7 Li NMR has been used to differentiate between ionic and metallic lithium in tin-based ion conducting glass [28.212]. Goward et al. use 7 Li to track the behavior of the lithium environment in charge-cycled ion conducting glass, identifying the presence of a lithium nanoparticle environment [28.213].
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
Transition Metal Ions. As some transition metal ions are stable in diamagnetic configurations, they may be studied by NMR rather than EPR. Some typical examples are listed here. Scandium 45 Sc (I D 7=2) has many desirable spectroscopic properties, with high natural abundance (100%) and high gyromagnetic ratio and moderate nuclear quadrupole moment. The chemical shift reference for 45 Sc is a dilute solution of Sc.NO3 /3 [28.105]. 45 Sc spectra of scandium-containing glasses were first reported by Mohr et al., who compared 1-D and MQMAS 45 Sc spectra of scandium aluminophosphate glasses to model oxides [28.218]. 31 P45 Sc REAPDOR and 45 Sc31 P REDOR were used to probe the homogeneity of the glass network. On the basis of their MQMAS and HETCOR data, Mohr et al. concluded that scan-
dium ions were evenly distributed through the network, with no clustering present. Kelsey et al. used 45 Sc to investigate the effect of pressure on the local environment of scandium on a 2 wt:% Sc2 O3 aluminosilicate glass, finding that there was an approximately 5% change in the chemical shift of the peak of the high-pressure sample [28.219]. Pahari et al. used 45 Sc as part of a comprehensive study of scandium aluminosilicate glasses containing significant (1520 mol%) fractions Sc2 O3 [28.220]. They found that the 45 Sc MAS central transition was significantly broadened by both CSA and quadrupolar interactions, with an isotropic chemical shift consistent with a six-coordinate scandium environment. Vanadium has two NMR-active isotopes, 50 V and 51 V. The former is not used due to poor abundance, integer nuclear spin, relatively low sensitivity, and its radioactive nature. 51 V is of high abundance (99:8%), reasonably high gyromagnetic ratio, and fairly low quadrupole moment, making it an attractive nucleus for NMR study. 51 V spectra are referenced to neat VOCl3 (0 ppm) [28.105], with various secondary shift references in use. 51 V NMR has focused on the relative quantification of different vanadium coordinations. The first 51 V study of vitreous V2 O5 found two distinct environments, which the authors attributed to four- and fivefold coordinate vanadium [28.221]. Similar results were found in sodium-vanadophosphate and sodium–borovanadophosphate glasses [28.222, 223]. Lapina et al. used high-temperature 51 V NMR to investigate the vanadium mobility in alkali sulfovanadate glasses [28.224]. Molybdenum is a somewhat challenging element for the NMR investigation of glasses. Its two NMR-active isotopes, 95 Mo and 97 Mo, have low abundance, and similarly low gyromagnetic ratios. The slightly greater sensitivity and significantly lower nuclear quadrupole moment generally make 95 Mo the target of NMR studies [28.225]. However high field strengths, 95 Mo NMR is typically feasible at natural abundance and without specific sensitivity enhancement techniques. Machida and Eckert used 95 Mo to deduce the local molybdenum structure in silver ion-conducting glasses, using crystalline molybdenum compounds as structural models [28.226]. Four- and six-coordinate molybdenum was identified in sodium molybdenum phosphate glasses by Santagneli et al. using a Hahn-echo pulse [28.227]. Nicoleau et al. have recently used 95 Mo to probe the behavior of molybdenum in model nuclear waste glasses, concluding that increasing MoO3 content leads to the formation of hydrated molybdate phases [28.228]. Lanthanum. Despite the generally positive spectroscopic properties (100% natural abundance, moderately
981
Part C | 28.4
Rubidium has two NMR-active isotopes, 85 Rb and Rb. While 87 Rb is the less-abundant isotope (27:9%), its significantly greater gyromagnetic ratio makes it the more sensitive nucleus, and the typical spectroscopic choice. 87 Rb NMR spectra are referenced to a dilute solution of RbCl [28.105]. Due to the significant quadrupolar broadening of 87 Rb spectra, there have been very few 87 Rb NMR investigations into glass structure. Michaelis et al. report the first 87 Rb spectra in an oxide glass, finding the spectra to have a single featureless resonance [28.214]. The significant narrowing of the peak at 21:1 T indicates that quadrupolar interactions are the primary broadening mechanism. Schneider et al. apply 87 Rb QCPMG to rubidium lithium phosphate glasses, finding that the estimated mean quadrupole product and peak center of gravity both decrease with decreasing RbC content [28.215]. Cesium has one NMR-active isotope, 133 Cs, with 100% natural abundance and moderate gyromagnetic ratio. The nuclear quadrupole moment of 133 Cs is extremely small, but 133 Cs spectra of glass still show significantly broadened peaks due to the significant chemical shift range. Due in part to the extremely small quadrupole moment, 133 Cs generally relaxes slowly, often requiring long experimental times. The 133 Cs NMR resonance of glassy environments is generally a broad, featureless peak. The isotropic chemical shift of the glass peak generally increases with cesium content [28.211, 216]. As CsC is replaced by other monovalent cations in phosphate glasses, Schneider et al. determined that the magnitude of the change in ıiso is dependent on the identity of the substituting cation, with NaC and AgC causing smaller changes than LiC [28.215]. 133 Cs NMR is effective in probing glass-ceramic composites, and is used to identify precipitating crystalline phases from model nuclear waste glasses [28.217]. 87
28.4 Magnetic Resonance Studies of Glass
982
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Characterization of Glasses
high gyromagnetic ratio), 139 La NMR has only recently been broadly applied due to the large quadrupole interaction of the 139 La nucleus. Only one oxide .LaAlO3 / has been reported under MAS conditions, and most early spectra were collected under static frequency-swept spin-echo conditions [28.229, 230]. The WURST-QCPMG pulse sequence has enabled rapid collection of broad 139 La peaks, with application to a broad range of crystalline compounds [28.231], as well as less-ordered crystalline materials [28.232]. While at the time of writing no 139 La NMR spectra of lanthanum-containing glasses have been reported in the literature, the barriers to the use of 139 La NMR spectroscopy in glasses seem imminently surmountable.
Part C | 28.4
Other Main Group Elements. Gallium has two NMRactive nuclei, 69 Ga and 71 Ga. Both are quadrupolar (I D 3=2) nuclei, and both are quite abundant, with natural abundances of 60% and 40%, respectively. 71 Ga is somewhat more sensitive, with a larger gyromagnetic ratio, but both nuclei are commonly observed. 71 Ga has a lower quadrupole moment than 69 Ga, generally leading to narrower spectra. Both nuclei are referenced to a 1:1 molar aqueous solution of Ga.NO3 /3 (0 ppm) [28.105]. The first application of 69;71Ga NMR in glass was by Zhong and Bray in their study of binary cesium gallate glasses [28.233]. Four- and six-coordinate gallium sites were identified by a combination of static and MAS NMR. Mao et al. used 71 Ga MAS NMR to determine the exclusively tetrahedral coordination of gallium in a gallium germanate chalcogenide glass [28.234]. Bureau et al. used an early implementation of the Czjzek model to describe the 69;71Ga behavior of amorphous gallium fluorides [28.204]. The above article is also an example of the use of VOCS to homogeneously excite very wide peaks. Le Caër, Bureau, and Massiot have also used 71 Ga spectra of gallium glasses as model systems for the extension of the Czjzek model [28.56]. Gallium NMR spectroscopy is also useful for the investigation of glass-ceramic composites. Rozé et al. used 71 Ga NMR to probe the crystallization of a germanium gallium selenide glass, concluding that the formation of a gallium-containing crystalline phase initiates widespread crystallization [28.235]. Sulfur is an important element in many industrially and scientifically interesting glasses, but has not been the subject of significant NMR investigation. Like 17 O, 33 S is of low natural abundance (0:76%); this is sufficiently low for isotopic enrichment to provide significant signal enhancement, though not so low as to preclude measurements on natural abundance samples. 33 S has a low gyromagnetic ratio and moderate nuclear quadrupole moment, resulting in poor sensitivity
and significant quadrupole broadening. The chemical shift range of 33 S is quite broad, spanning approximately 700 ppm [28.236]. However, the chemical shift range of sulfates and sulfides is very restricted in comparison, with isotropic chemical shifts ranging from 321 to 362 ppm with respect to CS2 (0 ppm) [28.237]. 33 S NMR spectroscopy has had limited application to glasses, with only sulfur-doped silicates being investigated [28.237, 238].
28.4.3 EPR Studies of Glass Unless a glass contains ions that are stable in paramagnetic configurations or contains a large fraction of defects, it will not exhibit an EPR spectrum. On the other hand, these two features, namely paramagnetic ions and defects, are two of the more important aspects for developing optical properties in glass. Both will be considered briefly here. Paramagnetic Ions If a glass contains paramagnetic ions, typically transition metals, the unpaired spin density can be probed with EPR spectroscopy. Not all transition metals are stable in paramagnetic configurations; those that are include Cr3C , Cu2C , V4C , and Ti3C (see [28.8, 239] for reviews). An example of Cr3C is shown in Fig. 28.25, in which Cr3C is doped into antimony phosphate glass [28.240]. These authors note that with no added Cr3C the glasses exhibited no EPR spectrum, while at low and high Cr3C content the spectra showed marked changes. These features could be assigned to octahedral coordination environments at low doping levels, and the presence of additional features due to ferromagnetic coupling between the Cr3C ions at high content (Fig. 28.25). In contrast, the ions giving rise to the unpaired spin density need not be transition metals. Work on a photothermorefractive (PTR) glass has shown that in fact antimony is a key paramagnetic center. In this type of glass exposure to light is necessary to initiate a chemical reaction and the development of a refractive index change. Typical PTR glass uses both cerium and silver, and it was thought that the photoinitiated step Ce3C C AgC ! Ce4C C Ag
(28.7)
was the initial process. However, careful EPR study has shown that the expected splitting patterns associated with 107 Ag and 109 Ag, both spin 1/2 nuclei, are absent, while the splitting patterns could be well explained by interaction with antimony sites; Fig. 28.26 [28.241]. The differences arise because 121 Sb and 123 Sb have spin 5/2 and 7/2 respectively and thus give very dif-
Nuclear Magnetic Resonance and Electron Paramagnetic Resonance Studies of Glass
a) EPR first derivative absorption (arb. u.)
28.4 Magnetic Resonance Studies of Glass
983
b) EPR first derivative absorption (arb. u.) g = 5.11
1
g = 5.11 2
1
0
g = 1.97
0
g = 1.97
g = 2.49
–1 0
1000
2000
3000
4000 5000 6000 Magnetic field (G)
0
1000
2000
3000
4000 5000 6000 Magnetic field (G)
Fig. 28.25a,b EPR spectra of (a) 3 mol% and (b) 6 mol% Cr3C doped antimony phosphate glasses, specifically 0:2ŒSb.PO3 /3 n -.0:77/Sb2 O3 :0:03Cr2 O3 (a) and 0:2ŒSb.PO3 /3 n -.0:74/Sb2 O3 :0:06Cr2 O3 (b). Reprinted from [28.240] with permission from Elsevier
50 dB, 2.0 μW 21 dB, 1.6 mW (G) Sb 121
Sb
123
Sb
2500
5000
7500
(I) (J)
Part C | 28.4
0
(H)
1000 Magnetic field (G)
Fig. 28.26 EPR spectrum of a photothermorefractive
(PTR) glass, (G), along with simulations based on antimony (Sb) as the paramagnetic center. (H) natural abundance Sb, (I) and (J) the two spin-active Sb isotopes. Reprinted from [28.241] with permission from Elsevier
ferent splitting patterns than silver. Therefore, the mechanism in Scheme 28.7 is much better understood as Ce3C C Sb5C ! Ce4C C Sb4C Sb4C C AgC ! Sb5C C Ag
(28.8) (28.9)
In this way EPR proves to be a key technique for following chemical processes that involve generation of paramagnetic species in glass. Defects in Glass In the context of EPR spectroscopy, defects in glass refer to points of unsatisfied electron valence, leading to unpaired spin density and hence EPR signals. Such defects are largely absent in well-annealed, clean glass, but can be induced (or appear naturally) from a variety
3342
3344
3346
3348 3350 Magnetic field (G)
Fig. 28.27 X-band CW EPR spectra of the E 0 defects in fused quartz, as a function of irradiation power. Reprinted from [28.243] with permission from Elsevier
of causes, such as radiation and particle bombardment, and atom substitution. Even in silica (fused quartz) there are a variety of possible defects, which give rise to subtly different EPR spectra [28.242]. An example is shown in Fig. 28.27, where the EPR spectrum of the well-studied E0 defect in fused silica is shown as a function of irradiation power [28.243]. The E0 defect arises from the unpaired electron on a three-coordinate silicon; in other words, one of the
984
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Characterization of Glasses
Fig. 28.28 2-D-HYSCORE
EPR spectrum of induced paramagnetic centers in B2 O3 glass. Reprinted from [28.244]. Copyright 1998 by the American Physical Society I
Part C | 28
four valence electrons in silicon is unpaired, leading to a defect center and also paramagnetism, hence and EPR signal. In nominally defect-free glass, defects can be added through particle bombardment, in order to generate paramagnetic centers. This method was used for example by Kordas and co-workers to study B2 O3 -derived glasses [28.244]. Interpretation of the induced defect sites was complicated by the interaction with the abundant, quadrupolar 11 B nuclei, but by use of pulsed methods such as ESEEM and HYSCORE (Sect. 28.3.4) the interaction of the defect centers with the nearby atomic centers could be quantified. Figure 28.28 shows a 2-D-HYSCORE spectrum of paramagnetic centers in B2 O3 glass [28.244]; the weak off-diagonal peak intensities were interpreted as arising from couplings to distant boron atoms. These couplings were interpreted with the aid of quantum chemical calculations as consistent with defect center interactions with broxol ring and nonring boron in the glass. In this way the EPR experiments were used as a probe of glass structure even though the parent glass gives no native EPR signal.
Frequency (MHz) 10 τ = 168 ns
(+, +)
8
6
4
2
0 (+, –) –2
–4
–6 0
2
4
6
8 Frequency (MHz)
28.5 Summary Despite its length, this chapter in no way would qualify as a full review of NMR and EPR studies of glass: the field is simply far too large and continues to grow. We have chosen to emphasize experiments for structural characterization of glassy solids, and have essentially left out for instance the many interesting ways that
NMR and EPR can be used to characterize dynamics. Nevertheless, structure is the largest area in which magnetic resonance is used in glass science, and as such we hope that this chapter has provided a useful introduction into the methods, experiments, and results of current use in this field.
References 28.1 28.2 28.3 28.4 28.5
M. Affatigato: Modern Glass Characterization (Wiley, Hoboken 2015) A. Abragam: Principles of Nuclear Magnetism (Oxford Univ. Press, Oxford 1961) C.P. Slichter: Principles of Magnetic Resonance, 3rd edn. (Springer, New York 1989) K. Schmidt-Rohr, H.W. Spiess: Multidimensional NMR and Polymers (Academic, London 1994) A. Schweiger, G. Jeschke: Principles of Pulse Electron Paramagnetic Resonance (Oxford Univ. Press, Oxford 2001)
28.6
28.7
28.8
E.R. de Azevedo, T.J. Bonagamba: Molecular dynamics and local molecular conformation in solid materials studied by nuclear magnetic resonance, Braz. J. Phys. 36, 61–74 (2006) S.E. Ashbrook: Recent advances in solid-state NMR spectroscopy of quadrupolar nuclei, Phys. Chem. Chem. Phys. 11, 6892–6905 (2009) D.L. Griscom: Electron spin resonance. In: Glass: Science and Technology. Advances in Structural Analysis, Vol. 4B, ed. by D.R. Uhlmann, N.J. Kreidl (Academic, Boston 1990) pp. 151–251
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28.9
28.10
28.11
28.12 28.13
28.14
28.15
28.16
28.17
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28.21
28.22
28.23
28.24
28.25
28.26
28.27
28.28
28.29
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28.31
28.32
28.33
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28.36
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R.R. Ernst, G. Bodenhausen, A. Wokaun: Principles of Nuclear Magnetic Resonance in One- and Two-Dimensions (Clarendon, Oxford 1987) M. Emshwiller, E.L. Hahn, D. Kaplan: Pulsed nuclear resonance spectroscopy, Phys. Rev. 118, 414 (1960) A.C. Kunwar, G.L. Turner, E. Oldfield: Solid-state spin-echo fourier transform NMR of 39 K and 67 Zn salts at high field, J. Magn. Reson. 69, 124–127 (1986) H.Y. . Carr, E.M. Purcell: Effects of diffusion on free precession in nuclear magnetic resonance experiments, Phys. Rev. 94, 630 (1954) S. Meiboom, D. Gill: Modified spin-echo method for measuring nuclear relaxation times, Rev. Sci. Instrum. 29, 688–691 (1958) F.H. Larsen, H.J. Jakobsen, P.D. Ellis, N.C. Nielsen: Sensitivity-enhanced quadrupolar-echo NMR of half-integer quadrupolar nuclei. Magnitudes and relative orientation of chemical shielding and quadrupolar coupling tensors, J. Phys. Chem. A 101, 8597–8606 (1997) J.A. Tang, L.A. O’Dell, P.M. Aguiar, B.E.G. Lucier, D. Sakellariou, R.W. Schurko: Application of static microcoils and wurst pulses for solid-state ultrawideline NMR spectroscopy of quadrupolar nuclei, Chem. Phys. Lett. 466, 227–234 (2008) L.A. O’Dell: The WURST kind of pulses in solidstate NMR, Solid State Nucl. Magn. Reson. 55, 28– 41 (2013) L.A. O’Dell, R.W. Schurko: QCPMG using adiabatic pulses for faster acquisition of ultra-wideline NMR spectra, Chem. Phys. Lett. 464, 97–102 (2008) I. Hung, Z. Gan: On the practical aspects of recording wideline QCPMG NMR spectra, J. Magn. Reson. 204, 256–265 (2010) L.A. O’Dell, A.J. Rossini, R.W. Schurko: Acquisition of ultra-wideline NMR spectra from quadrupolar nuclei by frequency stepped WURST–QCPMG, Chem. Phys. Lett. 468, 330–335 (2009) P.-K. Wang, C.P. Slichter, J.H. Sinfelt: NMR study of the structure of simple molecules adsorbed on metal surfaces: C2 H2 on Pt, Phys. Rev. Lett. 53, 82 (1984) E.R.H. Van Eck, W.S. Veeman: The determination of the average 27 Al-31 P distance in aluminophosphate molecular sieves with SEDOR NMR, Solid State Nucl. Magn. Reson. 1, 1–4 (1992) T. Gullion, J. Schaefer: Rotational-echo doubleresonance NMR, J. Magn. Reson. 81, 196–200 (1989) A.W. Hing, S. Vega, J. Schaefer: Measurement of heteronuclear dipolar coupling by transferredecho double-resonance NMR, J. Magn. Reson., Ser. A 103, 151–162 (1993) C.P. Grey, A.J. Vega: Determination of the quadrupole coupling constant of the invisible aluminum spins in zeolite HY with 1 H/27 Al TRAPDOR NMR, J. Am. Chem. Soc. 117, 8232–8242 (1995) T. Gullion: Measurement of dipolar interactions between spin-1/2 and quadrupolar nuclei by ro-
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28.19
E. Fukushima, S.B.W. Roeder: Experimental Pulse NMR: A Nuts and Bolts Approach (AddisonWesley, Reading 1981) M.E. Smith, K.J.D. Mackenzie: Multinuclear Solid State NMR of Inorganic Materials, Pergamon Materials Series (Pergamon, Amsterdam 2002) J. Herzfeld, A.E. Berger: Sideband intensities in NMR spectra of samples spinning at the magic angle, J. Chem. Phys. 73, 6021–6030 (1980) W.T. Dixon: Spinning-sideband-free NMR spectra, J. Magn. Reson. 44, 220–223 (1981) W.T. Dixon: Spinning-sideband-free and spinning-sideband-only NMR spectra in spinning samples, J. Chem. Phys. 77, 1800–1809 (1982) D. Massiot, F. Fayon, M. Capron, I. King, S. Le Calvé, B. Alonso, J.-O. Durand, B. Bujoli, Z. Gan, G. Hoatson: Modelling one-and two-dimensional solidstate NMR spectra, Magn. Reson. Chem. 40, 70–76 (2002) U. Werner-Zwanziger, K.W. Chapman, J.W. Zwanziger: Multinuclear NMR study of zinc dicyanide, Z. Phys. Chem. 226, 1205–1218 (2012) S. Chenu, U. Werner-Zwanziger, C. Calahoo, J.W. Zwanziger: Structure and properties of NaPO3 –ZnO–Nb2 O5 –Al2 O3 glasses, J. Non-Cryst. Solids 358, 1795–1805 (2012) B. Langer, I. Schnell, H.W. Spiess, A.-R. Grimmer: Temperature calibration under ultrafast mas conditions, J. Magn. Reson. 138(1), 182–186 (1999) D. Massiot, C. Bessada, J.P. Coutures, F. Taulelle: A quantitative study of 27 Al MAS NMR in crystalline YAG, J. Magn. Reson. 90, 231–242 (1990) M.E. Smith, E.R.H. van Eck: Recent advances in experimental solid state NMR methodology for half-integer spin quadrupolar nuclei, Prog. Nucl. Magn. Reson. Spectrosc. 34, 159–201 (1999) A. Samoson, E. Lippmaa: Excitation phenomena and line intensities in high-resolution NMR powder spectra of half-integer quadrupolar nuclei, Phys. Rev. B 28, 6567 (1983) F.M.M. Geurts, A.P.M. Kentgens, W.S. Veeman: 27 Al nutation NMR of zeolites, Chem. Phys. Lett. 120, 206–210 (1985) A.P.M. Kentgens: A practical guide to solid-state NMR of half-integer quadrupolar nuclei with some applications to disordered systems, Geoderma 80, 271–306 (1997) E. Kupce, R. Freeman: Adiabatic pulses for wideband inversion and broadband decoupling, J. Magn. Reson., Ser. A 115, 273–276 (1995) D. Massiot, I. Farnan, N. Gautier, D. Trumeau, A. Trokiner, J.P. Coutures: 71 Ga and 69 Ga nuclear magnetic resonance study of ˇ-Ga2 O3 : Resolution of four-and six-fold coordinated Ga sites in static conditions, Solid State Nucl. Magn. Reson. 4, 241– 248 (1995) A. Medek, V. Frydman, L. Frydman: Central transition nuclear magnetic resonance in the presence of large quadrupole couplings: Cobalt-59 nuclear magnetic resonance of cobaltophthalocyanines, J. Phys. Chem. A 103, 4830–4835 (1999)
References
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28.43
28.44
28.45
28.46
28.47
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28.50
28.51
28.52
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Electron paramagnetic resonance (EPR) studies on the photo-thermo ionization process of photothermo-refractive glasses, J. Non-Cryst. Solids 452, 320–324 (2016) A. Alessi, S. Agnello, G. Buscarino, Y. Pan, R.I. Mashkovtsev: EPR on radiation-induced defects in SiO2 . In: Applications of EPR in Radiation Research, ed. by A. Lund, M. Shiotani (Springer, Heidelberg 2014) pp. 265–298 D.G. Mitchell, R.W. Quine, M. Tseitlin, V. Meyer, S.S. Eaton, G.R. Eaton: Comparison of continuous wave, spin echo, and rapid scan EPR of irradiated fused quartz, Radiat. Meas. 46, 993–996 (2011) Y. Deligiannakis, L. Astrakas, G. Kordas, R.A. Smith: Electronic structure of B2 O3 glass studied by one-and two-dimensional electronspin-echo envelope modulation spectroscopy, Phys. Rev. B 58, 11420 (1998)
Josef W. Zwanziger Dept. of Chemistry Dalhousie University Halifax, Canada [email protected]
Josef Zwanziger holds the Canada Research Chair in NMR Studies of Materials at Dalhousie University, and is a Professor of Chemistry. He holds a BA from the University of Chicago, a PhD from Cornell University, and did postdoctoral work at the University of California, Berkeley. His primary research areas are the structure, mechanics, and optical properties of glasses.
Ulrike Werner-Zwanziger
Courtney Calahoo Dept. of Chemistry Dalhousie University Halifax, Canada
Courtney Calahoo is a Doctoral Candidate in Chemistry at Dalhousie University. She holds a BSc from McGill University. Her research involves glass structure and mechanics studies in mixed ion glasses and glass surfaces.
Alexander L. Paterson Dept. of Chemistry Dalhousie University Halifax, Canada
Alexander Paterson is a Doctoral Candidate in Chemistry at Dalhousie University. He holds a BSc from the University of Manitoba. His research involves structure and modeling studies of ferroelectric nanocomposites.
Part C | 28
Ulrike Werner-Zwanziger is Adjunct Professor in the Department of Chemistry at Dalhousie University, and Solid-state NMR Coordinator in the Nuclear Magnetic Resonance Research Resource. She holds degrees from the Westfälische WilhelmsUniversität Münster, and did a postdoctoral at the University of California, Berkeley. Her research centers around solid-state NMR methods development and application to materials.
Dept. of Chemistry Dalhousie University Halifax, Canada [email protected]
995
Refractive Ind 29. Refractive Index of Optical Materials
Jean-Louis Meyzonnette, Jacques Mangin, Michel Cathelinaud 29.1 29.1.1
Basic Parameters and Specifications .. Accuracy Requirements ......................
29.2
Main Properties of the Refractive Index...................... Propagation of Light .......................... Chromatic Dispersion of the Refractive Index....................... Reflection and Refraction by Transparent Media ........................ Energy Considerations ........................ External and Internal Reflections ........ Case of Thin Films ..............................
29.2.1 29.2.2 29.2.3 29.2.4 29.2.5 29.2.6 29.3 29.3.1 29.3.2 29.3.3 29.3.4 29.3.5
Measurement of the Refractive Index of Bulk Materials............................... Minimum Deviation Angle Through a Prism ................................ Littrow Method.................................. Methods Based on Grazing Incidence and Total Internal Reflection .............. Brewster Angle Method ...................... Ellipsometric Methods........................
Temperature Dependence of the Refractive Index...................... 29.4.1 Basic Considerations .......................... 29.4.2 Measurement of the Temperature Dependence of the Refractive Index n.; T / ............ 29.4.3 Thermo-Optic and Refractive Index Dispersion ........................................
996 996 998 998 999 1001 1003 1003 1006 1008 1008 1011 1012 1013 1014
29.4
29.5 29.5.1 29.5.2 29.5.3 29.5.4 29.5.5 29.5.6
Spectrophotometric Determination of Refractive Indices.......................... Some Useful Properties of Spectrophotometers....................... Case of Bulk Materials ........................ Refractive Index Measurement of Homogeneous Dielectric Thin Films . Case of Inhomogeneous Dielectric Thin Films ......................................... Case of Metallic Films Deposited on a Transparent Substrate ................. Optical Constant Determination by the Bilayer Metallic-Dielectric Method ............................................
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References................................................... 1040
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_29
Part C | 29
This chapter deals with the use of methods for measuring the refractive index of optical materials. It contains five sections: The first section recalls some bases of the electromagnetic theory of light leading to the main characteristics of the index of refraction, and their consequences in geometrical optics (Snell– Descartes laws), in the spectral transmission and absorption of optical media, or the polarization of light beams at interfaces between optical media. The second section describes the more or less classical panel of methods that have been devised to measure refractive indices of bulk materials: these are essentially based upon either the refraction or reflection of light inside prisms (minimum deviation angle, Littrow methods,. . . ) polarizing properties of optical boundaries (ellipsometric, Brewster configurations). While the previous section consists of refractive index characterization at a given temperature, the third section is dedicated to the dependence of the refractive index upon the temperature: the normalized thermo-optic coefficient (NTOC) is defined here and an experimental set-up specially designed for this purpose by one of the authors is described in detail. The last section is concerned with the fact that most optical components are thin film coated in order to improve their performance in transmission, reflection or absorption. Since spectrophotometry is extensively used to characterize these coatings, the operating principle of spectrophotometers is recalled, as well as the main parameters of these deposited films that one can expect to extract by using this technology from spectrophotometric measurements. Various spectrophotometric procedures are described to determine the optical constants of optical “systems” (bulk and thin film compounds) in the case of homogeneous or inhomogeneous films, slightly absorbing or not.
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Characterization of Glasses
29.1 Basic Parameters and Specifications The speed of light in vacuum, designated as c, is a physical constant for any type of electromagnetic radiation. For a monochromatic radiation of frequency , the wavelength 0 is then given by the relation 0 D
c :
(29.1)
Part C | 29.1
When light travels through a transparent, homogeneous material, its frequency remains unchanged, but its speed of propagation is modified (reduced) from c to v , so that its wavelength becomes D v = . The ratio between these quantities is the absolute index of refraction n of the medium: n D c=v D 0 =. If two media, 1 and 2, have respective indices n1 and n2 , the ratio n1;2 D n1 =n2 D v2 =v1 D 2 =1 is designated as the relative refractive index of the first medium relative to the second. Along with its wavelength, the other parameters of a light beam that are modified by the refractive index of the optical materials it encounters are its direction of propagation, split into both reflected and refracted beams at the interface, the energy it carries (attenuation or absorption by the atoms of the medium), and its state of polarization (direction of vibration). These effects are frequency dependent because they result from the mutual interaction between the incident electromagnetic field and the electrons of the medium under consideration. Frequency dependence and its effects may be analyzed by means of the basic electromagnetic theory of light. Among the parameters influencing the refractive index of a medium, we will mention the number of atoms per unit volume, related to its density m , and its chemical structure, converted into specific refractivity R in the following H. A. Lorentz formula n 1 D Rm : n2 C 2 2
(29.2)
Hence, gases have lowest refractive index values (close to one), as compared to liquids (typically between 1.3 and 1.6) and solids (between 1.3 and 4). In most experimental set-ups, refractive indices of solids and liquids are not measured in vacuum but in the presence of ambient atmosphere. This must be taken into account for specific applications (aeronautical, space or satellite optical systems), since the result from such measurements is the relative index of the medium with respect to that of air. nrelative D
nabsolute : nair
(29.3)
In the visible domain, the refractive index of air is around 1:00029, so the relative difference between absolute and relative indices is about 3 104. The specific refractivity R of a medium depends upon the frequency of the incoming light. This defines the dispersion of the medium, i. e., the change in the refractive index with respect to wavelength or (less commonly) frequency or wavenumber P D 1=. In the visible domain (380 nm < < 780 nm), glasses are generally specified by the value of their refractive index nd near the center of the domain ( D 587:6 nm at the d spectral line of He) and their dispersion by the Abbe number, defined as Abbe number D
nd 1 : nF nC
(29.4)
All optical glasses are classified in the Abbe diagram (Fig. 29.1), where (nF nC ) is the difference of indices between two hydrogen spectral lines: F (in the blue, D 486 nm) and C (in the red: D 656 nm). The influence of temperature on the refractive index of a medium is characterized by its thermo-optic coefficient, dn=dT, i. e., the change in refractive index per degree Celsius. This particular point will be treated in Sect. 29.3. Pressure also plays a role on the refractive index of media, particularly in gases, for which the molecular density is proportional to the pressure. This also affects liquids to a lesser degree. As far as solids are concerned, large pressure stresses and strains may induce birefringence in the medium, i. e., different values of refractive index depending upon the state of polarization of the incoming light.
29.1.1 Accuracy Requirements Because of its numerous influences on the behavior of any medium with respect to incident light, an accurate evaluation of its refractive index is of prime importance in all areas of optics: optical design, imaging and nonimaging applications, optical telecommunication, laser optics, atmospheric and space optics, bio-photonics, thin film coatings. To give a few examples:
Optical telecommunication Optical telecommunication is based on beam guiding by means of total reflection inside step index fibers or gradient index fibers that require perfect refractive index monitoring. Low-attenuation coatings As optical systems become more and more complex and involve an increasing number of components, reflection phenomena at each interface must be re-
Refractive Index of Optical Materials
29.1 Basic Parameters and Specifications
Fig. 29.1 Abbe
Refractive index nd (λ = 587.6 nm)
1.9
1.8
1.7
1.6
FK PK PSK BK BaK SK K LaK SSK BaLF KF LaSF LaF BaF BaSF LLF LF F SF ZK KzSF
Fluorite crown Phosphate crown Dense phosphate crown Borosilicate crown Barium crown Dense crown Crown Lanthanum crown Very dense crown Barium light flint Crown/flint Lanthanum dense flint Lanthanum flint Barium flint Barium dense flint Very light flint Light flint Flint Dense flint Zinc crown Special short flint
66
1.5
LaSF
21
90
80
LaF
8 14
21
5
10
4 57
1 4
2 BaK 5 7 ZK7
KzFS4
9
KF
2
4
5
LF
KzFS2 5
10
5
19
F
3
BaLF
K
2
2
5
4
1
LLF
5
70
60
50
40
20 Abbe number
(29.6)
(29.7)
In equation (29.7), K is a coefficient taking into account the system complexity (number and thicknesses of refractive components), and average and n are the average values of the wavelength and refractive index over the spectral domain. For highresolution systems typical of aeronautical and space applications, a value of K close to 5 106 m1 is appropriate if the average wavelength is expressed in m units. Table 29.1 lists some orders of magnitude of the refractive index accuracy that is required by optical designers for high-quality systems, relative to average values of wavelengths and refractive indices. Atmospheric corrections For applications in which long atmospheric distances are being traversed by light, tiny fluctuations
Part C | 29.1
n D K.n 1/average :
where r1 and r2 are the radii of curvature of the front and back surfaces, respectively, and n is the refractive index at that wavelength . Hence, for a monochromatic system, the uncertainty n on the value of the refractive index induces the following uncertainty f on the focal length f
In more complex optical systems, close to the diffraction limit, the uncertainties on the refractive indices of the various optical components over some spectral domain (visible, near-IR or thermal IR) must be low enough so as to maintain a negligible root mean square (RMS) value of the optical
30
path difference (OPD) induced by chromatic aberration onto the output wave-front. Quality criteria such as those of Maréchal or Strehl are generally required (typically: OPDrms < =10). Without getting into too much detail, one may show that this condition leads to the following constraint upon the accuracy of refractive index measurement required at each wavelength
duced to minimal values. This is generally achieved by depositing thin film coatings with refractive indices that are known as precisely as possible. Optical design In the simple case of a monochromatic system (at some wavelength ) made up of a thin lens, its focal length f is given by the well-known formula 1 1 1 D .n 1/ ; (29.5) f r1 r2
f n D : f .n 1/
KzFS11
52 4
8
KzFSN5
BaF
2
2
SK
11
7
51
SSK
15
16 14
BaSF
10
14
1 64 15
KzFS12
64
5
11
10
3
9 12
22
7 53
10
4
7
2
35 34
6 56
33
34
LaK
SF 45
47 43 36
32
33A
10 BK
FK
40
44
diagram of optical glasses (after Schott catalog [29.1])
57
9 41
53
52A 51A
31A
31
3
PK
46A
46
PSK
51
997
998
Part C
Characterization of Glasses
Table 29.1 Specifications on refractive index accuracy of bulk materials for high-quality optical systems Refractive index n (visible) average D 0:5 m n D 1:5 1 106 nD2 n D 4 (Ge)
n (near IR) average D 1:5 m 3 106
in refractive index induced by local temperature changes produce phenomena such as turbulence. Optical range-finding High-precision distance measurements, which are based upon time-of-flight range-finding techniques,
n (35 m) average D 4 m
n (812 m) average D 10 m
2 105 6 105
5 105 1:5 104
are degraded by uncertainties in the refractive index of the intermediate medium. This is the case, for instance, in astronomy experiments involving the precise measurement of the distance between the Earth and the Moon.
29.2 Main Properties of the Refractive Index 29.2.1 Propagation of Light Maxwell Equations in Vacuum These equations set relations between the electric and magnetic fields of radiation propagating inside a medium. Written as follows in the SI international set of units, they are the starting point for evaluating the refractive index of the material,
Part C | 29.2
r D D ; @B ; r E D @t r B D 0 ; @D ; (29.8a) r H D jC @t with @D @D @D C C (29.8b) r DD @x @y @z and the vector @Ez @Ey @Ex @Ez @Ey @Ex ; ; ; r ED @y @z @z @x @x @y (29.8c)
where E is the electric field vector, D the electric displacement field, H the magnetic field, B the magnetic induction, the free electric charge density and j the free current density. In the case of dielectric, homogeneous media such as a good-quality glass, j D D 0, and hence Maxwell’s equations reduce to @H ; @t
r H D 0 ; @E ; r H D " @t
r
@H @2 E D" 2 : @t @t
(29.10)
Then, by taking the second equation, we get
@H r .r E/ D r @t
D "
@2 E : @t2 (29.11)
Noting that A D r .r A/r .r A/ D r 2 A and taking into account the fact that r E D 0 we find E D
1 @2 E 1 with v D p : 2 2 v @t "
(29.12)
This is the equation of propagation of the electric field E (the same result can be derived concerning the magnetic field), leading to the value of the speed of propagation of light, which is, in vacuum 1 D 3 108 m=s; "0 0 1 since "0 D nF=m and 0 D 4 107 H=m : 36
cD p
In a transparent medium other than vacuum, one obtains " D "r "0
and
D r 0 :
(29.13)
For dielectric materials such as glasses, r 1, and hence c p n D D "r ; (29.14) v
r E D 0 ; r E D
where " and are the dielectric permittivity and magnetic permeability, respectively. By taking the derivative of the last equation relative to time, one obtains
(29.9)
which corresponds in optics to the so-called refractive index n of the medium.
Refractive Index of Optical Materials
Case of Transparent and Absorbing Media It is convenient to take the refractive index as a complex parameter. Going back to Maxwell’s equations (29.8a)– (29.8c), complex solutions in terms of plane waves (in z-direction), sinusoidally modulated with respect to time t with angular frequency ! are written in the form h i i ! t n c z C'
E .z/ D E0 e
;
(29.15)
where the complex refractive index is set as n D n i ;
(29.16)
similarly, the complex absolute dielectric permittivity of the medium can be written as " D n 2 D "0 i"00 :
(29.17)
The solution (29.15) is referred to the simple case of a harmonic wave propagating along the z axis in an isotropic medium, E being perpendicular to H and both lying in a plane normal to the z direction. ' represents a phase at origin t D 0 and z D 0. The coefficient ’ characterizes the absorption of the electromagnetic wave at angular frequency ! and is determined from spectroscopic measurements. Now, following Beer–Lambert’s law, the intensity I.z/ of a beam after propagation length z in an optical material is given by I.z/ D I0 e˛z ;
(29.18)
where I0 is the intensity of the incident light. Note that in terms of electric field attenuation, (29.18) corresponds to a field E.z/ (29.19)
since I.z/ / jE.z/j2 , E0 being a real. Hence, the basic equations that can be drawn for nonconductive and nonmagnetic media are 4
2 ! D ; c n 2 2 D "0 I 2n D "00 ; ˛D
" r
" ."0 i"00 / D D : "0 "0
29.2.2 Chromatic Dispersion of the Refractive Index Kramers–Kronig Relations One of the most useful ways to determine the real and imaginary parts of the complex refractive index is to perform spectroscopic measurements over the whole frequency range, that is from ! D 0 to ! ! 1. Kramers–Kronig (K–K) relations derive from the causality principle generally acknowledged in physics, which states that the response of a system subjected to a given excitation cannot exist before this excitation has taken place [29.2]. The system should be homogeneous, stable in time, and exhibiting a linear response. Basically, if f .t/ represents the response in the time domain, the causality principle states that we must have f .t/ D 0 8t < 0 :
(29.23)
One method for obtaining the K–K relations is to start by multiplying the f .t/ function by the Heaviside H.t/ step one, which does not change anything to relation (29.23), and going then to the frequency domain by taking the Fourier transform F.!/ of the product 1 F.!/ D p 2
ZC1 f .t/H.t/ei!t dt :
(29.24)
1
Detailed calculations following formula (29.24) can be found, for instance, in [29.3, 4]. It is found that in terms of the frequency dependence of the real and imaginary parts of the dielectric constant, the K–K relations may be expressed as 2 " .!/ 1 D P 0
"00 .!/ D
Z1 0
2! P
! 0 "00 .! 0 / 0 d! ; ! 02 ! 2 Z1 0
(29.25)
"0 .! 0 / 1 0 d! ; ! 02 ! 2
(29.26)
(29.20)
where P denotes the Cauchy principal value of the improper integrals of rational functions g.! 0/ (29.21)
n is the real refractive index which obeys the Snell– Descartes relationship, while is the so-called extinction coefficient; both depend on the angular frequency !. The complex dielectric function or relative dielectric permittivity " r is written as
Z1 P
g.! 0 /d! 0
0
2 6 lim 4
Z!
!0
0
(29.22)
999
g.! 0 /d! 0 C
Z1
3 7 g.! 0/d! 0 5 :
!C
(29.27)
Part C | 29.2
˛z
E.z/ D E0 e 2 ;
29.2 Main Properties of the Refractive Index
1000
Part C
Characterization of Glasses
In practice, for bulk optical materials, the refractive index n and extinction coefficient are deduced from the reflection spectra performed under (nearly) normal incidence. From the Fresnel formulas, R D r.!/r .!/ represents by definition the normal reflectance. The complex reflection coefficient r .!/ undergoes a phase change '.!/ and is written as r .!/ D jr .!/j ei'.!/ where jr .!/j is the complex reflectivity modulus. As a result of K–K relations we have 2! P '.!/ D
Z1 0
! ln r.! 0 / 0 d! : ! 2 ! 02
(29.28)
The refractive index and extinction coefficient can finally be derived from spectroscopic measurement through the use of Fresnel formulas in normal incidence 1 r2 .!/ ; n.!/ D 1 C r2 .!/ 2r.!/ cos '.!/ 2r.!/ sin '.!/ :
.!/ D 1 C r2 .!/ 2r.!/ cos '.!/
(29.29) (29.30)
Part C | 29.2
Thus, reflectance spectra allow one to calculate r.!/ and the phase change '.!/ undergone by the reflected beam. This holds for the case of an optically polished, flat front face of a bulk sample which is exposed to an impinging beam and set in a free space (near-vacuum condition). From a technical point of view, care must be taken to avoid an eventual contribution of the rear face of the sample to the reflected intensity; this can be realized, for instance, by shaping the material in a slightly wedged form. The case of a double-sided polished sample is examined in Sect. 29.5.2, Plane-Parallel Plate with Two Polished Surfaces. Sellmeier’s Formula This subsection recalls the basic equations that have led to the dispersion formula of the refractive index, in view of their further use in Sect. 29.4.3 for a rigorous formulation of their temperature dependence. The Maxwell equations (Sect. 29.2.1) are the constitutive formulas that describe at a macroscopic scale the response of a dielectric medium to an applied electric field E, irrespective of the atomic structure of the material. When determining the refractive index, the main parameter to be taken into account is the absolute complex permittivity " of the medium, which is related to the polarization P induced by the field P D "0 ." r 1/E :
(29.31)
With respect to microscopic analysis, the Lorentz model introduces the mean molecular polarizability ˛p
and assumes to first order that the polarization P at a mesoscopic scale is the sum of the mean polarizability of each molecule forming the material over the unit volume of matter. For weak fields, to a first approximation, the polarization P induced by a field E should be linear, described in the simplest form by P D "0 E ;
(29.32)
where is defined here as the complex dielectric susceptibility of the material, related to the abovementioned permittivity by the straightforward relationship D 1 " r
(29.33)
Speaking now in terms of mean molecular polarizability ˛p , it was shown that the effective field E0 acting on a molecule (Lorentz’s local field) is given by E0 D E C
P ; 3"0
(29.34)
larger than the average electric field E in the dielectric [29.5]. From these considerations, the mean molecular polarizability ˛p was related to the dielectric constant " (or the square of the refractive index n in Maxwell theory) through the so-called Lorentz–Lorenz formula ˛p D
3"0 n2 1 3"0 " 1 D N "C2 N n2 C 2
(29.35)
where N is the number of molecules per unit volume. The corresponding total electric moment P is P D Np D N˛p E0 ;
(29.36)
where p is the molecular elementary electric moment. For interaction of light with matter, we have to account for the frequency dependence of the response to an applied harmonic field E of angular frequency !. A molecule which consists of heavy nuclei surrounded by light particles (electrons) will undergo a local electric field E0 , as mentioned above. Assuming no motion of the nuclei, E0 will generate a harmonic motion of the electrons, bonded to the nuclei through a restoring force of amplitude F1 proportional to the displacements x from their equilibrium position (Hooke’s law) F1 D kf x ; where kf is the restoring constant.
(29.37)
Refractive Index of Optical Materials
Consider the example of one electron, which will also be subjected to the Lorentz force F2 proportional to its electric charge e and the local field E0 F2 D eE0 :
(29.38)
If me is the mass of the electron and neglecting the existence of a damping term (resisting force), due to energy dissipation and some friction between atoms, the equation of motion will take the simplest form @x C kf x D eE0 : @t2
(29.39)
For a harmonic field of the form 0
E D
E00 ei!t
(29.40)
and looking to a solution x D x0 ei!t ;
(29.41)
we get xD
eE0 2 ; me !0 ! 2
(29.42)
where s !0 D
kf me
(29.43)
n2 1 D
P D Ne x D N
e2 E0 2 : me !0 ! 2
(29.44)
Combining (29.35), (29.42) and (29.44) will give the variation of the refractive index n with angular frequency !, that is, chromatic dispersion, described by Ne2 n2 1 : D n2 C 2 3"0 me !02 ! 2
(29.45)
Of course, at the scale of a unit volume of matter, one may presume the occurrence of many resonance frequencies similar to the simplest case described above, so that (29.45) should reasonably be read as e2 N X n2 1 fi ; D n2 C 2 3"0 me i !i2 ! 2
(29.46)
X i
!i2
i ; !2
(29.47)
where we set i D
Nfi e2 : 3"0 me
(29.48)
In the above description, only electrons were considered, assuming that they easily move with respect to the applied field because of their low mass me ; (29.47) was shown to be quite satisfactory in the case of gases, particularly at short wavelengths. However, going towards infrared wavelengths we have to take into account the motion of nuclei, and (29.47) must also include resonance frequencies specific to lattice vibrations of optical materials [29.6]. Thus two sets of terms generally appear in Sellmeier’s dispersion formula when it is used to predict the value of the refractive index of a compound over its spectral region of transparency. High values of !i account for the UV cut-off, while lower values account for the infrared edge beyond which the material becomes opaque. In most cases, two poles added to a constant term are quite sufficient to accurately describe the chromatic dispersion.
29.2.3 Reflection and Refraction by Transparent Media Snell–Descartes Relationships Let us consider a monochromatic plane-polarized wave of modulus E0 that is incident upon the boundary separating two transparent media, 1 and 2, inside which the respective speeds of propagation are v1 and v2 , with corresponding refractive indices n1 D c=v1 and n2 D c=v2 . If E.x; y; z; t/ is the electric field of the incident wave and Er .x; y; z; t/ and Et .x; y; z; t/ are the electric fields of the reflected and transmitted waves, respectively, one must write the classical continuity equations at the interface, i. e., equality between the tangential components of E C Er and of Et as well as those for the magnetic fields. These equalities must pertain at all times, which means that the frequencies of these three waves must be the same; hence one may omit the effect of time and consider only the complex amplitudes. The plane of incidence is defined by the propagation vector and the normal to the interface. If we choose the xyz axes such that the xz plane is the plane of incidence
Part C | 29.2
is the resonance angular frequency of the un-driven electron. The elementary moment p D e x is to be extended up to the scale of the unit volume, and summing these contributions gives the total polarization
1001
where Nfi is the number of electrons oscillating at resonance angular frequency !i . From formula (29.46) it was shown [29.5] that the frequency dependence of the refractive index n is described through Sellmeier’s dispersion formula
2
me
29.2 Main Properties of the Refractive Index
1002
Part C
Characterization of Glasses
(Fig. 29.2), the direction cosines of the incident plane wave are then ˛1 .D .k1 ux /=jk1 j/ˇ1 .D .k1 uy /=jk1 j D 0/ and 1 .D .k1 uz /=jk1 j/ where ux , uy and uz are the unit vectors along the x, y and z axes, respectively. The incident electric vibration may be written, in complex notation, as
The second result leads to the well-known relationship sin .1 / D sin 10 and n1 sin .1 / D n2 sin .2 / ; (29.52)
where 1 , 10 , and 2 are the angles of incidence, reflection and refraction of the beam, respectively.
E D E0 exp Œik1 .˛1 x C 1 z/ ; 2 ! : with k1 D n1 D c 1
(29.49)
Fresnel Equations at an Interface At the interface between two homogeneous, isotropic, lossless dielectric media, Maxwell equations must be completed by boundary conditions imposing continuity between tangential components of both electric and magnetic fields, i. e.,
The reflected and transmitted vibration amplitudes will be written as
Er D r E0 exp ik1 .˛10 x C ˇ10 y C 10 z/ ; (29.50) Et D t E0 exp Œik2 .˛2 x C ˇ2 y C 2 z/ ;
ET1 D ET2
where ˛10 , ˇ10 , 10 are the direction cosines of the reflected wave, and ˛2 , ˇ2 , 2 are those of the transmitted wave, with k2 D n2 .!=c/ D 2 =2 . Writing continuity conditions at the boundary (z D 0) leads to the following results ˇ10 D ˇ20 D 0
The first result expresses the fact that the incident, reflected and refracted rays lie in the same plane, i. e., the plane of incidence.
E| |
c)
Part C | 29.2
H
ξ
E⊥ k1 Plane of incidence
E
k'1
Hr
k1
E
ux
Er
θ1 ux θ2
uz
Ht Et k2
uz
Hr
Boundary
θ2
uy
k'1
H k1
Er
θ1 Boundary
θ1
Boundary
(29.53)
Transverse Electric or TE Wave. Electric vector perpendicular to the plane of incidence.
b) E
HT1 D H T2 :
The mathematical expressions of reflectance and transmittance, which are derived by writing the continuity conditions at the boundary, depend upon the angle of incidence and the orientation of the electric and magnetic vectors relative to the plane of incidence. We will examine two cases of plane polarized light, first with the electric vector perpendicular to the plane of incidence, and then parallel to it.
and k1 ˛1 D k1 ˛10 D k2 ˛2 : (29.51)
a)
and
uz Ht Et
kt
ux
General case: ξ ≠ n /2 (n = 0, 1, 2)
E perpendicular to the plane of incidence (ξ = /2)
E parallel to the plane of incidence (ξ = 0)
Fig. 29.2a–c Electric, magnetic and propagation vectors: (a) general case of linearly polarized incident wave; (b) transverse electric incident wave; (c) transverse magnetic incident wave
Refractive Index of Optical Materials
The possible relative orientations of electric, magnetic and propagation vectors are drawn in Fig. 29.2b. The total tangential component of the electric vector is E C Er in the first medium and Et in the second (in complex notation). For the magnetic vector, they are .H Hr / cos .1 / and Ht cos .2 /. Denoting r? as the amplitude reflection coefficient (in the literature, one also finds rs , rTE or r ) and t? (or ts , tTE , t ) as the amplitude transmission coefficient, and taking into account the fact that H D E= v D nE= c, noting that the ratio H=E appears as the optical admittance Y, one obtains 1 C r? D t? and .1 r? /n1 cos.1 / D t? n2 cos.2 / :
(29.54)
Taking into account the Snell–Descartes law, that is n1 sin.1 / D n2 sin.2 ), this equation system leads to the following results sin .1 2 / and sin .1 C 2 / 2 cos .1 / sin .2 / t? D : sin .1 C 2 /
r? D
(29.55)
These two quantities are real, which means that the phase changes at the interface may be only 0 or . t? is always positive (no phase change), and r? is negative if 1 > 2 (i. e., n2 > n1 ), or positive if 1 < 2 (i. e., n2 < n1 ). In the case of near-normal incidence, these formulas become simpler n2 n1 n2 C n1
and t? D
2n1 : n2 C n1
(29.56)
Transverse Magnetic or TM Wave:. Electric vector lying in the plane of incidence. If the amplitude reflection and transmission coefficients are denoted rk (or rp , r ) and tk (or tp , t ), the orientation of the electric, magnetic and propagation vectors is as shown in Fig. 29.2c, which leads to the following continuity conditions 1 C rk cos .1 / D tk cos .2 / 1 rk sin .2 / D tk sin .1 /
29.2.4 Energy Considerations We must recall here that optical metrological instruments are sensitive to optical powers or fluxes (i. e., optical energy flow per unit time), while previous results are derived from reflection and transmission coefficients calculated at the scale of local electric fields E. These coefficients must be converted into corresponding measurable, energetic quantities. This can be done simply by considering that the energy flow per unit time of a beam of light (i. e., its flux or power P) is equal to the product of its energy density per unit area, dW=dS, times the beam cross section S and the speed of propagation of light, v . Since the energy density per unit area is proportional to "E2 , where " is the dielectric constant of the medium involved, the correspondence between the power of the incident beam and the power of the reflected or transmitted beam may be written as 0 dW 1 2
P2 B C S2 v2 D @ dS A : dWinc S1 vinc Pinc dS
(29.59)
In the case of reflection, the incident and reflected beams have identical cross sections and propagate through the same medium (i. e., with the same dielectric constant " and speed of propagation of light); hence the reflectance R is Er 2 Pr D D r2 : (29.60) RD Pinc Einc For the transmitted beam, the transmittance T is TD
"2 cos .2 / n1 2 tan .1 / 2 Pt t ; (29.61) D t D Pinc "1 cos .1 / n2 tan .2 /
taking into account that " D n2 .
29.2.5 External and Internal Reflections
and hence to the following expressions for both amplitude reflection and transmission coefficients tan .1 2 / and tan .1 C 2 / 2 cos .1 / sin .2 / tk D : sin .1 C 2 / cos .1 2 /
Here again, these coefficients are real; hence phase changes can be only 0 or . In the case of near-normal incidence, one finds the same results as for the previous case.
and (29.57)
rk D
(29.58)
1003
External Reflection External reflection is said to occur when n1 < n2 , for example, when light propagates from air into glass or from air into water. Here, again, we will first consider the case of polarized light, with the E vector being either perpendicular or parallel to the plane of incidence; then we will consider the case of natural light, and finally the case of linearly polarized light along some arbitrary direction.
Part C | 29.2
r? D
29.2 Main Properties of the Refractive Index
1004
Part C
Characterization of Glasses
Fig. 29.3 Amplitude reflection coefficient r? and reflectance R? versus incidence angle, from air to glass of refractive index n D 1:5 (TE wave)
1.00 0.75 0.50 Reflectance R⊥
0.25 0.04 15° –0.20
30°
45°
60°
75°
90° Incidence angle
–0.25 Amplitude reflection coefficient r⊥
–0.50 –0.75 –1.00
E Vector Perpendicular to the Plane of Incidence. Variations in r? with respect to the angle of incidence 1 are shown on the graph in Fig. 29.3 in the case of an interface of air with a glass of refractive index 1.5: r? starts at 0:2 for normal incidence and reaches 1 for grazing incidence (1 D =2). Corresponding values of R? evolve from 4% up to 100%. E Vector Parallel to the Plane of Incidence. rk starts from the same value of 0:2, as above for normal incidence, and changes in sign while crossing the zero value when 1 C 2 D =2, i. e., when reflected and refracted beams are perpendicular to each other. In that configuration, sin.2 / D cos (1 /; hence
n1 sin.1 / D n2 cos.1 / and consequently tan .1 / D
n2 : n1
(29.62)
This particular angle of incidence, for which the electric vector is parallel to the plane of incidence is not reflected at all is called Brewster’s angle. It has a value of about 56ı 200 for a glass of refractive index 1.50. Reflectance decreases from 4% at normal incidence down to zero at Brewster’s angle, then increases sharply up to 100% for grazing incidence, as shown in Fig. 29.4. Case of Natural Light. Light radiated from most natural sources is unpolarized, i. e., made up of a super-
Part C | 29.2
1.00 0.75 0.50 θ B = 56° 20' 0.25 Reflectance R| |
0.04
15° –0.20
30°
45°
60°
75°
90° Incidence angle
–0.25 Amplitude reflection coefficient r || –0.50 –0.75 –1.00
Fig. 29.4 Amplitude reflection
coefficient rk and reflectance Rk versus incidence angle, from air to glass of index n D 1:5 (TM wave; B corresponds to Brewster angle)
Refractive Index of Optical Materials
position of electric vectors vibrating along all possible directions. Such light may be considered as having two perpendicular components, Ek and E? , of equal amplitude but without any phase correlation. The reflectance for each of these components will be either Rk or R? , and generally, reflected light will be partially polarized: it will be completely depolarized for 1 D 0 and 1 D =2 and totally polarized (perpendicular to the plane of incidence) for 1 D B . Case of Light Linearly Polarized Along Some Arbitrary Direction. If the electric vector E is at angle with the plane of incidence (Fig. 29.2a), it can be decomposed into two in-phase components Ek D E cos. / and E? D E sin. / :
(29.63)
After reflection, one will get 0 Ek0 D rk E cos 0 and E? D r? E cos 0 :
sin .L / D
n2 ; n1
(29.67)
by setting s
sin2 .1 / 1 : n22;1
(29.68)
This leads to the fact that sin .1 2 / and sin .1 C 2 / are complex conjugates, as well as tan .1 2 / and tan .1 C 2 /. Therefore, both moduli of rk and r? equal unity, and the corresponding incident energies are totally reflected Rk D R? D 100% :
(29.69)
Figure 29.5 shows reflectance values Rk and R? versus the angle of incidence 1 in the case of a glass-to-air internal reflection (n1 D 1:5; n2 D 1:0).
1.00 0.75
θ B = 33° 40'
0.50 R⊥
0.25
R| |
θ L = 41° 50'
0.04 15°
30°
45°
60°
75°
90° Incidence angle
Fig. 29.5 Reflectance (R? and Rk ) of a glass-to-air interface versus incidence angle; B and L represent the Brewster and limit angles, respectively
Part C | 29.2
Internal Reflection Internal reflection is said to occur when n1 > n2 , which may arise, for instance, when a beam propagating inside a piece of glass hits the glass/air boundary. Equations (29.55), (29.58), (29.60) and (29.61), which give the characteristic parameters of the reflected and transmitted waves, still hold, provided that 1 is changed into 2 and vice versa. Three cases may thus occur:
(29.66)
one gets sin .2 / D .sin .1 //=n2;1, and cos .2 / becomes purely imaginary, s sin2 .1 / 1 D ˙i m cos .2 / D ˙i n22;1
mD
Since the coefficient of tan . / is always > 1, the plane of vibration tends to diverge from the plane of incidence.
n2 ; n1
the refraction angle 2 does exist, and part of the light is transmitted towards the outside (external) medium. For 1 D L , 2 D 90ı , and the emerging beam appears as grazing along the interface, following the boundary between the internal and external media. For an incidence angle 1 greater than L , the angle of refraction 2 no longer exists, but one may nevertheless introduce virtual values of sin .2 / > 1 and pure imaginary values for cos.2 / in the abovementioned expressions. By writing now
(29.64)
(29.65)
1005
As long as 1 remains smaller than a so-called limit angle L , satisfying the relationship
n2;1 D
Since these two components are in phase, the reflected vibration will still be linearly polarized, at an angle 0 with the plane of incidence such that 0 0 E? r? tan D 0 D tan Ek rk cos .1 2 / tan . / : D cos .1 C 2 /
29.2 Main Properties of the Refractive Index
1006
Part C
Characterization of Glasses
An interesting feature in the case of total internal reflection is the occurrence of a so-called evanescent wave in the external medium: when applying equations (29.49) and (29.50) to this case .1 > L /, one gets the following expression for the transmitted field E t D t E0 exp Œi k2 .˛2 x C 2 z/ ; with ˛2 D sin .2 / ; and 2 D cos .2 / D ˙i m :
Thus '? is an advance phase shift that increases from 0 for 1 D L up to for 1 D =2 2. In the case of an incident TM wave, which is the component parallel (Ek ) to the plane of incidence), one gets tan .2 1 / tan .1 C 2 / sin .1 / cos .1 / C im sin .2 / D sin .1 / cos .1 / im sin .2 / D exp i 'k :
(29.70)
rk D
(29.71) (29.72)
Taking into account that k2 ˛2 D k1 ˛1 D k1 sin 1 and that i k2 2 z becomes a real quantity, one may write E t D t E0 ek2 m z exp Œi k1 x sin .1 / :
As in the case of a TE wave, there is also an advance phase shift at reflection, such that
(29.73)
One will note that the minus sign has to be kept in the expression of cos .2 / in (29.72) to avoid the propagation of an infinitely increasing energy in the output medium. As a consequence, the transmitted wave creeps along the boundary, while at the same time its amplitude decreases exponentially along the z axis, which explains why it is called an evanescent wave. We can also analyze the phase shift arising in the case of total internal reflection, depending on the polarization state of the beam: 1. In the case of an incident TE wave, which is the component perpendicular (E? ) to the plane of incidence, the amplitude reflection coefficient may be written as sin .1 2 / sin .1 C 2 / sin .2 / cos .1 / C im sin .1 / D sin .2 / cos .1 / im sin .1 / D exp.i '? /
r? D
Part C | 29.2
(29.74)
and the phase shift '? at reflection is given by q ' sin2 .1 / n22;1 ? tan : (29.75) D 2 cos .1 /
(29.76)
tan
' k
2
D
q sin2 .1 / n22;1 n22;1 cos .1 /
:
(29.77)
This phase shift starts at 0 for 1 D L and increases up to for 1 D =2. Figure 29.6 shows the difference: 'k '? versus the angle of incidence, in the total reflection regime between glass (n D 1:5) and air.
29.2.6 Case of Thin Films Transfer Matrix Formulation A simple extension of the above analysis occurs in the case of a thin, plane-parallel film of material covering the surface of a substrate [29.7, 8]. The presence of two (or more) interfaces means that a number of beams will be produced by successive reflections, and the properties of the film will be determined by the summations of these beams. We denote the waves propagating along the direction of incidence and those propagating in the opposite direction by the symbols C and , respectively. The interface (b) located between the film and the substrate of Fig. 29.7 can be treated in the same way as for a simple boundary. By considering the tangential components of
/2 3/8 ∆φ = φ| | – φ⊥ /4 /8 0
θ L = 41° 50'
15°
30°
45°
60°
75°
90°
Incidence angle
Fig. 29.6 Phase shift difference in the total reflection regime for a glass (n D 1:5)-to-air interface, versus incidence angle
Refractive Index of Optical Materials
29.2 Main Properties of the Refractive Index
1007
So that C C E1a ; Ea D E1a
Incident plane wavefront
C C H1a : Ha D H1a
n0 Boundary (a)
Incident medium
θ0 d1
Thin film n1
z
Fig. 29.7 Plane wave incident on a thin film
the fields, there is no wave traveling within the substrate, and all C waves can be summed. Thus, at the substrate-thin film interface (b), the tangential components of E and H are (
C C E1b Eb D E1b C Hb D Y1 E1b Y1 E1b ;
(29.78)
where Y1 is the optical admittance defined as the ratio of the tangential components C E1b
Optical Properties of a Coating The procedure described in the preceding section can be extended to the general case of a stack of N layers, where the resulting characteristic matrix is simply the product of the successive individual matrices corresponding to the sequence performed during the coating process used. Starting from the substrate, one can take into account, step by step, each of the various appearing interfaces through the product of the corresponding matrices, to finally connect the field tangential components (EA , HA ) and (ES , HS ) drawn in Fig. 29.8 " # Y N sin ' i Yj j cos 'j EA ES D ; (29.84) HA H S iYj sin 'j cos 'j jD1 where the optical phase change 'j introduced by the jth layer) is defined by the expression 'j D
2 nj i j dj cos j ;
(29.79)
n0 R
1 EA HA
The field at the other interface (a) is obtained by taking into account the phase change ' (or phase shift) of the wave 'D
2 n1 d1 cos .1 / ;
(29.80)
where d1 is the thickness of the layer. Note that 1 is obtained by applying the Snell– Descartes relationship (29.52): n0 sin .0 / D n1 sin .1 / C C i' E1a D E1b e ; i' E1a D E1b e ; C C i' H1a D H1b e ; i' H1a D H1b e :
(29.81)
(29.85)
ES HS nS
T
Fig. 29.8 Diagram showing a multilayer coating de-
posited on a substrate considered as infinite. EA and HA represent the tangential components of fields at the upper interface. ES and HS are the tangential components of the field at the coating/substrate interface. nS and n0 are the refractive indices of the substrate and the input medium, respectively
Part C | 29.2
1 Hb D C Eb ; 2 Y1 1 Hb D C Eb ; E1b 2 Y1 1 C C D Y1 E1b D .Hb C Y1 Eb / ; H1b 2 1 H1b D Y1 E1b D .Hb Y1 Eb / : 2
These relations can be written in a matrix form such as i cos ' sin ' Eb Ea Y 1 D ; (29.83) Ha Hb cos ' iY1 sin ' where the 22 matrix is characteristic of a homogeneous thin film and often called its Abeles matrix.
Substrate ns
Boundary (b)
(29.82)
1008
Part C
Characterization of Glasses
where nj is the refractive index of the jth layer, j its extinction coefficient and dj its mechanical thickness; is the wavelength and j the angle of incidence inside the jth layer, determined by using the Snell–Descartes law, N is the number of layers, and Yj D
nj i j cos j
for p-polarization (TM-wave or k),
n0 for p-polarization, cos .0 / Y0 D n0 cos .0 / for s-polarization. Y0 D
Then speaking in terms of admittances, we get for a coating of N-layers [29.7, 8] " #! sin ' QN i Yj j cos 'j B 1 : (29.86) D jD1 C Y s iYj sin 'j cos 'j The reflectance at an interface (a) is
Yj D nj i j cos j
ˇ ˇ ˇ ˇ ˇ Y0 B C ˇ2 ˇ Y0 YA ˇ2 ˇ ˇ Dˇ R D jrj2 D ˇˇ ˇY C Y ˇ : Y0 B C C ˇ 0 A
for s-polarization (TE-wave or ?). The optical admittance at the interface is expressed by the relation Y D H=E. Note that the admittance of a thick absorbing substrate is equal to nS i S YS D cos .S /
The transmittance is TD
for p-polarization,
YS D .nS i S / cos .S /
for s-polarization,
(29.87)
4Y0 Re.YS / jY0 B C Cj2
;
(29.88)
where Re.YS / is the real part of YS and the absorptance is A D 1RT :
and for the incident medium (n0 )
(29.89)
29.3 Measurement of the Refractive Index of Bulk Materials
Part C | 29.3
The methods and set-ups used for measuring the refractive indices of bulk materials are based on the index-induced phenomena described in Sect. 29.2.3, mainly angular deviation of light by refraction through prisms, and also, to a lesser degree, total internal reflection including critical angle, and in some cases Brewster angle measurements.
29.3.1 Minimum Deviation Angle Through a Prism The minimum deviation method is recognized as the most accurate for measuring the refractive index of bulk materials. It consists in illuminating a prism of known apex angle ˛ by a monochromatic collimated beam of wavelength , and then measuring the minimum value ım of the deviation angle between input and output beams by means of a goniometer. Figure 29.9 shows a typical graph of deviation angle ı versus the angle of incidence . Minimum deviation occurs when rays inside the prism are perpendicular to the bisector of apex angle, hence when input and output beams are symmetrical with respect to that bisector.
At wavelength and temperature T, the refractive index of the prism material is then given by the following relationship n .; T/ D
sin .Œ˛.T/ C ım .; T/ =2/ : sin Œ˛.T/=2
(29.90)
The fact that the deviation angle is stationary in the neighborhood of this configuration somewhat alleviates the precision constraints on the setting of the corresponding incidence angle. Expected Accuracy The main experimental uncertainties that are to be taken into account for evaluating the affordable accuracy on the measured value of n.; T/ are as follows:
˛ upon the measurements of the apex angle of the prism, inducing a partial uncertainty n;˛ D .@n=@˛/ ˛ ı upon the measurements of the deviation angle from the prism, inducing a partial uncertainty n;ı D .@n=@ı/ ı
Refractive Index of Optical Materials
a)
b)
29.3 Measurement of the Refractive Index of Bulk Materials
1009
δ (°) 57.5 55.0 Limit incidence angle: θ 0 = arcsin(nsin[α – arcsin(1/n)]) 52.5
α
50.0 δm
47.5
θ θρ
45.0 42.5 40.0 37.5
δm
35.0 20
25
30
35
40
45
50
55
60
65
70
75
80
85
90 θ (°)
Fig. 29.9a,b Minimum deviation configuration; deviation angle through a prism
T upon the measurements of the temperature T of the prism, inducing n;T D .@n=@T/ T where .@n=@T/ is the value of the thermo-optic coefficient of the material, i. e., the change in its refractive index per ı C upon the measurements of the wavelength of the illuminating beam, inducing n; D .@n=@/ where .@n=@/ is the dispersive power of the material.
Considering that these uncertainties are uncorrelated, one may write that the global variance in the refractive index is the sum of all contributing variances
@n D @˛ ˛ ˛ ˛ C ım ˛ C ım cos sin sin cos 2 2 2 2 ; 2 ˛ 2 sin 2
Even with commercial equipment, the minimum deviation method is quite satisfactory for most materials in the visible range. In the infrared, strict precautions must be taken concerning the size of the prisms, the precision of the angular measurements and the temperature of the room, for a number of reasons. First, the angular measurement accuracy degrades as the wavelength increases from UV, to visible, and up to infrared, since it depends upon the (wavelength/pupil size) ratio and the signal-to-noise ratio. Second, many infrared materials are semiconductors, and their thermo-optic coefficients may be much larger than those of glasses of the visible domain (typically, one hundred times larger for germanium, for instance). Hence, in the IR domain, specific constraints are imposed upon the pupil size (> 30 mm), the surface quality (flatness better than =10, usually measured
(29.92)
s
(29.91)
@n D @˛
1 sin2
˛
˛ C ım n cos 2 2 ˛ : (29.93) 2 sin 2
Considering that the optimal value of apex angle ˛ must be chosen in accordance with the expected value of n (˛ decreases as n increases), and varies widely from one material to another, we choose to evaluate .@n=@˛/ with respect to n and the angle of incidence, considered as being the same for all materials. The following expressions make use of some characteristics of the minimum deviation configuration: If r is the angle of the refraction, sin . / D n sin .r / and ım D 2 ˛ sin . / ; ˛ D 2 arcsin n
(29.94)
Part C | 29.3
2 2 2 2 n2 .; T/ D n;˛ C n;ı C n;T C n; :
in the visible), temperature, (T < 0:1 K) and, in some cases, humidity and pressure. A rough evaluation is given next concerning the dependence of the refractive index accuracy upon uncertainties on ˛ and minimum deviation ım . Taking the partial derivative of n with respect to ˛, one gets
1010
Part C
Characterization of Glasses
Table 29.2 Contribution of the various sources of uncertainties on ˛, ı, and T to the index measurement accuracy by means of the minimum deviation method
MgF2
ZnS
ZnSe
Si
Ge
( m) 2.325 3.39 10.6 2.325 3.39 10.6 2.325 3.39 10.6 2.325 3.39 10.6 2.325 3.39 10.6
1.3
˛ (ı ) 72
n˛ 106 1.7
2.2
41
9
13
2.4
37
12
15
3.4
26
29
21
4
22
40
24
napprox
nı 106 7.9
dn=d n 106 (nm1 ) 106 7.4 7.4 11 22 53 265 9.6 9.6 10 20 14 71 10 10 4.6 9.2 6.5 33 18 18 7.1 14 0.2 1 68 68 30 60 0.7 3.5
dn=dT 106 (K1 ) 1
nT 106 0.1
40
4
60
6
150
15
400
40
2 n 105 2.2 4.7 53 3.7 5.2 14.4 4.6 4.5 8.4 8.8 8.5 8 18.5 17 12
Table 29.3 Relative percentages of various uncertainty contributions on apex angle ˛, deviation angle ı, wavelength and temperature T to the overall refractive index uncertainty
MgF2
ZnS
ZnSe
Si
Part C | 29.3
Ge
( m) 2.325 3.39 10.6 2.325 3.39 10.6 2.325 3.39 10.6 2.325 3.39 10.6 2.325 3.39 10.6
napprox 1.3
2.2
2.4
3.4
4
2 n 105 2.2 4.7 53 3.7 5.2 14.4 4.6 4.5 8.4 8.8 8.5 8 18.5 17 12
˛ D 100 (%) 3 0.5 0 22 12 1.5 27 28 9 46 49 55 18 22.5 42
one gets p n cos . / n n2 sin2 . / @n D : @˛ 2 sin . /
(29.95)
Similarly, one gets the following result for @n=@ı, where ı is deduced by measuring twice this deviation between two symmetrical positions of the prism with respect to the axis of the incident beam @n n D : @ı 4 tan . /
(29.96)
Table 29.2 shows a comparative evaluation between the expected accuracy of the minimum deviation method for the measurement of refractive indices of
nı D 600 (%) 51 11 0 50 25 3 44 45 15 24 26 30 6 5 16
D 1:2 nm (%) 46 88 100 23 60 95 20 18 73 18 12 0 58 50 0
T D 0:1 K (%) 0 0 0 5 2.5 0 9 9 0 12 13 15 18 22.5 16
various infrared materials: magnesium fluoride, zinc sulfide, zinc selenide, silicon and germanium. For this evaluation, the angle of incidence is the same for all samples ( D 50ı ), ˛ D 100 , ı D 600 , T D 0:1 ı C and D 1, 2 and 5 nm respectively at 3 different wavelengths: 2.325, 3.39 and 10:6 m. The results from this analysis indicate that the respective contributions of the various parameters vary widely from one sample to another and for a given sample from wavelength to wavelength. Table 29.3 lists these relative weights for the above-mentioned materials. Most national metrological laboratories such as PTB in Germany [29.9], LNE in France or NPL in Great Britain are equipped with this method to measure refractive indices with respect to air, at least in
Refractive Index of Optical Materials
a) 1st measurement:
reference input beam direction in the abscence of prism
29.3 Measurement of the Refractive Index of Bulk Materials
b) 1st measurement:
autocollimation on metallized side of prism
1011
Fig. 29.10 (a) Front face autocollimation and (b) Littrow configurations
α Goniometer
Goniometer
2nd measurement: deviated beam direction with normal incidence on front face of prism
2nd measurement: autocollimation on metallized side after prism rotation of angle + δ
α
α δ Goniometer
Goniometer δ
Fig. 29.11 Typical experimental set-up and prisms for Littrow configuration Parabolic Right angle prism primary mirror Off-axis collimator
Coated side
Ge prism
Detector
Goniometer Light source
Monochromator
the UV, visible and near-infrared domains, for measurements at ambient temperature. One may mention the NIST and the NASA Goddard Space Flight Center, which are able to measure absolute refractive indices down to cryogenic temperatures, up to the mid-infrared [29.10–13].
29.3.2 Littrow Method Two other arrangements, derived from the minimum deviation method, have found use in measuring the refractive index of bulk materials. The first, called the front face autocollimation method (Fig. 29.10a), consists in illuminating a prism under normal incidence upon the input face and measuring the corresponding
ZnSe prism
deviation of the output beam. It was widely used for the first characterizations of infrared materials between 1950 and 1980 (Optical Science Center, Tucson, University of Arizona, Institut d’Optique, Paris). It has been replaced in several labs (Schott Glasswerke, Institut d’Optique) by the Littrow method (Fig. 29.10b), in which the impinging beam hits the second face of the prism under normal incidence and is then retro-reflected by this optical face. The configurations of these set-ups are shown schematically in Fig. 29.10, with corresponding relationships between ˛, ı and n; a typical set-up for the Littrow configuration is shown in Fig. 29.11. Analysis of these techniques shows that they are less accurate than the minimum deviation method, typically
Part C | 29.3
Beam splitter
1012
Part C
Characterization of Glasses
by respective factors of 2 (Littrow set-up) and 4 (autocollimation on front face).
29.3.3 Methods Based on Grazing Incidence and Total Internal Reflection Grazing Incidence The principle behind measuring refractive index by grazing incidence is as follows: when a ray propagating inside a medium of refractive index n1 is launched under grazing incidence (1 D 90ı ) at the interface with a medium of index n2 > n1 , it is refracted inside the second medium along the direction of the limit angle L such that n1 sin .L / D : (29.97) n2 If an incident beam, comprising rays under grazing incidence, converges at some point I (Fig. 29.12) of such an interface, the beam refracted in the second medium disappears beyond the angle L , thus defining a well-contrasted separation line between the clear and dark areas. If the second medium is a reference of precisely known refractive index, the measurement of the refractive index n1 emerges from the measured value of the limiting direction L .
Part C | 29.3
Practical Set-Up: Pulfrich Refractometer In a Pulfrich refractometer, the sample to be characterized is placed on top of a reference glass shaped like a cube, the horizontal and output faces of which are precisely polished and approximately normal to each other (angle ˛ 90ı on Fig. 29.12). In order to reduce stray light reflections from the interface, some immersion liquid whose index is matched to the reference cube is also deposited between the reference and the sample. The illuminating beam, containing rays that are parallel to the interface, is first refracted into the reference cube under
the limit angle L , then refracted out of it under the angle of refraction 3 . The refractive index of the sample, nsample , may be obtained from nref , ˛ and 3 by the relationship nsample D sin .˛/
q n2ref sin2 .3 / cos .˛/ sin .3 / ; (29.98)
where the angle 3 is measured by means of a goniotelescope, also used as autocollimator, by pointing the normal to the output surface of the reference cube and the direction of the limit between dark and bright areas. In the visible domain, where the Pulfrich refractometer is exclusively used, the uncertainty that can be expected is on the order of 104 . Total Internal Reflection If a ray is incident from medium 1 of index n1 , onto a medium 2 of index n2 < n1 , it is totally or partially reflected back towards the first medium if the angle of incidence is either greater than or less than the limit angle L , respectively. Hence, if the interface is illuminated by a beam converging at some point I (Fig. 29.13) of the interface, there results, by reflection back to the first medium, a separation line between a bright and a dark region. This method may give rise to two different configurations, one of which does not require that the illuminating light propagate through the sample. In this case, this method is of particular interest for measuring refractive indices of absorbing media that cannot be characterized by prism or grazing incidence methods. The Abbe refractometer is essentially intended for measuring the refractive index of liquids, viscous fluids or gels. It is composed of two identical reference prisms, one for illumination and the other for measurement purposes. They are of known, high refractive index (nref > 1:7), and of standardized shape (right an-
Partially reflected beam
Converging incident beam
Input rays at grazing incidence
Totally reflected beam
Sample I
Output rays at limit angle
α θL
Luminance inside the field of view of the telescope
θ3
Refracted beam
Reference cube, nref Gonio-telescope
Fig. 29.12 Configuration of Pulfrich
refractometer
Refractive Index of Optical Materials
29.3 Measurement of the Refractive Index of Bulk Materials
Partially reflected beam
Fig. 29.13 Abbe refractometer configuration for transparent media
Abbe prisms refractive index nref Input beam
1013
Totally reflected beam
I γ
α
θL
θ3
β
Telescope
Sample, nsample Flat mirror Limiting direction of totally reflected rays
gle triangle, with angles ˛ D 60ı , ˇ D 90ı , D 30ı ). The hypotenuse side of the measurement prism is set horizontally so that small amounts of liquids can be poured on top of it. If the liquid medium to be characterized is transparent, the illumination prism is deposited face-down on top of the measurement prism to spread the liquid uniformly between the two prisms, so that the resulting layer behaves optically as a thin and parallel face plate (Fig. 29.13). The rays that propagate with an angle of incidence larger than the total internal reflection angle L are totally reflected back into the upper prism, while the others are partially reflected, and partially refracted into the measurement prism below that angle L sin .L / D
nsample : nref
(29.99)
a)
b)
29.3.4 Brewster Angle Method In this method, the sample is shaped as a plane-parallel face plate and illuminated by a collimated, linearly polarized beam, at the vicinity of the Brewster angle (Fig. 29.14a). If the electric vector of the incident R 1.0 0.9
Polarizer Source
E⊥ E ξ
θ2 θ1
E| |
S, n1
Transmitted beam
R| | R⊥ R| | /R⊥ (ξ = 45°) R (ξ random) n = 1.50
0.8 0.7 0.6
n1
Goniometer Reflected beam Analyzer
0.5 0.4 0.3
θ Β = 56.25°
0.2 Detector
0.1 0.0
0
10
20
30
40
50
60
70
Fig. 29.14a,b Brewster angle method: General configuration (a), and (b) reflectance versus incidence angle
80
90 θ1 (°)
Part C | 29.3
By adapting (29.98) to this configuration, one finds q 2nsample D 3Œn2ref sin2 .3 / sin.3 / : (29.100)
One may note that, in this configuration, the dark region in the output beam is perfectly black, since no radiation is transmitted beyond the total reflection angle. Hence, the contrast between these two regions is quite good. If the liquid is opaque, the illuminating prism is of no use, and the sample is then illuminated from below, through the hypotenuse side of the measurement prism. In this case, the contrast is not as high, since the fraction of incident rays with incidence angles below the total reflection angle are partially reflected, but it is usually sufficient to give access to the refractive index of opaque liquids not measurable by other means. Abbe refractometers are used extensively in the chemical and food industries.
1014
Part C
Characterization of Glasses
Fig. 29.15 Possible improvement in refractive index measurement by Brewster angle determination
∂ ln (R| | /R⊥) / ∂θ1 2.5 2.0 1.5 1.0 0.5 0.0 –0.5 –1.0 n = 1.50
–1.5 –2.0 –2.5 –3.0 –3.5 50
θB 51
52
53
54
55
56
57
58
59
60
61
Part C | 29.3
beam is parallel to the plane of incidence, Rk drops to a minimum value when the sample is rotated back and forth around this angle of incidence, 1 D B , for which n D tan.B /. The precision of this configuration is rather poor, however, because the Rk curve is stationary around the Brewster angle of incidence. The accuracy may be somewhat improved by polarizing the input beam at 45ı with respect to the plane of incidence, and by recording the curves of both Rk and R? relative to the incident angle 1 and solving for n from the best fit between experimental and theoretical curves (Fig. 29.14). A further improvement in accuracy may be obtained by applying a minor modulation d1 around each angle of incidence and recording the resulting modulations dRk and dR? [29.14]. As shown on Fig. 29.15, the Brewster angle B is then the value of the incidence angle, for which there is a discontinuity of the first derivative of Rk @ ln R? D0: (29.101) @1 The uncertainty in refractive index of this method is on the order of 104 .
29.3.5 Ellipsometric Methods Ellipsometry is widely used in refractive index measurements of bulk (or stacked) samples [29.15–29]. It gives rise to a large number of methods and configurations that cannot all be covered here. That is why
62
63
64
65 θ1(°)
a selection has been made in this section that covers the operating principle and basic parameters of this technique, and is limited to the description of two classical configurations. Operating Principle and Measurement Parameters Through the use of Fresnel formulas, equations (29.29) and (29.30) show how the refractive index n.!/ and extinction coefficient .!/ of a bulk material may be derived from spectroscopic measurements of the amplitude complex reflectance of the medium under normal incidence. In these equations, the phase change '.!) between reflected and incident waves at the boundary results from K–K relation (29.28). In a more extensive use of Fresnel formulas, ellipsometry is based upon specific apparatuses (ellipsometers) in which the sample (either bulk or stacked) is illuminated under oblique incidence by a monochromatic beam having a well-controlled state of polarization. The refractive index of the sample is then computed from the measurement of the amplitudes and states of polarization of the incident and reflected waves, respectively. By expanding the amplitude reflection coefficient (29.55) of an optical boundary, for the oblique incidence angle 1 of a wave polarized perpendicularly to the incidence plane (TE polarization), one gets sin.2 1 / ETE,r D ETE,inc sin.2 C 1 / 0 1 q 2 2 2 n cos. / n n sin . / 1 1 C 2 1 B 1 D@ q A (29.102) n1 cos.1 / C n22 n21 sin2 .1 /
r? D
Refractive Index of Optical Materials
and similarly, for an incident linearly polarized wave parallel to the plane of incidence (TM polarization) ETM,r ETM,inc tan.2 1 / D tan.2 C 1 / 1 0 q n1 2 2 2 n cos. / C n n sin . / 2 1 1 2 1 C B n2 C: DB q A @ n1 n2 cos.1 / C n22 n21 sin2 .1 / n2
rk D
(29.103)
Hence, r? and rk , which are real if both media are lossless ('? D 'k D 0 or ), and complex if one or both of the media are absorbing ('? ¤ 'k ), may be written as r? D jr? j exp.i '? / and ˇ ˇ rk D ˇrk ˇ exp.i 'k / :
(29.104)
Let a monochromatic polarized beam of electric field Einc be incident upon the interface between two media of refractive indices n1 and n2 with the incidence angle 1 Einc D ETE cos.! t k r C 'TE / C ETM cos.! t k r C 'TM / :
(29.105)
Er D jr? j ETE cos.! t k r C 'TE C '? / ˇ ˇ C ˇrk ˇ ETM cos.! t k r C 'TM C 'k / : (29.106)
A comparison between (29.105) and (29.106) shows that, if the incident electric field is not perpendicular or parallel to the plane of incidence (jETE j and jETM j ¤ 0), the states of polarization of the reflected and the incident beams differ from each other: for instance, if the input beam is plane-polarized ('TE D ˙'TM / and if the medium under test is nonabsorbing (n2 real), the reflected beam is also plane-polarized, but in a different direction, if the medium is nonabsorbing, and it is elliptically polarized if the medium is absorbing. Since the angle of incidence 1 and the refractive index n1 of the first medium (usually air) are known parameters, the change in the state of polarization at reflection is a function of the unknown refractive index n2
1015
to be measured, and it is possible to deduce the refractive index n2 by measuring r? and rk . Since n2 D n i , there are two unknowns, and two equations are necessary to fully characterize n2 . In practice, ellipsometric techniques are devised to measure the quantity e , the complex reflectance ratio, rk over r? ˇ ˇ ˇrk ˇ
rk exp i 'k '? e D D r? jr? j D tan exp.i/ : (29.107) where 2 Œ0ı ; 90ı and 2 Œ180ı ; C180ı , the two basic parameters being measured, are such that tan is the ratio between the (amplitude) attenuation of the TM and TE components of the electric vector, and is the difference between their phase lags at reflection. In the particular case of a bulk material, expansion of (29.107) leads to the following expression of n2 s 1 C e 2 2 n2 D n1 sin 1 1 C tan 1 : (29.108) 1 e Two Main Methods Among the numerous methods used in ellipsometry, this section describes two of the more common, namely the nulling technique and the modulation technique by rotatable components. More complete reviews, concerning for example the techniques of multiple-angleof-incidence ellipsometry (MAIE), spectroscopic ellipsometry (SE), or variable-angle spectroscopic ellipsometry (VASE), may be found in references [29.15–18, 27–29]. Nulling Technique. The configuration of the nulling technique (Fig. 29.16) comprises a monochromatic source (laser or filtered source), a polarizer, a compensator (such as a quarter wave plate) an analyzer, and a detector. The linearly polarized output wave from the polarizer is converted into an elliptically polarized wave by the compensator, which is oriented in such a way that the light reflected by the sample is linearly polarized. The analyzer is then oriented perpendicularly to the plane of polarization in order to obtain extinction (nulling) of the reflected beam. The ellipsometric parameters of the sample are directly derived from the respective orientation angles of the polarizer, of the compensator and ˛ of the analyzer, with respect to the plane of incidence, by means of the following relationship tan
exp.i/ D tan ˛
tan tan. / : 1 C i tan tan. / (29.109)
Part C | 29.3
where ETE and ETM are its components perpendicular and parallel to the plane of incidence, respectively, with phases 'TE and 'TM . The reflected electric field Er is then
29.3 Measurement of the Refractive Index of Bulk Materials
1016
Part C
Characterization of Glasses
Fig. 29.16
Angles between P, C, A polarizing directions and plane of incidence
Source
ξ
Circular or un-polarized
α
γ
Linear polarizer (P)
Configuration of a nulling ellipsometer
Detector
Compensator (C)
Nulling analyzer (A)
Sample Linear
Elliptic
Linear
Extinction
Fig. 29.17
Source
Modulation ellipsometer in the rotating analyzer configuration
Rotating analyzer Detector
Linear polarizer
Sample Linear
Elliptical
Modulated flux
State of polarization
Part C | 29.3
Even when automated, this method is rather slow because of the search for the minimum value of the output signal from the detector, but it is quite accurate. Modulation Techniques by Means of Rotating Components. These techniques consist in periodically modulating the state of polarization of the beam by rotating the polarizer, the compensator or the analyzer. If the rotating element is the polarizer, then the source must be circularly polarized, or unpolarized, as perfectly as possible. If it is the analyzer, then the detector must not be polarization-sensitive. If it is the compensator, these constraints on both the source and the detector are relaxed, but the compensator must be carefully calibrated spectrally and well aligned. Time Dependence of the Detector Output (Case of an Ellipsometer with Rotating Analyzer). Let us consider the configuration of Fig. 29.17, in which the (stationary) polarizer is linearly polarized along some axis at angle with the plane of incidence.
The parallel (p) and perpendicular (s) components of the electric vector are then Ep D E0 cos
and
Es D E0 sin :
(29.110)
After reflection of the wave from the sample, these components become Ep0 D rk Ep D r? E0 tan Es0
exp.i/ cos ;
D r? Es D r? E0 sin :
(29.111)
The complex amplitude a.t/ at the exit of the analyzer is obtained by summing the projections of the components Ep0 and Es0 onto the polarizing direction of the analyzer (Fig. 29.18), hence a.t/ D Ep0 cos ˝t C Es0 sin ˝t ;
(29.112)
where ˝ is the angular speed of rotation of the analyzer a.t/ / sin sin ˝t C tan
exp.i/ cos cos ˝t : (29.113)
Refractive Index of Optical Materials
29.4 Temperature Dependence of the Refractive Index
1017
from the detector, which can be expressed as follows with respect to its average value I0
TE axis
I.t/ D 1 C A cos 2˝t C B sin 2˝t : I0
Rotating analyzer
Where A and B are the Fourier coefficients of this function at its fundamental frequency, with
E0
E0 sinξ
AD
Incident E0
r⊥E0 sinξ ξ Ωt
r | | E0 cosξ
Fig. 29.18 States of polarization
1 C tan2 cot2 cos2 sin2 D ; 1 C tan2 cot2 cos2 C sin2 (29.118)
and BD
Since the flux on the detector is proportional to the modulus square of the amplitude, one gets
F.t/ / Œsin sin ˝t C tan Œsin sin ˝t C tan
tan2 tan2
E0 cosξ
TM axis ( | | plane of incidence)
F.t/ / a.t/a .t/ ;
(29.117)
sin 2 tan
cos
C sin2 2 tan tan cos : D 1 C tan2 cot2 tan2
cos2
(29.114)
exp.i/ cos cos ˝t exp.i/ cos cos ˝t : (29.115)
After development and simplification, the following relationship is obtained F.t/ / tan2
cos2 C sin2 C cos 2˝t tan2 cos2 sin2 (29.116) C sin 2˝t sin 2 tan cos :
The ellipsometric angles and of the sample are then derived from the above quantities by ˇr ˇ ˇ 1C Aˇ ˇ ˇ tan D ˇ ˇ jtan j and ˇ 1Aˇ ˇr ˇ ˇ 1 ˇˇ ˇ cos D B ˇ (29.120) ˇ: ˇ 1 A2 ˇ The sign of , which depends upon the (left or right hand) type of the elliptical polarization of the reflected beam, cannot be determined from the flux detected in this set-up. In order to solve this ambiguity, a complementary measurement is needed, by means of a compensator of known slow and fast axes.
29.4 Temperature Dependence of the Refractive Index 29.4.1 Basic Considerations Temperature is one of the most important parameters affecting the value of the refractive index of bulk (dielectric) optical materials. At a macroscopic scale, we consider the material as a stack of identical molecules, each linked to the others through some kind of binding forces. From Lorentz’s theory, mentioned in Sect. 29.2.2, Sellmeier’s Formula, if p is the elemental polarization associated with a molecule placed in an electric field E, we have p D ˛p "0 E, where ˛p represents the molecular polarizability. The polarization P at the scale of the unit volume V of material will be P D Np D N˛p "0 E, N being the density number of molecules. For one mole
of matter, for instance, we have P D .NA m ˛p =M/"0 E, NA being the Avogadro number, M the molecular weight and m the mass density. In this case the volume V that is to be considered will be the molar volume. Both the m and ˛p parameters are temperature-dependent, and thus so is the refractive index. Several attempts have been made to accurately describe the thermo-optic coefficients (TOC) dn=dT of optical materials [29.30–36]. Predicting their thermal behavior over the whole spectral range of transparency is also of the utmost importance for proper implementation in nonlinear optical devices where highpower lasers are employed in frequency conversion arrangements.
Part C | 29.4
Hence the signal flux upon the detector is a periodic function of time, which varies at twice the frequency of rotation of the analyzer. So does the output current I.t/
(29.119)
1018
Part C
Characterization of Glasses
Table 29.4 Thermo-optic coefficient dn=dT (106 K1 ) and volume expansion coefficient ˛v (106 K1 ) of some ionic crystals and selected glasses Compound Ionic crystals LiF
Part C | 29.4
LiCl LiBr LiI NaF NaCl NaBr NaI KF KCl KBr KI RbF RbCl RbBr RbI CsF CsCl CsBr CsI KRS 5 (TlBr 48%, TlI 52%) CaF2 SrF2 BaF2 UV-Vis glasses d Lithosil SiO 2 d N-BK7 d N-SF6 d LF5 Clearceram-Z regular
Wavelength ( m)
dn=dT 106 (K1 )
0.633
18b;c
0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 0.633 10.6 0.633 0.633 0.633
31.7b 38.8b 48b 16.8b 32.2b 38.6b 45.9b 23.2b 31.7b 36.6b 43.75b 25.1b 39.4b 44.9b 56.3b 41.7b 77.4b 84.75b 96.25b 235 10.4 12.7 16
0.633 0.633 0.633 0.633 0.633
10 2.5 0.43 2.3 13.9
One way to evaluate the TOC is to start from the Clausius–Mossotti relationship (analogous to (29.35), which connects the dielectric permittivity " of a medium to its molecular polarizability ˛p . It was first proposed for static electric fields and then extended to the case of alternating fields within the framework of the local field theory developed by H. Lorentz. For one mole of matter, the formula is written as NA m ˛p "1 D : "C2 3M
(29.121)
Taking the derivative with respect to T gives @" 3 ." C 2/2 @T @˛p @˛p @m dV NA C m C D ; ˛p 3M @T @T T dT @T V (29.122)
˛v 106 (K1 ) a
References
99.6b 102.9c 131.4b;c 150b;c 177b;c 100.5b;c 123.3b;c 125.4b;c 134.1b;c 94.2b;c 109.5b;c 115.5b;c 120.9b;c 82.5b;c 108b;c 111b;c 117b;c 111b;c 135 141.6b;c 145.8b;c 174 56.7 55.2 55.2
[29.37–41]c
1.56 21.9 27 24.9 6
[29.37, 40, 41] [29.40–42] [29.40] [29.37, 39–41] [29.37, 39, 40] [29.37, 39, 40] [29.37, 39, 40] [29.37, 40], [29.37, 40], [29.37, 40] [29.37, 40] [29.37] [29.40] [29.40] [29.40, 41] [29.38] [29.40, 41] [29.39, 41] [29.39, 41] [29.39] [29.39, 42–45] [29.39, 43] [29.39, 43, 45] [29.42] [29.46–48] [29.46–48] [29.46, 46, 48] [29.49]
for which a dependence of ˛p on both V and T is assumed. For an isotropic material, and considering a volume V as that of a sphere of radius R, we have dV=dT D 3V˛L , ˛L being the usual linear thermal expansion coefficient: ˛L D .1=R/.dR=dT/. Recasting (29.122) then yields 1 @" ." 1/ ." C 2/ @T @˛p V @˛p 1 C : D ˛L 1 ˛p @V T 3˛p @T V (29.123)
For materials exhibiting a high thermal expansion coefficient, such as alkali halides, for instance, the TOC is negative, while it is positive in covalent compounds, due to a pre-eminent contribution of the change in polarizability. We can also predict, from (29.13), which is further described in Sect. 29.4.3, Theoretical
Refractive Index of Optical Materials
29.4 Temperature Dependence of the Refractive Index
1019
Table 29.4 (continued) Compound IR glasses Germanate glass 9754 Amtir 6 (As40 S60 ) IRG 6 Schott (As40 Se60 ) Gasir 1 Gasir 5 IRG 22 IG 2 (Ge33 As12 Se55 ) IRG 23 IG 3 (Ge30 As13 Se32 Te25 ) IRG 24 IG 4 (Ge10 As40 Se50 ) AMTIR 1 (Ge33 As12 Se55 ) AMTIR 2 (AsSe) ZBLAN
Wavelength ( m)
dn=dT 106 (K1 )
˛v 106 (K1 ) a
References
1.060 5 5 10.6 10.6 5 3.39 5 3.39 5 3.39 3.39 10.6 0.633
10.4 8.6 (25 to 78 ı C); C9.3 (20 to 65 ı C) 33.5 55 32 67.7 67.7 103.8 105.2 21.5 23 77 30 14.75
18.6 64.2 62.4 51 23.5 36.3 36.3 40.2 40.2 61.2 61.2 36 67.2 60
[29.42] [29.44] [29.46] [29.50] [29.50] [29.46] [29.51] [29.46] [29.51] [29.46] [29.51] [29.44] [29.44] [29.45]
Values deduced from referenced linear ˛L expansion coefficients: ˛v D 3˛L Values calculated at 0:6328 m (He-Ne laser line) from recommended data of [29.38] c From [29.41, 52] d Selected glasses are referred to Schott catalog denomination [29.46]; for the same glasses different names can be found in [29.47, 49] and [29.48]. A convenient comparative table is given in [29.49]. a
b
n2 1 dn D .˛v C ƒ0 ˛v C 0 / ; dT 2n
(29.124)
after having shown that the polarizability ˛p may exhibit a linear dependence on temperature T and written as ˛p .T/ D ˛p0 Œ1 C .ƒ0 ˛v C 0 / T ;
(29.125)
˛v is the volume expansion coefficient, i. e., V1 dV ; the dT parameters ƒ0 and 0 have been recast in the form 2n m @n ƒ0 D 1 2 ; n 1 @m
2 d ln n 1 2n m @n C ˛v 2 0 D : dT n 1 @m
(29.126)
(29.127)
Thermo-optic measurements were performed on several glasses and cubic ionic crystals. It appeared that
for glasses, the change in polarizability due to pure temperature effect is dominant as compared to the contribution of volume variation. The converse was true for ionic crystals, where the change in the lattice parameter becomes dominant, leading to a negative value of dn=dT. This behavior is illustrated in Table 29.4, which gives for comparison dn=dT and ˛v data known for ionic cubic crystals (alkali halides Ia–VIIa and alkaline earth fluorides CaF2 , BaF2 ) and for some typical Schott, Hoya, Hikari, Ohara and specialty IR glasses.
29.4.2 Measurement of the Temperature Dependence of the Refractive Index n.; T / Direct Measurement The temperature dependence of the refractive index n.; T/ can be obtained directly by using the minimum deviation method if the prism is mounted in an adequately temperature-controlled cell and illuminated with an appropriate wavelength-selecting setup. Indeed, among the various methods described in Sect. 29.3, it appears to achieve the best accuracy. However, if a wide temperature range is to be explored, this would require the use of an air-tight evacuated and thermal insulated enclosure, along with additional optical components allowing entry and exit of the light beam, which obviously will alter the accuracy of measurements. Such problems have been overcome to some extent at NASA Goddard Space Flight Center with
Part C | 29.4
Considerations, that the thermo-optic coefficient in the transparent region decreases with angular frequency !, while becoming divergent in the vicinity of both UV and IR cutting edges. Ramachandran [29.36] also took into account the change in density, which induces a net change in polarizability, in addition to a change in polarizability due only to the change in temperature. This is formally equivalent to what can be identified in (29.122). From this point of view, he derived the following equation describing the TOC of optical glasses
1020
Part C
Characterization of Glasses
the development of the Cryogenic High-Accuracy Refraction Measuring System (CHARMS), which enables accurate measurements of n.; T/, mostly dedicated to proper implementation of optical materials for space applications at cryogenic temperatures [29.10, 11, 53, 54]. Despite appearing equally well suited for isotropic, homogeneous and perfectly transparent materials, some disadvantages can still be noted:
Part C | 29.4
It is known that the highest accuracy is obtained with prisms of quite large dimensions (say a few cm2 in aperture), leading to considerable thermal time constants and to an eventual occurrence of thermal gradients in the sample. The measurement procedure is of a step-by-step type, with regularly spaced temperature intervals and suitable sample soaking times. These operating constraints induce unavoidable time-consuming measurements. Subjected to a rise in temperature, any (homogeneous) material would exhibit an increase in its absorption coefficient, and consequently, the beam could progressively more or less lose its original transverse symmetry of intensity while traveling inside the prism. This is particularly true for semiconductors like (cubic) germanium for instance. For large temperature excursions and/or rather high absorption values, such a phenomenon could lead to a shift of the maximum of irradiance onto the pupil of the detection system and a slight widening of the diffraction pattern in the focal plane of the detection system. This qualitative description is illustrated in Fig. 29.19, which shows that the location of the irradiance maximum is shifted towards the summit of the prism. In the case of anisotropic materials, accurate measurements must be performed in polarized light and require a set of prisms which must be precisely cut with respect to appropriate crystallographic direc-
Imax
Incoming beam
Imax
"Absorbing medium"
Emergent beam
Fig. 29.19 Prism method in the case of an absorbing material. The transverse profile of intensity becomes asymmetric at the exit of the prism
tions that depend on the space group of the material. This can be adequately realized at room temperature, say T0 , and the principal refractive indices could thus be accurately measured at T0 using the minimum of deviation method. However, if the material undergoes a temperature change from T0 to T, its intrinsic anisotropic character will induce internal strains; these could distort the initial shape of the prism, depending on the symmetry class that it belongs to [29.55]. Thus, when dealing with thermal behavior of refractive indices, the the minimum deviation angle method does not appear to be convenient. Most of the above-mentioned difficulties inherent in direct measurement of the refractive index as a function of temperature can be overcome by using differential interferometric methods, which are described in the next section. Interferometric Methods: Normalized Thermo-Optic Coefficients (NTOC) It is known that interferometric methods may be used advantageously to determine a material’s thermo-optic coefficients with high accuracy. However, they give only what we have called the normalized thermo-optic coefficient (NTOC) [29.56, 57], namely ˇNTOC D
1 dn n dT
(29.128)
instead of the more commonly used TOC, defined as dn=dT. Temperature dependence measurements of NTOCs can be performed at several discrete laser wavelengths by using specifically developed interferometric arrangements that enable accuracy of around a few 106 K1 [29.58]. Also, data can be obtained on relatively small parallelepiped-shaped specimens (say a few mm2 in aperture and about 7 mm in length), which ensures a low thermal time constant while overcoming the problem of nonhomogeneous absorption described above. The first attempts to obtain accurate measurements using interferometric means can be attributed to setups developed at the US National Bureau of Standards [29.59], improved over the years and used to characterize the thermal behavior of numerous materials [29.60–62]. Of course, many techniques were then elaborated, employing various Fizeau, Fabry–Pérot, Michelson or Mach–Zehnder based interferometric arrangements. Some examples will be found in references [29.63–65]. In all cases, the principle is based on measuring the number of fringes N passing in front of a detector when subjecting a sample to a temperature change T. Regardless of the technique employed, the
Refractive Index of Optical Materials
determination of the temperature dependence of the refractive index requires measurements of both thermal expansion and changes in optical path. For a sample of thickness L and refractive index n, the linear thermal expansion and normalized thermo-optic coefficient (NTOC) are given by ˛L D dŒln.L/=dT and ˇNTOC D dŒln.n/=dT, respectively. Defining as well the coefficient for normalized thermal changes in optical path (NTCOP), that is NTCOP D dŒln.Ln/=dT, the NTOC is obtained from the straightforward relationship ˇNTOC D NTCOP ˛L . As an example, we describe below an original arrangement that was specifically designed for the determination of the thermo-optic coefficients of bulk nonlinear optical (NLO) materials [29.58], for which accuracy on dn=dT of about 105 is required. Obviously, its use can easily be extended to any optical one, and particularly to (isotropic) glasses, seeing that in such case and for NTCOP measurements, the polarization state of the beam with respect to dielectric axes of the medium is not so stringent.
reflected beam then overlaps that of the reference arm (path BS1 , M1 , M3 and RP) at the recombination plate RP to give a fringe pattern which is recorded by photodetector D1 . Detector D2 , external to the enclosure, enables convenient observation of the fringe pattern on a screen and verification of its spatial stability. The highest measurement accuracy is achieved by inserting a piezo-transducer PZT on mirror M1 , which allows phase modulation and subsequent phase detection of the fringe shift induced by applying a linear ramp of temperature to the sample through temperature control TC (Pt 100 thermistor) of the oven. The temperature of the sample is given by a Cu/constantan thermocouple glued on one of its sides. The optical source is a frequency/intensity-stabilized He-Ne laser emitting at wavelength ; a phase shift of 2 (i. e., fringe spacing), induced by a variation in temperature T, corresponds to a change in length L of =2. With phase modulation, two consecutive zero responses on the photo-detector D1 correspond to an optical path variation of =4. Thus, if N is the number of recorded fringes in the first case, the linear expansion coefficient will be given by ˛L D N=.2LT/. In the second case we will get twice as many fringes, which moreover are detected unambiguously while crossing a zero response on D1 . With such improvements, the typical accuracy on linear dilatation coefficient measurements is close to 3 107 K1 for a sample of 5 mm in length examined over a 10 K temperature interval. It is temperature-dependent, reaching zero at T D 0 K. As long as the material does not exhibit strong structural modification within the explored temperature interval, ˛L .T/ may always be accurately fitted to a power series in T as ˛L .T/ D a0 C
m X
ak T k :
(29.129)
kD1
A schematic layout and a picture of the apparatus are given in Figs. 29.20 and 29.21, respectively.
PZT M3
Vacuum enclosure M1
Thermocouple Oven
W1
TC (Pt100) BS2
BS1
Laser
W2 RP
D2
S M5
M6 D1
M2 Metallized optical faces
1021
M4
Fig. 29.20 Lay-out of an absolute interferometric dilatometer used for thermal expansion measurements
Part C | 29.4
Dilatometric Measurements. Measurements of linear thermal expansion are performed by using an absolute laser interferometric dilatometer acting as an optical gauge. The corresponding modified Mach–Zehnder set-up is entirely mounted in a vacuum enclosure and provided with a thermostated base plate, as depicted in Fig. 29.20. The parallelepiped-shaped sample S is located at the center of an oven in a nearly blackbody configuration to avoid any occurrence of thermal gradient. Two silica windows W1 and W2 allow entering and leaving of light from the vacuum enclosure. The beam of a frequency-stabilized He-Ne laser is divided into two paths by the beam splitter BS1 . The plane and parallel optical end faces of the specimen are goldmetallized and act as mirrors M5 and M6 in the sample arm. After reflection on the front face M5 , the beam is sent by successive reflections on BS1 , M2 , M4 , and beam splitter BS2 to the back surface M6 of S. The
29.4 Temperature Dependence of the Refractive Index
1022
Part C
Characterization of Glasses
Base plate D1 Oven and sample Towards D2 Thermal shield Incoming beam
Vacuum enclosure
BS1
RP
BS2
Fig. 29.21 Photograph of an absolute interferometric dilatometer; red and yellow beams correspond to the sample and reference arms, respectively. Not shown: the laser source located on the right side of the picture. RP: recombination plate; BS1,2 : beam splitters; D1,2 : light detectors and PZT: piezotransducer
PZT
Part C | 29.4
Determination of Normalized Thermo-Optic Coefficients. Normalized thermal changes in optical path NTCOP NTCOP are obtained by removing metallization M5 and M6 . The same sample S is mounted in a specific vacuum cell which reproduces identical thermal working conditions as those used in the dilatometer. Appropriate translation and rotation stages enable accurate orientation of the sample relative to the direction of the incident beam. A Fabry–Pérot interference pattern is generated by multiple reflections on the optical end faces; the fringe shift induced by applying a linear ramp of temperature to the sample is observed by reflection and continuously recorded on photo-detector D1 after being reflected by the semi-reflecting plate BS, as shown in Fig. 29.22. An analyzer crossed with respect to the orientation of the front polarizer allows permanent control of the spatial stability and eventual structural changes in the sample during all heating runs by recording on detector D2 the intensity of the transmitted beam which is imaged outside the vacuum cell. BaF2 windows W1 and W2 enable convenient switching of laser sources from the UV-Vis up to the IR spectral ranges. With such an arrangement, the typical accuracy in the determination of NTCOP of a sample similar
D1
to that described above, and exhibiting a refractive index n D 1:5 with an uncertainty around 104 , is close to 2 107 K1 . Accuracy in the NTOC determination ˇTOC D NTCOP ˛L may thus be expected to lay around less than a few in 106 K1 .
29.4.3 Thermo-Optic and Refractive Index Dispersion Theoretical Considerations In a manner somewhat similar to the works proceeding from a microscopic description of the matter, and which have led, for instance, to the Lorentz–Lorenz and Sellmeier formulas, Gosh [29.66] proposed a model based on three energy levels of absorption between the valence band and the conduction band of the material. The characteristic energies associated with each process are Eelec , Eisen and Eexcit , corresponding to so-called average electronic, isentropic and excitonic absorption band gaps, respectively. Eelec is the gap energy between the valence and the conduction bands, and Eexcit corresponds to the energy in the creation of an electron–hole entity, while Eisen is defined as a fitting gap that lies between the excitonic band and conduction bands. The
Vacuum enclosure Thermocouple Oven TC (Pt100)
Laser BS
W1
S
Optical end faces
Analyzer D2 W2
Fig. 29.22 Optical lay-out used for measurements of thermal changes in optical path
Refractive Index of Optical Materials
energy levels are depicted in Fig. 29.23 In the case of isotropic media, considering that the isentropic band is the geometric mean of the electronic and excitonic absorption bands, further analysis gives the following temperature dependence of the refractive index n linked to its thermo-optic coefficient dn=dT dn 2 1 dEexcit 2 2n D n0 1 3˛L ; dT Eexcit dT (29.130)
where ˛L is the linear thermal expansion coefficient, D
2
2 : 2i
(29.131)
Conduction band Isentropic band
in 104 in the mid-IR region, and for samples of large aperture. At a fixed temperature T0 , the data may be fitted to the simple Sellmeier relationship (29.47) mentioned in Sect. 29.2.2, Sellmeier’s Formula and written in the slightly modified form l X ˇ n2 ./ˇT D A C 0
iD1
2
Bi ; 2i
(29.132)
where A is a constant, and the summation extends over a finite number l of oscillators i resonant at wavelengths i D .2 c/=!i , with c being the speed of light. Parameters Bi depend on the strength of each oscillator that is to be taken into account to achieve best fitting procedure. Two sets of terms are introduced formally to account for UV and IR cutting edges, beyond which the material becomes opaque. Now, considering that (29.132) is also temperaturedependent, and then taking the logarithmic expression, we get " #! l X .Bi =A/.T/ 1 lnŒn.; T/ D ln A.T/ 1 C : 2 2 2i .T/ iD1 (29.133)
Over the range of transparency, far enough from cutting edges, the dispersion is represented by the summation term, which emphasizes only slight and monotonically wavelength-dependent deviations from the mean value A.T/, that is l X .Bi =A/.T/ 1: 2 2i .T/ iD1
(29.134)
Having defined the normalized thermo-optic coefficient ˇNTOC D .1=n/.dn=dT/, we may write ˇNTOC .; T/ D
1
ˇ 2n2i ˇT
dA.T/ X 1 dBi .T/
C 2 2 .T/ dT dT i iD1 0 ! l X 2Bi .T/i .T/ di .T/ C :
2 2 2 dT iD1 .T/ l
i
(29.135) Electrons
Excitonic band
Eelec
Eisen Eexcit Valence band Holes
Fig. 29.23 Schematic representation of the energy levels of optical glasses. After [29.66]
1023
Now ˇNTOC .T/ data may always be accurately fitted to a power series of temperature to better than 107 K1 accuracy ˇNTOC .; T/ D c0 ./ C c1 ./T C C cm ./T m m X D cj ./T j : 0
(29.136)
Part C | 29.4
is called the normal dispersive parameter, is the photon wavelength and i the isentropic band wavelength, lying in the UV region between the excitonic and the electronic absorption bands. n0 is the lowfrequency refractive index in the IR region. The shift of lattice absorption with temperature is assumed to be negligibly small [29.66]. It has been shown quite recently that a rigorous description of the thermal behavior may be obtained in a much more comprehensive manner [29.57]. Despite being described as deduced from a semi-empirical model, Sellmeier equations have long been accepted as giving the best representation of the refractive index dispersion of any optical material over its entire transparency window. Thus, in accordance with other authors [29.67], we would recommend fitting recorded refractive index data by using this formulation. Direct measurements of the dispersion n./ are usually obtained from various noncoherent impinging light sources and at room temperature, say T0 , by employing prism methods performed in the minimum deviation configuration. From a literature survey it can be estimated that mean values of best affordable accuracies lie around 105 in the visible spectral range, with a few
29.4 Temperature Dependence of the Refractive Index
1024
Part C
Characterization of Glasses
Determined experimentally, the cj values must be consistent with (29.135) and will therefore be written according to cj ./ D
1 ˇ 2n2 ˇ
X1 C
T0
l X
iD1
1 2 2i .T/
Xi
! l X 2Bi .T/i .T/ 0 C
2 Xi ; 2 2 iD1 i .T/ (29.137)
obtained from (29.135) by putting
Part C | 29.4
dA.T/ ; X1 D dT dBi .T/ (29.138) Xi D and dT di .T/ : Xi0 D dT Equation (29.137) represents a set of .2l C 1/ linear equations with unknown parameters X1 , Xi and Xi0 , which can readily be solved by using a simple vectorial formalism, if NTOC data are obtained at a number of .2l C 1/ laser wavelengths suitably chosen in the transparency window of the material. A set of .2l C 1/ experimental values of the cj values will allow us to determine the temperature-dependent dispersion formula (29.132), which is obtained by integrating equation (29.136) and knowing the dispersion equation at room temperature T0 . This gives 2 3 m X cj ./ jC1 jC1 .T T0 /5 : n.; T/ D n.; T0 / exp 4 jC1 jD0 (29.139)
The refractive index could also be written in a Sellmeier like formulation n2 .; T/ D .A C A/ C
l X iD1
Bi C Bi
; 2 2i C .2i / (29.140)
.2i /
where A, Bi and are functions of temperature T and obtained by integrating equations (29.138) ZT A D
ZT X1 dT;
T0
ZT .2i /
D
Bi D
Xi dT
and
T0
Xi0 dT :
T0
(29.141)
Expression (29.140) is reminiscent of the pure empirical ones proposed in the case of LiNbO3 [29.68, 69] and MgO-doped LiTaO3 crystals [29.70]. Accuracy: Temperature Dependence of an ONL Interaction in RbTiOPO4 If ˛L and NTCOP are the uncertainties associated with measurements of thermal expansion and changes in the optical length of a sample of length L examined over a temperature interval T, the uncertainty on NTOC is used by ˇNTOC D ˛L C NTCOP
T L T n 1 L 1 .nL/ C NTCOP C C : n L T nL T
D .˛L C NTCOP /
L
C
(29.142)
From experience, estimates of all sources of uncertainty lead us to conclude that the order of magnitude of ˇNTOC is of a few 106 K1 in most cases. Note that such an assertion is based on linear optics measurements and classical uncertainty calculation (i. e., without any statistical consideration). However, confirmation of this has been clearly evidenced through nonlinear optics experimentation that is described below. The temperature dependence of the second harmonic generation (SHG) 1:0642 m ! 0:532 m was studied in the case of an RbTiOPO4 (RTP) single crystal [29.71]. Apart from the requirement for accurate knowledge of the dispersion equations at a fixed temperature T0 , it is known that any temperature variation in the crystal will alter the doubling efficiency. In such critical processes, refractive index modifications are to be characterized at least down to the fifth decimal place. RTP belongs to the anisotropic orthorhombic mm2 symmetry class; therefore, three Sellmeier equations analogous to (29.132) must be considered to characterize the dispersion of the refractive indices nx , ny and nz along the three principal dielectric axes Ox , Oy and Oz of the crystal, respectively. Interferometric measurements of the corresponding three principal thermal expansion coefficients of RTP were obtained from 30 ı C to C130 ı C by using a frequency-stabilized He-Ne laser. The NTOC values were determined over the same temperature interval from measurements of normalized coefficients of changes in optical path performed at four CW laser wavelengths and with appropriate polarization direction of the light with respect to the X, Y and Z axes. Single-mode CW lasers were used: an argon ion tuned at 0.4578 m, two He-Ne emitting at 0.6328 and 3.39 m, and a Nd:YAG at 1:0642 m. Linear behavior of ˛L .T/ coefficients was observed, with ˛z < 0, while
Refractive Index of Optical Materials
29.4 Temperature Dependence of the Refractive Index
1025
Fig. 29.24 NTOC dispersion obtained
dn / ndT (×10 –6 °C –1) 20.0
for RTP at room temperature (20 ı C) and starting from refractive index dispersion given in [29.71]. Circles correspond to experimental data and lines to fitting results; black, blue and red refer to X, Y and Z polarizations, respectively
18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
the NTOCs exhibit quadratic behavior; they are given in Fig. 29.24 for illustration. Type II eo-e second harmonic generation (SHG) is a nonlinear optical interaction where an extraordinary photon combines with an ordinary photon at the fundamental wavelength to give an extraordinary wave at =2. The SHG 1:0642 m ! 0:5321 m is governed by the phase mismatch k, written as
2 =2 k.T/ D 2n .T/ n .T/ C nz .T/ ; (29.143)
1 cos2 ' sin2 ' D C : n2 .'/ ny2 n2x
(29.144)
Phase-matched interaction corresponds to k D 0, which is for n=2.T/ D
1 n .T/ C nz .T/ : 2
(29.145)
In biaxial RTP and starting from the dispersion equations used in [29.71], this occurs at T0 D 20 ı C for
φpm (°) 57 56 55 54 53 52 –20 0
20 40 60 80 100 120 140 160 180 200 220 Temperature (°C)
Fig. 29.25 Predicting the temperature dependence of the
phase-matching angle in the (X; Y) plane of RTP for the SHG of Nd:YAG lasers. Full curve: theory, from (29.145); the black squares correspond to recorded experimental maxima of efficiency
phase-matching angle 'pm D '0 D 55:82ı . The temperature dependence of 'pm is determined by numerically solving (29.145) and by using the n.T/ values derived from NTOC measurements following the procedure described in Sect. 29.4.3. The result is drawn as a full curve in Fig. 29.25, which gives the predicted evolution of the phase-matching angle 'pm from 20 ı C up to 230 ı C.
Part C | 29.4
n=2.T/ and both n .T/, nz .T/ are the temperature and orientation-dependent refractive indices at the second harmonic and fundamental waves, respectively. In the (X; Y) crystallographic plane and for an impinging internal angle ' referred to the X axis, the refractive index n is given by
3.5 4.0 Wavelength (μm)
1026
Part C
Characterization of Glasses
29.5 Spectrophotometric Determination of Refractive Indices Spectrophotometers are widely used in industry and in research laboratories for determining the spectral transmittance, reflectance and absorptance of optical materials. This section starts by recalling some of their basic characteristics and methods, which will be helpful for understanding how they can be used for the measurement of the refractive index and extinction coefficient of bulk and coated samples. The following cases are then covered in successive steps: bulk materials, homogeneous thin films, inhomogeneous thin films, metallic films on transparent media, and optical constant determination by the bilayer metal-dielectric method.
29.5.1 Some Useful Properties of Spectrophotometers This subsection deals with some of the basic characteristics of spectrophotometers, starting with a description of their main constituents. It then defines their coherence length and the measurable quantities that are of particular interest for characterizing the refractive indices of films and of coated or uncoated samples. As the V-W procedure is very commonly used, its configuration is presented here, along with some typical spectral results in transmission and reflection. Structure and Main Components of a Spectrophotometer The main components of standard spectrophotometers are the following (Fig. 29.26):
Part C | 29.5
1. The light source, which is chosen in connection with the spectral domain of interest. In the UV, deuterium lamps operate from 195 to 380 nm; in the visible and near-IR, the sources are usually of the tungsten halogen type (from 320 to 1000 nm) or Xenon lamps (from 190 to 1100 nm), and blackbodies are used to cover the IR. 2. A monochromator, responsible for filtering the input light inside a narrow bandwidth (or spectral resolution) around some wavelength of interest and for scanning (or not) this selection over the spectral domain of investigation. 3. A telescopic goniometer, responsible for adjusting the size, the direction, and in some cases the polarization of the beam of light that illuminates the sample. This component monitors the angle of incidence of the beam upon the optical sample under test. 4. The sample to be characterized, generally in the shape of a plane-parallel plate. In most spectrophotometers, the test sample is characterized by com-
paring the fluxes collected from it with those obtained in the same configuration from a reference sample (specially designed for the task). Hence, the test and reference samples are alternately illuminated in similar conditions. 5. The detection and its associated signal processing electronics, which convert the different (reflected, transmitted, scattered) collected amounts of flux into recordable electric signals. Hence, it is important to note that most of the optical parameter values delivered by a spectrophotometer, such as transmittance or reflectance, are dimensionless and represent the ratios between the same quantities (fluxes) measured from the test and reference channels under similar configurations. The reference sample (or channel) plays an important role, since it is used as a scale and defines the so-called baseline of the instrument. Coherence Length of the Spectrophotometer The coherence length (Lc ) of the spectrophotometer is defined by (29.146) below Lc D
20 1 D ; ı0 ı P 0
(29.146)
where 0 is the mean wavelength of the spectrally filtered beam, and ı0 or ı P 0 its full width at half maximum (FWHM), expressed in wavelength (ı) (m or nm) or in wavenumber .ı P 0 / (cm1 ) units. The value of this coherence length is of prime importance because the shape of the output spectral data (such as spectral reflectance or transmittance) from the spectrometer depends upon the ratio between the sample thickness and Lc . As will be shown in Sect. 29.5.1, Measurable Quantities, the incident beam is separated into two or more beamlets that recombine on the sensitive area of the detector after bouncing back and forth between the sample boundaries. If the corresponding optical path difference (OPD 2nd for quasi-normal incidence) is much less than the coherence length, these interfering waves retain some mutual coherence, and their recombination gives rise to interference phenomena, converted as ripples on the spectral graphs. The lower the ratio (OPD/Lc ), the higher the mutual coherence beam, and the higher the ripple contrast. Conversely, if OPD Lc , the interfering beams are un-correlated. Their recombination does not give rise to static interference, and the corresponding spectral graphs are smooth. Figure 29.27 shows the graph, over the 900940 cm1 domain, of the spectral transmittance
Refractive Index of Optical Materials
29.5 Spectrophotometric Determination of Refractive Indices
Fig. 29.26 Operating principle of a spectrophotometer used for measuring the transmitted flux of a sample defined by Tg ./˚./, where Tg ./ is the global spectral transmittance (respectively, global spectral reflectance Rg .// and ˚./ the incident flux
Φ (λ)
Dispersive device
Lamp
∆λ0
(monochromator single or double)
(tungsten halogen lamp, ...)
Incident flux Φ (λ)
λ0
Reflected flux Rg (λ) Φ (λ)
1027
λ
Test sample or reference sample Transmitted flux Tg (λ) Φ (λ) Detection system: detector (Si, PM, ...) and conversion current–voltage
Tg (λ) Φ (λ)
Sample signal measurement (Volt): Tg (λ) Φ (λ) λ
Measurable Quantities As mentioned in Sect. 29.5.1, Structure and Main Components of a Spectrophotometer, the sample under test (either bare or coated substrate) transmits, reflects and/or absorbs parts of the incident pencil of light which is spectrally filtered at some wavelength (scanned over the spectral domain of interest), and the spectrophotometer outputs are the detector signals in response to the corresponding collected fluxes. This
Spectral transmittance T 1.0 . ∆v0
0.9
0.8
Part C | 29.5
of a 514 m thick plate of polycrystalline isotropic diamond (ndiamond 4) obtained from a Bomem Fourier transform infrared spectrometer, of spectral resolution ı P 0 D 0:04 cm1 . In this example, Lc D 1=ı P 0 D 25 cm 2ndiamondd 4 mm, which explains the rather high contrast (C D .Tmax Tmin /=.Tmax CTmin / 25%) of the ripples. The fringe spacing, or free spectral range P 0 (i. e., the difference between two adjacent wavenumbers of identical state of interference), given by (29.146) equals about 4 cm1 and the resulting number of oscillations (ratio between 40 cm1 , the covered spectral range, and 4 cm1 , the free spectral range), is around 10, as confirmed in Fig. 29.27 [29.5, 72]. The black curve is from experimentation, and the red curve corresponds to the theoretical fit obtained by using a one-pole Cauchy’s model for the dispersion of the refractive index [29.5, 72]. In practice, it is advisable to choose a substrate of appropriate thickness (i. e., Lc ) with respect to the resolution ı0 in order to better highlight the interference features specific to multilayer.
0.7
0.6
0.5 900
910
920
930 . 940 v = 1/λ (cm –1)
Fig. 29.27 Spectral transmittance of a 514-m thick plate
of diamond from 900 to 940 cm1 . P 0 is the nominal free spectral range (i. e., fringe spacing) in the explored spectral interval from [29.72]
subsection briefly describes the methodology used to derive the optical parameters of the sample, i. e., the refractive index and extinction coefficient of the substrate and of its coating, as well as the film thickness, from
1028
Part C
Characterization of Glasses
the measured values of the global spectral reflectance, denoted Rg ./, and the global spectral transmittance, denoted Tg ./, of the sample. For this purpose, the sample is generally shaped as a plane-parallel plate of high quality, with polished surfaces, in order to avoid any deviation or other type of modification of the reflected and transmitted beam spots onto the sensitive area of the detector and hence to ensure optimal detection of all fluxes of interest. Figure 29.28 shows the case of a nonabsorbing sample, of refractive index ns ./ and thickness ds , illuminated under quasi-normal incidence; its upper boundary is coated over only half of its surface by the thin film for characterization purposes, and the lower one is not coated at all. The surrounding medium should be air, of refractive index n0 ./1. In typical spectrophotometric experiments, three configurations of sample illumination are necessary in order to provide the expected information, according to Fig. 29.28a: in configuration 1, on the left hand side, the downward-propagating incident beam hits the bare part of the sample (both interfaces of the substrate are uncoated). At the center, the sample is translated in such a way that the same downward-propagating incident beam first hits the coated part of the upper surface of a)
Configuration 1
Incident flux Фinc (λ)
the sample and then its uncoated rear surface. On the right side of Fig. 29.28a, the incident beam propagates upwards and first hits the (uncoated) lower surface of the sample and then the coated surface (in practice, the sample is turned upside down). Let the (unknown) spectral reflectance and transmittance of the film (as deposited on the substrate) be denoted R./ and T./ for a downward propagation of the light (i. e., for rays incident from air to film), and R0 ./ and T 0 ./ (D T./) for an upward direction of propagation (i. e., for an incident beam propagating from the substrate to the film); the spectral reflectance and transmittance of each uncoated boundary are denoted Rs ./ and Ts ./, respectively (Fig. 29.28b) [29.5, 7, 73, 74]. Without getting into detailed calculations, we can show that the flux reflected by the sample is the sum of the flux reflected from the first encountered interface and the multiple fluxes carried by the beams that propagate inside the substrate and bounce back and forth from its interfaces (coated or not). This summation of fluxes (and not of field amplitudes) is justified by the fact that the coherence length of the incident beam should be much less than the sample thickness. Similarly, the flux that is transmitted by the sample is
Configuration 2
Reflected flux Фr1 (λ) = Rg1 Фinc (λ)
Configuration 3
Фr2 (λ) = Rg2 Фinc (λ) Фinc (λ)
Ф t3 (λ) =Tg3 Фinc (λ)
Part C | 29.5
Thin film Non absorbing substrate
Fig. 29.28a,b Transmitted flux Ф t1 (λ) =Tg1 Фinc (λ)
Ф t2 (λ) =Tg2 Фinc (λ) Фr3 (λ) = Rg3 Фinc (λ)
Фinc (λ)
b) Rs (λ), Ts (λ)
T (λ)
yA (λ) ys (λ)
Non absorbing substrate (ns (λ), es) Rs (λ), Ts (λ)
R' (λ) 1
1
R (λ) T (λ)
Thin film
Typical illuminating configurations of the sample with corresponding measured quantities (fluxes ˚) (a), and parameters of the sample that can be extracted from these measurements (b)
Refractive Index of Optical Materials
29.5 Spectrophotometric Determination of Refractive Indices
1029
Table 29.5 Computed values of global spectral reflectance and transmittance for the three illuminating configurations of Fig. 29.28 (case of a nonabsorbing bulk material) Configuration
Spectral reflectance
1
Rg1 ./ D
2
Rg2 ./ D R./ C
3
Rg3 ./ D Rs ./ C
Spectral transmittance
2Rs ./ 1CRs ./ T 2 ./Rs ./ 1Rs ./R0 ./ Ts2 ./R0 ./ 1Rs ./R0 ./
the sum of the directly transmitted flux and the multiple contributions that have been bouncing back and forth inside the substrate. Table 29.5 gives the theoretical expressions of the global spectral reflectance Rg ./ and global transmittance Tg ./ of the sample corresponding to the reflected and transmitted fluxes as measured in the three configurations of Fig. 29.28a. The equivalence among the respective ratios between the experimentally measured reflected or transmitted fluxes and the incident flux, and the corresponding expressions of the reflectance or transmittance of the sample as expressed in Table 29.5 yield the optical parameters of the sample. For a transparent substrate, the spectral reflectance Rs ./ and transmittance Ts ./ of each uncoated boundary, given by the Fresnel formulas under normal incidence, lead to the refractive index ns ./ of the bulk material ns ./ n0 ./ 2 Rs ./ D and ns ./ C n0 ./ Ts ./ D 1 Rs ./ : (29.147)
Tg ./ C Rg ./ D 1 :
(29.148)
If there are light losses along the optical path inside the sample due to absorption and/or scattering, the energy conservation law becomes Tg1 ./ C Rg1 ./ C ƒ1 ./ D Tg2 ./ C Rg2 ./ C ƒ2 ./ D Tg3 ./ C Rg3 ./ C ƒ3 ./ D 1 ;
1Rs ./ 1CRs ./
Tg2 ./ D
T./.1Rs .// 1Rs ./R0 ./
Tg3 ./ D
T./.1Rs .// 1Rs ./R0 ./
If scattering is negligible, for each wavelength, the values of the three unknown R./, R0 ./ and T./ can be extracted from the three experimental values of Rg2 ./, of Rg3 ./ and of Tg2 ./, and hence we can compute the film admittances YA ./ and Ys ./, defined in Sect. 29.2.6, Optical Properties of a Coating, and considered here at the respective film interfaces with air and with the substrate, by the following expressions ˇ ˇ ˇ n0 ./ YA ./ ˇ2 ˇ ; R./ D ˇˇ (29.150) n0 ./ C YA ./ ˇ ˇ ˇ ˇ ns ./ Ys ./ ˇ2 ˇ : and R0 ./ D ˇˇ (29.151) n ./ C Y ./ ˇ s
s
It must be noted that the computation of R./, R0 ./ and T./ differs from that of Rg ./ and Tg ./ because the evaluation of YA ./ and Ys ./ results from the vector sum of the field amplitudes of the beams bouncing back and forth from the boundaries of the coating, since the film thickness should be much smaller than the coherence length of the incident light. At wavelengths for which the substrate is slightly absorbing ( s ¤ 0), these parameters may be evaluated in a similar manner, on the condition, however, that the substrate thickness ds is taken into account. Under this condition, the expressions of the measured transmittance and reflectance become ˛s ds T./Ts ./ exp 2 ; Tg2 ./ D (29.152) 1 Rs ./R0 ./ exp.˛s ds / T 2 ./Rs ./ exp.˛s ds / ; Rg2 ./ D R./ C 1 Rs ./R0 ./ exp.˛s ds / (29.153)
Rg3 ./ D Rs ./ C
Ts2 ./R0 ./ exp.˛s ds / 1 Rs ./R0 ./ exp.˛s ds /
;
(29.154) (29.149)
where the ƒ values are the spectral loss coefficients including the absorptance (A) and scattering (TIS, defined in Sect. 29.5.1, The V and W Configurations), with: ƒ./ D A./ C TIS./
where ˛s D .4 =/ s is the absorption coefficient. The V and W Configurations In order to correctly measure the above-mentioned quantities, it is critical that a unique and stable source is utilized and that the same detector is used to collect the
Part C | 29.5
The experimental verification of the equality at the right-hand side of (29.147) confirms the fact that the material of the substrate is transparent. At each wavelength, if the optical coating and the substrate are neither absorbing nor diffuse, the energy conservation law may be written for each configuration in the following manner
Tg1 ./ D
1030
Part C
Characterization of Glasses
flux. It is also important that the configurations for the test and the reference samples are as similar as possible, hence the interest in the so-called V-W configuration, which is described in this subsection. Figure 29.29a,b shows the optical set-up of this method, which can be modified from its V configuration for measuring the spectral transmittance of the sample into its W configuration for the spectral reflectance, by means of a retractable mirror that stops the transmitted beam and redirects the reflected beam towards the final mirror without any modification in the external path. The angle of incidence is generally around 8ı . As shown in Fig. 29.29c, the fraction Rsp ./ of the incident light reflected from a surface propagates along the direction specified by the Snell–Descartes law and corresponds to the specular reflection of that surface. The other fraction Rd ./ of the reflected light, a)
which is scattered over all the other directions in space, corresponds to the diffuse reflection of the surface. Consequently, the global reflectance Rg ./ of the surface is the sum of these two contributions Rg ./ D Rsp ./ C Rd ./ :
It can be shown that scattering of light originates from the surface roughness: if the surface is modeled as a Gaussian random surface of root mean square (rms) roughness r (supposed to be small compared to the wavelength of the incident beam), its specular reflectance is related to its global reflectance and to the rms roughness of the surface by the following relationship [29.75–77] 16 2 r2 cos2 ; (29.156) Rsp ./ D Rg ./ exp 2 Mirror
b)
Mirror
(29.155)
Retractable mirror
Sample
Sample Aperture
Aperture
Aperture
Tg Ф (λ0)
Ф (λ0)
Aperture
Ф (λ0)
Rg Ф (λ0) Mirror
Mirror Mirror
Mirror
Part C | 29.5
Mirror
Mirror Detector for specular reflectance
c) Ф (λ0) θ
θ
Rg (λ0) Φ (λ0)
Rsp (λ0) Φ (λ0)
Detector for diffuse reflectance
Rd (λ0) Φ (λ0)
Rough surface
Integrating sphere Sample
Fig. 29.29 (a) V-configuration, (b) W-configuration, (c) Integrating sphere used for measuring the specular and diffuse reflectance of a rough surface
Refractive Index of Optical Materials
where is the angle of incidence of the illuminating beam. Consequently, the diffuse reflectance of such a rough surface is Rd ./ D Rg ./ Rsp ./
Sample with Only One Flat (Polished) Surface In this subsection, it is supposed that the front surface of the sample is flat and well polished, and that the rear surface is rough (diffuse). The V-W method does not allow access to the transmittance of this kind of sample, and consequently it can only deliver the spectral reflectance Rs ./ of its front surface, without any information on both transmission and absorption of the sample itself. However, if the Sellmeier formula of the constitutive material is known, it should be consulted to help check the experimental values of Rs ./, because this formula is a valuable tool for characterizing the dispersion of glasses and crystals. In fact, most optical glass manufacturers mention the Sellmeier coefficients of their materials in their catalogs. If one does not know the material of the sample, the K–K relationships (29.28)–(29.30) may be used to deduce its refractive index and extinction coefficient from the experimental values of the spectral reflectance (Sect. 29.2.2, Kramers–Kronig Relationships) obtained by the W method. Since the reflectance measurements are realized inside a limited range (!1 –!2 ), in order to correctly apply the K–K relationships, one must analytically extrapolate the experimental reflectance values outside this range by means of an adjusted formula, such as
16 2 r2 cos2 Rg ./ : 2
Typically, the percentage of the scattering in the light being reflected by the surface is specified by the total integrated scattering, or TIS, of the surface, equal to 16 2 r2 cos2 Rd D : Rg 2
(29.158)
Typical Transmittance and Reflectance Outputs It was shown in Sect. 29.5.1, The V and W Configurations that the spectral reflectance Rg ./ and transmittance Tg ./ of plane-parallel samples can be obtained from the V-W configuration of conventional spectrophotometers. This is illustrated in Fig. 29.30a,b by the spectral transmittance graphs of several 2 mm thick samples. Figure 29.30a concerns slabs of TAS (Te20 As30 Se50 ) and 2S1G (Ge15 Sb20 S65 ), and Fig. 29.30b a silicon plane-parallel plate, polished on both sides. The curve in Fig. 29.30b shows the presence of the silicon cut-off wavelength at around 1100 nm, below which the light is completely absorbed before reaching the rear interface. In the transparency domain ( > 1100 nm), some light reaches the second interface and rebounds from it, so that the sample reflectance is very close to 2Rs =.1 C Rs /, where Rs is the reflectance at the interface air/sample.
for ! 0 < !1 Rs .! 0 / D Rs .!1 / and for ! 0 > !2 Rs .! 0 / D Rs .!2 /
!0 !2
a ; (29.159)
where a is an adjusted parameter (0 < a < 4).
Part C | 29.5
a) Tg (%)
Rg , Tg (%) 100
b)
80
2S1G
70
80 60 TAS
50
60
Tg
40 Thickness = 2 mm
30
40
Rg Transparent zone
20
20
Absorption zone
10 0 400
600
800 1000 1200 1400 1600 1800 2000 Wavelength (nm)
0
500
1000
1500
2500 2000 Wavelength (nm)
Fig. 29.30 (a) Spectral transmittance of two infrared bulk materials (2S1G and TAS) measured with the V configuration for normal incidence with air as reference. (b) Spectral reflectance and transmittance of a thick (2 mm) silicon sample
polished on both surfaces
1031
29.5.2 Case of Bulk Materials
(29.157)
TIS D
29.5 Spectrophotometric Determination of Refractive Indices
1032
Part C
Characterization of Glasses
Alternatively, another extrapolation can be used [29.78]. The computational method for calculating '.!/ must converge with high accuracy. Since it must take into account the singularity, and to divide into a number of domains adapted to the !-broadband, for the integration calculation, the result of '.!/ directly gives the values of ns and s mentioned in Sect. 29.2.2 Kramers–Kronig Relationships ns D
n0 Œ1 Rs .!/
p ; 1 C Rs .!/ 2 cos Œ' .!/ Rs .!/ p 2n0 sin Œ' .!/ Rs .!/ p : and s D 1 C Rs .!/ 2 cos Œ' .!/ Rs .!/ (29.160)
The absolute uncertainties are ˇ ˇ ˇ .1 C R / cos ' 2pR ˇ ˇ s s ˇ ns D ˇ ˇ RS p p 2 ˇ 1 C Rs 2 Rs cos ' Rs ˇ ˇ ˇ ˇ ˇ 2Rs .Rs 1/ sin ' ˇ ˇ Cˇ ˇ and p p ˇ 1 C Rs 2 Rs cos ' 2 Rs ˇ ' ˇ ˇ ˇ ˇ .Rs 1/ sin ' ˇ ˇ s D ˇ ˇ p p ˇ 1 C Rs 2 Rs cos ' 2 Rs ˇ RS ˇ ˇ ˇ 2R .1 C R / cos ' 2pR ˇ s s ˇ ˇ s Cˇ ˇ : ˇ 1 C Rs 2pRs cos ' 2 pRs ˇ ' (29.161)
Part C | 29.5
The accuracy of the K–K method is directly linked to the accuracy and value of '.!/ for the extinction coefficient s . If we assume that the contribution of the light reflected from the (diffuse) second surface is negligible, we find that the uncertainty in the value of the refractive index is on the order of n D 2% if Rs D 1 103 Plane-Parallel Plate with Two Polished Surfaces In this case the light, having traversed the plate, may be efficiently reflected back from the rear surface towards the front surface, as shown in Fig. 29.28, and consequently, some information can be collected concerning the absorption and transparency spectral domains of the material (Fig. 29.30b). The expressions (29.152) and (29.153) become (29.162) and (29.163), respectively
Rs 1 C .Ts2 R2s / exp.˛s ds / ; Rg D 1 R2s exp.˛s ds /
(29.162)
˛s ds exp 2 ; Tg D 1 R2s exp.˛s ds / Ts2
(29.163)
with 4
s ; (29.164) where ds denotes the sample thickness. In the transparency domain, where Tg ¤ 0, the refractive index ns is given by the analytic formulation below q n0 1 C 2Rg R2g ns D : (29.165) Rg 1 ˛s D
The associated absolute uncertainty is q n0 1 C 2Rg R2g q Rg : ns D .1 Rg /2 2Rg R2g
(29.166)
Thus it is found that ns is around 0:5%, and the absolute error Rg is on the order of 103 . In the totally absorbing zone, where Tg ./ D 0, one can use the K–K relation mentioned in Sect. 29.2.2, Kramers–Kronig Relationships. For materials of low absorption such that Tg ./ C Rg ./1 and for samples of known thickness ds , analytical expressions cannot be obtained, and a computational method must be used in order to extract the values of the optical constants (ns and s ). It is important to note that the sample reflectance yields information on the optical band gap (Eg ) of the material. The value of the corresponding cut-off wavelength g , ( g (in m) D 1:24=Eg (in eV)) is obtained by solving @2 Rg =@2 Dg D 0 [29.79]. We will see later how the optical constants (n; ) of a nontransparent substrate (or opaque metal layers) can be determined at normal incidence with the help of a transparent dielectric.
29.5.3 Refractive Index Measurement of Homogeneous Dielectric Thin Films The determination of the optical parameters of weakly absorbing thin films is a problem commonly encountered in various sectors of applied physics, particularly in the microelectronics and thin film technologies [29.80]. In order to optimize the design and fabrication of multilayers, it is essential to know precisely the refractive indices and extinction coefficients of the coatings. We will consider here the case of systems that are made up of a nonabsorbing substrate coated with an absorbing thin film, as shown in Fig. 29.31a and specified as follows:
Refractive Index of Optical Materials
a) T, R
29.5 Spectrophotometric Determination of Refractive Indices
1033
b) Tg2
1.0
1.0
Bare substrate
0.8
0.8 Tg2 Rg2 R'g3 Tg1 Rg1
0.6 0.4 0.2
Bare substrate Tmax
0.6 0.4 High
Moderate
Weak
Zero
0.2 Bare substrate
0.0
400
600
800
1000
1200
1400 1600 1800 Wavelength (nm)
0.0
400
600
800
1000
1200
1400 1600 1800 Wavelength (nm)
Fig. 29.31 (a) Spectral reflectance and transmittance of a bare and then coated substrate. (b) Spectral transmittance Tg2 ./ of a substrate with a homogeneous film, showing the envelopes of its maximum and minimum values
Figure 29.31b shows the spectral transmittance Tg1 ./ (Table 29.5) of the bare substrate and the spectral transmittance Tg2 ./ of the coated substrate. Tg2 ./ oscillates between two envelopes corresponding to its maximum (Tmax ) and minimum (Tmin ) values. In the same Fig. 29.31b, one notes the presence of four zones, which are defined by the value of the ratio zA between the maximum transmittance of the coated substrate and the transmittance of the bare substrate (zA D Tmax =Tg1 ) [29.81]. These zones correspond to high (zA < 0:4), moderate (0:4 < zA < 0:8), weak (0:8 < zA < 0:99) and null (zA D 1) absorption of the sample (o). As far as reflectance is concerned, a similar behavior is observed, showing alternate maxima and minima. As previously described in Sect. 29.5.1 Coherence Length of the Spectrophotometer, the oscillations observed between the two envelopes are interference fringes, and the spacing of these fringes is directly linked to the
physical thickness of the film relative to the wavelength, as is their number, which is also linked to the bandwidth of the covered domain. We also note that the envelopes of Tmax (or Rmin ) converge towards the transmittance (or reflectance) of the bare substrate, in the case of films with weak or no absorption at all. This characteristic is generally the signature of a homogeneous layer. Over the spectral domain without any absorption, the theory [29.7] demonstrates that the locations of minima of transmittance (or maxima of reflectance) correspond to the value Ymax D n2 =ns of the optical admittance with ˇ ˇ ˇ n0 n2 ˇ2 ˇ ns ˇ (29.167) Rmax D ˇ ˇ : ˇ n 0 C n2 ˇ ns The expression of the refractive index is then s p n0 ns 1 C Rmax : nD (29.168) p 1 Rmax In the weak absorption spectral domain of the film, the maximum value Tmax of the transmittance and the minimum value Rmin of the reflectance are affected. Manifacier et al. [29.81] demonstrated that the solution to the refractive index is expressed in terms of Tmax and Tmin r q n D "1 C (29.169) "21 .n0 ns /2 ; with
"1 D
n20 C n2s Tmax Tmin C 2n0 ns : 2 Tmax Tmin (29.170)
Part C | 29.5
1. Its materials are isotropic and homogeneous, i. e., there is no variation in the refractive index throughout the film. 2. Both boundaries of the film are ideally flat, smooth and infinitely thin, i. e., without any transition layer. 3. The ambient medium is nonabsorbing and with a refractive index of n0 D 1. 4. The (nonabsorbing) substrate is a plane-parallel plate; Rs ./ and Ts ./ are the spectral reflectance and transmittance of each boundary, respectively. 5. The global spectral quantities Tg ./ and Rg ./ measured in the V-W configuration yield the theoretical reflectance R./ and R0 ./ and the transmittance T./ values of the coating defined by (29.87) and (29.88).
1034
Part C
Characterization of Glasses
This method consists in detecting (Fig. 29.31) the wavelengths for which reflectance is maximal and transmittance minimal. Ohlidal et al. [29.82] suggest that the index of refraction is equal to v u p u 1 C Rmax 2 C ns Tmin t : (29.171) n D ns 2 p ns 1 Rmax C Tmin Once the values of the refractive index are known at the wavelengths of two successive maximum (Tmax ) or minimum (Tmin ) values of the spectral transmittance, the film thickness d is given by dD
1 2 : 2 Œn.2 /1 n.1/2
Refractive index 2.6
2.5 nmax
2.4
2.3 nmin 2.2
(29.172)
The extinction coefficient of the film is given by 1R ln : (29.173)
D 4 d T
Part C | 29.5
As far as uncertainties are concerned, if ns = Rmax D Tmin D 1 103 , and if ¢1 D ¢2 D 1 nm, then the relative uncertainties are n =n D 0:2% on the refractive index of the film and ¢d =d D 2% on its thickness. Since the optical constants (n; ) are functions of wavelength, an iterative process involving smoothing steps of reflectance and transmittance and interpolation of the envelopes Rmax and Tmin is necessary to extract their values. These steps are important, since the value of the wavelength corresponding to Rmax (or Tmin ) is the key for determining the thickness of the film. In fact, in order to extract the refractive index, the extinction coefficient and the thickness of the film from the measurements of the reflectance and transmittance of the system, this method, called the R-T method, is an inverse problem. The analytical expressions of n, , and d given by (29.171), (29.172), and (29.173) are being used as starting computational solutions to extract R./ and T./. The advantage of this method is that it is not based on any approximation law for the refractive index (Cauchy, Sellmeier, . . . ). However, it is necessary that the spectral reflectance graph show at least one maximum in order to determine the film thickness. It must be noted that there is an infinite number of solutions for the refractive index values at the wavelengths corresponding to Tmax and Rmin , hence a very large error bar in the vicinity of these wavelengths. In contrast, the resolved value of the refractive index is unique at the wavelengths corresponding to Tmin and Rmax . In order to increase the sensitivity of the results, choosing a high refractive index for the substrate can be useful when characterizing low-index films. The terms high index and low index are defined in relation to the
400
500
600
700 800 Wavelength (nm)
Fig. 29.32 Typical result given by the R-T method about
the refractive index of a ZnS thin film
reflectance of the uncoated substrate: a film has a high index value if the reflectance of the film is higher than that of the substrate, and vice versa. Figure 29.32 shows the spectral curve of the refractive index of a zinc sulfide (ZnS) thin film in the visible range, as obtained with the R-T method. The green curve corresponds to the average value of the refractive index. On either side of this curve, one finds the upper and lower limits (˙n ) of the uncertainty of the method, computed on the basis of a homogeneous layer with uncertainty values on reflectance and transmittance measurements equal to R D T D 1 103 . However, we do observe that this uncertainty becomes much larger in the vicinity of wavelengths where the bare and coated substrates have similar reflectance.
29.5.4 Case of Inhomogeneous Dielectric Thin Films Depending upon the deposition process and conditions, the spectrophotometric results may show that the maximum transmittance and minimum reflectance values of the coated substrate do not coincide with the transmittance or reflectance of the uncoated substrate (Fig. 29.33), whereas it is found that the energy conservation law, R./ C T./ D 1, is verified. Spectrophotometry is utilized for the characterization of inhomogeneous films, particularly in the case of columnar or porous films, or films with a graded composition (Fig. 29.34). In order to account for the inhomogeneity of a film, one may either consider the coating as being made up of N homogeneous sublayers with a linear index variation, or use the Jacobsson method [29.83], which is based on a matrix that takes into account the index variation
Refractive Index of Optical Materials
29.5 Spectrophotometric Determination of Refractive Indices
1035
Fig. 29.33 Spectral reflectance and
T, R 1.0
transmittance of an inhomogeneous film deposited on a transparent substrate
Ts (λ)(boundary of bare substrate)
0.8 T(λ)
0.6
0.4 R(λ)
0.2
Rs (λ) (boundary of bare substrate)
0.0
a)
400
0.3
R
500
600
700
800 900 Wavelength (nm)
b)
naverage = 2.22; nmin = 2.19; nmax = 2.25
ni
n decrease n constant n increase
0.25
Refractive index
∆n
ň nd
0.3
ns
0.25
na
0.3 Boundary of bare substrate
0.25 0 500
700
900
Substrate (ns)
Air (n0)
d
0
Thickness
Fig. 29.34 (a) Comparison between the spectral reflectance of a transparent inhomogeneous layer and that of a layer with a linearly graded index (positive or negative gradient) (b) Simulation of a linearly graded index by N homogeneous layers for the case of a linearly decreasing gradient (from substrate to air). nL stands for average value of refractive index
with thickness. For normal incidence, the characteristic transfer matrix that links the electric field from one boundary to another is 2 s n.ˇ/ cos .ˇ/ n .0/
6 6 MD6 6p 4 i n.ˇ/n .0/ sin .ˇ/
sin .ˇ/
2
Rmin D
3
ip 7 7 s n.ˇ/n .0/ 7 7 n .0/ 5 cos .ˇ/ n .ˇ/ (29.174)
with ˇ D
The values of minimum reflectance are given by
0
(29.175)
2 :
(29.176)
It must be noted that the Rmin values of the inhomogeneous film spectral reflectance differ from the Rs ./ values of the bare boundary (Fig. 29.34a). This criterion is to be used for differentiating inhomogeneous from homogeneous films. The optical admittance Ymax at Rmax is
Zd n.z/dz :
n0 n .ˇ/ n .0/ ns n0 n .ˇ/ C n .0/ ns
Ymax D
n.ˇ/n.0/ : ns
(29.177)
Part C | 29.5
1100 Wavelength (nm)
Inhomogeneous layer
1036
Part C
Characterization of Glasses
Thus the R-T method is well adapted to determining the refractive index of inhomogeneous films. With the starting solution to the relationship (29.171) established by Ohlidal et al. [29.82], the numerical method explains optical properties of the film and extracts its optical constants and thickness. This method was developed by Borgogno et al. [29.84]. Other models exist, such as that of linear gradient films which have been developed by Jacobsson [29.83] or by an approach of inverse synthesis of optical coating [29.85].
29.5.5 Case of Metallic Films Deposited on a Transparent Substrate This section deals with moderately or highly absorbing metallic films. In the case of a completely opaque layer (Ts D 0), since film admittance is equal to nm i m , it is sufficient to determine Rs ./ and R0s ./ in order to compute the refractive index and extinction coefficient (nm and m ) of the film. If the thin metallic film is not quite opaque, Rs ./, R0s ./ and Ts ./ are required. Analytical expressions of the optical properties Ts ; Rs ; R0s ;
1 C Rs 1 Rs 1 C R0s 1 R0s ; ; ; Ts Ts Ts Ts (29.178)
Part C | 29.5
can be found in papers of Heavens [29.73], Abeles [29.86] and Tomlin [29.87]. These terms (29.178) are a priori sufficient to extract the optical constants (nm and m ) and the thickness of the metallic film (dm ), assumed to be homogeneous. If a very thin metallic film is deposited, the search for its parameters can be based on a power series of dm =. If dm = 1, a first-order development [29.88], under normal incidence, allows us to compute the product of the metallic layer parameters 2nm m dm in equations (29.179a)–(29.179c), depending on experimental measurements 2nm m dm D
ns ./ 2 ns ./ n0 ./
Rs ./ R0s ./ Ts ./
;
(29.179a)
1 Rs ./ Ts ./ ns ./ 2 Ts ./ As ./ D ns ./ ; (29.179b) 2 Ts ./ 1 R0s ./ Ts ./ n0 ./ ; 2nm m dm D 2 Ts ./ 2nm m dm D
(29.179c)
R0s
(A0s )
where and Rs .As / are the film reflectance (absorptance) on the substrate and air sides, respectively, and Ts is its transmittance.
This development shows how it is difficult to correctly evaluate the optical constants of a very thin metallic layer. Although the method described above delivers a partial solution, which is the product of nm ,
m , and dm , it remains inadequate.
29.5.6 Optical Constant Determination by the Bilayer Metallic-Dielectric Method Since metallic layers can be inhomogeneous, depending on their deposition process and conditions, there is a need for a more efficient method dedicated to determining their optical properties. That is the goal of the bilayer metallic–dielectric method, explored below in two modes: the Rs -Rc method for opaque metallic films, and the Rs Ts Rc Tc method for non-opaque films. The Rs -Rc Method for Opaque Metallic Films Let the thick and opaque metallic layer to be characterized, of optical constants nm and m , be deposited upon a transparent substrate, be considered as a substrate. The spectral reflectance of its front surface Rs ./ is measured, and the spectral transmittance of its front and rear surfaces, Ts ./, is set equal to 0. Then, a dielectric film is deposited on top of the metallic film, and the spectral reflectance Rc ./ of the coated metallic film is measured under the hypothesis that there is no physico-chemical interaction at the metal-dielectric interface. Figure 29.35a shows the two phases of the Rs Rc method, and Fig. 29.35b the typical corresponding spectral reflectance graphs. At each wavelength, one can write the following set of equations 1 C Rs 2 Rs C m2 D 4n20 ; nm n0 1 Rs .1 Rs /2 (29.180)
m D
n2d
C n20
2n0 1 tg'd C 2nd nd .n2d n20 / sin 2'd 1 C Rs 2 .n cos2 'd C n20 sin2 'd / 1 Rs d
2 1 C Rc nd nm ; (29.181) 1 Rc
with 'd D .2 =/nddd the phase shift introduced by the dielectric film of thickness dd . One will note that, in the nm , m plane, (29.180) represents a circle centered at the point of coordinates nm D n0 .1 CpRs /=.1 Rs / and m D 0, having a radius equal to 2n0 Rs =.1 Rs /; (29.181) is that of a straight line ( m D m0 CA nm ) representative of a linear depen-
Refractive Index of Optical Materials
a)
b)
Rs
1
spectral reflectance Rs ./ of metallic film alone, and Rc ./ of the same metallic film coated with a dielectric film
Rs Rc
0.80 0.70
Rc
1
1037
Fig. 29.35 (a) The two configurations of the Rs -Rc method (b) corresponding
R
0.90
Opaque metallic film
29.5 Spectrophotometric Determination of Refractive Indices
0.60
Dielectric film
0.50
Opaque metallic film 0.40 400
600
800 1000 Wavelength (nm)
dence of m with respect to nm of slope A The solution to the problem of index determination is given by the coordinates of the intersection points between the circle and the straight line. As shown by Fig. 29.36, there may be several solutions. One way to eliminate this ambiguity is to make measurements on two systems coated with layers of the same metal but of different dielectric thicknesses; then the solution is unique. The measurements should be carried out for a large number of wavelengths over the spectral range of interest. It can been shown, at the wavelengths where Rs D Rc , that 'd D p (p integer) for the wavelengths of intersection where the slope of the Rc curve is positive (Fig. 29.35b). For these wavelengths, the equation (29.181) shows that the extinction coefficient m ! 1. If the wavelength values for which 'd D .p C 1=2/ , the formulas (29.181) allow us to determine the
Straight lines
5
nm D
m2 D
2
1
0
1
2
3
4
5
lutions of the optical constants of a metallic substrate or opaque metal layer (nm D 2, m D 4) and nd D 2:35 for two phase retardations 'd D =4 and 'd D 3 =4
(29.182b)
The investigated spectral range can be limited at will. No analytical extrapolation, as is the case for K–K relations. No use of approximate laws for the optical constants, as is the case in R-T method. In situ reflectance measurements (Rs and Rc ) can be performed. The method is applicable to materials with strong to moderate absorption zones. The disadvantages of this method are:
6 nm
Fig. 29.36 Graphical representation of the search for so-
.n0 nm / Rs .n0 C nm / : .Rs 1/ 2
These expressions of refractive index and extinction coefficient can be considered as the starting solutions for iterative calculations. Considering realistic values of uncertainties on the reflectance, the refractive index and the thickness of the dielectric layer (such as Rs D Rc D 0:1%, nd D 0:2% and d D 1:5 nm), the resulting rms uncertainties on nm and m are similar, between 1% and 2%. Although this method is less accurate than the one based on the K–K relations, it has the following advantages:
3
0
and (29.182a)
2
Circle
4
.n4d n40 / 1 C Rc 1 C Rs 2n0 n2d n20 1 Rc 1 Rs
The dielectric film must be homogeneous. The dielectric layer parameters (nd and d) must be precisely characterized. Two reflectance values must be measured.
Part C | 29.5
κm
refractive index nm and the extinction coefficient m by
1038
Part C
Characterization of Glasses
The method accuracy is low for weakly absorbing layers. The method is critical if one needs to know accurate wavelength values. Improving the accuracy necessitates the use of highindex dielectrics.
This Rs -Rc method has been successfully used to measure the refractive indices of materials such as aluminum, chromium, hafnium and nickel [29.89]. Figure 29.37 shows the experimental characterization of these opaque metallic films [29.89] with this method. For each of these metals, a high-refractive-index (> 2) dielectric layer was associated with the metallic film. In the case of aluminum, nickel and chromium, a)
R s , Rc
n m , κm 16.0
1.00
the films were deposited via electron beam deposition (EBD) technology and a BAK 600 coating system, and then covered by a ZnS dielectric coating. In the case of hafnium, the dielectric coating was in hafnium dioxide (HfO2 ), both films being deposited using reactive low-voltage ion plating (RLVIP) technology and a BAK 800 coating system. The optical measurements were carried out using the V-W configuration (incidence angle of 8ı ) of a Perkin-Elmer spectrophotometer model LAMBDA-19. Figure 29.38 shows the spectral curves for each of these bilayers, i. e., Rs ./ (metallic layer alone) and Rc ./ (metal C dielectric layers), along with the optical constants (nm and m ) of the opaque metallic films resulting from the use of the Rs -Rc method. These results are in agreement with those obtained on bulk materials [29.21, 90]. b)
R s , Rc
n m , κm 8.0
0.60 Rs
Rs
0.90
12.0
6.0 0.40
Rc
0.80 Rc
8.0
4.0
0.70 κm
nm
0.20 4.0
0.60
2.0 κm
nm 0.50 500
Part C | 29.5
c)
600
700
R s , Rc
0.0 800 Wavelength (nm) n m , κm 4
0.50
0.00 400
d)
R s , Rc
n m , κm 4
0.80
Rs 0.40
Rc
0.0 800 1000 Wavelength (nm)
600
κm 3
0.60
3 Rs
0.30
nm
2
2
0.40 nm
0.20 κm
1
0.10
0.20
1 Rc
0.00 300
400
500
600
0 700 800 Wavelength (nm)
0.00 400
500
600
0 700 800 Wavelength (nm)
Fig. 29.37a–d Experimental characterization of opaque metallic films by the Rs -Rc method: (a) aluminum, (b) chromium, (c) hafnium, (d) nickel
Refractive Index of Optical Materials
a)
b) T
29.5 Spectrophotometric Determination of Refractive Indices
Fig. 29.38a,b Schematic showing the Rc
T
Rs nd , dd n m , κm, d m
Dielectric film Thin metallic film
n m , κm, d m
Transparent substrate
Ts
1. Potential transmittance is equal to 100% only if all constituents (coatings and substrate) are nonabsorbing (which is the case for dielectric film). 2. If the system is made up of transparent substrate with a non-opaque metallic layer D
Ts ; .1 Rs /
that, if sT ¤ cT , one may consider that there exists some chemical interaction between metallic and dielectric film, at interface and/or bulk film. Now, if it is assumed that there is no such interaction, one may consider that optical admittance of thin metallic film is Ym D Xm iZm , where Xm and Zm are functions of the optical constants and thickness of the metallic film. In that case Xm stands for nm and Zm stands for m in (29.180) and (29.181). In the case of very thin metallic films, it is more difficult to identify the three parameters nm , m and dm . This can be accomplished by numerical calculations [29.92] with a complex strategy using different merit functions of Ts , Rs , Rc , and Tc [29.89, 91], where:
Rs and Ts are the air-side reflectance and transmittance of the single metallic film. Rc and Tc are the air-side reflectance and transmittance after deposition of the dielectric layer on metallic film.
3.00
Now, if one considers the case of a thin metallic film, dm = 1 the Wolter relations (29.179) give important information on the optical constants and thickness of the metallic film.
n m, κm κm
nm
2.00
1.00
2nm m dm D
(29.183)
where As and Ac are the absorptance of the following coatings, respectively: metal alone and metal C dielectric. The most important information from (29.183) is
0.00 0
20
40
60 Thickness (nm)
Fig. 29.39 Simulation of optical constants, versus thick-
ness of a nickel layer at D 600 nm (after [29.91])
Part C | 29.5
where Ts and Rs are the transmittance and the reflectance of the system, respectively (Fig. 29.38a). 3. After deposition of the nonabsorbing dielectric, for the bilayer (metal C dielectric), the potential transmittance is given by cT D Tc =.1 Rc / D sT (Fig. 29.38b).
As ns 2 Ts Ac ns ; D 2 Tc
parameters and measured quantities of a bilayer system: (a) transparent substrate coated with a non totally opaque metallic film (b) same system covered with an additional dielectric layer
Tc
Case of Metal-Dielectric Bilayer with Non-Opaque Metallic Layers In this case, the metallic film may be traversed by some fraction of the illuminating beam, and its thickness dm plays an important role. In contrast to the Rs -Rc method, as described in Fig. 29.35, four spectral measurements (Rs ./, Ts ./, Rc ./ and Tc ./) are necessary to obtain the three unknown parameters (i. e., nm , m , and dm ). Figure 29.38 shows the corresponding schematic. Electromagnetic theory shows that the potential transmittance T of any element of a coating system is defined as the ratio of the output to the input irradiances, the input being the net irradiance rather than the incident: T D T=.1 R/. Therefore:
T s
1039
1040
Part C
Characterization of Glasses
This strategy for determining optical constants is based on the use of the expressions of .1 R/=T and .1 C R/=T [29.7, 87, 89, 93]. This strategy has been used for nickel films of different thicknesses, obtained by an electron beam deposition technique; the results delivered by the numerical algorithm for these three parameters are satisfactory for all thicknesses. However, a notable discrepancy is observed for each parameter (nm ; m ) if one compares the results obtained for different thicknesses, which means that metallic films are inhomogeneous [29.89, 91]. A simulation (Fig. 29.39) based on the change in compactness inside a metallic layer [29.91], including the Maxwell-Garnett model, has been successfully developed to fabricate a broadband absorber (absorptance
A > 99%) which operates over the visible [29.89–91, 94]. In conclusion, measuring the refractive index is a more difficult task for a non-opaque metallic film than for a dielectric film. Furthermore, it is important to note that the layer model must be chosen in connection with its deposition technology, and that the best results are obtained with homogeneous layers. Spectrophotometry is a simple tool to use, well adapted to the ex situ and in situ characterization of thin films and for the determination of optical constants. It provides guidance for choosing the appropriate layer model. Every three years, at its Optical Interference Coatings conference, the international optical coating community launches a measurement challenge [29.95– 98].
References 29.1
29.2
29.3
29.4
29.5
Part C | 29
29.6 29.7 29.8
29.9 29.10
29.11
29.12
SCHOTT AG: Interactive Abbe diagram, https:// www.schott.com/advanced_optics/english/ knowledge-center/technical-articles-and-tools/ abbe-diagramm.html (2018) N.G. Van Kampen, F. Lurçat: Causalité et relations de Kramers-Kronig, J. Phys. Radium 22, 179–191 (1961) V. Lucarini, J.J. Saarinen, K.-E. Peiponen, M.E. Vartiainen: Kramers-Kronig Relations in Optical Materials (Springer, Berlin, Heidelberg 2005) J.F. Ogilvie, G.J. Fee: Equivalence of Kramers-Kronig and Fourier transforms to convert between optical dispersion and optical spectra, MATCH Commun. Math. Comput. Chem. 69, 249–262 (2013) M. Born, E. Wolf: Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge Univ. Press, Cambridge 1999) A. Hadni: Essentials of Modern Physics Applied to the Study of the Infrared (Pergamon, Oxford 1967) H.A. Macleod: Thin-Film Optical Filters, 4th edn. (CRC, Boca Raton 2010) F.S. Forman, A.V. Tikhonravov: Basics of Optics of Multilayer Systems (Edition Frontieres, Gif-surYvette 1992) National Metrology Institute of Germany: https:// www.ptb.de/cms/en.html (2015) D. Tentori, J.R. Lerma: Refractometry by minimum deviation accuracy analysis, Opt. Eng. 29(2), 160– 168 (1990) D.B. Leviton, B.J. Frey, T.K. Kvamme: High accuracy, absolute, cryogenic refractive index measurements of infrared lens materials for JWST NIRcam using CHARMS, Proc. SPIE 5904, 222–233 (2005) B.J. Frey, D.B. Leviton: Cryogenic High Accuracy Refraction Measuring System (CHARMS): A new facility for cryogenic infrared through farultraviolet refrac-
29.13 29.14
29.15 29.16
29.17
29.18
29.19 29.20
29.21 29.22
29.23 29.24
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29.25
29.26
29.27
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29.29
29.30
29.31
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29.33
29.34
29.35
29.36
29.38
29.39 29.40 29.41
29.42 29.43
29.44 29.45 29.46
29.47 29.48 29.49 29.50 29.51 29.52
29.53
29.54
29.55 29.56
29.57
29.58
29.59
29.60
29.61
29.62
29.63
29.64
29.65
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29.66
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29.73
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29.75
29.76
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29.78
29.79
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fractory metals, Int. J. Thermophys. 12, 643–656 (1991) G. Gosh: Model for the thermo-optic coefficients of some standard optical glasses, J. Non-Cryst. Solids 189, 191–196 (1995) W.J. Tropf, M.E. Thomas, T.J. Harris: Optical and physical properties of crystals and glasses. In: Handbook of Optics, Vol. II, ed. by M. Bass (McGraw-Hill, New York 1995) M.V. Hobden, J. Warner: The temperature dependence of the refractive indices of pure lithium niobate, Phys. Lett. 22, 243–244 (1966) D.H. Jundt: Temperature-dependent Sellmeier equation for the index of refraction, ne , in congruent lithium niobate, Opt. Lett. 22, 1553–1555 (1997) I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, G. Gadret: Linear and nonlinear optical properties of MgO:LiTaO3 , Appl. Phys. B 96, 423–432 (2009) J. Mangin, G. Mennerat, P. Villeval: Thermal expansion, normalized thermo-optic-coefficients, and condition for second harmonic generation of a Nd:YAG laser with wide temperature bandwidth in RbTiOPO4 , J. Opt. Soc. Am. B 28, 873–881 (2011) W. Tropf, M.E. Thomas: Infrared refractive index and thermo-optic coefficient measurement at APL, Johns Hopkins APL Tech. Dig. 19, 293–298 (1998) O.S. Heavens: Measurement of optical constants of thin films. In: Physics of Thin Films (Academic, New York 1964) M. Cathelinaud: Les méthodes spectrophotométriques pour la détermination d’indice de couches minces. In: CNRS/ROP Workshop Metrol. Refract. Indices, Paris, 24–25.11.2008 (2009), http:// www.rop.cnrs.fr/spip.php?article349 P. Bousquet, F. Flory, P. Roche: Scattering from multilayer thin films: theory and experiment, J. Opt. Soc. Am. 71(9), 1115–1123 (1981) A. Piegari, F. Flory: Optical Thin Films and Coatings: From Materials to Applications (Woodhead, Oxford 2013) C. Amra: Light scattering from multilayer optics. I. Tools of investigation, J. Opt. Soc. Am. A 11, 197–210 (1994) S. Adachi: Model dielectric constants of GaP, GaAs, Gasb, InP, InAs, and InSb, Phys. Rev. B 35(14), 7454– 7463 (1987) V. Kumar, S.K. Sharma, T.P. Sharma, V. Singh: Band gap determination in thick films from reflectance measurements, Opt. Mater. 12, 115–119 (1999) P.S. Hauge: Polycrystalline silicon film thickness measurement from analysis of visible reflectance spectra, J. Opt. Soc. Am. 69(8), 1143–1152 (1979) J.C. Manifacier, J. Gassiot, J.P. Fillard: A simple method for the determination of the optical constants, n, k and the thickness of a weakly absorbing thin film, J. Phys. E Sci. Instrum. 9, 1002–1004 (1976) I. Ohlidal, K. Navrfitil, E. Schmidt: Simple method for the complete optical analysis of very thick and weakly absorbing films, Appl. Phys. A 29, 157–162 (1982)
29.83
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29.90
29.91
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29.93
29.94
29.95
29.96 29.97
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Refractive Index of Optical Materials
References
1043
Jean-Louis Meyzonnette Institut d’Optique Graduate School Palaiseau, France
Jean-Louis Meyzonnette received his degrees from the Institut d’Optique (Orsay, France) and the Institute of Optics (University of Rochester, USA). He worked as a Research Scientist in the Optronics Department of Thomson-CSF Avionics Division (1975-1990). In 1990, he joined the Institut d’Optique as a Professor in Instrumental Optics. He retired from the Institut d’Optique in 2012 and now acts as an independent consultant.
Jacques Mangin Laboratoire Interdisciplinaire Carnot de Bourgogne Dijon, France
Jacques Mangin received his PhD from the University of Nancy, France, where he joined the Far-Infrared Laboratory as a Researcher at the CNRS. After a Postdoctoral position at Lawrence Berkeley National Laboratory, he joined the Department of Optical Materials at LICB, Burgundy University, Dijon, where he was in charge of the growth of optical crystals, metrology of thermo- and electro-optical properties of materials and nonlinear optics.
Michel Cathelinaud Institute of Chemical Sciences Rennes, UMR CNRS 6226 University of Rennes 1 Rennes, France [email protected]
Michel Cathelinaud, a CNRS Research Engineer with a PhD from the University of Aix-Marseille, France, has over 20 years of experience in the design, manufacture, and characterization of optical coatings for terrestrial and space applications. He joined ISCR in October 2013 to work on chalcogenide thin films after 6 years as Deputy Head of Mission for Resources and Skills in Technology (MRCT Paris) of CNRS (DGDS / MI).
Part C | 29
1045
Neutron and 30. Neutron and X-Ray Diffraction of Glass
Laurent Cormier
A basic characterization of amorphous materials is usually obtained using diffraction measurements. Indeed, amorphicity is revealed by the absence of sharp Bragg peaks in the angular diffraction pattern, signaling the lack of long-range order and periodicity. However, diffraction patterns obtained by scattering from x-rays, electrons or neutrons contain much more structural information, often overlooked, about the atomic organization of disordered materials. X-ray and neutron diffraction are pioneering tools to get information on the atomic arrangements of noncrystalline materials, alongside the older x-ray diffraction investigations [30.1–3], which are still routinely used as structural experimental techniques. The success of diffraction methods is partly due to the fact that they give the most direct access to the atomic structure (in particular interatomic distances and coordination numbers), and diffraction data can be easily compared to simulations, which is widely used to validate interatomic potentials in molecular dynamics. Another advantage of this technique is that it probes both the shortand intermediate-range order, being very sensitive to the nature and extent of disorder in glasses and liquids, and is an essential probe to understand the structural differences between glasses and their crystalline counterparts. Finally, various environments have been developed, allowing high temperature and/or high pressure measurements to be carried out.
Diffraction by Noncrystalline Materials ............... 30.1.1 Scattering of Neutrons and X-Ray ....... 30.1.2 The Static Approximation ................... 30.1.3 The Faber–Ziman Formalism............... 30.1.4 The Bhatia–Thornton Formalism .........
1046 1046 1046 1046 1047
The Debye Equation ........................... Real-Space Functions......................... Fourier Transformation....................... Data Processing .................................
30.2
Complementarity of Neutron and X-Ray Diffraction........................ 1051
30.3
Determination of the Structural Parameters ....................................... 1053
30.4 Difference Methods ........................... 30.4.1 Neutron Diffraction with Isotopic Substitution (NDIS)......... 30.4.2 Anomalous X-Ray Diffraction (AXRD) .... 30.4.3 Coupling X-Ray and Neutron Diffraction .....................
1048 1049 1050 1051
1054 1054 1055 1056
30.5
Reverse Monte Carlo and Related Methods ........................ 1057
30.6
Case Studies of Glass Investigation by Neutron and X-Ray Diffraction ...... The Low-Q Features ........................... The Polymeric Network....................... Cation Sites in Glasses........................ Cationic Arrangement at Medium Range Distances................ Nonhomogeneous Distribution of Cations .........................................
30.6.1 30.6.2 30.6.3 30.6.4 30.6.5
In Situ High Temperature/High Pressure Diffraction. .......................... 30.7.1 High-Temperature Experimental Techniques ....................................... 30.7.2 Case Studies of Temperature-Induced Modifications .................................... 30.7.3 High-Pressure Experimental Techniques ....................................... 30.7.4 Case Studies of Pressure-Induced Modifications ....................................
1061 1061 1064 1066 1067 1067
30.7
30.8
1068 1069 1070 1078 1078
Conclusion and Perspectives .............. 1083
References................................................... 1083
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_30
Part C | 30
30.1
30.1.5 30.1.6 30.1.7 30.1.8
1046
Part C
Characterization of Glasses
30.1 Diffraction by Noncrystalline Materials 30.1.1 Scattering of Neutrons and X-Ray The fundamental aspects of the scattering processes have been completely described elsewhere [30.4–7] and we will present only a brief outline of the theory. In a conventional diffraction experiment (Fig. 30.1a), the quantity measured by the detector in the small solid angle d˝ at the scattering angle 2 is the differential cross-section d=d˝ (in barn/steradian), defined as number of quanta of wavelength scattered per unit time into d˝ 1 d D N d˝ N˚./d˝ D I.Q/ ; (30.1)
with N the number of scattering units in the sample and ˚./ the incident flux of quanta at wavelength . Q (in Å1 ) is the magnitude of the scattering vector (Fig 30.1b) for an elastic scattering, i. e., ki D kf (or in the static approximation, ki kf ) QD
4 sin :
(30.2)
The differential cross-section may be separated as a distinct term and a self term [30.8] I.Q/ D F.Q/ C
n X ˛
c˛ bN2˛ ;
(30.3)
Part C | 30.1
with F.Q/ the total interference function, and c˛ and b˛ the atomic concentration and scattering length of the chemical species ˛ respectively. The neutron scattering length, b, which measures the strength of the interaction between the neutron and the nucleus, can be positive or negative and is expressed in fm (1015 m). All the structural information is contained in the interference function that is simply related to a structure factor S.Q/ by the relation F.Q/ F.Q/ S.Q/ D P 2 C 1 D N 2 C 1 ; b ˛ c˛ b˛
(30.4)
with S.Q ! 1/ D 1 and S.Q/ 0. The Fourier transform of the structure factor gives a pair distribution (correlation) function, g.r/, describing interatomic interactions in real space [30.5] 1 g.r/ 1 D 2 2 r0
0 D
NA d I A 1024
(30.6)
NA being the Avogadro number and A the atomic weight of the sample.
30.1.2 The Static Approximation In a diffraction experiment, the x-ray or neutron is usually detected without a monochromator being placed between the sample and the detector. In such a case, the experiment is not exactly elastic (as it would be if ki D kf in Fig. 30.1b) and energy exchange could occur within the sample due to interactions of neutrons or x-ray photons with thermal vibrations. The static approximation considers that such energy transfers are negligible compared to the incident energy (ki kf ). This approximation works well for x-ray diffraction due to the energy of the incident photon but is not a valid assumption for neutron diffraction so that, in practice, inelasticity corrections have to be taken into account [30.8, 9]. This approximation allows a decoupling between structural and dynamical information [30.5]. The static approximation considers that the energy exchange „! is small compared to the incident energy E0 . The „! energy corresponds to a characteristic time, , so that the condition „! E0 corresponds to the condition t0 , with t0 the time characteristic for vibrations or relaxations [30.6]. It implies that the time taken by the neutron (or x-ray photon) to pass from one atom to the next is small compared to an atomic motion. Therefore, a scattering event probes only the static structure of the specimen giving an instantaneous snapshot of the structure. A neutron or x-ray elastic diffraction measurement consists of time-averaging snapshots taken by each incident neutron or x-ray photon.
30.1.3 The Faber–Ziman Formalism For polyatomic materials, the total structure factor is a weighted sum of all partial structure factors S˛ˇ .Q/ in the Faber–Ziman formalism [30.10] X W˛ˇ S˛ˇ .Q/ ; (30.7) S.Q/ D ˛;ˇ
Z1 Q.S.Q/ 1/ sin.Qr/dQ ; 0
where r is the interatomic distance, and 0 (atoms Å3 ) is the atomic number density expressed as a function of the macroscopic density, d (g cm3 )
(30.5)
where W˛ˇ are the weighting factors and S˛ˇ .Q ! 1/ D 1. The partial structure factors are identical for
Neutron and X-Ray Diffraction of Glass
Q (Å–1) 20
a) Detector
1047
Q = kf – ki
b)
15
kf
ki
Sample 10
30.1 Diffraction by Noncrystalline Materials
2θ
Source 5 2θ λ
I (Q)
Fig. 30.1 (a) Conventional setup for a diffraction experiment. A monochromator can be placed between the source and sample, which is the case for synchrotrons or steady-state reactors. To obtain true elastic scattering, a monochromator should also be placed between the sample and the detector. (b) Scattering from a single atom by an incoming radiation with wavevector ki of magnitude 2 =, and a scattered wavevector kf
x-ray photons and neutrons since they only depend on the structure. In contrast, the weighting factors are independent of the structure but are different when considering diffraction by x-ray photons or neutrons. As a result, the total structure factors, S.Q/, have significant differences in peak positions and intensities between the two diffraction methods (Fig. 30.2). At this point, it is necessary to distinguish between diffraction processes for x-rays and neutrons. For x-rays, the quantity equivalent to the neutron scattering length is the atomic form factor, f .Q; E/, which is dependent on both the energy of the incident photon and Q. f .Q; E/ corresponds to the scattering by the electron cloud (while the neutron scattering length b indicates scattering by the nucleus) and its amplitude increases with atomic number Z (while b can be considered usually as a constant). b and f are tabulated in [30.11– 14]. Due to the Q-dependence of the form factors, the expression for the weighting factors is slightly different
W 0 ˛ˇ D x-ray
c˛ cˇ K˛ Kˇ .2 ı˛ˇ / ; P 2 ˛ c˛ K˛
(30.10)
with K˛ the effective number of electrons for species ˛. With this simplification, the weighting factor is a constant and the pair distribution function has a simpler formulation X x-ray W 0 ˛ˇ g˛ˇ .r/ : gx-ray .r/ D ˛;ˇ
The partial pair distribution function, g˛ˇ .r/, gives the probability of finding an atom of type ˇ at distance r from an atom of type ˛ taken at the origin (average distribution of atoms ˇ around an atom ˛ at the origin) and vice-versa, since g˛ˇ .r/ D gˇ˛ .r/. For a system with n components, there are n.n C 1/=2 independent partial structure factors (or partial pair distribution functions, PPDFs). A detailed understanding of the structure requires the complete determination of the set of partial structure factors (or PPDFs) that describe the environment of each atomic species.
30.1.4 The Bhatia–Thornton Formalism
(30.8)
where the Kronecker delta .ı˛ˇ / takes into account that S˛ˇ .Q/ D Sˇ˛ .Q/. In the case of the neutron, the Fourier transform in (30.5) is straightforward while, for x-rays, it is the Fourier transform of a product of two functions that gives, in real space, the convolution of the Fourier transforms of each function X neutron W˛ˇ g˛ˇ .r/ gneutron .r/ D ˛;ˇ
g
x-ray
x-ray .r/ D FT W˛ˇ ˝ g˛ˇ .r/ ;
(30.9)
An alternative formalism for the partial structure factors has been proposed by Bhatia and Thornton for a binary system based on the local density and concentration [30.16]. These partial functions correspond to the density fluctuations (topological contribution), SNN .Q/, the concentration fluctuations (chemical contribution), SCC .Q/, and the correlations between the two, SNC .Q/, b b 2 SNC .Q/ C S.Q/ D SNN .Q/ C 2 SCC .Q/ ; hbi hbi (30.11)
Part C | 30.1
c˛ cˇ b˛ bˇ .2 ı˛ˇ / P 2 ˛ c˛ b˛ c˛ cˇ f˛ .Q; E/fˇ .Q; E/.2 ı˛ˇ / x-ray W˛ˇ .Q; E/ D ;
P 2 ˛ c˛ f˛ .Q; E/ neutron W˛ˇ D
where ˝ is the convolution sign between two functions. To avoid the complex definition of gx-ray .r/, the weighting factors can be simplified
1048
Part C
Characterization of Glasses
Partial structure, S αβ(Q)
Weighting factors, Wαβ(Q)
×
b) S N(Q) – 1
a)
Total structure factor, S(Q)
=
c) S N(Q) – 1
0.2
0.2 Neutron
SGeGe(Q) – 1 0
WOO
0.5
0
WGeO –0.2
0
10
20
30 Q (Å–1)
0.2
–0.2
WGeGe
0 SGeO(Q) – 1
0
10
20 Q (Å–1)
0
0
10
20
30 Q (Å–1)
20
30 Q (Å–1)
SX(Q) – 1 SX(Q) – 1
–0.2 0
10
20
30 Q (Å–1)
X-ray
WGeGe 0.5
0
WGeO
0.2 S OO(Q) – 1
0
–1 WOO
–0.2
0
10
20
30 Q (Å–1)
0
0
10
20 Q (Å–1)
0
10
Fig. 30.2 (a) For GeO2 glass, the three partial functions S˛ˇ .Q/ contain the structural information. (b) Each partial structure factor can be multiplied by their respective neutron weighting factors (top), which are constant, or by their respective x-ray weighting factors (bottom), which are Q-dependent. (c) The sum of all S˛ˇ .Q/ multiplied by their weighting factors gives the total structure factor for neutron (top) or x-ray (bottom). Due to the different weighting factors, the total structure factors are different, though the structural information (contained in the S˛ˇ .Q/ functions) is the same. The figure is adapted from [30.15]
where hbi D c˛ b˛ C cˇ bˇ
and
Their use is limited, as it is restricted to binary materials, but several examples can be founded in Salmon’s works [30.17–19].
b D jb˛ bˇ j :
Part C | 30.1
These functions are related to the Faber–Ziman partial ones by simple linear combinations, but they emphasize different aspects of the atomic structure as they separate information on the topological order .SNN .Q// from information on the chemical order .SCC .Q// SNN .Q/ D c2˛ S˛˛ .Q/ C 2c˛ cˇ S˛ˇ .Q/ C c2ˇ Sˇˇ .Q/ SNC .Q/ D c˛ cˇ Œc˛ S˛˛ .Q/ .c˛ cˇ /S˛ˇ .Q/ cˇ Sˇˇ .Q/ SCC .Q/ D c˛ cˇ c˛ cˇ ŒS˛˛ .Q/ C Sˇˇ .Q/ 2S˛ˇ .Q/ C 1 : (30.12)
30.1.5 The Debye Equation For a set of N identical atoms in an isotropic specimen, Debye has shown that the structure factor can be simplified as [30.20] S.Q/ D 1 C
n 1 X X sin Qr˛ˇ : N ˛D1 Qr˛ˇ
(30.13)
ˇ¤˛
Each characteristic interatomic distance r˛ˇ in the sample corresponds in S.Q/ to a damped sine wave of period Q D 2 =r˛ˇ . Long-period fluctuations in Q-space give rise to short-range distances and viceversa [30.21].
Neutron and X-Ray Diffraction of Glass
a) g(r) (b Å–2)
30.1 Diffraction by Noncrystalline Materials
1049
b) D(r) (b Å–2)
3 0.5 2
0
1
– –4r 2ρ 0 b2 0 0
2
4
6
8
10 r (Å)
c) T(r) (b Å–2)
–0.5
0
2
4
6
8
10 r (Å)
8
10 r (Å)
d) RDF(r) (b Å–2)
2
14 12 10
– –4r 2ρ 0 b2 1
8 6 4 – –4r 2ρ 0 b2
2 0 0 0
2
4
6
8
10 r (Å)
0
2
4
6
Fig. 30.3a–d Relation between the different real-space functions (see text) for a 61CaO-39Al2 O3 glass [30.22]: (a) The pair distribution function, g.r/; (b) the differential correlation function D.r/; (c) the total distribution function T.r/; and (d) the radial distribution function RDF.r/
30.1.6 Real-Space Functions
Another commonly used function is the differential (or reduced) correlation function D.r/ .D.r ! 1/ D 0/
g.r/ D
.r/ ; 0
(30.14)
where .r/ is the r-dependent atomic density (g.r ! 1/ D 1 and g.r ! 0/ D 0), defining the number of atoms within a sphere or radius r [30.21]. For a polyatomic specimen, the partial pair distribution function g˛ˇ .r/ is the number of atoms of type ˇ between distances r and r C dr from an atom ˛ g˛ˇ .r/ D
n˛ˇ .r/ : cˇ 0 4 r2 dr
(30.15)
D.r/ D 4 rbN2 0 Œg.r/ 1:
(30.16)
In this function, only deviations from the average atomic density 0 are considered. The (total) radial distribution function RDF(r) or the total distribution function T.r/ are also used RDF.r/ D 4 r2 bN2 0 g.r/ RDF.r/ T.r/ D r D 4 rbN2 0 g.r/ :
(30.17)
An excellent account of these different definitions is given by Keen [30.23].
Part C | 30.1
Different functions (Fig. 30.3) can be used in real space, which are all related to the pair distribution function g.r/, describing the local fluctuations in density around the unit
1050
Part C
Characterization of Glasses
30.1.7 Fourier Transformation Effect of Q-Range As shown in Fig. 30.4a, access to high Q-values (i. e., high Qmax ) is required to achieve high real-space resolution. With a small Qmax value, the dramatic peak broadening results in an overlapping of atom–atom contributions. A high Qmax value allows us to resolve two close interatomic distances. The Q-range accessible experimentally is determined by (30.2). The values of are restricted to 2 D in a scattering measurement. The possibility of increasing the Q-range is thus achieved essentially by using high incident energy (short incident wavelength ) either from synchrotron sources for x-rays or from spallation sources for neutrons. An example is provided by Petkov et al. that used high energy x-ray diffraction (HE-XRD) with Qmax D 40 Å1 in aluminosilicate glasses [30.24]. The Si–O and Al-O distances, only separated by 0:15 Å, can be clearly differentiated. Using a neutron spallation source, similar Qmax values can be reached. With such a diffraction experiment, the two P–O distances existing within a PO4 tetrahedra can be resolved [30.25]. The two P–O components at 1:43 and 1:58 Å correspond to the terminal and to the bridging oxygen atoms, respectively. a) D(r) (b Å–2)
Finally, we should note that increasing the upper-Q limit increases the noise in real space so that sufficient counting statistics at large Q-values are needed, which increases the time for measurement. Effect of Truncation The data accessible in diffraction experiments are limited in Q W Qmin Q Qmax : The Qmin limit does not affect the Fourier transform since low values can be accessed experimentally and since the structure factor is multiplied by Q in the Fourier-sine transform. However, the fact that the Fourier transform cannot be integrated to infinite Q results in the appearance of peak broadening and parasitic lobes around the peaks in D.r/, particularly at low r values. This truncation of the upper-Q limit is equivalent to multiplying the interference function F.Q/ D QŒS.Q/ 1 by a modified M.Q/ function Z1 2 D.r/ D M.Q/F.Q/ sin.rQ/dQ 0 ( 1 when Q Qmax with M.Q/ D (30.18) 0 when Q > Qmax : b) D(r) (b Å–2)
Qmax = 7 Å–1
15
3 Qmax = 10 Å–1 Qmax = 15 Å–1
Lorch
10
2 Qmax = 17 Å–1 Exponential Qmax = 20 Å–1
Part C | 30.1
1
5
Qmax = 30 Å–1 Qmax = 40 Å–1 0
0
1
2
3
4
5
6
7
8 r (Å)
No M(Q) 0
0
0.5
1
1.5
2 r (Å)
Fig. 30.4 (a) Example showing how the Qmax limit in the Fourier transform of the structure factor affects the resolution in real space for a 61CaO-39Al2 O3 glass [30.22]. (b) Influence of the data truncation without modification function and
with two modification functions (exponential and Lorch)
Neutron and X-Ray Diffraction of Glass
The introduction of M.Q/ is equivalent to a convolution of the correlation function with a peak shape function, P.r/, which is the cosine transform of M.Q/ [30.26] 0
Z1
D .r/ D
D.r/P.r u/du 0
2 with P.r/ D
Z1 M.Q/ cos.rQ/dQ :
(30.19)
30.2 Complementarity of Neutron and X-Ray Diffraction
1051
The Q resolution of the instrument adds another exponential dampening effect to the real-space information [30.30]. This has no effect at short r distances but prevents extraction of pair correlation information beyond 50 Å [30.31]. For glasses and liquids, structural fluctuations are not discernible at large r (isotropic medium) and the atomic density .r/ tends to 0 at large r so that integration can be truncated safely at r 2 nm.
30.1.8 Data Processing
0
If M.Q/ is a step function, P.r/ is a sinc, giving important termination ripples. The effect of truncation can be partly suppressed by using different M.Q/ functions damping the data cutoff at Qmax . This effect is illustrated in Fig. 30.4b. The primary modification function is a Lorch function [30.27] ( sin.rQ/ when Q Qmax rQ M.Q/ D (30.20) 0 when Q > Qmax ; with r D =Qmax , corresponding to a resolution length in real space. These smoothly decaying functions reduce unphysical oscillations, but at the expense of further broadening of the peaks in D.r/. More sophisticated functions using r-dependent real-space broadening were recently proposed in order to minimize the broadening near the first peak [30.28, 29].
The purpose of a diffraction experiment is to measure I.Q/ and make all the necessary corrections to extract S.Q/. The data treatment has been described in numerous papers for neutrons [30.4, 7, 32] or xrays [30.4, 7, 28, 33]. Absolute intensities can be determined for neutrons thanks to the measurement of standard references with known scattering cross-section, such as vanadium. However, for materials with a high inelasticity or major absorption corrections (for example, Li or H), care is necessary in the analysis of neutron diffraction data. The normalization is not straightforward for x-rays and can lead to uncertainties in the determination of the coordination numbers. All sources have adequate codes to correct the data and we could cite mainly GUDRUN for neutron spallation sources [30.34], CORRECT for steady-state neutron reactors [30.35], and GUDRUNX [30.28] or PDFgetX3 [30.36] for x-ray sources. Once S.Q/ is correctly obtained, the Fourier transformation allows us to obtain real-space information.
30.2 Complementarity of Neutron and X-Ray Diffraction Neutron and x-ray diffraction techniques are often associated to provide additional information on the structure of disordered materials (Table 30.1). These two meth-
ods allow access to wide Q-range domains and thus offer a good resolution of bond lengths and numbers of first neighbors. Neutron diffraction has significant dif-
X-ray diffraction Interaction with electronic cloud f .Q; E/ atomic form factor Strong variation of scattered intensity with Information on high-Z elements Weak scattering for low-Z elements Weak contrast for elements with close Z f varies with the energy ) anomalous scattering Small samples Radiation can cause damage No magnetic information
Neutron diffraction Interaction with the nucleus b neutron scattering length Constant, independent of Not a monotonous function of Z Light elements are visible (H, Li, N, O, etc.) Possibility to distinguish elements with close Z b can vary at some energies for some elements ) anomalous scattering limited b varies among isotopes of the same element ) isotopic substitution Large samples Radiation can cause activation Magnetic information is possible
Part C | 30.2
Table 30.1 Comparison of neutron and x-ray diffraction
1052
Part C
Characterization of Glasses
a) Scattering length (fm)
b) Scattering amplitude (fm) 5
58
Ni
46
Ti
2
H
4
10
3 6
Li 2
0
X-rays
7
Li 1 48
Ti
Neutrons 62
–10
0
20
Ni 40
60
80 Atomic number, Z
0
0
0.2
0.4
0.6
0.8 1 sinθ/λ (Å–1)
Fig. 30.5 (a) Erratic evolution of neutron scattering lengths as a function of the atomic number, Z (solid curve), with the slowing increase in potential scattering (dashed curve). (b) Evolution of the x-ray and neutron scattering amplitudes as
a function of sin =
Part C | 30.2
ferences with x-ray diffraction [30.7]. While an x-ray photon is scattered by the atomic electron density, the uncharged neutron interacts directly with the (small) atomic nucleus. As a result, neutrons can be used to study the structural position of light elements such as H or Li and are thus well suited to study aqueous solutions, glassy ices or glass electrolytes for solidstate batteries. Conversely, x-ray diffraction is sensitive to high-Z elements. These two techniques are thus complementary because they are sensitive to different elements (Fig. 30.2). Neutron scattering lengths exhibit a nonmonotonous evolution as a function of the atomic number, Z, and are Q-independent, while x-ray atomic form factors directly depend on Z and decrease to zero at large Q-values (Fig. 30.5). This will limit Qmax values that are obtainable, particularly for samples containing low-Z elements. Neutron interaction with
a given atom nucleus does not vary straightforwardly with Z, as it does in the case for x-rays, but may be very different between two neighboring elements and even between isotopes of the same element. This last property is at the basis of the isotopic substitution method (Sect. 30.4.1). For x-rays, the possibility that the atomic form factor varies close to the absorption edge of a specific element allowed the development of the anomalous scattering method (Sect. 30.4.2). The coupling of the two diffraction methods was widely used to study borate and phosphate glasses with high ionic conduction. The glassy borate and phosphate networks could be studied more specifically with the neutron diffraction results, while the organization of the elements responsible for the ionic conduction (alkali oxides or salts) could be investigated by x-ray diffraction [30.25, 37–41].
Neutron and X-Ray Diffraction of Glass
30.3 Determination of the Structural Parameters
1053
30.3 Determination of the Structural Parameters Structural information is easier to visualize and extract in real space (Fig. 30.6). The peak position directly gives the average interatomic bond length, r˛ˇ , between an atom ˛ taken at the origin and an atom ˇ at the distance r˛ˇ . Provided that there is limited overlap with other interatomic contributions, a great precision can be achieved: the Si–O bond length has been determined at 1:605 ˙ 0:003 Å using neutron diffraction [30.42]. The coordination number, N˛ˇ , defines the average number of neighbors ˇ around an atom ˛, and it can be calculated by integrating the area under the ˛–ˇ peak
N˛ˇ and ˛ˇ factors are closely correlated and subject to more uncertainties. The coordination number is the least accurate parameter because it varies strongly with the slope at the origin or the Q-range, and the accuracy decreases in the case of overlapping peaks. The ability to use different functions (total or partial), which must give the same information, can provide guidance on the accuracy of the values. These three parameters are often obtained by performing a Gaussian fit of the peak, allowing r˛ˇ , N˛ˇ and ˛ˇ to vary.
(30.21)
" # W˛ˇ N˛ˇ .r r˛ˇ /2 exp (30.22) g˛ˇ .r/ D q 2 2 2˛ˇ cˇ r 2 ˛ˇ
where the integration limits .r1 r2 / define the coordination shell. These limits are not always well defined, in particular in the case of partial overlap with another contribution, which affects the accuracy. The width of the peak ˛ˇ gives a measure of the distribution of interatomic distances due to both static structural and thermal disorder. However, the determination of ˛ˇ is not direct since a peak broadening results from the limited-Q integration of the structure factor giving the correlation function.
The weighting factors W˛ˇ are calculated from tabulation of b and f [30.11–14] and the atomic fraction, c, is provided by the chemical analysis of the samples. The D.r/ and T.r/ functions should be preferred as the finite Qmax results in a symmetric peak broadening for these functions [30.43]. To take into account the Qmax truncation, Gaussian functions have to be convoluted by a resolution function in real space given by the Fourier transform of the Lorch function [30.44].
Zr2 N˛ˇ D 4 0 cˇ
g˛ˇ .r/r2dr ; r1
D(r) 4 1st coordination sphere
3 Area: average coordination number
2
r dr
2nd coordination sphere
1
0
1
2
3
4
5 r (Å)
Fig. 30.6 Correlation function and
real-space information
Part C | 30.3
Peak position: average bond length
0
1054
Part C
Characterization of Glasses
30.4 Difference Methods
Part C | 30.4
The D.r/ function is informative but dominated by the correlations that have large weighting factors, e. g., usually Si–O, O–O and Si–Si in silicate glasses for neutron diffraction measurements. On the other hand, above 3 Å, the various contributions are superimposed, the contributions with small weighting factors being overlapped by those having large weighting factors. It becomes extremely difficult above 3 Å to deconvolute the various contributions for a multicomponent material. The use of structural models can offer an interpretation of D.r/ but this is of course not unequivocal. For a system with n-components, there are n.n C 1/=2 partial structure factors (or PPDFs) that one wants to retrieve to describe the structure. The detailed understanding of the atomic structure requires the complete determination of the set of partial structure factors, which means that n.n C 1/=2 distinct experiments are required. In simple systems, this can be obtained by applying different contrast variation methods. For multicomponent glasses or liquids, these techniques allow the extraction of structural information for one specific element that is otherwise buried beneath other contributions with strong weighting factors. The only element in S.Q/ that is not structure or composition dependent is the neutron scattering length, b, or the atomic form factor, f .Q; E/. b can vary significantly in amplitude or sign from one element to another or between isotopes of the same element. The first property is used in isomorphic substitutions (exchange of elements playing an identical role in the structure [30.45]) while the second led to a more rigorous method of contrast, that of isotopic substitution. f can change close to the absorption edge characteristic of a given element due to anomalous dispersion. The contrast variation is thus the possibility of modifying the scattering power (b or f ) of a specific element to extract the partial functions associated to this element. The higher the contrast variation, the higher the reliability of the results.
30.4.1 Neutron Diffraction with Isotopic Substitution (NDIS) The isotopic substitution method was used for the first time by Enderby et al. to retrieve the three partial structure factors of a liquid Cu-Sn alloy [30.46]. This technique is based on the measurement of the neutron diffraction (ND) by two samples, prepared rigorously identically (thus assuming the same structure, i. e., same c˛ , cˇ and g˛ˇ .r/) but with different isotopic concentrations for one species, here called M. One can measure
two total structure factors from these two samples, where only the weight of the partial structure factors involving M can vary X S.Q/ D c˛ cˇ b˛ bˇ ŒS˛ˇ .Q/ 1 ˛;ˇ¤M
C
X
˛ ˛¤M
c˛ cM b˛ bM ŒS˛M .Q/ 1
C c2M b2M ŒSMM .Q/ 1 ; X S0 .Q/ D c˛ cˇ b˛ bˇ ŒS˛ˇ .Q/ 1 ˛;ˇ¤M
C
X
˛ ˛¤M
c˛ cM b˛ b0M ŒS˛M .Q/ 1
C c2M b02 M ŒSMM .Q/ 1 :
(30.23)
The difference technique consists of subtracting these two quantities and therefore eliminating all terms not involving M, since they are identical. The subtraction gives the first difference function, M .Q/, which is the sum of the partial structure factors centered on the element M. After Fourier transformation, the M-centered pair correlation function is obtained Z 2 M .Q/Q sin.Q/dQ GM˛ .r/ D X D2 c˛ cM b˛ bM b0M gM˛ .r/ ˛¤M
C c2M b2M b02 M gMM .r/ :
(30.24)
We have thus a chemically selective probe. The resulting function is analogous to the difference calculated by anomalous x-ray diffraction (Sect. 30.4.2) or to the Fourier transformation of the EXAFS (extended x-ray absorption fine structure) signal obtained by x-ray absorption spectroscopy. Additionally, it is possible to measure three samples and thus to obtain two first differences, M .Q/ and 0M .Q/, M .Q/ D 2
X
c˛ cM b˛ bM b0M ŒSM˛ .Q/ 1
˛¤M
C c2M b2M b02 M ŒSMM .Q/ 1 X c˛ cM b˛ b0M b00M ŒSM˛ .Q/ 1 0M .Q/ D 2 ˛¤M
002 C c2M b02 M bM ŒSMM .Q/ 1 : (30.25)
Neutron and X-Ray Diffraction of Glass
The weighting factors depend on the difference of the scattering lengths of M for the terms M–˛ (˛ ¤ M) while the term M–M depends on the difference of the square of the scattering lengths. Therefore, a judicious choice of the isotopic composition of the three glasses allows us to equalize the quantity b D bM b0M and 0 b D b0M b00M . This condition is easily obtained b0 D
b C b00 : 2
(30.26)
The subtraction of these two functions in (30.25) gives the second difference function, .M /.Q/, in which only the M–M correlation is present 2 1 .M /.Q/ D c2M bM b00M ŒSMM .Q/ 1 : 2 (30.27)
This function is of course related to a pair correlation function that directly describes the distribution of the element M within the structure Z 2 .M /.Q/Q sin.rQ/dQ GMM .r/ D 00 2 2 bM bM D cM gMM .r/ : (30.28) 2
1055
the scattering lengths are not always known precisely). Errors can therefore quickly accumulate and seriously contaminate the second difference, making its extraction delicate. The first difference has the advantage of reducing the problems associated with systematic errors: corrections of inelasticity and multiple scattering are largely eliminated in the subtraction. However, we must be aware that those terms reappear in the second difference. For a binary system, the treatment can be summarized in matrix form 2 3 3 2 2 2 S1 .Q/ c˛ b˛ c2M b2M 2c˛ cM b˛ bM 4S2 .Q/5 D 4c2˛ b2˛ c2M b02 2c˛ cM b˛ b0M 5 M 2 2 2 002 c˛ b˛ cM bM 2c˛ cM b˛ b00M S3 .Q/ 3 2 S˛˛ .Q/ 4S˛ˇ .Q/5 ; Sˇˇ .Q/ ŒS.Q/ D ŒAŒX.Q/ ; (30.29)
with S1 .Q/, S2 .Q/ and S3 .Q/ the three distinct measurements and changing the isotopic state of the element M. The formal solution consists of obtaining the partial functions by matrix inversion ŒX.Q/ D ŒA1 ŒS.Q/ :
(30.30)
A few elements (H, Li, Ti, Ni, Cr, Dy) have isotopes with both positive and negative scattering lengths, so that an isotopic mixture can be prepared with a null average scattering length. For a binary system having an element with a zero scattering length, the partial structure factor for the other element is directly measured in a single experiment. This null isotopic substitution technique has been used in several cases: for Dy and Ni in a Dy7 Ni3 metallic glass allowing the separation of all partial functions [30.48] or in liquid NiSe2 to isolate the Se–Se partial structure factor [30.49].
30.4.2 Anomalous X-Ray Diffraction (AXRD) X-ray diffraction (XRD) is widely used as a complementary technique to neutron diffraction (Sect. 30.2) and can also allow the determination of partial functions through a difference method. The structure factor determined by XRD is the sum of all the partial structure factors as shown in (30.7) but, contrary to b, the atomic form factors f depend upon Q and the incident energy, E. It is possible to change f .Q; E/ at the absorption edge energy, Eedge , of a specific element, leading to the technique of anomalous x-ray diffraction (AXRD) [30.50, 51].
Part C | 30.4
The first limit of NDIS is the small number of elements with isotopes that are suitable. X-rays (with anomalous diffraction) allow access to more elements but they cannot probe light ones such as hydrogen or lithium. These isotopes should be stable and must not be too absorbent. It is necessary that the difference between the scattering lengths of isotopes is large enough, typically b > 3 fm, to get a first and a second difference. A lower b may give access only to a first difference, especially for atomic concentrations less than 3 at:%. A recent study has demonstrated that the oxygen isotope substitution method can be carried out using O16 and O18 isotopes with a b of only 0:142 fm [30.47]. In their experiments, the authors found a 0:5% difference between the O–H and O–D bond lengths in water, supporting a competing quantum effects model. Many errors can seriously limit the accuracy (and even correctness) of the difference functions. This method, in contrast to anomalous x-ray diffraction, uses several specimens synthesized under the same conditions and it is assumed that they have the same structure. Each sample should be identical with the exception of the isotopic composition of M. This means that the concentration of each element must be perfectly known. The isotopic ratios of M must also be determined to be able to properly assess bM for each sample (although
30.4 Difference Methods
1056
Part C
Characterization of Glasses
The atomic form factor has a complex nature f .Q; E/ D f0 .Q/ C f 0 .E/ C if 00 .E/ ;
where f0 .Q/ is the usual energy-independent term that controls the Q-dependence. f 0 .E/ and f 00 .E/ are the real and imaginary parts corresponding to the anomalous term. Near an absorption edge, they change drastically giving different scattering. In an AXRD experiment, the scattering intensities for a single sample are measured at two different energies (Fig. 30.7), one close to the absorption edge Eedge (where the variation of f is the highest) and another one several hundred eV below Eedge (to avoid problems of absorption and fluorescence above Eedge ). The subtraction of the two measured intensities gives a first difference function X M .Q/ D DW˛M ŒS˛M .Q/ 1 ; (30.32) ˛ ˛¤M
with DW˛M .Q/ the differential weighting factor for the pair ˛–M c˛ cM D fM f˛ fM f˛ DW˛M D : (30.33) D.jhf ij2 /
Part C | 30.4
The difference function limits information to the environment around the specific element, M, but this limitation is not a handicap because it allows us to isolate a signal that is overlapped in the total distribution function by stronger correlations. Though AXRD can be obtained at three different energies, allowing the extraction of a second difference function, the contrast to retrieve a partial function M–M is low and this method has been little used. An example is the study of the distribution of Ba in silicate glasses [30.52]. Anomalous diffraction can also be obtained for certain energies using neutrons [30.53], but this is restricted to a limited number of elements (e. g., Sm). An advantage of AXRD is that a large number of elements are available, especially considering the possibility of using K or L absorption edges for lowand high-Z elements, respectively. The major limitation concerns the accessible Q-range that is limited by the choice of the absorption edge energy, Eedge D
f', f'' (arb. u.)
(30.31)
hc : edge
Given this wavelength edge , a maximum momentum
λ1
λ2
λ3
λ4 f'' f'
X-ray energy
Fig. 30.7 Variation of f 0 and f 00 near an absorption edge
energy Eedge (2 , 3 ). AXRD usually considers two experiments at the edge (2 or 3 ) and far below the edge (1 ) where f 0 and f 00 are almost constant, rather than above the edge (4 ) due to oscillations in f 00
transfer of Qmax D 4
sin max edge
can be obtained. In practice, a minimum Eedge of 10 eV is necessary to get a Qmax 10 Å1 . Therefore, AXRD is suited for elements of Z 26 (iron K-edge absorption). As an example, this technique has been applied to Gex Se1x glasses at energies close to the Ge and Se Kedge absorption. The partial functions show a gradual change with x but intermediate-range structure probed by prepeak position in the SSeSe .Q/ partial structure factor indicates that the stiffness transition at x D 0:20 can be observed [30.54].
30.4.3 Coupling X-Ray and Neutron Diffraction One possibility of determining the difference function is by combining neutron and x-ray data, which can be realized on the same sample [30.4]. A first-order difference function can be obtained, though the sources of errors are important due to different experimental setups and resolutions and due to the Q-dependence of the form factors.
Neutron and X-Ray Diffraction of Glass
30.5 Reverse Monte Carlo and Related Methods
1057
30.5 Reverse Monte Carlo and Related Methods Despite the development of experimental techniques, our representation of the glass structure remains partial. The use of simulations can help to better constrain structural models. Since correlation functions are one-dimensional, the construction of three-dimensional structural models can be used to describe the isotropic three-dimensional (3-D) arrangements characteristic of glass structures. Different modeling techniques associated with fitting of the experimental diffraction data have been developed, in particular reverse Monte Carlo (RMC) and empirical potential structure refinement (EPSR). These are analogs for disordered materials to the Rietveld refinement methods for crystalline powder patterns. An analogy can be pointed out between the g.r/ and the pair potential V.r/ (Fig. 30.8). The low-r part represents the repulsion of two neighboring atoms defining the distance of closest approach between atoms. This mimics the Coulombic repulsive term in V.r/ that hinders the particles from colliding. The peak position and width between two neighboring atoms in g.r/ mimics the form of the pair potential (energy position and depth of the potential well), i. e., the attractive term of the potential. Molecular dynamics and Monte Carlo techniques have been more widely used. Molecular dynamics (MD) allows for tracking of the movements of a set of atoms interacting within a given potential force field as a function of time and also of the temperature/pressure. Information on the liquid dynamic behavior at the glass transition temperature or on the glass structure can be obtained. This method has been applied to a large number of oxide glasses [30.55, 56]. However, for reasons of computational time, quenching rates are significantly higher than those obtained experimentally [30.57]. In addition, the determination of potential a) g(r)
correctly representing the atomic interactions is difficult. As an alternative to this approach, the Monte Carlo method uses potentials and randomly moves atoms to minimize the energy of the system [30.58]. These models can be compared to experimental data to test the validity of simulations over different length scales or to improve the pair potentials. The evaluation of the (dis)agreement between simulation and experiment should require a factor of goodness of fit, such as the one proposed by Wright [30.59] 2 !1=2 P
i Texp .ri / Tsim .ri / P 2 R ; (30.34) i Texp .ri / with Texp and Tsim the experimental and simulation total distribution functions respectively. If the agreement is not satisfactory, other techniques can be used for elucidating the detailed atomic structure based on fitting the experimental diffraction data (and possibly additional structural information). The reverse Monte Carlo (RMC) method involves iteratively moving a set of atoms randomly to reproduce the experimental data, without recourse to interatomic potentials [30.60, 61]. After each random move, the difference between experiment and model is calculated and, if the move improves the agreement, the atomic displacement is accepted, otherwise the structure change is allowed with some probability to avoid local minima. This procedure is repeated until a satisfactory refinement of the experimental data is achieved. Additional constraints such as the density, known coordination numbers, etc., can greatly improve the final RMC model. RMC allows the generation of atomistic models in quantitative agreement with diffraction data, and structural information extracted from these models can improve our understanding of the glass structure. b) V(r)
Part C | 30.5
Atomic repulsion
Minimum of the pair potential r (Å)
Fig. 30.8a,b Analogy between (a) the pair distribution function and (b) the interatomic pair potential (see text)
r (Å)
1058
Part C
Characterization of Glasses
The initial model is a key parameter in RMC modeling. Large atomic boxes are required, containing several thousands of atoms. Random configurations are usually chosen but, after RMC fitting, such structures yield models with important and unrealistic entropic energies. Indeed, RMC is a maximum entropy approach giving the most disordered structure that is in accord with the experimental data. MD simulations offer more realistic starting models if interatomic potentials are available [30.62]. Even with the best current MD simulations, differences in peak positions and intensities exist with the experimental data. We present in Fig. 30.9a a comparison between neutron data and MD simulations obtained on a MgSiO3 glass with pair interaction potentials [30.63], showing small discrepancies in the structure factors between experiments and MD. These models can therefore be adjusted by using the RMC method to obtain atomistic structures in agreement with the experimental data (Fig. 30.9b). Several software packages can be used to realize this RMC fitting process: RMC++ [30.64], RMC_POT [30.65] or RMCProfile [30.66], all available at http://www.isis2.isis.rl.ac.uk/rmc/. Some of these programs now incorporate an extensive use of interatomic potential functions. The coupling between experiments and RMC allows a better interpretation of the experimental data obtained on multicomponent glasses, since different partial structure factors or partial pair distribution can be extracted. Figure 30.10 shows the results obtained on a SrSiO3 glass by simultaneously refining ND (Fig. 30.10a) and AXRD at the Sr K-edge (Fig. 30.10b), allowing us a) F N (Q)
to obtain a first difference function centered on Sr (Fig. 30.10c). This example shows the interest of coupling the two diffraction techniques due to different weighting factors: ND is most sensitive to the pairs associated with the silicate network and XRD will be heavily weighted by the pairs associated with strontium. This study allowed understanding of the arrangements of the Sr cations in glasses and the similarities with crystals of equivalent composition [30.41]. The analysis of correlation functions reveals that strontium has a different environment and a different distribution within the structure if it acts as a modifier or charge compensator. A RMC development is meant to improve interatomic pair potentials used in classical MD simulations. Indeed, by calculating partial pair distributions before and after the RMC procedure, it is possible to determine the pairs that have varied the most and require an optimization of their potential parameters. Figure 30.11 compares the Ca-O pair before and after the RMC adjustment, which highlights the need for a lower Ca-O bond length to achieve a good agreement with the experimental data. This type of approach allowed the modification of the Ca-O pair potential [30.67]. Much of our existing knowledge about the atomic structure of metallic glasses is based on RMC and diffraction measurements (as well as MD simulations) [30.69–71]. Efficient atomic packing is a fundamental principle underlying the formation and stability in such systems. RMC structural models for binary nickel-based and zirconium-based metallic glasses have been obtained [30.70], enabling knowledge of the threedimensional positioning of the atoms. The short-range b) F N (Q)
0.1
0.1
Exp MD
Exp MD
Part C | 30.5
0.0
0.0
–0.1
–0.1
–0.2
–0.2
0
4
8
12
16
20
24 Q (Å–1)
0
4
8
12
16
20
24 Q (Å–1)
Fig. 30.9 (a) Comparison between neutron structure factors obtained experimentally (solid line) and by MD simulations for a MgSiO3 glass. (b) Comparison between neutron structure factors obtained experimentally (solid line) and after
running RMC starting with the MD simulations
Neutron and X-Ray Diffraction of Glass
a) Sneutron (Q) Sr–Sr S–O
30.5 Reverse Monte Carlo and Related Methods
gCa–O (r) 6
1059
MD MD + RMC
5
O–O
0.5
0
0
2
4
6
8
Si–Sr
4
Si–O Si–Si
3
S(Q)
2
10 Q (Å–1)
b) Sx-ray (Q)
0
3
Sr–Sr Sr–O O–O Si–Sr Si–O Si–Si
2 1 0
S(Q)
–1 –2 0
c) S
diff
2
4
6
8
10 Q (Å–1)
(Q)
4 Sr–Sr
2
Sr–O Si–Sr
0
∆(Q)
–2
2
4
6
8
10 Q (Å–1)
Fig. 30.10a–c Total structure factors obtained by (a) neutron diffraction, (b) x-ray diffraction and (c) structure factor of first difference determined by anomalous x-ray diffraction at the Sr K-edge for a SrSiO3 glass, compared with the weighted partial structure factors determined by RMC modeling
2
3
4
5
6
7
8 r (Å)
Fig. 30.11 The Ca-O pair distribution function calculated by molecular dynamics (solid line) and adjusted by RMC (dashed line) for a 61CaO-39Al2 O3 glass. There is a displacement of the first peak at 2:44 Å in the MD model to 2:35 Å after RMC. The figure is adapted from [30.68]
order (SRO) is characterized by solute-centered clusters (various polyhedra of around 9 to 13 atoms), each of which is made up of a solute atom surrounded by a majority of solvent atoms. The intermediate-range order (IRO) is constructed by packing of these polyhedral clusters with appreciable icosahedral medium-range order (Fig. 30.12), regardless of the short-range order within the clusters. Icosahedral order has a fivefold rotational symmetry that is incompatible with translational symmetry and favors glass-forming ability. Another method based on the refinement of diffraction data is empirical potential structural refinement (EPSR) modeling [30.72]. This tool uses realistic intraand intermolecular potentials that constrain the atomic positions in the simulation box. An empirical potential is introduced as a perturbation to the arbitrary potential functions, generated from the difference between measured and calculated structure factors or radial distribution functions. A Monte Carlo refinement of this empirical potential is successively obtained as the atoms or molecules are moved, enabling the best possible agreement with the experimental data. As for RMC, a 3-D atomic model is obtained, consistent with the measured diffraction data. This method has been particularly developed for molecular systems, such as water (Fig. 30.13).
Part C | 30.5
–4 0
1
1060
Part C
Characterization of Glasses
a) Fraction Ni81B19 Ni80P20 Zr84Pt16
0.25
0.2
0.15
0.1
0.05
0
555
433
b)
544
444
〈0,3,6,0〉
666
c)
322
422
655
532
311
d)
〈0,4,4,3〉
421 533 Cluster neighbor pairs 〈0,2,8,1〉
VS 〈0,3,6,0〉
〈0,3,6,0〉
FS
〈0,2,8,0〉
〈0,3,6,3〉
〈0,0,12,0〉 〈0,2,8,1〉
FS
ES
ES ES FS
〈0,3,6,0〉 FS
〈0,3,6,0〉
〈0,2,8,0〉
FS 〈0,2,8,0〉
〈0,2,8,2> FS
〈0,2,8,2〉
Fig. 30.12 (a) Cluster neighbor analysis showing that the local clusters (solute-centered polyhedra) exhibit icosahedral order. (b–d) Typical packing of clusters showing fivefold symmetry detailed for (b) Ni81 B19 , (c) Ni80 P20 and (d) Zr84 Pt16
metallic glasses, respectively. FS, ES and VS stand for face-sharing, edge-sharing and vertex-sharing, respectively. Reprinted from [30.70]
Part C | 30.5
Neutron and X-Ray Diffraction of Glass
30.6 Case Studies of Glass Investigation by Neutron and X-Ray Diffraction
a) g(r)
1061
b) HDA LDA
9 8 7 6
OO
5 4
OH 3 2 HH
1 0
0
1
2
3
4
5
6
7
8 r (Å)
15 Å
15 Å
15 Å
Fig. 30.13 (a) Intermolecular PPDFs of high-density amorphous (HDA) and low-density amorphous (LDA) water (Sect. 30.7.4, Amorphous Forms of H2 O) at 80 K. (b) Three-dimensional arrangement of the oxygen atoms around a water molecule (spatial distribution function) showing the first, second and third O neighbors (from left to right) for crystalline ice at 220 K, LDA at 80 K, liquid water at 298 K [30.24], and HDA at 80 K. Reprinted with permission from [30.73]. © 2002 by the American Physical Society
30.6 Case Studies of Glass Investigation by Neutron and X-Ray Diffraction 30.6.1 The Low-Q Features
Part C | 30.6
In the structure factors, it is often useful to consider the domain at low Q-values. For simple glasses, three peaks, Q1 , Q2 and Q3 , are characteristic features that scale roughly with the interatomic distance d (Fig. 30.14): Q1 d ' 23, Q2 d ' 4:64:9, Q3 d ' 7:78:9 [30.74]. At these peak positions correspond ordering at different length scales: nearest-neighbor separation for Q3 , size of the local network-forming motifs for Q2 and arrangements of these motifs on an intermediate range for Q1 . Note that some low-Q features are not present for some classes of glasses (e. g., Q1 and Q2 are absent in metallic glasses) or are not observable for some diffraction methods (e. g., Q2 is present in neutron diffraction data for SiO2 but absent in the x-ray diffraction data).
The low-Q region is usually dominated by the peak Q1 , referred to as the first sharp diffraction peak (FSDP), but several peaks or shoulders can coexist in chemically complex glasses. The features at low Qvalues have attracted considerable attention as they are a characteristic of topological organization at the IRO (Fig. 30.15). If the low-Q feature at position Q1 is isolated and Fourier transformed, it gives in r-space a decaying sine function with periodicity 2 =Q1 . The correlation length in real space of the decaying oscillations corresponds to the full half width maximum (FHWM) of the Q1 peak, 2 =FHWM, giving typical values of 1525 Å [30.75]. This feature is seen in a wide range of disordered systems, persisting even into the liquid state. Its intensity is highly sensitive to disorder (e. g., in neutron bombarded SiO2 , the peak becomes weaker) and ex-
1062
Part C
Characterization of Glasses
Q[S(Q) – 1]
Structure factor S(Q) 6 Q1 Q 2 Q 3
1.5 5.4 Å
1
5
7.8 Å
Pd42.5Ni7.5Cu 30P20
8.9 Å
0.5 4 GeSe2
30 Å
0 –0.5
3
11.1 Å
0
2
4
6
8
10 Q (Å–1)
1
Fig. 30.15 Interference function, QŒS.Q/ 1 of a K2 TiSi2 O7 glass obtained by Fourier transformation of D.r/ truncated at different values of r (dashed lines), chosen as even nodes of D.r/. The experimental interference function (solid lines) is shown for comparison. A value of r D 8:9 Å is necessary to fully reproduce the peaks, particularly the one at 1:12 Å1
0
controversial [30.97–100]. Several general explanations have been proposed for the universal origin of this peak.
SiO2 2
Se
0
5
10
15
20 25 30 35 Scaled scattering vector Qd
Fig. 30.14 Typical structure factors obtained by neutron
diffraction (solid curves) or x-ray diffraction (broken curves) for various glasses as a function of the scaled scattering vector Qd. The figure is adapted from [30.74]
Part C | 30.6
hibits anomalous behavior with pressure [30.76–79], temperature [30.80–83], pressure/temperature [30.84– 86] and composition [30.87–92]. For instance, the peak intensity decreases with P and increases with T unlike the normal behavior of the other peaks. This anomalous T-dependence suggests a similar origin as the anomalous low-frequency, low-T vibrational properties. Relationships with system dynamics or fragility have been suggested [30.93]. Whether included or not in the Fourier transformation, the low-Q feature is not related to a well-localized real-space feature in the correlation function, indicating that it corresponds to subtle organization at intermediate range. The difference function indicates that the main contribution usually comes from cation–cation correlation in the materials [30.50, 80, 94, 95] though other authors suggest that the low-Q features appear primarily from density fluctuations and not concentration fluctuations [30.96]. Although essential to the understanding of IRO, the origin of the peaks present in this region remains
Quasicrystalline Organization, Quasi-Bragg Peak or Quasiperiodic Arrangement The position of these low-Q features in glasses, melts and simple liquids often appears at similar scattering vectors as strong Bragg peaks in compositionally equivalent crystals, suggesting a general correspondence. It was proposed that these peaks result from a broadening of the Bragg reflections corresponding to periodic anisotropic spacing of limited coherence length in real space [30.99, 101–103], or as structures in layers existing in chalcogenide glasses [30.77, 81, 82]. Liquids can also present these structures with intensities sometimes greater than in glasses. As it seems improbable that the liquid is more organized than the glass, the stronger intensity seems an indication that the layer models do not work [30.98]. However, this intensity increase is not inevitably related with a more ordered structure [30.101–103]. It was suggested that, with the temperature increase, a relaxation of the constraints of the arrangements provokes an increase of the intralayer correlations [30.81, 82]. It was also considered that in glasses such as SiO2 , layer structure is improbable. Gaskell and Wallis [30.100] used various models developed for silica glass to show that they contain planar corrugated sheet structures associated with reasonably well-defined interplanar spacings
Neutron and X-Ray Diffraction of Glass
30.6 Case Studies of Glass Investigation by Neutron and X-Ray Diffraction
similar to f111g planes of ß-cristobalite. They interpret these quasi-Bragg planes as the origin of the low-Q peak in SiO2 glass. Since, in most glasses, the low-Q peak position corresponds closely to the position of a strong diffraction peak (often the lowest Q feature) of a corresponding crystalline phase, these similarities suggest a general explanation: the remaining quasi-Bragg planes (distorted, imperfect and not necessarily plane) in the glasses are similar to those present in the related crystalline phases (Fig. 30.16). This model does not imply a layer glass structure and has connections with the Elliott’s model of interferences between the network and voids [30.104]. On the other hand, this model received the support of modeling [30.105] and is connected with liquid models [30.106, 107]. Although not indicating a microcrystallite model, this interpretation emphasizes the important similarities between glasses and crystals in the organization at intermediate distances, which is also seen in the analysis of the first difference functions (Sects. 30.6.4 and 30.6.5). Correlations Between Clusters and Voids Price and Moss [30.97] have suggested an explanation based on the packing of the basic structural or molecular units, which are observed in some tetrahedral molecular compounds [30.109]. One problem is that these clusters are ill defined and the structure between these clusters is not specified. For liquids like CCl4 , the a)
b)
1063
diffracted intensity is a sum of inter- and intramolecular terms. The low-Q peak appears as a combination of a strongly Q-dependent intermolecular term (decreasing with Q) and the wing of the first normal diffraction peak (increasing with Q). Dixmier and Blétry [30.110, 111] emphasized the role of holes for tetravalent vitreous structures, which has been used by Elliott for a broader interpretation [30.98, 112]. Elliott considers that these low-Q features derive from the chemical organization at short distance of the interstitial voids around cation-centered clusters, which can be for example the SiO4 tetrahedra in silicates (Fig. 30.17). It was shown that the lowest Q and most intense peak originates from a rapidly decaying intercluster structure factor, i. e., simply an artifact resulting from the addition of a rapidly decreasing intramolecular form factor and the increasing intercluster structure factor at small Q [30.98]. It can be noted that, in the correlation functions, low atomic occupation zones around 5 Å are present [30.113]. The behavior in pressure, temperature and composition can be qualitatively explained by this model. For instance, the empty space within the structure reduces in volume as pressure is applied [30.112, 114]. Correlations Between Q1 and the Reduced Volume Simplifying the Debye formula in (30.13) for a diatomic gas composed of two atoms of scattering c) Scattered intensity (arb. u.) (111)
(110) Li
(111)
(020) (111)
KLi
(100) (140)
b a b
Na
c c
0 a
1
2
3 Q (Å–1)
Fig. 30.16 (a) The structure of c-Li2 Si2 O5 showing planes parallel to (111) in c-Li2 Si2 O5 , which are associated with the strong peak at 1:71:8 Å1 in (c), and can be associated with a similar feature in the corresponding glasses. (b) Projection of the structure along [100] showing corrugated planes of Si2 O5 units. Planes parallel to (020) (horizontal, black) and (110) (inclined, green) are shown and are associated with the weak features at 1 Å1 in (c). (c) Experimental neutron diffraction data (dashed curves) for disilicate glasses containing Li, K=Li and Na compared with simulated neutron diffraction data calculated from the crystal structures (solid curves). The disorder is simulated by considering crystallites 2 nm in size (meaning not a microcrystallite model). Adapted after [30.108]
Part C | 30.6
(120)
1064
Part C
Characterization of Glasses
Fig. 30.17a–c Structure factors calculated for different
a) Structure factor S(Q)
models and normalized in Q to the position of the principal peak Q3 determined by the nearest-neighbor distance. (a) A dense random packing structure (typical to metallic glasses), (b) a tetravalent structure (e. g., a-Si), and (c) a 4 W 2 structure (e. g., a-GeSe2 ). Q1 and Q01 correspond to FSDP and Q2 to a second sharp diffraction peak with the same origin but different length scales. Brown circles in (b,c) are four-coordinated atoms, brown squares are two-coordinated atoms, and beige circles are voids. Adapted after [30.110, 115] J
Q3 3
2
1
0
0
1
2
3 Q/Q3
b) Structure factor S(Q) 3
Q3 2 Q'1 1
0
0
1
2
3 Q/Q3
c) Structure factor S(Q) 3
2
For Q D 0, the intensity is equal to 4b2 and after several oscillations tends to 2b2 , i. e., the sum of the intensities diffracted by the two atoms of the molecule (Fig. 30.18b). The function presents a succession of maxima and the first and highest diffraction maximum is obtained by setting the derivative of (30.35) with respect to .Qd/ to zero, which gives the Ehrenfest relation [30.116, 117] 2 4 sin m QD D 1:23 : (30.36) d The position of this peak is associated with the principal diffraction peak .Q3 /. As a consequence, the position Q3 is inversely proportional to the mean atomic spacing and the third power of Q3 scales inversely with the volume. In metallic glasses, it was used to determine the thermal expansion coefficient by following the variation of Q3 with temperature [30.118]. A power law relationship is proposed between the reverse of the principal peak position, 2 =Q3 , and the glass volume Va D 0 =.NA M/ for various metallic glasses [30.119]. The following relationship corresponds to the plot in Fig. 30.19 Q3 Va0:433 D 9:3 ˙ 0:2 :
Q3
(30.37)
Q2 Q1
1
Part C | 30.6
0
0
1
2
3 Q/Q3
The power of 0:433 is significantly different to 1=3, which would be expected for crystals, and this has been interpreted as indicative of a fractal network with a fractal dimensionality of .0:433/1 D 2:31 [30.119]. This correlation is convenient to understand the relative volume (density) change with pressure (Sect. 30.7.4, Polyamorphism in Metallic Glasses).
30.6.2 The Polymeric Network power b, at a distance d from each other (Fig. 30.18a), we obtain [30.116] S.Q/ /
X ˛ˇ
sin Qr˛ˇ sin Qd 2 b˛ bˇ D 2b 1 C : Qr˛ˇ Qd (30.35)
Neutron diffraction is one of the most widely used methods to study glass structures. In particular, the quantitative structural information on network formers and on the polymeric network can be obtained through the total correlation functions, in which the pairs associated with the glassy matrix are dominant. Pure silica
Neutron and X-Ray Diffraction of Glass
a)
30.6 Case Studies of Glass Investigation by Neutron and X-Ray Diffraction
Fig. 30.18 (a) Representation of a gas
b) >VLQ Qd Qd @ d
composed of a diatomic molecule with an interatomic distance d. (b) The scattering power per molecule of a diatomic gas showing successive maxima
Qd
1065
Qd
Fig. 30.19 Power law scaling of
Q3 (Å–1) 3.0 Fit:
Q3 Va0.433
= 9.3
2.9 2.8
the peak Q3 as a function of the atomic volume Va . Both axes are in a logarithmic scale. The symbols represent the experimental points for various metallic glasses. Adapted after [30.119]
2.7 2.6 2.5 2.4 2.3 2.2 2.1 13
15
20
25
35 Va (Å 3)
.BO4 / [30.39]. The BO3 =BO4 ratio can be tracked according to the composition and excellent agreement is obtained with RMC experiments. Various studies have been conducted on borate and phosphate ionic glasses often combining ND, XRD and RMC modeling. It has been shown that IRO of the borate network decreases with an increase in doping salt concentration, and that the borate network forms a chain structure with AgI salt ions cross-linking these chains, while (Li,Na)(Cl,Br) salt ions enter the structural free volume and dilate the borate network [30.40]. NDIS was also used to extract the different PPDFs in the glassy network. In particular, in a GeSe2 glass [30.94, 123], all pairs have been determined. The basic structural units are GeSe4 tetrahedra arranged with both edge and corner sharing. The chemical order existing in oxide glasses is broken as homonuclear (ho-
Part C | 30.6
and borate glasses have been widely studied with this method [30.42, 120, 121]. In phosphate glasses, it was possible to separate the contributions between the bridging oxygen anions and nonbridging oxygen anions around a phosphorus atom [30.25]. Such data provide constraints on the polymerization of the chains of PO4 tetrahedra according to modifier oxide contents. Coupling ND and XRD with RMC allowed the building of structural models. These models showed for example that two alkalis present in glasses were distributed homogeneously [30.37]. The addition of salts in these glasses (for instance AgI [30.122]) leads to the expansion of the network, which promotes the formation of paths for ionic diffusion. In borate glasses, large Q-values enable discrimination of two distances corresponding to threefold coordinated boron .BO3 / and fourfold coordinated boron
30
1066
Part C
Characterization of Glasses
mopolar) bonds have been evidenced by NDIS. Ion conductive chalcogenide glasses have been also extensively studied by this method to determine the interaction between the network and the added salts [30.124–127].
tion of the Ti site as a square-based pyramid. Contrary to EXAFS, which shows a single distribution [30.130], the NDIS method is able to solve the two Ti–O distances, thanks to the wide available Q-range that gives a better real-space resolution. Some examples of first difference functions obtained by NDIS for cations in silicate and aluminosilicate glasses are presented in Fig. 30.21 [30.131]. Important similarities exist in these functions, regardless of the cation concentration (e. g., 5:9 at:% for Ni in Ca2 NiSi3 O9 [30.132] versus 14:3 at:% for Li in LiAlSiO4 [30.133]) or the glassy matrix (e. g., Li in a silicate, Li2 Si2 O5 [30.134] or an aluminosilicate, LiAlSiO4 ). Structural oscillations are discernible up to 10 Å in GM˛ .r/ functions, which indicates a cationic arrangement very well defined at mediumrange distances. All GM˛ .r/ functions have a first sharp peak that results from the first shell of oxygen neighbors, indicating very well-defined cationic sites in glasses. These sites present cation–oxygen distances and coordination numbers that may be similar to those observed in compositionally equivalent crystals, often with a low coordination number and a small radial disorder (Li at the center of a tetrahedral sites, Ti at the center of a pyramidal site). However, cations with higher field
30.6.3 Cation Sites in Glasses AXRD and NDIS are chemically selective methods, similar to EXAFS, but they have the advantage of being able to probe the structure with better accuracy [30.128] and larger distances (typically 10 Å). The use of isotopically substituted materials gives similar information to AXRD but for different elements, with better experimental counting statistics and the ability to directly extract the cation–cation distances and coordination numbers. The interest of the first difference function (Sect. 30.4.1) can be understood in Fig. 30.20, which shows the correlation functions determined in a complete study on a K2 TiSi2 O7 glass with isotopic substitution of Ti [30.129]. In the first difference function, GTi˛ .r/, we observe that Si–O and O–O correlations, having important weights, are eliminated. It appears then that the first layer of oxygen neighbors surrounding Ti can be deconvoluted into two distinct Ti–O distances at 1:68 and 1:96 Å, which allows the unambiguous determinaD(r) 1.5
1
K 246TiSi 2O7
0.5
K 248TiSi 2O7 0
Part C | 30.6
–0.5 1.68Å
4O 1.96Å 1O 1.68Å
–1
Ti–Si
Fig. 30.20 Differential correlation
1.96Å
Ti–K Ti–Ti Ti–O2
Ti– 48Ti
46
–1.5 0
2
4
6
8
10 r (Å)
functions obtained for a K2 TiSi2 O7 glass containing 46 Ti isotopes (top curve) and 48 Ti isotopes (middle curve) compared with the first difference functions (46 Ti–48 Ti, lower curve) for Ti. Insert shows the TiO5 site. Adapted after [30.129]
Neutron and X-Ray Diffraction of Glass
30.6 Case Studies of Glass Investigation by Neutron and X-Ray Diffraction
also exists for Ca and Ni: the GM˛ .r/ function presents a broad contribution at large r-values, though an exact determination is difficult.
GMα(r)
30.6.4 Cationic Arrangement at Medium Range Distances
Ti 1 Ni
Ca
Li
0 0
1067
2
4
6
8
10 r (Å)
Fig. 30.21 Comparison of first difference functions,
GM˛ .r/ for Ti in K2 TiSi2 O7 , Ni and Ca in Ca2 NiSi3 O9 (solid curve) and Ca in CaSiO3 (dotted curve), Li in LiAlSiO4 (from top to bottom). Adapted after [30.131]
30.6.5 Nonhomogeneous Distribution of Cations Second-order difference functions (Sect. 30.4.1) have been obtained for Ti [30.129], Ni [30.132], Ca [30.138] and Li [30.134] in silicate glasses [30.139]. These functions reflect the distribution of cations in the glassy network and reveal significant similarities. Figure 30.22 shows the well-defined M–M correlation functions. The presence of a first short cation–cation distance indicates a nonhomogeneous distribution of these elements in the glass structure as a homogeneous distribution consisting of a compact arrangement of spheres would give a first cation–cation distance at 6 Å (RMM D .6 0:63= 0 cM /1=3 ). In CaSiO3 glass, it was concluded that nearest-neighbor Ca–Ca distances can be associated with edge-sharing sixfold coordinated Ca–O polyhedra [30.138]. In Ca2 NiSi3 O9 glass, edge-sharing linkages are proposed between trigonal bipyramids for NiO5 sites [30.132]. On the other hand, the nearest-neighbor Ti–Ti distance indicates cornersharing polyhedra, charge compensated by adjacent alkalis in K2 TiSi2 O7 glass [30.129]. The region extending up to 910 Å indicates a significant IRO. For all studied cations, if R1 is the first p M–M distance, the second p one appears close to 3R1 and the third close to 7R1 . In addition, the
Part C | 30.6
strength have lower coordination numbers in glasses compared to crystals. This is the case of Ca2C (coordination number 8 in the CaNiSi2 O6 crystal and coordination number 6 in the Ca2 NiSi3 O9 glass) and Ni2C (coordination number 6 in the CaNiSi2 O6 crystal and coordination number 5 in the Ca2 NiSi3 O9 glass). The effects of radial disorder can also be quantified by NDIS. The main cation–oxygen correlations show standard deviations that are similar for all glasses, 0:1 Å. Very well resolved site geometries are found by using extended Q-ranges. Good contrast of Ti isotopes allowed the deconvolution of two Ti–O distances separated by 0:3 Å in K2 TiSi2 O7 glass [30.129]. Site distortions were also assessed in the case of Li [30.133– 135]. Lithium is always fourfold coordinated in the oxide glasses, but differences are observed. The local environment around Li in aluminosilicate glasses is strongly distorted (3O at 2:02 Å and 1O at 2:32 Å) with a stronger distortion and a larger average distance than for silicates. RMC modeling showed that the LiO4 tetrahedra share edges with the AlO4 tetrahedra in the LiAlSiO4 glass, which involves short distances (Si,Al)–Li ( 2:62:7 Å) and long Li–O distances. These distances and the Li site distortion in LiAlSiO4 are related to the role of Li as a charge compensator in aluminosilicates, unlike a network modifying role in silicates where LiO4 and SiO4 tetrahedra share corners. These data replicate those observed in compositionally close crystals and show that the local geometry of the Li site reflects important differences in the structural organization at longer distances. Asymmetric distribution
Between 3 and 5 Å, all GM˛ .r/ functions present several contributions related to second and further neighbors (Fig. 30.21). These peaks are close to those observed in compositionally equivalent crystals, which indicate that the glass structure retains some structural features of crystals. However, the presence of contributions beyond 5 Å in crystals is contrary to a model of microcrystallites [30.136]. Contrary to crystals, there is a structural deficit around 56 Å for all the studied cations. Difference functions obtained by AXRD exhibit the same lack of correlations (e. g., for Sr in silicate glasses [30.137]). Beyond 5 Å, large contributions centered at 7 and 9 Å are observed and are not comparable to the distances in crystals. The distance at 5 Å can therefore be regarded as the size limit of the structural organizations that are similar in crystals and glasses. However, a large order persists beyond 5 Å as can be found by calculating a second difference by NDIS or by MD calculations.
1068
Part C
Characterization of Glasses
Fig. 30.22 Cation-cation distribu-
GMM(r) R1
tion, GMM .r/, in glasses obtained by Fourier transformation of the second difference functions for Ti in K2 TiSi2 O7 , Ni and Ca in Ca2 NiSi3 O9 Ca, and Li in LiAlSiO4 (from top to bottom). Adapted after [30.139]
3R1 2R1
Ti 7R1
0.04 Ni
2R1
7R1
Ca
0
Li
–0.04
0
2
4
6
p distance at 2R1 , which is characteristic of a tridimensional arrangement of polyhedra, is absent. This information reflects a cationic structural organization that has a strong bidimensional character in these glasses [30.138] and deviates from the completely random cationic arrangement as historically suggested by Warren and Pincus [30.140]. Diffraction studies reveal a more ordered glass structure and the second difference function is the more convincing experimental evidence for clustering and percolation domains in silicate glass structure [30.141], consistent with the modified random network model proposed by Greaves [30.142].
8
10 r (Å)
Similar M–M distances were observed by XRD in borate or silicate glasses containing heavy elements, since the M–M pair dominates the experimental structure factors. These studies show correlations near 4:7 and 10 Å due to cation–cation pairs in silicate and borate glasses [30.143–148] on a very wide range of compositions (365 mol% nonnetwork former oxides). A study by AXRD at the Sr K-edge in silicate glasses has also shown Sr–Sr distances at 7 Å [30.137]. These heterogeneous structures are strengthened by numerical calculation such as MD [30.149] or RMC [30.150, 151], which are able to reproduce cation-rich regions.
30.7 In Situ High Temperature/High Pressure Diffraction Part C | 30.7
Direct studies of the structure of glasses at high temperature and high pressure address important fundamental questions and are of great interest in different domains of research such as material science or geophysics. Structural changes induced by temperature can govern important properties or phenomena: the glass transition occurs in supercooled liquids and experimental and simulation studies are now consistent with subtle structural reorganization at intermediate range; nucleation/crystallization are events occurring in the supercooled state and in situ experiments can be useful to probe transient phases; and glasses are studied as analogs for melts or liquids in industrial furnaces or for natural magmas, although significant structural differ-
ences can exist between glass and melt and a detailed understanding of such differences is important to understand the behavior and properties at high temperature. Since the first extensive diffraction studies of liquids by Waseda [30.152, 153], important experimental developments have been obtained allowing investigation of very high temperature and increasing the accuracy of diffraction data. The structure of liquid and amorphous materials at high pressure is crucial for geophysicists interested in silicate melts relevant to earth and planetary sciences, but also to material scientists wishing to obtain new materials with novel properties. In situ investigation is mandatory because pressure-induced mod-
Neutron and X-Ray Diffraction of Glass
ifications, such as coordination changes, are usually reversible.
30.7.1 High-Temperature Experimental Techniques In an ND experiment, vanadium can be used as a resistive element since this material has mainly an incoherent scattering and gives negligible Bragg peaks. Using several sheets of vanadium as shielding, temperatures up to 1200 ı C can be reached, just before softening of vanadium (Fig. 30.23a). The advantage of such a furnace is that large sample volume can be used and measurements are carried out in high vacuum, minimizing statistical noise. Samples are contained in silica tube containers (e. g., for chalcogenide glasses) or in vanadium cells (e. g., for oxide glasses). Some commercial heating devices are also available in synchrotrons, providing controlled atmospheres. However, these furnaces give access to a limited range of temperature (< 1500 ı C at best), which prevents the investigation of refractory materials or liquids melting at very high temperatures. In large facilities (neutron sources or synchrotrons), levitation techniques became widely available during the past twenty years. Various experimental setups to levitate a sample have been developed and were reviewed by Hennet et al. [30.154]: 1. Electromagnetic levitation (EML) [30.155] 2. Electrostatic levitation [30.156] a)
b)
30.7 In Situ High Temperature/High Pressure Diffraction
1069
3. Acoustic levitation [30.157] 4. Gas flow such as gas film levitation [30.158] 5. Aerodynamic levitation [30.159, 160]. They are containerless methods useful for avoiding heterogeneous nucleation from the cell walls or contamination between the sample and the container. The technique is also useful to extend the glass domain and explore the structure of glass compositions that are not quenchable in crucibles. The aerodynamic levitation (CNL, conical nozzle levitation) is the most popular tool [30.161] and consists of levitation by a gas jet (usually argon) of a glass bead placed on a levitator composed of a water-cooled conical nozzle (Fig. 30.23b). Using CO2 or YAG laser heating, temperatures up to 3000 ı C can be reached. Since nucleation is hindered due to the lack of interfaces with a container, supercooled liquids can be investigated a few hundred degrees below the melting point. The sample bead is small (few mm in diameter) and only partially interacts with the incoming radiation, so a very low experimental and stable background is required. Using neutron sources, measurement times are typically several hours, requiring a good stability of the bead in the gas jet. Using synchrotrons, time-resolved experiments are possible since diffractograms are acquired in a few ms with good counting statistics. A major drawback is the volatilization that can occur and experimenters must be attentive that the evaporation rate remains extremely low for the duration of the experiment.
Mirror Laser 1
Pyrometer Bell jar Glass bead Nozzle (V or Al)
Camera
Part C | 30.7
Cell Furnace
Gas Mirror
Laser 2
Fig. 30.23 (a) Picture of a vanadium furnace positioned inside the bell jar of the 7C2 diffractometer at LLB (Saclay, France). (b) Schematic representation of an aerodynamic levitation setup used for diffraction experiments on a neutron source or a synchrotron. The glass sphere is levitated by a gas jet and heated using two lasers (from top and bottom to reduce thermal gradient)
1070
Part C
Characterization of Glasses
30.7.2 Case Studies of TemperatureInduced Modifications Temperature Evolution of the Low-Q Features The FSDP (Sect. 30.6.1) in silica decreases in amplitude up to 1036 ı C as expected [30.80] and as observed for the other peaks, with a normal Debye–Waller behavior. This is in contrast to the anomalous temperature dependence of the FSDP in oxide and chalcogenide glasses [30.98]. This normal behavior for silica is associated with the nearly zero thermal expansion coefficient and the dominant effect of thermal vibrations. The position of the FSDP sometimes shifts to lower Q-values with increasing temperature as shown in Fig. 30.24a for a 15Na2 O-10CaO-75SiO2 glass (window glass composition) where the Q1 peak position is shifted from 1:72 Å1 in the glass to 1:62 Å1 in the liquid at 1000 ı C [30.162]. But this does not necessarily imply an important change at intermediate range. Indeed, thermal expansion (decrease of the density) has a similar effect, since the third power of Q1 scales inversely with the volume (Sect. 30.6.1, Correlations Between Q1 and the Reduced Volume). The FSDP increases in intensity in glasses (e. g., As2 Se3 up to the glass transition temperature, Tg [30.82]) and even persists in the liquid state. This is a) S(Q)
remarkably evident in alkali silicate melts. In K2 Si2 O5 , the first peak at Q1 D 0:97 Å1 in the neutron structure factor presents drastic changes when temperature exceeds Tg (Fig. 30.24b), with a marked increase in intensity [30.83]. RMC modeling indicates that this peak has important contributions from the partial functions involving oxygens (mainly BO–BO and Si–BO correlations while BO–NBO and Si–NBO have antiphase contributions, where BO and NBO are bridging and nonbridging oxygen anions respectively). This peak is related to the structural organization of the silicate network supporting the concept of cation channels. Evolution of Short-Range Order with Temperature The pioneering diffraction works using levitation focused on investigation of refractory materials such as Al2 O3 [30.160, 163]. They revealed a decrease of the Al coordination number on melting. However, the Q-range and counting statistics were very limited and the neutron/x-ray diffraction were recently revisited [30.29], taking advantage of the experimental advances and the development of new detectors. In this new study, the authors also combined their diffraction data with RMC modeling and they evidenced that AlO4 and AlO5 units dominate the melt, in an approximate b) S(Q) 1.2
1.0 1.0
0.8 0.9 0.6
Part C | 30.7
0.4 300 K 823 K 1273 K
0.8
0
1
2
3
4 Q (Å–1)
300 K 730 K 830 K 1350 K
0.2 0
1
2
3
4 Q (Å–1)
Fig. 30.24 (a) Evolution of the low-Q features in the neutron structure factors for a 15Na2 O-10CaO-75SiO2 glass/melt showing the shift of the first peak towards lower Q-values. The figure is adapted from [30.162]. (b) Evolution of the low-Q features in the neutron structure factors for a K2 Si2 O5 glass/melt showing the dramatic increase in the intensity of the first peak. Data were obtained using a Joule vanadium furnace on the 7C2 diffractometer at LLB (Saclay, France). Adapted after [30.83]
Neutron and X-Ray Diffraction of Glass
ratio of 2 W 1. Al–O–Al connections are dominated by corner sharing but a significant amount of edge sharing exits ( 16%). The structure of .CaO/x .Al2 O3 /1x glasses and liquids have been widely studied by CNL [30.164–167]. Coupled with MD simulations [30.164, 165], ND and XRD measurements indicate that Al is predominantly in tetrahedral positions, with 20% of fivefold coordinated Al at x D 0:33 and fewer AlO5 units as the CaO content decreases. Ca is predominantly sixfold coordinated in distorted octahedra but with a broad range of coordination environments (Fig. 30.25). Another study agrees with AlO4 tetrahedra but found a lower coordination Ca–O number of 5 in the melt [30.166]. This discrepancy results from different fitting criteria (cutoff distance for instance) and the difficulty in separating the Ca–O pair from the overlap of other contributions. It is also found that the structure for the eutectic liquid (64 mol% CaO) does not change significantly with temperature between 1600 and 1970 ı C. HE-XRD has been used to investigate the liquid– liquid (L–L) transition between two forms of Y2 O3 Al2 O3 glass with low density (LD) and high density (HD) [30.168]. The authors have associated structural changes with the onset of the L–L transformation that affects the Al and Y environment. The low- and highdensity configurations calculated by MD simulations are shown in Fig. 30.26 and these models exhibit changes that match the difference in the experimental diffraction patterns. The main change in structure on liquid–liquid transition is not an Al coordination change Position (Å) 1.9
1071
but rather an increase in IRO seen as changes in the coordination polyhedra of Y3C and in connectivity and arrangement of Al and Y polyhedra [30.169, 170]. AXRD has been rarely used to investigate glass/melt modifications. However, this technique has been combined with CNL to investigate the liquid structure of Y2 O3 [30.172]. The Y–O coordination of 67 and the Y–Y coordination of 12 imply the preservation of the close packing existing in the high-temperature polymorph. An unusually sharp main diffraction peak suggests a high degree of chemical order. In alkali borate glasses, boron atoms can be present in triangular or tetrahedral sites. Using high-resolution neutron diffraction, a detailed analysis of the first peak in real space reveals two different B–O nearestneighbor distances at 1:37 and 1:47 Å, corresponding to BO3 and BO4 units, respectively [30.39]. In pure B2 O3 melt, the temperature-induced structural evolution has been described, using in situ neutron/x-ray diffraction, as a gradual opening of boroxol rings above Tg [30.121, 173]. The structural changes of the local boron environment have also been quantified by ND in alkali borate glasses (Fig. 30.27), showing a partial conversion of BO4 units present in the glass to BO3 units in the melt [30.171, 174]. This conversion implies the formation of nonbridging oxygens (NBOs) and the disappearance of bridging oxygens (BOs). Using NDIS (7 Li=6 Li isotopic substitution), the environment around the alkali atoms was also shown to vary (Fig. 30.28). The first Li–O distance in the DLi˛ .r/ shortens by
Ca–O coordination number 5.4 Tg Glass 5.2
Tf
Liquid
30.7 In Situ High Temperature/High Pressure Diffraction
Supercooled liquid
1.8
5.0 4.8
Part C | 30.7
1.7
4.6 4.4
1.6
4.2 4.0
Position of the 1st peak Ca–O coordination number 1.5 2000
1800
1600
1400
1200
1000
800
3.8 600 400 Temperature (°C)
Fig. 30.25 Evolutions of the posi-
tion of the Al–O peak in the pair distribution functions obtained by neutron and x-ray diffraction and the average Al–O coordination number upon cooling a liquid CaAl2 O4 from 1900 ı C. Adapted after [30.167]
1072
Part C
Characterization of Glasses
a)
Fig. 30.26a,b
b)
Possible configurations for HD (a) and LD (b) glasses quenched from Y2 O3 Al2 O3 liquids obtained by RMC modeling of the neutron and x-ray diffraction data. Reprinted from [30.170], © 2006, with permission from the Royal Society of Chemistry
a) D(r)
b) D(r)
15
15 KB2 KB2
10
10 NB2 NB2
5
LB2
5
B–O
Glass Liquid 0
0
1
2
3
4
5
6
7
8 r (Å)
0
1
LB2
2 r (Å)
Fig. 30.27 (a) Differential correlation functions, D.r/, for the glass (solid lines) and the liquid (dashed lines) for K2 B4 O7 (KB2), Na2 B4 O7 (NB2) and Li2 B4 O7 (LB2), from top to bottom. (b) Low-r part of the D.r/ functions showing the shift
Part C | 30.7
towards low r-values with increasing temperature. Adapted after [30.171]
0:02 Å in the liquid state, which is due to the shorter Li–NBO distance compared to the Li–BO ones. Therefore, a higher number of NBOs is expected in the first coordination sphere of Li in liquids and the Li structural role evolves from charge compensator in the glass, associated with BO4 units, to modifier in the melt, associated with NBOs [30.175]. In SiO2 , the temperature has little effect on the SiO4 tetrahedra that remain the main structural units in silicate melts, with a coefficient of thermal expansion of the Si–O bond estimated by ND at .2:2 ˙ 0:4/ 106 K1 [30.176]. The D.r/ function of silica
shows a small decrease of the Si–O–Si mean bond angle and an expansion of the network between 5 and 9 Å (Fig. 30.29), but an important IRO persists in the liquid state [30.177]. In silicate glasses, substantial changes in cation coordination number are important in order to understand melt properties such as melt/crystal partitioning, transport, and ionic conduction. In the binary MgO-SiO2 system, the average Mg–O coordination numbers decrease on cooling from 5:2 in the liquid to 4:5 in the glass, using in situ XRD and RMC fitting [30.178]. This change in structure allowed the authors to conclude that
Neutron and X-Ray Diffraction of Glass
a) Q*F(Q) (b Å–1)
30.7 In Situ High Temperature/High Pressure Diffraction
1073
b) D(r) (b Å–2) 300 K 1273 K
2
Li–O
Li–B
2
3
0.1
7–LB2 1.5
1 6–LB2
0
0.5 diff 6 – 7 0 0
2
4
6
8
10
12
14 16 Q (Å–1)
–0.1
0
1
4 r (Å)
Fig. 30.28 (a) Interference functions, QŒS.Q/ 1, at 300 K (solid lines) and at 1273 K (dotted lines) for Li2 B4 O7 containing 7 Li isotopes (7LB2) and 6 Li isotopes (6LB2) and first difference function (diff 6 – 7) extracting the Li-centered partial functions. (b) First difference function in real space showing the shift of the first Li–O bond distance towards lower r-values in the liquid state. Adapted after [30.175]
a) SX(Q)
b) GX(r) 1.6
10
12
8
4
1.2 6 4.4
4.8
5.2
1.4
8
1.6
1.8
Experiment
Liquid 2100 °C 2 Hot glass 1600 °C
4
Classical MD
Ab initio MD
0
0 0
5
10
15 Q (Å–1)
2
4
6 r (Å)
Fig. 30.29 (a) Experimental x-ray structure factors for SiO2 . Insert: second peak emphasizing the main changes between the glass (dashed) and the liquid (solid). (b) Top curves: experimental x-ray correlation functions for the glass (dashed) and the liquid (solid). Middle curves: classical MD simulations. Bottom curves: ab initio simulations. Insert: shift in experimental data of the Si–O peak. Reprinted with permission from [30.177]. © 2007 by the American Physical Society
Part C | 30.7
Glass 25 °C
1074
Part C
Characterization of Glasses
the distorted magnesium percolation domains occur in liquids with lower MgO contents compared to glasses. The structure of iron-bearing silicates glasses was measured using HE-XRD combined with laser-heated aerodynamic levitation [30.179]. The technique is particularly well suited to investigating such liquids as certain compositions (Fe2 SiO4 ) are not quenchable and their structure can only be studied in situ. The Gaussian fit of the correlation function indicates two Fe–O distances at 1:93 and 2:20 Å (Fig. 30.30), corresponding to FeO4 and FeO6 polyhedra, respectively. The coexistence of these two states has important implications for the partitioning behavior of iron or transport of magmas.
formation on the Ca environment has been extracted from NDIS experiments using CNL [30.181]. A decrease of the intensity of the first Ca–O bond peak at 2:42 Å is observed in the liquid compared to the glass, which is attributed to the distortion of polyhedra. There is also a decrease in the average coordination number for Ca or a redistribution of Ca–O bond lengths to longer distances in the melt. The structure of metallic melts has been mainly studied using the EML environment, from the liquid state to a large undercooling [30.182]. In Ni, Zr and Fe metallic melts (Fig. 30.32), icosahedral short-range order (ISRO) has been evidenced though larger polytetrahedral aggregates (such as dodecahedra) are prevalent in the liquid state. This ISRO appears as a split peak of the second peak in S.Q/. It is present already above the melting temperature and becomes more pronounced in the undercooled metastable state. NDIS experiments were carried out on Ni36 Zr64 alloys using Ni isotopic substitution (Fig. 30.33), which allowed the extraction of all the partial functions [30.183]. The EML is advantageous in the case of NDIS since large samples can be levitated, improving good counting statistics. These partials indicate a preference of Ni–Zr nearest neighbors suggesting a pronounced chemical SRO. A high nearest-neighbor coordination number of 13:9 is deter-
Evolution of Intermediate-Range Order with Temperature XRD measurements were performed on aerodynamically levitated CaSiO3 droplets [30.180]. When cooled, the presence of isosbestic points is observed on the correlation functions (Fig. 30.31), reproduced by MD simulations, which are used to characterize the polymerization process. A linear behavior is evidenced in the melt while a rapid growth is observed just above Tg and near 1:2 Tg . The MD simulations show more edgeshared polyhedra and fewer corner-shared polyhedra in the glass model than the liquid one. Local structural ina) T(r)
b) T(r) 4
4
FeO4 FeO4 SiO4
3
3 FeO6
FeO6
SiO4 2
2
O–O
O–O
Part C | 30.7
1
1
0
1.5
2.0
2.5
3.0 r (Å)
0
1.5
2.0
2.5
3.0 r (Å)
Fig. 30.30a,b Neutron total distribution functions, T.r/ (black circles), for (a) liquid fayalite Fe2 SiO4 and (b) liquid ferrosilite FeSiO3 [30.179]. The red dashed curve is the Gaussian fit of the Si–O peak. The chained curves are the Gaussian fits of the first and second Fe–O peaks, due to FeO4 tetrahedra and FeO6 octahedra, respectively. The black dashed curve is the approximate contribution for the O–O pair correlation. The solid curve is the sum of the fitted Gaussians. Reprinted with permission from [30.179]. © 2013 by the American Physical Society
Neutron and X-Ray Diffraction of Glass
a) DCaO(r) (Å–2)
Running CaO coord.
8
8 6
Glass Liquid
4 2
4
0 2.0
2.6
3.2
3.8 r (Å)
0
0
4
8
12
16 r (Å)
4
6
8 r (Å)
–2
b) ΔD(r) (atoms Å ) 0.4
0.2
0
–0.2 0
2
c) Connectivity (%) 80
Corner 60
Edge 20 Face 0
0
0.4
0.8
T/Tm
Fig. 30.31 (a) NDIS data showing the Ca–O partial distribution function, DCaO .r/ (solid), for the liquid CaSiO3 compared with the MD simulation for the glass (dashed) and liquid (solid). The insert presents the Ca–O running coordination number determined by MD simulations. Reprinted with permission from [30.181]. © 2012 American Chemical Society. (b) Difference of the x-ray correlation function, D.r/ D DT .r/ D0 .r/, where the highest temperature D0 .r/ at 1900 ı C has been subtracted. The isosbestic points are marked with arrows. The figure is adapted from [30.180]. (c) Changes in the connectivity between Ca polyhedra for the liquid/glass MD models of CaSiO3 as a function of temperature. Reprinted with permission from [30.180]. © 2010 by the American Physical Society J
was also employed to measure NDIS for NiSi and NiSi2 alloys [30.184]. Both alloys exhibit a strong tendency to heterocoordination within the first coordination shell. In particular, the tendency to form Si–Si covalent bonds with somewhat greater distances influences the atomic structure of the NiSi melts. The structure of complex metallic alloys has been recently investigated showing the development of the ISRO upon cooling [30.185, 186], with important consequences for glass stability. Rapid changes in the atomic structure of liquid tellurium has been shown by HE-XRD [30.187]. The structural evolution allows a better understanding of the density anomaly and the semiconductor-metal (SC-M) transition. Twofold and threefold local coordination coexists with a majority of the formers, which are slightly more present at lower temperature. The density maximum near the melting point reflects the temperaturedependent changes in chain lengths (longer chains at low T), ring distribution (larger rings at low T) and cavity volumes that are more abundant but with smaller sizes at low T. Cavities in the interchain regions at low temperatures explain the density minimum. The broadening of bond angle distribution at high temperatures is related to the SC-M transition. ND and HE-XRD measurements have been carried out on TeX4 (X D Cl, Br) liquids, in which chalcogens have covalent bonds and halides have ionic bonds [30.188]. Tellurium is present in tetrahedral coordination with Cl or Br. The intense FSDP suggest a pronounced intermediate-range structure that consists of Te2 X8 dimers, different to the monomeric gas and the tetrameric solid Te4 X16 (s) ! Te2 X8 (l) ! TeX4 (g) :
mined. In contrast to most melts of pure metals or of metallic alloys, ISRO was not observed in the Ni36 Zr64 melts, which could result from the large difference of the atomic radii .RZr =RNi D 1:29/. The CNL technique
1075
A broader composition range of Te1x Clx liquids, outside the glassy domains, has been investigated by ND [30.189]. Contrary to Cl-rich compositions, the ND
Part C | 30.7
40
30.7 In Situ High Temperature/High Pressure Diffraction
1076
Part C
Characterization of Glasses
a) g(r)
a) S(Q) 3.0
4 T = 1435 K
3
T = 1465 K
2 1
2.5 60
T = 1605 K T = 1765 K
2.0
T = 1905 K
1.5
Ni36Zr64
nat
Ni36Zr64
58
0
Ni36Zr64
1.0 2
3
4
5
6
7
8
9
10
11 r (Å)
0.5
b) g(r) 0
1
4 T = 1670 K
3
T = 1730 K T = 1750 K
2
3
3
4
5
6
7
8
9
10 11 Q (Å–1)
b) S NN, SCC, S NC 4
S NC
T = 1830 K T = 1870 K
1
3 S CC
0
2
3
4
5
6
7
8
9
10
11 r (Å)
2
c) g(r) 1
4 3
T = 1830 K
0
T = 1890 K
2
T = 2135 K
S NN
0
2
4
6
8
10 Q (Å–1)
c) S NiNi, SZrZr, S NiZr
T = 2290 K
1
6 0
2
3
4
5
6
7
8
9
10
11 r (Å)
S NiZr 5 4
Fig. 30.32a–c Neutron diffraction structure factors at different temperatures for (a) Ni melts, (b) Fe melts and (c) Zr
3
melts. Adapted after [30.182]
2
SZrZr
S NiNi
Part C | 30.7
structure factors of Te-rich liquid alloys exhibit a weak FSDP due to a chain network structure. As the Cl content increases, the structure progressively evolves from a chain network to a molecular-like behavior, the final member being Te2 Cl8 dimers.
1 0 0
2
4
6
8
10 Q (Å–1)
Fig. 30.33 (a) Neutron diffraction total structure factors
Thermodiffraction Thermodiffraction is time-resolved diffraction acquisition at high temperatures. Diffractograms can be completed in up to 80ı in 2:5 min acquisition times with ND [30.190] and in few ms with XRD. Such measurements are particularly useful to follow the real-time evolution of nonisothermal nucleation. In a bioactive glass CaSiO3 -Ca3 .PO4 /2 , the growth and disappear-
for 58 Ni36 Zr64 , 60 Ni36 Zr64 , and nat Ni36 Zr64 at T D 1375 K. (b) Partial Bhatia–Thornton and (c) partial Faber–Ziman structure factors. Reprinted with permission from [30.183]. © 2009 by the American Physical Society
ance of the successive phases can be easily visualized on a two-dimensional (2-D) map (Fig. 30.34b), which is the projection of the 3-D thermodiffractograms
Neutron and X-Ray Diffraction of Glass
30.7 In Situ High Temperature/High Pressure Diffraction
Intensity (arb. u.)
a)
1375 1275 1175 1075 T (°C) 975 875 775 675
59 55 57 2θ 53 49 51 45 47 43 39 41 35 37 33 31 27 29
1077
Fig. 30.34 (a) Evolution with time of nonisothermal crystallization of a CaSiO3 -Ca3 .PO4 /2 glass showing neutron diffraction data collected from 600 to 1375 ı C at 5 ı C min1 ( D 2:5145 Å). (b) 2-D projection of the thermodiffractograms in (a). The crystallization events (growth or collapse) are directly visualized (Ap, Ca-deficient apatite; W-2M, wollastonite-2M; ps-W, pseudowollastonite; -TCP, -tricalcium phosphate). Reprinted from [30.190], ©2009, with permission from Elsevier
b) T (°C) 1350 α-TCP Ap ps-W 1250 – (202) (112) Ap α-TCP 00) (2 1150 ps-W (202) (331) –– 1050 (112) (132) W-2M W-2M 950 (151) (021) (320) 850 Ap Ap Ap Ap 750 (211) (300) (002) (111) (121) 650 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 2θ
a)
b) T (°C)
Intensity (arb. u.)
7500
324
324 304
T (°C) 304.5
35 37 39 41 43
285
2θ
285 35
37.5
40
42.5
45 2θ
3900
(Fig. 30.34a). The crystallization sequence with the domains of the different crystalline phases is clearly identified. A complex crystallization sequence has been demonstrated by neutron thermodiffraction of the Agx .Ge0:25 Se0:75 /1x glasses with x D 15, 25 [30.191]. In agreement with the Ag-Ge-Se phase diagram, the pri-
mary crystals are the two stable phases, i. e., Ag8 GeSe6 and GeSe2 . However, in situ measurements highlight an additional phase (Ag2 GeSe3 ), which is signaled by peaks located at 39ı and 50:2ı (Fig. 30.35). This phase is unstable and decomposes upon further heating, giving a new phase of Ag10 Ge3 Se11 composition along with the stable GeSe2 phase.
Part C | 30.7
Fig. 30.35 (a) Neutron thermodiffractograms for the Ag25 Ge18:75 Se56:25 glass. Graphs show a peak at 2 D 39ı , characteristic of the intermediate-phase Ag2 GeSe3 , whose intensity appears at 285 ı C and decreases above 320 ı C. (b) 2-D projection of the thermodiffractograms on (a) revealing the intermediate phase around 39ı . Adapted from [30.191]. © IOP Publishing. Reproduced with permission. All rights reserved
1078
Part C
Characterization of Glasses
30.7.3 High-Pressure Experimental Techniques Two general pressure cells are most currently used on large facilities: the diamond anvil cell (DAC) [30.192] and the large-volume press [30.193]. In the DAC (Fig. 30.36a), the sample is squeezed between the flat parallel culets of two opposed diamonds (single crystal, sometimes specially designed) and maintained between the diamond anvils by a hole drilled in a gasket. An inflated gas membrane transmits a mechanical force to the diamond table, pressing the diamonds together and increasing the pressure in the sample chamber. Resistance heating or laser heating can be used to generate high temperature. The advantage of DAC is that diamonds are transparent to x-rays. However, to achieve high pressure, the sample size must be very small ( 50 m thick and < 200 m in diameter). Note that large-volume DAC are currently developed on neutron sources (Spallation Neutrons and Pressure beamline at Oak Ridge, USA) to investigate disordered materials. Large-volume apparatus (Fig. 30.36b), like the Paris–Edinburgh (PE) press [30.196, 197], can be used for ND and XRD to achieve pressures up to 25 GPa. The PE press is composed of multi- or toroidal-type anvils and a metal gasket, usually TiZr for ND as this alloy has almost null scattering (Fig. 30.36c). A hydraulic press connected to the piston by a capillary is used to generate the force. A major advantage of PE presses is that large sample volume can be compressed compared to DAC: 100 mm3 for WC anvils, with pressure limited to 10 GPa, and 35 mm3 for sintered diamond, achieving pressures up to 25 GPa [30.198]. As the incident beam passes through the cell assembly and the diffracted beam is usually detected in the gasket plane, the background scattering is important. Moreover, this a)
b)
20–200 μm
Part C | 30.7
F
background is pressure-dependent, resulting from the deformation of the gasket with pressure. The data correction is thus tedious as the background is hard to subtract, especially for weakly scattering samples. Another limitation also existing for DAC is the angular exit aperture, which can restrict the accessible maximum Q.
30.7.4 Case Studies of Pressure-Induced Modifications A structural modification is usually the response to an applied pressure, modifying the properties of the material. Distinct amorphous states lead to the notion of polyamorphism or amorphous–amorphous (A–A) transition induced by pressure [30.199]. Considerable research using diffraction methods has been active on this topic in various glass systems, such as ice, oxides, chalcogenide or metallic alloys. The A–A transformation can be the viewable aspect of a liquid–liquid transition, which could be present in the supercooled regime [30.200]. Amorphous Forms of H2 O The polyamorphism in water has been the subject of numerous in situ diffraction studies to investigate the apparent first-order-like transition between the lowdensity amorphous water (LDA) and the high-density amorphous form (HDA). These two amorphous states have both a fully hydrogen-bonded tetrahedral network, with HDA having a structure close to that of liquid water at high pressure and LDA a structure close to ice 1 h (Fig. 30.13) [30.73]. The different structures are particularly evidenced in the gOO .r/ partial function determined by NDIS and combined with EPSR (Fig. 30.37a) [30.73]. The O–O coordination number increases from 3:7 in LDA to 5 in HDA indicating an additional fifth interstitial water molecule in HDA in Cylinder head
c) Sample 80 mm 3
V = 1×10 –4 – 0.06 mm 3
Sample Ruby 10–50 μm
Anvils 28 cm
Joint Piston
Joint
TiZr gasket
Diamond
Steel cBN die
13.5 cm
Fig. 30.36 (a) Illustration of diamond anvil cell. (b) Illustration of V4 large-volume Paris–Edinburgh press. On the cutting, the vertical access for the incident beam can be seen. The figure is adapted from [30.194]. (c) Cross-section of opposed anvils in the
Paris–Edinburgh press. Adapted after [30.195]
Neutron and X-Ray Diffraction of Glass
the first neighbor shell, which gives a less ordered HDA structure compared to LDA. The pressure applied to transform LDA to HDA results in the collapse of the second neighbor shell of water molecules that eventually become interstitial, as demonstrated by spatial density functions obtained from EPSR models based on the diffraction data (Fig. 30.37b) [30.202]. The interpenetrating network of water molecules stabilizes the HDA structure as this state can be recovered to ambient pressure. A third denser amorphous form of water (very highdensity amorphous, VHDA) has been discovered and can be differentiated from HDA by its diffraction pattern: its structure factor has a sharp first peak shifted to higher Q values compared to S.Q/ for HDA. This increase in the IRO is associated with a second interstitial water molecule [30.203], which is confirmed in the gOO .r/ partial function [30.204]. As in situ studies are possible, neutron diffraction has been used to follow the LDA ! HDA transition using the PE pressure cell [30.205, 206]. The structure factors exhibit a decreasing peak at 1:71 Å1 and a growing peak at 2:25 Å1 , attributed to LDA and a) gOO(r) HDL LDL
3 2 1 0
3
4
5
6
7 r (Å)
b) z
z y
x
y
x
II
I
Fig. 30.37 (a) gOO .r/ pair distribution functions for HDA and LDA as obtained by EPSR. The figure is adapted from [30.201]. (b) Three-dimensional arrangements of the oxygen atoms around a water molecule (spatial distribution functions) for HDA and LDA. The pronounced lobes render the spatial density functions for the first (I) and second (II) shells of water molecules, showing the collapse of the second O–O shell in HDA (lobes II). Reprinted from [30.202]. © 2000, with permission from the American Physical Society
1079
HDA, respectively. During the transition, changes in the position and height of the FSDP and in the position of the interstitial water molecule indicate distinct structural relaxation processes. A continuous series of metastable forms change the IRO during the transition and then structural relaxation in the second coordination shell of the LDA form appears [30.207, 208]. Density-Driven Transformation in B2 O3 B2 O3 glass has been investigated by XRD up to 9:5 GPa [30.209] and by ND up to 17:5 GPa [30.210]. The position of the first peak in S.Q/ is linearly shifted towards high Q-values upon compression. This change indicates a reorganization of the IRO, interpreted as the break of boroxol rings below 3:5 GPa. Above 3:5 GPa, the real-space function shows a change in boron coordination where BO3 units are converted to BO4 units. At 1114 GPa, the decomposition of boroxol rings is achieved as seen in the disappearance of the third peak in the distribution function and only the local boron conversion to BO4 takes place at higher pressure. Polyamorphism in SiO2 and GeO2 SiO2 and GeO2 are typical examples of strong tetrahedral network glass-forming systems. The polyamorphism of these glasses correspond to an A–A transition from an open network structure based on corner-linked tetrahedra at low pressure, to a network dominated by SiO6 or GeO6 octahedra at high pressure. These glasses were initially studied after decompression from high pressure allowing a permanent densification of the structure to be maintained [30.211– 213]. Such permanently densified glasses show mainly structural changes at IRO with a decrease in the A–O and O–O distances (A D Si, Ge) due to rotation of the A–O–A bond angles and distortion of the AO4 tetrahedra [30.211]. Coordination changes can only be addressed by in situ measurements as first demonstrated by x-ray absorption experiments [30.214]. The first in situ diffraction study has been reported using x-rays on SiO2 up to 42 GPa and has revealed a gradual increase of the mean coordination number around Si, nSi , from four to six above 10 GPa [30.215]. In the last decade, XRD and ND were widely used to investigate the pressureinduced structural modifications in SiO2 (using XRD [30.216–220] and ND [30.221]) and in GeO2 (using XRD [30.76, 222–224] and ND [30.76, 225, 226] including isotopic substitution of Ge (nat Ge/70 Ge/73 Ge) [30.227]). The structure factors for SiO2 and GeO2 are modified as the pressure is increased: the FSDP moves to higher Q-values and the principal peak becomes sharper in SN .Q/ and more discernible in SN .Q/. These changes
Part C | 30.7
I
II
30.7 In Situ High Temperature/High Pressure Diffraction
1080
Part C
Characterization of Glasses
indicate a decrease in IRO through the shrinkage and collapse of the open network structures. The analysis of the distribution functions allows more information on the local order to be obtained. At low pressure, the tetrahedral structure is preserved and densification proceeds via an increase in the packing of AO4 tetrahedra. The nSi increases above four at P > 10 GPa while the Si–O bond length does not increase initially but presents the appearance of a shoulder on its high-r side. The domain of coordination change is still debated but occurs mainly in the range 1040 GPa. The tetrahedral–octahedral change occurs at lower pressure in GeO2 by comparison with SiO2 [30.214, 228], with a nGe increase when P > 5 GPa [30.229]. The complete partial functions extracted from NDIS allowed the determination of the pressure dependence of the Ge–O–Ge bond angle [30.227]. As highly coordinated AO6 species are formed, the mean coordination number for O, nO , also increases. The transition domain is not necessarily a simple mixture of four- and sixfold coordinated sites and intermediate AO5 species can coexist. However, the experimental evidence of such AO5 species has not been unambiguously proven by diffraction methods, though MD simulations consistent with experimental data advocate, for instance, for SiO5 units over the window P 2045 GPa while SiO6 units dominate when P & 32 GPa [30.229]. Therefore, AO5 units should play a key role in the mechanism of polyamorphism.
The oxygen-packing fraction O has been proposed to rationalize the changes in the coordination number [30.230, 231]. The mean A–O coordination number nN O A shows an interesting dependence with O for a large number of glassy and liquid network-forming materials (Fig. 30.38). BO3 triangles and AO4 tetrahedra show a plateau of stability ending at O ' 0:44 and at O ' 0:59 respectively. At higher packing fractions, the conversion to BO4 or AO6 takes place. We can also note that SiO2 and GeO2 increase coordination at the same O . The upper limit of stability for AO4 tetrahedra corresponds to the packing fraction for a random loose packing (RLP) of hard spheres, i. e., RLP D 0:55 0:60, and nN O A increases rapidly as O approaches the expected packing fraction for a random close packing (RCP) of hard spheres, i. e., RCP D 0:64. For the latter packing, the transformation to an octahedral network is largely completed. Therefore, network-forming motifs govern the topological ordering and can be predicted based on O behavior. The evolution of Q1 position with pressure has a common behavior with O [30.74]. Chalcogenide Glass GeSe2 GeSe2 is representative of chalcogenide glasses in which the mechanism of pressure-driven network collapse can differ to that in oxide glasses due to the presence of edge-sharing GeSe4 tetrahedra and homopolar bonds. This glass was investigated by in situ
Coordination number n– OA
6
B2O3 GeO2 SiO2 (MgO)0.62(SiO2)0.38 CaSiO3 Basalt
Rutile
5
Part C | 30.7
4 c-B2O3
Fig. 30.38 Variation of the mean A–O
3 0.3
0.4
0.5
0.6 0.7 Oxygen packing fraction ηO
coordination number as a function of the oxygen-packing fraction O for oxide glasses and liquids under high pressure conditions. From [30.229]
Neutron and X-Ray Diffraction of Glass
XRD [30.232] and NDIS [30.233, 234]. NDIS is particularly useful since neutron and x-ray diffraction methods give essentially the same information due to similar scattering amplitudes for Ge and Se. The FSDP is shifted to a larger Q-value upon compression and almost vanishes at 9:3 GPa. The principal peak also moves to a larger Q-value but its height increases according to the pressure dependence for GeO2 . These changes were interpreted as a loss of the IRO associated with the FSDP and a dominant extendedrange ordering associated with the principal peak with increasing pressure, corresponding to the transformation from a strong low-density to a fragile high-density glass [30.229]. The first average peak in the pair distribution function, rN , slightly decreases with increasing density up to P 12:8 GPa, while the average coordination number, nN , remains at 2:67. At higher densities, rN and nN increase to accommodate a larger number of nearest neighbors. MD simulations indicate that, up to 8:2 GPa, the proportion of corner-sharing tetrahedra increases at the expense of edge-sharing tetrahedra, with a ratio from 1:3 to 1:7. According to MD simulations, homopolar bonds are largely present on the highly coordinated Ge and Se atoms and play a key role in the density-driven structural transformations. The pressure-induced structural modifications are continuous and occur on a broad pressure range, suggesting that densification is not an A–A transition. According to diffraction results, GeSe2 glass retains a semiconducting behavior. The structure of liquid GeSe2 has also been studied under pressure [30.236], showing changes in the IRO, as reflected by changes in the FSDP on a narrow pressure range between 4:1 and 5:1 GPa. These modifi-
Polyamorphism in Metallic Glasses The coordination change associated with bond lengthening observed in oxide glasses (Sect. 30.7.4, Density Driven Transformation in B2 O3 and Polyamorphism in SiO2 and GeO2 ) are not expected in nondirectional, densely packed metallic glasses (MGs). Indeed, these materials already have a high coordination number (1214) and are spatially compact. An in situ high-pressure XRD study on a La75 Al25 MG shows a gradual and completely reversible compression (Fig. 30.39) [30.235]. Based on ab initio MD simulations and RMC fitting, changes in atomic size ratio and coordination number were identified as a conversion of prism-type coordination to icosahedral short-range order. However, evidences of pressure-induced polyamorphism were recently reported in various MGs mainly based on Ce-Al alloys (Ce32 La32 Al16 Ni5 Cu15 [30.237], Ce55 Al45 [30.238], Ce75 Al25 [30.239], Ce75 Al23 Si2 [30.239] and Ce70 Al10 Ni10 Cu10 [30.84]), mostly using in situ high-pressure XRD measurements carried out on synchrotrons. The position of the main peak Q3 in the structure factors tracks with increasing pressure, showing a significant shift towards high Q-values in some narrow pressure range (Fig. 30.40). Similar to oxide or chalcogenide glasses, these changes are reversible when the pressure is released with an important hysteresis. The inverse position of the main diffraction peak, 2 =Q3 , can be estimated using a Voigt line profile after subtracting baseline. As seen previously (Sect. 30.6.1, Correlations Between Q1 and the Reduced Volume),
6
5
5
4
4
2 1 0
0
2
4
6
8 Q (Å–1)
40.2 GPa 26.7 GPa 17.0 GPa 6.8 GPa 1.5 GPa 0.1 GPa
3 2 1 0
0
2
4
6
8 Q (Å–1)
Fig. 30.39a,b X-ray structure factors for a La75 Al25 metallic glass at different pressures upon (a) compression and (b) decompression showing the reversibility of the changes. The dashed arrow emphasizes a shoulder that becomes
more apparent with increasing pressure. Adapted after [30.235]
Part C | 30.7
b) S(Q)
6
40.2 GPa 28.9 GPa 17.9 GPa 8.9 GPa 4.1 GPa 0.1 GPa
1081
cations were interpreted as a continuous evolution from a two-dimensional to a three-dimensional network.
a) S(Q)
3
30.7 In Situ High Temperature/High Pressure Diffraction
1082
Part C
Characterization of Glasses
a) Intensity (arb. u.)
0
2
3
4
6
p (GPa) 30
p (GPa) 30
25
25
20
20
15
15
10
10
5
5
0
0 0
8 Q (Å–1)
c) p (GPa)
3
4
2
3
4
6
8 Q (Å–1)
30
20
20
10
10
0
2
of XRD patterns of a Ce55 Al45 metallic glass in a diamond anvil cell upon (a) compression and (b) decompression. (c) The XRD intensity peak gradually shifts to high Qvalues during compression in the pressure range 2:013:5 GPa. (d) During decompression, the arrow at 2 GPa marks an abrupt shift towards low Q-values. Reprinted by permission [30.238]
d) p (GPa)
30
0
Fig. 30.40a–d Evolution
b) Intensity (arb. u.)
2
3
4
5
0
6 Q (Å )
0
5
–1
a) Intensity (arb. u.)
6 Q (Å–1)
b) 2/Q1 (nm) 1.5 GPa
0.28
24.4 GPa
0.27
Part C | 30.7
0.26 5 GPa 0.25 0.8 GPa 0.24 20
24
28
32
36
40 Q (nm –1)
0
5
10
15
20
25 p (GPa)
Fig. 30.41 (a) Evolution of XRD patterns of a Ce75 Al45 metallic glass. (b) Inverse Q3 positions as a function of pressure.
The black and red curves correspond to LDA and HDA respectively. Reprinted with permission from [30.240]. © 2010 by the American Physical Society
Neutron and X-Ray Diffraction of Glass
=Q3 can be correlated to the relative volume (density) change as a function of pressure. The plot of 2 =Q3 over pressure allows the observation of a clear transition between 1:5 and 5 GPa from a low-density state to a high-density state (Fig. 30.41). The transition starts from a LDA at low pressure, and goes through continuous densification ending with a HDA at high pressure. A large density difference is observed between the two polyamorphs. In Fig. 30.41, the volume collapse can be estimated with the 1=3 power law function giving about 8:6% volume reduction (2:9% in 2 =Q3 ). The suggested mechanism is an increase in Ce–Ce interactions leading to delocalization of some electrons in the 4f shells (from localized state 4f1 to delocalized state 4f0 ) under high pressure [30.238]. Ab initio MD simulations confirm this scenario, which causes a splitting of the Ce–Ce nearest-neighbor distance with one position experiencing a significant bond
References
1083
shortening. Unlike the structural transition in ordinary amorphous materials [30.199], MGs exhibit an electronic polyamorphism. This large electronic configuration change has also been observed in other bulk metallic glasses (lanthanide-based MGs [30.86]) indicating that this mechanism is common. The A–A configuration change is not restricted to MGs having an f electron: in Ca–Al MGs [30.79] a transfer of s electrons into d orbitals under pressure has been proposed to explain the A–A transition. A liquid–liquid phase transition in the monatomic liquid metal cerium has also been reported using in situ high-P=high-T XRD experiments [30.241]. At a given pressure, a high-density liquid transforms to a lowdensity liquid with increasing temperature. Again, the origin of this transition is due to delocalization of f electrons. It was proposed that this transition reflects the liquid–liquid critical point in the Ce phase diagrams.
30.8 Conclusion and Perspectives In this chapter, we have introduced the fundamental concepts of the neutron and x-ray diffraction methods, emphasizing the difference and complementarity of the two techniques, the possibility to extract more structural information using contrast methods (neutron diffraction with isotopic substitution or anomalous diffraction) and the clear contribution of refinement methods (RMC, EPSR) or MD simulations. The synergism between diffraction data and simulation/modeling techniques is now a routine procedure, beneficial for both tools and improving our current representation of the three-dimensional atomic arrangements in glasses. Oxide, chalcogenide and metallic glasses, among others, have been the subject of a tremendous number
of investigation using neutron/x-ray diffraction and we have thus chosen some representative examples to illustrate the invaluable information that can be determined from diffraction data, leading to a deeper understanding of the glass structure in many amorphous systems. The structural response to pressure and temperature is often an experimental challenge, which has been successfully met by diffraction. Results using in situ high pressure/temperature setups hold great promise for elucidating the structural behavior in glasses, and thus the changes in their physicochemical properties. Diffraction will continue to provide an excellent choice for future in situ high-pressure/temperature studies by continuing to push the experimental limits.
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Laurent Cormier IMPMC Sorbonne University – CNRS Paris, France [email protected]
Laurent Cormier obtained his PhD from the University Pierre and Marie Curie – Paris 6, France in 1997 and worked at the Cavendish Laboratory, Cambridge University (UK) before joining CNRS in 1999. His research focuses on understanding the structure of glass at short and medium range order in relation to transport, nucleation and crystallization properties. He received the Gottardi Prize from the ICG.
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31 First-Principles Calculation Wai-Yim Ching, Kansas City, MO, USA 32 Molecular Dynamics Simulations of Oxide Glasses Jincheng Du, Denton, TX, USA
33 Machine Learning for Glass Modeling Adama Tandia, Corning, NY, USA Mehmet C. Onbasli, Istanbul, Turkey John C. Mauro, University Park, USA
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_30
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This chapter describes the application of firstprinciples calculation to investigate the structure and properties of different classes of glasses. These include insulating glasses, three types of metallic glasses, and an example of an amorphous metal–organic framework as an emerging hybrid organic glass. First-principles calculation differs from the more popular molecular dynamics simulation and can provide more in-depth information on interatomic interactions. In many highly complex multicomponent glass systems, ab initio calculation may be the only viable method for realistic modeling. Here it is demonstrated that first-principles calculation is best accomplished by a combination of methods with different strengths and advantages. We introduce the novel concept of using total bond order density as a single quantum mechanical metric to assess the strength and cohesion in different types of glasses by providing some provocative examples of the limitations and
Glass is widely recognized as an important part of the materials world, with a history that spans more than 6000 years, from ancient times and the beginning of human civilization, through the various industrial revolutions. In today’s world, glass plays a pivotal role in the ever-changing technology affecting all aspects of everyday life. This was succinctly summarized in a short editorial by T. Vogt and T. Shinbrot [31.1]. Glass is a predominant part of noncrystalline materials constituting more than 95% of materials on Earth. Glass composition is highly diverse, involving almost all elements in the periodic table, with an extraordinary variety of properties ranging from very soft to superhard, from porous to densely packed, from easy to form to impossible to produce, from insulating to conductive, and from organic to metallic [31.2–4]. Such diversity leads to numerous applications, from window glass in churches to smartphone touch screens [31.5], from concretes and cements for construction materials to optical devices critical to many sophisticated instruments, from
31.1 31.1.1 31.1.2
Methods and Approach ..................... Model Construction............................ Electronic Structure and Interatomic Bonding ................... Physical Properties Calculation............
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First-Principles Calculation for Different Types of Glasses ............. 31.2.1 Insulating Glasses.............................. 31.2.2 Metallic Glasses ................................. 31.2.3 MOF Glasses ......................................
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Conclusions and Future Outlook......... 1119
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inadequacy in current theory for structure characterization of glasses. The chapter also highlights some urgent areas in glass research where firstprinciples calculations could play a more critical role.
materials affecting human health [31.6–8] to nuclear waste disposal [31.9], to those at the interior of the Earth’s mantle and interstellar matter, just to mention a few [31.10]. Throughout the long history of the development of glasses, the role of theory and simulation in glass research cannot be discounted. In the early days, all insight, intuition and experience was acquired by trialand-error processes in laboratories or kilns. The demand for new and better glasses at lower cost, with improved quality and easy processing, created the need for generalized theoretical concepts and a fundamental understanding of the key factors governing the behavior of different glasses. Various theories have been systematically developed, debated and refined as to how these ubiquitous nonequilibrium disordered materials can be best described: is it due to their composition, or is it controlled by the route of their preparation [31.11]? Such developments are always accompanied by simulations at different spatial and temporal scales for differ-
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_31
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ent purposes. Until recently, almost all simulation studies in glasses were carried out using classical molecular dynamics (MD) techniques, following from the early success of Monte Carlo simulations [31.12]. Over the years, MD simulations have been highly successful, accounting for many important advances [31.13, 14] involving almost all aspects of glass research, which are well covered in many reviews [31.15, 16] and in this handbook. A key element for MD simulation is the potential function used to describe the interactions of the atoms in glasses. They range from simple pairwise potentials such as the Lennard-Jones 6–12 potential or the Buckingham potential with three parameters, to more advanced and sophisticated multi-atom potentials such as the Mayer–Huggins potential for different glasses [31.17]. Some of these potentials used in MD actually have parameters derived from first-principles calculations on simpler crystalline phases, such as those used in reactive force fields [31.18] or in many other standard codes such as AMBER or CHARMM with specific force-field parameters [31.19, 20]. It is fair to say that the success of MD depends to a large extent on the appropriateness and the quality of the potential functions used. Because the potential functions in MD are empirical and parameterized, they can be used for much larger systems, up to hundreds of millions of atoms or more [31.21, 22], and run over a long simulation time for dynamic behaviors. Thus classical MD has advantages in both the space and time domains for materials simulation. Many excellent packages have been developed by a number of groups [31.23–25]. In particular, the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) program developed by Sandia National Laboratories [31.26] is extremely popular, and Nanoscale Molecular Dynamics (NAMD) [31.27] is a very versatile package designed chiefly for biomolecular systems. In recent years, the use of first-principles calculations for simulation of glass structures has gained much popularity. This can be traced back to the 1985 paper by Car and Parrinello [31.28], which reported that the electronic degree of freedom was no longer separated from the nuclear degrees of freedom, as in the case of classical MD. Such development arose from the need to improve the accuracy of simulation, especially for those glasses with complex structures and involving different types of constituent atomic species, where empirical potential functions used in classical MD sim-
ulations are difficult or impractical to obtain. This is also facilitated by the global availability and abundance of resources with high-performance computing (HPC) facilities and the development of many highly efficient computational packages based on density functional theory (DFT) [31.29, 30]. These developments enabled the use of first-principles calculations beyond crystalline materials or simple molecules, to noncrystalline glassy models of sufficiently large size and with specific design for their complexity. The loosely defined term first-principles generally implies that the calculation does not involve any experimentally determined or empirical parameters. It should be emphasized that first-principles calculations can be used to supplement or enhance the results from classical molecular dynamics, but can never replace MD, since many aspects of glassy material simulations require extremely large samples, long simulation time, and other attributes such as temperature-dependent behavior and longerrange defective structures, which are still limiting factors for first-principles techniques. This chapter focuses on the first-principles calculation of glasses, with examples of application to several types of glasses, including insulating glasses (mostly oxides), metallic glasses (MG) and emerging hybrid glasses. Many of the results discussed are either recently published or yet to be published by the author’s own research group. The chapter also briefly discusses specific cases of first-principles calculations from other authors with different perspectives. I sincerely apologize if I have inadvertently omitted work by other groups using the first-principles methods in glasses. A combination of several different computational methods is described, in particular the firstprinciples orthogonalized linear combination of atomic orbitals (OLCAO) developed by the author over the past 35 years, which is especially effective for complex noncrystalline materials. The main motivation for the work presented here is to gain a deeper understanding of the interatomic interactions in glasses, in addition to their geometric structures, which are typically not available from MD simulations. Of particular importance is the introduction of a new concept of using total bond order density (TBOD) as a viable quantum mechanical metric for assessing the properties of glasses. The chapter also highlights some pressing needs in current glass research where a first-principles approach could play a more critical role.
First-Principles Calculation
31.1 Methods and Approach
31.1.1 Model Construction Model construction is the most important step in glass modeling, tantamount to sample preparation or fabrication in the experimental component of glass research. Before we begin actual model construction, we must carefully consider factors such as the size of the model to be constructed, which must be large enough to be realistic, and the computational resources it will demand. Special attention is needed in the initial construction such that subsequent ab initio calculations of the model structure can lead to an important understanding of the fundamental issues that govern its properties or an explanation of specific observations in experiments. Since glasses are disordered systems, each glass model is of limited size, and with specific composition and chemical components, it may require at least several samples for a targeted glass. In many ways, one can consider simulations as another kind of experiment, where the equipment used is the computer hardware and software for the simulations. The results from reliable simulations, verified by comparison with available experimental data, can lead to valid conclusions and the formulation of a specific theory for glasses. An important consideration in model construction for glasses is recognizing the presence of short-range order (SRO) and intermediate-range order (IRO), and the absence of long-range order (LRO), in noncrystalline solids that leads to classical models such as hard sphere models (HS) in metallic glasses (MG) [31.31] and continuous random network (CRN) models in covalently bonded inorganic glasses [31.32]. The absence of LRO requires a model of sufficiently large size that the imposed periodic boundary conditions do not introduce any artifacts. Also important is recognizing what is intrinsic to a particular type of glass and what is extrinsic and is introduced by defects or impurities, which are unavoidable in real glasses. For example, in the case of silicate glass, the CRN model, where Si is always tetrahedrally coordinated with twofold coordinated bridging O atoms infinitely extended with no LRO, is a perfect paradigm of an intrinsic glass. When defects are introduced, such as broken bonds associated with under- or over-coordinated Si or O atoms, the glass model is no longer intrinsic. The same can be said when the glass contains impurities, intentional or unintentional, as in the case of alkali-doped silica. Since intrinsic glass is an ideal realization on theoretical grounds, whereas extrinsic glass is the laboratory norm, the distinction between them is murky at best. Thus, soda-lime glass is simply a mixed glass between Na2 O and SiO2 . The strategy in first-principles calculation involves first achieving an
understanding of the simpler intrinsic glass, and then modeling extrinsic glass to be as realistic and close as possible to real samples. Boundary conditions in glass modeling are another important consideration. Should the model have a free surface or be periodically extended? There are situations where specific modeling of the glass surface is necessary, such as in glass nanoparticles, where the surface area correlates with particle size, a key parameter in their characterization. Another example is special glasses, where the surface properties are extremely important, such as the Gorilla Glass developed at Corning for cellphone covers [31.5]. Almost all glass models will be three-dimensional (3-D), with sporadic cases of two-dimensional (2-D) or even one-dimensional (1-D) models in special situations such as in polymers in the form of linear chains [31.33, 34]. Glass models may also contain extended defective structures, such as grain boundaries (GB) in polycrystals, or they can be part of glassy films between crystalline grains, the so-called intergranular glassy films (IGF) [31.35–38]. For first-principles calculations of glasses, all models must be fully relaxed with the desired accuracy such that they can be used in the electronic structure analysis and for the calculation of physical properties using quantum mechanics. There are many popular computational packages, including the Vienna Ab initio Simulation Package (VASP) [31.39], Cambridge Serial Total Energy Package (CASTEP) [31.40], Quantum ESPRESSO [31.41] and ABINIT [31.42], using plane wave expansion and pseudopotentials for efficient force evaluation, since glass models are usually large. Other ab initio packages that are popular for crystals include WIEN2k [31.43], CRYSTAL [31.44] and ASCF [31.45]. They may be less effective for glasses but can also be used. In classical MD, a single potential energy surface (usually the ground state) is represented in the force field, a consequence of the Born–Oppenheimer approximation. If excited states, chemical reactions or a more accurate representation is needed, electronic behavior can be obtained from first-principles calculations. This has led to the development of ab initio molecular dynamics (AIMD) such as in Car–Parrinello molecular dynamics (CPMD), and has also been implemented in other packages such as VASP. The computational cost is much higher for AIMD than classical MD because of the quantum mechanical treatment of the electronic degree of freedom, and it is usually limited to much smaller models and shorter time steps. Currently, AIMD is generally limited to around 1000 atoms [31.46], whereas classical MD can be ap-
Part D | 31.1
31.1 Methods and Approach
1097
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Part D | 31.1
plied to systems several millions of atoms in size. Depending on the actual size of the model and the problem to be studied, the simulation time can range from 50 ps in AIMD to 20 ns or much longer in classical MD. A significant advantage of using AIMD in modeling glasses is the avoidance of empirical-based potentials used in classical MD and the ability to study reactions that involve breaking or forming covalent bonds, which correspond to multiple electronic states. AIMD usually produces a vast amount of information not available from empirical methods, such as density of electronic states (DOS) or other electronic properties. There are several popular software programs for ab initio molecular dynamics, including CPMD [31.47] for organic/biological materials and the above-mentioned VASP and Quantum ESPRESSO packages for inorganic materials, all of which utilize DFT [31.29, 30, 48]. To reduce the computational burden of full AIMD, special techniques can be implemented to create a hybrid classical/quantum potential, where the bulk of the system is treated classically but a small region is treated as a quantum system, usually undergoing a chemical transformation. The structure of glass models generated by classical MD, AIMD or a combination of methods and approaches is always characterized by the pair distribution function (PDF). The PDF of glasses can be measured experimentally using atomic or neutron scattering, and then used to validate the models constructed. The PDF and partial PDF (PPDF) for specific atomic pair types can also provide information about the coordination number and atomic bonding. These parameters are based on the geometry of the structure and are less quantitative than the bond order (BO) description for interatomic bonding (see next section). Thus, the PDF is the first order check in determining the quality of the glass models. It should be noted that experimental measurement of the PDF is extremely challenging, especially in the case of multicomponent glasses with atoms of comparable size. This is where simulations become most useful, since they provide the distribution of all atomic pairs based on their simulated atomic positions. A few examples illustrating this important point will be presented in Sect. 31.2.
31.1.2 Electronic Structure and Interatomic Bonding The electronic structure reflects the fundamental interactions between atoms at the electronic level based on quantum mechanics. This is the major difference from classical MD simulations, which provide structural information with geometric parameters such as bond lengths (BL), coordinate shells and PDF. First-
principles calculation provides additional information on the electronic structure and bonding, energy levels, density of states (DOSs), charge distributions and potential surfaces. Within the first-principles calculations for solids, there are generally two different approaches according to the basis functions used: either plane waves or localized orbitals. The plane-wave-based method using pseudopotentials is the primary computational tool for accurate force calculations and structural optimization. In describing interatomic interactions, one typically must find some schemes to fold back into atomic descriptions. The localized orbital method using atomic waves for basis expansion is a more natural way to describe interatomic bonding, and can be more economical when applied to sufficiently large noncyrstalline glass models, as will be discussed below in greater detail. One of the most effective means of calculating the electronic structure and bonding of glasses is the OLCAO method [31.49]. For glass simulations, it often uses models whose structures have first been optimized using VASP or other methods including classical MD. The OLCAO method uses atomic orbitals for basis expansion, which is an expedient and efficient approach for calculation of the electronic structure of glasses represented by supercells with a large number of atoms. The combination of these two DFT-based methods has been shown to be highly effective in the study of large, complex systems including crystalline and noncrystalline solids [31.50–56], liquids [31.57], large organic crystals [31.58, 59] and biomolecules [31.60– 64]. In addition to the usual calculation of the density of states (DOS) and partial DOS (PDOS), the evaluation of effective charges Q ˛ at each atom and bond order (BO) value (overlap population) ˛ˇ between any pair of atoms (˛, ˇ) based on Mulliken population analysis [31.65, 66] is of central importance ˛ˇ D
XX n occ
Q ˛
D
n n Ci˛ Cjˇ Si˛;jˇ ;
i;j
XX
n n Ci˛ Cjˇ Si˛;jˇ :
(31.1)
n i;j;ˇ occ
In (31.1), i; j represent the orbital quantum number and n n the band index, Cjˇ are the eigenvector coefficients of the wave function, and Si˛;jˇ is the overlap matrix between atoms ˛ and ˇ. The BO value ˛ˇ is a quantitative measure of the strength of the bond between a pair of atoms. The deviation of the effective charge Q ˛ from that of the charge of the neutral atom Q0˛ is sometimes called the partial charge (PC) of the atom. Although BO is not a quantum observable, it is far more useful and informative than pure geometric
First-Principles Calculation
31.1.3 Physical Properties Calculation The calculation of the physical properties of glasses is the major motivation for using the first-principles method on appropriately constructed models. The physical properties can be roughly divided into two types. The first type comprises properties that can be directly linked to experimental measurements such as density and composition, mechanical, optical and spectral properties, melting point and viscosity. The second type includes properties that cannot be directly measured but are important in explaining the measured properties, such electronic structure and bonding, glass-forming
ability, hardness, brittleness and ductility. For new or hypothetical glasses, such calculations can be considered as theoretical predictions to provide guidance for experimental exploration and research. Properties that are particularly important for glasses include mechanical and optical properties. These will be demonstrated in the next section when the results for specific glasses are presented. First-principles calculations provide the electronic wave and vibrational wave functions from the electronic and dynamic calculations, respectively. In the case of ab initio molecular dynamics, temperature-dependent properties can be investigated, which is a distinct advantage over static calculations. Classical MD shares this important advantage. Optical properties are especially critical for insulating glasses. For first-principles calculation with the OLCAO method, it is usually carried out in the form of interband optical transition within the one-electron approach. The imaginary part of the complex dielectric function "2 is evaluated first according to "2 .¯!/ D
e2 m! 2
Z dk3 BZ
X
jh
n .k; r/j
n;l
i¯r j l .k; r/ij2 fl .k/ Œ1 fn .k/ (31.2) ı ŒEn .k/ El .k/ ¯! : In (31.2), k is the point within the Brillouin zone (BZ) of a crystal in the usual description [31.18]. Since models for glass structures must be large in order to reflect the lack of LRO, only one k-point at the zone center .0; 0; 0/ is needed. Here, E D ¯! is the photon energy, ` and n represent the occupied and unoccupied states, respectively, n .k; r/ is the wave function for the n-th state with energy En .k/ at Brillouin zone point k, and f .k/ is the Fermi distribution function. The momentum matrix elements h n .k; r/jPj l .k; r/i from the ab initio wave functions are explicitly included, which automatically imposes the quantum mechanical selection rule. The real part of the dielectric function "1 .¯!/ is obtained from the imaginary part "2 .¯!/ via the Kramers–Kronig transformation [31.71], and P represents the Cauchy principle value of the integral "1 .¯!/ D 1 C
2 P
Z1 0
s"2 .¯!/ ds : s2 ! 2
(31.3)
From the complex dielectric function, the refractive index n can be estimated p from the square root of "1 at zero frequency or n D "1 .0/. The energy loss function (ELF) is also obtained. Peaks in the ELF are usually
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Part D | 31.1
parameters such as BL or coordination numbers. BO values are not strictly dependent on the BL between two atoms, but are affected by the distribution of other nearby atoms. Since BO is calculated from quantum mechanical wave functions and its value is dominated by the distance of separation of the two atoms ˛ and ˇ, in the discussion for BO, BL is still used to designate the pair, with the understanding that the BO value is not strictly dependent on the distance, but on the nature of quantum mechanical interactions between the two atoms. The Mulliken scheme is basis-dependent, and therefore its application must be confined to a specific method and with well-defined basis sets. It is most effective when a more localized basis set is used. In the present work with the OLCAO method, the BO is calculated using a minimal basis (MB) set, whereas for the self-consistent potential and electronic structure calculation, a full basis (FB) set is used [31.49]. Although there are other more elaborate methods for calculating BO values [31.67], they are generally limited to simpler molecules or crystals and are based on numerical evaluation on dense 3-D mesh. They are less efficient for analyzing multicomponent complex glass structures. The summation of all BO pairs gives the total bond order (TBO). The total bond order density (TBOD) is obtained from the sum of all BO pairs, normalized by the cell volume. TBOD is a single parameter of the electronic structure that reflects the internal cohesion of complex materials. Both the TBO and the volume of the cell are important for the TBOD. The TBO and TBOD can be resolved into partial bond order (PBO) and partial bond order density (PBOD), respectively, for any specific groups of atomic pairs within the different parts of the model. The use of TBOD and PBOD as a quantum mechanical metric for characterizing interatomic bonding has been demonstrated recently in a variety of materials [31.68–70]. This is the main focus of this chapter on first-principles calculations and will be discussed in greater detail for specific cases in Sect. 31.2.
31.1 Methods and Approach
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Part D | 31.2
identified as plasmon peaks for the collective excitation of electrons in the solid 1 ELF.¯!/ D Im ".¯!/ "2 .¯!/ ; D 2 (31.4) "1 .¯!/ C "22 .¯!/
slightly deformed structures are then fully optimized, keeping their volume fixed. The six stress components ij are calculated for each applied strain "j , and the elastic coefficients Cij are obtained by solving the tensor equation ij D
X
Cij "j :
(31.5)
ij
where Im represents the imaginary part. Also very important are the mechanical properties of glasses, which can be obtained rather easily using classical MD. However, first-principles calculation of mechanical properties is much more efficient, since it is based on the fully relaxed equilibrium structure. The calculation is based on linear elastic theory, although nonlinear behavior can be modeled using an ab initio approach with special computational design, as will be illustrated in Sect. 31.2.2, Ni60 Nb40 . In this chapter, we describe the approach we adopted, which has been quite effective. The mechanical properties of glass models are calculated using a strain–stress analysis method [31.72, 73]. A small strain of 0:5 (compression) and C0:5% (expansion) is applied to each independent strain element of the glass model. The
From the calculated Cij and its inverse, the compliance tensor Sij , we obtain the bulk modulus .K/, Young’s modulus .E/, shear modulus .G/, and the Poisson ratio ( ) using the Voigt–Reuss–Hill (VRH) approximation for polycrystals [31.74–76]. The Voigt approach [31.74] assumes a uniform strain in the structure and gives the upper limit of bulk modulus and shear modulus. The Reuss approach [31.75] assumes a uniform stress distribution and gives the lower limit. The average of the two is generally known as the Hill approximation for polycrystals [31.76], and is typically used for comparison with the measured values. It should again be noted that for large glass models, first-principles calculation of mechanical properties using this approach requires a large number of computer cores from HPC.
31.2 First-Principles Calculation for Different Types of Glasses Glasses can be roughly divided into several classes: 1. Inorganic glasses such as silicate glasses, the most common of which is amorphous silicon dioxide (aSiO2 ) or its composites such as soda classes (alkalidoped glasses) 2. Metallic glasses (MG), which is the noncrystalline form of metals and alloys with atomic components of mostly transition metals (Zr, Cu, Ni, Ti, Pd, etc.) and metalloids (Al, P, Se, etc.) 3. Organic glasses, which comprise mostly polymers or peptides with constituent organic elements C, O, N and H, intimately related to organic compounds and biological materials. More recently, a hybrid form of inorganic/organic glasses has emerged, with some fascinating properties and potential applications including zeolitic imidazolate frameworks or ZIF [31.77], a subclass of metal–organic frameworks (MOF) [31.78], which are topologically isomorphic with many different forms of zeolite. An even more general form of organic glasses is the new class of covalent organic frameworks (COF), where the covalently bonded atoms form framework structures [31.79]. In this chapter for first-principles calculations, we will focus on the inorganic glasses,
metallic glasses and recent results on a specific model of ZIF glasses [31.80].
31.2.1 Insulating Glasses The most prominent class of insulating glasses is silicate glass. Here we present some representative results of first-principles calculations for pure amorphous SiO2 (a-SiO2 ) glass, a-GeO2 glass, and their composites, using a large, near-perfect continuous random network (CRN) model, with no over- or under-coordinated Si or O atoms and reasonable ring statistics. Related modeling on alkali-doped a-SiO2 has been attempted [31.81, 82], with some work still in progress. The alkali ions break the silicate network, resulting in non-bridging oxygen (NBO), and making the multicomponent glasses even more complex in structure. It should be noted that Al2 O3 , CaO2 , B2 O3 , P2 O5 are also very good glass formers for the insulating glasses and have been studied extensively [31.83–85], albeit less so with first-principles methods. a-SiO2 Back in 1981, I reported the construction of an interesting a-SiO2 model with 162 atoms (54 SiO2 molecules)
First-Principles Calculation
low-energy vibrational mode was identified as originating from a branched chain of six Si and five O atoms approximately 13 Å in length. This gives an estimation of the range of atomic movement in the low-energy vibrations. More recently, the full optical and mechanical properties of this large glass model were obtained for the first time [31.90]. The most recent study focuses on densification of the model under homogeneous compression up to a pressure of 80 GPa [31.91]. By assessing a full spectrum of properties including atomic structure, bonding characteristics, effective charges, bond order values, electron density of states, localization of wave functions, elastic and mechanical properties, and interband optical absorption at each pressure, we reveal the pertinent details of this remarkable glass model under pressure. They all confirm the main conclusion that amorphous-to-amorphous phase transformation from a low-density to a high-density state occurs at pressures between 20 and 35 GPa in this nearly ideal a-SiO2 network model. The phase transformation is rooted in the change in bonding characteristics from a mixed ionic and covalent type at low pressure to a highly covalent type under high pressure, with concomitant variations in the coordination number. Figure 31.2 shows the variation in density with pressure, providing evidence of the transition from low density to high density at around 2035 GPa, and is in good agreement with reported experimental data [31.92–94]. Figure 31.3 shows the change in the BOD for Si–O bonds as a function of pressure in three ways: 'HQVLW\ JFP± > @ > @ > @ > @
b
c
a
Fig. 31.1 Tetrahedral sketch of the 1296-atom model of a-
SiO2
3UHVVXUH *3D
Fig. 31.2 Density as a function of pressure of a-SiO2 on densification [31.91]. Experimental data are from [31.92– 94]. Reproduced from [31.91] with permission from the PCCP Owner Societies
1101
Part D | 31.2
and with periodic boundary conditions [31.86]. This model has near-perfect local bonding, with no overor under-coordinated Si or O atoms, and a realistic distribution of ring structures. Such a near-perfect CRN model is extremely valuable and very difficult to construct due to the constraints imposed on strong directional covalent Si–O bonds across the periodic boundary, and would be equally difficult to obtain using classical MD simulations. This relatively small model contains mostly five- and six-membered rings (30 and 32%, respectively), a considerable number of seven- and eight-membered rings (18 and 17%), a small presence of nine-membered rings (3%) and no fourmembered rings. The model was originally obtained from a carefully built periodic model of amorphous Si [31.87] by inserting O atoms at the middle of the Si–Si bonds and rescaling the cell size to fit the density of silicate glass before relaxation by a simple Keatingtype potential [31.86]. Over the years, this 162-atom a-SiO2 model has been enlarged by a 222 extension, further refined using improved potential, and used as a representative intrinsic model for a-SiO2 of sufficiently large size (1296 atoms) to calculate many different properties [31.88– 91]. Figure 31.1 is a sketch of this periodic 1296-atom a-SiO2 model, which retains the same topology as the original 162-atom model. The model has been used to study properties including structure, coordination and bonding analysis, as well as the localization index (LI) of the band edge states etc. [31.88]. It was also used for phonon calculation after further refinement by four types of empirical potentials [31.91]. In particular, the
31.2 First-Principles Calculation for Different Types of Glasses
Part D
Glass Modelling
Part D | 31.2
(a) A linear plot of density versus pressure (b) A 2-D plot of Si–O BO distribution at different pressures depicted by color; also shows that the Si– O BO only roughly scales with BL (c) A 3-D plot of the same data as in (b) but a clearer illustration of the pressure dependence. These plots vividly demonstrate the innovative use of BO values and BOD in describing the complex process of amorphous-to-amorphous transition for a-SiO2 in the CRN model. Similar plots will be shown later in Sect. 31.2.2, Zrx Cu1x and Zrx Cuy Alz , for metallic glasses. The refractive index of the glass model as a function of the pressure is reported for the first time. The calculated real and imaginary parts of the dielectric function (" D "1 C i"2 ) for the a-SiO2 model at zero pressure is shown in Fig. 31.4. The "2 curve is shifted downward by 2:37 eV to match the three observed excitation peaks [31.95]. The calculation does not account for the presence of the excitonic peak (shaded) which is observed in both crystalline and amorphous SiO2 . The refractive index n will be affected by the presence of the excitonic peak in "2 .!/. To ascertain the difference in n due to the omission of the excitonic peak, we added a simulated Gaussian peak that has the same width and position as the experimentally observed peak, to mimic the effect of the excitonic peak (shaded gray peak in Fig. 31.4). The modified "2 .!/ and the subsequent "1 .!/ give a refractive index of 1:51, slightly higher than n D 1:46 without the simulated excitonic peak, but falling within the acceptable range of n of a-SiO2 . The calculation does not account for the underestimation of the bandgap due to the typical deficiency in methods based on DFT. If this effect is also taken into account, the calculated refractive index will be reduced slightly, giving a value closer to the experimental value of 1:458 [31.97]. Thus, it is possible to account for the excitonic effect in insulators by adding a simulated peak to the results from a conventional first-principles calculation based on one-electron theory, without invoking the more complicated many-body corrections. Additional details can be found in [31.49, 90, 91, 96]. a-GeO2 With the availability of the large CRN model for aSiO2 and the results for many of its properties using first-principles calculations, it is natural to extend it to another important insulating glass, a-GeO2 , by simply replacing Si with Ge, fully relaxing the model again, and repeating the calculation of its properties [31.96]. The application of germania glass, especially in fiber optics, has been fairly well documented [31.98]. The a-GeO2 model has the same topology as the a-SiO2 model, but their properties differ. The calculated TDOS
a)6L± 2ERQGRUGHUGHQVLW\
3UHVVXUH *3D
b)6L± 2ERQGRUGHU
*3D *3D *3D *3D *3D *3D *3D
c)
6L±2ERQGOHQJWK c *3D *3D *3D *3D *3D *3D *3D
6L ± 2 ERQ GRUG HU
3UHVVXUH *3D
1102
WK c HQJ O RQG E ±2 6L
Fig. 31.3a–c Bond order versus bond length in the densification of the 1296-atom model of a-SiO2 in (a) linear, (b) 2-D and (c) 3-D, plots. Reproduced from [31.91] with
permission from the PCCP Owner Societies
and PDOS for a-GeO2 and a-SiO2 are compared in Fig. 31.5a and b, respectively. Compared with the crystalline phase of c-GeO2 in the quartz structure, the DOS
First-Principles Calculation
31.2 First-Principles Calculation for Different Types of Glasses
imaginary parts of the dielectric function of a-SiO2 . Experimental data from [31.95]. Reprinted from [31.96] with permission from Elsevier
İ İ ([SW
([FLWRQLFSHDN
$GGHGWRPLPLF H[FLWRQLFSHDN
a)'26 VWDWHVH9
(QHUJ\ H9
Fig. 31.5a,b
b)'26 VWDWHVH9
7RWDO
7RWDO
2S
2S
2V
2V
*HG
6LG
*HS
6LS
± ± ± ±
*HV
± ± ± ±
6LV
(QHUJ\ H9
for a-GeO2 is broadened because of the variations in SRO and the lack of LRO in a-GeO2 [31.96]. Figure 31.5 reveals the difference in the electronic structure of a-GeO2 and a-SiO2 . The calculated bandgap of
Calculated TDOS and orbital-resolved PDOS of (a) a-GeO2 and (b) a-SiO2 . Reprinted from [31.96] with permission from Elsevier
(QHUJ\ H9
2:42 eV for a-GeO2 is much smaller than that for a-SiO2 (5:37 eV) and is also slightly smaller than the bandgap for c-GeO2 (2:66 eV). Both Si 3d orbitals and Ge 4d orbitals are empty orbitals; the presence of Si 3d and Ge
Part D | 31.2
Fig. 31.4 Calculated real and
İİ
1103
1104
Part D
Glass Modelling
Part D | 31.2
a)&RXQWV *H ± 2ERQGRUGHU b)&RXQWV 6L± 2ERQGRUGHU
Fig. 31.6a,b Comparison of the bond order distribution in (a) a-GeO2 and (b) a-SiO2 . Reprinted from [31.96] with
permission from Elsevier
4d components in the PDOS in the occupied valence bands in Fig. 31.5a,b reflects significant interaction of the d orbitals in Si and Ge with O. The slight differences between the electronic structures of these two glasses simply show that Ge is a larger atom with occupied
semi-core 3d orbitals, whereas there are no occupied d orbitals in Si. In Fig. 31.6, we compare the BO distributions between a-SiO2 and a-GeO2 , showing that a-SiO2 has stronger bonding than a-GeO2 , as reflected in the larger BO values, mainly because of the shorter Si–O bonds. Both plots show approximate Gaussian-type distribution as a result of a near-perfect CRN structure in both models. Figure 31.7 shows the calculated imaginary part of the dielectric function in a-GeO2 , which is quite different from that of a-SiO2 (Fig. 31.4). The blue dotted line in Fig. 31.7 represents the experimental data [31.99], which shows very good agreement with the calculation. The experimental "2 .!/ curve is shifted by 1:8 eV to the left to align with the calculated peak 1 in order to account for the gap underestimation. The "2 .!/ shows a steep rise at the threshold 2:7 eV, and two major peaks 1 (5:2 eV) and 2 (9:4 eV) match well with the measured data reported by Pajasová’s [31.99, 100]. The calculated spectrum also shows two minor peak features 3 and 4 at 10:5 and 12:7 eV, respectively, which are not sufficiently resolved in the experimental curve. There is no excitonic peak in a-GeO2 as in a-SiO2 , and it could be buried within the conduction band region [31.101]. Thus far, we have not presented any results on the mechanical properties of the 1296-atom model for a-SiO2 and a-GeO2 . They will be discussed in the following section as the end members (x D 1 and 0) of the expanded study on the mixture series (a-SiO2 )x (aGeO2 )1x of the two glasses. (a-SiO2 )1x (a-GeO2 )x With the models of a-SiO2 and a-GeO2 described above, it is natural to consider the mixture of these two
İİ İ İ ([SW
Fig. 31.7 Calculated real and imag-
inary parts of the dielectric function of a-GeO2 . Experimental data from [31.99]. Reprinted from [31.96] with permission from Elsevier
(QHUJ\ H9
First-Principles Calculation
x
a)
Three sizes of spherical particles were investigated, which revealed that particle size does affect the properties of the immersion models. However, the difference between confined particles and the extended region of the medium is relatively small [31.102]. This type of simulation provides deep insight into the properties of the mixture and nanocomposites of a-SiO2 and a-GeO2 glasses. Figure 31.9 shows the calculated refractive index n of (a-SiO2 )1x (a-GeO2 )x as a function of x, together with available experimental data. The refractive index is almost linear in x, but the slope of variation with x is steeper than the experimental data [31.103–105]. This is attributed to the fact that the calculated n for a-GeO2 is closer to the experimental data due to the smaller gap than that of a-SiO2 , which has an excitonic peak near the CB edge.
x
b
x
b a
c
b a
c
x
a
c
a
c
c
a
x
b
c
b
x
b
x
b a
a
c
b)
b
c
b a
c
b a
c
b a
c
b a
c
b a
c
a
Fig. 31.8 (a) Polyhedral structures of part I for (a-SiO2 )1x (a-GeO2 )x glass, 0 x 1. (b) Two-dimensional and three-dimensional illustration of six models of part II for spherical particle inclusion of one glass into the medium of the other glass. Reprinted from [31.102]
1105
Part D | 31.2
models [31.102]. Two types of mixture models were designed. In the first type, or part I, Si1x Gex O2 models are obtained by homogeneous random substitution of Si by Ge with x ranging from 0 to 1. Figure 31.8a shows a sketch of these models, including the end members of x D 0 (a-SiO2 ) and x D 1 (a-GeO2 ). The structural, electronic, mechanical and optical properties were obtained for the series [31.102]. The variations in the properties with x are analyzed and critically compared with available experimental data. The second type, or part II, investigates the properties of particle inclusion instead of homogeneous substitution for x D 0:5 (50% a-SiO2 and 50% a-GeO2 ). Six different models of particle immersion are constructed to test the difference in properties due to inclusion of spherical particles of one glass in the medium of the other glass (Fig. 31.8b).
31.2 First-Principles Calculation for Different Types of Glasses
1106
Part D
Glass Modelling
Part D | 31.2
31.2.2 Metallic Glasses
n *H2 ±VSKHUH 6L2 ±VSKHUH *H2 ±VSKHUHV 6L2 ±VSKHUHV *H2 ±VSKHUHV 6L2 ±VSKHUHV 5HI>@ 5HI>@ 5HI>@
x
Fig. 31.9 Calculated refractive index (n) as a function of x for (a-SiO2 )1x (a-GeO2 )x glass. The inset shows the magnified portion of the six models of part II, along with the data for x D 0:5 of part I. (See [31.102] for details)
The calculated elastic and mechanical properties of the Si1x Gex O2 (part I) models are listed in Table 31.1. This includes the results for the end members a-SiO2 and a-GeO2 . Only very limited experimental data are available for comparison. The Pugh modulus ratio of the shear to bulk modulus (G=K) is used as an indicator of whether the material is more brittle or ductile [31.108]. Table 31.1 shows that as x increases from 0 (a-SiO2 ) to x D 1 (a-GeO2 ), the G=K ratio decreases, or the glass gradually becomes more ductile. This conclusion is quite important, since both glasses are used as optical fibers. More detailed discussion can be found in [31.102].
Metallic glasses (MG) are a unique class of amorphous materials discovered only a little over a half-century ago by fast cooling of molten glass from above the melting temperature [31.109, 110]. Extension of MG to bulk metallic glasses (BMG) [31.111, 112] leads to an expanded array of applications, mainly due to the absence of grain boundaries in BMG [31.113, 114]. There are many outstanding reviews on MG and BMG [31.115– 119]. The first-principles calculation for MG using the early version of the OLCAO method can be traced back more than 30 years [31.120–129]. There have been relatively few attempts by other research groups to use first-principles calculations for the electronic structures of MG, because of the need for reasonably large periodic models. Most such calculations have used clusters of different geometric configurations to illustrate a particular point. These models generally ignore the effects introduced by the cluster surfaces, which could lead to spurious conclusions as to the electronic structure. Our early calculations also used smaller models and a less accurate method, but the models were periodic. They provided much insight on different types of MG and were quite pioneering in those days. Research on MG and BMG was revived about 6 years ago because of our ability to do much larger calculations, and the maturity and versatility of the OLCAO method [31.49]. In this section, we present some preliminary results on binary Zr-Cu and ternary Zr-Cu-Al BMG with periodic models of 1024 atoms. The main goal is to advocate the use of TBOD as a useful metric in the study of BMG, and to show the inadequacy in using the geometric parameters for structural characterization of BMG within prevailing theories such as free volume theory [31.130] and in assigning polyhedral units using a Voronoi tessella-
Table 31.1 Elastic modulus in units of GPa: Young’s modulus E, bulk modulus K and shear modulus G, Pugh’s modulus
.G=K/, Poisson’s ratio ( ) and six elastic constants Cij (GPa) (a-SiO2 )1x (a-GeO2 )x glass, 0 x 1 a-Si1x Gex O2 C11 C22 C33 C44 C55 C66 E K G
G=K a b
Makishima et al. [31.106] Bridge et al. [31.107]
xD0 102:16 89:00 101:45 34:97 40:68 38:33 88:95, 73a 44:28, 36:1a 38:17, 31:4a 0:165, 0:162a 0:862
x D 0:2 93:33 83:72 89:32 32:32 35:62 32:59 79:76 42:31 33:63 0:186 0:795
x D 0:4 80:94 72:75 81:23 28:68 31:91 29:77 70:86 38:08 29:78 0:19 0:782
x D 0:5 77:28 67:13 76:64 27:67 31:93 29:39 68:03 36:18 28:66 0:187 0:792
x D 0:6 72:67 65:01 70:05 24:72 29:7 26:8 63:01 34:22 26:4 0:193 0:771
x D 0:8 64:03 58:73 66:44 22:93 27:88 24:38 57:73 31:79 24:11 0:197 0:758
xD1 56:53 51:47 59:77 19:84 23:5 20:45 49:85, 43:3b 28:75, 23:9b 20:58, 18:1b 0:211, 0:192b 0:716
First-Principles Calculation
Zrx Cu1x and Zrx Cuy Alz We will use the binary Zrx Cu1x and ternary Zrx Cuy Alz as prototypical BMG to test some of our hypotheses related to the atomic-scale structures in MG. These two BMG systems have been well studied [31.132–148], producing a large collection of experimental data and very diverse conclusions. As such, they are well suited for use as benchmark systems upon which to test new concepts and approaches regarding the theory of MG. Despite several years of intense effort, most of the results presented here have not yet been published and are considered preliminary. In ab initio DFT calculations, the size of the BMG model has been limited to about 1000 atoms at most. We adopt a two-step approach to construct a series of 1024-atom Zrx Cu1x periodic models for Zr concentrations ranging from 32 to 55%. As will be explained later, the goal of this study
is to test the hypothesis of using TBOD as a parameter that can be correlated with the glass-forming ability (GFA) in Zrx Cu1x based on experimental data of film density measurements in the same range as a benchmark [31.149]. We start with classical MD simulation using LAMMPS [31.150] and the embedded-atom method (EAM) with well-established EAM potentials [31.24]. The models are annealed from 2000 to 300 K with long multistage MD steps of up to several hundred picoseconds. The MD-generated models are then fully relaxed using VASP [31.39], with no constraints on cell volume or shape (i. e., both volume and atomic position changes). The construction of these models is very tricky, and there is no assurance that the final relaxed structures will be close enough to those in real samples to produce accurate electronic structures. We have thus far constructed 17 Zrx Cu1x models for initial assessment with x ranging from 0:34 to 0:54, which is roughly the same as in [31.149]. In Table 31.2, the calculated total bond order and TBOD from the electronic structure results are listed, along with the volume and mass density of these models. The test for the glass-forming ability (GFA) using these data for Zrx Cu1x will be discussed after we first present some selected electronic structure results and the reasons for using TBOD to test GFA. To more carefully explore the concept of using TBOD to describe the internal bonding in BMG, we have also extended our first-principles calculation from the binary Zrx Cu1x to the ternary Zrx Cuy Alz system. It is well known that the inclusion of Al drastically
Table 31.2 First-principles calculation incl. total bond order (TBO) and total bond order density (TBOD) of 17 Zrx Cu1x
models (preliminary results) ID 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
Name Zr328 Cu696 Zr343 Cu681 Zr358 Cu666 Zr374 Cu650 Zr389 Cu635 Zr404 Cu620 Zr420 Cu604 Zr435 Cu589 Zr451 Cu573 Zr466 Cu558 Zr481 Cu543 Zr497 Cu527 Zr512 Cu512 Zr527 Cu497 Zr543 Cu481 Zr558 Cu466 Zr369 Cu655
Atomic % Zr 32:03 33:50 34:96 36:52 37:99 39:45 41:02 42:48 44:04 45:51 46:97 48:54 50:00 51:46 53:03 54:49 36:04
Cu 67:97 66:50 65:04 63:48 62:01 60:55 58:98 57:52 55:96 54:49 53:03 51:46 50:00 48:54 46:97 45:51 63:96
Volume (Å3 ) 16 044:276 16 211:666 16 385:371 16 571:365 16 738:197 16 882:613 17 068:420 17 278:339 17 465:693 17 585:667 17 755:120 17 955:229 18 144:629 18 270:668 18 461:494 18 635:664 16 516:317
Density (g cm3 ) 7:674 7:735 7:599 7:558 7:524 7:500 7:462 7:412 7:373 7:362 7:331 7:290 7:252 7:240 7:205 7:174 7:569
TBO
TBOD
520:689 521:655 522:269 523:653 524:552 525:526 526:340 527:169 527:359 529:821 530:475 530:528 531:594 534:421 534:002 535:470 522:783
0:03245 0:03218 0:03187 0:03160 0:03134 0:03113 0:03084 0:03051 0:03019 0:03013 0:02988 0:02955 0:02930 0:02925 0:02893 0:02873 0:03165
1107
Part D | 31.2
tion scheme [31.131] as the basic building blocks for MG [31.116]. Also in this section, results are presented for another MG Ni60 Nb40 in conjunction with experimental work on elastic deformation to demonstrate the applicability of first-principles modeling on mechanical properties for MG. Lastly, we present the work on Vitreloy (Zr41:2 Ti13:8 Cu12:5 Ni10 Be22:5 ), a multicomponent BMG, where no electronic structure calculations have ever been attempted. Multicomponent BMG are much easier to vitrify than BMG with fewer components. The focus here is to demonstrate the necessity of using AIMD to build structural models for Vitreloy and the effectiveness of the OLCAO method in describing the electronic structure in such complex systems.
31.2 First-Principles Calculation for Different Types of Glasses
1108
Part D
Glass Modelling
Part D | 31.2
changes the structure and properties of the Zr-Cu BMG [31.151]. Twenty-two such models for Zrx Cuy Alz are currently under investigation, with some preliminary results listed in Table 31.3. We now select two representative models, Zr50 Cu50 and Zr50 Cu40 Al10 , from the above lists of binary Zrx Cu1x and ternary Zrx Cuy Alz systems for presenting the first-principles electronic structure results. Figure 31.10 shows a ball-and-stick illustration of these two models. In Fig. 31.11, we plot the calculated BO versus the distance of separation, or the so-called bond length (BL), for every pair of atoms in the two models within
a distance of 4:5 Å. It is clear that there is a large distribution of BO values for a particular value of BL. Conversely, there is a large range of BL for a specific value of BO. In order words, the interatomic bonding in MG cannot be precisely defined in terms of a definitive BL, a geometric parameter. Any theory based on such parameters for interpretation is highly questionable. Figure 31.11 also shows that the general trend wherein BO values decrease with an increase in the so-called BL is true, but atomic pairs with separations well beyond the generally accepted BL contribute substantially to the TBO and cannot be ignored. On the other hand, the TBO value for the whole system normalized by the cell vol-
Table 31.3 First-principles calculation incl. total bond order (TBO) and total bond order density (TBOD) of 22 Zrx Cuy Alz
models (preliminary results) ID 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
Name Zr512 Cu512 Al0 Zr512 Cu410 Al102 Zr512 Cu430 Al82 Zr491 Cu492 Al41 Zr471 Cu471 Al82 Zr450 Cu451 Al123 Zr435 Cu435 Al154 Zr419 Cu451 Al154 Zr435 Cu461 Al128 Zr462 Cu408 Al154 Zr419 Cu400 Al205 Zr538 Cu435 Al51 Zr486 Cu512 Al26 Zr461 Cu512 Al51 Zr461 Cu486 Al77 Zr614 Cu307 Al103 Zr563 Cu358 Al103 Zr614 Cu358 Al52 Zr563 Cu410 Al51 Zr410 Cu512 Al102 Zr666 Cu307 Al51 Zr410 Cu563 Al51
Atomic % Zr Cu 50 50 50 40 50 42 48 48 46 46 44 44 42:5 42:5 40:9 44:1 42:5 45 45:1 39:8 40:9 39:1 52:5 42:5 47:5 50 45 50 45 47:5 60 30 55 35 60 35 55 40 40 50 65 30 40 55
Al 0 10 8 4 8 12 15 15 12:5 15:1 20 5 2:5 5 7:5 10 10 5 5 10 5 5
a)
b)
b
b
c
a
c
a
Volume (Å3 ) 18 144:629 18 504:271 18 371:668 17 965:541 17 893:246 17 048:541 17 730:644 17 507:915 17 590:756 18 024:009 17 606:786 18 590:275 17 879:205 17 661:299 17 752:031 19 671:835 19 052:541 19 466:063 18 871:133 17 246:186 20 050:613 17 730:644
Density (g cm3 ) 7:252 6:777 6:891 7:132 6:971 7:262 6:694 6:737 6:838 6:654 6:524 6:976 7:205 7:142 7:017 6:609 6:702 6:838 6:933 6:999 6:762 7:260
TBO
TBOD
531:594 549:746 546:914 538:808 545:369 540:796 559:672 563:697 557:422 561:813 575:372 542:155 536:633 541:580 546:519 552:963 553:255 546:416 543:664 550:962 549:074 540:830
0:02930 0:02971 0:02977 0:02999 0:03048 0:03172 0:03157 0:03220 0:03169 0:03117 0:03268 0:02916 0:03001 0:03066 0:03079 0:02811 0:02904 0:02807 0:02881 0:03195 0:02738 0:03172
Fig. 31.10a,b Illustrative sketch of the Zr50 Cu50 (a) and Zr50 Cu40 Al10 (b). Red: Zr; green: Cu; black: Al
First-Principles Calculation
&X± &X =U ±=U &X±=U %RQGOHQJWK c
c)
b)%RQGRUGHU
&X± &X =U ± =U &X ± =U &X ± $O =U ± $O $O ±$O %RQGOHQJWK c
d)
&X±&X =U±=U &X±=U
%
&X±&X =U±=U &X±=U &X±$O =U±$O $O±$O
% %
%
% % %
% 7RWDOERQGRUGHUGHQVLW\
%
7RWDOERQGRUGHUGHQVLW\
Fig. 31.11a–d BO versus BL in Zr50 Cu50 (a) and Zr50 Cu40 Al10 (b). Percentage of the BO components in Zr50 Cu50 (c) and Zr50 Cu40 Al10 (d)
ume or the TBOD is a valid parameter for characterizing the internal cohesion of the glass structure. It is also quite obvious from Fig. 31.11 that the addition of Al to the Zr-Cu system changes its properties, mainly because of the stronger BO of the Cu-Al pairs and at shorter BL. The lower part of Fig. 31.11 shows the contributions to TBOD from different atomic pairs. The above assertion of the inappropriateness of using geometric parameters to characterize the structure of MG can be further illustrated by plotting the distribution of spherical clusters with specific numbers of atoms enclosed with different BL cutoffs (radius of the sphere) in Fig. 31.12 for Zr50 Cu50 . The cluster radius of 3:5 Å has a distribution with a maximum at an atomic coordination of 12, close to the icosahedral structure that has been advocated by many researchers in MG. But Fig. 31.12 shows that the distribution of cluster size (total number of bonds in the cluster) according to the ill-defined coordination number for the cluster varies to
a high degree with the radius of the sphere or the cutoff distance, which cannot be precisely defined, as shown in Fig. 31.11. The histogram distribution also depends on the central atom (Zr- or Cu-centered). Moreover, it shows that even for a given radius, clusters of different sizes can coexist. Obviously, the situation in ternary Zrx Cuy Alz would be even more complicated than in the binary Zrx Cu1x . The notion of icosahedra or similar polyhedral clusters to describe the structural units in BMG is not substantiated by the results of first-principles calculations. Figure 31.13 is a snapshot of the atomic positions in Zr50 Cu40 Al10 , showing the locations of Zr, Cu and Al atoms in the spherical enclosure centered on a Cu atom. It clearly accentuates the lack of evidence of any icosahedral units or similar units based on the geometric length as a parameter in BMG, in strong contrast to the nature of interatomic bonding in inorganic glasses as discussed in the previous section.
1109
Part D | 31.2
a)%RQGRUGHU
31.2 First-Principles Calculation for Different Types of Glasses
1110
Part D
Glass Modelling
Part D | 31.2
a)7RWDOERQGV
b)7RWDOERQGV =U±=U =U±&X c
c
c
c
&RRUGLQDWLRQQXPEHU
=U±&X &X±&X c
c
c
c
&RRUGLQDWLRQQXPEHU
Fig. 31.12a,b Cluster size distribution in Zr50 Cu50 : Zr-centered (a), Cu-centered (b) Fig. 31.13 2-D projection of a Cu-
centered cluster with different radii
c c
c c
One of the hotly debated topics in BMG is its glassforming ability (GFA), which involves complex thermodynamic issues and many other factors related to interatomic interactions. The GFA of a BMG simply reflects its resistance to crystallization. We would like to use the results from the first-principles calculation to test the hypothesis that it may correlate with the TBOD as discussed above. In order to validate or refute this hypothesis, we undertake an ambitious task of model-
ing and calculating the TBOD for the 17 samples of Zrx Cu1x listed in Table 31.1. The construction of the models follows a sequence of steps starting with classical MD, followed by full relaxation using VASP as discussed earlier. The density variation in the 17 models is shown in Fig. 31.14, which indicates that the density obtained from the initial MD simulation underestimates the measured data, and ab initio relaxation significantly improves the density, bringing it into closer agree-
First-Principles Calculation
'HQVLW\ JFP±
31.2 First-Principles Calculation for Different Types of Glasses
9$63UHOD[HG ,QLWLDO0' > @
Part D | 31.2
7%2'
=U DW
=U
Fig. 31.15 Third-order polynomial fit of data for 17
Zrx Cu1x BMG models
Fig. 31.14 Density plot of 17 Zrx Cu1x models
ment. However, the data cannot faithfully replicate the measured density fluctuation used to explain the composition dependence of GFA in Zrx Cu1x [31.149]. We propose a hypothesis that the measured data for GFA in Zrx Cu1x may be explained by the TBOD, which describes the interatomic interactions at the quantum level, condensed into a single parameter, TBOD. TBOD includes both the structural aspect of the MG through its density and the interatomic interaction through BO distribution, and therefore reflects the internal cohesion of the glass that may correlate with the GFA, at least indirectly. We used the preliminary TBOD values for the 17 models listed in Table 31.2 and fit the data as a function of x to a third-order polynomial, which provides the general trend for the dependence of TBOD on x. This is shown in Fig. 31.15. Our hypothesis states that the deviation from this general trend at a specific composition is an indicator of higher or lower GFA. Figure 31.15 shows that there are deviations of individual points with a specific Zr concentration from the fit. This preliminary result is used to test the above hypothesis by comparing the deviations in TBOD with the measurement of the film thickness using a microcantilever with a fixed support [31.149]. The authors of [31.149] contend that the GFA in Zrx Cu1x is reflected in the density of the glass, hence the film thickness. Three compositions with Zr concentrations of 36, 44 and 49% have maximum film thickness, corresponding to maximum density, and are identified as a signature of high GFA. In Fig. 31.16, we show a comparison of the deviation of individual TBOD from the fit in Fig. 31.15 with experimental data, which has fairly large error bars [31.149].
1111
=U
Fig. 31.16 Qualitative comparison of GFA from experi-
mental film thickness (circles) and predicted by TBOD hypothesis (squares) as a function of Zr content. The numbers correspond to ID numbers in Table 31.2
The three peak structures are reproduced, but not at the exact composition. These results are encouraging, showing some possible correlation between GFA and TBOD in Zrx Cu1x . We are in the process of refining our calculations for higher accuracy, especially in the final relaxed structure, since they control the density of the models. It must be stressed that the above results for Zrx Cu1x and Zrx Cuy Alz are preliminary in nature, and research is still ongoing in order to further improve the accuracy. We expect it to be completed soon, assuming sufficient computer resources become available. We also plan to include the calculations of mechanical properties of these MG series and expand the list in
1112
Part D
Glass Modelling
Part D | 31.2
Zrx Cuy Alz such that we will have sufficient data to construct ternary maps to identify the best composition for specific properties, especially the shear modulus and the Poisson ratio. The bond order concept we proposed to characterize the structure of BMG is an important step forward in the theory of BMG. Pure geometric analysis of the structure of BMG is inadequate. This is very different from inorganic glasses discussed in Sect. 31.2.2, Zrx Cu1-x and Zrx Cuy Alz . Ni60 Nb40 First-principles calculation has been applied on large metallic glass models to study the deformation behavior of Ni60 Nb40 MG under tensile strain in conjunction with experimental measurements [31.152]. The goal is to answer the question of why Ni60 Nb40 MG films have a high elastic strain limit. Obviously, many factors contribute to its answer. We largely restrict our discussion in this section to the computational and modeling part of the study using the first-principles method. Ab initio simulations can validate some of the issues raised and provide the necessary insights. In addition, the electronic structure and mechanical properties of Ni60 Nb40 MG are calculated for the first time using first-principles methods, which is not part of reference [31.115]. Ultimately, all physical properties of any material are intimately related to its electronic structure. Similar to the procedures described for Zrx Cu1x and Zrx Cuy Alz in the previous section, we first build a periodic cubic box containing 1024 atoms (614 Ni and 410 Nb) to simulate the heating and cooling processes using LAMMPS [31.150] with EAM potential. The sample is heated to 2400 K and then quenched to 300 K at a cooling rate of 1011 K s1 with a constant pressure and temperature (NPT ensemble). The obtained configuration is then fully relaxed using VASP with no constrictions on cell shape or atomic positions, similar to the simulations for the Zr-Cu and Zr-CuAl BMG series described earlier. The relaxed model with cell parameters of a D 24:362 Å, b D 24:341 Å, c D 24:096 Å, ˛ D 89:53ı , ˇ D 89:87ı and D 90:03ı has a final density of about 8:571 g cm3 , in good agreement with the experimental value [31.153] of 8:5 ˙ 0:05 g cm3 . The electronic structure of this relaxed Ni60 Nb40 model is calculated using the OLCAO method [31.49]. Figure 31.17 shows the calculated total and partial DOS for the Ni60 Nb40 model under zero stress. The DOS consists of two rather broadened peaks. The one below the Fermi level EF centered at 2:0 eV is from Ni 3d orbitals, and the one at 2:4 eV above EF originates from Nb 4d orbitals. The Fermi level is located at the sharp slope in the DOS, with some evidence of a local minimum in the vicinity of EF . As is the case in many other
'26 VWDWHVH9FHOO 7RWDO 1L 1E
± ±
±
±
±
(QHUJ\ H9
Fig. 31.17 Calculated total and partial DOS of Ni60 Nb40
under zero stress
MG systems, we are unable to correlate the electronic structure of Ni60 Nb40 with other measured properties. An obvious target is to calculate the TBOD and ascertain its dependence on the strain, which can establish a connection between the TBOD and mechanical properties discussed below. The elastic coefficients and mechanical properties of this fully relaxed model are calculated using a strain-versus-stress approach [31.72] to obtain the following bulk mechanical properties: bulk modulus K D 192:7 GPa, shear modulus G D 43:6 GPa, Young’s modulus E D 121:7 GPa, and average Poisson ratio D 0:395 based on the Voigt–Reuss–Hill (VRH) approximation [31.76]. These values are comparable to the experimental data of K D 174:9 GPa, G D 48:2 GPa, E D 132:0 GPa and D 0:37 reported for a Ni50 Nb50 MG [31.154]. The model is then subjected to successive extension in the x direction, with 1% elongation in each step. At each step, the model is fully relaxed using VASP, and the cell dimensions in the other two directions and the volume are adjusted according to the directionally dependent Poisson ratio. The stress at each step and the atomic coordinates of the model are then recorded. The procedure of using the adjusted Poisson ratio in uniaxial tensile simulation for deformation behavior is extremely important for obtaining reliable results, since even at a size of 1024 atoms, the model is still considered small. We have previously used a similar procedure to study the tensile behavior of intergranular glassy films (IGF) in polycrystalline Si3 N4 [31.155], crystalline B4 C2 [31.156] and bioceramic crystal hydroxyapatite [31.157, 158]. The Ni60 Nb40 model, after extension to a strain of 7%, is then released (unloading) in stepwise fashion,
First-Principles Calculation
Vitreloy (Zr41:2 Ti13:8 Cu12:5 Ni10 Be22:5 ) The last project on metallic glasses we will discuss is on Vitreloy [31.160]. Vitreloy is a special class of 6WUHVV *3D
8Q
GL
QJ
/R
DG
LQ
J
D OR
6WUDLQ
Fig. 31.18 Stress–strain curve from VASP simulation for the Ni60 Nb40 upon loading and unloading (after [31.152])
multicomponent BMG having some of the most exciting properties, including resistance to a corrosive environment, unique mechanical properties and high tolerance to deformation. It can be easily molded into complex shapes, making it ideal for 3-D printing, at a significantly reduced cost. However, the nature of its electronic structure and interatomic bonding is totally unknown, because accurate models for Vitreloy are not available using classical MD, due to the unavailability of reliable potentials. Most of the existing data on Vitreloy were obtained by costly trial and error in the laboratory. We initiated perhaps the only firstprinciples calculation of the most well-known Vitreloy, Zr41:2 Ti13:8 Cu12:5 Ni10 Be22:5 (also known as Vit1), first introduced by Peker and Johnson in 1993 [31.161]. Vitreloy typically has more than five atomic species of vastly different sizes and a wide range of composition ratios. In Vit1, the atomic radius of Zr is 84% larger than that of Be. Vit1 has extraordinarily high GFA, with a low critical cooling rate (1 K s1 ) and superior mechanical properties [31.162]. A large body of experimental work has been undertaken for Vit1, establishing several key parameters. Vit1 has a glass transition temperature (Tg ) of 623 K [31.163], a crystallization onset temperature (Tx ) of 705:0 K, a melting onset temperature (Rm ) of 933:0 K, and relatively low density of 6:11 g cm3 . Other work includes differential scanning calorimetry (DSC) measurement to investigate the thermodynamic properties, reported by Busch et al. [31.164]. The only work at the atomic scale that we are aware of is atomistic calculations in terms of structure factors, pair correlation functions, coordinate numbers, bond pairs and Voronoi polyhedra analysis using AIMD [31.165] on a small 200-atom model. Since the atomic structure of Vit1 is not known, theoretical calculation of its electronic properties is nonexistent. Thus an understanding of atomic-scale interactions in relation to the SRO and medium-range order (MRO) of Vit1 is lacking. Here we report a recent first-principles calculation of the thermomechanical properties of Vit1 using AIMD on a sufficiently large model of 512 atoms [31.160]. The OLCAO method [31.49] is used to calculate the electronic structure and interatomic bonding. We first construct a model by randomly placing 512 atoms (211 Zr, 71 Ti, 64 Cu, 51 Ni and 115 Be.) with a composition close to Zr41:2 Ti13:8 Cu12:5 Ni10 Be22:5 in a periodic cubic supercell with a size of 2:0292 2:0292 2:0292 nm3 , consistent with the measured mass density. Next, this random model is subjected to simulated annealing and optimization using VASP [31.39]. We used AIMD at a constant pressure and temperature (NPT) ensemble, with the following specifications:
1113
Part D | 31.2
but the stress does not return to the original value at zero stress, in agreement with experimental data [31.152]. The results are shown in Fig. 31.18. The total computational resources expended on this project were quite significant; over 2:5 million processor hours at the National Energy Research Scientific Computing Center (NERSC) were used. The results of the first-principles tensile simulation of Ni60 Nb40 MG provide insight into how a superelastic limit can be achieved in an MG. Spatially inhomogeneous responses of single atoms and specific groups of atoms are found to change substantially with increasing external stress when the strain is over 2%, causing the intrinsic viscoelastic behavior. Again, this work points to the importance of tracing the atomic movements and the changes in their interactions as key elements for a fundamental understanding of mechanical behavior through changes in the electronic structure. Obviously, the analysis of the stress-versusstrain data can be further extended to include compression of the model and variations in the calculated TBOD as a function of strain. More detailed monitoring of the atomic movements at each strain rate will be very helpful. Investigating the change in BMG under isotropic pressure is highly desirable, as this can provide the much-needed evidence of correlated atomic motion and change in interatomic bonding, as was recently observed in Zr66:7 Cu33:3 BMG [31.159]. Unfortunately, current limitations in computational resources prevent us from proceeding with such analysis.
31.2 First-Principles Calculation for Different Types of Glasses
1114
Part D
Glass Modelling
Part D | 31.2
1. The PAW-PBE potentials [31.166] within the generalized gradient approximation (GGA) [31.167] 2. Electronic convergence criterion set at 104 eV, with an energy cutoff of 400 eV 3. Time step of 3 fs 4. A single point sampling. No significant improvement was observed when tested at the higher energy cutoff. We used a Langevin thermostat for NPT simulations, which is more suitable in light of the volume changes that occur during annealing and alloying [31.168]. The AIMD works in two stages. First, the 512-atom model was melted at temperatures above the melting temperature (932 K). Second, the melted model was quenched from 1500 to 300 K in eight sequential stages, with an average cooling rate of 6 1013 K s1 . At each stage of quenching, the model was held at the respective temperature for 600 time steps, and the thermodynamic fluctuations were closely monitored to ensure realistic quenching. After final relaxation at 300 K, we selected snapshot models from the 600 MD steps that were closest to 300 K. The selected models were then fully relaxed. The structure with the lowest total energy was chosen as the most appropriate model. The calculated density of 6:055 g cm3 for the final model is in good agreement with the experimental density of 6:11 g cm3 at 300 K. This procedure provides us with the most representative structure at room temperature [31.169]. The filtering procedure that we implemented within the process is crucial for obtaining a reliable structure. Figure 31.19 shows the final 512atom model of Vitreloy using AIMD.
The total pair distribution function (PDF) G.r/ of our model for Zr41:2 Ti13:8 C12:5 Ni10 Be22:5 is shown in Fig. 31.20a. A normalizing coefficient was used to align with the experimental data in the y-axis. The very good agreement with the experimental PDF [31.170] validates our model. The inset of Fig. 31.20a gives a more detailed comparison for r < 4 Å. In a multicomponent BMG, it is a great experimental challenge to resolve the total PDF into partial components, or PPDF. This is a daunting task for Vit1, with five different components. On the other hand, this information is readily available from the modeled structure. Figure 31.20b shows the contributions to the total PPDF from the eight most dominant pairs in the Vit1. The experimental observation of the first prominent peak at 2:3 Å actually consists of combinations of contributions from Be-Be, Ni-Be and Cu-Be pairs. The main broad peak centered at 2:75 Å consists of contributions from many pairs (Zr-Be, Zr-Cu, Zr-Ni and Zr-Ti), but the details are all buried in the superposition. Our PPDF indicates that the predominant contribution to the total PDF comes from Zr-Be and Zr-Cu pairs, whereas the slight shoulder around 2:98 Å is from Zr-Zr pairs, mediated by the Zr-Ti pair in between. It can be clearly seen that the first shell, defined as the distance for the first deep minimum (3:7 Å) in the PDF, is densely packed in this multicomponent BMG and cannot be used to define any atomic radii of the atoms to be used for potential functions, as is routinely performed in classical MD. The calculated total density of states (DOS) for this model is shown in Fig. 31.21, which is resolved into partial DOS for individual types of atoms. It appears that EF is located in the vicinity of a local minimum in the TDOS that has been frequently used to justify the stability of Vitreloy at this composition. However, such a conclusion is untenable, since: 1. The minimum is not prominent, and calculation is based on a single model with 512 atoms. 2. More importantly, no rigorous theory actually exists that can attribute the stability of BMG purely to an ill-defined nonquantitative parameter.
Fig. 31.19 Snapshot of a configuration from AIMD simu-
lation. Red: Zr, blue: Ti; green: Cu, yellow: Ni, gray: Be
TBOD would be a much more reliable parameter, but we will need many such calculations at different compositions to validate it. Nevertheless, the value of N.EF / and its composition is important for other properties, such as electrical conductivity and transport properties, in Vitreloy. The calculated value of N.EF / of 468:7 states per unit cell per volume (or 0:916 states per atom per eV) is a fairly large number for a metallic alloy. In Table 31.4, we list the contributions to N.EF /
First-Principles Calculation
b)3') WRWDO
3') WRWDO
'LVSODFHPHQW c
([S &DOFXODWHG
=U%H
=U&X %H%H
'LVSODFHPHQW c
=U1L 1L%H &X%H
=U=U
=U7L
'LVSODFHPHQW c
Fig. 31.20 (a) Total and (b) partial pair distribution function for Zr41:2 Ti13:8 Cu12:5 Ni10 Be22:5 3'26 VWDWHVH9FHOO %H ± ± ±
Fig. 31.21 Calculated DOS and PDOS of Zr, Ti, Cu, Ni and Be for Vitreloy
&X 7RWDO
1L
±
±
7L
=U
(QHUJ\ H9
Table 31.4 Energy values and contribution percentages for each component at the Fermi level PDOS (state/eV-cell) Contribution % to TDOS
Zr 250:969 53:54
Ti 106:455 22:71
from the five atomic species. The largest contribution is from Zr, followed by Ti, since EF is derived mostly from the Zr 4d and Ti 3d orbitals, and both Zr and Ti also have a large atomic percentage. Although Be has 22:5 at:% in Vit1, it has minimal contribution to N.EF /, since it has no occupied d electrons. Both Cu and Ni have 3d orbitals, but these states are well below the Fermi level. Next we present the results for effective charge Q . They are shown in Fig. 31.22, with the average values indicated. Also shown are the plots for the distribution
Cu 33:9444 7:24
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Part D | 31.2
a)3') WRWDO
31.2 First-Principles Calculation for Different Types of Glasses
Ni 42:519 9:07
Be 34:8595 7:44
Total 468:748 100
in the form of a histogram. We can see that the average Q values for the atom types are 3:46e for Zr, 3:87e for Ti, 11:74e for Cu, 10:39e for Ni and 2:49e for Be (with the elementary electron change e). The valence shell electrons in a neutral atom for these atoms are as follows: Zr (4), Ti (4), Cu (11), Ni (10) and Be (2). Therefore, on average, Zr and Ti lose 0:54 and 0:13e, respectively, whereas Cu, Ni and Be gain electrons in the amount of 0:74, 0:39 and 0:49e, respectively. The histogram distribution of the effective charges for each type of atom is depicted on the right panel in Fig. 31.22,
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Part D | 31.2
Fig. 31.22 Distribution of the calculated effective charge Q in the Vitreloy model
(IIHFWLYHFKDUJH Q Q &X e
Q 1L e
=U 7L &X 1L %H
Q 7L e Q =U
e
Q %H e
which shows a reasonable range in the form of a Gaussian distribution. Ti atoms appear to have a wider range of Q , from 2:0 to 5:8e, with an average of 3:87e, indicating a more diverse interaction with their neighboring atoms. However, it is possible for atoms in BMG to lose or gain electrons and deviate significantly from their average values. This is completely different from the case of inorganic glasses, where specific types of atoms either gain or lose electrons. This fact further demonstrates the complex nature of interatomic bonding in metallic glasses, especially in multicomponent BMG such as Vitreloy. All interatomic BO values are calculated for this Vitreloy model. The plots for the BO versus BL are not presented here given the large number of possible pairs distributed in a rather complicated pattern [31.160]. Similar to the case of Zr50 Cu50 and Zr50 Cu40 Al10 in Fig. 31.11, the scatter plot again shows that for a given pair of atoms with a fixed BL, there is wide range of values for the BO, and for a fixed BO value, the BL can span a fairly large distance of separation, supporting the assertion that the BL in BMG is an ill-defined quantity. Instead we show the percentage contribution to the TBOD from each pair in Fig. 31.23. Zr-Be and Zr-Zr have the largest contributions, with 13:65 and 15:74%, respectively, since they have the largest numbers of atoms and relatively strong BO values. This chart takes into account the effects of both the composition and the strength of the bonds. This information is far more useful than simply the composition or the size of the atoms.
1XPEHURIDWRPV
The above results underscore the need to use AIMD in the study of the structure and properties of multicomponent BMG such as Vitreloy. Detailed calculation of the electronic structure and bonding in Vitreloy at the density functional theory level is especially significant, since no such results are available. In such systems, the use of TBO, TBOD and PBOD as valuable parameters for characterizing the interatomic bonding is highly desirable. For future work, the use of larger models with different compositions could facilitate a systematic search for BMG with superior properties. Adequate computational resources would be required, but this is not an unsurmountable obstacle.
31.2.3 MOF Glasses First-principles calculations for glasses have recently been applied to a new class of amorphous solids, known as metal–organic frameworks (MOF) [31.80]. MOF have attracted immense attention from diverse disciplines of chemistry, physics, engineering, material sciences, and biological and biomedical sciences [31.171– 174]. An important member of the MOF family is the zeolitic imidazolate frameworks (ZIF), which display network topologies analogous to silica. In the network, the corner-sharing SiO4 tetrahedra are replaced by MN4 tetrahedra (M D a metal, Zn in this case) linked by imidazolate (Im) .C3 N2 H3 / anions (Fig. 31.24a). The chemically tunable porosity of ZIF is central to their potential application in gas storage and separation, drug delivery, heterogeneous catalysis and
First-Principles Calculation
31.2 First-Principles Calculation for Different Types of Glasses
=U1L
=U&X
=U 7L
=U%H
7L7L 7L1L 7L&X
=U=U
7L%H 1L1L &X%H 1L%H &X1L &X&X
a)
%H%H
b)
c)
+ =Q
=Q
& 1
1
&
&
+
+
b
c
b a c
a
Fig. 31.24 (a) Zn–Im–Zn unit of ZIF, (b) 162 atom a-SiO2 model (red balls: oxygen; green balls: silica), (c) a-ZIF model. Orange, blue, gray and white balls represent Zn, N, C and H, respectively
selective adsorption [31.175–178]. In addition to the large number of crystalline ZIF with well-defined zeolite structures, the emerging category of noncrystalline or amorphous ZIF glasses is of particular interest. They can be fabricated by melt-quenching the liquids upon melting [31.179], thereby transforming the crystalline phases to glasses by varying the temperature [31.180, 181] or pressure [31.182], or by ball milling [31.183]. Amorphous ZIF (a-ZIF) can be viewed as a model glass system for understanding the general features and properties of a novel hybrid inorganic/organic glass with no LRO but retaining a well-preserved SRO. There has been increased interest recently in the structure of ZIF glasses subjected to elevated temperatures near the crystalline-to-amorphous phase tran-
sition [31.180]. A-ZIF differ from insulating glasses described in Sect. 31.2.1 in the drastic difference in the IRO, with distances of separation in the range of 1020 Å. They have a well-preserved SRO, defined by the covalently bonded organic molecule or the linker, the IM in the present case. We have constructed the first a-ZIF model by converting it from the 162-atom a-SiO2 model described in Sect. 31.2.1 [31.43]. It is well known that ZIF are closely related to zeolitic silica polymorphs by virtue of their analogous tetrahedral connectivity. By replacing Si atoms with Zn atoms, and O atoms with the Im molecules, such that the Im bridge creates a Zn–Im–Zn angle close to 145ı, similar to the Si–O–Si angle in a-SiO2 , we obtain a viable a-ZIF model with 918 atoms that has the same network
Part D | 31.2
Fig. 31.23 Pie chart showing the contributions to the TBOD from all pairs of atoms for Vitreloy
7RWDOERQGRUGHUGHQVLW\ ec±
1117
1118
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Glass Modelling
Part D | 31.2
a)3'26 VWDWHVH9
b)%RQGRUGHU +
$ %
'
*
( & )
,
7RWDOD=,)
0 . /
D=,)
1
1
-
=,)
,P &
=,)]QL
+ =Q
=,)
± ± ± ±
&±& &±+ &±1 1±+ =Q±1
± ± ± ±
(QHUJ\ H9
(QHUJ\ H9
%RQGOHQJWK c
Fig. 31.25a,b Calculated DOS (a) and bond order distribution (b) in a-ZIF model. (Im D C3 N2 H3 ). Adapted with permission from [31.80]. Copyright 2016 American Chemical Society
topology. The fully relaxed a-ZIF model using VASP is illustrated in Fig. 31.24c. We have shown that this CRN model for amorphous ZIF that is not derived from a crystalline phase has a radial distribution function (RDF) in good agreement with measurements [31.184]. The calculated PDF is resolved into specific pairs including H atoms, which is beyond the resolution of experimental capability, demonstrating the power of first-principles modeling. Additional details are described in [31.80]. The electronic structure and bonding for a-ZIF are elucidated in great detail, showing considerable bond strength for Zn-N pairs. The calculated TDOS and partial PDOS of a-ZIF are shown in Fig. 31.25a. A large bandgap of 4:8 eV, which may be underestimated due to the typical deficiency of DFT methods, indicates that a-ZIF is a large-gap insulator. The PDOS also provides insight into interatomic bonding. For example, above 6:0 eV, the PDOS of Zn shows strong interaction with N and H atoms in IM. All of these data indicate that the electronic structure of a-ZIF bears a strong resemblance to the broadened spectrum of the molecule Im, where Im is the organic linker .C3 N2 H3 /1 with a nominal valence of
1. Figure 31.25b shows the distribution of the calculated BO versus BL up to 4 Å, which provides basic bonding information in a-ZIF. Also included for comparison in Fig. 31.25b are similar plots for crystalline ZIF, ZIF-4, ZIF-zni and ZIF-8 [31.80]. The narrow distributions of C-C, C-H, N-C and Zn-N pairs in a-ZIF and crystalline ZIF are almost identical, which indicates that the SRO in the a-ZIF model remains the same as in the crystalline phases. Zn connects with imidazolate via N-bonding, with a relatively large BO value and BL close to 2:0 Å. This is the key for maintaining the near-perfect tetrahedral Zn–N4 bonding with imidazolate. The calculated TBOD for a-ZIF is 0:0264e=Å3, which is smaller than that of its crystalline counterparts. ZIF-4 and ZIF-zni have TBOD of 0:0317 and 0:0396e=Å3 , respectively. This indicates that the crystalline phases have higher internal cohesion than the amorphous phase, even though their SRO are identical. However, the TBOD for ZIF-8 of 0:0276e=Å3 is close to that of a-ZIF, indicating much weaker internal cohesion than that of ZIF-4 or ZIF-zni, which can be attributed to the high porosity in ZIF-8 [31.80]. Based on the calculated electronic structure, the optical properties of this a-ZIF model are also calcu-
First-Principles Calculation
$ $ $
$
$
(QHUJ\ H9
(QHUJ\ H9
(QHUJ\ H9
b) İ
% %
%
%
%
c) (/) &
& &
& &
Fig. 31.26a–c Calculated optical properties of a-ZIF. (a) Imaginary dielectric function ©2 . (b) Real part of the dielectric function ©1 . (c) Energy loss function (ELF).
Adapted with permission from [31.80]. Copyright 2016 American Chemical Society
lated, which is shown in Fig. 31.26. This consists of frequency-dependent complex dielectric function and the electron energy loss function (ELF) as a function of photon energies up to 35 eV. Five prominent features (A1–A5) carry over from "2 .!/ to "1 .!/ (B1–B5)
and then to the ELF (C1–C5), with the largest peak C5 at 15:810 eV identified as the plasmon peak !p for the collective oscillations of the electrons in a-ZIF. The refractive index n of 1:327 for a-ZIF is obtained from the square root of "1 .!/ at zero frequency (excluding the vibrational effect). The ultralow refractive index in a-ZIF is attributed to its high porosity. We can speculate that n could be used as a convenient and measurable descriptor for characterizing a-ZIF films. The optical properties of crystalline ZIF phases (ZIF4, ZIF-zni and ZIF-8) are shown to be very similar to a-ZIF [31.80] because of the similarities in the SRO. In this section, a new class of MOF glasses, with a-ZIF as an example, is used to show the application of first-principles calculations for the organic–inorganic hybrid glasses, where classical MD will clearly have difficulties. The take-home message is the availability of a near-perfect CRN model for a-ZIF from a topologically similar a-SiO2 model. The calculated RDF is in good agreement with measurements [31.183]. The electronic structure and bonding for the a-ZIF show considerable bond strength in the Zn–N pairs, which is the key to maintaining the a-ZIF structure in rigid form. These results are very similar to those obtained for the three ZIF crystals—ZIF-4, ZIF-zni and ZIF-8—due to the identical SRO in a-ZIF. The calculated optical properties of a-ZIF show some unique absorption features and an ultralow refractive index of 1:327 related to the low-density porous structure. The high dependence on the absorption structures in a-ZIF and crystalline ZIF can be used to characterize and predict the different types of ZIF phases, especially in relation to their porosity, and thus their ability to encapsulate other molecules. It was recently shown that porous monolithic glassy MOF prepared using a sol–gel technique can take up huge amounts of methane gas, and with robust mechanical properties [31.185]. We plan to continue and expand such first-principles calculations in this emerging class of fascinating glasses. The behavior of an a-ZIF model under homogeneous compression and expansion are currently under investigation.
31.3 Conclusions and Future Outlook We have presented, in considerable detail, the simulation results for three classes of glasses using a firstprinciples approach. The ability to calculate many physical properties based on quantum mechanics instead of relying solely on structural information sets this approach apart from conventional molecular dynamics simulation, which has dominated the area of
glass simulation for many decades. Of particular importance is the introduction of the concept of TBOD as the single most useful parameter in the characterization of glasses, similar to experimentally quantifiable measurements such as mass density, melting point, freezing temperature, viscosity and elastic modulus. TBOD encompasses many glass properties including chemi-
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a) İ
31.3 Conclusions and Future Outlook
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Part D | 31.3
cal composition, volume, dimension, density, porosity, sample size, internal defects, aging and solvent effects, and temperature dependence within a single parameter. Many of these properties require sophisticated instrumentation and strict processing control to obtain experimentally. It is fair to say that first-principles calculation, in conjunction with MD simulations, can play a vital complementary role to what is not easily available or too costly for laboratory measurements. As noted at the beginning of the chapter, ab initio simulation can be considered another type of experiment where the instruments used are sophisticated computational packages, with rapidly increasing computing power now heading toward exascale in the next few years. Therefore, in using first-principles calculation for glass design, it is imperative to have key parameters that are easily quantifiable and understandable, instead of relying on a vast amount of simulation data, either numerically or in graphic form. TBOD fulfills this role. We now discuss what more can be done with firstprinciples calculations for glass research and development based on what has been recently achieved. We will succinctly summarize several projects currently under way or being contemplated, with the aim of contributing directly to the development of new and better glasses for high-level emerging technologies. In the inorganic glasses, the main issue will be the strengthening of glasses by chemical doping, or chemical strengthening, which modifies the network structure and local SRO, resulting in an ion-exchange effect and involving alkali (Li, Na, K) atoms [31.186, 187] or alkaline earth (Mg, Ca, Sr) atoms [31.137]. Despite great strides in research and development over the past half-century, large variations still exist in much of the reported data on measured properties, due to differences in samples and the way they were processed. Although silicate glass will remain the main component, mixed glasses with aluminate (Al2 O3 ), borate (B2 O3 ) and phosphates (P2 O5 ), resulting in a more complicated network structure, will be selectively investigated, including modeling of surfaces and graded dopant concentration distributions. For example, the Gorilla Glass developed by Corning, which is basically Na-doped alumina-silicate glass [31.5], was meticulously designed for special applications such as cell phone covers, for its durability and surface sensitivity. An important class of inorganic glasses that has not been discussed in this chapter is chalcogenide glasses. They typically contain much heavier elements than silicate glasses and have different types of interatomic bonding, resulting in very different structures, smaller bandgaps and some fascinating properties. The most common are binary compounds between group IV or
V elements (Ge, As) and group IV elements (S, Se, Te), but can also be multicomponent with other elements except O. They are less well studied than silicate glasses, especially with regard to using first-principles calculations. The electronic structure and interatomic bonding in chalcogenide glass are also very different from silicate glasses, with very interesting electronic and optical properties [31.188]. Chalcogenide glasses have special advantages in the development of infrared glass optics, with numerous promising applications [31.189]. Their physical properties such as high refractive index, low phonon energy and high nonlinearity make them ideal for use in laser technology and other special optical applications. Of particular interest is the GeSe2 crystal [31.190, 191] and glass [31.192–194]. When incorporated with impurities such as Ag [31.195] or mixed with other chalcogenide glasses [31.196, 197], their properties can be fine-tuned by controlling the composition to achieve the desired properties. There have been a considerable number of studies on chalcogenide glasses thus far, but they have been limited to small sizes [31.198–200]. We are in the process of extending our first-principles calculations to chalcogenide glasses using AIMD. Another, more complicated network inorganic glass is the group of phosphate-based glasses. Like silicate glasses, they have many crystalline polymorphs, including hydroxyapatite, and various forms of ditri- and polyphosphates with and without water molecules [31.201]. However, it is the amorphous or the glassy phase (bioactive glasses) that has many important and practical applications, especially in biomedical and health-related areas [31.202–206]. First-principles calculation for bioglasses is even more important, since its complex structure with multicomponent composition and the need to account for the solvent effect precludes any possible use of classical MD. Many such calculations have been carried out using ab initio MD [31.207, 208] or the calibrated force field approach in classical MD [31.209, 210]. The bioactive glasses are far more complex than the inorganic glasses described above, and involve many critical issues related to the physiological condition of living tissue, such as the solvent effect, hydrogen bonding, pH value, pKa index and much more. In this regard, accurate quantum mechanical calculations of interfacial and interatomic interactions in bioglasses involving phosphate and other components such as CaO2 and Na2 O complex environments are absolutely necessary. We have moved in this direction by first studying the complex structures and properties of pyrophosphate crystal containing the pentoxide P2 O5 group [31.59], and plan to move on to the next challenging task of simulating large bioglass models using AIMD.
First-Principles Calculation
do exist in nature. Last but not least, the area of bioglass, briefly mentioned above, where solvent effects play a critical role, should be actively pursued. This includes the incorporation of biological entities such as peptides, proteins and oligonucleotides into glass systems, where a fundamental understanding at the atomic level is still lacking. Issues related to genomic design, virus packing, hydrogen bonding and gene mutation, for example, which have never been encountered in traditional glass research, are unavoidable. This will be an enchanted land in computational materials science. The first-principles calculation of glass properties described in this chapter includes electronic structure, bonding, and mechanical and optical properties. Expansion to other properties more akin to experimental measurements, such as porosity, fracture, nanoindentation, hardness, viscosity, and temperature- and composition-dependent fragility .T; x/, is highly desirable. Thus far, important parameters including diffusion constant, interdiffusion (ion exchange) modeling and glass transition temperature have only been obtainable using classical MD. To this end, the use of ab initio molecular dynamics highlighted earlier must be adopted. It will still take some effort, using a combination of the two or additional methods, and perhaps with further development of the atomic orbital-based all-electron OLCAO method, to achieve these goals. The development of new computational methods and platforms and the adoption of materials informatics concepts based on a large collection of high-quality data generated from first-principles calculation, in parallel with experimentally measured data, will be of prime importance in years to come for glass research. Acknowledgments. I would like to acknowledge the contributions of many collaborators including the current and past graduate students, postdoctoral fellows and visiting scientists of the Electronic Structure Group at the University of Missouri-Kansas City; Professors Paul Rulis, R. Sakidja and Neng Li, Dr. Chamila Dharmawardhana, Dr. Sitaram Aryal, Ms. P. Adhikari, Mr. K. Baral and Dr. B. Walker. Special thanks go to Mr. Baral for making several figures and tables, and for careful checking of the references. I also thank many past and present collaborators on glasses started more than 40 years ago. This work has been supported in the past by DOE and NSF grants. Computational resources have been provided by the National Energy Research Scientific Computing Center supported by the DOE under contract no. DE-AC03-76SF00098 and by the University of Missouri Research Computing Support Services (RCSS).
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For metallic systems, which are an entirely different type of glasses, the focus will be on the more complex multicomponent glasses, or high-entropy alloys, where ab initio simulation is the only viable approach for providing information across an astronomical number of possibilities in compositional space. In the author’s opinion, we must go beyond the strict geometric description of the structures in metallic glasses, and focus on the atomic-scale interaction between all atoms and their correlated movements in order to formulate a more robust and predictive theory that can be tested by carefully designed experiments [31.159, 211]. In particular, the elastic and mechanical properties of metallic glasses should be connected more closely to atomic-scale theory based on collective bonding of the atoms [31.151]. There are tremendous opportunities in composite alloys of metallic glasses with exceptional high-strength applications such as in the SAM2X5-630 steel alloy [31.212]. Admittedly, this is a lofty goal, and it will take many years to determine whether substantial progress in this direction is possible. In a related system, similar to metallic glasses, is the simulation of molten salts, which is essentially a liquid above the melting temperature. Molten salts are fluorides used as coolants in nuclear reactors and have been developed and used worldwide [31.213, 214]. The development of special molten salts in reactor containers and their corrosive effects is of paramount importance in nextgeneration nuclear reactor technology. Ab initio modeling can certain play a key role. The current viable candidates for reactor molten salts at high temperature include Li2 BeF4 (FLiBe) and the complex ternary mixture of .LiF/x .NaF/y .KF/z (FLiNaK) with optimized mixing ratios [31.214, 215]. For glasses related to metal–organic frameworks, the goal is quite different, since the subject is still in the early stage of development. The main objective is ease of fabrication to enable large-scale applications, especially for use as screening materials for different gas molecules other than CO2 or methane [31.185, 216]. In this regard, parallel work with different classes of MOF crystals, some of which have very large unit cells, is imperative. Another emerging area of noncrystalline organic materials is COF [31.79, 217], a major extension of MOF, which include ordinary mundane materials such as fabrics. For structures of MOF and COF, the boundary between the crystalline and glass structures becomes ambiguous, and factors such as porosity, density and connectivity play a far more important role with regard to their properties and applications. The interfaces between organic and insulating glasses is another promising area, with many opportunities and unpredictable consequences. Some of these materials actually
31.3 Conclusions and Future Outlook
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References
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31.1 31.2
31.3 31.4 31.5 31.6
31.7 31.8 31.9
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31.11 31.12
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Wai-Yim Ching Dept. of Physics & Astronomy University of Missouri – Kansas City Kansas City, MO, USA [email protected]
Wai-Yim Ching is a Curators’ Distinguished Professor of Physics at the University of Missouri-Kansas City, USA. His research focuses on condensed matter theory and computational material science using first-principles methods. He has published over 435 journal articles and is an Academician of the World Ceramic Academy, a Fellow of AAAS, the American Ceramic Society, the American Physical Society, and the Royal Society of Chemistry.
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32. Molecular Dynamics Simulations of Oxide Glasses
Jincheng Du
32.1 32.2 32.2.1 32.2.2
A Brief History of MD ......................... Fundamentals of MD Simulations....... Empirical Potentials ........................... Algorithms for Integration of Equations of Motion ......................
32.2.3 Thermodynamic Ensembles, Temperature and Pressure Control in MD Simulations ............................. 1134 32.2.4 MD Simulation Packages..................... 1135 32.3 32.3.1
MD Simulations of Glasses ................. Procedure of Glass Structure Generation Using MD Simulations ........................ 32.3.2 Structure Analysis .............................. 32.3.3 Property Calculations ......................... Applications of MD Simulations in Oxide Glass Research ..................... 32.4.1 MD Simulations of Sodium Silicate and Soda Lime Silicate Glasses............ 32.4.2 MD Simulations of Aluminosilicate Glasses .................. 32.4.3 Simulations of Silica Glass/Water Interaction Using a Reactive Force Field................
1135
1135 1136 1139
32.4
1141
1141 1145 1148
1129 1130 1130
32.5
Outlook and Challenges .................... 1150
32.6
Conclusions ...................................... 1151
1133
References................................................... 1151
Since its development in the middle of last century, molecular dynamics (MD) simulations have been widely used in many natural science fields such as chemistry, physics, biology, and material sciences [32.1–3]. MD was first developed to study the interactions of hard spheres in the 1950s [32.4], followed by important advances in simulations of liquid argon with the Lennard-Jones potential by Rahman [32.5]. MD simulations of realistic systems began with the study of liquid water by Rahman and Stillinger [32.6]. The first MD simulations of glass was published in 1976 by Woodcock et al. to study silica glass using MD with the Born–Meyer–Huggins potential [32.7]. Since then, a number of papers have been published on MD simulations of silica and alkali silicate glasses [32.8– 10]. Simulations of more complicated and realistic glass
systems such as soda lime silicate [32.11], aluminosilicate [32.12, 13], phosphosilicate [32.14], and borosilicate glasses [32.15] have become possible, thanks to the ongoing development of interatomic potentials. In addition to the study of atomic structure and structure– property relationship of glasses, MD simulations have now been used to investigate more complicated processes in glasses such as ion-exchange strengthening [32.16], ionic conduction [32.17], and fracture and indentation of glasses [32.18]. As a result of these expanding capabilities to provide insight into the structure and behaviors of complex glass systems, MD simulations have become an effective tool in glass research and computational design of glass materials [32.19], used widely from university and national labs to industrial research environments.
32.1 A Brief History of MD
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_32
Part D | 32.1
Molecular dynamics (MD), one of the most important atomistic computer simulation methods, and its applications in glass simulations is introduced in this chapter. Essential ingredients of MD simulations such as empirical potentials, thermodynamic ensembles, integration algorithms, and procedures for glass structure generation, as well as structure analysis and property calculations, are covered. MD simulations of silicate-based glasses including silica glass, sodium silicate, soda lime silicate and sodium aluminosilicate glasses, silica glass/water interfaces are given as examples. Issues such as validation of simulated structure models, empirical potential development, and extending time and length scale of simulations are discussed. The chapter concludes with an outlook on future directions of MD simulations of glasses.
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Part D | 32.2
Ever since Zachariasen’s proposal of the continuous random network (CRN) model of silica glass structure [32.20], scientists have been seeking to build atomic structure models of glass, a material that lacks long-range order but has short-range structural features similar to that in crystalline materials. Bell and Dean built the first ball-and-stick model of amorphous silica by hand and it provided many insights into the structure of silica [32.21]. Later on the coordinates of this model were measured and used as input for structural relaxation using a computer [32.22, 23]. Of course, despite the insight gained into the structure of silica glass, there exist a number of restrictions for hand-built models such as the existence of surface atoms (like a cluster model in modern simulations), the limited size of the models that can be constructed, and the tedious process to hand build the model. The invention of the computer and advances in MD and other simulation techniques (such as Monte Carlo (MC)) made computer simulations of liquids—as shown by one of the
earliest applications of MD—and glass, which is essentially a super-cooled liquid, possible. Monte Carlo simulations [32.1], another important atomistic simulation method, have also been widely applied to the study of liquid structures but MC tends to sample equilibrium states consistent to Boltzmann distributions and it lacks a time scale in simulations. Therefore, MD simulations which can provide both structural and dynamic information have become the most widely used method for the simulation of liquids and glasses. The purpose of this chapter is to introduce the important ingredients of MD simulations of glasses, starting from the basics of MD simulations: empirical potential, structure analyses of simulation results, and methods to calculate different properties. This is followed by examples of MD simulations of several common oxide glass systems such as alkali silicate, soda lime, and aluminosilicate glasses. Finally, an outlook and a discussion of future challenges for MD simulations are presented.
32.2 Fundamentals of MD Simulations Molecular dynamics simulations involve numerical solution of Newton’s equations of motion of an assembly of atoms or molecules of a targeted system [32.2, 3]. MD simulations are carried out iteratively with a small time step, usually in the order of a femtosecond (fm), to ensure accuracy of the integrations of the equation of motions. MD simulations usually run from tens of picoseconds (ps) to hundreds of nanoseconds (ns), depending on the system and the time needed to reach an equilibrium state. Macroscopic properties such as pressure and energy are calculated using statistical mechanics principles depending on the thermodynamic setting or ensemble chosen to perform the simulations. Practical simulations include several hundreds to millions of atoms, usually with the applied three-dimensional (3-D) periodic boundary conditions to represent macroscopic systems that contain Avogadro’s number (6:02 1023 ) of atoms. To perform MD simulations, several choices have to be made before the actual calculations. These include the choice of interatomic potentials to describe the interactions between the particles, the type of boundary conditions, the type of thermodynamic ensemble, and the kind of numerical integrator. These will be explained in detail in this section.
32.2.1 Empirical Potentials In classical MD simulations, empirical potentials, or force fields, are used to describe the interatomic in-
teractions and are one of the most important inputs of MD simulations [32.3]. Potentials determine the accuracy, reliability, predictability, and reproducibility of the simulation results. The general form of potential U.r1 ; r2 ; r3 ; : : : ; rN / of a system is a function of the atomic coordinates of the N atoms. Total potential energy consists of the summation of one-body .U1 /, two-body .U2 /, three-body .U3 /, and higher order interactions depending on the complexity of the system of interest U.rN / D
X i
C
U1 .ri / C
XX
XXX i
i
U2 .ri ; rj /
j>i
U3 .ri ; rj ; rk / C : : :
(32.1)
j>i k>j
The one-body term is due to an external field, such as an applied electrical field. The two-body term is usually called pair interactions or pair potentials. According to the Born model of solids, the crystal lattice consists of infinite arrays of charged ion particles. Thus, for solids with high ionicity, pair interactions dominate and pair potentials, including the long-range Coulombic interaction and short range-interactions, are commonly used in simulations of ceramics and glass materials. The three-body term is also used to constrain bond angles, such as the O–Si–O bond angle to 109:47 for an ideal SiO4 tetrahedron. These interactions can be expressed
Molecular Dynamics Simulations of Oxide Glasses
in terms of interatomic distance rij and angles jik , U.rij / D
qi qj C U.rij / C U.jik / ; 4 rij 0
(32.2)
" U.rij / D 4"
rij
12
rij
6 # ;
(32.3)
where the r12 power term is for repulsion, the r6 power term for van der Waals interactions, and and " are parameters. Another commonly used pair potential is the Morse potential, U.rij / D Dij
2 1 eaij .rij r0 / 1 ;
(32.4)
in which repulsion is expressed in the exponential form, Dij , aij , and r0 are parameters. The Buckingham potential combines the LennardJones and Morse potentials, in the form of exponential repulsion and r6 van der Waals attraction, and is one of the most commonly used for ionic solids including the oxide glasses and ceramics. The Buckingham potential has the form Cij rij U.rij / D Aij exp 6 ; (32.5) ij rij where A, , and C are parameters. One difficulty with the Buckingham potential is when rij is too short and away from the potential well, the power term dominates and, as a result, the potential goes to negative infinity and creates unphysical fusion of atoms. This creates issues in simulations of glass and melts. At high temperatures, atoms can have high-enough kinetic energy
to overcome the barrier that leads to instability of simulations. This can be corrected by the addition of a 12– 18 Lennard-Jones potential or the Ziegler–Biersack– Littmark (ZBL) potential for shorter distances. The ZBL potential is a short-range repulsive potential, and is commonly used to study high-energy particle interactions with a solid surface in ion implantation or plasma/surface interactions. Du and Corrales [32.24] used a splice function to correct Buckingham potentials. The function has the form U 0 .rij / D Bij rijn C Dij rij2 ;
(32.6)
where B, D, and n are parameters. The function will be applied for a distance smaller than r0 , where r0 is defined as the r value when the third derivative of potential energy equals 0, and the A, B, and n parameters were chosen so that the potential, force, first and second derivative of force for U.r/ and U 0 .r/ are continuous at r0 . Among the published potentials, the set of potentials initially parameterized by D.M. Teter but later refined by Du and Cormack [32.25, 26] is one of the most successful for the modeling of multicomponent oxide glasses. It utilizes partial atomic charges (for example 1:2 for oxygen) and only contains pair potential interactions in the Buckingham form. Table 32.1 summarizes the Teter potential parameters A, , and C for common oxides in glasses. Pedone et al. [32.27] developed a set of partial charge potentials that combines the Morse potential form (32.4) and a Lennard-Jones term. The addition of the Cij =r12 term to the Morse form (32.4) strengthens the short-range repulsion. The potentials were fitted to silicate mineral structures and mechanical properties. This set potential used the same partial charge as the Teter potential listed in Table 32.1. The Morse potential parameters for some common oxide glass compositions are listed in Table 32.2. More oxides can be found in the original paper. Other commonly used potential forms include the Born–Meyer–Huggins which combines the exponential repulsion term and r6 and r8 attraction terms (i. e., an Table 32.1 Buckingham potential parameters for silicate and aluminosilicate systems [32.25] Pairs O1:2 -O1:2 Si2:4 -O1:2 Al1:8 -O1:2 Li0:6 -O1:2 Na0:6 -O1:2 K0:6 -O1:2 Ca1:2 -O1:2
Aij (eV) 2029:2204 13 702:905 12 201:417 41 051:938 4383:7555 20 526:972 7747:1834
ij (Å) 0:343645 0:193817 0:195628 0:151160 0:243838 0:233708 0:252623
Cij (eV Å6 ) 192:58 54:681 31:997 0:0 30:70 51:489 93:109
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Part D | 32.2
where the first term is Coulombic interaction. As it decays slowly with r.1=r/, the Coulombic term is also called long-range electrostatic interaction. Because of its slow convergence as a function of distance, methods such as Ewald summation and smoothed particle mesh Ewald are commonly employed to improve the calculation efficiency in Coulombic interactions. In the Ewald summation method, the Coulombic energy is split into a real space term and a reciprocal space term which enable accurate calculations of its contribution to total energy with reasonable computational cost. The second term U.rij / represents the short-range pair interaction which usually consists of a repulsion term at short distance and an attraction term for van der Waals forces due to dispersion interactions of the atoms. The Lennard-Jones potential is one of the first pair potentials to describe liquid and gas. The 12–6 Lennard-Jones potential is defined as,
32.2 Fundamentals of MD Simulations
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Glass Modelling
Table 32.2 Morse potential parameters for silicate and alu-
minosilicate systems [32.27] Pairs O1:2 -O1:2
Part D | 32.2
Si2:4 -O1:2 Al1:8 -O1:2 Li0:6 -O1:2 Na0:6 -O1:2 K0:6 -O1:2 Ca1:2 -O1:2
Dij (eV) 0:042395 0:340554 0:361581 0:001114 0:023363 0:011612 0:030211
aij
r0
Cij
(Å2 ) 1:379316 2:006700 1:900442 3:429506 1:763867 2:062605 2:241334
(Å)
(eV Å12 ) 22:0 1:0 0:9 1:0 5:0 5:0 5:0
3:618701 2:100000 2:164818 2:681360 3:006315 3:305308 2:923245
additional r8 attraction term to the Buckingham potential) Cij Eij rij 6 8 : U.rij / D Aij exp ij rij rij
(32.7)
Another form of potentials that have been used in the literature is the Gilbert–Ida type, which is again very similar to the Buckingham form with exponential repulsion and an r6 attraction term U.rij / D f0 .bi C bj / exp
ai C aj rij bj C bj
Cj Cj ; rij6 (32.8)
where ai , aj , bi , bj , ci , and cj are parameters for atom types i and j. Three-body potentials are also used in empirical potentials to constrain the bond angles. They are used for cations with partial covalent bonding and low coordination numbers, for example Si, B, and Al. Three-body terms have been widely used for oxide systems that utilized full atomic charges where they are necessary to maintain certain coordination numbers. Later development of potentials showed that effective two-body potentials with reduced atomic charge to account for the partial covalency of the bonding were capable of generating structures with polyhedron geometries such as a tetrahedron without three-body terms. Nevertheless, three-body potentials are still used in some empirical potential systems, especially in potentials that employ full atomic charges. Commonly used forms of threebody potential include the harmonic or screened harmonic k U.jik / D .jik 0 /2 ; (32.9) 2 rij rik k ; U.jik / D .jik 0 /2 exp 2 1 2 (32.10)
where jik is the angle of atoms i, j and k with the i atom in the middle and rij and rik are the distance between atoms i, j and i, k, respectively. k, 1 , 2 are parameters, and 0 is the target angle. Harmonic cosine or screened harmonic cosine are also commonly used 2 k
cos.jik / cos.0 / ; 2 2 k
cos.jik / cos.0 / U.jik / D 2 rij rik exp : 1 2
U.jik / D
(32.11)
(32.12)
More complicated potentials include those that have a polarization effect and those that are capable of describing chemical reactions. Ion polarization plays an important role in defect and surface simulations, as well as the calculations of properties such as dielectric constants. Ion polarization can be described by using the Shell model where a massless shell is introduced and the shell is linked to the ion core by a spring. Polarizable potentials were also developed for glass materials. Tilloca et al. developed a shell model (mainly on oxygen ions) and applied it to soda lime silicate and phosphosilicate compositions [32.28]. The polarizability of oxygen ions was introduced by the shell model in which the total atomic charge is distributed between the core and the shell which were coupled by a harmonic spring [32.28] 1 2 Ucs .rcs / D kcs rcs ; 2
(32.13)
where rcs is the distance between the core and shell and kcs the spring constant. In MD simulations, shell models can be treated dynamically (dynamic shell model), in which a small mass is assigned to the shell and it is treated like a regular particle, or statically (or relaxed shell model) in which shells have zero mass and they are relaxed to zero force at each of the MD steps. Potentials that are capable of describing chemical reactions, or chemical bond formation and breakage, are important to study the interactions of glass with the environment or interfaces with other materials, such as glass/water reactions and glass/metal or glass/polymer interfaces. As true chemical bond formation can only be described in quantum mechanics (QM), these potentials are usually more complex in functional forms and require more parameters than those described earlier for glass simulations. The reactive force field (ReaxFF) is an example of such a potential. ReaxFF [32.29, 30] is a bond-order based potential where the bond order of an atom depends on the interatomic distance. Another feature of ReaxFF is that the atomic charges
Molecular Dynamics Simulations of Oxide Glasses
Esys D Ebond C Eover C Eunder C Elp C Eval C Epen C Etors C Econj C EvdW C ECoul :
algorithm. The Verlet algorithm is based on Taylor expansions for the positions r.t/. 1 r.t C t/ D r.t/ C v .t/t C a.t/t2 2 1 C aP .t/t3 C O.t4 / ; 6 1 r.t t/ D r.t/ v .t/t C a.t/t2 2 1 aP .t/t3 C O.t4 / ; 6
(32.17)
(32.18)
where r.t/, v .t/, and a.t/ are position, velocity, and acceleration at time t, respectively. O.t4 / is the truncation error from the Taylor expansion in the order of the fourth power of the time step: t. The combination of the above two equations leads to the Verlet algorithm in the form,
(32.14)
More details of ReaxFF can be found in the literature [32.29–32]. First introduced to study hydrocarbons and reactions [32.29], ReaxFF has now developed to study various material systems and their interactions [32.30]. It has been applied to study glass/water interfaces [32.31] and reactions [32.32, 33], organic– inorganic hybrid glasses [32.34], and sol–gel processes [32.33].
32.2.2 Algorithms for Integration of Equations of Motion Molecular dynamics simulations consist of numerical, step-by-step, solutions of the classical Newton’s equations of motion f i D mi rRi D mi
@2 ri ; @t2
(32.15)
where f i is the force acting on atom i, t is time, and mi and ri are the mass and position of atom i. The forces can be calculated from derivatives of the potential energy versus interatomic distance fi D
@ U.r1 ; r2 ; r3 ; : : : ; rN / : @r
(32.16)
The description of a system of N interacting atoms through (32.16) leads to 3N second-order ordinary differential equations (ODE), which can be solved discretely by using the finite difference method. There exist large numbers of algorithms for integration of the equations of motion [32.1, 3]. Commonly used algorithms include Verlet, velocity Verlet, and the leap-frog
1133
r.t C t/ D 2r.t/ r.t t/ C a.t/t2 C O.t4 / : (32.19)
The velocities are thus not needed in the calculation of the positions. In (32.17), the truncation error is O.t4 /. Velocity can be calculated by using
v .t/ D
r.t C t/ r.t t/ C O.t2 / : 2t
(32.20)
The Verlet algorithm is easy to implement, stable, and the computer memory requirement is modest (a big deal in early MD simulations). However, it has the issue that velocities are not explicitly calculated and, when calculated from positions, have less precision (larger truncation error O.t2 / than that of position O.t4 /) and are calculated one step behind atom position. Several algorithms have been developed based on variations of the Verlet algorithm. The velocity Verlet algorithm computes positions, velocities, and accelerations at the same time t C t using values at time t. The velocity Verlet algorithm is fast, stable, relatively simple to implement, and does not compromise precision. It is probably the most widely used algorithm in MD. This algorithm is implemented as follows 1 r.t C t/ D r.t/ C v .t/t C a.t/t2 C O.t3 / ; 2 (32.21)
1 v .t C t/ D v .t/ C tŒa.t/ C a.t C t/ 2 (32.22) C O.t3 / : Both the position and velocity are calculated, stored, and have the same error O.t3 /. Another variation of
Part D | 32.2
are assigned dynamically depending on the local environments of each atom through the electronegativity equilization method (EEM) scheme. These two important features, together with others such as under- and overbonding energies, enable ReaxFF to study chemical reactions and heterogeneous bonding of different types of materials. The total system energy Esys in ReaxFF is a sum of the bond energy .Ebond/, energy penalty due to overbonding .Eover / and underbonding .Eunder /, lone-pair electron energy .Elp /, three-body valence angle term .Eval /, four-body torsion angle term .Etors /, conjugate energy .Econj /, and finally the van der Waals energy .EvdW / and long-range Coulombic energy .ECoul / [32.29, 30]
32.2 Fundamentals of MD Simulations
1134
Part D
Glass Modelling
Part D | 32.2
the Verlet algorithm is known as the leap-frog algorithm. In this algorithm, velocity is first calculated at time t C t=2. It is then used to calculate the positions r.t/ at time tCıt. The velocities are updated at half time steps and leap ahead of the positions, which makes the velocities and the positions leap one over the other (thus the origin of the name). The leap frog algorithm is expressed as follows 1 1 v t C t D v t t C tai .t/ ; (32.23) 2 2 1 r.t C t/ D r.t/ C v t C t t ; (32.24) 2 1 1 1 v .t/ D v t C t C v t t : 2 2 2 (32.25)
In the leap-frog method, velocities are calculated explicitly and the numerical imprecision is minimized. Unlike the other Verlet-type algorithms, the energy conserves well even at large time steps using the leap-frog algorithm. The disadvantage is that the positions and velocities are not synchronized, which means it is not possible to calculate the contribution of kinetic and potential energy at the same time. The general requirements of a good algorithm include fast speed, low memory requirement, and easiness to program. In addition to these requirements, additional considerations are needed while choosing an integration algorithm for MD simulations. This is because the most time-consuming part in MD simulations is the calculations of the forces acting on atoms, which are done at each of the time steps [32.3]. An important consideration is that the algorithms should allow for a long time step, t, conserve energy and momentum in long runs, and be time-reversible. Overall, computational cost and energy conservation are the major criteria in choosing integration algorithms.
32.2.3 Thermodynamic Ensembles, Temperature and Pressure Control in MD Simulations In molecular dynamics simulations, information such as atomic position and velocity are generated. The information in the microscopic world can be related to the macroscopic properties such as temperature, volume, and pressure by using statistical mechanics. A thermodynamic ensemble is a collection of all possible systems with different microscopic states that the real system may find itself in with the same common macroscopic states. The microstates are distributed over the phase space with a probability density % and the average value
hAi of a macroscopic property A is then an ensemble average and can be calculated as follows Z hAi D A.˝/%.˝/d˝ ; (32.26) where ˝ is a microstate. This implies that, in molecular dynamics simulations, the system should be allowed to evolve in time as long as possible so that it will eventually pass through all possible states. In this way, the system is assumed to reach ergodicity where the time average is equivalent to the ensemble average. The ergodic hypothesis is the most fundamental axiom in statistical mechanics. Thus, the goal in molecular dynamics simulations is to generate enough representative configurations and microstates, with which the time-averaged values can be used to calculate structural, dynamic, and thermodynamic properties of the targeted system. The commonly encountered ensembles in MD simulations include the microcanonical, canonical, and isobaric isothermal ensembles. The microcanonical ensemble represents systems where all microstates are constrained to the same number of atoms .N/, volume .V/ and energy .E/, hence it is also called the NVE ensemble. The microcanonical ensemble is the natural ensemble for MD simulations. As there is no external intervention in the ensemble, it is commonly used in the production run after the system reaches equilibrium to collect structural information and trajectories to calculate dynamic and other properties. The canonical ensemble corresponds to a collection of all systems with a thermodynamics state characterized by a fixed number of atoms, N, in a fixed volume V at a fixed temperature T (also called the NVT ensemble). Different thermostats can be applied to control the system temperature. This includes direct velocity scaling, which is considered to be a brute force method or, achieving the desired temperature by connecting the system to a thermal bath, for example the Berendson method [32.3]. The thermal bath acts as a source of thermal energy and the velocities are scaled each step in a way that the rate of temperature change is proportional to the difference of the actual and targeted temperature dT.t/ 1 D ŒTbath T.t/ ; dt
(32.27)
where T.t/ is temperature of the system, Tbath is the bath or targeted temperature, and is a coupling constant. The constant controls how strongly the system is coupled to the thermal bath. If is large, the system is weakly coupled to the thermal bath. If is small, then the coupling is strong. This results in exponential decay of the system toward the targeted temperature; the tem-
Molecular Dynamics Simulations of Oxide Glasses
perature change at each successive step is T, and the velocities are then scaled through . (32.28)
(32.29)
The methods to control temperature through temperature scaling are relatively easy to implement. However, they do not generate rigorous canonical averages that can sample all possible states of a system in thermal equilibrium with a heat bath [32.3]. Alternative methods such as stochastic collision and extended system, when properly implemented, do generate canonical averages. The stochastic method randomly reassigns velocity to a randomly selected subset of atoms according to the Boltzmann distribution at certain time intervals, simulating the situation that the system is in contact with a thermal bath. The Anderson thermostat is a stochastic method [32.3]. The stochastic nature of the method does not generate smooth trajectories. The extended system method considers the thermal reservoir to be an integral part of the system. A parameter is introduced to control the energy flow between the system and reservoir. The commonly used Nosé–Hoover method is such a method [32.3]. The canonical ensemble can be used to bring the system to equilibrium at a certain temperature. The isobaric isothermal ensemble is characterized by a fixed number of atoms, N, a fixed pressure, P, and a fixed temperature T (also called the NPT ensemble).
The NPT ensemble introduces pressure as a controlling parameter, thus structural changes or phase transition under pressure in systems can be simulated. As pressure is calculated as a virial based on the product of the distance and distance derivative of the potential function, it fluctuates much more than other quantities such as total energy and temperature. The pressure control is commonly implemented by changing the system volume, in ways similar to temperature control in microcanonical ensembles by connecting the system to a pressure bath.
32.2.4 MD Simulation Packages Several molecular dynamics codes are available and commonly used for MD simulations of glasses. These include DL_POLY, a general purpose classical molecular dynamics simulation package developed at Daresbury Laboratory (UK), and LAMMPS (large-scale atomic/molecular massively parallel simulator), a classical MD code developed at Sandia National Lab. Both codes can run in serial or parallel mode and are capable of simulating large systems. Other packages such as GROMACS (Groningen machine for chemical simulations), NAMD (Nanoscale molecular dynamics), GULP (general utility lattice program), CP2K, and NWChem can also be used to perform general MD simulations although some have additional functions such as quantum mechanical capabilities. Visualization of atomic structures (and sometimes dynamics) can be achieved with several software packages such as Material Studio (formerly Cerius2 ), VMD (Visual Molecular Dynamics), VESTA, OVITO (The Open Visualization Tool), or other packages.
32.3 MD Simulations of Glasses 32.3.1 Procedure of Glass Structure Generation Using MD Simulations To set up an MD simulation, the initial configuration needs to be chosen, either from experimental structure, previous simulation results, or simply randomly generated. Then the velocities of the atoms are assigned accordingly to the Maxwell–Boltzmann distribution at the temperature of interest. The initial velocities are often readjusted to set the total momentum to be zero. MD simulations can then start by calculating the forces acting on each atom and solving the equation of motion using algorithms discussed earlier. As force calculations involve each atom and are performed at each MD step, they are usually the most time consuming in MD simulations. There are techniques such as linked-cell
list or minimum-image convention to reduce the total amount of calculations at each of the MD steps to keep the computational cost at a minimum [32.1]. For systems started from random distributions, an energy minimization step is usually required to remove the high-energy atom positions before performing MD simulations. Once these are set up, the first stage of MD simulations is equilibration, in which the system is brought to equilibrium from the initial configuration. Various properties such as total energies, temperature, pressure, and atom movement are monitored to ensure equilibrium is reached. The second stage of MD simulations is the production stage. In the production stage, the microcanonical ensemble (NVE) is commonly used and no velocity scaling or thermal bath is attached to the system.
1135
Part D | 32.3
@t ŒTbath T.t/ ; s @t Tbath 1 : D 1C T.t/
T D
32.3 MD Simulations of Glasses
1136
Part D
Glass Modelling
Part D | 32.3
The commonly used procedure to generate glass structure using MD simulations is the simulated melt and quench process [32.35], i. e., melting a glass in a computer very similar to using a furnace in a lab. Firstly, the system temperature is increased enough to fully melt the initial configuration in a reasonable time (hundreds of picoseconds). Equilibration of the melt is practically assessed by checking if the average movements of atoms are larger than half of the simulation cell, the longest distance you can measure in a system with the periodic boundary condition that is usually applied in glass simulations. This is followed by the cooling (or quenching) step in which the temperature is brought down from the melting temperature to room temperature. This can be achieved in different ways, either through step cooling or continuous cooling, i. e., using very small steps, with linear or nonlinear temperature profiles. The melt and cooling steps can be done with constant volume (such as canonical or microcanonical ensembles) or constant pressure (isothermal isobaric ensemble), depending on the system or the systems of interest and the type of empirical potential employed in the simulations. How much time it uses in the cooling process determines the cooling rate of the glass formation. The cooling rate used in classical MD simulations is usually 110 K=ps, which is orders of magnitude higher than that required to form a glass in the lab (usually 1100 K=s). This high cooling rate suggests the higher fictive temperature of the simulated glasses. However, comparison of experimental and simulated glass structures show the close similarity of the short- and medium-range structures. This was explained by the smaller number of atoms in simulations as compared to macroscopic systems [32.31]. At room temperature, the system undergoes an equilibrium run with the NVT ensembles or NPT ensembles, which is finally followed by a production run with the microcanonical ensemble (NVE) when the configurations are recorded for final structure analysis of the glass.
32.3.2 Structure Analysis Compared to crystalline materials, glass and amorphous materials lack long-range order and are more complicated to characterize and describe. As a result, several structural analysis tools have been developed to characterize structures of glasses from MD simulations. Some of these provide a means of direct comparison with experiments, such as pair distribution functions, but others only provide structural information of the models but there is no direct experimental comparison. In this section, the commonly used pair distribution functions, in different forms, accumulated coordination numbers,
bond-angle distribution, Qn distribution, and ring size distributions are introduced. Radial Distribution Functions (PDF, TDF, RDF etc.) and Structure Factor The radial distribution function (RDF) or pair distribution function g.r/ is one of the most widely used functions for glass structure analyses. Although these distribution functions compress a three-dimensional structure into one-dimensional (1-D) interatomic distance, it provides a unique way to describe the structures that lack long-range order, such as glasses, amorphous materials, and melts. Additionally, experimental distribution functions can be obtained from diffraction experiments, such as x-ray, neutron, and electron diffractions and can be compared with those from simulations, which is highly valuable to validate simulated structure models. There are several forms of radial distribution functions, which can cause confusion in the literature on how they are used. The pair distribution function g.r/ represents the probability to find a particle in a spherical shell of thickness dr at the distance r from an arbitrarily chosen particle. The number of atoms dn.r/ at a distance between r and r C dr around an atom can be calculated from the ratio of the radial density function .r/, i. e., atom density at distance r from the chosen particle, and the average atom density 0 D N=V dn.r/ D .r/4 r2dr ; .r/ dn.r/ : g.r/ D D 0 0 4 r2 dr
(32.30) (32.31)
Other forms of distribution function can be defined based on g.r/ and .r/ [32.36]. For example, the total correlation function T.r/ has been widely used in comparison with diffraction experiments as T.r/ is the conventional form obtained from Fourier transformation of the experimental diffraction data. T.r/ is defined as, T.r/ D 4 r.r/ D 4 r0 g.r/ :
(32.32)
Other forms include the differential correlation distribution function D.r/ and the radial distribution function RDF.r/, D.r/ D 4 r..r/ 0 / D 4 r0 .g.r/ 1/ ; (32.33)
RDF.r/ D 4 r .r/ D rT.r/ D 4 r0 g.r/ : 2
(32.34)
Figure 32.1 shows plots of four types of distribution functions for the O-O pair from MD simulations of erbium-doped silica glass.
Molecular Dynamics Simulations of Oxide Glasses
a) gOO (r)
32.3 MD Simulations of Glasses
1137
b) tOO (r)
8
10
8 6
Part D | 32.3
6 4 4 2 2
0
0
1
2
3
4
5
6
7
8 r (Å)
c) dOO (r)
0
0
1
2
3
4
5
6
7
8 r (Å)
2
3
4
5
6
7
8 r (Å)
d) RDFOO (r) 40
10 8
30
6 4
20
2 0
10 –2 –4 0
1
2
3
4
5
6
7
8 r (Å)
0
0
1
Fig. 32.1a–d The distribution functions of the O-O pair from MD simulations of an erbium-doped silica glass. (a) Pair distribution function, gij .r/. (b) Partial total correlation function, tij .r/; the dotted line is 4 ro . (c) Differential correlation function, dij .r/. (d) Radial distribution function, RDF.r/; the dotted line is 4 r2 o . After [32.36]
From partial distribution functions, the partial structure factor can be obtained through Fourier transformation. The partial static structure factor can be calculated from partial pair distribution functions through the Fourier transformation [32.24], Sij .Q/ D ıij C 4 0 .ci cj / Z1 sin.Qr/ 2 r dr ; Œgij .r/ 1 Qr 1=2
(32.35)
0
where ıij is a delta function and the rest have the same meaning as before. The total static structure factor is
defined as, S.Q/ D
X .ci cj /1=2 Sij .Q/ :
(32.36)
i;j
The neutron-scattering static structure factor is obtained by weighting the partial static structure factor with 12 the neutron-scattering length bi . It can be expressed as,
P 1=2 Sij .Q/ ıij C .ci cj /1=2 i;j bi bj .ci cj / N S .Q/ D : P 2 i ci bi (32.37)
1138
Part D
Glass Modelling
Coordination Number and Accumulated Coordination Number The average coordination number (CN) is a common way to characterize the local structure of amorphous materials. The CN is usually calculated by the integration of the pair distribution functions.
Bond-Angle Distribution (BAD) The bond-angle distribution aijk provides information on the probability to find i, j, k atom triplets in certain bond angles hence determine the coordination environments around the center atom. aijk is defined as
Part D | 32.3
aijk . / D
Zr0 CN D nij .r0 / D 4
j gij .r/r dr ; 2
(32.38)
0
where nij is the coordination number of j around i, gij .r/ is the partial pair distribution function between i and j atom species, j is the number density of atom species j, and r0 is the cutoff distance. There are several ways to define the cutoff r0 for the integration. The cutoff distance r0 is normally defined by the first minimum in the pair distribution function gij .r/. Alternatively, the cumulative coordination number nij .R/ can be calculated with a different cutoff R ZR nij .R/ D
4 j gij .r/r2dr :
(32.39)
0
Figure 32.2a shows the partial total correlation functions for cation–oxygen and oxygen–oxygen pairs of an oxide glass and associated accumulated coordination number distributions (Fig. 32.2b). a)
T(r) PO SiO SrO CaO NaO
1.485
40
1.605 20
2.405 2.395 2.565
0
1 b) Accumulated CN 10.0
2
3
4 r (Å)
5.0 2.5 1
2
(32.40)
where Na is the total number of angles of interest, in the first coordination shell of the atom i, and ijk is the actual bond angle. The distribution aijk . / depends on how many atoms there are in the coordination shell of the triplets, which is usually defined by a cutoff distance. Averaging over all atoms of the same type, and an average over configurations of trajectories during the production run are usually adopted to improve the statistics. Qn Distributions Analysis Q distribution is terminology borrowed from solidstate NMR (nuclear magnetic resonance) studies of glasses. Qn represents a tetrahedron (e. g., SiO4 tetrahedron) with n bridging oxygens (BOs). In silica and silica-based glasses, Q4 stands for the silicon coordinated by four BO, Q3 stands for silicon coordinated to three BO and one nonbridging oxygen (NBO), Q2 stands for silicon coordinated to two BO and two NBO, etc. Information from the Qn distribution provides information on the glass network structure. The Qn distribution is statistical data of the percentage of each Qn species. From the Qn distribution, we can calculate the network connectivity (NC), which is defined as the average number of BO per tetrahedron [32.38] n
NC D
4 X
xi i
(32.41)
iD1
7.5
0.0
Na 1 X ıŒ .ijk /l ; Na lD1
3
4 r (Å)
Fig. 32.2 (a) Partial total correlation function T.r/ of SiO, P-O, Na-O, Ca-O, and Sr-O pairs. Bond distances are marked for each pair. (b) The accumulated coordination number distributions. After [32.37]
in which xi is the fraction of the Qi species. For silica glass, the NC equals 4. Addition of modifiers breaks the Si–O–Si bonds hence the network and the NC value decreases. Ring Size Distributions The ring size distribution is one of the most important ways of characterizing the medium-range structure of network glasses, particularly due to the lack of longrange order of glass structures. Corner-sharing silicon oxygen tetrahedra form rings of different sizes. Each silicon ion is considered as a vertex and the connection of two vertices is an edge. Ring size distribution only counts the primitive rings. A ring is primitive if the number of edges connecting any two vertices forms the
Molecular Dynamics Simulations of Oxide Glasses
32.3.3 Property Calculations Mechanical Property Calculations Mechanical properties can be calculated using static or dynamic methods. In static methods, one approach is the diagonalization of the Hessian matrix and the elastic constants can be obtained from where the macroscopic mechanical properties can be calculated [32.40]. Alternatively, strains according to the elastic constants are introduced and energies calculated, and the mechanical properties are then calculated based on the finite difference method. The dynamic method calculates the mechanical properties using tension testing, i. e., apply tensile strain to the simulation cell along certain directions and the properties are then calculated. In the static method, the stiffness matrix C is calculated first. The elements of the stiffness matrix are defined as the second derivative of the potential energy Rings per base Si 4 SiO2 10Na2O-90SiO2 20Na2O-70SiO2 30Na2O-70SiO2
3
.V/ over the strain ."/ [32.40],
1 Cij D V
@V @"i @"j
:
(32.42)
The compliance matrix S was calculated through inverse operation of the compliance matrix .S D C1 /. Macroscopic mechanical properties such as bulk modulus .K/, Shear modulus .G/, Young’s modulus .Y/, and Poisson’s ratio . / can then be expressed from the compliance matrix elements. K and G can be expressed with S and C elements using the Voigt–Reuss–Hill formalism [32.40]. The Voigt–Reuss–Hill method has been used to calculate isotropic polycrystalline elastic moduli from single-crystal anisotropic elastic constants [32.40]. The Voigt and Reuss definitions for bulk modulus K and shear modulus G are 1 KVoigt D ŒC11 C C22 C C33 C 2.C12 C C13 C C23 / ; 9 (32.43) KReuss D ŒS11 C S22 C S33 C 2.S12 C S13 C S23 /1 ; (32.44)
1 ŒC11 C C22 C C33 C 3.C44 C C55 C C66 / 15 (32.45) .C12 C C13 C C23 / ; 15
: GVoigt D 4ŒS11 C S22 C S33 .S12 C S13 C S23 / C3.S44 C S55 C S66 / GVoigt D
(32.46)
The Voigt–Reuss–Hill expression of K.KVRH / and G.GVRH / are the average of the Voigt and Reuss definition KVoigt C KReuss ; 2 GVoigt C GReuss : GVRH D 2 KVRH D
(32.47) (32.48)
Young’s modulus Y is defined as, 2
Yk D 1
0
1 Skk
.k D 1; 3/ :
(32.49)
Poisson’s ratio is calculated by averaging six components obtained from the compliance matrix 0
5
10
15
20
25 30 Ring size
Fig. 32.3 Ring size distributions of silica and sodium sili-
cate glasses (lines are cubic spline fitted). After [32.38]
1139
vxy D
S21 S31 S32 ; vxz D ; : : : ; vzy D : (32.50) S11 S11 S33
For an isotropic media such as glass, the bulk modulus .K/, shear modulus .G/, Young’s modulus .Y/, and
Part D | 32.3
shortest path, or the ring contains the minimum number of tetrahedra [32.39]. The ring size distributions of simulated silica and sodium silicate glasses are shown in Fig. 32.3. The y-axis is the number of primitive rings per base Si atom and the x-axis is the size of ring counted as the total number of Si atoms in the ring. Ring size distribution of silica shows a symmetric Gaussiantype distribution with a peak at the 6-membered ring. With modifier oxide e. g., soda added, the distribution becomes broader due to the creation of larger rings and the intensity of the peak at the 6-membered ring decreases [32.38].
32.3 MD Simulations of Glasses
1140
Part D
Glass Modelling
Poisson’s ratio .v / are related through Y 1 ; 3 .1 2 / 9KG ; YD .3K C G/
KD
(32.51) (32.52)
Part D | 32.3
and thus reduce the total independent mechanical constants to two. Alternatively, the elastic constant matrix can be obtained by solving the relationship between stress and strain tensors through a series of deformations introduced to a fully relaxed simulation cell. Sij D Cijkl kl ;
(32.53)
where, Sij are symmetric stress tensor elements, Cijkl are the fourth rank of the elastic constants, and kl are the symmetric strain elements. The number of distinct constants, reduced by symmetry is 21. Deformations of the stimulated configurations are applied from six directions .x; y; z; xy; yz; xz/, and zero energy minimization methods are employed to obtain the elastic constant matrix. Elastic moduli can then be calculated in the same way as mentioned above. The dynamic method involves simulated tensile testing by elongation of the simulation cell. This is achieved by rescaling the atom position r along the tensile direction: r D .1 C "/r0 where r0 is the initial position and " is the strain [32.41]. The effective strain rate (in the order 109 s1 ) is much higher than the experimental values due to the relatively short time samples in MD simulation. During the simulated tensile testing, the simulation box size is allowed to change in directions perpendicular to the elongation direction. The stress tensor at each step is calculated and then converted to the nominal stress tensor. Figure 32.4 shows a stress–strain diagram of silica and soda silicate glass under tensile testing [32.41]. Mechanical properties such as Young’s modulus, strength, and strain at failure can be extracted from the stress–strain curve. a) σ (GPa)
Diffusion Coefficient Calculations As in MD simulations, the time-dependent evolution of atom positions can be recorded hence dynamic properties can also be calculated from these trajectories. One of the most common dynamic properties is the selfdiffusion coefficient, which can be calculated from the mean square displacements (MSD) [32.42], + * n 1 X 2 2 hr .t/i D (32.54) jri .t/ ri .t0 /j ; n iD1 where r.t/ are position of an atom at time t. hi represent time average. MSD are usually calculated from trajectories under NVE runs after NPT or NVT equilibration at each temperature [32.27]. Figure 32.5 shows MSD of a simulated glass. In the logarithm scale (Fig. 32.5b), three typical regime behaviors of MSD are shown: the initial ballistic regime (hr2 .t/i proportional to t2 ), the long-time diffusion regime (hr2 .t/i proportional to t), and the crossover regime between ballistic and diffusion regime. Diffusion coefficient .D/ can be calculated from the diffusion regime of MSD through the Einstein relation [32.42] hr2 .t/i : t!1 6t
D D lim
(32.55)
MSD is usually averaged over particles of the same kind and over multiple time origins to improve the statistics during calculations. Diffusion coefficients can be calculated for different temperatures, from which the diffusion energy barrier can be obtained. The Arrhenius relationship of the diffusion coefficient is [32.37] Ea D D D0 exp ; (32.56) kB T where D0 is the pre-exponential factor, Ea is the diffusion energy barrier, T is the temperature, and kB is the Boltzmann constant.
b) σ (GPa)
14
8 Fiber Bulk
12
6
10 8
v-SiO2
6
Fig. 32.4a,b Stress–
NS20
4
4
2
2 0 0.0
0.1
0.2
0.3
0.4
0.5 ε
0 0.0
0.1
0.2
0.3
0.4
0.5 ε
strain curves of uniaxial tension for the bulk and nanowire of silica (a) and soda silicate (20%Na2 O80%SiO2 ) glasses (b) from MD simulations. Reprinted (adapted) with permission from [32.41]. Copyright 2015 American Chemical Society
Molecular Dynamics Simulations of Oxide Glasses
a) MSD (10–4 cm2/s)
32.4 Applications of MD Simulations in Oxide Glass Research
1141
b) MSD (10–4 cm2/s)
1000 1000
Na Ca Sr
800
100
10
400
1
200
0.1
0
Part D | 32.4
600
Na Ca Sr
0
10
20
30
40
50 t (ps)
0.01 0.01
0.1
1
10 t (ps)
Fig. 32.5a,b Mean square displacement versus time in linear (a) and logarithm scales (b) for 45S5 bioactive glasses at 2000 K. After [32.42]
Vibrational Spectra Calculations Vibrational spectroscopy such as Raman, FTIR, and inelastic neutron scattering are commonly used in glass structure characterizations. These spectroscopy methods are inherently related to the vibrational density of states in glasses (VDOS). VDOS can be calculated from the normalized velocity autocorrelation function (VACF) c.t/ [32.42], 2 hv .t/v .0/i ; c.t/ D hv .0/v .0/i
(32.57)
where v .t/ and v .0/ are velocity at time t and 0, and hi represents time averaging. The diffusion coefficient can also be calculated from the un-normalized VACF .c0 .t// through the Green–Kubo formula [32.1], 1 DD 3
Z1
c0 .t/dt :
(32.58)
0
Practically, because of the fact that fluctuation of VACF can last for very long times, the calculated D value can be influenced by the cutoff of integration. VDOS can be calculated through Fourier transformation of the velocity autocorrelation function through the following equation g.!/ D
2
Z1 c.t/ cos.!t/dt ;
(32.59)
0
where g.!/ is the VDOS, ! is the frequency of vibration, c.t/ is the velocity autocorrelation function, and t is time. In addition to the dynamic method, static methods such as diagonalization of the Hessian matrix or the finite difference method can also be used to calculate the vibrational frequencies [32.43], from which the VDOS can be obtained. The advantage here is that the normal modes corresponding to the vibrational frequencies can also be calculated.
32.4 Applications of MD Simulations in Oxide Glass Research 32.4.1 MD Simulations of Sodium Silicate and Soda Lime Silicate Glasses Alkali silicate glasses are archetypes of more complicated modified silicate glasses and have been extensively studied using MD simulations [32.38], which provide information on how the structure would change with addition of modifiers of silica network structures.
On the basis of the modified random network (MRN) model proposed by Greaves et al. [32.44], contrary to the conventional picture of modified silicate glass structures, the modifier cations do not just occupy the interstitial sites of the silica network but instead they segregate and form regions that are rich in alkali and nonbridging (NBO) ions. These regions connect the fragments of silica network structures. Structure models
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Part D | 32.4
of alkali silicate glasses from MD simulations support the MRN and provide additional insights such as medium-range orders in glasses [32.38]. Du and Corrales studied the alkali silicate xA2 O.100 x/SiO2 glasses across the glass formation ranges (x D 1540 for Li2 O, x D 1050 for Na2 O, and x D 1040 for K2 O) using MD simulations [32.24] with partial charge potentials listed in Table 32.1. The alkali–oxygen bond distance and coordination number changes depend on the alkali species and the composition. Table 32.3 shows the bond distance and coordination number of alkali silicate glasses. It can be seen that the Li–O distance is around 1:95 Å with the oxygen coordination number around lithium ions increasing from 3:2 to 3:8 with increasing Li2 O concentration from 15 to 40%. In sodium silicate glasses, the Na–O bond distance increases from 2:36 to 2:39 Å and the sodium coordination number increases from 4:4 to 5:1. Potassium silicate glasses have a larger K–O distance of around 2:77 and the potassium coordination number decreases slightly from 8:0 to 7:4. The contribution of BO, NBO, and FO (free oxygen, i. e., oxygen ions that do not bond to any silicon) can also be calculated from the simulations and their percentage are also provided in Table 32.3 [32.24]. It can be seen that there is a mixture of BO and NBO around the modifier cations, a picture similar to that in crystalline sodium silicates and the
MRN model [32.44]. For example in the sodium disilicate (Na2 O 2SiO2 ) crystal structure, Na ions have a coordination number of 5, with 60% of them being BO and 40% being NBO. One critical structure aspect in alkali silicate glasses, surprisingly with very few experimental and simulation studies, is the distribution of alkali ions in the glass structure. The distribution of alkali ions in the glass provides a means to check the structure models proposed. Du and Cormack characterized sodium ion distribution by calculating the second moment of sodium silicate glasses from MD-generated sodium silicate glass structures. The second moment, M2 , is defined as [32.45] M2 D 0:9562
2 0
4
4 ¯2
X
rij6 ;
(32.60)
j
where 0 is the vacuum permittivity, is the magnetogyric ratio, ¯ is Plank’s constant divided by 2 , and rij is the distance between atom i and j. Experimentally, Gee and Eckert [32.45] studied the spin echo resonance of sodium ions in sodium silicate glasses and used the second moment to characterize the spatial distribution of sodium ions in glasses. While the pair distribution function reduces the three-dimensional structure to one dimension, the second moment reduces the structure to
Table 32.3 Modifiers–oxygen bond length and coordination number in alkali silicate glasses obtained from MD simulations [32.24] Li2 O (%)
R Li–O (Å) (˙0:01 Å)
Total coord. # (cutoff 2:6 Å)
15 20 25 30 33:3 40 Na2 O (%)
1:93 1:95 1:95 1:96 1:95 1:96 R Na–O (Å) (˙0:01 Å)
3:22 3:35 3:48 3:57 3:68 3:76 Total coord. # (cutoff 3:0 Å)
10 20 30 33:3 40 50 K2 O (%)
2:36 2:38 2:39 2:39 2:39 2:39 R K–O (Å) (˙0:01 Å)
4:43 4:66 5:00 5:02 5:10 5:09 Total coord. # (cutoff 3:8 Å)
10 20 33:3 40
2:76 2:77 2:77 2:75
8:02 7:79 7:60 7:40
Percentage (%) NBO 67:6 72:5 74:0 78:0 79:0 82:3 Percentage (%) NBO 48:4 59:8 67:4 70:6 76:0 83:7 Percentage (%) NBO 30:6 45:3 58:4 65:5
BO 32:4 27:5 25:4 21:9 20:0 16:9
FO 0:0 0:0 0:6 0:2 0:9 0:9
BO 51:6 40:2 32:6 29:2 23:8 15:5
FO 0:0 0:0 0:0 0:1 0:2 0:8
BO 69:4 54:7 41:6 34:4
FO 0:0 0:0 0:0 0:1
Molecular Dynamics Simulations of Oxide Glasses
M2 (106 rad2/ms2) 35 30 25
been characterized from NMR for a wide range of alkali silicate glasses and in wide composition ranges, extensive comparison with experimental data is thus possible. Figure 32.7 shows the comparison of the Qn distribution of sodium silicate glasses from MD, NMR and a random distribution model. It can be seen that the trend of Qn distribution from MD follows that of NMR data well. The existence of a maximum of Q3 proportion at around 30% Na2 O is well reproduced in MD. However, quantitatively, the percentage of Q3 is smaller, and that of Q2 and Q4 higher, than experimental NMR values, suggesting 2Q3 , Q2 CQ4 reaction to the right direction, which is consistent with the higher fictive temperature of simulated glass structures. More recently, the comparison of Qn distribution in lithium silicate glasses between MD and NMR were made by Du and Chen [32.46]. Similar trends of Qn distribution were observed in lithium silicate glasses [32.46]. Other medium-range structure features include ring size distribution. The primitive ring size distribution for sodium silicate glasses is shown in Fig. 32.3. It can be seen that with increasing sodium oxide content, the peak at the six-membered ring decreases and the tail of the larger ring increases indicating that more open structures with larger rings are formed, again consistent with the MRN model suggesting regions with alkali ions and NBO segregation. Another way to characterize the medium-range structure change is from the first sharp diffraction peak (FSDP) in structure factors of glasses. FSDP has been seen as a signature of the medium-range
20 Qn distribution (%) 100
15 10
80
MD simiulation NMR results Random model Q4
5 0
60 0
10
20
30
40
50
60 70 Na2O (mol%) 40
Fig. 32.6 Comparison of second moments .M2 / of sodium
distribution from sodium silicate glasses with uniform/random distributions and those of several crystalline materials. Green triangle: uniform distribution; blue triangle: random distribution generated from crystalline sodium oxide lattice; cross: random distribution generated statistically with shortest Na–Na constraint; red circle: MD modeling; solid square: sodium silicate crystals calculated from structure data. Crystals are alpha (upper) and beta (lower) sodium disilicates, sodium metasilicate, and sodium othosilicate. Lines are used as a guide to the eye. After [32.38]
20
0
Q1
Q3
Q2 10
20
30
40
50 Na2O (mol%)
Fig. 32.7 Comparison of Qn distributions of simulated glasses with experimental NMR data and random distribution. Q4 : triangle; Q3 : square box; Q2 : circle; Q1 : cross. After [32.38]
1143
Part D | 32.4
a single number, which enables direct comparison of different models. The calculated second moment of Na ions as a function of Na2 O concentration is shown in Fig. 32.6. Also in the figure are the second moment calculated from the homogeneous distribution model based on the antifluoride Na2 O structure, those from a random distribution, and those from crystal structures of binary sodium silicates. The second moment of sodium in glasses is very different from those from an even or homogenous distribution, similar but slightly more random than those in the sodium silicate crystal structures, where sodium ions are also segregated with NBOs, and very similar to those from a random distribution. The results thus support a more segregated sodium distribution in glasses that is similar to the MRN model. In addition to the short-range structures, the medium-range structure can also be elucidated from MD simulations. The Qn distribution, a term borrowed from solid-state NMR and meaning the average number of bridging oxygens n per SiO4 tetrahedron, is one way to characterize the network arrangement at the medium-range level. As the Qn distribution has
32.4 Applications of MD Simulations in Oxide Glass Research
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Fig. 32.8 Neutron scattering total structure factors of silica and sodium silicate glasses (named after NSx, for xNa2 O-.100 x/SiO2 , x D 1050). After [32.24] J
S N (Q) 7 SiO2 6
Part D | 32.4
NS10 5 NS20 4
NS30
3
NS40
2
NS50
1
0 0
5
10
15
20
25 Q (Å–1)
order of network-forming glasses, with the exact origin still under debate [32.47]. The calculated neutron structure factor for silica glass and sodium silicate glasses
is shown in Fig. 32.8 for a wide composition range: xNa2 O-.100 x/SiO2, .x D 10 50/ [32.24]. The comparison of calculated and experimental neutron structure factors are in good agreement for silica glass and sodium disilicate glass [32.47]. The total structure factors were calculated from the partial pair distribution functions of the simulated glasses. The peak at 1:6 Å1 is the FSDP and it can be seen that the FSDP intensity decreases with increasing sodium content, suggesting a decrease of medium-range order. In addition to the peak position, the shape or FWHM (full-width at half-maximum) of FSDP was also considered to correlate to the mediumrange structure [32.24]. Addition of calcium to soda silicate significantly improves the mechanical properties and chemical durability. Because of reasonable physical, chemical properties and relatively cheap raw materials, soda lime silicate is the most-produced glass (over 90% in volume). The simulations of soda silicate glasses are otherwise very limited as addition of CaO increases the complexity of the alkali silicate glasses. Cormack and Du studied soda lime silicate glass with .25 x/Na2 OxCaO-75SiO2 (mol%) compositions using MD simulations [32.11]. Figure 32.9 shows the Na-O and Ca-O partial correlation function of 20Na2 O-5CaO-75SiO2 soda lime silicate glass [32.11]. The BO and NBO contributions are also shown. It can be seen that the
a) T (r)
b) T (r)
8
8
7
7
6
6
5
5 Na-O
4
4
3
3
2
Ca-NBO
2 Na-BO Na-NBO
1 0
Ca-O
1
2
3
4
5
Ca-BO
1 6 r (Å)
0
1
2
3
4
5
6 r (Å)
Fig. 32.9a,b Total correlation function T.r/ for Na-O (a) and Ca-O (b) pairs of a soda lime silicate glass .20Na2 O-5CaO75SiO2 /. The deconvoluted BO and NBO contributions are also included. Reprinted from [32.11] with permission from Elsevier
Molecular Dynamics Simulations of Oxide Glasses
32.4 Applications of MD Simulations in Oxide Glass Research
1145
Table 32.4 The coordination distribution of O around Al in sodium aluminosilicate glasses from MD simulations using
the Buckingham and Morse potentials [32.13] RAl/Na D NAl =NNa 1:5 1:0 0:6
Buckingham (%) 3 4 0:87 98:70 0:83 98:62 3:38 96:29
5 0:43 0:55 0:37
32.4.2 MD Simulations of Aluminosilicate Glasses Aluminosilicate glasses find wide industrial applications from container, display to fiber glasses. For example, the Corning Gorilla® glass used in display and touch screens belongs to the aluminosilicate glass family [32.13]. MD simulations help to deepen the understanding of the structure and structure–property relationships of these glasses [32.12, 13, 40, 48]. One important question in relation to the aluminosilicate structure is the coordination of aluminum ions as a function of composition and the precise charge compensation of Al. Xiang et al. [32.13] reported MD simulations of sodium aluminosilicate glasses by using MD simulations with two sets of popular potentials of the Buckingham and Morse form with parameters Fig. 32.10 (a) Quantification of different types of threebonded oxygen (TBO) atoms. Type 1 is the TBO bonded to three Al (noted as 3Al); type 2 is the TBO bonded to 2 silicon and one Al (noted as 2Si1Al); type 3 is the TBO bonded to one Si and two aluminum (noted as 1Si2Al). (b) Oxygen triclusters (left: 1Si2Al; right: 3Al) observed in aluminosilicate glasses from MD simulations. Brown ball: oxygen, dark grey ball: aluminum, light grey ball: silicon (after [32.13, 40]) I
4 93:26 93:33 97:3
5 6:74 6:08 2:36
6 0 0:28 0:34
shown in Tables 32.1 and 32.2. The simulated glass compositions had around 60 mol% of SiO2 with Al2 O3 increasing from 15 to 23%, and the remaining being Na2 O, hence covering peralkaline to peraluminus compositions. Table 32.4 lists the aluminum coordination number as a function of composition. It can be seen that majority of Al are four-fold coordinated, simulations with the Buckingham potential predicted small amounts of 5-fold coordinated Al .< 1%/ while the Morse potential predicted higher amounts of 5-fold coordinated Al (27%) and small amounts of 6-fold coordinated Al. With increasing alumina concentration, the amount of 5-fold coordinated Al increased. In addition to an increase of Al coordination, formation of oxygen triclusters is another way to compensate the charge around AlO 4 . This was indeed observed in MD simulations with the major types of tricluster being 3Al and 2Al1Si [32.13, 40]. Oxygen tricluster percentage as a function of glass composition is shown in Fig. 32.10. With increasing alumina content and Al/Na ratio from a) Oxygen coordination (%) 12 11 10 9 8
3Al 2Si1Al 1Si2Al
7 6 5 4 3 2 1 0 0.0
b)
0.5
1.0
1.5
2.0 RAl/Na
Part D | 32.4
Ca-O distribution has a much stronger first peak than Na-O, which is broader with a long tail. The average coordination number of Na is 5:0 with 56% of Na atoms having an NBO, while the average coordination number of Ca is 5:8 with around 72% of Ca atoms having an NBO. Although both have similar ionic radii, as a result the Na–O and Ca–O bond distances are very similar . 2:4 Å/, the higher field strength of Ca2C compared to Na1C leads to its stronger capability to compete for NBO and slightly higher coordination number, i. e., oxygen ions pack more loosely around Na than Ca [32.11]. The stronger bonding and higher packing density around Ca ions has significant structural implications on the properties. Because of the stronger bonding, Ca ions can bind the silica network pieces together more strongly. This led to muchimproved chemical durability and mechanical strength of soda lime silicate glasses as compared to soda silicate glasses.
Morse (%) 3 0 0:28 0
6 0 0 0
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a) K (GPa)
Part D | 32.4
60 58 56 54 52 50 48 46 44 42 40 14
b) G (GPa) Buckingham Morse
16
18
20
22 24 Al2O3 (mol %)
33 32 31 30 29 28 27 26 25 24 14
c) Y (GPa) 85 Buckingham Morse Exp.
80
Buckingham Morse Exp.
75 70 65
16
18
20
22 24 Al2O3 (mol %)
60 14
16
18
20
22 24 Al2O3 (mol %)
Fig. 32.11a–c Comparison of bulk (a), shear (b), and Young’s modulus (c) of sodium aluminosilicate glasses with Al/Na ratio from 1:5 to 0:6 from simulations with two sets of potentials and those from experiments (after [32.13])
300 K
2000 K
3000 K
4000 K
z x
y
Fig. 32.12 Snapshot of structure of ˇ-LiAlSi2 O6 as a function of increasing temperature from MD simulations. Reprinted from [32.49] with permission from John Wiley and Sons
0:5 to 1:5, the percentage of oxygen tricluster increases from 1 to over 8%. Mechanical properties of sodium aluminosilicate glasses have been calculated by the static method using the structures generated from MD simulations [32.13]. The calculated bulk moduli, elastic moduli, and shear moduli for simulations using the two sets of potentials are compared with those from experimental measurements. This is shown in Fig. 32.11 [32.13]. With increasing alumina content, the moduli all increased. This is in excellent agreement with the experimental trend and can be understood by the increased network connectivity from increasing alumina concentration. This also shows that although there are some numerical differences, both potentials correctly reproduce the trend of mechanical property change with composition. Ren and Du recently studied the structure and properties of lithium aluminosilicate glass in comparison to the two crystal polymorphs of the spodumene composition (LiAlSi2 O6 ) using MD simulations [32.49] with potentials listed in Table 32.1. The melting behaviors of these glasses and crystals were simulated
using MD simulations with the constant pressure (NPT) ensemble. Figure 32.12 shows the structure change of ˇ-LiAlSi2 O6 as a function of temperature and the volume changes of all three systems are listed in Fig. 32.13 [32.49]. It can be seen that at 2000 K, the basic crystal structure remains unchanged although there are some vibration-induced structure changes. At around 2700 K, melting begins and at 4000 K the crystal is completely melted. The melting behavior shows the important feature that ˇ-LiAlSi2 O6 and the glass form have very similar volume, which is considerably larger than ˛-LiAlSi2 O6 . While from the energy point of view, ˛- and ˇ-LiAlSi2 O6 have similar energies, both lower than that of the glass. For both glass and crystals, there is a jump or discontinuity at the melting point. The difference of the melting behaviors between the LiAlSi2 O6 glass and crystal polymorphs originates from the atomic structure of these systems. Figure 32.14 shows the Si–O and Al–O pair distribution functions of the three materials [32.49]. Si–O has very similar behaviors in all three systems while for the Al–O
Molecular Dynamics Simulations of Oxide Glasses
a) V (Å3)
32.4 Applications of MD Simulations in Oxide Glass Research
b) Econfig (eV) –550
700 α-LiAlSi 2O6 ß-LiAlSi 2O6 LiAlSi 2O6 glass
650
α-LiAlSi 2O6 ß-LiAlSi 2O6 LiAlSi 2O6 glass
–555 –560 –565
600
Part D | 32.4
–570 550 –575 500
–580 –585
450 –590 400
1147
0
1000
2000
3000
4000
5000 T (K)
–595
0
1000
2000
3000
4000
5000 T (K)
Fig. 32.13a,b Changes in volume (a) and configuration energy (b) per unit formula ˛-LiAlSi2 O6 , ˇ-LiAlSi2 O6 , and LiAlSi2 O6 glass as a function of temperature from MD simulations. Reprinted from [32.49] with permission from John Wiley and Sons
a) PDF (Si–O)
b) PDF (Al–O)
PDF (Si–O) α-LiAlSi 2O6 ß-LiAlSi 2O6 LiAlSi 2O6 glass
30
30
25
25
PDF (Al–O) α-LiAlSi 2O6 ß-LiAlSi 2O6 LiAlSi 2O6 glass
20
20
15
20
15
15
20
10 5
10
15
10
5
10
0 1.4
0 1.4 1.5
1.6
1.7
1.8
1.9
2.0 r (Å)
1.6
1.8
4
5
2.0
2.2
2.4
2.8 r (Å)
5
5 0
1
2
3
4
5
6
7
8
9
10 r (Å)
0
1
2
3
6
7
8
9
10 r (Å)
Fig. 32.14 (a) Si–O (b) Al–O pair distribution functions g.r/ for ˛-LiAlSi2 O6 , ˇ-LiAlSi2 O6 , and LiAlSi2 O6 glass at 300 K from MD simulations. Reprinted from [32.49] with permission from John Wiley and Sons
pair, the first peaks of the glass and ˇ polymorphs are very similar with a bond distance of 1:74 Å indicating a tetrahedron coordination. Conversely, the first peak of the ˛ polymorph is broader and located at a longer distance suggesting an octahedral environment for the aluminum. As we know in ˇ-LiAlSi2 O6 , aluminum substitutes one third of the silicon in the corner-sharing silica tetrahedral network structure with lithium ions acting as charge compensators. This is consistent with the four-fold coordination observed in the crystals. Interestingly, aluminum in LiAlSi2 O6 glass is also mostly
four-fold coordinated, which leads to the similar density of ˇ-LiAlSi2 O6 and the glass. In addition to the structures, dynamic properties such as ionic diffusion have also been studied using MD simulations. The diffusion coefficients .D/ were calculated from the mean square displacements detailed in Sect. 32.3.2, Coordination Number and Accumulated Coordination Number and shown in Fig. 32.15. It is found that the diffusion coefficient of lithium ions in the beta form and glass are significantly higher than that of the alpha form for temperatures below the
1148
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Glass Modelling
log D (cm 2/s) 4000 –3.0
T (K) 2000
3000
–3.5 –4.0
Part D | 32.4
–4.5 –5.0 –5.5 –6.0 0.25
α-LiAlSi 2O6 ß-LiAlSi 2O6 LiAlSi 2O6 glass 0.30
0.35
0.40
0.45
0.50 1000/T (1/K)
Fig. 32.15 Li ion diffusion coefficients in ˛-LiAlSi2 O6 , ˇLiAlSi2 O6 , and LiAlSi2 O6 glass (20003700 K) from MD simulations. Reprinted from [32.49] with permission from John Wiley and Sons
melting temperature. The slope of D versus 1=T of the two group materials are also quite different: the slope for ˛-LiAlSi2 O6 is considerably steeper than the other two suggesting a higher activation energy barrier. Indeed, the calculated activation energy barrier for ˛LiAlSi2 O6 is around 1 eV while that for ˇ-LiAlSi2 O6 and LiAlSi2 O6 glass has only about half of the value at around 0:5 eV [32.50]. This again can be explained by the structure difference of the three phases. In ˇ-LiAlSi2 O6 and LiAlSi2 O6 glass, the structure is relatively open and there is more free volume for lithium ions to diffuse while the structure of ˛-LiAlSi2 O6 is more closely packed, which makes lithium ion diffusion more difficult. MD simulations thus provide both structural, thermal, and dynamic (mainly diffusion) interpretations of LiAlSi2 O6 glasses and their difference from the crystal forms of the same composition [32.49].
breaking and formation. However, the recent development of the reactive force field (ReaxFF) [32.29] and its extension to silica/water systems [32.31, 32] enabled simulations of the silica glass/water systems. Forgaty et al. [32.31] developed water and related parameters to extend the silica/silicon ReaxFF potentials and applied them to MD simulations of silica glass/water interfaces. Quantum mechanical data, both energetic and structural, for water clusters, Si–O–H bond combination, angle distortion, and equation of states of silica and silicon were used as the training set. Additionally, binding and dissociation energies of silicic acid .Si.OH/4 / and polymerization of silicic acid from QM calculations were also included in the training set [32.31]. This development enabled reactive MD simulations of a system with 3000 atoms of silica glass and 2025 water molecules for 580 ps, a significant achievement at the time when the paper was published [32.31]. Hydroxylation of the silica surface occurred due to the hopping of hydrogen atoms through the top surface layers of silica glass to react with dangling bonds (or coordination defects) [32.31]. Figure 32.16 shows the silica/water interface generated using ReaxFF simulations after reaction in 1 ns simulations at an elevated temperature. It is shown that silanol bonds were formed at the interface during the hydroxylation. Furthermore, dissolved silicon atoms in the form of silicic acid .Si.OH/4 / monomer or dimers are observed in the bulk water region showing the dissolution behaviors of silica glass. The results show that ReaxFF is capable of simulating the silica/water interface and dissolution behaviors of silica glass. Several later studies [32.32, 33] were performed to improve the silica/water ReaxFF parameters of
32.4.3 Simulations of Silica Glass/Water Interaction Using a Reactive Force Field The ability to model glass/water interaction and reactions and the glass/water interface structures is of critical importance to understand the properties of glasses such as stress corrosion, chemical durability, bioactivity, and others [32.30, 51]. Most of the potentials for bulk glass simulations were not equipped for the simulation of reaction with water, as these potentials are not reactive meaning not capable of simulating bond
Fig. 32.16 Silica glass/water interface from ReaxFF-based
MD simulations (after [32.33]) using the refined ReaxFF parameters (after [32.32]). Yellow ball: silicon; red ball: oxygen; white ball: hydrogen
Molecular Dynamics Simulations of Oxide Glasses
a)
b)
32.4 Applications of MD Simulations in Oxide Glass Research
Fig. 32.17a–e Snapshots of a twomembered ring (a) reaction with
d)
e)
Forgarty et al. [32.31]. For example, Yoen and van Duin [32.52] found that while the Forgarty parameterization was able to describe the energy barrier for hydroxylation of unstrained Si–O–Si bonds it significantly underestimated that of the strained Si–O–Si bonds, such as those in the two-membered rings. This was corrected in the 2015 parameter set [32.52] to reproduce 2030 kcal=mol barriers from DFT (density functional theory) calculations. This improvement was further proved by comparing the two versions of ReaxFF with ab initio molecular dynamic simulations for the nanoporous silica/water system [32.32]. Figure 32.17 shows the mechanism (reaction steps) of a twomembered ring (Fig. 32.17a) opening in nanoporous silica through the formation of five-coordinated silicon (Fig. 32.17b), a hydrogen bond on a bridging oxygen (Fig. 32.17d), and eventually breaking of the Si–O–Si bond (Fig. 32.17e). The reaction energy barrier of water with a stand-alone two-membered ring from the two ReaxFF parameterizations for the silica/water system was also compared with DFT calculations [32.32]. The results show that the new parametrization [32.52] provided a much closer reaction energy barrier of 20:1 kcal=mol—as compared to 25:1 kcal=mol, the result from the nudged elastic band (NEB) calculations based on DFT [32.32]—than the 8:1 kcal=mol of the 2010 parameterization [32.31]. In a recent study, Rimsza and Du [32.33] used ReaxFF-based MD simulations to study silica/water in-
terfacial structures and their evolution with an aim to understand the dissolution gel structure of silica and borosilicate glasses. A model consisting of three regions of dense silica, porous silica, and water was constructed to mimic the porous silica gel formed after dissolution of the dissolvable species. After relaxation at different temperatures for up to 1 ns, the models represent the interface of the gel structure annealed at different temperatures. Figure 32.18a shows the pore size distribution and Fig. 32.18b the ring size distribution of the silica gel after annealing at different temperatures [32.33]. The higher annealing temperature represents a longer gel formation period. The gel relaxed at 300 K has a pore size centered at 3:7 Å, while the gel structures annealed at higher temperatures have wider pore size distributions, with larger pores created. This is because of continued dissolution reactions and the opening of the siloxane bonds by reaction of the gel with water [32.33]. At the same time the ring size distribution of the gel layer shows the opposite trend: an increase of five- and six-membered rings with annealing at higher temperatures. This suggests that the silica network has undergone reorganization which was also shown by the increase in higher n Qn species observed in NMR studies [32.53]. These results show that the reactive force field can be used for the study of the dynamic reaction of water with glass materials, as well as the complex interfacial behaviors at the water/glass interfaces [32.33].
Part D | 32.4
water through the intermediate steps (b–e) in a hydrated nanoporous silica structure using the refined ReaxFF parameters. Reprinted (adapted) with permission from [32.32]. Copyright 2016 American Chemical Society c)
1149
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Glass Modelling
a) Concentration
b) Ring concentration (#/Si)
0.30
0.18 Initial SGW-1 SGW-2 SGW-3 SGW-4
0.25 0.20
Initial SGW-1 SGW-2 SGW-3 SGW-4
0.16 0.14 0.12
Part D | 32.5
0.10 0.15 0.08 0.10
0.06 0.04
0.05 0.02 0.00 2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0 6.5 Pore size (Å)
0.00
2
4
6
8
10
12 14 Ring size
Fig. 32.18 (a) Pore size and (b) primitive ring size distribution as a function of annealing temperature in the gel layer. SGW-1: 300 K; SGW-2: 500 K; SGW-3: 700 K; SGW-4: 900 K. Reprinted (adapted) with permission from [32.33]. Copyright 2016 American Chemical Society
32.5 Outlook and Challenges Despite rapid progress and increasing applications of MD simulations in glass materials, several challenges still exist that need to be addressed by the community [32.25, 37, 50]. One of the first challenges is that of empirical potential development for MD simulations. Reliable, transferable, and efficient potentials are the key input in MD simulations. Although there are many developed silicate potentials, potentials for other glass formers, particularly potentials for borate-containing glasses to correctly reproduce the composition-dependent coordination changes, for example boron in borosilicate glasses [32.54], remain relatively underdeveloped. Methodologies to speed up and automate the potential development process such as machine learning and genetic algorithms need to be developed. In addition, development of potentials to study heterogeneous interfaces of glasses with other materials, such as glass/water interactions and glass/metal interfaces, are also needed [32.51]. There has been some progress in applying the reactive force field (ReaxFF) in MD simulations [32.34] of water/silicate glass interfaces but more work is needed for multicomponent systems. Conversely, ab initio-based MD [32.43, 55], in which the interatomic forces are calculated from first principles, may be the ultimate solution to the potential issue with the ever-increasing computing power and development of faster algorithms. However, at the moment, the systems that can be studied using AIMD (ab initio molecular dynamics) are
still limited to a few hundred atoms and relatively short times due to its very high computational cost. As shown in this chapter, the development and optimization of reactive force fields (such as ReaxFF) have already shown very promising results in modeling water/silica glass reactions and the associated complex interfacial behaviors. Other applications of ReaxFF include the study of the reactions in sol–gel processes [32.56]. Several other developments of reactive potentials such as the one by Mahadevan and Garofalini also show promise for the study of water/glass reactions [32.57]. Another challenge is the accessible time in MD simulations [32.37]. Parallel computing and faster algorithms help to bring simulation time down from picoseconds to microseconds in a system of a few thousand atoms. One of the most common critiques of glasses generated from MD simulations is their relatively high cooling rate, which is limited by the accessible simulation time. In addition, when sampling rare events such as diffusion at relatively low temperatures, long time period simulations are needed. Some simulation methods have been developed to address these challenges such as umbrella sampling, accelerated MD, and Monte Carlo-based methods [32.25]. Each of them can be applied to some situations but also have their limitations. Validation of simulation results with experimental structural data is another challenge, but some new
Molecular Dynamics Simulations of Oxide Glasses
As a result of the importance of MD and other simulations to glass research, the International Commission on Glass (ICG) formed a new technical committee (TC) on Atomistic Modeling and Simulation of Glasses in 2009 with John Mauro of Corning Inc. being the founding chair and the author of this chapter (J. Du) being the current chair since 2011. The focus of the TC27 is on developing the theoretical foundation for advancing the modeling and simulation of glassy systems. The TC has organized several roadmap sessions and a series of workshops on challenges of MD simulations of glasses and amorphous materials. The book based on the contributions of the first workshop [32.2] provides a summary of the state of the art in MD simulations, both in terms of methodology and applications, and provides a unique reference for the area of atomistic simulations of glasses.
32.6 Conclusions MD simulations have become a reliable method that is widely used to study the structures, properties, and structure–property correlations of glass materials. This chapter introduces the fundamentals and applications of MD simulations of glasses, with the aim to provide the readers with a broad picture of the field. Starting from the basics of MD simulations, structure analysis of glass structures from simulations, property calculations, applications of MD in alkali silicate, soda lime silicate, sodium and lithium aluminosilicate glasses were introduced. Challenges and future directions are also discussed. It is conceivable that,
with ever-increasing computing power and development of methodologies and new potentials, MD will play a more and more important role in future glass research. Acknowledgments. The author acknowledge financial support of the Center for Performance and Design of Nuclear Waste Forms and Containers, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0016584 and National Science Foundation DMR Ceramic (project # 1508001).
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32.3
32.4 32.5 32.6
M.P. Allen, D.J. Tildesley: Computer Simulation of Liquids (Clarendon, Oxford 1989) C. Massobrio, J. Du, P.S. Salmon, M. Bernasconi (Eds.): Molecular Dynamics Simulations of Disordered Materials: From Network Glasses to PhaseChange Memory Alloys, Springer Series in Material Science, Vol. 215 (Springer, Cham 2015) A. Leach: Molecular Modeling: Principles and Applications, 2nd edn. (Prentice Hall, Upper Saddle River 2001) B.J. Alder, T.E. Wainwright: Phase transition for a hard sphere system, J. Chem. Phys. 27, 1208 (1957) A. Rahman: Correlations in the motions of atoms in liquid argon, Phys. Rev. A 136, 405 (1964) F.H. Stillinger, A. Rahman: Molecular dynamics study of liquid water under high pressure, J. Chem. Phys. 60, 1545 (1974)
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L.V. Woodcock, C.A. Angell, P. Cheeseman: Molecular dynamics studies of the vitreous state: Simple ions systems and silica, J. Chem. Phys. 65, 1565 (1976) T.F. Soules: A molecular dynamics calculation of the structure of sodium silicate glasses, J. Chem. Phys. 71, 4570 (1979) C. Huang, A.N. Cormack: Structural difference and phase separation on alkali silicate glasses, J. Chem. Phys. 95, 3634–3642 (1991) C. Huang, A.N. Cormack: The structure of sodium silicate glass, J. Chem. Phys. 93, 8180–8186 (1990) A.N. Cormack, J. Du: Molecular dynamics simulation of soda-lime-silicate glasses, J. Non-Cryst. Solids 293–295, 283–289 (2001) L.R. Corrales, J. Du: Characterization of ion distributions near the surface of sodium containing
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developments in characterization also provide opportunities. X-ray and neutron diffractions have been the standard validation tool for glass structures from MD simulations [32.47, 48]. The challenge is to determine whether good agreement of the total structure factor or total correlation function ensure the best structure model. The development of combined MD and reverse Monte Carlo (RMC) simulations may be an opportunity to further validate and refine simulated structures [32.58]. More recently, development in characterization techniques such as solid-state NMR and imaging techniques with atomic level resolution provide unique opportunities to validate and guide MD simulation such as potential refinement. For example, combining MD and NMR has been shown to be a very useful way of generating structural insights into glass structure [32.59, 60].
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and sodium depleted calcium aluminosilicate glass melts, J. Am. Ceram. Soc. 89, 36–41 (2006) Y. Xiang, J. Du, M.M. Smedskjaer, J.C. Mauro: Structure and properties of sodium aluminosilicate glasses from molecular dynamics simulations, J. Chem. Phys. 139, 044507 (2013) J. Du, L. Kokou, J.R. Rygel, Y. Chen, C. Pantano, R. Woodman, J. Belcher: Structure of cerium phosphate glasses: Molecular dynamics simulations, J. Am. Ceram. Soc. 94, 2393–2401 (2011) H. Inoue, A. Masuno, Y. Watanabe: Modeling of the structure of sodium borosilicate glasses using pair potentials, J. Phys. Chem. B 116, 12325–12331 (2012) K.D. Vargheese, A. Tandia, J.C. Mauro: Molecular dynamics simulations of ion-exchanged glass, J. Non-Cryst. Solids 403, 107–112 (2014) J. Du, C.-H. Chen: Structure and lithium ion diffusion in lithium silicate glasses and at their interfaces with lithium lanthanum titanate crystals, J. Non-Cryst. Solids 358, 3531–3538 (2012) J. Luo, K.D. Vargheese, A. Tandia, G. Hu, J.C. Mauro: Crack nucleation criterion and its application to impact indentation in glasses, Sci. Rep. 6, 23720 (2016) J.C. Mauro, A. Tandia, K.D. Vargheese, Y.Z. Mauro, M.M. Smedskjaer: Accelerating the design of functional glasses through modeling, Chem. Mater. 28, 4267–4277 (2016) W.H. Zachariasen: The atomic arrangement in glasses, J. Amer. Chem. Soc. 54, 3841–3851 (1932) R.J. Bell, P. Dean: Properties of vitreous silica: Analysis of random network models, Nature 212, 1354–1135 (1966) P.H. Gaskell, I.D. Tarrant: Refinement of a random network model for vitreous silica, Philos. Mag. B 42, 265–286 (1980) A.C. Wright, M.F. Thorpe: Eighty years of random networks, Phys. Status Solidi (b) 250, 931–936 (2013) J. Du, L.R. Corrales: Compositional dependence of the first sharp diffraction peaks of alkali silicate glasses, J. Non-Cryst. Solids 352, 3255–3269 (2006) J. Du: Challenges in molecular dynamics simulations of multicomponent oxide glasses. In: Molecular Dynamics Simulations of Disordered Materials: From Network Glasses to Phase-Change Memory Alloys, Springer Series in Material Science, Vol. 215, ed. by C. Massobrio, J. Du, P.S. Salom, M. Bernasconi (Springer, Cham 2015) pp. 157–180 J. Du, A.N. Cormack: Molecular dynamics simulation of the structure and hydroxylation of silica glass surface, J. Am. Ceram. Soc. 88, 2532–2539 (2005) A. Pedone, G. Malavasi, M.C. Menziani, A.N. Cormack, U. Segre: A new self-consistent empirical potential model for oxides, silicates and silica based glasses, J. Phys. Chem. B 110, 11780–11795 (2006) A. Tilloca, N.H. de Leeuw, A.N. Cormack: Shellmodel molecular dynamics calculations of modified silicate glasses, Phys. Rev. B 73, 104209 (2006) A.C.T. van Duin, S. Dasgupta, F. Lorant, W.A. Goddard: ReaxFF: A reactive force field for hydrocarbons, J. Phys. Chem. A. 105, 9396–9409 (2001)
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T.P. Senftle, S. Hong, M.M. Islam, S.B. Kylasa, Y. Zheng, Y.K. Shin, C. Junkermeier, R. EngelHerbert, M.J. Janik, H.M. Aktulga, T. Verstraelen, A. Grama, A.C.T. van Duin: The ReaxFF reactive force-field: Development, applications and future directions, NPJ Comput. Mater. 2, 15011 (2016) J.C. Fogarty, H.M. Aktulga, A.Y. Grama, A.C.T. van Duin, S.A. Pandit: A reactive molecular dynamics simulation of the silica-water interface, J. Chem. Phys. 132, 174704 (2010) J.M. Rimsza, J. Yeon, A.C.T. van Duin, J. Du: Water-nanoporous silica interactions: Comparison of ReaxFF and ab initio based molecular dynamics simulations, J. Phys. Chem. C 120, 24803–24816 (2016) J. Rimsza, J. Du: Interfacial structure and evolution of the water-silica gel system by reactive force field based molecular dynamics simulations, J. Phys. Chem. C 121, 11534–11543 (2017) J. Rimsza, L. Deng, J. Du: Molecular dynamics simulations of nanoporous silica and organosilicate glasses using reactive force field (ReaxFF), J. NonCryst. Solids 431, 103–111 (2016) L.R. Corrales, J. Du: Thermal kinetics of glass simulations, Phys. Chem. Glasses 46, 420–424 (2005) J. Du: Molecular Dynamics Simulations of the Structures of Silicate Glasses Containing Hydroxyl Groups and Rare Earth Ions, Ph.D. Thesis (Alfred University, Alfred 2004) J. Du, Y. Xiang: Investigating the structure-diffusion-bioactivity relationship of strontium containing bioactive glasses using molecular dynamics based computer simulations, J. Non-Cryst. Solids 432, 35–40 (2016) J. Du, A.N. Cormack: The medium range structure of sodium silicate glasses, J. Non-Cryst. Solids 349, 66–79 (2004) X. Yuan, A.N. Cormack: Efficient algorithm for primitive ring statistics in topological networks, Comput. Mater. Sci. 24, 343–360 (2002) J. Du: Molecular dynamics simulations of the structure and properties of low silica yttrium aluminosilicate glasses, J. Am. Ceram. Soc. 92, 87–95 (2009) A. Pedone, M.C. Menziani, A.N. Cormack: Dynamic fracture in silica and soda-silicate glasses: From bulk materials to nanowires, J. Phys. Chem. C 119, 25499–25507 (2015) J. Du, Y. Xiang: Effect of strontium substitution on the structure, ionic diffusion and dynamic properties of 45S5 Bioactive glasses, J. Non-Cryst. Solids 358, 1059–1071 (2012) J. Du, L.R. Corrales: ab initio molecular dynamics study of the structure, dynamics, and electronic properties of lithium sisilicate melt and glass, J. Chem. Phys. 125, 114702 (2006) G.N. Greaves, A. Fontaine, P. Lagarde, D. Raoux, S.J. Gurman: Local structure of silicate glasses, Nature 293, 611–616 (1981) B. Gee, H. Eckert: Cation distribution in mixed alkali silicate glasses. NMR studies by 23 Na-f7 Lig and
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glass passivation by surface layers, Nat. Commun. 6, 6360 (2015) L. Deng, J. Du: Development of effective empirical potentials for molecular dynamics simulations of the structures and properties of boroaluminosilicate glasses, J. Non-Cryst. Solids 453, 177–194 (2016) J. Rimsza, J. Du: Ab initio molecular dynamics simulations of the hydroxylation of nanoporous silica, J. Am. Ceram. Soc. 98(12), 3748–3757 (2015) A.S. Cote, A.N. Cormack, A. Tilloca: Reactive molecular dynamcis: An effective tool for modeling solgel synthesis of bioglasses, J. Mater. Sci. 53, 9006 (2017) T.S. Mahadevan, S.H. Garofalini: Dissociative chemisorption of water onto silica and formation of hydronium ions, J. Phys. Chem. C 113, 11177 (2009) R.L. McGreevy: Reverse Monte Carlo modeling, J. Phys. 13, R877–R913 (2001) C. Bonhomme, C. Gervais, N. Folliet, F. Pourpoint, C.C. Diogo, J. Lao, E. Jallot, J. Lacroix, J.-M. Nedelec, D. Iuga, J.V. Hanna, M.E. Smith, Y. Xiang, J. Du, D. Laurencin: 87 Sr solid-state NMR as a structurally sensitive tool for the investigation of materials: Antiosteoporotic pharmaceuticals and bioactive glasses, J. Am. Chem. Soc. 134, 12611–12628 (2012) T. Charpentier, M.C. Menziani, A. Pedone: Computational simulations of solid state NMR spectra: A new era in structure determination of oxide glasses, RSC Advances 3, 10550–10578 (2013)
Jincheng Du Dept. of Materials Science & Engineering University of North Texas Denton, TX, USA [email protected]
Dr. Jincheng Du is a Professor of Materials Science and Engineering at the University of North Texas. He received his PhD in Ceramics from Alfred University and postdoctoral training at PNNL and the University of Virginia. He is an expert on atomistic simulations of glasses and amorphous materials and has published over 130 peer reviewed papers. Since 2011, he is the Chair of ICG’s technical committee “Atomistic Simulation of Glasses”. In addition, he currently serves as Chair-Elect of the Glass and Optical Materials Division of the American Ceramic Society.
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Na-f7 Lig spin echo double resonance, J. Phys. Chem. 100, 3705–3712 (1996) C. Chen, J. Du: Lithium ion diffusion mechanism in lithium lanthanum titanate solid-state electrolytes from atomistic simulations, J. Am. Ceram. Soc. 98, 534–542 (2015) J. Du, L.R. Corrales: The first sharp diffraction peaks in silicate glasses: Structure and scattering length dependence, Phys. Rev. B 72, 092201 (2005) J. Du, L.R. Corrales: Understanding lanthanum aluminate glass structure by correlating molecular dynamics simulation results with neutron and x-ray scattering data, J. Non-Cryst. Solids 353, 210–214 (2007) M. Ren, J. Du: Structural origin of the thermal and diffusion behaviors of lithium aluminosilicate crystal polymorphs and glasses, J. Am. Ceram. Soc. 99, 2823–2833 (2016) Y. Xiang, J. Du: Effect of strontium substitution on the structure of 45S5 bioglasses, Chem. Mater. 23, 2703–2717 (2011) J. Du, J. Rimsza: Atomistic computer simulations of water interactions and dissolution of inorganic glasses, NPJ Mater. Degrad. (2017), https://doi.org/ 10.1038/s41529-017-0017-y J. Yeon, A.C.T. van Duin: ReaxFF molecular dynamics simulations of hydroxylation kinetics for amorphous and nano-silica structure, and its reactions with strained atomic strain energy, J. Phys. Chem. C 120, 305–317 (2016) S. Gin, P. Jollivet, M. Fournier, F. Angeli, P. Frugier, T. Charpentier: Origin and consequences of silicate
References
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Machine Lear 33. Machine Learning for Glass Modeling
Adama Tandia, Mehmet C. Onbasli, John C. Mauro 33.2.3 Data-Driven Materials Modeling and Predictions ................................. 1165 33.3 33.3.1 33.3.2 33.3.3 33.3.4
Methods ........................................... Data Consolidation and Cleaning ........ Initial Data Modeling ......................... Genetic Algorithms ............................ Neural Networks ................................
33.4
Data-Driven Development for Glass Composition Design............. Neural Network-Based Composition Models for Predicting Glass Liquidus Temperature ..................................... Neural Network-Based Composition Models for Predicting Glass Viscosity............... Genetic Algorithm-Based Glass Models for Predicting Compositions for Desired Ranges of Young’s Moduli.............................. Genetic Algorithm-Based Glass Models for Predicting Compositions for Desired Ranges of Compressive Stress and Depth of Layer ............................
33.4.1
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33.4.4 33.1 33.1.1
Data-Driven Glass Research ............... 1155 Glass Research at Corning ................... 1156
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Development of Data-Driven Materials ................... 1161 33.2.1 Publicly Available Materials Databases ......................................... 1161 33.2.2 Examples of Successful Data-Driven Materials Development ...................... 1162
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33.1 Data-Driven Glass Research Glass researchers focus on developing high-quality crystalline (ceramic, glass-ceramic) and non-crystalline (glass, fiber) materials for functional and technological applications used ubiquitously in smart phones, television, transoceanic optical fibers, diesel particulate filters for vehicles, and biological test lab ware. Corning is one of the major glass research and development companies and established its industrial research laboratories in 1908 in Corning, NY, and has been focusing on inventing and refining new compositions and prop-
erties of glass since then. Corning has been among the inventors and developers of high technology glass and ceramic materials for advanced optics, commercial consumer electronics, display technologies, environmental technologies, optical fiber and communication systems, life sciences, and pharmaceutical development. The growing need for highly-functional, manufacturable, and inexpensive glasses has prompted glass researchers to use data-driven machine learning (ML) models to accelerate the development of glass and
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_33
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With abundant composition-dependent glass properties data of good quality, machine learningbased models can enable the development of glass compositions with desired properties such as liquidus temperature, viscosity, and Young’s modulus using much fewer experiments than would otherwise be needed in a purely experimental exploratory research. In particular, research companies with long track records of exploratory research are in the unique position to capitalize on data-driven models by compiling their earlier internal experiments for research and product development. In this chapter, we demonstrate how Corning has used this unique advantage to develop models based on neural networks and genetic algorithms to predict compositions that will yield a desired liquidus temperature as well as viscosity, Young’s modulus, compressive stress, and depth of layer.
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ceramic materials. Machine learning is a set of statistical and nonlinear algorithmic tools that can help make inferences about available data, i. e., Corning’s experimental results on glass composition–processing– property relations, and make predictions about glass properties for previously unexplored or partially explored composition/processing conditions. The key advantage in using these models is that once the models are trained with existing composition/property data to accurately predict test and evaluation data, new and accurate predictions of functional glass properties may become feasible across large composition and fabrication parameter spaces. Machine learning models and predictions can significantly accelerate predictions over prohibitively large composition spaces. A major barrier that prevents many researchers from using this advantage is the availability of sparsely experimental composition–processing–property data over compositions of interest. Since state-of-the-art glass materials can contain more than eight different kinds of oxides and substituents, parametric evaluations of structure– property relations are prohibitively expensive for traditional academic research programs. As a result, largescale initiatives including industrial research programs are essential to make use of the key advantages of ML models in glass research. In this chapter, we present how data-driven models can be used for functional glass development and discuss how they have enabled Corning’s industrial researchers to accurately evaluate the key glass properties across a composition and manufacturing parameter space that is prohibitively large for experimental trial and error. The chapter begins with an overview of Corning’s history of inventions in the field of glass compositions for display applications, damage resistance applications, optical lens applications, and optical fiber applications. Such a historic description is important not just as an evaluation of the development of glass science, but also particularly for this chapter because Corning has accumulated experimental and modeling results on glass and ceramic processing–property and structure relations for over more than a century. While developing each of these glass products and compositions with a multitude of different properties and compositions, Corning has generated a number of glass compositions and experimental data. With the growing demand for high-end smart phone and flat panel display applications, Corning accelerated the glass composition development by using data-driven methods such as statistical methods, artificial neural networks, and genetic algorithms for both engineering the end properties of glass as well as manufacturing properties such as liquidus temperature, glass viscosity,
compressive stress (CS), depth of layer, and Young’s modulus, which determine the development cost and the quality of the final glass product [33.1]. First, Corning’s history of functional glass products is briefly introduced. In the second section, other contemporary efforts to develop such materials databases, such as the Materials Genome Initiative, are discussed. In addition, a brief tutorial on initial data modeling (unsupervised learning, cluster analysis, and regression), genetic algorithms (GA) and neural networks (NN) is presented. In Sect. 33.4, five examples of data-driven models for glass development at Corning are presented; first, NN-based composition models for predicting glass liquidus temperature, second, NN models for predicting glass viscosity, and, finally, GA-based glass models for predicting desired ranges of CS, depth of layer, and Young’s moduli. Finally, new glass and other materials discovery opportunities with data-driven approaches are discussed.
33.1.1 Glass Research at Corning Corning’s focus on functional glass research spans tough, strong, and ultra-low CTE (coefficient of thermal expansion) borosilicates with different dopants and tunable glass transition temperatures to different fusion draw rates for controlling production throughput and yield. The data analysis and prediction methods as well as composition and process information presented herein are intended to describe Corning’s research and to guide the readers in doing similar data-driven studies on different materials databases. The Early Days After establishing one of the first industrial research laboratories in 1908, Corning developed heat-resistant and low CTE glasses as lanterns for railroad signaling systems in 1912, which significantly helped safe operation of railroads, as shown on Fig. 33.1. Building on this expertise, in 1913, Dr. Jesse Littleton, a Corning physicist, asked his wife Bessie to bake a cake on a piece of heat resistant glass developed in 1908. The glass held up beautifully throughout the baking process. After this experiment, the glass composition was refined and the highly durable cookware and laboratory glassware Pyrex® was born in 1915. Pyrex® glassware [33.2] is still very popular in today’s kitchens for its low CTE and its high and uniform thermal conductivity. The Pyrex® composition innovation was a major step that eventually yielded superior thermal shock-resistant glass components. A major stride for domestic lighting was made when William J. Woods, a former glassblower, and his colleague David E. Gray, an engineer, invented the
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In 1934, Corning’s scientist Dr. J. Franklin Hyde, who was an organic chemist, developed silicones, which is an engineered material that is a bridge between glass and plastic. Dr. Hyde’s early work on silicones was later applied in the development of products for the Dow Corning joint venture. Dr. Hyde’s experiments with vaporized liquids led to a process for producing a nearly pure silica compound, known as vapor deposition. This process was later used to develop high-purity fused silica and to prepare spacecraft windows, optical lenses, optical fibers, and telescope mirrors. Dr. Hyde’s experiments were recognized when he was inducted into the National Inventors Hall of Fame in 2000.
for railroad signal systems [33.3]
high-speed ribbon machine, which could blow 400 000 bulb blanks in a 24-h period. This rate is about five times the output of earlier machines. As a result, Corning was able to assist Thomas Edison in making the light bulb a widespread commercial utility. In addition, the ribbon machine was also used to manufacture radio bulbs in 1933. Because of this manufacturing innovation, the price of radio sets was driven down to make them affordable to consumers. While working on the ribbon machine (shown on Fig. 33.2), Corning also began producing large glass bulbs for cathode ray tubes (CRTs) for new test equipment such as an oscilloscope, which is a fluorescent screen of CRT that helps display the voltage oscillations as time-variant waveforms. After World War II These inventions eventually led to the first CRT television sets. With the outbreak of World War II in 1939, the demand for Corning’s CRTs increased, as these were a critical component of the US military’s radar equipment. Later in 1943, Corning developed an electrical process to seal the bulbs, which enabled the production of more than 3 million large tubes for this application. Like light bulbs, Corning revolutionized the television industry by inventing a process to mass produce TV picture tubes. Corning first developed a lead-free glass composition that was lighter and less expensive to produce. Next, Corning developed a new method of spin casting of television funnels, which made televisions become affordable for millions of people immediately. Thus, Corning then began its journey into the television market by manufacturing television glass in 1948.
Part D | 33.1
Fig. 33.1 Corning’s first major invention: low CTE glasses
Heat-Resistant Glass for Telescopes and Space Applications In 1935, Corning’s Dr. George McCauley designed and directed Corning’s production of a 200-inch mirror blank for the Hale Telescope at Mount Palomar, which was the world’s largest piece of glass at that time. This early disk was also made from Pyrex® . Thermal stability especially in optical imaging components is particularly critical for acquiring data with low noise and low drift. Specifically, the optical lenses and mirrors used in terrestrial stations or in space must have low CTE, microstructural stability against wide temperature and humidity fluctuations, stability against gamma ray exposure in space, which can be detrimental to optical transmission over the long-term, and heat exchange with other parts of the system. Corning’s Pyrex® was also engineered to weather these relatively harsher and different environments compared to the kitchen stove. This expertise was used later in 1961, 1990, and 1997 for the Mercury spacecraft windows, the Hubble Telescope, and the Subaru Telescope mirrors, respectively. In 1961, the Mercury spacecraft made the first successful American manned flight equipped with heatresistant windows manufactured by Corning. Corning went on to refine the glass compositions for windows for every manned American spacecraft, from Gemini and Apollo flights to the space shuttle and for numerous applications within the space industry. In 1990, Corning produced glass for the mirror of the Hubble Telescope. The aspheric mirror form focused images over the largest possible field of view through the telescope lens. In 1997, Corning prepared one of the largest pieces of man-made glass ever made for the Subaru Telescope mirror, which is a 27-ton contact lens-shape glass, more than 26 ft across and only a few inches thick. The thin profile of the Subaru Telescope mirror was designed such that 261 actuators on the reverse side of the mirror can constantly reshape its surface through tiny nudges that keep starlight precisely focused.
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Fig. 33.2 High-speed ribbon machine for blowing glass bulbs for lighting and radios [33.3]
Part D | 33.1 Development of Glasses for Daily Use Corning chemist Dr. Charles F. DeVoe developed a continuous melting process using electric melting. He also improved the stirring techniques to make up to 100 pounds (45 kg) of optical glass an hour. This method with increased production yield helped produce optical and ophthalmic glasses that are still used today. Dr. S. Donald Stookey made a major discovery in 1952 while heating a photosensitive glass developed by Corning. During the experiment, the oven malfunctioned and overheated. Dr. Stookey, however, discovered that the glass was still intact and in perfect shape except that it was white from microcrystallization. It was found that this new glass-ceramic material did not break when dropped. As a result, modern CorningWare® , which was a new family of materials, glass ceramics were discovered. Stookey was later awarded the National Medal of Technology in 1986 for his materials innovations and went on to be inducted into the National Inventors Hall of Fame in 2010. Major Corning scientists like Dr. George Beall also discovered glass-ceramic materials used in such products as Macor® machinable glass-ceramics (which have widespread use in the electronic and aerospace industries), Pyroceram® commercial tableware, and Visions® cookware. Glass-ceramic materials are composite materials that consist of a glassy amorphous matrix and micro-
crystalline phases consisting of one or more different chemistries dispersed across a material (Chap. 4). In glass manufacturing, crystalline phases are usually not wanted, as these phases scatter light and compromise glass manufacturability. Corning’s numerous glass composition development trials and errors yielded glass-ceramics with the fabrication advantages of glass as well as the special properties of ceramics. With a well-designed thermal treatment profile and history, properly-engineered microcrystalline phase structure and composition, and a host matrix glass composition, one can achieve low or zero porosity, high strength, high toughness, translucency or opacity, pigmentation, opalescence, low or even negative thermal expansion, high-temperature stability, fluorescence, machinability, ferromagnetism, resorbability or high-chemical durability, biocompatibility, bioactivity, ion conductivity, superconductivity, isolation capabilities, low dielectric constant and loss, and high resistivity and breakdown voltage. Glass-ceramics are valued for having the strength of ceramics but the hermetic sealing properties of glass. Development of Glasses for Drug Discovery and Life Sciences Contemporary drug discovery technologies mainly use fluorescent or radioactive labels and tags, which are
Machine Learning for Glass Modeling
Developing Optical Silica Fibers In 1970, Corning’s Robert Maurer, Donald Keck, and Peter Schultz developed the first optical silica fiber capable of maintaining the strength of laser light signals over significant distances. With the reduction of water vapor in the glass preform, the transmission losses for the fiber drawn from the fiber tower were also reduced (Chap. 41). This discovery paved the way for the commercialization of fiber optical infrastructure for telecommunications. For these discoveries, Maurer, Keck, and Schultz were inducted into the National Inventors Hall of Fame in 1993 and went on to receive the 2000 National Medal of Technology. Wiring optical fibers through apartment buildings requires numerous twists and turns, and each bending diminishes the fiber’s performance with bending loss and optical waveform dispersion. In order to eliminate fiber bending losses, Corning scientists Drs. Pushkar Tandon, Dana Bookbinder, and Ming-Jun Li developed the ClearCurve® optical fiber in 2007 by leveraging Corning’s decades of optical fiber research. The ClearCurve® fiber is able to transmit signals with minimal loss when bent at 90° angles. This capability helped bring a state-of-the-art highperformance optical link infrastructure to high-rise buildings, data centers, and enterprise networks. This
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invention has been possible through engineering the index profile and cladding structure of the preform prepared in the organic vapor deposition process and during the fiber drawing step. Modern Display Glass Development In display glass development, a key requirement on the glass product is achieving very low surface roughness, uniform surface dopant distribution, and processability across wide areas of glass (Chap. 45). In addition, the yield and the production rate and cost need to be controlled through modulating viscosity and controlled heating and cooling of glass. In 1964, Corning scientists Stuart Dockerty and Clint Shay developed the fusion overflow process to produce flat glass. In this method, molten glass flows down both sides of a tapered trough and rejoins at the bottom to form a single sheet of flawless glass. This fusion overflow glass method became the precursor to Corning’s liquid crystal display glass substrates. In the 1980s, as computers were being developed and research laboratories were working on active matrix liquid crystal displays (LCDs), a major challenge was faced due to the fact that ordinary glasses were not precise, stable, or durable enough to meet LCD requirements. Corning’s fusion flow process helped glass meet that requirement. After process refinements, Corning started to aid the LCD industry in making large, high-quality flat panel displays possible for various new applications. In 2007, Apple’s late chief executive officer Steve Jobs challenged Corning to find a cover glass for their first generation of iPhones and asked for cover glasses that were more damage-resistant than traditional materials such as soda-lime glass and plastic. Corning engineered the fusion draw process rate and parameters to establish ways to make glass thin and light enough for mobile devices and tough enough to resist scratches, bumps, and drops. This new damage resistant glass as shown on Fig. 33.3 is used in smart phones, slates, tablets, PCs, TVs, smart watches, and many other devices. A key invention in the development of damage resistant glassy products is chemical strengthening (Chap. 8), in which flat glass sheets are treated with salt baths after fusion draw to establish a CS state on the surface (30120 m from the surface, depending on the application). Stress concentration of the cracks on the surface are significantly eliminated or alleviated, and thus cracks cannot propagate. In 2008, Corning introduced the Gen 10 glass, which was one of the most dramatic leaps forward in size in the history of LCDs. Gen 10 offers approximately 70% more surface area than the previous size, Gen 8. A single sheet of Gen 10 glass can produce 15 42-inch pan-
Part D | 33.1
prone to false-positives and false negatives, as these fluorescent tags can bind nonspecifically and unintentionally on completely different proteins, which may happen to have the right binding chemistry. In order to minimize false identifications, Corning developed Epic® label-free which is integrated with 384 microwell plates and optical biosensors in each well. With this integrated and automated screening technology, 40 000 wells can be read in 8 h. The transmission properties of Corning glasses are used along with the integrated biosensors. Automation, biosensor integration and anti-fouling Corning Life Sciences glassware enable accelerated pharmaceutical discoveries for treating specific diseases. Based on its highly transparent glass preparation technology, Corning has developed the most fundamental biological laboratory glassware for cell cultures, liquid handling, filtration, reagents, microplates, stirring equipment and other essential glass components used in cancer drug development. In addition to optical transparency and mechanical strength, a key requirement in each of these components is anti-fouling. Corning achieves an extremely limited likelihood of anti-fouling and unintentional cell binding on glass by special internal surface functionalization of the glass flasks and containers that enable reuse without any cross-contamination.
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Part D | 33.1 Fig. 33.3 Fusion draw process enabled Corning to develop
flat, stable, and durable glasses for active matrix liquid crystal displays [33.3]
els at 2880 3130 mm (about 9 ft 10 ft). This increase in efficiency reduced costs, ultimately making LCD TVs more affordable for consumers. The introduction of Gen 10 glass was possible through Corning’s fusion draw manufacturing process development. Corning’s Glass Characterization As described in the previous sections, Corning has a rich history of developing glasses for different ap-
plications in which requirements can dictate vastly different compositions and manufacturing conditions. Table 33.1 shows some of the examples of these applications. In almost all of these applications, a new glass composition was developed or refined, and the manufacturing process needed to be either invented or tailored for the requirements (quality restrictions and throughput requirements). As a result of the glass melting and characterization experiments while preparing each of these products, Corning also established one of the most advanced glass composition characterization and property measurements. The characterization results include the structural (topology and defect structure, stoichiometry, microstructure), electrical, thermo-mechanical (glass transition temperature, viscosity, fictive temperature), and mechanical properties (elastic modulus, stress-strain profile) of different glass compositions at different temperatures. Each of these experiments was done with these characterizations iteratively. Although Corning’s history contains many serendipitous discoveries (i. e., glass-ceramics) originating from exploratory experimental trials and errors, each new commercial glass composition development takes at least 2 to more than 30 years and costs multiple millions of dollars. In order to minimize the glass composition development process, Corning used linear and nonlinear ML models and GAs to predict the liquidus temperature, viscosity, Young’s modulus, and other properties. In the next section, similar academic studies on data-driven materials composition models and predictions are presented.
Table 33.1 Examples of glass composition and manufacturing process innovations from Corning Application Glass lanterns for railroad signal systems Light bulbs, radio set bulbs, CRTs
Requirement on glass properties Low CTE Clear and transparent
TV tubes
Lead-free, lightweight, less expensive
(Non-fiber) optical components (lenses, mirrors) Space-grade glass
High-purity silica
Pyrex® , CorningWare® , Macor® , Pyroceram® , and Visions® cookware Biological laboratory glassware
Glass compositions were invented, their thermal manufacturing treatment profiles optimized Low CTE, optical transparency, anti-fouling New surface functionalization chemistries were and contamination developed Low optical transmission loss, low bending Outside vapor deposition process and equiploss and dispersion ment, preform treatment recipes were invented to minimize vapor content in fiber preforms. Fiber tower designs and fiber pulling process were engineered.
Optical fiber
Low CTE, microstructural stability against temperature and humidity fluctuations, stability against gamma ray exposure Low CTE, high thermal conductivity
Manufacturing process Glass melting and forming Ribbon machine invented for high-throughput blowing Spin casting of TV funnels had to be invented for increasing throughput Vapor deposition and forming processes invented New glass compositions
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33.2 Development of Data-Driven Materials
33.2.1 Publicly Available Materials Databases Data-driven materials discovery approaches use statistical models as well as ML algorithms, which are trained, tested, and validated using materials databases. An important part of this approach is to develop accurate materials databases with low cost. While one can use first principles approaches to calculate the electronic band structure, formation energy and crystalline structural stability and other thermodynamic parameters, a brute force calculation of properties for more than 10 million chemical compounds known today is prohibitively expensive and time consuming. As a result, major institutions such as NIST, the American Chemical Society (ACS), and the University of California at Berkeley (UC Berkeley) have started curating materials databases for known major crystal structures, phase diagrams, formation energies and other thermodynamic parameters. The first major publicly available materials database maintained at NIST is the Inorganic Crystal Structure Database (ICSD, SRD 84), which contains over 100 000 crystal structures that are known to exist and could potentially have useful functional properties [33.3]. The second major publicly available materials database is ACerS-NIST Phase Equilibria Diagrams Database, formerly known as Phase Diagrams for Ceramicists [33.4]. This database contains 26 000 phase diagrams for nonorganic systems, which were collected between 1964 and 1992 as part of the NIST and the American Ceramic Society collaboration. The third major database is the NIST Chemical Kinetics Database [33.5], which contains the kinetics results for thermal gas-phase chemical reactions. Over 38 000 separate reaction records over for over
11 700 distinct reactant pairs are maintained in the database. NIST also maintains a database of fracture toughness/fracture energy data for borate, germanate, phosphate, and silicate base glasses [33.6] (NIST Standard Reference Database 137). Other specialized NIST databases are available online [33.7]. Researchers led by UC Berkeley maintain The Materials Project, which contains open web-based access to computed information on known and predicted materials as well as analysis tools to design novel materials [33.8]. This online database contains crystal structure, electronic band structure, and other important parameters (elastic tensors, piezoelectric tensors, magnetic moments, etc.) for more than 66 000 inorganic compounds. One of the most promising aspects of this database is that the online and free web interface allows users to calculate the electronic band structure and other thermodynamic parameters if the desired compound is not found among the records. The web interface is connected to FireWorks open software for submitting calculation workflows to the supercomputer infrastructure managed by researchers at UC Berkeley. After the results are parsed and processed, they are saved in the materials database. This publicly crowd-sourced distribution of chemical compound investigations helps scale the materials database along composition spaces that the researchers find most promising. UC Berkeley groups have put a special emphasis on battery electrode materials due to growing scientific and technological interest on these materials. Although this is a scalable database, it is designed for low-throughput consumption via a graphical user interface. There are multiple major databases maintained by Springer Materials, National Institute for Materials Science (NIMS) MatNavi, Matweb, Citrination. Major specialized domain databases that consist of experimental data are SciGlass (database with more than 400 000 glass compositions and properties), Powder Diffraction Files (more than 384 000 diffraction records), ICSD (crystal structure records), NanoHub, Granta, and ASM (American Society for Metals) Phase Diagrams. Computational material property databases include AFLOWLIB, CatApp, Harvard Clean Energy Project, Materials Project, NoMaD (Novel Materials Discovery NOMAD Laboratory) and OQMD (Open Quantum Materials Database). NIST established several other scalable generalized and scalable materials databases: 1. ASM Structural Materials Data Demonstration Project [33.9] is currently in progress to provide an open data repository for metallic structural materials.
Part D | 33.2
On June 24, 2011, the President of the USA, Barack Obama, announced the inauguration of the Materials Genome Initiative (MGI), which is a multi-agency federal initiative designed to prepare the policies, resources, and the infrastructure required for US institutions to discover, manufacture, and deploy advanced materials twice as fast and at a fraction of the cost than it was necessary in the past [33.2]. As part of this initiative, the Departments of Energy (DOE) and Defense (DoD), the National Science Foundation (NSF), the National Institute of Standards and Technology (NIST), and the National Aeronautics and Space Administration (NASA), have invested more than $500 million in resources and infrastructure since 2011. As a result, several publicly available large-scale experimental and calculated materials databases have been curated [33.3].
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2. NIST Materials Data Curation System [33.10] is generalized data storage scheme for capturing, sharing, and transforming materials data into an XML structured format which is also amenable to transformation to other formats. The data are organized with user-selected templates encoded in XML Schema. 3. NIST Materials Resource Registry is an umbrella database of materials databases [33.11]. It is currently being developed to bridge the gap between existing resources and end users by allowing resources to be registered with associated metadata to aid in search and discovery. The information includes metadata related to materials science content (e. g., material classes, data acquisition methods, and microstructural information) as well as access policies, and communication protocols for search and retrieval. This metadata can be shared as part of a data network to create a searchable catalog for materials data discovery. 4. NIST Materials Informatics [33.12] database focuses on phase-based data which include thermodynamics, diffusion, molar volume, elastic properties, electrical conductivity, and thermal conductivity. It may be extended to two phase descriptions such as interfacial energies. Phase-based data includes both experimental and computational data. 5. Density Functional Theory (DFT) Informatics and Repositories [33.13] is a new materials database currently being built for atomistic simulations, calculation of phase diagrams (CALPHAD), and DFTbased studies. As scientific journals do not provide the necessary media for disseminating results (i. e., code, database, descriptions longer than 20 pages), this comparative structured database is expected to serve an open-source platform for sharing more extensive data such as DFT formation energy calculations for 100500 different atomic configurations in an alloy. This database is also expected to provide a comparative framework for understanding the effects of different DFT parameters on predicted material properties. 6. Web Force-Field (WebFF) [33.14] is a repository for soft materials such as polymers, colloids, gels, composites as well as pharmaceutical and various biological materials and it consists of a database, a software engine, and a web-client interface. The database supports a multi-table format where each table is a distinct force field. The software engine allows the input of chemical structures, automated force field assignment, output to support molecular dynamics (MD) calculations for open source software such as LAMMPS and GROMACS and insertion of new force fields into the database.
7. The Computational Materials Repository [33.15, 16] is an online data repository maintained by researchers at Technical University of Denmark. The repository includes the properties calculated using first principles for 2-D materials, van der Waals hetero-structures, organometallic halide perovskites, porphyrin-based dyes, new light harvesting materials, perovskite water-splitting, low symmetry perovskites, functional perovskites, calculated reaction, and activation energies for elementary coupling reactions occurring on metallic surfaces. A recent review article [33.17] on materials models based on large-scale databases explains the key challenges and opportunities and lists a non-exhaustive list of the major materials databases that researchers can access either freely or with a fee.
33.2.2 Examples of Successful Data-Driven Materials Development Since the size of each database is large, an exhaustive screening of each of these entries can be prohibitively time consuming even with a computational approach. As a result, researchers at NIST have been using high-throughput first principles calculations and density functional theory to quickly screen hundreds of materials for suitability in applications, based on thermodynamic and structural stability as well as band structure parameters. In one example [33.18], researchers at NIST integrated the x-ray diffraction (XRD) data from synchrotron beamline and ICSD records and used ML approaches to reduce the complexity of data and to rapidly home in on the underlying trend in multidimensional data. Specifically, they used an algorithm that they call mean shift theory to a large amount of XRD data and ICSD records to delineate and classify the structural evolution across compositional variation over the Fe-Co-Mo ternary phase diagram with minimal computational cost. The algorithm helped the researchers classify the structural phases on the ternary phase diagram. They applied this approach to identify a novel magnetic phase with enhanced magnetic anisotropy which is a candidate for rare-earth free permanent magnet. Ab initio calculations based on quantum mechanics, density functional theory, molecular dynamics, or lattice models are used to calculate the formation energies and predicting the most stable crystal structures for structures of less than about a thousand atoms (1-Dconfined, 2-D-confined or bulk systems) (Chaps. 31 and 32). Although ab initio calculations can be highly accurate, these calculations require significant com-
Machine Learning for Glass Modeling
Ei D
d X
˛ij ei C i .d/ ; jD1
where i .d/ is the error vector for alloy i. PCA consists of finding the proper basis set fej .d/g that minimizes the remaining square error d X
> i .d/ i .d/ iD1
for a given dimension d. These optimum basis vectors fej .d/g are called the principal components that are a set of orthogonal vectors ordered by the amount of variation of the original sample they can explain. These vectors are essentially new axes of a new 114dimensional space ordered according to the fraction of the data lying along that axis. The typical output for PCA is a plot of the root mean square error
(RMSE) as a function of dimension d. An error cutoff is picked based on the DFT calculation uncertainties (i. e., 50 meV=atom) and to describe the energies with a 50 meV error, only 9 dimensions are required instead of the original 114. It is, therefore, possible to perform far fewer than 114 calculations to parameterize the nine-dimensional space and then derive the other 105 energies through linear relationships given by the PCA. As discussed in a recent review [33.20], datadriven materials design is advantageous because one can use computational quantum mechanical and thermodynamic approaches to screen with high throughput and quickly eliminate sub-groups of combinatorial stoichiometric possibilities for different classes of materials. In addition, there is a wide variety of statistical and data mining techniques [33.1] to predict any property within an arbitrarily complex phase diagram. The methods used in many demonstrations [33.21–33] are similar. First, create a large database as one those listed on Table 33.2 containing the calculated thermodynamic and electronic properties of existing and hypothetical materials, and then intelligently interrogate the database using PCA, GA, NN, or other ML algorithms in the search of materials with the desired properties. These steps include the calculation of the thermodynamic and electronic structure of materials, systematic storage of data in repositories, and data analysis by screening the database based on descriptors, which are empirical relations between calculated microscopic parameters (i. e., formation and defect energies, atomic lattice environments, and topology, band structure, density of states, magnetic moments), and macroscopic properties such as mobility, susceptibility, and critical temperatures. Examples of such descriptors are shown in Table 33.3 [33.20]. Using such descriptors, one can define cost (or profit) functions, which can be embedded into the database searching and prediction models. These search and prediction models use GA, NN, data mining of spectral decompositions and Bayesian probabilities, refinement and optimization by cluster expansion, structure map analysis, and support vector machines to estimate properties with low RMSE. Descriptor-based data mining across materials repositories has been carried out [33.20, 23] for identifying new superconductors, zeolites, ferroelectric materials, polymers, magnetoresistive materials, metallic alloys, solar cell materials, thermoelectrics, luminescent materials, new materials for methanol fuel cells and solid oxide fuel cells, organic light-emitting diodes, automative coatings, ferromagnetic shape-memory alloys, waterborne coatings, thermoelastic shape-memory alloys, catalysts, organic dyes, battery cathode and anode materials, water photosplitting, carbon capture
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putational time and resources to the extent that an exhaustive ab initio analysis of even a binary phase diagram can be prohibitively expensive. A major feature and limitation of ab initio calculations is that these calculations do not explicitly use the results of previous calculations when studying a new composition or a new crystal lattice arrangement. As a result, researchers have proposed using heuristic models together with ab initio models: a large amount of experimental observations is used in order to extract rules that rationalize crystal structure with a few simple physical parameters such as atomic radii and electronegativities etc. [33.19]. In this approach, also referred to as data-mining of quantum calculations, researchers used principal component analysis (PCA) on over 6000 ab initio energy calculations and show that the energies of different crystal structures in binary alloys are strongly correlated between different chemical systems and use this correlation to accelerate prediction of structure and properties of new materials. They first calculated using density functional theory a library of energies for 114 different crystal structures in each of 55 binary metallic alloys. The alloys include all 45 binaries that can be made from row 4 transition metals as well as ScAl, AgMg, AgTi, CdTi, MoTi, PdTi, RhTi, RuTi, TcTi, and TiZr. About a third of the crystal structures in the library were chosen from the most common binary crystal structures in the CRYSTMET database for intermetallics [33.19]. The rest are superstructures of the face-centered cubic (fcc), bodycentered cubic (bcc), and hexagonal close-packed (hcp) lattices at various compositions. Next, they applied PCA to the 114-dimensional space to find an approximate linear dependency for the formation energies Ei for each alloy i. The formation energy Ei for alloy i is
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Table 33.2 List of major publicly available materials databases that can be used for building models Category Alloys Catalysts Chemical data
Computational
Part D | 33.2
Crystallography
General materials data
Glass Hard-copy sources
Hydrogen storage Materials characterization Minerals Nanomaterials Thermodynamics Thermoelectrics
Database name CINDAS High-Performance Alloys Database ASM Alloy Center Database CatApp PubChem Scifinder/ChemAbstracts Chemspider Reaxys AFLOWLIB Harvard Clean Energy Project Computational Materials Repository Web Force-Field (WebFF) NoMaD Open Knowledge Database of Interatomic Models (Open KIM) Open Quantum Materials Database NIST Interatomic Potentials Repository Materials Project Inorganic Crystal Structure Database CrystMet Crystallography Open Database Cambridge Crystallographic Data Centre Powder Diffraction File (PDF) Knovel Citrination NIST Materials Informatics SpringerMaterials NIST Materials Data Repository (DSpace) MatNavi (NIMS) Pauling File AIST Research Information Databases Granta CES Selector CRC Handbook Matbase MatDat MatWeb NIST Standard Reference Data NIST Standard Reference Data Total Materia International Glass Database System SciGlass Handbook of Optical Constants of Solids Pearson’s Handbook: Crystallographic Data Metallurgical Thermochemistry DOE Hydrogen Storage Materials Database 3D Materials Atlas American Mineralogist Crystal Structure Database Mindat NanoHUB Nanomaterials Registry CALPHAD databases (e. g., Thermocalc SGTE) ASM Phase Diagrams UCSB-MRL thermoelectric database TEDesignLab
Web address http://cindasdata.com/products/hpad http://mio.asminternational.org/ac http://suncat.stanford.edu/catapp http://pubchem.ncbi.nlm.nih.gov http://scifinder.cas.org http://www.chemspider.com http://www.elsevier.com/solutions/reaxys http://aflowlib.org http://cepdb.molecularspace.org http://cmr.fysik.dtu.dk http://mgi.nist.gov/web-force-field-webff http://nomad-repository.eu/cms http://openkim.org http://oqmd.org http://www.ctcms.nist.gov/potentials http://www.materialsproject.org http://cds.dl.ac.uk/cds/datasets/crys/icsd/llicsd.html http://cds.dl.ac.uk/cgi-bin/news/disp?crystmet http://www.crystallography.net http://www.ccdc.cam.ac.uk/pages/Home.aspx http://www.icdd.com/products/index.htm http://app.knovel.com/web/browse.v http://citrination.com http://mgi.nist.gov/calphad-data-informatics http://materials.springer.com http://materialsdata.nist.gov/dspace/xmlui http://mits.nims.go.jp/index_en.html http://paulingfile.com http://www.aist.go.jp/aist_e/list/database/riodb http://www.grantadesign.com/products/ces http://www.hbcpnetbase.com http://www.matbase.com http://www.matdat.com http://www.matweb.com http://www.nist.gov/srd/dblistpcdatabases.cfm http://www.nist.gov/srd/onlinelist.cfm http://www.totalmateria.com http://www.newglass.jp/interglad_n/gaiyo/info_e.html http://www.sciglass.info [33.34] [33.35] [33.36] http://www.hydrogenmaterialssearch.govtools.us http://cosmicweb.mse.iastate.edu/wiki/display/home/ Materials+Atlas+Home http://rruff.geo.arizona.edu/AMS/amcsd.phP http://www.mindat.org http://nanohub.org http://www.nanomaterialregistry.org http://www.thermocalc.com/products-services/thermodynamic http://www1.asminternational.org/AsmEnterprise/APD http://www.mrl.ucsb.edu:8080/datamine/thermoelectric.jsp http://www.tedesignlab.org
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Table 33.3 Examples of descriptors previously used for estimating functional properties of materials that were not previously known to have high figures of merit for a desired application Problem Finding stable structures for alloy systems (convex hull in energy-composition space)
Combination of material properties Formation enthalpy (Hf ) as a function of concentration (x) and the enthalpies (H) of components A and B.
Nanosintered thermoelectrics
and gas storage, topological insulators, and magnetic materials. In addition to descriptor-based data mining, a new layer of materials prediction methodology is emerging by combining materials imaging analysis, molecular dynamics, multiscale materials modeling, and ab initio dynamics simulations [33.37]. In this modeling toolbox, researchers are using imaging data in different scales (atomistic to microscopic) to algorithmically analyze defects, phase boundaries as well as stoichiometry distribution and correlation and analysis with multiscale modeling to refine fabrication process as well as material compositions. Corning’s successful commercial application of this new layer of image analysis and MLbased materials modeling will be presented in [33.38].
33.2.3 Data-Driven Materials Modeling and Predictions Data-driven materials modeling started impacting numerous industries, and its significance is expected to grow based on the development of new and more accurate prediction and classification algorithms; faster, larger scale, and accurate atomistic simulation tools as well as open-access materials data repositories that serve the needs for researchers. With the development of supercomputing capabilities, data mining algorithms, and efficient data storage infrastructures, researchers have never been closer to discovering new functional materials. Using these new capabilities as well as publicly available materials databases, one can discover new breakthrough optical and electronic materials within less than a few years, which would otherwise take multiple decades with a purely experimental iterative research program.
O thermo
hPi L
.˛.E/, fr / D Pm =Pin , Eg
Ep 0:5 eV ˛AB 45ı
While new tools, algorithms, and databases empower researchers, one needs to be careful about the potential challenges that researchers are currently facing. The most expensive and time-consuming step in datadriven materials modeling is first building or acquiring the materials database. Since materials databases must include the relevant important parameters for a given application; researchers must still build their own specialized data structure and materials database either by collecting data from the previous academic publications or calculating an extensive sample library of properties using first principles calculations. Publicly available databases provide more fundamental and general data such as crystal structure, electrical and optical properties for specific conditions, and wavelengths. A specialized materials discovery may need to build the relevant phase diagram, specify an efficient sampling method for the stoichiometry space, and establish plausible methods of eliminating sub-groups of materials based on either crystalline symmetry, microstructure evolution or other calculated order parameter or a descriptor. Then, screening the materials based on a descriptor function and an appropriate ML algorithm will be essential. After each of these steps, the predicted materials must be fabricated in the laboratory to validate predictions. Since this effort is an inherently multidisciplinary approach (involving database architecture, software engineering, materials science, data science and ML algorithms, electrical engineering or other domain-based materials and device specialization), the project planning and execution with multiple specializations is going to require collaborations across cross-functional teams. The next section focuses on the methods used at Corning to predict new glass compositions.
Part D | 33.2
Ratio of the average power factor (hPi) to the grain size (L) Power conversion efficiency of a solar cell Ratio of the maximum output power density (spectroscopic limited maximum efficiency) (Pm ) to the incident solar energy density (Pin )— a function () of the radiative electron–hole recombination current (fr ) and the photon absorptivity (˛.E/)—versus bandgap energy (Eg ) Morphotropic phase boundary Energy proximity between tetragonal, rhombopiezoelectrics hedra and rotational distortions (Ep ). Angular coordinate (˛AB ) of the energy minimum in the A–B off-centerings energy map for ABO3 systems
Descriptor Hf .x/ D H.A1x Bx /.1x/H.A/ xH.B/
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33.3 Methods This section describes the essential procedures and methods used for preparing the glass composition and property data for glass properties models development. First, initial data modeling, the methods used for identifying sub-groups of compositions and properties, are presented. The last two parts are tutorials for GA and NN with a materials science focus. This section prepares the reader for the actual models for data-driven composition development.
33.3.1 Data Consolidation and Cleaning Part D | 33.3
The predictive power and accuracy of any data-driven materials model is based on the accuracy and quality of the input data. Glass composition and property relations have been used in order to build the models. The training data contain weight percentages of each oxide as input variables. For outputs, the viscosities , Young’s modulus E values, glass transition temperatures Tg , densities as well as the liquidus temperatures TL are stored among many other output values. Typically, the experiments were done at different dates and by different staff. For each sample, an extensive sample preparation record (date, time, technician name, furnace name, many process conditions with 10 min intervals) is saved. In a separate step, the characterization reports (one for each of mechanical, electrical, chemical, rheological properties) for that sample are also recorded. Combining these records took multiple years, since when the experimental data were being acquired and the characterization reports were being prepared, the data-driven predictive modeling approach had not yet been developed. In addition, many of the records had to be entered manually into computers. As different staff had different naming conventions for files, a standardized automated processing for these thousands of files was unfortunately not possible. The records also had to be standardized when they were entered into computers, and this clean up procedure was also an iterative process that needed to be updated as more data were entered into the system. As a result, the data preparation involved extensive laborious manual work that lasted multiple years. Corning’s earlier glass composition development experiments focused on refining towards improving the glass properties for a specific product at the time. Some of those experiments, for instance, focused on Young’s modulus and related mechanical properties. If a glass sample with a given composition failed the Young’s modulus threshold, in most cases, no further experiments were done on that sample, and the other
mechanical, chemical, or rheological properties of the glass may not have beenr ecorded. These missing entries must be handled either using predictive models (i. e., interpolating Young’s modulus values between glasses with similar compositions) or the entire sample’s incomplete data row simply be ignored. In this clean-up process, the decision of whether to completely ignore the row or to carry out a different pre-process depends on the model being developed. If the model critically relies on numerous rows of missing entries (i. e., predicting viscosity without density or temperature or other relevant data), then the samples with missing rows needed to be ignored. If the model results can have strong dependence on the pre-processing procedures for filling in the gaps, then the model will likely not be accurate. In each of these data consolidation and clean-up steps, the purpose is to keep good-quality data and minimize useless data while preserving similar naming conventions.
33.3.2 Initial Data Modeling Unsupervised learning is a group of algorithms used for input datasets without labeled response variables. These algorithms were used because a divide-andconquer strategy allows distinguishing misbehaving or outstanding data entries (if any), helps categorize different composition groups, and classify and predict based on their generalized behavior (i. e., dopant dependence of CTE in alumino-borosilicate glasses) within a more controlled and lower-dimensional phase space. In this part, we describe cluster analysis, principle component analysis, and regression methods, which could be used to identify sub-groups in the training data sets to assess generalization capabilities of models built from such data sets. Cluster Analysis The composition space in the data could consist of more than ten dimensions where some parameters (i. e., dopant or host matrix constituent fractions) were systematically varied. Since manual identification of systematic variations in the input space is not feasible or reliable, a classification algorithm based on unsupervised learning was used. In unsupervised learning, one first calculates the proximity and similarity between each data point in the data, then defines a criterion function to maximize the quality of clustering based on the proximity and similarity metrics, and finally computes a clustering function whose values satisfy the criterion function for all data points when mapped to each data
Machine Learning for Glass Modeling
Fig. 33.4 Unsupervised learning and cluster analysis methods allow distinguishing systematic studies within the material composition space and help identify outlier (or misbehaving) data entries. Different colors indicate different classification indices assigned
Cluster Analysis of Material Composition Space 1. Assemble the database for more than ten constituents and their composition (10-D space), CTE, Young’s moduli, and viscosities. 2. Normalize CTE, Young’s moduli, and the viscosity scales. 3. Describe a proximity criterion function to determine groups of similar composition space based on distances f .x1 ; x2 ; : : : ; xN ; y1 ; y2 ; : : : ; yN ; / D f Œd.x1 ; x2 /. 4. The function gives numerical category values based on separation thresholds. 5. Customize the clustering function thresholds based on the desired properties, iterate until the classification converges. The values in the glass composition training data points span more than 15 orders of magnitudes, and their absolute nominal values cannot be used directly. For instance, there are significant absolute value differences between some parameters such as CTE (107 to 106 (K1 ) and weight percentages (105 to a few
101 ), and Young’s moduli (hundreds of GPa, 1011 ) and viscosities (10105 Pa s). In order not to cause one column to dominate distances based on their absolute values, each value is normalized initially before calculating the distances. A conversion formula is defined in the beginning for each property or entry column for converting these normalized values back to their original scales. After normalization, the distances between each data point can be found using either Euclidean distance, which is translation invariant, or using Manhattan distances or their generalized version, which is the Minkowski distance, as shown in Table 33.4 [33.39]. After distances have been calculated, similarity indices can also be calculated to specify if compositions are nearly identical. Then, a criterion function needs to be defined to set the rules for distinguishing different clusters. For instance, this function can impose multiple specific conditions such as eliminating hazardous dopants like lead for a given application (xPb D 0 condition) or requiring lead for an x-ray shield glass application (xPb > 106 ), impose distance threshold conditions based on overall calculated separations or material property differences (high versus low viscosity samples etc.). The definitions of the clustering criteria are the points where materials engineering and specifications for the given application may also be built into the models. Since models can later be trained with subsets of clusters (i. e., glass compositions with or without lead and their corresponding properties), one may filter for data in model training and the testing stage as well. After cluster criteria are defined, a clustering function is iteratively calculated such that all data entries are grouped to satisfy the criteria. This clustering function can be implemented with MATLAB and its toolboxes or R and its packages, or Python and its packages. The clustering algorithms can be grouped into three types [33.39]: hierarchical, partitional, and Bayesian. In the agglomerative hierarchical approach (i. e., inductive method), each data row can start as a separate cluster,
Table 33.4 Euclidean, Manhattan, and Minkowski distance definitions for use in clustering algorithms Minkowski distance dp .xi ; xj / D
ˇ PM ˇ k ˇx xk ˇp 1=p kD1
i
j
p: integer, used for p 1. Minkowski: a generalized distance metric
Euclidean distance, which is translation-invariant qP .k/ 2 M .k/ d.xi ; xj / D kD1 xi xj
Manhattan distance
Euclidean: translation invariant
Euclidean and Manhattan distances are specialized cases for Minkowski distances. This is a form of power mean.
d.xi ; xj / D
ˇ PM ˇˇ k x xk ˇ kD1
i
j
xi , xj : input or output values for i and j-th experiments for a given input or output property (denoted with index k) (i. e., silica .5/ .5/ 2 weight percentages compared for experiments 1297 and 1298 as x1297 x1298 , where silica wt% column has index 5), d.xi ; xj /: the distance between two data rows, M: dimensions of the space (i. e., total number of input and output columns)
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point in the data. Figure 33.4 shows the clustering steps. A cluster is defined as a collection of data items that are similar among them; dissimilar data items are grouped under different clusters.
33.3 Methods
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and based on differences and distance criteria, clusters can be merged. In the divisive hierarchical approach (i. e., deductive method), all data rows belong to one cluster and can then differentiate based on distance criteria and similarity metrics. Partitional algorithms can return a clustering function matrix that categorizes each row after a single iteration. These algorithms can either be based on spectral density of data, graph theoretic dependence of rows on each other, k-means (centroid averaging), and model-based implementations. The most commonly used method is k-means clustering, in which clustering can be completed in linear time, O.n/. In this clustering algorithm:
Part D | 33.3
1. k random data points (seeds) are chosen to be initial cluster centers. 2. Next, each data point in the materials data set is assigned to the closest cluster center. 3. Then, centers of clusters are calculated again by averaging the new members of the cluster. 4. After recalculating the cluster centers (or centroids), one tests whether the convergence criteria are met. These criteria can include: a) Specific composition restrictions as mentioned above. b) Mathematical descriptions such as whether or not there are no re-assignments of data points to new clusters, whether or not the change of centroids is below a change threshold, or the minimum decrease in the sum of squared error (SSE) is smaller than convergence threshold. This is defined as SSE D
k X X
d.x; mj /2 ;
jD1 x2Cj
where Cj is the jth cluster, mj is the centroid of the cluster Cj (the mean vector of all the data points in Cj ), and d.x; mj / is the distance between data point x and centroid mj . c) If convergence criteria are met, clustering is complete. If not, steps 2 and 3 are repeated. In the clustering algorithm implementation, one needs to make sure that the clusters are not sensitive to random seeds. Cluster analysis should be repeated many times to ensure that different random seeds do not alter how the data are clustered. In addition, outlier data points emerging from this clustering method can be individually analyzed by glass scientists, and these points can either be removed from analysis or clustering can be done with and without these outliers to
prevent any unintentional bias in cluster centroids. Visualization methods may help in reporting clusters and identifying outliers. Principal Component Analysis (PCA) PCA is a dimension reduction technique that allows omitting variables that do not have any significant effect on the desired glass property [33.40, 41]. It uses an orthogonal transformation to convert a mapping of possibly correlated columns (variables) into a set of values of linearly uncorrelated variables called principal components. The number of principal components is less than or equal to the number of original variables. The first principal component has the largest possible variance, and every next component has progressively lower variance values. The output of PCA is a set of vectors transformed out of the original data, and these output vectors form an uncorrelated orthogonal basis set. Since variance values depend on the absolute mean values of each variable, PCA output vectors strongly depend on the relative scaling of the initial variables. Therefore, before carrying out PCA, the variables must be normalized. Intuitively, PCA can be viewed as fitting a multidimensional ellipsoid to the data. The axes of the ellipsoid are principal components. Whenever the data have weak dependence on a variable, the variance with that variable is small, and the corresponding axis of the ellipse is also small. As a result, ignoring that variable or axis of the ellipsoid will not cause a significant loss in information, but instead this simplification will reduce the number of variables. In order to calculate the axes of the ellipse (i. e., a vector output), the data are centered first on the origin by subtracting the mean of each variable from the dataset. Next, the covariance matrix of the data and the corresponding eigenvalues and eigenvectors of the covariance matrix are calculated. After finding the eigenvectors, these eigenvectors are orthogonalized and normalized to unit vectors, so as to yield an orthonormal basis. This orthonormal basis constitutes the new axes for the ellipsoid fit to data. These new axes (or principal components) are linear combinations of the original variables. The proportion of the variance that each eigenvector represents can be calculated by dividing the eigenvalue (of a given eigenvector) by the sum of all eigenvalues. After PCA, one can define a variance threshold for an eigenvector to be significant and pick only the eigenvectors that have corresponding variance proportions above the threshold. This last step helps researchers determine the most significant variables in a glass composition project and focus on cluster analysis using those fewer and more important variables.
Machine Learning for Glass Modeling
There are a few important potential limitations of PCA:
Regression Analysis Since PCA may fail to capture nonlinear correlations among variables, regression analysis is necessary to distinguish whether there are hidden complex dependencies. In regression analysis, the conditional expectation (E.XjH) of variable X given H) is estimated when the independent variables are given. In other words, either a generalized linear model is constructed by using a multivariable linear superposition of independent variables or a least squares fit is solved numerically among variables to identify whether there is a nonlinear correlation.
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Below are a few ways to construct regression models: 1. Multivariable linear regression: This is a generalized linearization method that assumes one or more independent variables; Yi D ˛0 C ˛1 Xi1 C ˛2 Xi2 C C ˛n Xin C i ; where Xi1 to Xin are independent variables (or variables that are assumed to be independent), i is a normal error that is minimized when finding the numerical solution for the regression model; which are coefficients from ˛0 to ˛n . 2. Least squares regression model: This is a generalized nonlinear fitting model that assumes a more sophisticated nonlinear correlation between the variables. Since there are no closed-form solutions, one may either pick a Taylor expansion or a different basis set to fit the dependent variables behavior by minimizing the sum of the squared residuals S SD
n X
Œyi f .xi ; ˇ/2
iD1
3. Domain expert interpretation of statistically-identified causalities: Although correlations can be identified using regression analysis, identifying causality requires an extra layer of physical interpretation by glass scientists. Both linear and nonlinear regression models can be implemented in MATLAB, R, or Python.
33.3.3 Genetic Algorithms Genetic algorithms (GAs) are methods for solving constrained problems (especially optimization) based on a natural selection process that mimics biological evolution. In a classical numerical solution algorithm (i. e., Newton’s method solving the zeros of equations), one generates a single point at each iteration. The sequence of points progressively approaches the solution. In GA, however, instead of iterating on one point, a population of points are generated at each iteration, and the best point in population approaches the solution. A fundamental difference between classical algorithms and GA is that in GA, the next population is generated using random number generators and some clever combinations from the best solutions of the previous iteration instead of deterministic computation. GA are useful, particularly for global optimization problems where there are multiple ob-
Part D | 33.3
1. Strongly-dependent on initial data scaling and normalization: The relative ranges and values of each variable can distort the ellipsoid and alter the covariance matrix. As a result, the principal components will depend on the scale of the variables if they are not normalized. 2. Relies on linear variances and correlations: The variables may be linearly uncorrelated but may have a more complex nonlinear correlation. Then, PCA cannot capture the information gain from those cases, and the analysis may end up adding spurious variables instead of capturing the nonlinearly uncorrelated variables. 3. PCA assumes that when a variable has a large variance, the variable will have low covariance, hence high importance: This assumption helps eliminate the noise and pick up the major variables. However, in specific problems, called blind signal separation (or blind source separation), multiple signal sources can have almost equally significant effects and lead to a mixed signal response. In the case of glass compositions, for instance, different dopants may drive diffusion and oxide topology freezing, which may have competing or differential effects on CTE. In such multiple source effects that may lead to competing driving forces, running an independent component analysis (ICA) in addition to PCA is recommended. 4. Mean and covariance do not describe some distributions: Mean and covariance values are used mostly for Gaussian distributions, but there are many statistical distributions in which mean and covariance do not yield relevant information about the variables. As a result, one may need to have other ways of testing the significance of variables, such as information gain analysis (also known as Kullback–Leibler divergence [33.42, 43]), or Gram–Schmidt [33.1].
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jectives with competing requirements. GA can also be used for maximization, minimization, constrained optimization, multidimensional fitting, classification, and prediction problems. For data-driven glass composition discovery problems, one almost always optimizes with multiple competing objectives. As a result, this toolbox of algorithms is useful for composition development. Here is a step by step description of a simplified GA for solving a generic multi-objective optimization problem:
Part D | 33.3
1. The GA generates a random initial population of glass compositions. 2. The GA then evaluates the glass composition population based on their predicted properties and the fitness values: a) Scores each composition of the current population by computing its fitness value and normalizing these scores for comparisons. b) Picks a few candidates from the population (parents) based on their fitness. c) Some of the individuals in the current population that have lower fitness are chosen as elite. These elite individuals are passed to the next population (children). d) Children are produced either by making random changes to a single parent (mutation) or by combining the vector entries of a pair of parents (crossover). e) Replaces the current population with the children to form the next generation.
3. The GA then creates a sequence of new populations. At each step, the GA uses the compositions in the current generation to create the next population. 4. The algorithm stops when the output meets the stopping criteria. These criteria can include the maximum number of generations, the time limit for iterations, the fitness limit for the population (when the fitness function for the best point in the population is less than or equal to the fitness limit), and stall limits on generations (i. e., when the average change over each generation is less than a function tolerance limit).
33.3.4 Neural Networks Neural networks (NN) are a set of ML algorithms (supervised or unsupervised) that can be used to predict nonlinear behavior of different systems. A neuron is a nonlinear, parameterized function of input variables. Therefore, an NN is the composition of nonlinear functions of two or more neurons. The nonlinear nature of NNs can help identify nonlinear behaviors that may not otherwise be observed or captured properly in regression models or other linear techniques such as PCA. Despite the biological flavor of the term neural network, NNs in ML are pure mathematical constructs that consist of either feedforward or feedback networks (recurrent). For glass composition modeling purposes, this x0 = 1
x1 x1 x2 x2 x3 x3
g(x,w) x4
x4
xN xN N inputs
Hidden neurons
Output neurons
Fig. 33.5 Feedforward NN consisting of multiple n inputs, Nc hidden neurons, and No output neurons
N variable inputs, one bias input
Hidden neurons with sigmoid activation function
One linear output neuron
Fig. 33.6 Feedforward NN with a single hidden layer and
a bias input
Machine Learning for Glass Modeling
Nc X iD1
13 0 N X 4wNc C1;i tanh @ wij xj C wi0 A5 2
jD1
2
13 0 N X 4wNc C1;i tanh @ wij xj A5
iD1
jD0
where x is the input vector (size: N elements) and w is a vector of size .N C 1/Nc C .Nc C 1/. The hidden neurons are numbered from 1 to Nc , and the output neuron is indexed as Nc C 1. The parameter wij is assigned to a connection from neuron (or input edge) j to neuron i. The output function g.x; w / is a linear function of the parameters in the last connection layer (between the final hidden layer to the output neuron), and the connections between the inputs and the hidden layers are nonlinear functions of the inputs. In the topology shown in Fig. 33.6, there are N variable inputs and a bias input x0 . If the static NN is going to have a major linear component or an offset, one can add linear terms by introducing additional direct connections from inputs (x0 to xN ) to the linear output neuron. Thus, the formal description of a static NN with a single hidden layer becomes g .x; w / D
g .x; w / D wNc C1;0 C
D wNc C1;0 C
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33.4 Data-Driven Development for Glass Composition Design The design of glass compositions for a targeted application is a very long and tedious process because of the many different attributes required by the product, and the manufacturing technology. Product requirements vary from application to application. Many customer requirements are, generally, for display glasses, about strain point (SP), annealing point (AP), softening point (SfP), CTE, density, Young’s modulus (E), dimensional stability, and additionally CS, stress profile (SPr), depth of layer (DOL), and fracture toughness (FT) for strengthened glasses. At Corning Incorporated, we use the fusion draw technology to deliver surface pristine glass products. Such technology comes with known requirements for the manufacturability of a given glass composition. Some of the most important ones are the liquidus temperature, the viscosity at the liquidus temperature, and the temperatures at 20 Pa s and 3500 Pa s. Glass composition design can be seen mathematically as a multi-objective optimization with constraints on the sum of the variables (different oxides that make
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up the glass composition), the range of each variable (oxide). One objective function for each attribute can be given as a range (70 GPa E 85 GPa) or lowerbounded range (AP 800 ı C). There are many different ways to solve this mathematical problem. An experimental approach is based on using currently known insights built from years of practice of glass melting. This approach requires the melting of many glass compositions following an experimental path that is updated through iterative melt trials. Very often, glass scientists using this method make use of linear fittings of different glass properties to help them design the next set of trials for search of the potential optimal directions. Many existing commercial glass compositions had been designed this way. Through this trial-and-error minimization process, the likeliness to hit a glass composition that meets all requirements highly depends on the many years of expertise of the practitioner and the available budget (time, money). With access to a huge monetary budget and without any deadline, this trial-
Part D | 33.4
section focuses on feedforward networks. The description presented here follows the NN formalism in [33.1]. A feedforward NN (static network) is a nonlinear function of its inputs and their corresponding weighting parameters. So, a feedforward network consists of functions of its neurons which are nonlinear functions of inputs. Figure 33.5 shows a graphical representation of a feedforward NN in which information flows only in forward directions. In this graph representation, the vertices are the neurons, while the edges are the connections. Different from feedback networks, feedforward NN have a non-cyclic graph topology. The neurons at the outputs are called output neurons and the rest of the layers between the inputs and the output neurons are hidden networks. An important property of feedforward networks is that they are static: If the inputs are constant, then the outputs are constant as well. So, feedforward networks are also called static networks. A mathematical representation of the single layer static network in Fig. 33.6 that uses nonlinear sigmoid activation functions is shown below
33.4 Data-Driven Development for Glass Composition Design
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and-error approach, guided by local fittings and years of experience can be a viable route. One major hurdle, though, is the choice of the starting point of the search. Most of the time, the starting point is chosen to be a glass composition that has some attributes close to or identical to the ones of interest. This method will also greatly suffer if the glass to be designed has a large set of attributes to satisfy, especially when some of them are conflicting, which is the case when some oxides that optimize a given attribute also increase another attribute that is to be minimized. With years of practice of glass melting at Corning, a huge amount of compositions had been generated through the years. Even though these glasses are not based on regular design of experiments, they are very likely to cover a significant part of the composition space. Because of the way the glass compositions had been developed over time, one can expect to see some level of clustering in the set. A legitimate question to ask is: why not extend the usual linear regressions done on local spots to the whole compositions space covered by the existing and dormant glass data set? Of course, a linear regression might not work for all properties of interest, but the idea of using a robust modeling approach on the whole data set seems reasonable and very attractive. With the advent of faster computers and cheap random access memory (RAM) and storage, and especially with the development and maturing of new algorithms for nonlinear regression, such an exercise is appealing. It is called ML [33.44]. Basically, ML is an advanced form of applied statistics aimed at the use of computing power and sophisticated algorithms to help discover insights from data. The method grew from pattern recognition and computational learning theory, enabling machines to build mathematical models from a training data set. Iterative in nature, the algorithms learn from data to find hidden insights without being explicitly programmed where to search. Most of the key algorithms used in ML were already introduced in Sect. 33.3. The two most important properties for glass design are liquidus temperature and viscosity. The glass liquidus temperature TL is defined as the temperature at which the first crystalline phase precipitates from the melt of a given glass composition when the melt is cooled with very small rate. Accurate knowledge of the liquidus temperature is critical for many different reasons. When the glass is made with an isopipe, as it is the case at Corning Incorporated, it is important to know its value when the melt is flowing on the surface of the isopipe. The temperature of the melt at that stage can be maintained at a value higher than the liquidus temperature of the melt under consideration to avoid its
crystallization on the isopipe, which can damage a multimillion dollars piece of equipment. Depending on the targeted sheet thickness, the melt has to have a viscosity at the liquidus higher than a given value. This last requirement, among many others related to the melt during its transport from the steering tank up through the platinum pipes to the isopipe, describes the need to accurately know the viscosity–temperature curve for the glass melt. The viscosity becomes important based on its own rights. We see here that both the liquidus temperature and the viscosity–temperature curve are critical melt properties tightly related to the manufacture of surface pristine glass sheets when drawn from an isopipe. Most of the time, for display applications or for ion-exchange glasses for damage resistant layer, the knowledge of the viscosity–temperature is also important for customer attributes such as annealing temperature, softening temperature, or the viscosity at the given temperature value. There is no known accurate and generalizable physics-based models for glass melt liquidus temperature or melt viscosity for industrial glasses in display or damage resistance coating applications. The existence of huge data sets, coupled with robust ML techniques could be a viable route for the development of very predictive models for both liquidus and viscosity. An approach to finding glass compositions that meet both customer and manufacturing attributes is to use a fine grid search on the composition space and compute each property at the grid. One key challenge is the development of glass properties that are robust and accurate enough to make good predictions. Most of the methods employed in ML for the development of data-driven models require many parameters. In the case of NNs, one has to decide the number of layers, the number of neurons in each layer, the functional form to use for the activation function. Depending on the type of optimizer to be used, additional parameters such learning rate and momentum need to be added in the list of parameters. In the case of GA, key parameters to optimize for during the model design are population size, different probabilities for cross-over and mutation, along with the fraction of new random solutions to be generated at each iteration. Searching for the best architecture for either the NN or GA can be very much time consuming because of the number of possible combinations of parameters. One can use a grid search in which each variable is set to have all the possible values/state in its domain. This will then amount to thousands of simulations to run, especially, for instance, when we have continuous parameters such as the learning rate. Another option would be to randomly select values/states for the model parameters and
Machine Learning for Glass Modeling
33.4.1 Neural Network-Based Composition Models for Predicting Glass Liquidus Temperature The liquidus data we use in this study is a sample from our internal liquidus data. The sample is chosen to represent a historical data collection with clusters of different size. First, we use the whole data set and use NNs to build a model for liquidus temperature. The initial liquidus model is built using the chart in Fig. 33.7. Special care is required with data splitting. One wants each subset (training, validation, and testing) to have a similar distribution to the whole set. Methods based on Kullback–Liebler divergence are very handy for such splitting. The design of optimal NN architecSplit data 70% train, 20% validation, 10% testing
Design optimal NN architecture
Train optimal NN architecture
Select best model based on test set
Fig. 33.7
Flowchart describing the steps for the liquidus model development
ture will be based on incremental increase of model complexity through more neurons in any given layer or an increase of the numbers of hidden layers. For each architecture with a given complexity and number of parameters, a series of parameters training is conducted and the RMSE and R2 on the test set and validation set is recorded. The best architecture is the one with the smallest number of parameters, the least complex and for which the RMSE and R2 are about the same for all three sets (training, validation, and testing). It also is possible to include the choice of the activation function for each layer in the architecture as part of the optimization process, except the output neuron, which is kept as a linear activation function. R-squared (R2 ) is a statistical measure of how close the experimental and predicted data are close to each other. It is also known as the coefficient of determination. Once an optimal architecture has been identified, the next step is to train it for hundreds of times to increase the likeliness of finding a set of parameters that give a reasonable set of parameters that correspond to low values for the objective function. For this training, we found the optimal architecture to have two layers, the first one with ten neurons and the second one with eight neurons, both layers with a Gaussian activation function. A close look at the plot of the predicted liquidus in Fig. 33.8 for the test set suggests that there are points with high accuracy and others with low accuracy. If we also consider that the original data is historical data and, therefore, was not based on a design of experiments, it is reasonable to think that the original data might be a clustered data set. Let us run a k-means cluster analysis to have a better view of how the data is organized. Since we do not know a priori the number of clusters to consider, we will assume a number of clusters between 2 and 15. The choice of the optimal number of clusters to consider will depend on how well the chosen clusters separate from each other. This is determined by the similarity between elements of the same cluster. In 1986, Peter J. Rousseeuw defined a metric, referred to as silhouette, which is a robust way of interpretation and validation of regularity within clusters of data. The technique provides a concise graphical representation of how well each object lies within its cluster or how similar an object is to other members in its own cluster compared to other clusters. The silhouette ranges from 1 to 1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters. If most objects have a high value, then the clustering configuration is suitable. If many points have a low or a negative value, then the clustering configuration may have too many or too
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run the decided number of simulations and pick the architecture that gives the best model in terms of minimized error on a test set. This last approach will by no means guarantee access to the best model. Hopefully, there is another approach. The one method we use in this study is based on a Bayesian approach and is called Bayesian optimization (BO) [33.45, 46]. BO is a method of finding the maximum/minimum of an expensive cost functions. It is based on the Bayesian method to set up a prior over the model objective function and combine it with evidence to find the posterior function. BO is applicable to cases where we do not have a closed form formula for the objective function, but where we can collect observations of the objective function. In the following sections, we will describe details of the development of composition dependent models for three key glass properties, liquidus temperature, viscosity, and Young’s modulus.
33.4 Data-Driven Development for Glass Composition Design
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a) Measured TL (°C) 1400
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Fig. 33.8a–d Best liquidus model based on the whole data set. RMSE on all sets are about the same but higher than the experimental values ( 10 ı C). (a) Represents the training data, (b) validation data, (c) the test set or blind prediction, and (d) the whole data set
few clusters. The silhouette can be calculated with any distance metric. The average silhouette in each cluster for all 14 clusters we consider is plotted in Fig. 33.9. It appears that the data is best split in nine clusters. Further analysis of the different clusters shows the clusters population. We observe that, for the liquidus data in hand, the clusters have different population size. As we can see in Fig. 33.10, two clusters stand out with populations higher than 1100 compositions. The third largest cluster has about 500 compositions. The 6 remainders have populations lower than 300 compositions. Besides the cluster population, another characteristic is the average distance of a cluster population to the cluster centroid. The smaller the average distance, the more compact the cluster. We observe in Fig. 33.11 that the two most populated clusters (1, 9) have the smallest average distances to their respective centroids. Being the most populated
and most compact, clusters 1 and 9 are suitable to be used for building localized liquidus models. Using the same procedure for splitting the data into a training set, a validation set and a test set, we conducted a best architecture search for data in cluster 1. We end up finding the same architecture as when we used the whole set, but this is not necessarily the case for all situations. From Fig. 33.12, we can see a significant improvement of the predicted liquidus temperature for the test sets. Overall, the RMSE of the test set decreased significantly with the use of the largest cluster (14 ı C), compared to (23 ı C) when we used the whole data set. The liquidus model we built from the second largest cluster also has a lower RMSE on the test set (15 ı C). To make liquidus temperature predictions from both models requires that the composition of interest be a member of cluster 1 or cluster 9. This is very likely
Machine Learning for Glass Modeling
33.4 Data-Driven Development for Glass Composition Design
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Fig. 33.11 Average distance to centroid for all 14 clusters considered in the k-means cluster analysis
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Fig. 33.10 Cluster population for the liquidus temperature
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to be the case, since these clusters are the largest ones in the set. When using this approach for designing glass compositions with low liquidus temperature, one has to start by selecting compositions that are only in cluster 1 or cluster 9 and then use the corresponding clusterbased model to make the prediction. For a situation in which we have many different models from Nc different clusters, it is possible to consider an ensemble prediction which consists of building a model for each cluster, make a prediction from each cluster based model and take the ensemble average computed as the mean predicted value, which is the average from the cluster-based predictions scaled by the distance from the composition of interest to the centroid
Nc is the total number of clusters for which we have built a liquidus model from, Ti is the liquidus temperature predicted by the model built from cluster i, while di is the Euclidian distance from the point of interest to the centroid of the cluster i. The coordinates of the composition can be in mole percent (mol%), weight percent (wt%), or atomic percent (at:%), depending on the coordinates used to do the cluster analysis. As we can see from the model development described above, finding the right architecture for the NN model is tedious. We searched for the best architecture by starting with a simple one-layer model with a small number of neurons and we increased its size by one or two neurons at a time, for a fixed activation function. We increased the number of neurons depending on the ratio between the RMSE of the training and validation sets, which we want to keep close to one. At some point, we can insert a second hidden layer to resolve the nonlinearity of the liquidus temperature. Let us consider for a moment the number of variables that we can play with in the design of the NN architecture, without being explicit:
Number of hidden layers (1,2) Number of neurons in each layer (6–20) Activation function of each layer (tanh, sigmoid, inverse tangent) Learning rate (continuous number between 0.0001 and 0.1).
Part D | 33.4
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a) Measured TL (°C) 1600
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1200 RMSE = 16.5867 R2 = 0.88105
1100
Part D | 33.4
1100
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1300
RMSE = 17.9567 R2 = 0.84429
1100
1400 1500 Predicted TL (°C)
1100
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c) Measured TL (°C) 1600
d) Measured TL (°C) 1600
1500
1500
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1300
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RMSE = 16.6554 R2 = 0.8752
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1400 1500 Predicted TL (°C)
Fig. 33.12a–d Best liquidus model based on the data in the largest cluster. RMSEs on all sets are about the same, within few degrees of difference. They are higher than the experimental values ( 10 ı C) but much better than the RMSE obtained when the whole data set was used to build a global model. (a) Represents the training data, (b) validation data, (c) the test set or blind prediction, and (d) the whole data set
If we want to simulate all possible architectures, it will take an extremely long time. This is not feasible. One can choose to randomly select a few cases to run from the whole parameter composition space, without, of course, any guarantee of having the optimal architecture in the selected cases. Ideally, one would like to find the optimal NN architecture without having to run thousands of simulations. BO offers that possibility. Let us try rebuilding a liquidus model while splitting the data into two sets, a training set and a validation set, with the help of BO to find the best architecture, along with its modeling parameters such as the number of layers, the number of neurons in each layer, the learning rate, the momentum and the activation function for each hidden layer.
33.4.2 Neural Network-Based Composition Models for Predicting Glass Viscosity Viscosity is a measure of the resistance of the glass melt to shear deformation; it is a measure of the ratio between an applied shearingj force and the rate of flow of the liquid. The temperature dependence of the melt viscosity plays a significant role in defining the glass formability of a given composition. A viscosity model serves many purposes in the design of glass composition for targeted properties. A viscosity model could be used to extract key temperatures from the viscosity curve, temperatures such as the annealing point, the strain point, the glass transition temperature or the softening point, to name a few. The viscosity value that defines to each of the above temperature points varies
Machine Learning for Glass Modeling
(VFT) [33.48] models. The VFT is given by the equation log D A C
B T To
where A is a negative number, while both B and To are positive. The MYEGA models, defined by Mauro et al. more recently stands as log D A C
B C eT T
In which A is also negative, while both B and C are positive. While both models can give good fit to the viscosity/temperature data curve, it is not an easy task to make
Predicted TL (°C) 1500 1450 1400 1350 1300 1250 1200 1150 1100
RMSE = 11.9 °C R2 = 96.4%
1050
1000 1000
1100
1200
1300
1400 1500 Measured TL (°C)
Fig. 33.13 Best liquidus model based
on the validation set. Use of the BO framework helped improve the RMSE and R2 on the validation set
Predicted η (poise) 14 12 10 8 6 4 2
0
RMSE = 0.11 R2 = 99.84% 0
2
4
6
8
10
1177
12 14 Measured η (poise)
Fig. 33.14 Brute force fitting of
temperature dependent viscosity with NNs using a single layer with 11 neurons and tanh as an activation function
Part D | 33.4
slightly, depending on the research group, except for the glass transition temperature, which is set for a viscosity of 12 GPa. Of course, all these points are very important, and each of them ought to be predicted as accurately as possible. However, one viscosity point, for the fusion drawn process, stands out of the crowd: the viscosity at the liquidus temperature. For current fusion draw technology and for most commercially available display glasses, the viscosity of the liquidus must be approximately above 2000 Pa s. A high viscosity at liquidus helps the purpose of making glass sheets of various thicknesses and also helps prevent crystallization on the isopipe surface; the higher the viscosity, the slower the diffusion of the different glass components. Different models exist for glass viscosity (Chap. 3). The two we use most at Corning are the MYEGA [33.47] and the Vogel–Fulcher–Tammann
33.4 Data-Driven Development for Glass Composition Design
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Fig. 33.15 Brute force fitting of
Predicted η (poise) 14
temperature dependent viscosity with NNs using two layers (9, 6) neurons and tanh as an activation function. Architecture designed with BO
12 10 8 6 4 2
Part D | 33.4
0
RMSE = 0.09 R2 = 99.99% 0
2
4
6
8
10
12 14 Measured η (poise)
Fig. 33.16 Brute force fitting of
Predicted η (poise) 14
temperature dependent viscosity with NNs using the architecture shown in Fig. 33.18 (one layer, eight neurons with tanh). The architecture represents the MYEGA equation
12 10 8 6 4 2
0
RMSE = 0.06 R2 = 99.95% 0
2
4
6
8
10
the models composition dependent, meaning having the parameters as function of the glass compositions. Building accurate data-driven models for viscosity as a function of temperature and glass composition is not an easy task. Even with abundant experimental data, we found it difficult to obtain a good predictive model of viscosity with acceptable accuracy at all three viscosity regimes (Figs. 33.13–33.15):
Low viscosity: 17 poise Mid-range viscosity: 78:5 poise High viscosity: 8:513 poise.
Our experience when using a brute force NN model is that accuracy of the prediction deteriorates as we reduce the temperature (increase the viscosity) (Figs. 33.16 and 33.17). Figure 33.12 shows the valida-
12 14 Measured η (poise)
tion results on alkali contacting glass compositions. The architecture of the NN model was optimized based on multirestarts and grid searches for the optimal number of neurons for a single layer. With the use of BO, we improved the prediction of the validation set with a reduction of the RMSE (0:110:9) and an increase of the R2 (99:8499:9%). The improvement of the temperature and composition-dependent viscosity model is not really significant. We still observe a clustering of the predicted data around the mid and high viscosity ranges. The addition of an extra layer suggested by the BO method did not resolve the lack of accuracy in those ranges. Let us for a moment turn back to the VFT and MYEGA models. For a single composition, both VFT and MYEGA give a close to perfect fit of the tempera-
Machine Learning for Glass Modeling
33.4 Data-Driven Development for Glass Composition Design
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Fig. 33.17 Brute force fitting of temperature dependent viscosity with NNs using BO to find the best architecture to code the MYEGA equation. The architecture represents the MYEGA equation
Predicted η (poise) 14 12 10 8 6 4 2
0
2
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Part D | 33.4
0
RMSE = 0.04 R2 = 99.99% 12 14 Measured η (poise)
Fig. 33.18 Gray box fitting of temperature-dependent MYEGA viscosity with NN using a single layer with eight neurons and tanh as an activation function on a single layer
Bias 0
Al 2O3 1 K(0) B2O3 2
11 K(1)
Na2O 3
12 K(2)
K 2O 4
MgO 5
CaO 6
SrO 7
13
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M0
K(3)
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K(4)
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C ·1000 ·100 1000 · M0
K(5)
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B · M0 · K0 27 log η 26
16 K(6)
BaO 8
17 K(7)
SnO2 9
18
T 10
ture dependent viscosity curve. To illustrate a way of implementing a gray NN model, let us take the case
of the MYEGA model. If one figures out a way to build accurate models of A, B, and C MYEGA model
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Part D | 33.4
parameters as functions of composition, then one will have a very robust and accurate model. This modeling approach is feasible through the coding of the MYEGA equation. Without any architecture optimization, Fig. 33.18 shows a gray model of MYEGA. We see that the coding of the MYEGA equation through the NN architecture significantly reduces the clustering of the prediction in the mid and high viscosity ranges. The architecture was just chosen from a linear grid search for single layer architecture with the number of neurons varying from 7 to 15. The best architecture choice is based on the optimization of the RMSE of the validation set. Once we use the BO framework and put many model parameters, such as the number of layers, the number of neurons in each layer, the learning rate, the momentum, and the activation function for each hidden layer, as variables we found a much more accurate model, as we can see in the plot of the validation set.
33.4.3 Genetic Algorithm-Based Glass Models for Predicting Compositions for Desired Ranges of Young’s Moduli Young’s modulus is a critical glass property for many different applications. When alkali-free glasses are used in the thin film transistor manufacturing process, they are sought to have a high Young’s modulus to help reduce the distortions due to film stress. In the design of glass compositions with native damage resistance, compositions with low Young’s modulus are of critical interest. Glass compressive stress due to ion exchange is given by a formula in which the Young’s modulus is a key contributor CS D
BEC 1
where B is the network dilation coefficient, E Young’s modulus, C an atomic concentration variation, and the glass Poisson ratio. If everything is kept equal, the higher the Young’s modulus, the higher the compressive stress CS. Access to an accurate and robust model for Young’s modulus is very important for the design of glass compositions for different applications. The accuracy is important, but the module’s robustness is even more important. Young’s modulus is not readily measured for each glass that has been melted. This lack of systematic measurement led to scarcity of Young’s modulus data; therefore, the extrapolation of any Young’s modulus model can be a serious challenge. NNs are known to not extrapolate very well when a user deviates too far
from the space holding the training data. One way to extrapolate with confidence is to have a compositiondependent physics-based model, which we do not have yet. We have found GA modeling to be very interesting. When done properly with enough care, one can build models with much better extrapolation capabilities than NNs as shown in Figs. 33.19–33.21. A careful study of the GA shows that it is a very long and slow iterative process when applied to model development, which success, in terms of accuracy and robustness, depends on the size of the population under consideration and the number of trials. We have used an in-house GA modeling tool similar to Python. Once we constrained the tool to simple models by penalizing complexity and a large number of parameters of long and complex solutions, we found good Young’s modulus models that extrapolate on the data set on the side during the training. One extreme situation to build such models would be to extract data that are at the boundary of the whole data set and use it as a test set for validation and selection of the best model. Overall, we see that GA makes very good extrapolated predictions. If we use the same data splitting with an NN model, the results are not that good, as we can see in Fig. 33.22.
33.4.4 Genetic Algorithm-Based Glass Models for Predicting Compositions for Desired Ranges of Compressive Stress and Depth of Layer Glass strengthening is a very important attribute of glassy products for many of their contemporary applications such as damage resistance for hand-held devices. Glass compositions for chemical strengthening should be designed with as fast KC -for-NaC interdiffusion as possible. Although large values of the DOL can also be achieved by increasing the ion exchange temperature, this simultaneously lowers the compressive stress (CS) at the surface due to an increased rate of stress relaxation at elevated temperatures. A large DOL value is required to embed surface flaws and defects in the compressive stress layer. For glasses designed with a fixed DOL value (e. g., 50 m), significant cost savings can be achieved by increasing the diffusion rates of the exchanging ions and thus shortening the ion exchange treatment time. To enable the composition-dependent prediction of DOL, it is first important to understand the temperature dependence of DOL. The activation barrier for sodiumpotassium inter-diffusivity (HD ) can be computed by
Machine Learning for Glass Modeling
Frequency
Train-E (GPa)
33.4 Data-Driven Development for Glass Composition Design
Frequency 300
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Fig. 33.19 Modeling of Young’s modulus with GA. Compositions selected for the test set are the ones very far from their
closest neighbors, meaning the ones at the boundary. A look at their corresponding Young’s modulus shows that they have a higher Young’s modulus
assuming an Arrhenius temperature dependence, log D.T/ D log D.1/
HD kB T ln 10
where D is the mutual diffusivity and kB is the Boltzmann constant; D can be calculated based on the measured KC diffusion profile. Let us here consider a set of 28 silicate glass compositions, which do not exhibit any clear composition dependence on HD . Certainly, we find that this activation barrier for diffusive hopping is not affected by the bulk viscous flow behavior over this range of compositions (Fig. 33.23a).
This is in agreement with literature findings that ionic diffusion and viscous flow are decoupled at low temperatures, i. e., the breakdown of the Stokes– Einstein relation. To predict the composition dependence of DOL, we consider a simple linear regression model. To do so, we calculate D by combining the previous equation with the following equation for relaxation of mutual diffusivity, log D.t/ D log D.1/
t C Œlog D.0/ log D.1/ exp D
Part D | 33.4
300
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Fig. 33.20 GA
Predicted E (GPa) 90
makes good predictions for the compositions in the training set
88 86 84 82 80 78 76 74
Part D | 33.4
RMSE = 0.55 GPa R2 = 95.8%
72
70 70
72
74
76
78
80
82
84
86 88 90 Experimental E (GPa)
Fig. 33.21 GA makes good predictions for the compositions in an extrapolated region
Predicted E (GPa) 95 90 85 80 75 70
RMSE = 1.11 GPa R2 = 98.4%
65
60 60
65
70
75
80
85
90 95 Experimental E (GPa)
where t is the ion exchange duration and D is the diffusivity relaxation time. We find that D is typically around 8 h and is, thus, independent of composition for this composition space, i. e., we assume D D 8 h in our model calculations. The difference between log D.0/ and log D.1/ in the previous equation has also been found to be relatively composition independent and equal to 0.1 (with D in units of cm2 =s). Moreover, we set HD equal to 1:12 eV, since this was the average value found in Fig. 33.23b. Then, we calculated D.1/ using a simple linear regression model, D.1/predicted D ŒAl2 O3 D.1/Al2 O3 C ŒNa2 OD.1/Na2 O C : : : ; which includes the weighted contributions from the different oxides to D.1/. We minimized the sum of squared errors by changing these values and obtained
a very good prediction of the measured DOL values (Fig. 33.24). The CS is given by, CS D
BE.csurf cbulk / BEC D 1 1
where B is the network dilation coefficient, E is Young’s modulus, is Poisson’s ratio, and csurf and cbulk are the potassium concentration at surface and bulk, respectively; CS is created at the surface as a result of ion exchange and depends on both ion exchange temperature and time. Unlike DOL, which increases with both temperature and time, CS decreases with both temperature and time as a result of stress relaxation. A simple exponential function can be accurately fitted to the time evolution of compressive stress. Extrapolating CS back to t D 0 gives CS as a result of purely elastic strain with no stress relaxation. As stress relaxes, elastic strain
Machine Learning for Glass Modeling
33.4 Data-Driven Development for Glass Composition Design
1183
Fig. 33.22 NN makes poor predictions
Predicted E (GPa)
for the compositions in an extrapolated region
95 90 85 80 75 70
RMSE = 2.11 GPa R2 = 93.4%
65
65
70
75
80
a) Log D (cm 2/s)
85
90 95 Experimental E (GPa)
Part D | 33.4
60 60
b) ∆HD (eV) 1.3
–9.4 Glass 1
–9.6
Glass 2 Glass 3
–9.8
1.2
–10.0
1.12 eV –10.2
1.1
–10.4 –10.6
1.0
–10.8 –11.0
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410 ºC
370 ºC 1/T (K –1)
0.9 5.3
5.4
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5.6
5.7 5.8 5.9 6.0 Activation barrier for viscous flow (eV)
Fig. 33.23 (a) Temperature dependence of the mutual diffusivity for three different glass compositions, showing constant slope and thus activation barrier for sodium-potassium inter-diffusivity (HD ). (b) HD as a function of the activation barrier for viscous flow calculated from the measured viscosity data
is transformed into plastic strain. The strain " can be then calculated as the product of CS and (1 /=E. Using CS.0/, we obtain the purely elastic strain, which is plotted in Fig. 33.25a as a function of CS.0/. As expected, the linear elastic strain increases approximately linearly with the initial compressive stress. By assuming that 90% of available sodium ions are exchanged at the surface, we can also calculate the lattice dilation coefficient, B, since ".0/ is equal to the product of B and C.0/. A plot of the lattice dilation coefficient as a function of the linear elastic strain is shown in Fig. 33.25b. Three sets of glasses are shown in Fig. 33.25, which have different Na2 O concentrations in the base glasses.
For each set of glasses, B increases linearly with the elastic strain. At higher Na2 O concentration, we find that B is smaller for a given elastic strain, i. e., the created compressive stress at a higher elastic strain is smaller. In other words, stress relaxation is facilitated with increasing alkali concentration in the glass. It is generally believed that a high strain point or glass transition temperature is required to obtain a high compressive stress due to ion exchange. However, when considering CS extrapolated to zero time, there is no influence of stress relaxation, and we, thus, find a relatively weak correlation between the initial CS and the glass transition temperature. Remarkably, if we transform this plot into a network dilation description, we
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Fig. 33.24 Comparison of measured and predicted values of DOL for 28 silicate glass compositions
Model DOL (μm) 160 140 130 100 80 60
Part D | 33.4
40 20 0
0
20
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a) ε (%)
b) B (ppm/(mol% K 2O))
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7000 0.9
↓Na2O Fixed (Na2O) ↑Na2O
1.0
1.1
1.2 ε (%)
Fig. 33.25 (a) Linear elastic strain " as a function of the initial compressive stress at 410 ı C for 28 silicate compositions. (b) Network (lattice) dilation coefficient B as a function of the linear elastic strain for three sets of glasses with different
contents of Na2 O in the base glasses
find a linear dependence of the network dilation coefficient on the glass transition temperature. This shows that network dilation is controlled by the bulk glass network topology, since the glass transition temperature is quantitatively related with the topological constraints of
the glass network. Therefore, a prediction of the composition dependence of the network dilation coefficient from constraint theory is possible. Eventually, this leads to a prediction of the composition dependence of CS created by ion exchange.
Machine Learning for Glass Modeling
33.5 Conclusions and New Glass Research Opportunities
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Fig. 33.26 Blind predictions of GA-based models for DOL (a) and CS (b)
a) Modeled DOL (μm) 80 70 60 50 40
R2 = 0.9483
30
30
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70 80 Experimental DOL (μm)
b) Modeled CS (MPa) 800 750 700 650 600 550 500
R2 = 0.9768
450
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A pure data-driven approach based on GA, as described earlier, can generate a pure mathematical formula of CS and DOL as functions of glass composition, time, temperature, and the sample thickness model, once validated with experimental data from blind prediction, could be used in an inverse problem approach to
design compositions meeting conditions of process, and customer attributes for compressive stress, along with other ones. Figure 33.26 is a result of blind predictions of DOL (Fig. 33.26a) and CS (Fig. 33.26b) models built from the method described above with GA.
33.5 Conclusions and New Glass Research Opportunities In this chapter, we described Corning’s glass innovations and how it developed a robust data-driven streamline for glass composition design. After an overview of similar data-driven materials modeling and prediction studies, we briefly presented the data cleaning, GA, and NN methods used for the data-driven development
of glass compositions. At the end of 2015, Corning’s damage resistant glassy products had been used in over 4.5 billion devices, including smart phones, tablets, notebook computers, smart watches, automotive glass, touch panels, and in interior architecture and design. Billions of current other devices and many more to
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come can claim some sort of connections with Corning either because of the LCD substrate or the high performance display used as carriers. Performance models-based topological constraint theory, data-driven models for CS and DOL, as well as integrated computational materials engineering (ICME) approaches that incorporate both materials design for performance and manufacturing-related models are key approaches to consider in the design of glass compositions for damage resistance applications. Using data-driven GA and NN models, it is possible to predict and engineer glass liquidus temperature, Young’s modulus, viscosity values, CS, and DOL of glass samples. Using topological constraint theory, some of the predicted compositions could be eliminated. . . In addition, empirical models based on a fusion draw process can help identify and eliminate fusion line zirconia defects in the fusion draw process. With previously established empirical and fundamental models of both glass structure and the glass fusion draw process, it is possible to minimize the number of experimental iterations not just in the materials selection stage (Stage I) but all the way down to manufacturing engineering (Stage III). Data-driven materials modeling and prediction allows researchers to accelerate the materials invention process by screening tens of thousands of different chemical compositions and their corresponding predicted or measured properties. For an application with a desired set of materials property specifications, a database of materials properties must be constructed by using publicly available crystal structure, phase diagram, and other optical, electronic, and magnetic properties. In addition, first principles and multiscale modeling techniques should also be used to construct a list of calculated properties for a range of sample compositions. After that, data simplification methods such as PCA, ICA, data cleaning, and cluster and regression analysis techniques should be used to identify the properties that have the most significant effects on the desired end properties. Finally, GA and NN models should be used to predict the properties of a given stoichiometry over an entire chemical composition space to identify (new) compositions with outstanding or desired physical properties. Eliminating a subgroup in a composition space (i. e., due to crystalline symmetry restrictions, known behavior of dopants, etc.) can help simplify the NN and GA models’ parametric sweep over the phase diagram. In terms of fundamental glass research, we believe that data-driven predictive modeling of chemical compositions and their corresponding physical properties offers numerous opportunities, especially in the following areas [33.49, 50]:
1. New glass compositions with minimal crack propagation: Damage resistant glass compositions are engineered to alleviate crack propagation and failure modes originating from external impact. Although chemical strengthening on the surface of glass reduces stress concentration and the likelihood of crack propagation, new failure modes that penetrate deeper than the strengthened surface are emerging due to new use cases. In addition, different form factors such as automobile windshields, smart watches, tablets, or smart phone scales cause differences in stress distribution and concentration profiles. Enhancing glass mechanical strength both through the bulk glass composition and through the surface dopant profile are ongoing efforts needed by consumer electronics. Data-driven predictive modeling can help identify new outstanding surface dopants, bulk chemical compositions, and the effect of any other post-processing recipes that can enhance the ductility and fracture toughness of the glass. 2. New electrical, optical, and magnetic properties of glass: Glass is one of the foundational constituents of our civilization. For numerous applications such as hand-held consumer electronics, architectural components, display devices, automobiles, kitchen appliances, telecommunication devices, and highdensity memory components, functionalizing glass to achieve piezoelectricity, magnetism, ferroelectricity, quantum memory states, photo elasticity, magneto-optical, and other useful properties can help integrated glass circuits and devices. Datadriven predictive modeling can help identify the appropriate host glass composition and dopant elements and combinations that can achieve outstanding electrical, optical, and magnetic properties. First principles calculations based on DFT and phenomenological theory can help build a library of doped functional glass compositions. After building such a library, data-driven methods can guide compositions that may be outstanding and useful for functional glass applications. Although damage resistant glass compositions now only focus on mechanical and rheological properties of glass, there are numerous opportunities in engineering new functionalities. 3. Nonlinear photonic property engineering in glass and fiber: Nonlinear optics enable researchers to design a wide variety of devices including frequency-doublers, amplifiers, supercontinuum generators, functional wideband lasers, detectors, sensors, and waveguides, which can enhance the communication bandwidth significantly while enhancing propagation distances and lower-
Machine Learning for Glass Modeling
of silicate glasses. Improving our understanding of structure–property relations as a function of silicate glass chemistry will be very valuable in the design and discovery of new industrial glasses. Data-driven approaches can help identify the chemistry dependence of properties of silicate glasses. 7. Borate and phosphate glass chemistry and their corresponding structure–property relations: Other major oxide glasses, such as borate and phosphates, offer interesting scientific challenges, as well as useful technological applications. Multiple different effects can be observed when incorporating these network-forming oxides into a silicate glass matrix. Data-driven approaches can help identify structure–property relations previously not known for these glass chemistries. 8. Glass-ceramics with high strength and toughness, low CTE, and high transparency: Glass-ceramics can exhibit high strength and toughness. In addition, these oxides have engineered glass as well as ceramic phases; they can have low CTE as well. An important target is to achieve glass ceramics with both high toughness and a high degree of transparency; however, modeling these structures is highly complex because of the length and time scales involved, as well as the quenched kinetics that lead to a variety of competing diffusion and crystallization mechanisms and properties. As a result, using data-driven approaches can be the best (or even the only) modeling technique for refining glass ceramics for high strength, toughness, transparency, and low CTE. 9. Non-traditional glass chemistries: Bulk metallic and chalcogenide glasses have attracted significantly growing interest in recent decades due to their unique behaviors. For instance, metallic glasses have brittle-to-ductile transition, which yields increased fracture toughness. Chalcogenide glasses have unique optical properties for infrared bands. These materials are fundamentally different from silicate, phosphate, or borate glasses in terms of their chemistries and optical, thermal, and mechanical properties. Since the length and timescales relevant for the functionalities of these materials can span more than nine orders of magnitude, molecular dynamics or other approaches can have significant limitations for engineering or understanding the properties of these materials. Data-driven approaches can help identify the compositions that can help optimize multiple functionalities with respect to a vast range of elemental constituents whose behaviors are only partially understood.
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ing bit error rates. In particular, low noise erbiumdoped fiber amplifiers, low-loss optical fibers, and photodetectors with high sensitivity have revolutionized optical communications. Data-driven approaches can help engineer fiber-based nonlinear effects by helping fiber researchers home in on the right chemical compositions that can amplify with lower noise. Since many of the nonlinear photonic mechanisms are known both on phenomenological and atomistic levels, data-driven approaches and their results can also be validated through fundamental photonic device modeling and engineering as well. 4. Engineered acoustic properties of glass: Acoustic properties of glass have not been largely explored previously because glass has traditionally been used for its outstanding optical transmission and mechanical strength. With new glass applications as in automobile windshields, the need for enhancing sound transmission loss in the audible range (20 Hz–20 kHz) has become more important. While acoustic band structure engineering on windshield with multilayer structures can enhance sound reflectivity, ultimately, the glass composition and the corresponding intrinsic acoustic phonon band structure determine the sound transmission loss. Data-driven applications can help glass scientists design new bulk glass compositions with minimal weight and maximum sound transmission loss. 5. Rational control of thermal properties of glass: Thermal properties of glass are tightly connected to acoustic properties, since these properties originate from the intrinsic electronic band structure of glass. Thermal properties such as heat capacity, CTE, and thermal conductivity are strongly related to phonon density in each glass composition. Engineering acoustic properties of glass can open up new handles in the rational control of thermal properties of glass through electronic band structure engineering. Since virtually all of the periodic table is available to glass chemists, a data-driven approach to narrowing down the outstanding host and dopant chemistries is essential both for a better understanding of the dependence of thermal properties on different chemistries and for refining and controlling the thermal properties of glass. 6. Structure–property relations as a function of silicate glass chemistry: Silicate glasses are by far the most important and best-known class of glasses. Despite their ubiquity, the complex structures of silicate glasses are still partially understood. Rigorous chemical analysis and experimental studies are required for fully understanding of the structure
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10. High-pressure glass formation: Corning’s approach to fabricating state-of-the-art glasses include fusion drawing of glass melt at high temperature and reasonably lower viscosities. A major open research area is high-pressure glass formation, which readily occurs for volcanic and magmatic systems. Today’s current glass production is normally performed at ambient pressure. Since high-pressure experiments can also be expensive, data-driven approaches on volcanic and magmatic glasses can help develop pressure-based glass fabrication methods. These new methods can simplify or enhance new combinations of glass properties, which may not necessarily form by thermal history. 11. Polyamorphism: In polyamorphism, two glasses of identical chemistries may display different shortrange structural ordering. This difference in shortrange order leads to large differences in observed properties. Since the glass chemistries that may exhibit this effect are not well understood, one may construct a record of polyamorph glasses and their
corresponding chemistries. Then, running a datadriven model can help identify the most important parameters and defect chemistries and conditions that may alter the short-range order for identical chemistries. Acknowledgments. Section 33.4.4 was reprinted (adapted) with permission from J.C. Mauro, A. Tandia, K.D. Vargheese, Y.Z. Mauro, and M.M. Smedskjaer: Accelerating the design of functional glasses through modeling, Chemistry of Materials 28, 4267– 4277 (2016). Copyright (2016) The American Chemical Society. Adama Tandia would like to thank Russell Magaziner for valuable discussions regarding the content and flow of the document, Deenamma Varghese and Venkatesh Botu for many discussions about applications of machine learning to glass properties predictions, colleagues at Corning, too many to list, for valuables suggestions and feedback during many years of ML tools development and validation.
References 33.1 33.2 33.3
33.4
33.5
33.6
33.7
33.8
33.9
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Machine Learning for Glass Modeling
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The case of multi-functional ABX half-Heusler filled tetrahedral structures, Adv. Func. Mater. 22, 1425 (2012) E.D. Palik (Ed.): Handbook of Optical Constants of Solids (Academic, Burlington 1998) P. Villars (Ed.): Pearson’s Handbook Desk Edition (ASM International, Materials Park 1997) O. Kubaschewski, C.B. Alcock (Eds.): Metallurgical Thermochemistry, 5th edn. (Pergamon Press, Oxford 1979) A.G. Kusne, D. Keller, A. Anderson, A. Zaban, I. Takeuchi: High-throughput determination of structural phase diagram and constituent phases using GRENDEL, Nanotechnology 26(44), 444002 (2015) M.C. Onbaşlı, A. Tandia, J.C. Mauro: Mechanical and Compositional Design of High-Strength Corning Gorilla® Glass. In: Handbook of Materials Modeling, 2nd edn., Vol. 2, ed. by W. Andreoni, S. Yip (Springer, Cham 2019) T. Mueller, A.G. Kusne, R. Ramprasad: Machine Learning in Materials Science: Recent progress and emerging applications. In: Reviews in Computational Chemistry, ed. by A.L. Parrill, K.B. Lipkowitz (2016), https://doi.org/10.1002/9781119148739.ch4 S.V. Kalinin, B.G. Sumpter, R.K. Archibald: Big– deep–smart data in imaging for guiding materials design, Nat. Mater. 14, 973 (2015) S. Ullman, T. Poggio, D. Harari, D. Zysman, D. Seibert: Massachusetts Institute of Technology 9.54: Computational aspects of biological learning. In: fall 2014 course notes, http://www.mit.edu/~9.54/ fall14/slides/Class13.pdf I.T. Jolliffe: Principal Component Analysis (Springer, New York 2002) M. Ringner: What is principal component analysis?, Nat. Biotechnol. 26, 303 (2008) S. Kullback, R.A. Leibler: On information and sufficiency, Ann. Math. Stat. 22, 79 (1951) S. Kullback: Information Theory and Statistics (Wiley, New York 1959) B. Shahriari, K. Swersky, Z. Wang, R.P. Adams, N. de Freitas: Taking the human out of the loop: A review of Bayesian optimization, Proc. IEEE 104, 148 (2016) J.C. Mauro, Y. Yue, A. Ellison, P.K. Gupta, D.C. Allan: Viscosity of glass forming liquids, PNAS 160(47), 19780–19784 (2009) H. Vogel: Das Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten, Phys. Z. 22, 645–646 (1921) Materials Innovation Case Study: Corning’s Gorilla Glass 3 for consumer electronics 2016), https:// mgi.nist.gov/sites/default/files/uploads/user124/ Materials Innovation Case Study_Gorilla Glass 3_020816.pdf J.C. Mauro: Grand challenges in glass science, Front. Mater. 1, 20 (2014)
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References
1190
Part D
Glass Modelling
Adama Tandia Science and Technology Division Corning Inc. Corning, NY, USA [email protected]
Adama Tandia received his PhD from Paul Sabatier University, France. He worked at the Department of Applied Mathematics at Northwestern University prior to joining the Department of Modeling & Simulation at Corning Inc. in 2000. Adama is an expert in applications of molecular modeling and machine learning for materials design and process optimization.
Mehmet C. Onbasli Dept. of Electrical and Electronics Engineering Koç University Istanbul, Turkey [email protected]
Mehmet C. Onbasli worked on model-driven composition development as a Research Scientist at Corning Inc. before he became an Assistant Professor at Koç University, Istanbul. He earned his B.S. in Electrical and Electronics Engineering from Bilkent University (2010) and a PhD in Materials Science and Engineering from Massachusetts Institute of Technology (2015).
John C. Mauro
Part D | 33
Dept. of Materials Science and Engineering The Pennsylvania State University University Park, USA [email protected]
John C. Mauro is a Professor of Materials Science and Engineering at Pennsylvania State University and co-inventor of Corning Gorilla® Glass products. He has received numerous international awards, including the Kreidl Award, Weyl Award, Gottardi Prize, Pilkington Award, Stookey Award, Fulrath Award, and Zachariasen Award. John is a Fellow of the American Ceramic Society.
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34 Industrial Glass Processing and Fabrication Mathieu Hubert, Painted Post, USA
37 Amorphous Thin Film Deposition Virginie Nazabal, Rennes, France Petr Němec, Pardubice, Czech Republic
35 Batch Chemistry and Reactions Oscar S. Verheijen, Eindhoven, The Netherlands Mathieu Hubert, Painted Post, USA
38 Sol-Gel Glasses Lisa C. Klein, Piscataway, NJ, USA
36 Glass Shaping Romain Laniel, Rennes, France Mathieu Hubert, Painted Post, USA Mathieu Miroir, Rennes, France Antoine Brient, Rennes, France
39 Glass Recycling Ronan Lebullenger, Rennes, France François O. Mear, Lille, France
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_33
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Mathieu Hubert
Glass is among the most widely produced materials in the world, with a global annual production of over 100 million tons [34.1, 2]. Due to its versatility, it can be found in a wide range of applications, from the ubiquitous windows, screens or bottles to more specialized usages such as glass for sealing applications. Most of the industrially produced glasses are prepared using similar steps, via melting of raw materials, homogenization of the melt, conditioning, shaping and cooling. Numerous postprocessing steps such as cutting or polishing can be applied. Depending on the type of glass prepared and the quantity produced, the processing and fabrication techniques employed may differ greatly from one type of glass to another. Since the first man-made glass articles, some millennia ago, the processing of glass has been constantly improving to produce better, cheaper products, while decreasing the energy demand and the environmental impact of the glass fabrication process. In this chapter, the basics of industrial glass production are described, from the selection of the raw materials to the delivery of a homogeneous glass melt to the forming process. The different types of furnaces employed for different types of production are described, and the importance of process and furnace modeling in modern glass making is highlighted.
34.1
Brief Overview of Global Glass Production ................ 1194
34.2
Industrial Glass Compositions and Process Overview........................ 1198
34.3 Raw Materials and Batch Preparation 34.3.1 Raw Materials Selection ..................... 34.3.2 Typical Raw Materials in Industrial Glass Making..................................... 34.3.3 Batch Preparation.............................. 34.4 Importance of Redox in Glass Making 34.4.1 Redox in Glass................................... 34.4.2 Effect of Redox on Glass and Melt Properties ........................... 34.4.3 Characterization of the Redox State ..... 34.5
1200 1200 1201 1204 1206 1206 1206 1207
34.5.1 34.5.2 34.5.3 34.5.4 34.5.5 34.5.6
Glass Melting, Fining and Conditioning.............................. Batch Melting.................................... Primary Fining .................................. Refining and Conditioning ................. Homogeneity and Defects .................. Shaping, Finishing and Inspection ...... Storage .............................................
1208 1208 1209 1210 1211 1211 1213
34.6 34.6.1 34.6.2 34.6.3 34.6.4 34.6.5 34.6.6 34.6.7
Industrial Glass Furnaces................... Heat Transfer and Convection Patterns . Regenerative Furnaces ....................... Recuperative Furnaces ....................... Oxygen-Fuel Furnaces ........................ All-electric Melters ............................ Refractory Materials ........................... Environmental Aspects .......................
1213 1214 1215 1216 1216 1217 1217 1218
34.7 34.7.1 34.7.2 34.7.3 34.7.4 34.7.5
Modeling of Industrial Processes ....... Introduction ..................................... Energy Balance Models ...................... CFD Modeling in Glass Melting Tanks ... Modeling of Forming Processes ........... Furnace Control .................................
1219 1219 1220 1221 1225 1226
34.8
Conclusions ...................................... 1227
References................................................... 1227
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_34
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Industrial Gla
34. Industrial Glass Processing and Fabrication
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Part E | 34.1
34.1 Brief Overview of Global Glass Production Glass is everywhere around us in our everyday life, in a wide variety of colors and shapes, with a multitude of applications ranging from the highly visible and ubiquitous glass panels (screens, windows), containers (bottles, jars) or tableware, to the less visible (yet just as important) applications such as fiberglass for reinforcement and insulation, or glass for electronics (sealant/solder glass). No single type of glass can be used for all these usages, and all these applications require different glasses, with compositions tailored to meet specific requirements [34.3]. Industrial glass furnaces are typically specific to each type of production (especially in terms of forming of the glass, see Chap. 36), and can be classified by sectors, Flat 32.3%
Container 48.9%
Automotive glass 10% Furniture & internal glass ~ 19%
Glass market 136 mt
Solar glass 0.7%
Glass market 44 mt
Flat glass
Frits 1.8% Speciality 7.5% Art 2%
e. g., container glass, flat glass, fiberglass, tableware, specialty glass, etc. Each sector can be divided into subsectors. For instance, the fiberglass market can be divided into insulation fiber, reinforcement fiber, mineral wool, and optical fiber submarkets, while flat glass can be divided into automotive glazing, windows, furniture/internal glass and solar glass submarkets (see illustration in Fig 34.1 – display glass not represented here). Container glass and flat glass are the two largest sectors, amounting respectively to approximately 4550% and 30% of the world production in terms of weight of glass produced [34.2]. Fiberglass production (including reinforcement, insulation and mineral wool fibers)
Fig. 34.1 Distribution of the glass market in 2007, with specific focus on the flat glass market. After [34.2]
Reinforcemetn 2.7% Insulation 2.4%
Mineral wool 2.9%
Building windows 70%
11 21
16 260
4 42
59
12
2
8
22 6
5 40
97 107
55
31
54
11
8 10
18
49 38
7
8 8 3
4
5
22
3 22 11
8 7
Fig. 34.2 Global distribution of glass companies and groups in the world (December 2017). Figure courtesy of glassglobal Group (plants.glassglobal.com)
Industrial Glass Processing and Fabrication
Table 34.1 Nonexhaustive list of companies producing di-
verse types of glass in the world. The country indicated corresponds to the company’s headquarters. Several of the companies listed below operate in several countries and produce several types of glass Float glass AGC (Asahi Glass Company) Cardinal Guardian Cebrace Pa¸sabahçe Vitro KCC NSG – Pilkington Saint Gobain Fuyao Glass Industry Group Co Ltd Xinyi Glass Holding Ltd CSG Holding Co. Ltd Tableware glass Arc Bormioli group Libbey Fengyang Ruitailai Glassware Co Pa¸sabahçe Royal Leerdam Crystal Shandong Heishan Glass Group Shaoxing Jielong Glassware Co. Ltd World Kitchen LLC Yuncheng Huachuang Industry Co Nadir Figueiredo Container glass Si¸ ¸ secam Anchor Glass Ardagh Glass BA Vidro Bangkok Glass Gerresheimer Guangdong huaxing glass co Hindusthan National Glass & Industries Owens Illinois Piramal Glass Rockwood & Hines Shandong Glass Verallia Vetropack Specialty glass and fiberglass Corning Schott Nippon Electric Glass Owens Corning Fiberglass Rockwool Johns Manville Lanxess Knauf Insulation Jushi’s group Shandong Taishan Fiberglass Co., Ltd
Japan USA USA Brazil Turkey Mexico Korea Japan France China China China France Italy USA China Turkey NL China China US China Brazil Turkey USA Ireland Portugal Thailand Germany China India USA India China China France Switzerland USA Germany Japan USA Denmark USA Germany UK China China
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Part E | 34.1
and specialty glass manufacture each represent about 10% of the world glass production. As indicated, the global glass production reached 136 mt (million tons) in 2007 [34.2]. The distribution of the glass production per sector, and for the flat glass subsector for that year (2007–excluding display glass), is represented in Fig. 34.1. Actual production of flat glass amounted to 65 mt in 2014 [34.4] (50% produced in China, 15% in Europe, 10% in North America, the remaining 25% being produced in the rest of the world), while container glass production reached about 50 mt that same year [34.5]. According to figures collected by the glassglobal Group, more than 1270 glass companies and groups can be counted in the world (see overview of the distribution of the glass companies in the world in Fig. 34.2, with a focus on Europe in Fig. 34.31), with a total of about 2400 furnaces producing glass in 95 countries worldwide, for a total capacity of over 200 mt per year (data from August 2017) [34.1]. The majority of the furnaces produce container glass (more than 1100 furnaces), flat glass (540 furnaces) and tableware (close to 400 furnaces). Table 34.1 presents a list of selected companies representing different glass production sectors (flat glass, container glass, tableware, specialty glass and fiberglass). Given the very large number of companies producing glass in the world, this table is not meant to be exhaustive nor representative of companies’ market shares. It should only be taken as an illustration of the diversity of the glass production in the world. It should be noted that some of the companies listed in this table produce more than one type of glass, though listed in only one category. Global glass production is not evenly distributed in the world, and furnace locations depends on factors such as local market demand, availability of local resources for raw materials and/or energy, local regulations, and import/export of glass from other countries. Some examples of the geographic distribution of glass furnaces in different parts of the world are shown in Figs. 34.4–34.6. Figure 34.4 shows the location of flat glass furnaces in China (China possessing the largest share of flat glass production in the world). Distribution of container glass furnaces in Europe is shown in Fig. 34.5, while Fig. 34.6 illustrates container and tableware furnaces in the United States. All these different sectors, subsectors and companies produce different types of articles and products, using different glass compositions, raw materials, furnaces, forming strategies, etc. The following paragraphs provide an overview of the glass production process and describe some of the specificities for each type of production.
34.1 Brief Overview of Global Glass Production
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11 5
19
6
7
16 102
32
11
2
14
9
5
20 3
24 13
3
2
Fig. 34.3 Zoom in on the distribution of glass companies and groups in Europe (December 2017). Figure courtesy of
glassglobal Group (plants.glassglobal.com) Fig. 34.4 Flat glass furnaces in mainland China (December 2017). Figure courtesy of glassglobal Group (plants.glassglobal.com)
Industrial Glass Processing and Fabrication
34.1 Brief Overview of Global Glass Production
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Part E | 34.1
Fig. 34.5 Distribution of container glass furnaces in Europe (December 2017). Figure courtesy of glassglobal Group (plants.glassglobal.com)
Fig. 34.6 Location of tableware and container glass furnaces in the USA (August 2017). Figure courtesy of glassglobal Group (plants.glassglobal.com)
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Part E | 34.2
34.2 Industrial Glass Compositions and Process Overview In industrial glass fabrication, the choice of the composition produced is based on three main considerations: 1. Product requirements: the glass must present properties fulfilling the specifications of the targeted application. 2. Process requirements: some elements may be added to the composition in order to facilitate the process and/or allow for lower production costs or higher production rates (the impact of the addition of these elements on the glass properties must of course be acceptable). 3. Costs: the costs for producing the glass should be in accordance with the market acceptance. The final composition results from the best compromise between these three aspects. There are almost as many glass compositions as there are glass products, but some main glass families can be defined. An overview (nonexhaustive) of typical industrially produced glass families is given in Table 34.2. The main constituting oxides in these
glasses, as well as typical applications they are used for, are also indicated. Some typical compositions for different types of glasses are given in Table 34.3. It has to be noted that, even though compositions are usually expressed as percentage of oxides in the glass, the structure of a glass is not a mere blend of these different oxides. The elements are indeed part of a complex structure, as described in more detail in other chapters of the present book. In that respect, while the composition of soda-limesilicate (SLS) glasses is often expressed in the glass industry in the form of a SiO2 b Na2 O c CaO d X (X D other elements/oxides), with a, b, c and d in wt%, a more correct way to express the composition would be Sim Nam Cao Xp : : :Os , with m C n C o C p C C s D 100%). Industrial glass production is a complex, energyintensive process. It follows a series of steps, illustrated in Fig. 34.7. These steps comprise selection of the raw materials and preparation of a batch, melting and fining of the glass melt at high temperatures, conditioning and shaping of the glass article, followed by various poten-
Table 34.2 Overview of main industrial glass families, compositions and applications Glass family Soda lime silicate
Main constituents Na2 O CaO SiO2
Sodium borosilicate
Na2 O B2 O3 SiO2
E-glass C-glass
CaO Al2 O3 B2 O3 SiO2 (can also be boron-free) Na2 O CaO B2 O3 SiO2
S-glass LCD glass Lead crystal glass Vitreous silica
MgO Al2 O3 SiO2 Al2 O3 CaO B2 O3 BaO SiO2 PbO K2 O SiO2 SiO2
Applications Flat glass (windows), tableware Container glass (bottles and jars) Lamp glass (lighting), lenses Laboratory glass, tubing Cooking utensils, headlights Reinforcement for plastics/polymers Fibers for printed circuit boards Glass wool for insulation Glass fiber for reinforcement Glass fiber for reinforcement Substrate glass for displays Art glass, tableware, enamels Telecommunications, halogen lighting Lab equipment, optical elements
Table 34.3 Examples of typical glass compositions (nonexhaustive list) Glass Container glass Flint Green Float glass Pyrexo˝ E-glass C-glass D-Glass Glass wool Crystal glass
Oxide content (wt%) SiO2 B2 O3 Al2 O3
Na2 O
72.5 72 70 80.6 54.5 54.0 7080 64 58.5
14 15 14 4.0 0.8 – 25 15.5 1.5
– – – 13.0 6.6 10.0 1521:5 4.5 –
1.5 1 1 2.3 14.0 14.0 02 3.5 –
K2 O
CaO
MgO
Others
0.5
11 8.5 9 – 22.1 17.5 01 7 –
– 2 5 – 0.6 4.5 – 3 –
< 0.05 Fe2 O3 , 0.2 SO3 0.4 Fe2 O3 , 0.05 SO3 0.25 Cr2 O3 0.08 Fe2 O3 , 0.3 SO3 0.1 misc. traces 0.5 TiO2 , 0.2 Fe2 O3 , 0.5 F2 – – 0.25 Fe2 O3 , 0.15 SO3 27 PbO
– 0.8 – 0.2 – 02 1.2 13
Industrial Glass Processing and Fabrication
Batch preparation (weighing, mixing) Melting (batch-to-melt conversion) Fining of the melt Conditioning Forming Annealing Post-processes & inspection
Fig. 34.7 Typical steps in the glass-making process
tial postprocessing steps. Homogeneity of the batch and melt is of crucial importance for obtaining good-quality products. While these steps are typical for the production of most types of glasses, their relative importance in the complete process, as well as the strategies and tools involved, may differ greatly from one type of product to another. They depend notably on the composition of the glass, the type of product prepared and the level of quantity required. Modern industrial glass furnaces can be typically divided into three main sections: the batch house, the hot end, and the cold end. The batch house, upstream of the furnace, is where the raw materials necessary for the preparation of the glass are stored and the glass batch (or mix of the raw materials) is prepared and delivered to the furnace. The hot end corresponds to the part of the furnace where melting, forming and annealing processes occur. The cold end, downstream of the forming and annealing processes, is where postprocessing such as coating, cutting and inspection take place. An examFeeder of materials
Regenerator
Melting furnace
ple of an industrial float glass production line is shown in Fig 34.8. This chapter will focus mainly on the glass processing line until the forming, i. e., on the processes involved upstream and in the melting tank (or melting furnace). A typical industrial glass melting tank is illustrated in Fig. 34.9. The batch is prepared in the batch house and fed via a batch charger into the furnace, typically on top of a bath of molten glass at high temperature. The batch will then undergo a series of reactions and processes to produce a glass melt. The heat necessary for these reactions is typically provided by flames above the melt, and by the hot molten glass below the batch. The flames are provided by burners placed above the melt in the melting tank, typically running using an air/gas (natural gas) or oxygen/gas mix as fuel. Some furnaces use heavy oil instead of natural gas. The choice of fuel can depend on several factors, including the type of melter used, availability of fuel sources, costs, and purity required for the fuel (oil tending to have more impurities than natural gas). The temperatures in the furnace can be controlled by controlling the ratio of the combustibles in the flame and/or their flow through the burners. After the batch-to-melt conversion, the melt is fined and homogenized, before reaching the working end via a throat. In the working end, the melt is conditioned before the forming process. Inside the melting tank, the melt is homogenized and transported by convection currents, generated by temperature gradients within the melt. Typical flow patterns are represented by arrows on Fig. 34.9. These flows generally create two loops, with a spring zone at the location where the temperature is the highest, called the hot spot. The spring zone corresponds to the location in the furnace where the glass flow rises upwards (see illustration in Fig. 34.9). The convection patterns and residence time of the melt in the furnace will depend notably on the design of the furnace, temperature profiles, process parameters, and quantity of glass produced. Industrial melting is a continuous process, and for economic reasons the melting tanks must operate without interruption for several years (up to 20 years in
Fig. 34.8 Schematic illustration of Refining furnace
Float bath (forming)
Annealing
Cutting
Inspection
a float glass production line. The melting and refining furnace can be up to 65 m long and 25 m wide, while the annealing furnace can be up to 120 m long. The entire line (including cutting and inspection) can be over 500 m long. Picture courtesy of Asahi Glass Co. Ltd
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Selection & preparation of raw materials
34.2 Industrial Glass Compositions and Process Overview
1200
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Glass Processing
Part E | 34.3
Batch house
Melting Tank
Batch charger
Flames
Fig. 34.9
Working end
Schematic illustration of an industrial glass melting tank
Hot spot
Spring zone Batch Melting & sand grain dissolution
Primary fining & melt homogenization
some cases). All the different steps must therefore be carefully controlled and optimized to allow for proper operation and production of glass articles with a good quality over that period. In this chapter, the steps involved in the glassmaking process are described, from the selection of the raw materials used for commercial glass applications to the industrial melting processes. The different
Forming
Throat Refining & Conditioning
types of furnaces found in the modern glass industry are detailed. The importance of the choice of materials for their construction and the main energetic and environmental aspects are summarized. Finally, the advantages offered by furnace modeling for optimization of the processes are presented. Glass forming and glass postprocessing (e. g., cutting, polishing) are described in detail in Chap. 36.
34.3 Raw Materials and Batch Preparation The properties of a glass strongly depend on its composition, and the raw materials used for its preparation must be chosen carefully [34.6]. The raw materials used can also have an impact on the melting process itself. Glass production therefore starts with a careful selection of the raw materials. Calculation of the batch recipe and thorough batch preparation are also essential for the quality of the final product.
34.3.1 Raw Materials Selection The selection of the raw materials is based on several criteria, including composition and presence of impurities, availability, stability, melting/dissolution characteristics and costs (costs being influenced by all the aforementioned criteria). Raw materials can be either from mineral sources (e. g., sand) or prepared by chemical processes, such as sodium carbonate (or soda ash, Na2 CO3 , produced by the Solvay process). Mineral ingredients are usually cheaper, but often contain impurities and show some composition variability over time. Chemical ingredients
show higher purities and less variation in composition, but usually come at a higher cost. Impurities in the raw materials may lead to undesired effects in the final glass and/or damages during the process. Typical impurities of concern include coloring oxides (e. g., iron and chromium oxides), heavy minerals (e. g., zircon), organic materials or volatile species. The composition and purity of the raw materials should be checked thoroughly and regularly. Availability of the raw materials is of importance, as glass producers must make sure the suppliers can provide enough quantity of the raw materials to allow for the continuous production process. Proximity of the source of raw material can represent a significant advantage in terms of transportation costs. Stability of the raw materials must also be considered, especially when using hygroscopic raw materials, as it will impact consideration of the handling and storage strategies. The melting and dissolution characteristics of raw materials have a significant impact on the energy required for the batch-to-melt conversion. The grain size distribution is of high importance, especially for sand,
Industrial Glass Processing and Fabrication
34.3 Raw Materials and Batch Preparation
Boron is another major network former, used in borosilicate glasses (expressed as B2 O3 in the glass) [34.7]. Depending on the type of glass prepared, as well as the quality and costs considerations, it may be introduced either as mineral borate such as colemanite (2CaO 3B2 O3 5H2 O), borax penta- or decahydrate (Na2 O 2B2 O3 5H2 O or Na2 O 2B2 O3 10H2 O respectively) or chemical forms such as boric acid H3 BO3 or boron oxide (B2 O3 ).
34.3.2 Typical Raw Materials in Industrial Glass Making
Network Modifiers Network modifiers, added to batches in order to reduce the melting temperature and viscosities of glass melt, are typically alkali or alkaline-earth elements (expressed as R2 O and MO, with R D Li, Na, K and M D Ca, Mg, Ba, Sr, . . . ). They allow for increased melting rates and lower melt viscosities. However, alkalis decrease the glass chemical durability. Replacing part of the alkali oxides by alkaline-earth oxides will increase chemical durability. Alkali and alkaline-earth oxides can be introduced in the batch as carbonates, such as soda ash (Na2 CO3 ), potash (K2 CO3 ), or limestone (CaCO3 ). Barium and strontium are also typically introduced as carbonates (BaCO3 and SrCO3 respectively). Dolomite, a doublecarbonate mineral, (1x)CaCO3 xMgCO3 (x may vary as function of the dolomite source), is often employed in glass production, simultaneously introducing calcium and magnesium to the glass. It has to be noted that dolomite and limestone may be subject to decrepitation [34.8]. In this case, the CO2 released from the carbonate at high temperature can build up within the grain and eventually lead to its explosion (decrepitation). Part of the decrepitating grain may be entrained by the flue gases (so-called carry-over) in the melting atmosphere above the batch and thus not enter the melt. Other sources of alkali and alkaline-earth elements typically include minerals such as nepheline, kaolin, spodumene and feldspars (see above), or cullet (crushed recycled glass, reintroduced in the batch as a raw material, providing the oxides contained in the cullet glass used).
The raw materials used in glass making are usually categorized by the function they provide to the final glass and/or in the melting process. Materials are typically divided into different categories: network formers, network modifiers, intermediates, coloring elements, fining agents (for removal of bubbles from the melt), redox active species (to oxidize or reduce the glass melt) and melting accelerants (promoting melting of the glass at lower temperature and/or formation of early melting phases). Nucleating agents may also be added for production of glass-ceramics. A nonexhaustive overview of typical raw materials found in industrial glass production is given in the following paragraphs. It has to be noted that some raw materials can be included in several categories, such as sodium sulfate, which is both a fining agent and an oxidizing species. Network Formers Network formers are the backbone of the glass and correspond to oxides, which can form a glass on their own. SiO2 is by far the most common network former found in commercial glasses (Table 34.3). Sand is usually the main source for SiO2 . Only sand presenting sufficient purity (often 99:5% or higher) can be used for industrial glass making. The degree of sand purity required depends on the type of article to be produced. Glasses with higher purity requirements (which corresponds typically to glasses with the highest degree of optical transmission required) require higher purity sand (and other high purity raw materials), which often means that additional sand purification steps must be carried out before it can be used for production. A significant amount of the SiO2 introduced in industrial batches can also originate from recycled glass (cullet). Other minerals used in industrial glass making, such as kaolin (Al2 O3 2SiO2 2H2 O), nepheline (Na2 O Al2 O3 2SiO2 ), spodumene (Li2 O Al2 O3 4SiO2 ) and feldspar (alkali aluminosilicate) contain SiO2 , which will integrate into the final glass composition.
Intermediates Oxides Intermediates cannot form a glass on their own when prepared in the practical conditions found in industrial glass melting. However, they fully integrate into the structure of the glass network (formed by network formers) and provide higher stability, decreased tendency to crystallize, and increased chemical resistance. Alumina (Al2 O3 ) is the most commonly used intermediate oxide in industrial glass making. It can be introduced as pure alumina in the batch or alumina hydrate (Al2 O3 3H2 O). Alumina is a refractory material,
Part E | 34.3
which is integrated into the melt by dissolution of the sand grains, as described in more detail in Chap. 35. Raw materials can be processed before their delivery, e. g., to reduce their grain size to desired specifications or to remove impurities. Additional processing steps usually induce higher costs. In general, glasses with higher quality requirements have more stringent specification for raw materials purity, leading to higher costs involved in the raw material selection process.
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and is hard to dissolve in the glass melt. In order to facilitate its incorporation into the melt, it can also be introduced via minerals such as kaolin, feldspars, or furnace slags (byproducts of steel-making blast furnaces). Part of the alumina may come from cullet. Zirconia (ZrO2 ) is another intermediate oxide used in some glass types, and is typically introduced either as pure zirconia or as zircon silicate (ZrSiO4 ). Fining Agents Fining agents are added to the batch to enhance the removal of dissolved gases and gas bubbles trapped in the melt during the melting process (e. g., due to the release of CO2 from carbonate raw materials). Fining agents are typically added in small quantities (below 1 wt% in the batch). The most widely used fining agent in glass production is sodium sulfate (Na2 SO4 ), also called salt cake. It is the compound of choice for fining of soda-lime-silicate glasses and E-glass. Salt cake is typically added together with a redox active species (oxidizing or reducing agent) to influence its chemistry in the batch [34.9–11]. Sulfur may also be added as gypsum (CaSO4 ) or pyrite (FeS2 ). Sodium sulfate becomes much less efficient when fining of melts above 1450 ı C is required, as this temperature is roughly the maximum temperature at which sodium sulfate releases the fining gases SO2 and O2 . For some borosilicates and other high melting glasses, the viscosity of the glass in this temperature range is still high and would not allow for an efficient growth and rise of the fining bubbles in the glass, resulting in a poor fining (i. e., in a final glass full of seeds and bubbles). For these glasses, fining agents releasing fining gases at higher temperatures, where the melt viscosity is lower, must be used. Such fining agents include sodium chloride (NaCl), cerium oxide (CeO2 ) or tin oxide (SnO2 ). In lead-glasses, or when the use of sulfates is not acceptable, fining agents such as antimony or arsenic oxides (Sb2 O3 and As2 O3 respectively) can also be used in combination with an oxidizing agent. The use of arsenic is nowadays limited, due to regulatory constraints. The chemistry of glass fining is described in more detail in Sect. 34.5 and in Chap. 35. Oxidizing and Reducing Agents The redox (oxidation-reduction) state of the glass is of extreme importance in (industrial) glass making. Indeed, as explained in more detail in Sect. 34.5, some properties of the glass and of the melt are highly dependent on the redox state of the species it contains. Some elements can be added to the batch to modify this redox state, to bring the melt/glass either to a more oxidized or a more reduced state. These are called oxidizing
agents or reducing agents respectively. Typical oxidizing agents in glass making include nitrates (sodium or potassium nitrate, NaNO3 or KNO3 respectively) and sulfates (e. g., Na2 SO4 ). The most common reducing agents include carbon (or cokes, which contain high levels of carbon) and blast furnace slags. Organic contaminants, which may come in relatively large quantities in recycled cullet (Chap. 39) have a strongly reducing effect. Redox control can therefore be challenging when using a large amount of cullet in the batch. Coloring Elements Color is an important aspect in glass fabrication, and a large array of colors may be produced, based on the addition of specific elements to the batch. Typically, coloring agents are added in small proportions, below 1 wt%. Comprehensive information on color in glass can be found in the reference books by Weyl [34.12] and by Bamford [34.13]. The most commonly found coloring element is iron, for which coloration in soda-lime-silicate glasses depends on its redox state. Ferrous iron (Fe2C ) gives a bluish tint to the glass, while more oxidized ferric iron (Fe3C ) gives a yellowish, less intense tint. Iron may come as an impurity in the raw materials used (from sand notably), or added on purpose to the batch, typically as iron oxide (Fe2 O3 ), or in combination with chromium in chromite (FeCr2 O4 ). Chromium is mostly present in glasses in its trivalent form Cr3C , giving a typical emerald-green coloration to the glass. Only in very oxidizing conditions can chromium be found in its hexavalent form Cr6C , while in very reducing conditions Cr2C can also be present (giving a light blue coloration to soda-lime-silicate glasses [34.14]). Note that the presence of hexavalent chromium is undesired and avoided in glass products due to its carcinogenic nature. In certain redox conditions, when ferric iron and sulfides coexist in the glass, they form a chromophore Fe3C S2 called the amber chromophore, responsible for the typical brown-amber coloration widely used for container glass [34.11, 15]. While iron is often present as a contaminant in the glass and sulfur is present from the salt cake used for fining, elements such as pyrite (FeS2 ) or furnace slags (usually rich in sulfides) can be purposely added for the production of the amber glasses. An illustration of the optical transmission spectrum of container glasses containing iron and chromium, and corresponding colors, are shown in Fig. 34.10. The typical absorption peaks of Cr3C in the glass at 450 and 650 nm, as well as Fe3C (iron in its oxidized form) at 380 nm, are clearly visible for the green glass. The
Industrial Glass Processing and Fabrication
34.3 Raw Materials and Batch Preparation
transmission spectrum for colored container glasses (thickness D 3 mm) showing characteristic spectral signatures for the absorption of Fe3C (circle), Fe2C (diamond), Cr3C (triangles) and the amber chromophore (square). Picture courtesy of Si¸ ¸ secam
90 80 70 60 50 40 30 20 10 0 300 350 400 450 500 550 600 650
70
750 800 850 900 950 1000 1050 1100 1150 1200 Wavelength (nm)
amber glass shows a strong absorption of the amber chromophore at 420 nm, as well as the characteristic large absorption peak of Fe2C (iron in its reduced form) centered at 1050 nm. The olive green glass, a reduced glass that contains both the amber chromophore and Cr3C , shows a combination of their spectral signatures (note the strong absorption around 1050 nm, characteristic of reduced glasses containing Fe2C ). Several coloring agents are introduced in the batch directly in their oxide form, such as cobalt (Co3 O4 ) for deep blue coloration, manganese (MnO2 ) for purple or copper oxide (CuO) for light blue glasses. On the other hand, some elements can be added to decolorize the glass, i. e., to reduce its tint and increase the perceived transparency. Selenium is commonly used for this purpose, by addition of small amounts (some hundreds of ppm), either in the form of pure elemental selenium or other compounds such as zinc selenate (ZnSeO4 ) [34.16]. Glass producers can periodically manufacture glass with different colors in the same melting tank. For instance, bottle glass makers can switch from clear bottles (or flint bottles) to green or amber bottles during specific production campaigns, to fulfill their market needs. Glass melting tanks contain large amounts of molten glass that circulates within the melter, with residence times of a few hours to a few days. It thus takes several days to go from one color to another, i. e., ensuring that the initial color package is removed and that the new color package is well homogenized in the molten glass. The transition glass produced during a color change is not suitable for commercialization (out of color spec-
ifications), and it is therefore critical to ensure that the transition from one color to another is as fast as possible. The transition glass is often reused as raw material (cullet) in the batch. The control of the transition glass composition, and particularly in the coloring elements it contains, is critical in calculating how much of this cullet can be introduced in the batch. For instance, for a transition going from a colored glass to a clear glass, only a limited amount of the transition glass, which will contain a decreasing amount of coloring element, can be introduced in the batch. The transition glass can also be stored and used for subsequent color changes, when the targeted concentrations in coloring elements in the final glass allow for use of this specific transition glass cullet. Each company has its strategies for allowing fast and efficient color changes (e. g., rate at which the coloring elements are added/removed in the batch, overdoping or underdoping the element, change in the melting tank process parameters, etc.). Computational fluid dynamics (CFD) modeling is sometimes used to simulate color changes in a given melting tank and optimize the parameters that allow for achieving the fastest transition possible [34.17]. A color change can be either the addition of color, i. e., starting from a clear glass and going to a colored glass by addition of a coloring element (e. g., chromium to produce green glass), or removing of the coloring elements from the batch to go to a clear (flint) glass. Some color changes, such as going from a flint to an amber glass, may also require a change in the glass redox state (see the importance of redox in Sect. 34.4).
Part E | 34.3
Fig. 34.10 Optical
Transmission (%) 100
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Melting Accelerants Some compounds are added to the batch to promote the batch-to-melt conversion at lower temperatures. Their action may arise from different principles (which can be concurrent), including formation of low viscosity eutectic melt phases at low temperature, decreasing the surface tension of the molten phases, or promoting heat transfer within the batch. Typical melting accelerants include fluorspar (CaF2 ), lithium carbonate (Li2 CO3 ), spodumene, sodium sulfate (or salt cake, Na2 SO4 ), potassium and sodium nitrates and blast furnace slags. Cullet, which can enhance the heat transfer from the flames to the batch blanket [34.18], can also act as a melting accelerant. Cullet Over the past decades, glass recycling has taken on increasing importance in the glass-making process, with recycled glass (or cullet) amounting to up to 95% of the batch for certain types of production (see more detail on glass recycling in Chap. 39). The cullet used may be either internal cullet (glass rejects from production reintroduced into the furnace that produced it), or external cullet (coming from collection banks or processing plants). External cullet may be delivered as sorted by color/type or as mixed cullet. Internal cullet is of known composition and usually less contaminated than external cullet, which has a composition that may be subject to higher fluctuations. The use of cullet brings several advantages. As cullet is a previously melted glass, the energy needed to melt it again is lower, as no energy is required to provoke reactions between raw materials. Therefore, increased use of cullet leads to decreased energy consumption for melting of a batch. The volume of gases released from the batch may be lowered as the amount
of other raw materials is reduced (less carbonates releasing CO2 from the batch). Cullet may also act as flux, promoting melting of the batch at lower temperatures. However, cullet may contain significant amounts of impurities and organic contaminants. In addition, the possible fluctuation of composition of the cullet over time (especially for external cullet) makes the control of the composition of the glass produced more complex.
34.3.3 Batch Preparation After careful selection of the raw materials, the batch recipe allowing for preparation of the desired glass composition must be calculated. After batch calculation, the batch is prepared and conveyed to the melting tank. The proper execution of these different steps is crucial for the preparation of a glass product of good quality. Batch Calculation Many aspects have to be considered when calculating the composition of a batch for preparing the desired glass. The concentration of the relevant oxides in each of the raw materials employed must be known. For instance, limestone CaCO3 contains only about 56% of the relevant oxide CaO, the rest corresponding to CO2 that will be released during the melting process. Many raw materials contain carbonates, nitrates or water, which will dissociate at higher temperatures and release volatile species (CO2 , NO2 , H2 O, etc.), which will evaporate from the batch. The weight loss associated with the release of these volatile species, called melting losses, has to be accounted for in the batch calculations. The nature and concentration of impurities (typically iron oxide, halogens, etc.) in each raw material should also be known and integrated into the batch calculation.
Table 34.4 Simplified example of batch calculation for an industrial glass prepared from sand, soda ash, limestone,
dolomite and sodium feldspar. Part 1: Batch components and quantities Raw material Sand Soda ash (Na2 CO3 ) Limestone (CaCO3 ) Dolomite .1 x/CaCO3 xMgCO3 Sodium feldspar (Na2 O Al2 O3 SiO2 )
Composition (wt%) 99.95 SiO2 0.05 Fe2 O3 50 Na2 O Rest CO2 56 CaO Rest CO2 30.5 CaO 22% MgO Rest CO2 68.7 SiO2 19.5 Al2 O3 11.8 Na2 O Total
Quantity in batch (kg) 1000
Melting loss (kg CO2 )
350
Amount of oxide entering the glass (kg) 999:5 SiO2 0:5 Fe2 O3 175 Na2 O
150
84 CaO
66
200
61 CaO 44 MgO
95
80
55 SiO2 15:6 Al2 O3 9:4 Na2 O 1444
1780
175
336
Industrial Glass Processing and Fabrication
Table 34.5 Simplified example of batch calculation for an industrial glass prepared from sand, soda ash, limestone, dolomite and sodium feldspar. Part 2: Resulting glass composition
SiO2 Na2 O CaO MgO Al2 O3 Fe2 O3 Total
Total oxide in glass (kg) 1054.5 184.4 145 44 15.6 0.5 1444
Glass composition (wt%) 73.04 12.81 10.01 3.00 1.10 0.04 100
Storage, Batch Weighing and Transport to the Furnace The raw materials used in industrial glass making are usually delivered to the plants by truck, train or ships, mainly in the form of powders, and are stored in silos. Modern batch houses are equipped with different silos for the individual raw materials. Enough raw materials should be stored at the plant site in order to prevent any interruption in the production in case of temporary problems in the delivery chain. The raw materials needed for the batch are weighed before being mixed together. Typical industrial batches are several hundreds to several thousands of kilograms. Different weighing systems must be used for weighing major components such as sand (several thousands kg/batch) and minor components such as coloring agents (some hundreds g/batch). The homogeneity of the glass produced is strongly dependent on the homogeneity of the batch prepared and introduced into the furnace. Efficient mixing is thus crucial. Industrial mixers such as blenders, rotating drums or pan mixers are used. In order to reduce the risk of segregation or demixing of the batch during preparation and transport to the melting tank, small amounts of water may be added (typically 24 wt%). This process is called batch wetting. In some cases, the batch can be further processed to prepare pellets or briquettes, which allow for improved batch homogeneity and product quality. However, these processes induce higher costs for the batch preparation. After mixing, the batch is transported to the melting tank via transport belts, screw conveyors or pneumatic transport. Precautions must be taken to avoid as much as possible any contamination during the transportation of the raw materials and of the batch. The batch is then introduced into the furnace through a so-called batch charger, or dog house (Fig. 34.9), feeding continuously the batch on top of the melt. The batch charging rate is adjusted to introduce the right amount of batch for keeping a stable level of the melt in the melting tank (thus adjusted for the rate at which the melt is drawn at the other end of the furnace for the forming process, i. e., the pull rate of the furnace). Once introduced in the furnace, the batch will undergo a series of steps leading to its conversion into a melt (Chap. 35).
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Typical industrial batches are expressed in wt%. A simplified batch calculation for a soda-lime-silicate glass prepared using sand, soda ash, limestone, dolomite, sodium feldspar, and without cullet, is given in Tables 34.4 and 34.5. Note that the final glass obtained contains iron oxide, coming from impurities in the sand used. Due to the melting losses (from CO2 release from the carbonate raw materials), 1780 kg of batch has to be introduced to produce 1444 kg of glass. Note that the batch calculation presented above is a very simplified one, with only a few raw materials with limited amounts of impurities. Industrial batches usually contain a larger number of components, with high levels of impurities. In addition, the composition of the cullet, when used in the batch, may vary, and should be monitored regularly to adjust the batch composition and maintain a stable glass production. Therefore, industrial batches are typically calculated using more elaborate spreadsheets or software, which can integrate other parameters influencing the calculations (moisture content in the batch, evaporation of small amounts of some components from the melt, carry-over of batch particles by the flue gases, etc.). It is important to consider these potential deviations in order to correct the batch recipe and ensure production of the desired glass. Redox has a significant impact on the glass-making process, and is typically taken into account when calculating the batch recipe, by calculating a so-called batch redox number. The importance of redox and calculation of the batch redox number are detailed in Sect. 34.4 of this chapter.
34.3 Raw Materials and Batch Preparation
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34.4 Importance of Redox in Glass Making 34.4.1 Redox in Glass Redox is one of the most important parameters in industrial glass making [34.19]. Glasses (and glass melts) usually contain species that can be found in different oxidation states. The equilibrium between their reduced and oxidized forms can strongly influence the glass and melt properties. The most typical multivalent species found in glass is iron, found mainly as (oxidized) ferric iron Fe3C or (reduced) ferrous iron Fe2C . A glass melt will contain a certain amount of dissolved oxygen, either chemically dissolved as oxygen ions O2 bonded to polyvalent ions in the glass, or physically dissolved as O2 molecules or oxygen atoms without bonds to other glass components. Bridging oxygens in the glass network are not chemically active, while nonbridging oxygens influence the glass basicity [34.20]. These latter forms of oxygen do not influence the redox state of the glass/melt. During chemical dissolution of oxygen, oxygen molecules may pick up electrons from multivalent ions, creating O2 ions, according to O2 C 4e • 2O2
(34.1)
These electrons can originate from the multivalent ions dissolved in the glass. Some examples of redox reactions in glass include (oxidation from left to right, reduction from right to left). Cr3C • Cr6C C 3e Fe2C • Fe3C C e
(34.2) (34.3)
In the glass melt, in the presence of dissolved oxygen, these reactions can be written as Cr2 O3 C 1:5O2 • 2CrO3 2FeO C 0:5O2 • Fe2 O3
(34.4) (34.5)
It has to be noted that redox equilibria depend on temperature and by consequence evolve during the heating or cooling of the glass melt. Also, different multivalent species can react together if present simultaneously in the melt, such as Cr3C C 3Fe3C • Cr6C C 3Fe2C S4C C 6Fe2C • S2 C 6Fe3C
(34.6) (34.7)
The latter reaction can notably occur in reduced melts and is shifted to the right-hand side during cooling of the melt, leading to the formation of the
amber chromophore (Fe3C S2 ), giving to the glass the well-known amber coloration typical of beer bottles [34.15]. The redox state of a glass (or a melt) is thus defined as the equilibrium between the different multivalent species it contains, and characterizes the level of oxidation (oxygen concentration level). The amount of dissolved oxygen in the melt depends mainly on the presence and amount of oxidizing species (supplying oxygen to the melt) or reducing species (reacting with oxygen and absorbing it) in the raw materials. Specific compounds can be added to influence this redox state. Oxidizing agents such as sulfates, nitrates or polyvalent ions in their most oxidized form, will oxidize the melt by supplying oxygen. Reducing agents such as carbon/cokes, reduced forms of the polyvalent ions, or organic components, will reduce the melt. Indeed, carbon, cokes or organic components react with oxygen to form CO and/or CO2 gas, which will then escape the melt, reducing its content of dissolved oxygen.
34.4.2 Effect of Redox on Glass and Melt Properties Redox has a strong impact on different aspects of the glass-melting process. First, it impacts the color of the glass produced, and is thus critical for products for which color is of importance. For instance, iron present as Fe3C in the melt will give a slight yellowish tint to the glass, while iron present as Fe2C will yield a stronger (at equivalent concentration) bluish tint. This arises from the different optical absorptions of iron in its different oxidation states. In soda-lime-silicate glasses, ferric iron (Fe3C ) induces a relatively weak absorption with a band centered around 380 nm, while ferrous iron (Fe2C ) leads to a broader and stronger absorption in the visible and near-infrared centered around 1050 nm [34.12, 13]. These differences in absorption properties also have a great influence on the properties of the glass melts at high temperatures. Reduced melts, i. e., melts containing more reduced iron Fe2C , will absorb more strongly the radiation from the flames above the melt, which emit mainly in the near- and mid-infrared. The redox state of the melt has thus a significant impact on the heat transfer from the flames to the melt, which in turn has an effect on temperature profiles and flow patterns in the melting tank. The cooling rate of the glass melt, an important factor in the forming process, also depends (to a certain extent) on its redox state.
Industrial Glass Processing and Fabrication
34.4.3 Characterization of the Redox State In the final product (cold glass), the redox state is typically defined as the ratio between Fe2C and Fe3C in the glass, as iron is present in the vast majority of glass articles (added intentionally or present as an impurity). The most commonly used parameter in industrial glass making is the Fe2C =Fetotal ratio, representing the ratio of iron present as Fe2C as compared to the total concentration of iron in the glass (both expressed as wt% Fe2 O3 in the glass). The concentration of Fe2C can be calculated using the Beer–Lambert law, from optical measurements of the characteristic and well-quantified absorption of ferrous iron (band centered at 1050 nm) in glass samples. The total concentration of iron in the glass can be measured chemically. Glasses with higher Fe2C =Fetotal ratio are more reduced, while lower values indicate more oxidized glasses. In glass melts, where optical properties cannot be practically measured inside the furnace, the redox state is characterized by the so-called partial oxygen pressure in the melt, or pO2 .T/, corresponding to the oxygen partial pressure in equilibrium with dissolved oxygen in the glass melt. The higher the amount of oxygen dissolved in the melt, the more oxidized it is, and the higher pO2 value measured. The redox state of the melt is obtained using sensors dipped inside the melt (e. g., inserted from the top in the feeder canals in the fur-
nace using water-cooled casings, before the forming, where the melt temperature is lower than in the melter itself to increase the sensor lifetime), measuring the difference in partial pressure of oxygen compared to a reference [34.22]. As compared to the Fe2C =Fetotal ratio, measured on the glass article produced (i. e., after the complete glass making process), measurement of the redox state of the melt inside the furnace allows for an earlier monitoring in the process, enabling faster reaction in case of undesired variations. It must however be noted that continuous measurement of the redox inside the melt at high temperature is challenging and can lead to fast corrosion of the sensors. In the batch, the redox state is often characterized using the so-called batch redox number (or Simpson redox number, named after the developer of the method for its calculation) [34.23, 24]. The contribution of each raw material in the batch is calculated by multiplying its redox factor (negative for reducing species, positive for oxidizing species, 0 for nonredox active species) to the relative weight of the raw material per 2000 kg of sand in the batch. The sum of the redox contributions from all redox active species in the batch gives the final batch redox number [34.21]. The redox factors for selected species are indicated in Table 34.6. The redox of the final glass produced does not only depend on the redox of the batch. The melting conditions in the furnace (atmosphere, residence time, temperature profiles, etc.) will also have an influence. There exists however a certain correlation between ranges of values for the batch redox and the glass redox. Specific glass colorations are obtained in typical glass redox ranges, corresponding to typical batch redox values. Industrial producers usually try to maintain or adjust the batch redox to obtain the desired color. Examples of redox values and corresponding colors for soda-lime-silicate glasses are given in Table 34.7 (see also Fig. 34.10 for illustration of some of these glass colors). It has to be emphasized that the use of large quantities of external cullet (often contaminated, with contamination levels that may vary over time) makes the control of the redox very challenging for the production of many types of glasses. The higher risk of product
Table 34.6 Examples of redox factors for selected reducing and oxidizing raw materials (from [34.21]) Reducing components Raw material Cokes (85% C) Fluorspar (CaF2 ) Furnace slag Pyrite (FeS2 )
Redox factor 5.70 0.10 0.07 to 0.09 1.20
Oxidizing components Raw material Sodium sulfate (Na2 SO4 ) Sodium nitrate (NaNO3 ) Iron oxide (Fe2 O3 ) Gypsum (CaSO4 2H2 O)
Redox factor C0.67 C0:32 C0:25 C0.70
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In addition, the sulfur chemistry in glass melts is dependent on redox, and the fining and foaming behavior of the glass melt will highly depend on the redox state of the melt [34.9]. The fining mechanisms for sulfate-fined glasses, representing roughly 90% of the total glass production, are described in Chap. 35. Some types of glasses require oxidizing conditions to be produced, while others require reducing conditions, and every glass melt type has its optimum redox state, which can be adjusted by adjusting the amounts of oxidizing or reducing agents added. Therefore, a good knowledge and control of the redox is crucial in industrial glass making. In order to allow for monitoring of this parameter, different methods can be used to characterize the redox state at different stages in the process: batch, melt, or final product.
34.4 Importance of Redox in Glass Making
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Table 34.7 Typical batch redox number and Fe2C =Fetotal ranges for different SLS glass colors (from [34.21]) Color White/colorless Green Dead leaf/feuille morte Amber
Batch redox number 0 to C20 15 to 0 25 to 15 30 to 20
color variations with higher cullet content can limit the maximum amount of recycled glass acceptable in the batch. This is especially true for colors such as olive green or dead leaf, which can be produced only in narrow redox ranges. Production of glass colors that are less sensitive to redox variations, such as emerald green (obtained by addition of chromium in the
Fe2C =Fetotal in the glass 0:100:40 0:400:60 0:600:75 0:750:90
glass) typically allow for use of larger amount of cullet in the batch. Colorless glasses, such as window glass or clear glass bottles, require minimizing the amounts of impurities (mainly iron and chromium, which give a coloration to the product), thus leading to a limitation of the amount of cullet that can be used (typically in the range of 2040 wt% in the batch, or lower).
34.5 Glass Melting, Fining and Conditioning Once introduced in the melting tank, the batch will undergo a series of steps to obtain a homogeneous melt to be delivered for the forming process. First, the batch will be converted into a primary melt. While part of the raw materials can react rapidly and form low-melting phases, other compounds such as sand require more time and higher temperatures to integrate into the melt (dissolution of the sand grains). During the batch-tomelt conversion, a large amount of gases are released, and the rough, seedy melt obtained right after this stage contains a large amount of bubbles and of dissolved gases. The fining of the melt at high temperatures allows for the removal of the majority of the bubbles, yielding a clear melt at with only a few small bubbles (seeds) remaining. The temperature of the melt is then lowered to the temperatures required for the forming process. This step is called the conditioning of the melt. During this cooling step, the remaining small seeds in the melt are reabsorbed, during the so-called refining process. These different steps are illustrated in Fig. 34.11. Characteristic temperatures at which the different processes occur for SLS glasses are given as indications. On the right-hand side of this figure, typical weights of the batch and melt along the process are indicated for a SLS batch prepared without cullet. Typically, 1200 kg of batch is required to produce 1000 kg of glass, as approximately 20 wt% of the batch is lost, mainly by release of CO2 from the carbonates raw materials. At the beginning of the melting process, the first melt obtained is inhomogeneous and contains undissolved particles and bubbles. During the different processes, the melt will be homogenized and rid of bubbles and undissolved particles, to yield a homogeneous clear melt before the forming process. The good running and
completion of all the different steps is crucial for the quality of the final product prepared. Industrial glass furnaces are designed to promote the good sequence of these processes.
34.5.1 Batch Melting The batch is introduced on top of the molten glass as a blanket or as islands. It is then heated both from the top, by the flames and the hot flue gases in the combustion space, and from the bottom by the hot glass melt. Due to the rate of heat transfer through the batch, the central part of the batch will heat up more slowly, Homogenization
Batch introduction
Batch 25 °C
≈ 1200 kg
Batch melting
Rough melt 1200 °C
≈ 1001 kg
Sand grain dissolution
Seedy melt 1400 °C
≈ 1001 kg
Fining
Clear melt 1500 °C
≈ 1000 kg
Refining and conditioning
Conditioned melt 1250 °C
1000 kg
Fig. 34.11 Essential steps occurring in glass melting tanks.
For a typical soda-lime-silicate batch without cullet, approximately 1200 kg of batch is required to produce 1000 kg of glass. Approximately 20% of the weight of the batch is released as gas during the batch-to-melt conversion. Adapted from [34.25]
Industrial Glass Processing and Fabrication
Flames Combustion space (> 1500 °C)
Heat transfer Temperature profile
Batch
Convection flow
Batch tip
Hot glass melt (1400 °C)
Fig. 34.12 Schematic representation of heat transfer to the batch on top of the molten glass in an industrial furnace
heat flux in the melting tank. The rates of batch conversion processes depend on the reaction kinetics and the diffusion rates of the dissolving components in the melt, both of them being strongly determined by temperature. Heat transfer into and within the batch blanket is thus very important for the rate of the initial melting, and is the limiting factor for the melting reactions. The compactness of the batch and grain sizes may have an important effect on heating rate and contact area between reacting grains and thus on the overall reaction rates, especially in the regime of solid-state reactions. The batch may be introduced as pellets or granules to promote the reactions and increase melt homogeneity [34.26]. However, pretreated batches are most costly and may limit the interest of this solution for some glass producers. Use of higher cullet content in the batch can also increase the batch conversion rates, but the amount of cullet that can be introduced may be limited in terms of product quality. Dissolution of sand particles and other slowly dissolving components such as alumina or zircon depends on grain size, temperature, convection flows in the furnace and composition of the glass (e. g., presence of aggressive low-melting phases) [34.27]. All these parameters must be controlled and optimized to ensure that all sand grains and other slow-reacting refractory components are fully integrated into the melt within the melting tank and are not found in the final product as undissolved particles, i. e., defects leading to rejection of the product.
34.5.2 Primary Fining During the melting of the batch, a large amount of gases are released, originating typically from carbonate decomposition (CO2 ), carbon/cokes (CO2 and/or CO), evaporation from hydrated raw materials (water vapor), and decomposition of nitrates (O2 , N2 =NOx ) and/or sulfates and sulfides (SO2 , S2 , etc.). Some air may be trapped in the batch blanket or come from cracks in the melting tank walls, while furnace atmosphere gases (N2 , Ar, H2 O, CO2 , etc.), volatile glass and batch components (e. g., halogens or alkalis), gases released by refractories, or contamination of the melt by e. g., products of electrodes corrosion, may also be found in the melt. Part of the gases released may dissolve in the melt, but after melting, the amount of gas trapped is in very large excess compared to their solubility limit in the melt. This leads to the formation of numerous bubbles. It has to be noted that the gases released from the melting of the batch (mainly CO2 and SO2 ) can have a mixing effect within the batch blanket, increasing the dissolution rate of the sand grains. They must however be removed from the melt. Right after the melting stage,
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leading to a temperature gradient within the batch just after its introduction into the furnace, as illustrated in Fig. 34.12. Typical thickness of the batch blanket ranges from 10 to 20 cm. The batch-to-melt conversion occurs mainly by reactions within the batch blanket and implies a series of chemical reactions, comprising typically decarbonation, dehydration, solid-state reactions, formation of low-melting eutectics, and dissolution reactions. The nature and sequence of reactions depend notably on the batch composition and on the heating rate within the batch blanket. These reactions are described in detail in Chap. 35, and will thus not be covered extensively in the present chapter. First, aggressive melt phases are formed in the heated batch piles or blanket. These melt phases, which can be either formed by eutectic reactions between batch components (e. g., alkalis) or by melting accelerants (if added in the batch), will strongly attack and largely dissolve the components that are difficult to dissolve, such as sand or feldspar/china clay particles. Then, the melt phases formed flow from the batch blanket area into the glass melt, and the batch blanket becomes increasingly thinner at the batch tip, as shown in Fig. 34.12. Some of the sand particles arrive undissolved in the glass melt itself, and will have to further dissolve by diffusion of SiO2 into the molten glass. It is important to emphasize that sand is generally incorporated in the glass melt by dissolution and not by melting, as melting of silica requires temperatures above 1723 ı C, which are not achieved in typical melting tanks. The batch-to-melt conversion is a relatively rapid process, but is also the most energy-consuming step, with an energy demand representing 8090% of the net
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glass melts contains typically on the order of hundreds of thousands of bubbles per kg of melt. As bubbles are undesired in most commercial products, the removal of these bubbles from the melt is essential. The process of removing bubbles from the melt is called fining. Insufficient fining of the melt may result in the presence of bubbles in the final product and thus to its rejection. In the product, defects related to fine bubbles are usually referred to as seeds, while larger bubbles are called blisters. The bubbles can be removed from the melt either by buoyancy effects, i. e., rising to the surface of the melt, or by chemical dissolution of the gases into the melt. The former process corresponds to the primary fining, while the latter corresponds to the secondary fining, or refining. The bubbles, whose density is lower than that of the melt, will tend to rise to the surface. The rising velocity of the bubbles is proportional to the square of their radius and inversely proportional to the melt viscosity, following Stoke’s law [34.6]. Lower melt viscosities (i. e., higher temperatures) and larger bubbles are thus beneficial for an efficient primary fining. In industrial glass making, the removal of bubbles is promoted by the addition of so-called fining agents to the batch. These compounds will release gases at high temperatures, i. e., when the viscosity of the melt is low. These gases will diffuse into the existing bubbles, increasing their diameter, and thus accelerating their ascension to the surface of the melt. They will also promote the diffusion of the other dissolved gases into the bubbles. The process of high temperature decomposition of the fining agent in a low viscosity melt thus results in simultaneous bubble growth, gas stripping and acceleration of the bubble ascension rates. As different types of glasses present different temperature–viscosity profiles, the fining agent must be carefully chosen as to release the fining gases in the appropriate viscosity range, i. e., at an appropriate temperature range for the given glass melt. Indeed, release of the fining gases at too low temperatures would lead to the formation of numerous small bubbles, which will have difficulty in rising to the surface in a highly viscous melt. These bubbles could then end up in the final product, leading to it being rejected. Sodium sulfate (NaSO4 ), or salt cake, is the most ubiquitous fining agent in industrial glass making. It is the fining agent of choice for many types of glass such as container glass, float glass, E-glass or insulation wool, and is therefore the most widely used fining agent [34.28]. The advantage of sodium sulfate comes from its versatility, as the fining onset temperature, i. e., the temperature at which it reacts and releases fining gases (SO2 , together with O2 in mildly reduced and ox-
idized melts), depends on the redox state of the melt and can be adjusted in the 11001450 ı C temperature range by adjusting the batch/glass redox. When fining is required at temperatures above 1450 ı C, other fining agents can be employed, such as sodium chloride (NaCl) or tin oxide (SnO2 ). When the presence of sulfur is undesired in the glass, antimony oxide may be used as a fining agent (described in Sect. 34.3.2). The different fining reactions involved with these different fining agents are described in more detail in Chap. 35. The amount of fining agent added to the batch should be sufficient to allow for good fining of the melt, i. e., efficient stripping of the gases dissolved in the melt, but should not be too high. Indeed, excessive fining may lead to the formation of foam on top of the glass melt, which can entrain defects in the glass and be detrimental in terms of heat transfer from the combustion atmosphere to the melt, as foam can act as an insulation layer on top of the melt [34.29–32]. The amount of fining agent introduced in the batch should thus be optimized, and the optimum concentration of fining agent will depend notably on the type of glass produced, the batch composition, the redox state of the melt and the combustion atmosphere. Furnace design and convection patterns in the melting tank also play a major role in the fining process. As fining is promoted by higher temperatures, these patterns should be such that all the melt experiences temperatures high enough for efficient fining. In certain furnaces, bubblers, i. e., pipes blowing large bubbles (typically air) from the bottom of the melting tank, are added to induce forced convection and promote rising of the melt from the bottom of the melting tank to the surface (see spring zone schematic in Fig. 34.9), enhancing fining. Electrodes (also called boosting electrodes) can also be inserted in strategic locations in the furnace to locally increase the melt temperatures and influence flow patterns. Indeed, while cold glass is typically insulating, glass melts at high temperatures are electrically conductive (for alkali-containing glasses) and can be heated by the Joule effect through current injected via these electrodes, often referred to as boosting electrodes. An illustration of the impact of bubblers and boosting electrodes is shown in Fig. 34.15. After the primary fining process, the resulting melt should be lean in dissolved gases and only a small amount of seeds should remain. These remaining seeds are then reabsorbed by the melt during the secondary fining (or refining) process.
34.5.3 Refining and Conditioning As illustrated in Fig. 34.2, in the working end of the furnace the melt is progressively cooled from the high
Industrial Glass Processing and Fabrication
34.5.4 Homogeneity and Defects As described in the previous sections, homogeneity of the melt and absence of impurities is a crucial parameter in the glass-making process. The presence of inhomogeneity leads to defects [34.33, 34] and risks of rejection of the final product. Inhomogeneity may come from different sources and lead to different types of defects. Poor fining and/or reboil issues lead to the presence of bubbles (seeds or blisters). In practice, it is very complex to remove all seeds and blisters from the melt, and
most commercial products still contain some. A maximum acceptable number of seeds per weight or volume of glass articles, or seed count, is defined for each product and depends on type of product and specific requirements. For instance, the maximum acceptable seed count is typically higher for bottles than for glass windows (for which optical features are among the most important properties). In any case, the presence of large bubbles usually leads to automatic rejection of the product, whatever the quantity observed. An example of a bottle containing large bubbles is shown in Fig. 34.13a. Undissolved batch particles can also be found in the final product, as so-called stones. Careful raw material selection (notably grain size), batch preparation, melt composition, residence time and convection patterns in the furnace are crucial parameters to avoid formation of these stones. Stones may also originate from pieces of refractories falling in the melt, or from crystallization of the melt in cold areas of the furnace (also known as devitrification). Poor mixing, demixing, or volatilization of components from the surface of the melt (leading to local variation in the composition) can lead to the formation of cords or striae in the product. The variations in composition produced lead to local variations in the optical properties, making their identification by visual inspection relatively easy. External cullet may contain (among others) pieces of glass-ceramics, which would not dissolve in the glass melt, metals, or coloring oxides. These contaminants, when introduced into the batch, can lead to defects in the final products. Some illustrations of defects in container glasses are shown in Fig. 34.13b–d. The analysis of the defects (stones, seeds, cords, etc.) can allow for identification the origin of the problem. Glass companies perform defect analysis on a regular basis in order to take actions to eliminate or reduce defect occurrence.
34.5.5 Shaping, Finishing and Inspection After the conditioning, the refined melt is shaped into a glass article. Shaping processes differ vastly depending on the type of article produced (flat glass, bottles, glassware, fibers, etc.). The shaping processes are described in Chap. 36, and will not be described further in the present chapter. It should however be noted that glass furnaces are designed specifically for the production of a given type of article, and are dedicated to the production of that type of article for the lifetime of the furnace. A float glass furnace may produce flat glass with different thicknesses or colors during its lifetime, but will never produce fibers or bottles.
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temperatures required for the fining processes, down to the lower temperatures required for the forming process. In other words, the melt is progressively brought from a relatively low viscosity, allowing for the efficient removal of bubbles, to a higher viscosity allowing for an efficient and a well-controlled forming process. This step corresponds to the conditioning of the melt. The solubility of most gases in the melt increases with decreasing temperatures. Because a temperature decrease will reverse the fining reactions (meaning that the fining gases will be chemically reabsorbed), the fining gases (e. g., O2 , SO2 ) can redissolve into the melt during controlled cooling. The remaining seeds will thus shrink and disappear, being reabsorbed within the melt. This mechanism is especially important for the remaining smaller bubbles (< 100 m), which are hardly able to rise in the melt during the primary fining step. The secondary fining step takes place in a rather narrow temperature window and can only be efficient if the melt is sufficiently lean of dissolved gases after the primary fining process. As the solubility of gases in the melt can strongly decrease with increasing melt temperature (especially for SO3 ), great care should be taken to avoid local hot spots or reheating of the melt during the conditioning step. In such cases, the solubility limit may be locally exceeded, leading to the formation of new bubbles in the working end. These bubbles will not have sufficient time to escape the melt before the forming process and will end up as defects in the final product. The formation of these bubbles due to local reheating during conditioning is called thermal reboil. Other types of bubble formation mechanisms during melt conditioning are possible. Too strong agitation of the melt may lead to mechanical reboil, while local melt inhomogeneity can lead to chemical reboil issues. Conditioning of the melt is the last step before forming. At the end of the feeder (or canal in the case of float glass production), the melt must present high thermal homogeneity, a critical parameter to ensure good performance in the subsequent steps.
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a)
b)
c)
d)
Fig. 34.13a–d Examples of defects in glass bottles: (a) bubbles (indicated by arrows), (b) metal inclusion, (c) cobalt streak and (d) glass-ceramic inclusion. Defects shown in pictures (b–d) originate from contaminants in the batch. Pictures courtesy of American Glass Research
After the shaping of the article, coatings are typically applied to the surface of the glass article to increase scratch performance and thus the performance of the article over its lifetime. In the case of glass containers, two types of coatings are applied by chemical vapor deposition (CVD): tin oxide (using mostly tin(IV) chloride SnCl4 as a precursor) just before the annealing (hot-end coating) and a polymer after the annealing, when the glass is colder (cold-end coating). The hot-end coating ensures the adhesion of the cold-end coating, which itself helps to improve the mechanical resistance of the glass as well as adhesion of labels or other decorative elements. In the case of flat glass, coatings may be applied online (as the glass is produced on the float line) or offline (after the glass has been cut, on a separate line). A large array of coating technologies (CVD, physical vapor deposition (PVD), sputtering, etc.) can be used to apply different types of coatings (e. g., lowemissivity or self-cleaning coatings) [34.35, 36]. These will not be detailed in this chapter. Coatings applied on fiberglass are described in Chap. 36. The articles produced should be free of defects and comply with the specifications defined to meet the customer requirements. Inspection of the articles is therefore a critical step. Inspection of the glass can be made both online and offline, and depends on the type of article produced. Online inspection systems are typically applied on all the lines producing glass containers and float glass (see illustration of a float glass online inspection system in Fig. 34.14) and allow for inspection
of 100% of the production. These systems are designed to control the presence of defects (bubbles, seeds, inclusions), control the thickness of the product (especially for float glass) and detect the presence of residual stress in the article (due to poor annealing, presence of inclusions, or uneven wall thickness distributions in bottles for instance). If the product presents defects or falls outside of the specifications defined, it is automatically rejected. Depending on the nature of the defect leading to rejection, the rejected glass may be reused or not as cullet in the batch. In parallel to the automated online inspections, operators are typically present to sample Scanner
Laser
Detector
Fig. 34.14 Schematic illustration of a laser scanner (on-
line) inspection system on a float glass line
Industrial Glass Processing and Fabrication
34.5.6 Storage The glass articles may not be used right after production, and may need to be stored for significant periods
of time before being delivered to the customer. Besides economic considerations not detailed here [34.39], it is important to ensure that the articles do not evolve/deteriorate before being delivered. Containers are typically packaged in compartmented cardboard boxes, while bottles are stored in bulk on pallets, arranged in stacks separated by layer sheets. The pallets are wrapped using packaging material, allowing preservation of the glass from external contaminations and shocks. It should be noted that high-humidity conditions should be avoided during the storage, as these promote weathering of the containers [34.40] Storage is particularly critical in the case of float glass. Indeed, it is well known that glass can suffer from stress corrosion and static fatigue when subject to a constant load, which can be enhanced in the presence of humidity [34.41, 42] (see also Chap. 7). The storage conditions of the float glass sheets should thus ensure that these mechanisms are reduced as much as possible. The glass sheets are thus stored in a tilted position to reduce stresses [34.37], and acidified interleaving coatings are typically used to separate the sheets, both to decrease glass-to-glass contact and inhibit corrosion, weathering and staining of the surface. More detail on these acid interleave coatings can be found in [34.43, 44]. It should be noted that besides storage, great care should be taken during all the operations requiring handling of the glass, so as to not damage the articles, the surface condition of the glass being critical for its mechanical properties and its performance during use.
34.6 Industrial Glass Furnaces While artisanal production and some high-end, lowquantity productions use pot furnaces, most industrial glass production is based on continuous melting tanks. In pot furnaces, or day tanks, the batch is melted, fined, homogenized and conditioned within the same pot, before being extracted from the pot for forming (manual or semiautomatic blowing, casting, rolling, etc.). The operations are discontinuous, a new batch being introduced only once the previous batch has undergone the entire process up to production of the glass article. Large continuous melting tanks are used to produce products such as container glass, flat glass (float and rolled), tableware, fiberglass, glass wool and most types of specialty glass production (tubes, display glass, glass-ceramics, lighting bulbs, etc.) [34.45]. Depending on the type of glass/articles produced, the pull rate, i. e., the quantity of glass melt drawn out of the furnace per unit of time (typically expressed as tons per day, TPD),
can vary typically from 2 to 1000 TPD (for large float glass furnaces). Glass making is an energy intensive process, with large amounts of energy required for the batch-to-melt conversion (typically 8090% of the heat input in the melting tank) and for maintaining the melt and combustion atmosphere at high temperatures. The theoretical minimum energy input required for glass melting is around 2:6 MJ=kg glass (or 2:6 GJ=t) for soda-limesilicate glasses. However, the heat transfer from the combustion atmosphere to the batch and melt are limited, and most of the energy input is lost through the exhaust gases (or flue gases). In order to increase the energy efficiency of the furnaces, different heat recuperation strategies have been developed and now equip most of the industrial glass melting tanks. The main strategies include regenerators or recuperators (heat exchangers) for preheating the combustion air, oxygen-
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articles at given frequencies for manual, offline inspections. The proper identification of defects (nature and frequency) can allow for definition of their source (e. g., issue arising from the batch, melting, fining or forming) and correct the process. In the case of float glass, the edges of the glass ribbon formed typically concentrate more stresses and defects (due to contact with the rollers in the float bath, see Chap. 36) and are removed on the cutting line. The ribbon is then cut into large panels by scoring the surface with diamond wheels, and the panels are then removed from the line using suction cups to avoid damaging the surface. These panels may later be cut to smaller size to produce specific articles (windshields, windows, etc.). Additional postprocessing steps can also be applied, such as edge polishing, additional coatings, lamination, or thermal tempering [34.37]. These steps may occur at the glass plant or off-site. In the case of tempered glass, the glass panels often undergo additional inspection steps after tempering to detect the potential presence of nickel sulfide (NiS) stones, a defect that may lead to spontaneous breakage of the tempered glass but which cannot be detected by online inspection, the NiS stones being too small (see [34.38] for more detail about NiS stones in tempered glass).
34.6 Industrial Glass Furnaces
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Base
Electric boosting
Bubbling
Fig. 34.15 Examples of flow patterns in a glass melting tank, ob-
tained by CFD modeling. The implementation of electric boosting or bubbling in the tank can promote and modify the flow patterns. © CelSian Glass & Solar
fuel firing, and electric melting. These strategies allow for current modern furnaces to achieve high efficiencies, with most furnaces showing energy consumptions ranging from 3:28 GJ=t (depending on the type of glass produced, furnace design and age, combustion strategy, etc.) [34.28]. The following subsections focus exclusively on the most commonly found furnaces in the current industrial glass production. It has to be noted that several projects have been carried out to evaluate new melting concepts [34.27], including for instance segmented melters [34.46], submerged combustion melters [34.47] and plasma melters [34.48] (including also in-flight melting furnaces [34.49]). Though these concepts have been proven of interest, their use remains limited in today’s industrial glass production.
34.6.1 Heat Transfer and Convection Patterns As illustrated in Figs. 34.9 and 34.12, heat is transferred from the flames to the batch and to the melt. The flames, obtained from combustion of fossil fuel (mostly natural gas) with preheated air or oxygen, radiate mainly in the infrared and partly in the visible part of the electromagnetic spectrum. Part of the heat radiated by the flames will heat the crown (roof of the furnace), which will in turn radiate as well and contribute to the heat transfer to the batch and melt. Within the melt at high temperature, currents (or glass melt flow patterns) are generated, both by pull and by free convection of the melt. The large temperature gradients observed over the depth of the molten glass bath lead to density differences within the melt, creat-
ing the free convection flows. These convection patterns also play a major role in the heat transfer within the melt. Examples of convection flows in a glass melting tank are presented in Fig. 34.15. The temperature profiles within the melting tank and the position of the hot spot (point where the temperature is the highest) can be adjusted, to a certain extent, by adjusting the combustion parameters such as the fuel distribution in the burners. Bubblers can be added in strategic locations to promote the convection flows, while electrodes can also be added to boost the energy input, electric current releasing latent energy in the melt by the Joule effect. The impact of implementing bubbling or electrode boosting on the convection patterns in a melting tank is illustrated in Fig. 34.15. In this example, it can be seen that the tank without electric boosting or bubbling (top part of the figure) shows only one large convection loop, which may lead to poor or insufficient homogenization of the melt. By implementing electric boosting (middle picture), two loops are created in the melter, improving the melt recirculation and homogenization. The impact on temperature profiles (illustrated by the color gradient on the picture) is also clearly visible. Implementing bubblers instead of electric boosting (see bottom picture in Fig. 34.15) has a different impact on the convection patterns in this melter. While a second convection loop is created, the position of this loop is different as compared to the case with electric boosting. The temperature profiles are also different. This figure illustrates how, for the same melting tank (i. e., with a fixed design), the flow patterns and temperature distribution in the melt can be modified by implementing additional strategies in the melter. It has to be noted that bubbling and electric boosting can be implemented simultaneously in a glass furnace. The flow patterns are critical to the quality of the final glass produced. Once introduced in the melting tank, batch particles may follow a large number of trajectories until the working end, leading to a wide residence time distribution and potential quality differences depending on the path they followed. The convection patterns should be such that the minimum residence time of any particle in the furnace is sufficient to allow for production of a melt with good quality. In other words, no particles should be able to reach the end of the furnace without being fully reacted and integrated into the melt. In some cases, weirs or dams are built inside the furnace to bring the glass melt from the bottom of the tank to the surface, improving fining and homogeneity. A schematic of a furnace including bubblers, boosting electrodes and a weir is shown in Fig. 34.16.
Industrial Glass Processing and Fabrication
34.6 Industrial Glass Furnaces
glass melting tank (end-port regenerative container glass furnace) equipped with bubblers, electrodes and a weir. © SEPR/SAINT-GOBAIN SEFPRO
Burner ports Bubblers Weir
Batch charger
Boosting electrodes
34.6.2 Regenerative Furnaces A regenerator is a heat recuperation system consisting of a regenerator chamber in which refractories (called checkers) are stacked. The principle of regenerative furnaces, invented by Siemens in the 1850s, is illustrated schematically in Fig. 34.17. The checkers are not represented in this figure. An illustration of the checkers can be seen in the regenerators in Fig. 34.16 (appearing in blue and gray in the regenerators). Regenerators come in pairs in industrial furnaces, with alternating heat recuperation and heat restitution cycles. In one cycle the checkers are heated up by flue gases from the combustion atmosphere. In the following cycle the heat is transferred to combustion air, this preheating allowing for more efficient use of the en-
Burner
Feeder
ergy input. In order to allow for efficient combustion air preheating and good thermal homogeneity in the furnace, these cycles alternate on a regular basis. The switching of a given regenerator (or set of regenerators) from a heat recuperation cycle to a heat restitution cycle is called a firing reversal, and occurs typically every 2030 min in industrial furnaces. No flames can be produced during the firing reversal. The duration between the time a regenerator is switched from heat recuperation (no firing from that side, as the hot flue gases are moving from the top of the regenerator to the bottom – right side regenerator in Fig. 34.17) to heat restitution (flame produced from that side, as the combustion air is moving from the bottom of the regenerator to the top, where to burner is – left side regenerator in Fig. 34.17) should be as short as possi-
Crown Melting tank Flame Glass bath
Cold air Regenerator
Hot air Regenerator r o t a r e n egeR Regenerator
Combustion air
Fig. 34.17 Principle of a regenerative glass furnace
Part E | 34.6
Fig. 34.16 Schematic of an industrial
Regenerators
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ble to avoid a decrease in temperature in the melting tank. Regenerators may be placed on the side or at the back of the furnace. The former case is referred to as cross-fired regenerative furnaces. Typically, these furnaces are equipped with four to eight burner ports on each side. When regenerators are placed in the back wall of the melting tank, the furnaces are referred to as end-port-fired furnaces (or U-flame furnaces). The flames produced are generally longer in the case of endport-fired furnaces as compared to cross-fired furnaces, allowing for lower structural heat losses. However, the temperature profiles may be easier to adjust in the case of cross-fired furnaces. Schematics of end-port and cross-fired furnaces are shown in Figs. 34.16 and 34.18 respectively. Regenerative cross-fired furnaces are usually employed for float glass production, with pulls in the 5001000 TPD range. Smaller cross-fired furnaces can be found for production of containers and tableware, with pulls ranging from 100 to 600 TPD. Regenerative end-port-fired furnaces are typically used for container and tableware glass production, as this configuration usually leads to good energy efficiency and cost effective production for the production volumes for this type of articles, with typical pulls of 100400 TPD.
34.6.3 Recuperative Furnaces In the case of recuperative furnaces, the hot flue gases escaping the combustion space pass through recuperators (usually one or two per furnace) in which the heat is transferred to the combustion air in concurrent or in countercurrent flow. Recuperators, typically made out of high-temperature-resistant alloys, are relatively cheap compared to regenerators, do not require firing reversals and are simpler in construction. Contrary to regenerators, they do not contain refractory checkers. However, the combustion air preheating is less
efficient. Recuperative furnaces are typically equipped with a large number or burners (515 per side, depending on the size of the furnace), controlled independently, allowing for good control of the temperatures profiles in the melting tank. The functioning principle of recuperators in a recuperative furnace is illustrated in Fig. 34.19. The hot flue gases from the melting tank are directed towards a heat exchanger (the recuperator) and preheat the combustion air, which is then sent to the burners to produce the flames above the tank. These recuperators do not contain refractory checkers. Recuperative furnaces are typically smaller than regenerative furnaces and are used for production of fiberglass, tableware and container glass. Typical pull rates for recuperative furnaces are in the 20400 TPD range.
34.6.4 Oxygen-Fuel Furnaces Most regenerative and recuperative furnaces run using fuel and air as the oxidant. Oxygen-fuel (or oxyfuel)fired furnaces use pure oxygen as the oxidant, considerably reducing the volumes of flue gases produced as there is no dilution by nitrogen from the air. Oxyfuelfired furnaces have in general similar designs to recuperative furnaces, with multiple burners (typically four to six) on each side of the melting tank. Oxyfuel-fired furnaces are usually not equipped with heat recuperation systems, though recuperators can be found in some cases. The advantage of oxyfuel furnaces resides in their lower design costs (no heat recuperation system), lower flue gas volumes, lower environmental footprint and reduced fuel consumption. However, pure oxygen is costly and the additional costs related to oxyfuel firing may exceed the gain provided by the reduction in fuel consumption. In addition, oxyfuel furnaces usually require the use of refractories with higher quality, thus higher costs.
Regenerators Doghouse
Working end
Waist/neck Regenerators
Canal Spout/lipstone
Fig. 34.18 Schematic of a side-port regenerative float glass furnace. © SEPR/SAINT-GOBAIN SEFPRO
Industrial Glass Processing and Fabrication
34.6 Industrial Glass Furnaces
tive furnace. © Nikolaus Sorg GmbH & Co. KG
Oxyfuel-fired furnaces are usually relatively small in comparison to regenerative and recuperative furnaces. They are typically used for production of some technical glasses, fiberglass, glass wool, and for some tableware and container glass production. Typical pulls are in the 2400 TPD range. Some examples of very large oxyfuel-fired float furnaces exist, with pulls up to 800 TPD [34.28].
34.6.5 All-electric Melters Though many regenerative, recuperative or oxyfuel furnaces apply some electric boosting in the melt, the main source of energy is provided by the combustion system. In the case of all-electric furnaces, all the energy is supplied by electrodes inside the melt. All-electric furnaces are typically vertical melters, with the batch covering the entire surface of the melt. All the melting, fining and homogenization processes occur in the vertical direction. In this configuration, the batch is only heated from the bottom by the hot melt. Therefore, allelectric melters are sometimes referred to as cold-top furnaces. The temperature gradients within the melts are controlled by electrodes inserted inside the melt. The absence of a firing system above the batch brings a significant advantage for melting glasses that are sensitive to evaporation, as the temperatures at the top of the batch are low (hence the name cold-top furnaces). This makes all-electric melting especially in-
teresting for production of glasses with high contents of lead (e. g., lead crystal), fluorine (e. g., opal glass), chlorine (e. g., NaCl-fined glasses), boron (borosilicates), or alkalis (e. g., soda-lime-silicates). All-electric furnaces are typically found in tableware, tubing, fiberglass and flaconnage/perfume bottle production, with pull rates from 2 to 200 TPD. The main limitation of this type of furnaces remains the cost of electricity, which can be too high for economic feasibility of electric melting in some regions. An example of an all-electric furnace is given in Fig. 34.20. Note that all-electric furnaces are equipped with burners, whose only function is to initiate the melting process at the start of the furnace operation. Once a first melt is obtained in the furnace, the burners are switched off and the furnace operates only with electric energy.
34.6.6 Refractory Materials Glass melting tanks are built with refractory materials that must sustain high temperatures and corrosive environments over the lifetime of the furnace, which typically spans from 520 years depending on the type of furnace and the type of glass produced (requiring different temperatures and which can be more or less corrosive). Different types of refractory materials are used at different places in the furnace [34.50]. This is illustrated in Figs. 34.16 and 34.18, in which dif-
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Fig. 34.19 Illustration of a recupera-
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Fig. 34.20 Illustration of an all-
Batch feed Batch blanket Electrodes
electric furnace. The batch blanket covers the entire surface of the melt, which is heated up by electrodes. © 2016 Toledo Engineering Co., Inc. All rights reserved. www.teco.com
Glass melt
ferent colors represent different types of refractories used. It is essential to use suitable refractories in the different parts of the furnaces to ensure the good operation of the furnace. The important factors to consider for the selection of the refractories include their temperature resistance and stability at high temperatures, taking into account the maximum operating temperatures they will face. Thermal shock resistance and thermal expansion must be taken into account, especially during the first heating of the furnace. In any case, thermal cycling should be avoided, when possible, during the furnace operation. Thermal conductivity of the refractory is also important, in terms of insulation provided or heat exchanges. The mechanical resistance and potential deformation under load (creep) must be considered for the operational range considered. In the combustion chamber, the temperatures in the crown (the roof of the furnace) can reach levels between 1550 and 1700 ı C (higher temperatures typically observed in furnaces for borosilicate glasses or glassceramics), and the refractories must be resistant to the combustion atmosphere and potential chemical attacks by the flue gases and volatile components. The refractory materials exposed to molten glass are operated at about 11001550 ı C in most cases. The refractory materials should not dissolve or detach into the melt (which would result in inhomogeneity, cords, or undesired colorization of the glass). The temperature in the regenerators typically varies between 1550 ı C (at the top) and 500 ı C (at the bottom). In the regenerators, the top layers of the checkers are exposed to high temperatures and carry-over (dust) and condensation of volatile species from the melt. Fused-cast AZS (alumina-zirconia-silicate) refractories are commonly found in contact with the melt and for side walls for soda-lime-silicate glasses. It has to be
noted that the refractories located at the melt level, i. e., refractories in contact simultaneously with the glass melt and the combustion atmosphere, must be particularly considered. At this point, the so-called melt line, corrosion rates are at the highest. In many furnaces, the refractories at the metal line are cooled down by air-cooling on the outside in order to slow down the corrosion processes. Specific refractories with higher corrosion resistance, such as chromium oxide bricks, can also be used at the metal line. However, their use in furnaces producing soda-lime-silicate glasses is usually limited, as the cost of these refractories is significantly higher than fused-cast AZS. In furnaces used for the production of glasses requiring relatively high temperatures, like E-glass fibers (low-alkali), fused-cast AZSs are usually not suitable and chromium oxide bricks are used for construction of the melting tank. The furnace crown is usually made out of silica bricks (corrosion by alkalis evaporated from the melt may occur). Magnesia-based bricks, mullite (3Al2 O3 2SiO2 ), spinel (MgAl2 O4 ), or zirconia (ZrO2 ) bricks are commonly found in the regenerators (the composition can depend on their location in the regenerator). It is important to note that not only the chemical composition of the refractory should be considered, but also the microstructure and macrostructure (grain sizes, binding phases), and level of impurities. The quality of the refractory will have an impact on the costs, which is a major aspect in the final choice.
34.6.7 Environmental Aspects During industrial glass-making processes, a large amount of gases can be generated from the combustion and from the batch reactions, and glass manufacturers have to comply with strict regulations to limit emis-
Industrial Glass Processing and Fabrication
measured. Primary NOx reduction measures include combustion optimization (optimized burners) and reduction of the combustion air supply (i. e., stoichiometry of the flames or use of oxyfuel firing [34.51]). Secondary NOx reduction strategies involve selective reduction of the NOx into N2 by reaction with ammonia or urea in selective catalytic reduction (SCR) systems. CO2 is one of the main sources of emissions, originating mainly from the combustion processes (for fuel-fired furnaces) and partly from the batch reactions. Strong efforts are undertaken to reduce these CO2 emissions [34.52], including strategies such as increased recycling, improved energy efficiency, additional waste heat recovery systems or raw material/batch reformulation. It is important to consider that while the use of electric energy in the furnaces (boosting or all-electric melting) reduces the CO2 emissions related to combustion, the electricity generation process itself often involves consequent CO2 releases. The use of greener, sustainable and renewable energy sources are among the solutions considered by the glass industry for decreasing the environmental impact of glass making in the future.
34.7 Modeling of Industrial Processes The modeling of glass furnaces using computational simulations started around 1965 [34.53], and with the development of advanced mathematical tools, it has since taken an increasingly important part in the glass industry and in its optimization. A wide range of models have been developed, with different levels of complexity, for simulating different parts of the process at the micro- and macroscale. Rather than an in-depth description of the different models used in the glass-making process and the principles they are based on, this section presents some concrete applications and achievements they enable. The strength of these tools and their importance in the future of the glass industry is highlighted. A detailed description of the models used in the glass industry can be found in [34.54].
34.7.1 Introduction Industrial glass making is a complex process, involving an incredibly large number of reactions and phenomena, which are often interrelated, each one influencing one or several other reactions. Changing one parameter in the process settings (may it be in the batch, in the furnace design, in the combustion settings, in the pull rate of the furnace, etc.) will thus often have a consequence
in more than one place in the furnace, and can have significant impacts on the product quality and/or on the operational efficiency. Glass furnaces are harsh environments, operating at very high temperatures and closed environments, often making the direct observation of many phenomena inside the melting tank difficult. In addition, industrial glass making involves continuous production of several tens to hundreds of tons per day, in furnaces that must withstand these conditions for durations as long as possible (in terms of return on investment on the production infrastructure). Errors in the operation and/or unanticipated effects from a trialand-error approach can have dramatic consequences on the production (on the product or on the furnace itself), leading to major losses and considerable financial repercussions. In addition, the response of the furnace to changes carried out by operators can often be counterintuitive. For all these reasons, the ability to predict or anticipate the consequences before an action is taken represents a considerable advantage, and has been a major driving force in the development of glass-process modeling. Nowadays, almost every new furnace is modeled before being built in order to identify potential flaws and optimize their design [34.55]. Though it is not possible to replicate the entire industrial glass-making process at the lab scale, and thus
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sions to the environment [34.28]. The main gaseous species of concern include NOx , mainly arising from the combustion processes, and SOx , arising from the fuel and from the fining processes for sulfur-fined glasses. Lower quantities of alkaline species such as NaOH and KOH, harmful gases such as HCl and HF, or heavy metals from impurities in the raw materials, can also be found in the untreated waste gases. In the production of borosilicate glasses, borate species (alkali borates such as NaBO2 and KBO2 , or metaboric acid HBO2 ) may also be found. Industrial furnaces are usually equipped with systems allowing for the treatment of the waste gases and limit their release in the environment, such as bag filter or electroprecipitators (EPs). In EPs, gases such as SOx , chlorines and fluorines react at a temperature of approximately 450 ı C with an adsorption agent, Ca.OH/2 , to produce solid compounds (CaSO4 , CaCl2 or CaF2 respectively). These reactions produce a dust, called EP dust, which is then treated in special plants or reintroduced, to some extent, as raw material in the batch. NOx reduction, a major challenge in the glass industry, can rely on either primary or secondary reduction
34.7 Modeling of Industrial Processes
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to simulate the outcome of changes in process parameters in an industrial furnaces in small-scale setups, it is possible to build models describing individual phenomena. This includes, for instance, development of models for sand grain dissolution, bubble formation and behavior (i. e., for the fining process), corrosion mechanisms, or evaporations from melts. These models can then be used as inputs for more complex CFD models, based on numerical analysis and algorithms simulating the interactions between the different variables involved within the boundary conditions of the furnace. These CFD models allow for the simulation of the complex processes occurring within the furnace and the evaluation of the outcome of different scenarios (e. g., impact of changes in the glass composition, modification of the combustion settings, addition of bubblers or electrical boosting, etc.). These models are thus highly valuable in the glass industry, as they enable visualization of the different phenomena occurring in the furnaces, and also the ability to anticipate the impact of planned changes in the process parameters. Mathematical simulations can thus guide the furnace operators in their decision-making process, and allow for an optimization of the settings, taking into account the different consequences of a given parameter change on the global process. CFD models can also be used to evaluate the efficiency of the production in terms of energy consumption. Glass making is energy intensive, and glass producers have a strong incentive to optimize their energy consumption. Indeed, a significant amount of the energy input does not go to the batch and melt, and is lost via the flue gases and structural heat losses (around 50%, depending on the efficiency of the furnace – see also Fig. 34.22). The balance of the energy input and output can be modeled using so-called energy balance models. In the following sections, energy balance models and CFD models are described. In particular, the numerous possibilities they offer and their value in the glass-making process are highlighted with some modeling results. It has to be emphasized that, while the models described in this chapter result from calculations, they rely on input based on experimental results and/or measured industrial process data. The quality of the output of the models is thus dependent on the quality of the input data. As a consequence, processes for which measured data are lacking, or for which the available information is limited, yield limited possibilities in the development of accurate models simulating properly the actual situation. In the same manner, as the quality of the models is judged on their accuracy in representing actual processes, the validation of the models is a critical and essential step. Comparison of the modeled and mea-
sured values is crucial and is the criterion for judging the validity of the results obtained from simulation.
34.7.2 Energy Balance Models A good knowledge of the energy consumption of the furnace and the balance between the energy input and energy output is essential for ensuring optimal efficiency of the furnace and identifying the potential sources of improvement. Energy balance modeling tools are designed to provide an energetic map describing how much energy actually goes to the batch and melt, and how much is lost at different places in the furnace. An example of a flow diagram for an energy performance model of a glass furnace is given in Fig. 34.21 [34.56]. Energy balance models are based on a relatively simplified representation of the furnace design, including its dimensions, structural elements (i. e., types of refractories used at different places in the furnace), potential heat recuperation systems, and the different sources of energy input (amount of fuel and its calorific value, electric boosting, etc.). The energy demand for the reactions (calculated based on thermodynamic models), and the heat capacity of the glass and flue gases (taking into account their composition) are integrated into the calculations. A set of different process values measured within the furnace, such as glass outlet temperature (measured with thermocouples), temperature of the flue gases before and after heat recuperation systems, flue gas composition, leakages and air infiltration within the furnace, wall losses, pull rate of the furnace, etc., are included as input data. The output of the model describes the distribution of the energy usage within the furnace, and thus gives a picture of its energy efficiency. An example of the calculated output for a regenerative furnace is shown in Fig. 34.22. The values in this example are expressed as percentage of the total energy consumed (total amount of energy expressed in MJ/t of glass produced). Knowledge of the energy balance of the furnace is the first step in the identification of the solutions possible to reduce the energy consumption and thus reduce the costs related to energy. These solutions often involve good housekeeping of the furnace (e. g., proper insulation, avoiding leakages, optimization of combustion parameters). Energy balance models can also be used for evaluating the impact of different scenarios, i. e., the impact of modifying different process settings (e. g., cullet content in the batch, batch humidity, regenerator efficiency, etc.) on the energy consumption of the furnace [34.57]. They also present the advantage of requiring only relatively limited computational power while providing valuable information to the glass producers.
Industrial Glass Processing and Fabrication
Gap near burner
Guess for total heat added
Fumace oterating pressure
Design variables
Cooling air velocity Number of burner Burner air nozzle diameter
Furnace air/flue gas leakage calculations
Fuel composition Glass composition Moisture in batch and cullet Cullet % Glass draw
Combustion species Fuel stoichiometric calculation
Combustion zone stoichiometric calculation
Heat loss from air leakage Heat loss from flue gas leakage Mass of air Mass of flue gas
Heat loss from flue gas Flue gas outlet temperature
Glass reaction calculation
Regenerator calculation
Oxygen % at regenerator outlet
Furnace design capacity Furnace design details
Oxygen % at furnace outlet
Gas from glass reaction
Furnace design characteristics
Melting area
Air leakage
Flue gas leakage
Fuel consumption Ambient conditions
Fuel calorific value Fuel calculation
Furnace geometry calculation
Raw material composition Glass outlet temperature
Heat of reaction for glass Heat of reaction and heat carried by glass
Furnace operating characteristics
Total heat added in furnace
Heat loss batch gas Heat carried with glass Heat loss from batch moisture
Furnace geometry
Color of glass
Heat loss from regenerator wall
Furnace wall losses
Heat loss from furnace area wall
Fig. 34.21 Flow diagram for a glass furnace energy performance model. After [34.56], with permission from Elsevier Other structural losses 12%
To glass melt 41%
Melting tank wall losses 5% Regenerator wall losses 5%
34.7.3 CFD Modeling in Glass Melting Tanks
Cold flue gases 25% Evaporation 3%
sions from the furnace, or furnace lifetime (corrosion mechanisms at different places in the melting tank). The simulation and optimization of these parameters requires more complex, computational fluid dynamics (CFD) modeling tools.
Reactions 9%
Fig. 34.22 Example result from energy balance modeling of a regenerative glass furnace, expressed here as percentage of the total amount of energy. The values are indicative only
However, these models do not allow for in-depth visualization of the processes inside the melting tank, such as combustion, flow patterns or temperature distribution within the melt. Energy balance models also do not provide information on product quality, emis-
Computational fluid dynamics is widely used in today’s glass industry, as highlighted by the strong activity of the ICG (International Commission on Glass) Technical committee TC21 Modeling Melting [34.53]. CFD is based on the discretization of the geometry of the furnace/part of the furnace modeled into a large number of small volumes (typically several hundreds of thousands to several millions) and iterative procedures to solve, for each volume, the balances for mass, momentum, energy and chemical species conservation equations (coupled, nonlinear partial differential equations). CFD modeling of the glass-making process typically relies on finite volumes [34.58]. As described previously, glass making involves a significant number of reactions and mechanisms. While different simple models have been developed
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Gap in flux line
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to simulate them individually, advanced computational tools and capacities are required in order to simulate processes involving these different reactions simultaneously. The number of parameters taken into account and their interrelations can have a significant impact on the complexity of the simulation, and thus on the computational power/time needed to obtain the results. One of the challenges in the development of more accurate modeling tools lies in the balance between the gain in accuracy of the model (or increase in the number of parameters taken into account) versus the computational power required to run the simulations. Thus, the models available may be more or less complex, and the choice to use one or another may depend on the accuracy required. Different models have been developed, yielding steady-state or time-transient results, and taking into account different processes such as batch melting, fining, foaming, redox, volatilization, NOx formation, refractory corrosion, boosting, bubbling, etc. The following subsections give a few examples of the possibilities offered by CFD modeling. It has to be noted that the extent of the opportunities offered by CFD in the glassmaking process encompass a much larger range of possibilities than the limited selection presented in the following paragraphs. Temperature Distribution and Flow Patterns In industrial melting tanks, the modeling of the combustion process and heat transfer from the flames to the melt and within the melt, are of particular importance [34.58, 59]. Indeed, these parameters will have a great influence on the temperature profiles in the combustion atmosphere and within the melt, which will themselves have a significant impact on many of the chemical reactions occurring (melting, fining, corrosion of the refractories, etc.). Given the design of the glass furnaces and the limited points of access for placing thermocouples, it is not practically possible to know the temperature profiles by relying on measurements only. Modeling is therefore essential for calculating the temperature distributions, and their impact, in the complete melting tank. Examples of modeling of the glass melt surface temperature, and glass melt flow patterns in a flat glass furnace, are shown in Figs. 34.23 and 34.24 respectively. It can be seen in Fig. 34.23 that the temperatures at the surface of the melt are coldest close to the batch area (on the left of the picture), and in the refining area (on the right of the picture). The hot spot, where the temperatures are the highest, is located close to the center of the melting tank. The furnace simulated in this case is equipped with a bubbler row at the center of the
furnace. The bubblers push the colder glass from the bottom of the tank up to the surface, resulting in locally colder melt surface temperatures right above the bubbler row. Figure 34.24 shows the glass flow patterns in the furnace. The combustion system above the melt (i. e., the flames in this case) is also modeled. This model also integrates modeling of the batch melting, and the batch coverage and thickness evolution as it progresses inside the furnace are illustrated in the picture (left side). These models show the behavior of the melt and flames within the furnace, for a given set of process parameters. These parameters can be varied in the model (e. g., change in the burner settings, increase in the furnace pull, addition of boosting electrodes, etc.), and the comparison of the final modeling results allows for evaluation of the impact on the operation, e. g., in terms of energy usage, glass quality, or furnace lifetime. The optimization of these different parameters can lead to significant improvement of the stability and/or performance of furnaces, which translates to significant savings for industrial companies. In addition, the use of models allows for the evaluation of the impact of these different scenarios before implementing them in the furnace, thus reducing the risk associated with errors or unexpected consequences. As glass melting tanks are very complex, implementation of wrong process parameters can be difficult to correct and lengthy to recover from, which can induce significant production losses. Figures 34.23 and 34.24 show examples of modeling of the glass melt flows and temperature distribution. CFD modeling can also be used to model temperature distributions within the combustion atmosphere above the melt, as illustrated in Fig. 34.25. The outcome of such a simulation can for instance be used to identify potential critical spots for corrosion of the refractories in the crown of the furnace. The results of the modeling study can also be compared to temperatures measured inside the combustion atmosphere (using suction pyrometers), in order to assess and validate them. It has to be noted that accurate modeling of the heat transfer and temperature distribution within the melt is of particular importance in furnace forehearths and feeders, i. e., the parts of the furnace before the melt leaves to the forming process [34.58, 60]. In those areas, the temperature homogeneity is critical, and CFD modeling is a very powerful tool to visualize the phenomena occurring and for process optimization. It has to be noted that in the parts of the furnace where the depth of the melt is shallow, or for very transparent melts (for low- and ultralow iron containing glasses), the use of spectral radiation models is needed for accurate modeling [34.59].
Industrial Glass Processing and Fabrication
1200
1300
1400
1530
Fig. 34.23 Modeling of the glass melt
surface temperature calculated with GTM-X CFD model, for a float glass furnace equipped with a bubbler row. Picture courtesy of © CelSian Glass & Solar
Fig. 34.24 Modeling of the float glass
melting tank using GTM-X CFD model. The picture shows the position and shape of the flames, coverage of the batch on top of the melt, and flow patterns in the furnace. © CelSian Glass & Solar
1460 1370
1400 1400
1590 1510 1500
1440 1430 1410 1400 1480 1410 1390 1380 1420
1580
1550
1590
1540 1570
1520 1550 1520
1580
Fig. 34.25 Modeling of the temperature distribution in the combustion atmosphere above the melt using GTM-X CFD
model. © CelSian Glass & Solar
Particle and Bubble Tracing Glass quality is a baseline aspect of industrial production, and the presence of defects such as unmolten batch particles or bubbles can lead to rejection of the products. The melting tanks must be optimized to ensure that all raw materials experience sufficient time at a temperature high enough to fully react and integrate into the melt (especially sand, which dissolves relatively slowly). In the same manner, all bubbles should be removed during the fining and refining process. These processes are highly dependent on the melt temperature and flow patterns notably in the melting tank. Chemistry and redox of the melt also play an important role. A series of dedicated experimental studies have been used to derive models for sand grain dissolu-
tion [34.61] in glass melts. The output of such models can be integrated into CFD models to calculate the trajectories of the sand grains in the melting tank, taking into account the flow patterns and temperature profiles in the furnace (Fig. 34.24). These simulations, called particle tracing studies, are usually run for scenarios where a high number of particles are released from the batch, and all the possible trajectories the particles can follow in the melting tank are calculated. The results show whether all particles (e. g., sand grains) have sufficient time to be completely dissolved in the glass, and thus whether some may reach the end of the melting tank undissolved. If the CFD model shows that a large number of particles are likely to leave the melting tank unreacted, several parameter variations on the particle
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Fig. 34.26 Example of a particle
tracing study for a container glass furnace using GTM-X CFD model. The result of the simulation shows the path for a particle from the batch to the feeder. © CelSian Glass & Solar
a) 0
150
Bubble size (μm) 300 450 600
b) 0
150
Bubble size (μm) 300 450 600
Fig. 34.27a,b Bubble tracing analysis in a float furnace using GTM-X CFD model, showing the trajectory of bubbles as well as the evolution of their diameter along their residence in the melting tank; (a) base case and (b) furnace with bubbler row moved 2 m downstream in the furnace. © CelSian Glass & Solar
trajectories can be simulated to optimize the furnace settings (number, position and settings of the burners used, use of electrodes in the melting tank, temperature profiles imposed in the furnace) and lead to decreased amounts of defects in the glass. In the same manner, particle tracing studies by CFD modeling can be used to model different scenarios and anticipate the potential impact of planned changes in furnace settings on the glass quality, or to calculate residence time and particle paths in a furnace. An example of a particle tracing study in a container glass furnace is shown in Fig. 34.26. Similar tracing studies can be used to follow bubble behavior in the melting tank. In such cases, models based on experimental studies of bubble formation and behavior in glass melts [34.62, 63] as a function of vari-
ous parameters (glass composition, temperature, redox, etc.) are used as inputs into the CFD modeling. Figure 34.27 shows the results for bubble tracing in a glass furnace for a furnace with a bubbler row, and the impact of moving this bubbler row two meters downstream in the melting tank (for the same furnace, producing the same glass, with similar combustion settings). The impact of position of the bubbler row can be clearly seen, with a significantly lower number of bubbles reaching the end of the tank when it is moved two meters downstream. These results show that a lower amount of bubbles can be expected in the final product when the furnace design is changed to the second case (Fig. 34.27b). These results can be compared with the practical experience of the glass producer, comparing
Industrial Glass Processing and Fabrication
34.7 Modeling of Industrial Processes
the amount of bubbles measured in the final products before and after optimization of the furnace. Evaporation from the Melt Environmental impact of glass production and releases from the furnace are also a major concern for the glass industry, with strict regulations enforced in many countries. Modeling can be used to simulate evaporation from the glass melts. For instance, evaporation of species such as borates or NaOH from the melt can lead to increased corrosion of the crown of the furnace and increased formation of dust. Understanding the evaporation process for this species is therefore of high interest to better control it and limit its potential consequences. Experiments at the lab scale are used to derive models for evaporation of species from the melt, as a function notably of the glass composition, melt temperature, and composition and velocity of the flue gases above the melt [34.64–66]. The results from these models can be integrated into more complex CFD models in order to simulate the evaporation rates of given species from the melt in industrial glass melting tanks. Figure 34.28 shows the results for metaboric acid (HBO2 ) evaporation from a furnace producing borosilicate glass. It can clearly be seen that the evaporation rates are highest close to the central part of the melting tank, where the melt temperatures are the highest. Such a model can be used to evaluate the impact of a planned change in the furnace settings (e. g., change in the type of combustion used in the furnace) on the evaporation, and then anticipate the consequences (corrosion of the crown, dust formation, etc.). It can also be used to optimize the current settings of the furnace in order to minimize the evaporation.
34.7.4 Modeling of Forming Processes The forming processes found in the glass industry are various and can be significantly different depending on the type of article produced (press-blow or blow-blow for containers, drawing for fibers, tin bath process for float glass; see Chap. 36). During glass forming, the glass undergoes significant changes in temperature and viscosity over a short period of time, coupled with significant geometry variations, typically involving various degrees of deformation, heat transfer and radiation processes. The glass goes from a low-viscosity melt with a Newtonian behavior to a high-viscosity article with an elastic behavior, passing through a regime of viscoelastic behavior, for which understanding and experimental data on the glass behavior are limited and complex to obtain. Modeling of forming processes is therefore a very challenging task. As described in [34.58], modeling of the forming processes is a relatively new area of computational research as compared to modeling of melter and forehearth, and a significant number of challenges remain to be resolved in this field. Significant progress has been made over the last decade, and a large number of companies and institutes are dedicating their efforts to the development of more powerful simulation tools for the different forming processes [34.67–69], notably in the framework of the ICG Technical committee TC25 Modeling Forming. An example of modeling results from the simulation of the blow-blow process for forming of container glasses is shown in Fig. 34.29. The evolution of the shape from the glass gob to the glass bottle, and temperature distribution within the article, are shown.
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Fig. 34.28 HBO2 concentrations above the glass melt obtained from CFD calculations in the combustion chamber for a furnace producing borosilicate glass. © CelSian Glass & Solar
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Part E | 34.7 Fig. 34.29 CFD modeling of selected time steps occurring during the forming of a glass container by the blow-blow
process. The modeling shows the evolution of the glass shape and temperature distribution in the article during the process. Picture provided by Nogrid GmbH
Fossil fuel Manipulated variables
Crown temperatures (TC)
Oxy boost Time→ E‐Boost Time (hours)→ Pull
Measurable disturbance variables
Bottom temperatures (TC)
Cullet % Time→ Time (days)→
Fig. 34.30 Example of process variables taken into account in a furnace control system, and their influence on temperatures in an industrial furnace. © CelSian Glass & Solar
34.7.5 Furnace Control Models can be integrated in-line in the furnace control loop and fed in real time by the process data measured at various locations in the melter. Such model-based control systems rely on the use of reduced models, built around historical process data of the furnace, and boundary limits derived from process optimization studies. The process data are continuously monitored. When deviations are measured, the model calculates the corrections required and automatically adjusts them. The use of reduced models is motivated by the need for fast calculation times, allowing for the real-time control of the furnace [34.70]. These model-based predictive control systems therefore allow for a stabilization of the process, re-
ducing the risk of overshoot, which may occur when the corrections of the settings are performed manually. These systems provide an autopilot control system, assisting the operators in the choice of the correct settings for an optimal operation, and thus a minimization of the instabilities (often synonymous with decreased efficiency and/or increased production losses). With the development of more efficient and faster models, model-based control systems are nowadays taking on increasing importance in the modern glass-making industry. An example of how such a model-based control system can be built is shown in Fig. 34.30. The full CFD model is used as a virtual version of the furnace, to build the database that is used in the response model. The model, based on a database of known (modeled) parameters for this furnace, allows us to predict the
Industrial Glass Processing and Fabrication
control loop allows us to anticipate the response of the furnace, and to automatically adjust the input energy setting (manipulated variables) to mitigate these disturbances and return to the nominal, stable settings in the shortest time possible. The automated control based on the models is often faster and more reliable than adjustments made by operators, allowing for more stable operation.
34.8 Conclusions Glass processing is a complex process, involving a series of steps, each critical in the production of a final product with good quality. Though the number of glass compositions industrially produced is extremely large, the processing steps are similar in all cases: definition of the composition, selection of the raw materials, batch preparation, melting, fining, forming, annealing and postprocessing. The technical considerations, reactions involved, and energy requirements for each step can differ greatly depending on the type of glass produced. Glass melting tanks, which can produce up to several hundreds of tons of glass per day, continuously and for several years, must be optimized to ensure that the melt delivered before the forming process is of high chemical and thermal homogeneity, and free of defects and bubbles. Several types of melting tanks exist, and
modern furnaces are equipped with energy recuperation systems improving their efficiency. While glass has been produced for millennia, the glass industry keeps innovating and developing strategies towards better, cleaner, and more efficient production. The relatively recent development and improvement of mathematical modeling has allowed for significant improvement in the understanding and optimization of the industrial processes. Notably, advanced process control, using modeling integrated into the control loops, is increasingly used in the glass industry and will continue equipping more and more furnaces. Use of cleaner energy sources (e. g., solar), decarbonation, increased energy efficiency, and development of more flexible melters (allowing faster changes between production of different types of articles) represent key areas for the future of the glass industry.
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glassglobal Group: glassglobal Plants, https:// plants.glassglobal.com Green Rhino Energy: Value Chain Activity: Manufacturing Solar Glass, http://www.greenrhinoenergy. com/solar/industry/ind_15_solarglass.php C.R. Kurkjian, W.R. Prindle: Perspectives on the History of Glass Composition, J. Am. Ceram. Soc. 81(4), 795–813 (1998) Glass For Europe: World Market Structure, http:// www.glassforeurope.com/en/industry/globalmarket-structure.php Ceramic Industry: Worldwide glass containers market to see modest growth through 2020, http://www.ceramicindustry.com/articles/95295worldwide-glass-containers-market-to-seemodest-growth-through-2020 (2016) J.E. Shelby: Introduction to Glass Science and Technology, 2nd edn. (Royal Society of Chemistry, London 2005) M. Hubert, A.J. Faber: On the structural role of boron in borosilicate glasses, Phys. Chem. Glasses 55(3), 136–158 (2014)
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D. Dollimore, J.G. Dunn, Y.F. Lee, B.M. Penrod: The decrepitation of dolomite and limestone, Thermochim. Acta 237(1), 125–131 (1994) R. Beerkens: Sulphur chemistry and sulphate fining and foaming of glass melts, Glass Technol. 48(1), 41–52 (2007) R.G.C. Beerkens: Sulfate decomposition and sodium oxide activity in soda–lime–silica glass melts, J. Am. Ceram. Soc. 86(11), 1893–1899 (2003) R.G.C. Beerkens, K. Kahl: Chemistry of sulphur in soda-lime-silica glass melts, Phys. Chem. Glasses 43(4), 189–198 (2002) A. Weyl: Coloured Glasses (Society of Glass Technology, Sheffield 1992) C.R. Bamford: Colour generation and control in glass. In: Glass Science and Technology, Vol. 2, ed. by CBLS (Elsevier, Amsterdam 1977) M. Hubert, A.J. Faber, F. Akmaz, H. Sesigur, E. Alejandro, T. Maheara, S.R. Kahl: Stabilization of divalent chromium Cr(II) in soda-lime-silicate glasses, J. Non-Cryst. Solids 403, 23–29 (2014)
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response of the furnace to a change in so-called manipulated variables – here being the share of fossil fuel (natural gas), oxy-boost (oxygen boosting in the flame) and electrical energy (E-boost), and measurable disturbance variables – in this case, change of pull rate of the furnace and percentage of cullet added in the batch, on the furnace temperatures (crown temperatures and temperature at the bottom of the melter). The CFD-based
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S. Drogue, S. Breininger, R. Rurz: Minimization of NOx emissions with improved oxy-fuel combustion: Controlled pulsated combustion. In: A Collection of Papers Presented at the 54th Conference on Glass Problems: Ceramic Engineering and Science Proceedings, ed. by J.B. Wachtman Jr. (Wiley, Chichester 2008) pp. 147–158 British Glass Manufacturers Confederation: A Clear Future, UK Glass Manufacturing Sector Decarbonisation Roadmap to 2050 (British Glass, Sheffield 2014) H.P.H. Muijsenberg: ICG TC21 modeling of glass melting processes – How reliable and validated simulation tools can help to improve glass melting efficiency and productivity. In: 73rd Conference on Glass Problems, ed. by S.K. Sundaram (Wiley, Chichester 2013) pp. 227–248 D. Krause, H. Loch: Mathematical Simulation in Glass Technology, Schott Series on Glass and Glass Ceramics (Springer, Berlin, Heidelberg 2002) p. 477 H. Li, Z. Xing, S. Xu, S. Liu: 3D simulation of borosilicate glass all-electric melting furnaces, J. Am. Ceram. Soc. 97(1), 141–149 (2014) V. Sardeshpande, U.N. Gaitonde, R. Banerjee: Model based energy benchmarking for glass furnace, Energy Convers. Manag. 48(10), 2718–2738 (2007) A. Lankhorst, L. Thielen, J. van der Dennen, M. del Hoyo Arroyo: Application of an energy balance model for improving the energy efficiency of glass melting furnaces. In: 74th Conference on Glass Problems, ed. by S.K. Sundaram (Wiley, Chichester 2014) pp. 51–68 M.K. Choudhary, R. Venuturumilli, M.R. Hyre: Mathematical modeling of flow and heat transfer phenomena in glass melting, delivery, and forming processes, Int. J. Appl. Glass Sci. 1(2), 188–214 (2010) A.M. Lankhorst, L. Thielen, P.J.P.M. Simons, A.F.J.A. Habraken: Proper modeling of radiative heat transfer in clear glass melts. In: 73rd Con-
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Mathieu Hubert Dept. of Corning Glass Technologies Corning Research & Development Corporation Painted Post, USA [email protected]
Mathieu Hubert received his PhD from the Universities of Rennes 1, France, and Arizona, USA, in 2012. He joined CelSian Glass & Solar in 2013 as a Glass Scientist/Technologist, performing consulting and contract R&D for the glass industry worldwide. In 2016, he joined Corning as a Development Scientist, working on new display glasses and specialty materials.
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34.51
References
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Batch Chemis 35. Batch Chemistry and Reactions
Oscar S. Verheijen, Mathieu Hubert 35.1
Overview of the Batch Melting Process 1231
35.2
Heat Transfer Processes ..................... 1236
35.3 35.3.1 35.3.2 35.3.3
Different Types of Batch Reactions ..... Dehydration Reactions ....................... Solid-State Reactions ......................... Formation of (Eutectic) Primary Melt Phases.............................................. 35.3.4 Dissolution Reactions.........................
1239 1239 1240 1241 1242
35.4
Reaction Kinetics .............................. 1243
35.5
Silica Conversion ............................... 1244
35.6 Fining Reactions ............................... 35.6.1 Bubble Growth and Ascension in Glass Melts.................................... 35.6.2 Sulfate Fining.................................... 35.6.3 Halide Fining .................................... 35.6.4 Oxygen Fining ................................... 35.6.5 Impact of Cullet and Raw Material Composition ........... 35.7
1245 1246 1247 1250 1252 1253
Conclusions ...................................... 1254
References................................................... 1254
35.1 Overview of the Batch Melting Process In a continuous glass melting furnace, the glass batch (i. e., the mixture of raw materials) is fed on top of the glass melt and pushed into the furnace. In the melting tank, the batch either spreads out and forms a so-called batch blanket or separates into individual batch-islands. The batch blanket, initially mostly 1020 cm thick, floats on top of the glass melt and is heated both from the bottom side (by the hot glass melt) and from the top (by the radiating flames and combustion space). Freshly molten glass leaves the bottom side of the batch blanket and enters the strong recirculation flow directed from the glass melt surface hotspot position towards and underneath the batch blanket in the direction of the batch charging wall. Thereafter, the glass
melt flows downwards and returns along the bottom of the melting tank towards the throat separating the melting tank from the working end or refining area (Fig. 35.1). The freshly molten glass melt still contains large amounts of bubbles (mainly containing CO2 and N2 ) and undissolved batch particles like SiO2 and other slow-dissolving oxides. Proper fining is required to ensure that batch bubbles are released from the glass melt before entering the feeders that deliver the glass melt to the forming process. Sufficiently high glass melt temperatures and residence times are of key importance to prevent the situation in which the undissolved species that might still be present in the fresh glass melt are transported to the forming process without being
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_35
Part E | 35.1
In industrial glass production, a batch composed of a mix of raw materials is introduced in the furnace at high temperatures, to be converted into a glass melt, which will then be shaped into the desired article. The batch-to-melt conversion is a critical process, involving a sequence of reactions (dehydration, solid-state reactions, formation of primary melt phases, dissolution of sand grains), the nature and rate of which depend on both thermodynamics and kinetics. Heat transfers to the batch are of major importance, as the rate of batch-to-melt conversion has a direct impact on the energy required for melting the glass, and therefore on the production costs. After the batch-to-melt conversion, the melt will contain a large amount of bubbles and dissolved gases, and a proper fining is required to obtain a product with good quality. In this chapter, the different reactions taking place during the batch-to-melt conversion and the fining of the melt are described. Specific attention is given to the heat transfer mechanisms, kinetics, and the silica (sand) grain dissolution mechanisms. The consequences of batch-to-melt and fining reactions in an industrial furnace (foaming, refractory corrosion) are also mentioned.
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Fig. 35.1 Day hopper
Return flow for batch heating
Generation of blisters from refractory Refining and Bubble absorption Hotspot and evaporation Conditioning of melt Thermal homogeneity
Part E | 35.1
Zone for sand grain dissolution Batch melting • 40–60 min • 80–90% of net heat flux
Spring zone and primary fining
completely dissolved and thereby leading to glass defects. Both fining and complete dissolution of raw material components is supported by the presence of two glass melt recirculation loops in the glass furnace melting tank. Next to the major recirculation loop mentioned above, a smaller second recirculation loop might be present. This second recirculation loop transports glass melt from the so-called spring-zone at the glass melt surface towards the front wall (also sometimes referred to as bridge-wall or throat-wall), subsequently downwards to the bottom wall, and finally returning upstream towards the batch charging wall. This bottom flow directed towards the batch charging wall prevents a shortcut flow of freshly molten glass melt along the bottom wall towards the throat and thereby prevents glass with poor quality entering the forming area. The presence of a second recirculation loop is promoted by the presence of bubblers, electrodes, and/or a dam wall located around 1=2 to 2=3 of the length of the melting tank. Both the forced release of large bubbles in the glass melt and the local intense heating of the glass melt by electric boosting forces the glass melt flow at the bottom of the melter towards the glass melt surface creating the second recirculation loop. This recirculation loop is further stimulated by a steep temperature gradient in the combustion space between the hotspot area and front wall. In a glass furnace both primary and secondary fining takes place. Primary fining is the enhanced ascension of enlarged batch bubbles, air inclusions, and blisters generated from refractory that is in contact with the glass melt due to the release of fining gases at high temperatures. Primary fining mainly occurs in the hotspot area of the melting tank. Secondary fining or refining relates to the process where the gases from remaining small bubbles are reabsorbed in the glass melt during cooling. This latter process takes place in the last part of the
Schematic presentation of a glass melting furnace with throat and a double glass melt recirculation loop system in the melting tank
Return flow from working end
melting tank close to the throat area and subsequently in the working end/refining area. After refining, the glass melt is cooled down in the working end/refining area before it enters the feeders/ forehearths where the glass melt is further thermally homogenized before it is delivered to the forming process. During the batch melting process, high volumes of CO2 gas are released as result of calcination reactions. About 1420% of the mass of a normal soda-limesilica batch is reacted into volatile CO2 . This means that from 1 kg of normal batch about 100 l of gas at normal pressure and room temperature (or about 500 l gas at the furnace temperature level) are released in the furnace. Besides CO2 gas, the melting losses consists of water vapor (several mass percent depending on the batch humidity, water content of the cullet, and presence of hydrated raw materials) and any possible evaporation products (SO2 , HBO2 , HCl, NaCl, HCl, KOH, PbO, Pb, NaOH, Se-components, etc.). As a consequence of the production of large volumes of batch gases, primary foam might be formed on top of the batch blanket hampering the heat transfer from the combustion space into the batch blanket and thereby increasing the energy consumption of the furnace. Whether primary foam is formed depends on the batch composition, the thickness of the batch blanket (a thicker batch blanket results in an increase in batch gas release per surface area), and the heating of the surface layer of batch blanket (to limit primary foam formation, fast sintering of melt phase formation at the top of the batch blanket should be prevented to avoid early stage closure of the batch surface layer restricting the release of batch gases). For instance, the use of calcined raw materials reduces the volume of batch gases released compared to batch based on carbonates, which may reduce foaming, as illustrated in Fig. 35.2, for a glass containing soda ash (Na2 CO3 ) and either car-
Batch Chemistry and Reactions
35.1 Overview of the Batch Melting Process
1233
Fig. 35.2 Example of CO2 gas release from a glass batch containing soda ash and either carbonated or burnt dolomite. The insert pictures show the foaming on top of the glass melt at 900 ı C with permission of CelSian
CO2 release (arb.u.) Carbonated dolomite Burnt dolomite
Part E | 35.1
200
200
400
500
600
700
800
900
1000 1100 1200 1300 Temperature (°C)
bonated or burnt dolomite .1 x/CaCO3 xMgCO3 or .1 x/CaO xMgO, respectively. The batch with burnt dolomite shows lower CO2 releases, notably in the 800900 ı C temperature range. As can be seen in the insert of Fig. 35.2, the foaming observed on top of both batches at 900 ı C is considerably reduced, for this specific glass, when using burnt dolomite. Batch melting is also the source of some of the glass furnace emissions. Next to the release of CO2 and H2 O as a result of decomposition and dehydration reactions occurring in the glass batch, the presence of fine raw material components, like for instance fine cullet and fine sand, in combination with relatively high flue gas velocities directed over a batch blanket with an unsintered and/or unmolten top layer, will result in carry-over (entrainment of unmolten raw material components by the hot flue gases flowing over the batch blanket) of the fine batch components in the flue gas. In addition to these entrained batch particles, carry-over can be enhanced by decrepitation of dolomite and/or limestone. Decrepitation is the process of explosive fracturing of dolomite and/or limestone as result of the pressure build-up of CO2 within the (dolomite) lattice until it exceeds the mechanical strength of the grains resulting in the bursting of the grain [35.1]. Recycling of filter-dust (the fine-grained condensates, mainly salt cake, formed during cooling of flue gases and captured with bag filters, electrostatic precipitators, or cyclones) further supports the increase of carry-over. Generally, the addition of water to the batch raw materials to limit segregation during transport of (mixed) raw materials also prevents excessive carry-over. In the case of preheating glass batches aiming at reduced glass furnace energy consumption, raw materials are dried before being charged to the furnace. As a con-
sequence of charging a dry batch, increased carry-over of raw material components may be encountered when implementing batch preheating systems. Carry-over components are easily entrapped in the top layers of regenerators which are refractory waste heat recovery systems that reclaim heat from the hot flue gases and subsequently preheat the combustion air to reduce glass furnace energy consumption. Both carry-over components and condensates formed during cooling down in the flue gases in the regenerators lead to deterioration of the regenerator’s checker-work (stack of refractory bricks required for heat exchange from the hot flue gases and towards the cold combustion air) and thereby a reduced regenerator performance. Carry-over can be limited by proper choice of raw materials (selection of carbonates with low decrepitation tendency and avoiding overly fine batch particles) and optimization of burner settings aiming at lowering flue gas velocities in the batch area. Figure 35.3 shows for three situations the total amount of evaporated volatile species and carry-over particles in the top and the bottom of a regenerator of a soda-lime-silica glass-producing furnace. The total amount of evaporated species and carry-over batch particles is expressed in mg per standard normal m3 flue gas normalized to 8 vol:% oxygen. Figure 35.3 distinguishes Na2 SO4 , CaSO4 , and MgSO4 deposits. The rest concentration comprises the total concentration of nonsulfate species like SiO2 , PbO, and cullet. Situation 1 refers to the situation where the sodalime-silica glass furnace had no batch preheating system installed and was melting their standard fine batch. The batch contained 25% of raw materials with a grain size < 100 m. The concentration of species before and after the regenerator amounts to 190 and 130 mg=m3
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Concentrations in flue gas (mg/m 3, 8% O2) Situation 1:
Situation 2:
Situation 3:
600 500
Part E | 35.1
Rest MgSO4 CaSO4 Na2SO4
400 300 200
Fig. 35.3 Total concentration of evaporated volatile species and carryover components in the top and bottom of a regenerator of a soda-lime-silica glass-producing furnace for three situations. (1) Without a batch preheating system, (2) with a batch preheating system with a relatively high content of fine particles in the batch (fine batch), and (3) with a batch preheating system with a relatively low content of fine particles in the batch (coarse batch). With permission of CelSian
100 0
Top
Bottom
Top
Bottom
Top
(at 101 325 Pa and 0 ı C), respectively. Situation 2 refers to the situation of melting the same batch in the same furnace when a batch preheating system is installed. It is observed from Fig. 35.3 that the concentrations of species before and after the regenerator have increased to 530 and 270 mg=m3 (at 101 325 Pa and 0 ı C) respectively. This indicates that implementing a batch preheater system increased the total amount of dust and carry-over material. Also, the amount of species condensing in the regenerator (indicated by the difference of species concentration before and after the regenerator) increased after installing the preheating system. However, avoiding very fine raw material components in the batch reduces the increased dust and carry-over rate to normal values as indicated by the measurement results for situation 3. In situation 3, the batch melted in the same furnace only contains 3% of raw materials with a grains size less than 100 m. Also the amount of flue gas components condensing in the regenerator decreased. Batch evaporation of volatile components such as salt cake (Na2 SO4 ), chlorides, and other species containing sodium and/or sulfur results in the formation of Na2 SO4 droplets and condensates during cooling of the flue gas in the heat recovery system leading to fouling and degeneration of the heat recovery system (Fig. 35.4). Before entering the burner ports, volatile sodium species (both released during batch melting and by (reactive) evaporation from the hot glass melt surface) may also react with refractory materials like the silica bricks in the glass furnace superstructure. NaOH vapors react both with silica grains and the wollastonite binder phase forming binary or ternary low-melting
Bottom
silicates. 2NaOH(g) C SiO2 (s) ! Na2 O SiO2 (l) C H2 O(g) (35.1)
2NaOH(g) C CaO SiO2 (l) ! Na2 O CaO SiO2 (l) C H2 O(g)
(35.2)
Besides converting and consuming the silica crown, these alkaline vapors might also lead to glass defects when the low-melting silicates formed drip along the superstructure side-walls incorporating alumina and zirconia from the AZS refractory side-walls. These alumina- and/or zirconia-enriched silicate phases might result in the formation of crystalline species and/or highly viscous knots that are the source of defects in the glass product. Although the batch blanket occupies only a small part of the volume of a glass melting tank, understanding the reactions and processes taking place during batch melting is of key importance to be able to optimize batch melting in view of energy consumption, emissions, glass quality, and the lifetime of heat recovery systems and the furnace superstructure. Batch melting is an energy-consuming process step, requiring about 8090% of the energy required to produce high-quality glass. Notwithstanding the relatively short time to melt batch in a glass furnace (in the order of 4060 min), the average residence time of container glass in a glass furnace is about 1 day to ensure sufficient glass quality. To support fast batch melting, the major part of the combustion energy is directed to the batch blanket, whereas only a small remaining part is
Batch Chemistry and Reactions
35.1 Overview of the Batch Melting Process
1235
Fig. 35.4 2NaOH(g) + SO2(g) + ½O2(g) → Na2SO4(l,s) + H 2O(g)
Isotherm above which NO Na2SO4 condensation occurs
Deposition of Na2SO4 droplets Isotherm below which Na2SO4 solidifies
Temperature (°C) 500 600 700 800 900 1000 1100 1200 1300
used to keep the glass melt for a sufficiently long time at elevated temperatures ensuring proper fining. Maximizing the glass furnace pull rate (amount of glass pull out of the furnace per time unit), while meeting the everincreasing glass quality requirements and minimizing energy consumption, requires in-depth knowledge of the batch-to-melt conversion and of the heat transfer processes taking place during batch heating. For improved understanding of batch heating and melting, both experimental and modeling research studies have been executed on the various aspects of batch melting, including heat transfer to and in the glass batch [35.3–9], chemical energy demand of glass batches [35.9–12], batch reactions [35.9, 12–22], kinetics of calcination reactions [35.9, 23–27], and dissolution kinetics of silica sand [35.9, 22, 28–33]. To study the occurrence of batch reactions by analyzing the release of gases and the formation of (intermediate) reaction products, a series of different analyzing techniques have been applied, including primarily differential thermal analysis (DTA), thermal gravimetrical analysis (TGA), evolved gas analysis (EGA),
x-ray diffraction (XRD), hot-stage microscopy, scanning electron microscopy with energy-dispersive x-ray spectroscopy (SEM-EDX), and tomography [35.21]. To further reveal, on a quantitative basis, the conversion mechanism(s) and kinetics of batch heating and melting, combining the results of these different techniques and elaborating on detailed (kinetic) batch models is required to be able to make predictions of batch behavior on the industrial scale based on results from the laboratory and/or pilot scale. In this chapter, the different key aspects in the batchto-melt conversion and the different types of reactions occurring in industrial glass production are described. First, the heat transfer mechanisms to the batch are presented. Then, the different types of reactions that can occur in typical industrial batches are detailed. Besides the thermodynamics of glass melting, the key aspects of kinetics of batch reactions are presented, with a specific emphasis on silica (sand) conversion. Finally, the fining reactions (essential in producing a good-quality glass product without bubbles and seeds) are described, for different types of fining agents commonly found in the glass industry.
Part E | 35.1
Na2SO4 droplet formation regime
Simulated condensation and solidification of Na2 SO4 during cooling of flue gases in a regenerator [35.2] with the authorization of CelSian
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Glass Processing
35.2 Heat Transfer Processes
Part E | 35.2
Figure 35.5 shows a schematic overview of the heat transfer processes towards and into a batch blanket. Glass melt flows from the hotspot area downstream towards the batch blanket and transfers heat both via radiation and convection when flowing underneath the batch blanket. The top layer of the glass batch is heated mainly by radiative heat transfer and only to a limited extent by convective heat transfer from the hot flue gases flowing over the batch blanket. For a given batch composition, the heat transfer towards the batch blanket, the subsequent heat penetration to its interior, and the rate of energy consumption by chemical reactions are decisive for the time required for complete batch conversion. The heat flux on both sides of the batch blanket is in the order of 40100 kW=m2 [35.4, 6], depending on the effective radiation temperature and emission coefficient of the combustion space, the batch-, glass-, and foamtemperatures and emissivity, and the temperature of the glass melt flowing underneath the batch blanket. The heat conductivity of a powder batch is low, especially at temperatures below the onset temperature for primary melt formation starting around 800850 ı C for soda-lime-silicate (SLS) glasses (Fig. 35.6). Typical values for heat conductivity in the solid-state regime of glass batches range from 0:20:6 W=.m K/ [35.9]. Starting from the onset temperature of formation of primary melt phases, the thermal heat conductivity of the glass batch increases steeply with temperature to values exceeding 10 W=.m K/ at temperatures beyond 1300 ı C. As the batch blanket has low heat conductivity in the solid-state regime, steep temperature gradients are set over the thickness of the batch blanket. Figure 35.7 shows an example of measured temperature profiles at various times in a batch layer with an initial thickness of about 6 cm which is exposed at t D 0 to high
temperatures on both the top side (combustion space side) and the bottom side (glass melt side) of the batch layer. This figure shows that on both sides of the batch layer the temperature increases steeply with temperature, whereas the temperature of the core of the batch layer remains relatively low over a long period. Only after 24 min does the core temperature of the batch layer reach 1000 ı C. According to this figure, temperature differences of 800 ı C can be observed over a distance of only 2 cm. Above the onset temperature of primary melt phase formation, the heat conductivity of the glass batch starts to increase, resulting in lower temperature gradients at glass batch temperatures of 1000 ı C. As a result of the relatively large differences in heat conductivity values Heat conductivity (W/(m K)) 12 10
Flint glass Fourcault glass Libbey–Owens glass Amber glass Tube glass
8 6
Glass
4 2 Powder batch 0
250
500
750
1000 1250 Temperature (°C)
Fig. 35.6 Heat conductivity versus temperature for a pow-
der batch and glass. After [35.4], with the authorization of Deutsche Glastechnische Gesellschaft
Combustion space 1500 °C Heat transfer Gas release
Reaction zone See Fig. 10 Glass melt layer
Temperature profile Normal batch
Reaction zone
Glass level
See Fig. 10 Glass melt flow Thickness
Heat transferred Glass melt 1400 °C
Fig. 35.5 Schematic overview of the melting process of a batch blanket in a glass furnace. After [35.34], with the authorization of Deutsche Glastechnische Gesellschaft
Batch Chemistry and Reactions
35.2 Heat Transfer Processes
Fig. 35.7 Temperature profile in
Temperature (°C) Glass melt
Batch layer
1400
Combustion space Phase boundary: batch blanket–combustion space
1200
20 800
a batch blanket on top of a glass melt, measured experimentally. The x-axis shows the thickness of the batch layer (between 0 and 60 mm); the glass melt is located at negative x-values. The y-axis shows the batch temperature as a function of position in the batch layer (and glass melt) and time. After [35.34], with permission of the Society of Glass Technology
16 600 12 400
8 4 min
200 Thickness batch layer at t = 0: ±60 mm –20
0
20 60 40 Batch layer thickness (mm)
as a function of temperature, the residence time of batch particles in the solid-state regime (charging temperature up to 800850 ı C) is relatively large compared to the time the converting glass batch remains in the temperature range of 8501300 ı C. According to [35.35], when applying a simple heat transfer model (neglecting the chemical energy demand) to estimate the time required for batch heating and melting for a 10 cm thick batch blanket, batch particles remain in the solid-state regime for about 20 min, whereas the further heating-up to 1200 ı C requires about only 23 min. This results in a total time required for heating and melting (assuming the heat transfer at the batch boundaries is not the rate-limiting step for batch-to-melt conversion) of about 25 min. Figure 35.7 confirms this typical value for batch heating and melting as for a batch thickness of 67 cm about 28 min is required for heating up to a temperature of 1200 ı C. The batch remains for about 20 min in the solid-state regimes and about 8 min in the batch conversion regime. According to Fig. 35.7, typical heating rates in the center of the batch (above 800 ı C) equal about 50 ı C=min, whereas at the batch boundaries the heating rates exceed a few 100 ı C=min. Pelletized batches (batches composed of agglomerated raw materials) show higher heat conductivity values than powdered batches. The increase in heat conductivity is attributed to the larger penetration depth of radiative energy in the batch blanket because of the deeper pores in a pelletized batch. Therefore, the
heating of a batch composed of pellets is enhanced (provided that enough heat is being supplied to the batch) compared to a normal batch. In addition to increased heat conductivity, also the heat transfer from the combustion space into the pelletized batch might be increased [35.4]. The time saving for batch heating and melting when using a pelletized batch instead of a powder batch is in the order of 1015 min. Generally, pelletized batches are prepared by agglomeration of raw materials from a wetted batch using a rotating disk or drum. Envisioned advantages of pelletized batches comprise improved glass quality/homogeneity, enhanced reactivity due to more intense contact between raw material grains, reduced carry-over, and enhanced heat transfer. As an illustration, the CO2 gas releases from three batches with similar compositions, but with different initial grain size distribution and compaction, are shown in Fig. 35.8. It clearly appears that, for a batch of similar composition, the use of finer raw materials promotes the reactions towards lower temperatures. Pelletizing the batch reduces the temperatures at which the reactions take place even further, due to a combination of both better heat transfers and better contact between the different raw materials in the batch. Preheating glass batches gives another possibility to reduce the batch melting time. In the temperature range of the relatively low heat conductivity of a normal batch (20300 ı C), the batch is preheated externally by using the heat content of the hot flue gases.
Part E | 35.2
t = 28 min 24
1000
0
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Glass Processing
CO2 release (arb. u.) Base batch Fine batch Pellets from fine batch
Part E | 35.2
300
400
500
600
700
800
900 1000 1100 1200 Temperature (°C)
Fig. 35.8 CO2 releases for a soda-lime-silicate batch of similar composition, using coarse raw materials (base batch), finer raw materials, and finer raw materials pressed into pellets
A reduced time for batch heating and melting can also be realized by using cullet (internal waste glass or glass waste collected externally via glass recycling bins or other cullet collection systems) in the batch. The reason for this is two-fold: melting of cullet does not require energy for chemical reactions and the heat conductivity of glass is higher than heat conductivity values of powder materials (Fig. 35.9). In addition, as cullet is amorphous it is transparent for radiative heat, in contrast to crystalline raw material components that are opaque for radiation. Therefore, the use of cullet also increases the effective heat conductivity at temperatures where radiative heat transfer becomes predominant over conductive heat transfer. Figure 35.9 shows the temperature-dependent values for the heat diffusivity ˛ (˛ D =. cp /) for three different batches: 1. A batch composed of only raw material components 2. A batch composed of only cullet 3. A batch composed of 50% cullet and 50% raw materials. The heat diffusivity is the quotient of the heat conductivity and the product of the density and heat capacity cp . The thermal diffusivity values have been derived from time-dependent temperature profile measurements similar to those shown in Fig. 35.7. A study by Faber et al. [35.7] concluded that cullet increases the heat conductivity of glass batches and thereby reduces the batch heating time (in the case of cullet fractions exceeding 50%). The impact of cullet on heat conductivity has been shown to be dependent on cullet share, cullet size, and glass color. Cullet enhances the heat
Heat diffusivity (10 –6 m 2/s) 4.5 Cullet 4 50% cullet + 50% batch Normal batch 3.5 3 2.5 2 1.5 1 0.5 0 500 600 700 800 900
1000 1100 1200 Temperature (°C)
Fig. 35.9 Heat diffusivity of glass batches with different
levels of cullet, for TV panel batches (barium strontium silicate glasses). Data from [35.11]
conductivity of glass batches as radiative heat from the combustion space penetrates deeper in the batch blanket compared to opaque batch particles. The penetration of radiative heat by cullet is largest for low-absorbing cullet like flint glass, larger particle size, and increased share of cullet in the batch blanket. Because of the large temperature differences over the thickness of a batch blanket, the type and rate of batch reactions taking place during batch melting are strongly position dependent. The relatively short period within the batch-to-melt conversion zone (compared to the solid-state regime) results in a thin batch-tomelt conversion zone (indicated as a reaction zone in Fig. 35.10) compared to the batch thickness. Whereas the relatively cold core of the batch blanket is composed of solid batch particles surrounded by entrapped air and ascending hot batch gases released during calcination reactions in the bottom part of the batch blanket, the reaction zones are threephase systems comprising primary melt phases, batch gases, and unreacted and undissolved batch particles. During heating of the batch, and as a function of temperature, a series of different types of reactions take place. These batch reactions include water evaporation and dehydration reactions, solid-state reactions, reactive and thermal calcination reactions, melt-phase forming reactions, and reactive and diffusive dissolution processes of slow-dissolving oxides. The rate of the conversion process depends on the kinetics of the governing chemical reactions and the diffusion rates of the slow dissolving oxides in the formed melt phases. Both processes, chemical reactions and diffusion processes, are strongly determined by temperature, local batch composition, local atmosphere composition, and particle grain sizes.
Batch Chemistry and Reactions
a)
b) Bottom of batch blanket
Top of blanket Combustion space: 1500 °C
Melts
Dissolution of sand grains
Sand grains
Loose batch
Gas Carbonates (soda/lime)
Melting reactions
Melting reactions Dissolution of sand grains
Gas Sand grains
Batch
Fig. 35.10a,b Detailed schematic representation of the melting process of batch. These schematics correspond to (a) top side and (b) bottom side of the batch blanket as depicted in the insets of Fig. 35.5. After [35.34], with the permission of Deutsche Glastechnische Gesellschaft
Glass melt: 1400 °C
35.3 Different Types of Batch Reactions As described above, different types of reaction may occur in a glass batch, depending notably on the nature of the raw materials used and the temperatures involved. The different types of reactions in typical industrial soda-lime-silicate glass batches are schematically summarized in Fig. 35.11, and described in the following paragraphs.
35.3.1 Dehydration Reactions Dehydration corresponds to the release of water from the batch. The water may either come from molecular water in hydrated raw materials, or in the form of water adsorbed at the surface of the raw materials or intentionally added to the batch. Indeed, in order to reduce batch segregation during transport and batch charging, water can be added to the batch to a level of 13 wt%. This adsorbed water, i. e., not chemically bound to the
raw materials, evaporates at about 100 ı C. As water evaporation is a highly endothermic process, excess of water in the batch should be prevented to save on energy consumption. It also has to be noted that some raw materials may react with water at low temperatures. In the case of soda ash- or potash-containing batches, water should not be added below 35:4 ı C to prevent hydration of hydrophilic soda ash and potash resulting in segregated lumps in the batch. The bonded water, i. e., the water present in the form of hydrated raw materials such as hydrated soda, kaolin .Al2 O3 2SiO2 2H2 O/, or borax pentahydrate .Na2 O 2B2 O3 5H2 O/, is released at higher temperatures, exceeding the water boiling point (100 ı C). For instance, the use of kaolin in E-glass type batches will lead to dehydration during batch heating at elevated temperatures, in the range of 400700 ı C. The soda-monohydrate .Na2 CO3 H2 O/, which may form by
Dissolution reactions
Formation of primary melt phases Solid-state reactions Dehydration reactions 0
200
400
600
800
Fig. 35.11 Schematic summary 1000
1200 1400 Temperature (°C)
of the reactions occurring during batch-to-melt conversion for a sodalime-silicate glass
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Part E | 35.3
Layer glass melt
35.3 Different Types of Batch Reactions
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Glass Processing
hydration of the soda ash in the batch when the wetting is performed below 35:4 ı C, will dehydrate at about 109 ı C.
35.3.2 Solid-State Reactions
Part E | 35.3
Solid-state reactions refer to reactions between solid raw materials, as for instance the reaction between carbonates in the batch, forming binary or ternary carbonates. In soda-lime-silicate batches, soda ash (Na2 CO3 ) can react with either MgCO3 and/or with limestone (CaCO3 ) to form double carbonates (double-salt). Na2 CO3 (s) C MgCO3 (s) ! Na2 Mg.CO3 /2 Œ300550 ı C
(35.3)
Na2 CO3 (s) C CaCO3 (s) ! Na2 Ca.CO3 /2 Œ550850 ı C
(35.4)
The temperatures between brackets indicate the temperature range at which these reactions predominantly occur. The exact temperature at which these solid-state reactions start to take place depends on the reaction kinetics. Although solid-state reactions might by thermodynamically favored already at low temperatures, the rate of this type of reactions is generally low because of the limited contact area between solid particles and the low diffusion coefficient of reactants (soda ash and MgCO3 or CaCO3 ) through the formed solid-phase reaction product, thus preventing further reaction. The reaction rate of double-salt formation depends on limestone or dolomite particle size and is enhanced by finer limestone, higher CO2 vapor pressure, increased batch humidity, and increased temperature. Next to solid-state reactions with formation of solid species only (e. g., double-salt), solid-state reactions during batch melting leading to the combined formation of a solid product and release of CO2 also occur. These reactions are called calcination reactions. Soda ash can react with silica sand, forming sodium meta-silicate and/or sodium disilicate. Na2 CO3 (s) C SiO2 (s) ! Na2 O SiO2 (s) C CO2 (g)
(TGA). During calcination reactions carbonate raw materials decompose forming CO2 and leaving an oxide behind. One can distinguish both reactive and thermal calcination. Reactive calcination refers to the decarbonation of a raw material by reaction with a different raw material component, for instance the decomposition of soda ash by reaction with silica sand as described by (35.5) and (35.6). As solid-state reactions are generally governed by solid-state diffusion through the formed reaction product, the reactive calcination of soda ash by reaction with silica sand, in the solid-state regime, is limited. Thermal calcination is the decarbonation of raw materials when exceeding the calcination temperature. Thermal calcination of limestone in a CO2 -rich atmosphere occurs at around 910 ı C. CaCO3 (s) ! CaO(s) C CO2 (g)
Dolomite calcination follows a 2-stage reaction mechanism. MgCO3 CaCO3 (s) ! MgO (s) C CO2 (g) C CaCO3 (s) Œ650 ı C (35.8) ı
CaCO3 (s) ! CaO(s) C CO2 (g) Œ910 C
Degree of dolomite calcination 1.0
(35.6)
Because calcination reactions are accompanied with weight loss (release of CO2 ), the kinetics of calcination reactions can be monitored by means of evolved gas analysis (EGA) and thermal gravimetric analysis
in N2
0.8
0.6 in CO2 CaCO3(s) → CaO(s) + CO2(g)
Œ700850 ı C
Na2 CO3 (s) C 2SiO2 (s) ! Na2 O 2SiO2 (s) C CO2 (g) Œ700850 ı C
(35.9)
Similar to the calcination reaction described in the previous paragraph, the reaction rate can be monitored by means of EGA and TGA techniques. Figure 35.12 shows the conversion of dolomite as a function of temperature when heated in both an N2 atmosphere
0.4 (35.5)
(35.7)
MgCO3·CaCO3(s) → MgO(s) + CaO(s) + 2CO2(g)
0.2
0.0 800
MgCO3·CaCO3(s) → MgO(s) + CO2(g) + CaCO3(s)
900
1000
1100
1300 1200 Temperature (K)
Fig. 35.12 Conversion of dolomite as a function of tem-
perature when heated in both an N2 atmosphere and a CO2 atmosphere in the case of a heating rate of 10 K=min (after [35.9])
Batch Chemistry and Reactions
35.3.3 Formation of (Eutectic) Primary Melt Phases The formation of melt phases enhances the batch-tomelt conversion rate because of the higher mobility (diffusion coefficient) of reacting species through the
formed (intermediate) reaction product. In addition, low-viscosity melt phases will flow away from the reacting solid particles, thereby promoting new contact and further reaction between the solid components (Fig. 35.8). A melt phase that is formed can be either a molten pure substance such as soda ash, which melts at 850 ı C, or a melt phase that is formed by eutectic melting of two solid-state components. For instance, the system sodium metasilicate .Na2 O SiO2 / and sodium disilicate .Na2 O2SiO2 / shows a eutectic at about 840 ı C, whereas a eutectic melt phase is already formed at about 800 ı C when sodium disilicate and silica react with each other. Figure 35.13 shows the binary SiO2 -Na2 O phase diagram. The x-axis represents the mole percent of SiO2 in the binary system whereas the y-axis indicates the temperature in ı C. The melting
Temperature (°C) 1700 Cristobalite + liquid
1600
1500
1470°
Liquid 1400
1300
1200
Na2O + liquid
2Na2O · SiO2 + liquid
1100
Tridymite + liquid Na2O · SiO2 + liquid
1000
2Na2O · SiO2 + Na2O · SiO2
Na2O ·2SiO2 + liquid
900
867°
30 NaO2
40
Na2O ·2SiO2 + Na2O · SiO2
50
60
Quartz + liquid Na2O ·2SiO2
Na2O · SiO2
700
2Na2O · SiO2
800
Na2O ·2SiO2 + quartz I II
707° 678°
Fig. 35.13 Binary phase diagram of
III 70
80
90 100 SiO2 (mol%)
SiO2 and Na2 O (after [35.36]) in ı C. The x-axis represents the mole percent of SiO2 in the binary system
1241
Part E | 35.3
and a CO2 atmosphere in the case of a heating rate of 10 K=min. From this figure it can be seen that the decomposition of the MgCO3 part of dolomite is independent of CO2 pressure, whereas the CaCO3 decomposition is retarded with increasing CO2 pressure. On the basis of TGA experiments, the preexponential factor and reaction activation energy of the various calcination reactions occurring during batch conversion can be evaluated.
35.3 Different Types of Batch Reactions
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Part E
Glass Processing
Part E | 35.3
temperatures of the pure species SiO2 , Na2 O 2SiO2 , and Na2 O SiO2 are 1710, 874, and 1089 ı C, respectively. However, mixtures of these crystalline species melt congruently at lower temperatures as shown in Fig. 35.13 and listed in Table 35.1. The onset temperature of primary (eutectic) melt formation decreases with increasing silica content in the sodium silicate phases. Table 35.1 lists eutectic melting points for the melt system composed of SiO2 and Na2 O. Alongside eutectic temperature, the viscosity of the primary melt phase also has an impact on the onset and intensity of the conversion of silica in the aggressive alkaline primary melt phases. Although the onset temperature of primary (eutectic) melt formation decreases with increasing silica content in the sodium silicate phases, the viscosity of these primary phases decreases with increasing alkaline content and thereby lowers the reactivity of the primary melt phase. The double-salt Na2 Ca.CO3 /2 , which is the predominant salt phase formed during batch-to-melt conversion, melts at around 820 ı C and thereby also supports the increase of batch-to-melt conversion. Moreover, because of the salt-like behavior of the double carbonate, the viscosity of the formed melt phase is rather low, further enhancing the conversion rate of silica grains in these primary melt phases. As the onset for batch-to-melt conversion relates to the formation of (pure or eutectic) primary melt phases, two different conversion routes are considered when melting soda-lime-silica batches: the carbonate route and the silica route. The carbonate route is thought to predominate at fast heating rate of the batch ( few 100 ı C=min), whereas with moderate and low heating rates, the silica route is favored. The carbonate route involves the formation of a double carbonate (Na2 Mg.CO3 /2 ) and/or (Na2 Ca.CO3 /2 ) or a triple carbonate (Na2 MgCa.CO3 /3 ), at temperatures below 800 ı C. At about 820 ı C, the most predominant double carbonate Na2 Ca.CO3 /2 melts and forms a low-viscosity high-alkaline melt phase that is highly reactive towards silica grains. The double-carbonate melt phase forms a ternary silicate phase when reacting with silica grains, while releasing CO2 . Table 35.1 Eutectic melting temperatures of different
combinations of Na2 O-SiO2 crystalline species Eutectic melting crystalline species Na2 O 2SiO2 and SiO2 Na2 O 2SiO2 and Na2 O SiO2 2Na2 O SiO2 and Na2 O SiO2
Eutectic melting temperature (ı C) 800 840 1020
It is assumed that reactive soda ash calcination leading to the formation of sodium disilicate takes place when large limestone grains are used and the doublesalt formation is limited. The silica route corresponds to the route where, above 800 ı C, the eutectic melt of sodium disilicate and silica is formed. Upon heating, this melt phase reacts with the remaining soda ash increasing the alkalinity of the primary melt phase, whereas at the same time silica grains further dissolve in the primary melt phases as the SiO2 solubility in these primary melt phases increases with increasing temperature. Because of the low viscosity and the high alkalinity of a double carbonate, the carbonate route is expected to result in faster batch-to-melt conversion compared to the silica route.
35.3.4 Dissolution Reactions At 1200 ı C, most of the batch components have reacted, resulting in a glass melt containing a large amount of batch bubbles and some undissolved raw material components. Generally, the dissolution rates of sand or alumina raw materials in the (primary) melts are the most critical in order to achieve complete batch-freemelt conversion, especially for coarse-grained sand or alumina carriers. The batch-free time, i. e., the time needed to complete the conversion of all raw materials to a melt, is mainly determined by this dissolution process. Undissolved sand grains, and other slow-dissolving batch components, will dissolve further at increased temperature levels into the glass melt. This dissolution process can be compared to dissolution of sugar in water. SiO2 dissolves from the interface of sand particles into the surrounding glass melt. The SiO2 concentration in the glass melt at the interface with the sand particle equals the solubility of SiO2 in this melt at the prevailing temperature. The SiO2 concentration difference at the interface with sand grains and the bulk of the melt phase defines the driving force for sand grain dissolution. As the SiO2 solubility generally increases with temperature, the rate of sand grain dissolution increases with temperature. This increased dissolution rate is also supported by a increased SiO2 diffusion coefficient at higher temperatures as the consequence of a reduced glass melt viscosity. The required dissolution time for the largest sand particles may rise up to several hours, depending on the grain size, the temperature and glass (melt) composition and local convection flows (stirring will decrease the dissolution time).
Batch Chemistry and Reactions
35.4 Reaction Kinetics
1243
35.4 Reaction Kinetics
@ i D k f . i / @t
(35.10)
in which i is the conversion of batch component i, t is time, k is the reaction rate constant, and f . i / is the socalled reaction mechanism function for conversion of batch component i. Table 35.2 lists the main generally applied reaction types and their function f . / derived from the reaction mechanism. Similar to homogeneous gas-phase reaction kinetics, the reaction rate constant k is assumed to be temperature dependent according to the Arrhenius equation k D Ae
Ea RT
Equation (35.12) describes the rate of a heterogeneous reaction both far and close to thermodynamic equilibrium in which kf is the reaction rate of the forward reaction, Keq is the reaction equilibrium constant, Ka describes the ratio of the actual activities of the reactants and the reaction products, ai is the activity of species i, nr is the number of participating reactants, and nrp is the number of reaction products. r D kf f . / Qnrp
Ka avi i 1 ; Keq iD1
nr Y
vj jD1 aj vi iD1 ai
Ka D Q n r
(35.12)
:
(35.13)
The forward reaction of a reversible reaction is favored in case Ka < Keq , whereas the backward reaction is favored in case Ka > Keq . As an example, for the thermal calcination of limestone given by CaCO3 (s) ! CaO(s) C CO2 (g)
(35.14)
(35.11)
in which A is the pre-exponential factor, Ea is the reaction activation energy, R is the gas constant, and T the temperature in K. Equation (35.10) can be regarded as a kinetic equation describing the reaction rate of a heterogeneous reaction which occurs far from thermodynamic equilibrium. To predict the kinetic behavior of a heterogeneous reaction close to thermodynamic equilibrium, the reaction equilibrium has to be taken into account in (35.10). Because of the excessive release of CO2 gas during batch melting, the CO2 vapor pressure in the batch interior will be rather high, thereby affecting the rate of calcination reactions. The actual CO2 vapor pressure has to be taken into account to describe in a quantitative manner batch calcination reactions.
Ka equals the partial CO2 pressure (pCO2 ) as the activities of the pure solid species CaCO3 and CaO equal unity. The reaction rate r is now described by pCO2 ;a : (35.15) r D kf f . / 1 pCO2 ;eq In the case where limestone decomposes by reaction with glass melt components, e. g., SiO2 which is bonded in the glass matrix, the reactive calcination of limestone can be described by CaCO3 (s) C SiO2 (l) ! CaO SiO2 (l) C CO2 (g) (35.16)
and the reaction rate r is given by
Table 35.2 Reaction type and reaction mechanism func-
tion as described in [35.9] Reaction type N-th-order chemical reaction
f ./ .1 /N
1-D diffusion
1 2
2-D diffusion
1 ln.1 /
3-D diffusion (Jander’s type)
1:5.1 /2=3 1.1 /1=3
3-D diffusion (Ginstling–Brounstein type)
1:5 .1 /1=3 1
2-D phase-boundary reaction
2.1 /1=2
1-D phase-boundary reaction
3.1 /2=3
r D kf f . / aSiO2
1
aCaOSiO2 ;a pCO2 ;a aSiO2 ;a pCO2 ;eq
: (35.17)
Activities of the glass melt components SiO2 and CaO SiO2 listed in (35.20) deviate from unity and will affect the reaction rate. The activities of oxide components in glass melt systems depend on composition and temperature and can be calculated using thermodynamic models as described in [35.37, 38]. Generally, decomposition of carbonates is enhanced when the oxide from the carbonate is incorporated in the glass melt during
Part E | 35.4
Batch conversion can be regarded as a heterogeneous process comprising diffusion and chemical reaction processes. Generally, four types of processes are distinguished, i. e., one-dimensional (1-D), two-dimensional (2-D), or three-dimensional (3-D) diffusiongoverned processes, or a chemical reaction-governed process [35.9]. The general equation of the rate of a heterogeneous reaction is given by
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Glass Processing
the calcination reaction. Therefore, cullet has a major impact on batch-to-melt conversion. By preference, sand grains should react with soda ash to limit the amount of residual sand grains, after batch melting, that only slowly dissolve in the glass melt and thereby lengthen the time for complete batch conversion. The
addition of cullet, especially fine cullet, retards the reactivity of glass batches and should be avoided. Large pieces of cullet have only limited impact on preferential consumption of soda ash and have the benefit of increased batch heating rate reducing the overall batch melting time.
Part E | 35.5
35.5 Silica Conversion Quantitative description of sand grain conversion depends on the stage of the batch melting process. Different conversion mechanisms of silica reaction with soda ash have been proposed in the literature. Hrma and Marcial described the dissolution process/reaction of sand grains in mixtures of sand and soda ash by five different stages [35.32]: 1. An initial stage, which is controlled by a surface reaction of sand with soda ash during which a sodium silicate melt phase is formed (i. e., the so-called silica route), which surrounds the sand grain. This phase is generally referred to as the phase of primary melt formation; in the primary melt phase formation stage, three different reactions might occur dependent on the ratio of soda ash and silica. 2Na2 CO3 (l) C SiO2 (s) ! 2Na2 O SiO2 (l) C 2CO2 (g)
(35.18)
Na2 CO3 (l) C SiO2 (s) ! Na2 O SiO2 (l) C CO2 (g)
(35.19)
Na2 CO3 (l) C 2SiO2 (s) ! Na2 O 2SiO2 (l) C CO2 (g)
(35.20)
2. A transient stage, which is controlled by both the surface reaction and nonsteady-state diffusion of reactants and reaction products. During this stage, the thickness of the melt phase around the sand grain increases with time. The transport of reactants and reaction products in the melt phase is determined by diffusion and convective flow of the glass melt surrounding the sand grain. The convection of the glass melt can either be caused by free (buoyancy) convection due to density gradients in the glass melt or by forced convection due to the effect of ascending gas bubbles on the melt. 3. A stationary stage during which the SiO2 concentration at the sand grain interface is in thermodynamic equilibrium with the SiO2 in the sand grain.
4. A disappearance stage, during which the sand grain dissolution is enhanced by the reducing sand grain size. 5. A homogenization stage, during which local variations in SiO2 concentration in the formed melt phase are smoothed out. Beerkens [35.31] defined three sequential stages for silica conversion comprising a reactive stage (similar to the first stage described by Hrma and referred to as the primary melting phase formation stage), a transient, and a quasistationary stage. Beerkens did not provide a detailed quantitative description of the conversion mechanism of sand grains in the reactive stage as extensive research on a fundamental understanding of the mechanism of reactive conversion of silica by reaction with soda ash has so far not resulted in one unambiguous description of this process. Recently, Grynberg et al. [35.22] reported that melting experiments between soda ash and silica below the melting point of Na2 OSiO2 have been the topic of various research studies. Experiments have been performed with different grain sizes, partial CO2 pressures, and bulk compositions leading to nonconsistency in the reaction kinetic parameters. In his recent study, Grynberg systematically studied the progress of the formation of Na2 O SiO2 as a function of atmosphere composition and grain size starting from a mixture of 64 wt% SiO2 and 36 wt% Na2 CO3 (corresponding to a final glass composition of 75% SiO2 and 25% Na2 O). On the basis of the results of the investigation, two reaction mechanisms are proposed. The first mechanism prevailing at low CO2 partial pressure is governed by the thermal decomposition of solid sodium carbonate forming metallic Na (in a dry atmosphere) and/or NaOH vapors (in a wet atmosphere). 1 Na2 CO3 (s) ! 2Na(s) C O2 (g) C CO2 (g) (35.21) 2 Na2 CO3 (s) C H2 O(g) ! 2NaOH(g) C CO2 (g) (35.22)
Batch Chemistry and Reactions
In the presence of SiO2 the sodium vapors recombine to Na2 O SiO2 . 1 SiO2 C 2Na(s) C O2 (g) ! Na2 O SiO2 (s) 2 (35.23)
s
@r D h.m,i wi m,b wb / @t
(35.25)
in which s is the density of the silica grain, r is the radius of the sand grain, t is time, h is the mass transfer coefficient, m,i and m,b are the temperature-dependent densities of the glass melt close to the silica grain surface and in the bulk of the glass melt, and wi and wb are the weight fractions of SiO2 close to the silica grain surface and in the bulk of the glass melt. The mass transfer coefficient h is described by 1 1 1 D C h hr hd
(35.26)
in which hr is the mass transfer coefficient for the reactive conversion of silica, whereas hd is the mass transfer coefficient for the diffusion-controlled conversion of silica. Beerkens did not provide an explicit expression for hr , but proposed an empirical relation for reactive conversion of silica grains based on experimental data of residual crystalline silica as a function of time and temperature obtained by means of laboratory melting trials. The expression for the mass transfer coefficient for the diffusion-controlled conversion of silica is based on available Sherwood relations taking into account free and forced convective flow conditions around the silica grain particles.
35.6 Fining Reactions As described in Chap. 34, the glass melt right after batch-to-melt conversion contains a high amount of dissolved gases and gas bubbles (typically 0:03 mm to several mm in size). The most abundant gases in the melt and/or bubbles typically include CO2 , N2 , O2 , SO2 , Ar, water vapor, CO, and NO. These gases may arise from the different batch reactions described in this present chapter, from melt–refractory interactions, or from the melting atmosphere. From a production point of view, in terms of quality of the final product to be released on the market, it is important to remove as much as possible of the dissolved gases and bubbles. This is achieved by the fining and refining processes, corresponding respectively to the re-
moval of the gas bubbles by ascension to the glass melt surface, and the reabsorption of the remaining dissolved gases in the melt upon cooling before the forming process. Good fining and refining of the melt are crucial steps, and failure to achieve a good degree of bubble and dissolved gas removal can lead to the occurrence of a high level of defects in the final product. In order to promote the fining mechanisms, i. e., the efficient removal of dissolved gases and bubbles, fining agents are added to the batch (amounts typically below 1 wt% in the batch). The goal of the fining agent is to produce fining gases, which will contribute to the removal of the bubbles, at the temperatures at which the glass achieves its lowest viscosity in the melting tank
Part E | 35.6
The degree of conversion for this mechanism is linear with time and the reaction activation energy is in the order of 440490 kJ=mol. The second mechanism, which governs at high CO2 partial pressure, relates to the direct formation of Na2 O SiO2 at the contact point of soda ash and silica grains. For this specific case, the reaction rate is dominated by solid-state diffusion of soda ash and/or silica through the Na2 O SiO2 reaction layer leading to a conversion rate proportional to t0:5 and the reaction activation energy is in the order of 100160 kJ=mol. As local conditions (CO2 partial pressure, particle sizes, and composition) will vary during batch melting, conversion kinetics of soda ash and silica will vary locally. Gouillart et al. [35.21] also studied the reaction between soda ash and silica in the solid-state regime (by means of in situ tomography) and revealed that different reaction paths occur as a function of temperature and local composition. According to Beerkens’ model, in the last two stages, dissolution of silica is governed by diffusion of SiO2 in the surrounding melt phases. In the transient stage, the concentration gradient of SiO2 in the surrounding melt phase strongly depends on time with a high gradient (resulting in relatively fast dissolution)
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in the initial part of this stage and a moderate concentration gradient in the last part of the transient stage. During the quasistationary stage the SiO2 concentration gradient at the silica grain surface is assumed to be constant. Beerkens described the dissolution rate of silica grains by
SiO2 C 2NaOH(g) ! Na2 O SiO2 (s) C H2 O(g) (35.24)
35.6 Fining Reactions
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Part E | 35.6
(i. e., where the temperature is the highest in the melting tank). To be efficient, it should be ensured that all the melt transiting through the continuous melter reaches the level of temperatures required for the fining reactions to occur. The process of high-temperature decomposition of the fining agent in a low-viscosity melt will result in simultaneous bubble growth, gas stripping, and increased bubble ascension rates, allowing for their efficient removal. The efficiency of the fining is dependent on several factors, including the melt composition, redox state, furnace conditions (temperatures, flow patterns, residence time, atmosphere, . . . ), nature and concentration of the fining agent. Therefore, depending on the type of glass produced and on the melting conditions, different fining agents may be used, and fining mechanisms can differ. In the next sections, the principle of fining and the chemistry of the most commonly used fining agents in the glass industry are described.
35.6.1 Bubble Growth and Ascension in Glass Melts The diffusion of gases from the melt into a bubble occurs when the vapor pressure of a given gas in the melt exceeds that of the same gas in the bubble. The bubble will grow if the sum of the equilibrium pressures of the dissolved gases in the melt exceeds the gas pressure in the bubbles. The pressure in the bubble pbubble is given by 2 pbubble D p0 C gH C ; (35.27) r where p0 is the furnace pressure or pressure above the melt (Pa), is the melt density (kg=m3 ), g is the acceleration of gravity (9:81 m=s2 ), H is the height of the glass melt above the bubble (m), is the surface tension of the molten glass surrounding the bubble (N=m), and r is the bubble radius (m). pbubble is the total pressure of all P gases i in the bubble (Pa), according to pbubble D pi [35.39]. The solubility of the gases in the melt usually decreases with increasing temperature, leading to an increase in the internal gas pressure in the melt, and thus increased tendency for these gases to diffuse into the bubbles. Gas release typically occurs when the internal pressure of the gases inside the melt becomes larger than 1 bar. The role of a fining agent is to promote bubble growth by diffusion of the fining gases into the bubbles. With increased bubble size and increased concentration of the fining gases inside the bubble, the partial pressure of the gases initially present in the bubble decreases. This disturbs the equilibrium between the melt and the bubble, consequently leading to further diffusion of this
gas from the melt to the bubble. In other words, the fining gas and the bubble growth induced by the diffusion of the fining gases leads to a dilution of the other gases, and promotes the diffusion of these species from the melt to the bubble. Therefore, the fining agent not only promotes the formation of larger bubbles, but also leads to a stripping of the dissolved gases in the melt. It has to be noted that the composition of the atmosphere above the melt, and especially the water content, can have an influence on the fining process. Indeed, higher water content in the atmosphere will lead to a higher content of water in the melt. During the fining process, part of the water will diffuse into the bubbles, diluting the other gases it contains. This entrains a stronger dilution of the other gases inside the bubble, which in turn leads to an increased diffusion of the other gases into the bubble [35.40–42]. This water dilution effect is well known from the glass industry, in which significant foaming issues were observed when changing the combustion parameters (going from airfuel firing to oxygen-fuel firing, water content in the atmosphere increasing significantly) while keeping the batch recipe constant (including the amount of fining agent). With higher water content in the atmosphere, a higher amount of fining gases was released from the melt due to this dilution effect, leading to an excessive gas release and to foaming. The ascension rate of the bubbles in a glass melt, v , follows Stoke’s law according to the equation [35.43– 45]
vD
cgr2 ;
(35.28)
where v is ascension speed of the bubble in the glass melt (m=s), c is a constant (from Stokes’ law, with c D 2=9), g is the acceleration of gravity (9:81 m=s2 ), is the melt density (kg=m3 ), r is the bubble radius (m), and is the melt viscosity (Pa s). The ascension rate is thus proportional to the square of the bubble radius and inversely proportional to the melt viscosity. In other words, bubble removal will be most efficient for large bubbles in a low-viscosity melt. This is illustrated in Fig. 35.14, where the time required for bubbles with different sizes to ascend by 1 m in a glass is calculated. These calculations are performed for a standard sodalime-silicate container glass (see typical composition in Chap. 34), and assuming constant temperature in the melt across the 1 m of bubble ascension. This graph also highlights the crucial role of the temperature at which the fining agent is active in the melt. If the fining occurs at a too low temperature, i. e., in a highly viscous melt, the efficiency of the fining process will be hindered. Fining agents must be chosen so
Batch Chemistry and Reactions
Time (h) 300 1350 °C 1300 °C 1400 °C 1450 °C 1500 °C
250
200
35.6 Fining Reactions
Fig. 35.14 Calculated time required for a bubble to rise by 1 m in a standard soda-lime-silicate container glass melt, as a function of the bubble size and melt temperature
Part E | 35.6
150
100
50
0 50
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250
300
350
400 450 500 Bubble diameter (μm)
as to lead to the growth of the bubbles in a temperature range where the melt has a low viscosity. Different fining agents are used in the glass industry. These fining agents have different chemistries in glass melts, and different temperature ranges over which they are active (temperature range at which they release gases allowing for bubble growth and faster ascension). Therefore, the choice of the fining agent is made depending on the type of glass melted and/or the melting temperatures in the furnace. In the next paragraphs, three main categories of fining agents are presented, based on the type of fining gas they mainly release: sulfate fining, oxygen fining, and halogen fining.
35.6.2 Sulfate Fining Sulfur-based fining agents are by far the most ubiquitous in the glass industry, sodium sulfate Na2 SO4 (or salt cake) being used for fining of container glass, float glass, E-glass, glass-wool, as well as some tableware, tube, and technical glasses [35.40, 44–46], which represent about 90% of the world glass production (in terms of tonnage). It has to be noted that, while the primary goal of the addition of salt cake to the batch is for fining, this compound also helps to improve melting kinetics by improving reactive dissolution of sand grains and reducing the surface tension of the primary molten phases [35.40, 45, 46]. It is also an oxidizing agent, supplying oxygen to the glass melt. Finally, sulfur can have an impact on the glass coloration. Indeed, the combined presence of reduced sulfur, sulfide S2 and oxidized iron Fe3C , can lead to the formation of the so-called amber chromophore, yielding the characteristic brown color found in many glass bottles.
The sulfate chemistry and the fining onset temperature for sodium sulfate are highly dependent on the redox state of the melt. Na2 SO4 dissolves in the silicate melt and can decompose at high temperatures or may react with reducing components at lower temperature [35.40, 47, 48]. In oxidized melts, thermal sulfate decomposition is often the main sulfate fining mechanism. 1 Na2 SO4 (l) ! Na2 O(l) C SO2 (g) C O2 (g) (35.29) 2 SO2 and O2 are thus the fining gases, while the sodium integrates the melt. This equation can also be rewritten (with O2 : oxygen ion in the melt). 1 2 SO2 4 ! O (l) C SO2 (g) C O2 (g) 2
(35.30)
The temperature at which this reaction takes place (fining onset temperature) is typically in the 14301480 ı C range in soda-lime-silicate glass melts. Part of the sodium sulfate may react at lower temperatures with sand grains still undissolved in the melt. Na2 SO4 C nSiO2 (s) 1 ! Na2 O .SiO2 /n C SO2 (g) C O2 (g) (35.31) 2 This reaction typically occurs at temperatures of 1100 ı C or higher, and can lead to early SO2 and O2 release in the oxidized melt. In the presence of reducing components (e. g., cokes, CO, organic contamination), some sulfate will react to produce sulfides (S2 , written as sodium sulfide
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Na2 S in the following equations). Examples of reactions leading to the formation of sulfides include 2C C Na2 SO4 ! 2CO C Na2 S 4CO C Na2 SO4 ! 4CO2 C Na2 S 4C C Na2 SO4 ! 4CO C Na2 S
(35.32) (35.33) (35.34)
Part E | 35.6
The formation of sulfides in the melt occurs at relatively low temperature, typically around 700800 ı C. The sulfides formed may then react with the remaining sulfates via sulfate-sulfide reactions (S2 C 3SO2 4 ! 4SO2 C4O2 ). Examples of sulfide-sulfate reactions include Na2 S C 3Na2 SO4 C xSiO2 ! .Na2 O/4 .SiO2 /x C 4SO2 (g)
(35.35)
xNa2 S C yNa2 SO4 C pSiO2 y 3x O2 ! .Na2 O/.xCy/ .SiO2 /p C .x C y/SO2 C 2 (35.36)
These reactions typically occur in the temperature interval 10001350 ı C. Fining occurs thus at lower temperatures in reduced melts as compared to oxidized melts. Sulfates can also react directly with reducing agents in the 9001100 ı C range. C C 2Na2 SO4 C mSiO2 ! CO2 C 2SO2 C .Na2 O/2 .SiO2 /m
(35.37)
CO C Na2 SO4 C nSiO2 ! CO2 C SO2 C .Na2 O/ .SiO2 /n
(35.38)
Note that in most of the reactions occurring in reduced melt, only SO2 is acting as a fining gas, while in oxidized conditions sulfates lead to the production of both SO2 and O2 as fining gases. Concentration CO2 (vol%) 10 CO2 CO SO2 O2
8
In very reduced conditions (i. e., in the case of addition of large amounts of reducing agents in the batch, and/or presence of a high amount of organic impurities), other reactions may take place, leading to the formation of other fining gases such as S2 (3S2 C SO2 4 ! 2S2 C 4O2 ), for instance 3Na2 S C Na2 SO4 C qSiO2 ! .Na2 O/4 .SiO2 /q C 2S2 (g)
(35.39)
The mechanisms described above highlight the importance of the redox and its influence on fining, especially in the case of sulfate fining. Indeed, the redox state of the melt will influence the fining onset temperature and the extent to which all these reactions (and sequence of reactions) will take place. The more reduced the melt, the lower the temperatures at which the fining will take place. In the same manner, it is possible to tune the temperature at which the fining takes place by controlling the redox of the melt (addition of reducing or oxidizing agents). Therefore, sulfate fining can be efficient in a large range of temperatures, i. e., for a large range of products, explaining its popularity in the glass-making industry. Figures 35.15 and 35.16 show the gas evolution from soda-lime-silicate glasses containing sodium sulfate as fining agent, but with different redox states: oxidized (Fig. 35.15) versus reduced (Fig. 35.16). On these figures are represented the concentrations of the gases evolved from the batch and melt and entrained in a carrier gas purging the surface of the crucible in which the batch is melted [35.49]. The melting is done with a constant heating ramp from room temperature up to 1550 ı C. The graphs show the evolution of the gases CO2 (from the carbonate raw materials), CO (mainly from organic contamination and reducing agents), SO2
Concentration CO and SO2 (vol. ppm) 1000
Thermal sulfate decomposition
6
800
600 Sulfide–sulfate reaction
4
400
2
200
0 500
600
700
800
900 1000 1100 1200 1300 1400 1500 Temperature (°C)
0
Fig. 35.15 Gas evolution from an oxidized soda-lime-silicate glass containing sodium sulfate as fining agent
Batch Chemistry and Reactions
Concentration CO2 (vol%) 10 CO2 CO SO2
8
Concentration CO and SO2 (vol. ppm) 1000 Sulfide–sulfate reaction
0 500
Fig. 35.16 Gas evolution from
a reduced soda-lime-silicate glass containing sodium sulfate as fining agent
600
400
Direct reaction sulfate with reducing component
600
700
800
Part E | 35.6
2
1249
800
6
4
35.6 Fining Reactions
200
900 1000 1100 1200 1300 1400 1500 Temperature (°C)
and O2 (from the fining agent). It can be seen that while the CO2 evolution is similar in both cases, significant differences can be observed for the evolution of the other gases. The oxidized batch (Fig. 35.15) shows significantly lower CO release, due to a lower initial amount of reducing components. Note that, as the amount of carbonates introduced in SLS batches is typically much higher (in the order of several wt%) than the amount of fining agent (typically below 1 wt%), the amount of CO2 released from the batch and melt is higher than the amount of fining gases released. Thus, to facilitate the reading of Figs. 35.15 and 35.16, the concentrations of CO2 and that of the other gases (CO, O2 , and SO2 ) are expressed in different units (vol.% and vol. ppm, respectively) and shown on different axes on these figures. The release of the fining gases SO2 and O2 from the melt is also significantly impacted by the glass redox. In the case of the reduced melt (Fig. 35.16), part of the sulfur is released starting at around 900 ı C, and most of the SO2 release occurs between 1100 and 1400 ı C, due to sulfide–sulfate reactions. In the case of the oxidized batch, while some SO2 release occurs in the 11001350 ı C range due to sulfide–sulfate reactions, a significant amount of SO2 is released around 1450 ı C due to thermal sulfate decomposition (not observed in the reduced batch). The SO2 release is also correlated to O2 release in the case of the oxidized melt. The comparison between Figs. 35.15 and 35.16 clearly highlights the shift of fining gas release towards lower temperatures with more reduced batches. For sulfate fining, the control of the redox is of utmost importance, and disturbances such as unexpected introduction of organic impurities in the batch can have a dramatic impact on the fining behavior of a melt. The optimal fining range depends on the glass produced and
0
can be optimized (to a certain extent) by controlling the redox (addition of oxidizing or reducing agents). Fining being related to the partial pressure of the gases in the melt, the fining onset temperature will also be influenced by the initial amount of the fining agent introduced in the glass. This is illustrated in Fig. 35.17 for float glass melts with different initial amounts of sulfate added. It can clearly be seen that, with higher initial sulfate addition, the temperature at which the pressure of the fining gas reaches 1 bar (the fining onset) is shifted towards lower temperatures. It has to be noted that sulfur coming from cullet (when the cullet contains dissolved sulfur) also contributes to the fining of the melt, and must be taken into account when calculating the initial amount of fining agent to be added to the batch. Pressure (bar) 3 0.25 wt% SO3 2.5 0.5 wt% SO3 0.75 wt% SO3 2 1.5 1 0.5 0 1550
1600
1650
1700
1750
1800 1850 Temperature (K)
Fig. 35.17 Total fining gas pressure in dry-oxidized molten
float glass melt due to decomposition of sulfate for three different sulfate concentration levels. Reprinted from [35.47], Copyright (2003), with permission of Wiley
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Fig. 35.18 Sulfur retention (SO3
Sulfur retention (wt%)
in glass) in a sulfate-fined sodalime-silicate glass after melting at 1400 ı C in different redox conditions. The redox state is expressed as the logarithm of the oxygen partial pressure in the melt at 1400 ı C. For indication only, approximate values of the corresponding batch redox number and Fe2C =Fetotal ratio in the final glass are also given
0.8 0.7 0.6 0.5
Part E | 35.6
0.4 0.3 0.2 0.1 0 –8
–7 –30
–6 –20
80
–5 –10 70
–4 0 60
–3 +10 40
–2
–1 log pO2 +20
25
Batch redox number
15 Fe2+/Fe tot (%) in final glass
Besides fining temperatures, the sulfur solubility in the melt also depends on its redox state. As illustrated in Fig. 35.18, the sulfur retention in SLS glass melts (expressed as wt% SO3 retained in the melt after melting and fining) is the highest for very oxidized (high partial pressure of oxygen pO2 in the melt, high batch redox number, low Fe2C =Fetotal ratio in the glass), or very reduced glasses (low partial pressure of oxygen pO2 in the melt, low batch redox number, high Fe2C =Fetotal ratio in the glass), and reaches a minimum in the intermediate range. While sulfur is retained in the glass as sulfate 2 (SO2 4 ) in oxidized glasses, it is present as sulfide (S ) in very reduced glasses. In the intermediate range, it may be present in both forms, leading to sulfide–sulfate reactions and thus increased amount of sulfur release from the melt (thus decreased retention). Sulfur may also be present as sulfite (SO2 3 ) in this redox range, though this species shows less stability than sulfides and sulfates in glass melts. The color of amber glasses (and colored glasses including an amber component, such as antique or olive greens) can only be obtained when sulfides are present in the glass (for SLS glasses) [35.44, 46, 48, 50]. Therefore, these glasses are melted in relatively reduced conditions, and typically have a Fe2C =Fetotal ratio of 0:650:85. For these glasses, the fining occurs thus at relatively low temperatures as compared to oxidized glasses, and they typically present low levels of retained sulfur. For these glasses, pyrite (FeS2 ) or blast furnace slags (generally containing high amounts of sulfides) are sometimes employed as fining agents instead of sodium sulfate.
In some cases, e. g., when addition of sodium to the glass is not acceptable, gypsum .CaSO4 2 H2 O/ or barium sulfate (BaSO4 ) can be used as an alternative to salt cake. While the use of sulfate-based fining agents is appropriate for numerous types of glasses (soda-limesilicate and some borosilicates) due to the large range of fining temperatures they allow, up to 14501500 ı C, they may have limited or no efficiency for glass types requiring melting temperatures higher than 1550 ı C such as hard borosilicates and alumino-silicates. For these high-melting glasses, sulfate fining would lead to the release of the fining at temperatures where the melt viscosity is relatively high. As an illustration, the time required for a bubble to rise by 1 m in a glass melt in a Pyrex® -type glass as compared to a soda-lime-silicate (SLS) container glass is shown in Fig. 35.19. At similar temperatures, the time required for the bubble to rise is significantly higher for the Pyrex® -type glass, even for relatively large bubbles. For this type of glass, other fining agents have to be used. Typical high-temperature fining agents employed include halide salts, tin oxide, or cerium oxide.
35.6.3 Halide Fining The chemistry of halide fining differs quite significantly from that of sulfate fining. The solubility of halide in glass is limited, and decreases with decreased amount of alkali in the melt. It is significantly lower in neutral borosilicate glasses (Pyrex® -type glasses) as compared to soda-lime-silicate glasses, and even lower in hard
Batch Chemistry and Reactions
35.6 Fining Reactions
Fig. 35.19 Calculated time required
Time (h) 300
for a bubble to rise by 1 m in a standard soda-lime-silicate container glass melt (SLS, solid lines) and a Pyrex® -type glass melt (dashed lines), as a function of the bubble size, at 1400 and 1500 ı C
1400 °C 1400 °C 1500 °C 1500 °C
250
200
Part E | 35.6
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1251
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150
200
250
300
350
400 450 500 Bubble diameter (μm)
borosilicates (alkali-lean borosilicates such as E-glass). When an excess of halide is added to the melt, phase separation occurs, and a phase consisting mainly of one or more halide salts is formed. When in excess, the halide salt vapor pressure from the melt is almost the same as the pure compound, and above a certain temperature, when its vapor pressure exceeds 1 bar, it evaporates and entrains the fining effect in the melt. The fining action is therefore not based on a dissociation reaction, but on the evaporation of the pure halide salt out of the melt. The fining onset temperature, i. e., the temperature at which the halide salt starts to evaporate, depends on its concentration in the melt, the glass composition (mainly its alkali content), and on temperature. Sodium chloride, NaCl, is the most used halide salt as fining agent in glass-making. The fining onset temperature as a function of the chlorine content in the melt is shown in Fig. 35.20, for a ternary soda-lime-silicate (16Na2 O-10CaO-74SiO2 , in wt%), a neutral borosilicate (Pyrex® -type), and a hard borosilicate (alkali-lean borosilicate) glass [35.51]. It can be seen from this graph that relatively low amounts of chloride in the melt are required for the fining of the borosilicate glasses, for a fining action in the 15001650 ı C range, i. e., in the temperature range at which these glasses are melted in industrial melting tanks. It can also be seen that for SLS glasses, an initial amount of more than 1:5 wt% of chlorine would be necessary to obtain fining around 1450 ı C. Therefore, for these glasses, sulfate fining is more appropriate. Other halide salts could be used, such as NaBr and NaI. The solubility of these salts in glass melts
Temperature (°C) 1750 Hard borosilicate Neutral borosilicate SLS glass
1700 1650 1600 1550 1500 1450 1400
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4 1.6 Cl (wt%)
Fig. 35.20 Calculated fining onset temperature as a function of chlorine content in the glass melt for an SLS glass, a neutral borosilicate, and a hard borosilicate for pNaCl D 1 bar. Adapted from [35.51]
decreases with increasing ionic radius of the halide, namely ŒI < ŒBr < ŒCl . As a consequence, lower amounts of NaI would be required as compared to NaCl in order to obtain the same fining onset temperature [35.51]. However, the use of iodine and bromine would lead to potential environmental issues, the authorized amounts for the release of these halides being often strongly restricted. The emission of chlorides, while being less strictly limited than bromides and iodides, are still a challenge for glass industrials. Indeed, the chlorine evaporated during fining may react upon cooling of the flue gases to form the highly corrosive HCl gas.
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It may also react with sulfates and oxygen, leading to increased particulate emissions, according to the following equation. 1 2NaCl C SO2 C H2 O C O2 2 ! Na2 SO4 .particulates/ C 2HCl
(As2 O3 ) is added in combination with oxidants, e. g., nitrates (NaNO3 ) to convert trivalent arsenic into pentavalent arsenic which will be dissolved into the melt as As2 O5 . 5As2 O3 C 4NaNO3 ! 5As2 O5 C 2Na2 O C 2N2
(35.40)
Part E | 35.6
The HCl formed can be highly corrosive to the furnace environment as well as to the mold material (metallic molds) used in the forming processes. Because of this high corrosiveness, combined with the higher temperatures required for the fining of glasses using halides as a fining agent—which are usually higher than the temperatures encountered in SLS glass production, making the furnace environment even harsher—furnaces producing chlorine-fined glasses generally have a shorter lifetime than those that produce sulfate-fined glasses. The furnaces producing halide-fined glasses (usually considered as special glasses) have typical lifetimes of 57 years. SLS furnaces, running at lower temperatures and in which the SO2 and O2 gases released are less corrosive than HCl, have lifetimes spanning typically over more than 10 years, sometimes up to 18 to 20 years [35.44]. It has to be noted that a significant part of the chlorine added in the mix of raw materials may evaporate directly from the batch, especially in furnaces with flame combustion. The initial amount of fining agent must therefore be adjusted to compensate for this evaporation and ensure a sufficient fining of the melt. The use of electric furnaces (cold-top furnaces) allows for a reduction of this phenomenon and reduced chlorine addition to the batch.
35.6.4 Oxygen Fining The fining agents used for oxygen fining rely on the reduction of the fining agent at high temperature, leading to the release of oxygen. These fining agents are therefore introduced in the batch in their oxidized form, usually in combination with oxidizing agents in order to maintain the high oxidation state of the fining agent up to high temperatures. Different types of fining agents relying on oxygen release are used in the glass industry. Depending on the nature of the compound, the temperature range at which the fining will take place varies. Arsenic and Antimony Oxides Arsenic oxide is an important fining agent up to a temperature of 14001500 ı C for glasses being melted under strongly oxidizing conditions. Arsenic trioxide
(35.41)
Arsenates (arsenic in 5C valence state) can also be used. During fining, in the molten glass, at temperatures exceeding 1250 ı C, oxygen gas starts to be formed, creating arsenic(III) oxide. As2 O5 ! As2 O3 C O2 (g)
(35.42)
Arsenic oxide was the compound of choice for the fining of art glass (e. g., crystal glass) and some optical glass. However, more stringent environmental restrictions have led to a strong reduction of its applications in the glass industry. Arsenic oxide has notably been placed on the list of substances of very high concern (SVHCs) by the European Chemical Agency (ECHA), in the framework of the REACH (registration, evaluation, authorization, and restriction of chemicals) regulations, and its use in production prohibited in Europe after March 2015 (exceptions can be made by authorities in some specific cases, for specific applications). Arsenic oxide use as a fining agent is still authorized in other parts of the world, such as Asia. Given the increasingly strict regulations on this fining agent, arsenic oxide has been partly replaced by antimony oxide, though the quality (notably optical quality) of the antimony-fined glasses is lower than arsenic-fined glasses [35.52]. The fining principle for antimony oxide is similar to that of arsenic oxide, and it is also applied together with an oxidant. Sb2 O5 ! Sb2 O3 C O2 (g)
(35.43)
The temperature range for the redox reaction leading to the release of oxygen as a fining gas is lower than for arsenic oxide. Tin Oxide and Cerium Oxide The reduction reaction leading to the release of oxygen when tin oxide (SnO2 ) is added to the melt (together with oxidizing agents) occurs at higher temperatures than arsenic and antimony oxides. The oxygen release typically occurs in the 15001630 ı C range. 1 SnO2 ! SnO C O2 (g) 2
(35.44)
Batch Chemistry and Reactions
1 2 CeO2 ! Ce2 O3 C O2 (g) 2
(35.45)
35.6.5 Impact of Cullet and Raw Material Composition Fining agents are added on purpose to the batch to lead to the release of gases in the melt and remove bubbles and seeds arising from the batch-melting reactions. Some of the compounds described in the previous sections may enter the batch as impurities in the raw materials, or from the cullet used in the batch (which may represent a significant fraction of the batch). Indeed, cullet corresponds to recycled glass and every element it contains will be introduced to the glass melt. The most abundant type of glass found on the market is soda-lime-silicate glass and when recycled (SLS glasses being typically sulfate-fined), such cullet can add a significant amount of sulfur to the batch. Thus, when a piece of recycled SLS glass re-enters a batch as cullet, the sulfur it contains will enter the melt, and can assume an active role in the fining processes. As illustrated in Fig. 35.18, SLS glasses can retain a significant amount of sulfur. The amount of sulfate retained as well as the oxidation state of the sulfur retained depend strongly on the redox state of the glass and on its melting temperature. Therefore, a given amount of cullet may not bring the same amount of sulfur nor the same balance of sulfur redox species (ratio of sulfates and sulfides in the glass). Oxidized glasses such as clear glass have a higher concentration of retained sulfur (retained as sulfates) than reduced amber glasses (sulfur retained as sulfides). This has several consequences when considering fining of glasses melted from a batch containing a large amount of cullet:
For a given quantity of cullet in a batch, a higher amount of sulfur will come from the cullet if using only clear glass cullet, and thus lower amounts of sodium sulfate would need to be introduced to have the right amount of sulfur required to properly fine
the glass. If, for the same glass melted under the same conditions, only amber cullet was used, less sulfur would come from the cullet, and more of the fining agent would have to be added. For batches containing a mix of oxidized and reduced cullet, then the cullet will bring a mix of sulfides and sulfates. As described in (35.35) and (35.36), sulfates and sulfides can react together at relatively low temperatures to lead to the formation of SO2 and thus participate in the release of gases in the melt. Thus, the cullet mix used will also have an influence on the temperatures at which the fining gases are released. The redox state of the cullet introduced will also have an impact on the redox state of the glass produced from it—which will influence the sulfate— and thus the fining chemistry. Thus, variations in cullet quantities and redox conditions will have a strong impact on the fining behavior of a given glass melt, and control of the cullet is a major challenge for the glass industry. One must keep in mind that cullet can be the main raw material used in some industrial glass batches, and that SLS furnaces typically produce several hundreds of tons of glass per day (thus using several hundreds of tons of cullet on a daily basis). In addition, cullet may bring some organic contamination, which will reduce the melt, which will in turn impact the sulfate fining chemistry. Glass producers may introduce oxidizing agents to their batch to counter the impact of organic contamination, but as the amount of organic contamination present in the cullet may fluctuate over time, defining the proper amount of oxidizing agent to maintain a given redox state is challenging [35.57].
Cullet can also contain some of the other elements that are typically used as fining agents, such as halogens (chlorine, fluorine), arsenic, or antimony. In the same manner, some of these elements (e. g., halogens, sulfur) can be found as impurities in the raw materials. The concentration of these elements is typically small (in the order of some tens to some hundreds of ppm in most cases), and therefore their impact on the fining mechanisms is usually limited, if not negligible. However, these may be released from the batch and/or melt, and lead to emissions from the furnace. As the regulations on emissions are stringent, while the impact of these impurities on fining may be limited, they may still pose serious challenges to the glass producers, who need to implement emission-reduction strategies to limit their release to the environment. More details on environmental concerns can be found in Chap. 34.
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Tin oxide is often used for the fining of alkali-free high-melting glasses, such as LCD glasses [35.53] or aluminosilicates [35.54]. For these glasses, the need to avoid any alkali in the glass prevents the use of NaCl as the fining agent. It has to be noted that, for the different fining agents based on the release of oxygen, other oxides of polyvalent cations may be added to the melt which can also contribute to fining, such as cerium oxide (CeO2 ) [35.55, 56].
35.6 Fining Reactions
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35.7 Conclusions
Part E | 35
Batch-to-melt conversion is a crucial step in industrial glass production. It results from a complex sequence of reactions, including dehydration reactions, solid-state reactions, formation of primary melt phases, and dissolution of the more refractory raw materials such as sand or alumina. The reactions taking place depend on the composition of the batch and thermodynamics, but also on kinetics. The heat transfers to the batch therefore play a key role in the conversion of the batch into a melt free of undissolved particles. Following the batch-to-melt conversion, the glass melt will contain a high amount of dissolved gases and bubbles, which must be removed in order to obtain a glass article of sufficiently good quality to be commercialized. Proper fining is thus an essential step in the glass-making process. Fining also involves spe-
cific chemical reactions, in which the choice of the right fining agent, the temperatures involved, and the glass redox play a major role. A proper batch-to-melt conversion, and a good sequence of the different reactions in the time during which the melt resides in the furnace, will define the quality of the product. As highlighted in this chapter, the different reactions taking place in the batch and in the melt can also have a significant impact on other aspects of glass melting, such as foaming, carry-over, or corrosion of refractories. Batch-to-melt conversion and related reactions occurring at different places in an (industrial) glass furnace are still major topics of investigation in the glass industry. Significant efforts are exerted by the glass producers in order to allow for faster, cheaper, and/or less energy-demanding glass production.
References 35.1
35.2
35.3
35.4 35.5
35.6
35.7
35.8
35.9
35.10 35.11
35.12
D. Dollimore, J.G. Dunn, Y.F. Lee, B.M. Penrod: The decrepitation of dolomite and limestone, Thermochim. Acta 237(1), 125–131 (1994) O.S. Verheijen, A. Habraken, A. Lankhorst, H. Gramberg, S. Lessmann, M. van Kersbergen: Detailed modeling of glass furnace regenerators. In: 12th ESG Conf., Parma (2014) C. Kröger, H. Eligehausen: Über das Wärmeleitvermögen des einschmelzenden Glasgemenges, Glastech. Ber. 32(9), 362–373 (1959) M. Daniels: Einschmelzverhalten von Glasgemengen, Glastechnische Berichte 46(3), 40–46 (1973) P. Costa: Untersuchung des Einschmelzverhaltens von pelletiertem Gemenge zur Glasherstellung, Glastech. Ber. 50(1), 10–18 (1977) W. Trier, K.L. Loewenstein: Glass Furnaces: Design, Construction and Operation (Society of Glass Technology, Sheffield 1987) A.J. Faber, R.G.C. Beerkens, H. de Waal: Thermal behaviour of glass batch on batch heating, Glastech. Ber. 65(7), 177–185 (1992) R. Conradt, P. Suwannathada, P. Pimkhaokham: Local temperature distribution and primary melt formation in a melting batch heap, Glastech. Ber. 67(5), 103–113 (1994) O.S. Verheijen: Thermal and Chemical Behavior of Glass Forming Batches, Ph.D. Thesis (Technical Univ. Eindhoven, Eindhoven 2003) C. Kröger: Theoretischer Wärmebedarf der Glasschmelzprozesse, Glastech. Ber. 26(7), 202–214 (1953) R. Conradt, P. Pimkhaokham: An easy-to-apply method to estimate the heat demand for melting technical silicate glasses, Glastech. Ber. 63, 134–143 (1990) C. Madivate, F. Muller, W. Wilsmann: Thermochemistry of the glass melting process—Energy require-
35.13 35.14
35.15
35.16
35.17
35.18
35.19
35.20
35.21
ment in melting soda-lime-silica glasses from cullet-containing batches, Glastech. Ber. 69(6), 167– 178 (1996) C. Kröger: Gemengereaktionen und Glasschmelze, Glastech. Ber. 25(10), 307–324 (1952) F.W. Wilburn, S.A. Metcalfe, R.S. Warburton: Differential thermal analysis, differential thermogravimetric analysis, and high temperature microscopy of reactions between the major components of a sheet glass batch, Glass Technol. 6(4), 107–114 (1965) K. Kautz, G. Stromburg: Untersuchungen der Vorgänge beim Einschmelzen von Glasgemengen im Gadrientofen, Glastech. Ber. 42(7), 309–317 (1969) P. Hrma: Reaction between sodium carbonate and silica at 874 °C < T < 1022 °C, J. Am. Ceram. Soc. 68(6), 337–341 (1985) C.A. Sheckler, D.R. Dinger: Effect of particle size distribution on the melting of soda-lime-silica glass, J. Am. Ceram. Soc. 73(1), 24–30 (1990) K.S. Hong, R.E. Speyer: Thermal analysis of reactions in soda-lime silicate glass batches containing melting accelerants: I, One- and two-component systems, J. Am. Ceram. Soc. 76(3), 598–604 (1993) K.S. Hong, S.W. Lee, R.E. Speyer: Thermal analysis of reactions in soda-lime silicate glass batches containing melting accelerants: II, Multicomponent systems, J. Am. Ceram. Soc. 76(3), 605–608 (1993) L. Stoch, S. Kraishan: Interface phenomena accompanying the early stages of glass batch reactions: A model study, Glastech. Ber. 70(10), 298–305 (1997) E. Gouillart, M.J. Toplis, J. Grynberg, M.-H. Chopinet, E. Sondergard, L. Salvo, M. Suéry, M. Di Michiel, G. Varoquaux: In situ synchrotron microtomography reveals multiple reaction path-
Batch Chemistry and Reactions
35.22
35.23
35.25
35.26
35.27
35.28
35.29 35.30
35.31
35.32
35.33
35.34
35.35 35.36
35.37
35.38
35.39
35.40
35.41
35.42 35.43
35.44
35.45
35.46
35.47
35.48
35.49
35.50
35.51
35.52
35.53
35.54
35.55
R.G.C. Beerkens: Modeling of the melting process in industrial glass furnaces. In: Mathematical Simulation in Glass Technology, ed. by D. Krause, H. Loch (Springer, Berlin Heidelberg 2002) pp. 17–72 R. Beerkens: Sulphur chemistry and sulphate fining and foaming of glass melts, Glass Technol. 48(1), 41–52 (2007) A.J. Faber, O.S. Verheijen, J.M. Simon: Redox and foaming behavior of e-glass melts. In: Advances in Fusion Processing of Glass III, ed. by J.L. Vorner, T.P. Seward III, H.A. Schaeffes (American Ceramic Society, Westerville 2004) pp. 71–82 P. Laimbock: Foaming of Glass Melts, Ph.D. Thesis (Technical Univ. Eindhoven, Eindhoven 1998) J.E. Shelby: Introduction to Glass Science and Technology, 2nd edn. (Royal Society of Chemistry, London 2005) B.M. Scalet, M.G. Munoz, A.Q. Sissa, S. Roudier, L.D. Sancho: Best Available Techniques (BAT) Reference Document for the Manufacture of Glass, JRC Reference Report (European Commission, Brussels 2013) R. Falcone, S. Ceola, A. Daneo, S. Maurina: The role of sulfur compounds in coloring and melting kinetics of industrial glass, Rev. Mineral Geochem. 73(1), 113–141 (2011) M. Hujova, M. Vernerova: Influence of fining agents on glass melting: A review, Part 1, Ceramics-Silikaty 61(2), 119–126 (2017) R.G.C. Beerkens: Sulfate decomposition and sodium oxide activity in soda–lime–silica glass melts, J. Am. Ceram. Soc. 86(11), 1893–1899 (2003) R.G.C. Beerkens, K. Kahl: Chemistry of sulphur in soda-lime-silica glass melts, Phys. Chem. Glass. 43(4), 189–198 (2002) M. Rongen, M. Hubert, P. Marson, S. Lessmann, O. Verheijen: Laboratory facilities for simulation of essential process steps in industrial glass furnaces. In: 75th Conf. Glass Probl. (Wiley, Hoboken 2015) pp. 223–234 P.C. Ross, D.D. Myers: Amber glass—40 years of lessons learned. In: The 66th Conf. Glass Probl. (Wiley, Hoboken 2008) pp. 129–139 D. Kopsel: Solubility and vaporization of halogenides, Glastech. Ber. Glass Sci. Technol. 73(C2), 43–49 (2000) P. Hartmann: EU regulations threaten availability of raw materials for optics, https://spie.org/ membership/spie-professional-magazine/spieprofessional-archives-and-special-content/2014_ april_archive_spie_pro/euro-regulations?SSO=1 (2014) K.D. Kim, H.K. Kim: Redox behavior of Sn and S in alkaline earth borosilicate glass melts with 1 mol% Na2 O, J. Korean Ceram. Soc. 46(3), 271–274 (2009) M.J.M. Comte: Aluminosilicate glasses with improved fining behaviour, Patent US 8722554 B2 (2014) V.V. Vargin, G.A. Osadchaya: Cerium dioxide as a fining agent and decolorizer for glass, Glass Ceram. 17(2), 78–82 (1960)
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35.24
ways during soda-lime glass synthesis, J. Am. Ceram. Soc. 95(5), 1504–1507 (2012) J. Grynberg, E. Gouillart, M.-H. Chopinet, M.J. Toplis: Importance of the atmosphere on the mechanisms and kinetics of reactions between silica and sodium carbonate, Int. J. Appl. Glass Sci. 6(4), 428–437 (2015) P.K. Gallagher, D.W. Johnson: The effects of sample size and heating rate on the kinetics of the thermal decomposition of CaCO3 , Thermochem. Acta 6, 67– 83 (1973) P.K. Gallagher, D.W. Johnson: Kinetics of the thermal decomposition of CaCO3 in CO2 and some observations on the kinetic compensation effect, Thermochem. Acta 14, 255–261 (1976) J.M. Criado, A. Ortega: A study of the influence of particle size on the thermal decomposition of CaCO3 by means of constant rate thermal analysis, Thermochem. Acta 195, 163–167 (1992) M. Olszak-Humienik, J. Mozejko: Kinetics of thermal decomposition of dolomite, J. Thermal Anal. Calorim. 56, 829–833 (1999) B.V. L’vov: Mechanism and kinetics of thermal decomposition of carbonates, Thermochem. Acta 386, 1–16 (2002) D.W. Ready, A.R. Cooper: Molecular diffusion with a strong moving boundary and spherical symmetry, Chem. Eng. Sci. 21, 917–922 (1966) M. Muhlbauer, L. Nemec: Dissolution of glass sand, Am. Ceram. Soc. Bull. 64(11), 1471–1475 (1985) L. Bodalbhai, P. Hrma: The dissolution of silica grains in isothermally heated batches of sodium carbonate and silica sand, Glass Technol. 27(2), 72– 78 (1986) R.G.C. Beerkens, H.P.H. Muijsenberg, T. van der Heijden: Modelling of sand grain dissolution in industrial glass melting tanks, Glastech. Ber. Glass Sci. Technol. 67, 179–188 (1994) P. Hrma, J. Marcial: Dissolution retardation of solid silica during glass-batch melting, J. Non-Cryst. Solids 357, 2954–2959 (2011) P. Hrma, J. Marcial, K.J. Swearingen, S.H. Henager, M.J. Schweiger, N.E. TeGrotenhuis: Conversion of batch to molten glass, II: Dissolution of quartz particles, J. Non-Cryst. Solids 357(3), 820–828 (2011) A. Ungan, R. Viskanta: Melting behavior of continuously charged loose batch blankets in glass melting furnaces, Glastechnische Berichte 59(10), 279–291 (1986) NCNG: Glass Technology Course Textbook (2012) E.M. Levin, C.R. Robbins, H.F. McMurdie: Phase Diagrams for Ceramics (The American Ceramic Society, Westesville 1964) FactSage: Centre for Research in Computational Thermochemistry, Ecole Polytechnique, http://gtttechnologies.de/factsage (Montreal, Quebec 1976– 2018) B.A. Shakhmatkin, N.M. Vedishcheva, C.A. Wright: Thermodynamic properties: A reliable instrument for predicting glass properties, Proc. Int. Congr. Glass, Edinburgh 1, 52–60 (2001)
References
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35.56
K.D. Kim, H.K. Kim, J.H. Kim: Behavior of oxygen equilibrium pressure in CRT glass melts doped with Sb and Ce ions from the viewpoint of fining, J. Korean Ceram. Soc. 44(8), 419–423 (2007)
35.57
M. Hubert, A.J. Faber, H. Sesigur, F. Akmaz, S.R. Kahl, E. Alejandro, T. Maehara: Impact of redox in industrial glass melting and importance of redox control. In: 77th Conf. Glass Probl. (Wiley, Hoboken 2017) pp. 113–128
Oscar S. Verheijen
Part E | 35
CelSian Glass & Solar B.V. Eindhoven, The Netherlands [email protected]
Oscar Verheijen received his PhD from Eindhoven University of Technology, the Netherlands, in 2003. Following various positions within TNO, he joined CelSian Glass & Solar in 2013 as Business Development Manager focusing on sustainable glass production comprising energy and emissions reduction and process innovation and optimization.
Mathieu Hubert Dept. of Corning Glass Technologies Corning Research & Development Corporation Painted Post, USA [email protected]
Mathieu Hubert received his PhD from the Universities of Rennes 1, France, and Arizona, USA, in 2012. He joined CelSian Glass & Solar in 2013 as a Glass Scientist/Technologist, performing consulting and contract R&D for the glass industry worldwide. In 2016, he joined Corning as a Development Scientist, working on new display glasses and specialty materials.
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Glass Shapin 36. Glass Shaping
Romain Laniel, Mathieu Hubert, Mathieu Miroir, Antoine Brient
36.1
Overview of the Glass-Shaping Process ............................................. 1257
36.2
Shaping of Glass at High Temperatures........................ Viscosity and Annealing ..................... Shaping Strategies ............................. Towards New Glass-Shaping Strategies From High- to Low-Temperature Processes ..........................................
36.2.1 36.2.2 36.2.3 36.2.4
36.3 Glass Shaping at Low Temperatures ... 36.3.1 Material Removal in Glass at Low Temperatures.......................... 36.3.2 Glass Grinding................................... 36.3.3 Abrasive Water Jet Cutting .................. 36.4
1258 1258 1260 1274 1274 1275 1275 1278 1282
Conclusions ...................................... 1287
References................................................... 1288
36.1 Overview of the Glass-Shaping Process The ability to shape a material is of critical importance when it comes to developing any application based on it. In that respect, glass is a wonderful material due to its unique viscoelastic properties and the progressive increase in viscosity of a glass melt when its temperature decreases. This specificity has long been exploited by glass makers, who have been shaping glass in all kinds of forms and for all kinds of applications for millennia. Indeed, thanks to the ability to shape glass in virtually all forms, combined with outstanding properties that can be tuned by adjusting its composition, glass is found everywhere in our everyday life: art, packaging (bottles of all sizes and shapes), tableware (drinking glasses, plates, dishes), labware, architecture and construction (windows, light bulbs, lighting tubes, insulation, reinforcement in composite materials), transportation (windshields), optics (lenses, fibers), displays (TVs, laptops, smartphones,
and tablets), electronics (sealants in a large variety of applications), etc. The shaping of a glass article, whatever its final shape or final application, often results from the combination of a series of process steps. The production of most articles includes a shaping step carried out during the cooling of a molten glass melt. This process can be followed by one or several postprocessing steps at lower temperatures, which can include cutting, grinding, or polishing steps. The type of shaping process at high and low temperatures highly depends on the type of article to be produced (bottles, glass plates, fibers, . . . ) and the final dimensions and finish desired for the final product. In the first part of this chapter, the process of shaping at high temperatures is described. After highlighting the importance of glass viscosity in these processes, the main strategies employed in the glass
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_36
Part E | 36.1
The possibility to shape glass easily and in all kind of forms for applications in our everyday life is one of the key factors to its success. The fabrication of a glass article comprises a succession of steps, often starting from a hot glass melt that is shaped during its cooling. The product can then be worked at lower temperatures, to modify its dimensions or its surface finish. In this chapter, the shaping processes at both high and low temperatures are presented. In a first part, the different forming processes (shaping at high temperature) developed by the glass industry are illustrated, and a specific emphasis is given to glass viscosity, a key parameter in these processes. In the second part of the chapter, the shaping processes occurring at low temperatures, such as cutting or grinding, are described. In this section, specific attention is given to the mechanical behavior of the glass during the process as well as to machining parameters.
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industry for the various types of glass articles produced are presented. In the second part, the processes for shaping glass articles at low temperatures are described. As the mechanical properties of glass and
machining parameters play a major role in the behavior of the articles during shaping at low temperatures, the key mechanical parameters involved are emphasized.
36.2 Shaping of Glass at High Temperatures
Part E | 36.2
Glass shaping at high temperature is an essential step in the glass-making process. For most glass products, it corresponds to the transition from a glass melt at high temperature to an object with final, or semifinal, shape. In industrial glass making, the shaping at high temperatures, or forming, occurs after the melting and conditioning of the melt (Chap. 34). Forming thus involves simultaneous cooling of a melt and shaping into the desired shaped object. During the process, the viscosity of the glass increases by several orders of magnitude, from the low viscous melt to viscosities high enough to allow it to retain its shape under its own weight. The fast cooling often associated with the forming induces a lot of stresses within the product, which need to be removed to ensure proper mechanical properties of the final article. Forming is thus followed by an annealing step to remove these stresses in the glass, before it is cooled down to room temperature. The formed product can then be processed using various postprocessing steps, such as coating, cutting, grinding, or polishing. In industrial glass processing, these different steps occur successively in continuous production lines [36.1]. An example of a continuous glass manufacturing line for the production of flat glass is given in Fig. 36.1. The successive steps of melting, conditioning (and refining), forming, annealing, cutting, and inspection are illustrated. Depending on the type of article to be produced, several forming techniques exist [36.2–4]. Typical forming processes include:
Drawing: fiber glass, flat glass, tube glass, LCD (liquid crystal display) glass Blowing: containers, bulbs Pressing: tableware, containers, TV panels (CRT (cathode ray tube)) Centrifuging: insulation glass wool Rolling: wired glass, patterned glass Casting.
It has to be noted that some shaping processes at high temperatures do not start from a glass melt but from a glass substrate or glass powder previously prepared (either by melting and quenching of a glass or frit, or other synthesis methods such as sol–gel). Use
of glass frits as sealant (e. g., glass-to-metal seals in applications such as batteries [36.5]) or glass fritting for production on filters (for labware notably) are some examples of such processes. These processes will not be described further in this chapter.
36.2.1 Viscosity and Annealing The degree of cooling required during the forming process depends on the heat content of the glass product and the rate of production, i. e., the duration of the contact between the glass being shaped and the forming material (e. g., the molds for container glass). The degree of cooling must be sufficient to allow for an increase in viscosity leading to a product of high enough viscosity to retain its shape after forming. The deformation rate during forming must also be controlled. Too rapid deformation rates in the viscoelastic regime may lead to formation of cracks, decreasing the strength of the product. In case the deformation rate or the force applied during cooling is too low, the strong increase in viscosity may prevent good shaping of the article. Viscosity of the glass melt is thus the most important property during the forming process (Chap. 3). Though the official SI unit for viscosity is the Pa s, the poise (1 Pa s D 10 poise, or 1 poise D 0:1 Pa s) is usually preferred in industrial glass making. The different forming processes involve different methods and different deformation forces, depending on the glass products. These different processes usually involve processing of the glass at specific viscosities. As different types of glasses show different viscosity– temperature profiles, the forming processes occur at characteristic temperatures defined as specific viscosity values or ranges, illustrated in Fig. 36.2 (viscosities calculated from Fluegel’s model [36.6]). The main characteristic temperatures used in glass making, and the corresponding viscosity values, are as follow:
Melting point: D 102 poise (101 Pa s). This temperature does not correspond to a physical melting point. It corresponds to a temperature at which the viscosity is considered good for obtaining a well-
Glass Shaping
Feeder of materials
Melting furnace
Float bath (forming)
Annealing
Cutting
Inspection
Fig. 36.2
log10 η (Pa s) 16
Annealing point
Stresses relieved within 15 h Stresses relieved within 15 min
12
10
8
Softening point
Release from mold Slow blowing Slow pressing
6
Rapid blowing
SLS glass Working point
LCD glass Glass-wool
Viscosity curves for different glass families and characteristic temperatures commonly used in the glassmaking industry. Viscosity is expressed in Pa s. Note that poise is often used as the viscosity unit in the glass industry, with 1 Pa s D 10 poise
Rapid pressing Glass drawing
Lead-crystal 2 400
Melting point
Pyrex 600
800
1000
1200
fined melt with good homogeneity within the melting tank. Working point: D 104 poise (103 Pa s). Most forming processes occur at viscosities of 102 106 Pa s, i. e., 103 107 Pa s. This range is called the working range. Depending on the type of article desired, i. e., the forming technology used, the viscosity at which the process occurs will vary, as illustrated in Fig. 36.2. Softening point: D 107:65 poise (106:65 Pa s), or Littleton softening point (defined by American Society for Testing Material (ASTM) C338-93 [36.7]). At this viscosity, glass deforms under its own weight at a rate of 1 mm=min. In practice, the glass after the forming must be released at a temperature below this point, to avoid deformation of the article during further processes (annealing and further processes).
1400
1600 T (°C)
Strain point: D 1014:5 poise (1013:5 Pa s). Temperature at which the stresses generated during forming can be released within about 15 h. Below this temperature, relieving the internal stresses is practically impossible. Annealing point: D 1012:4 poise (1011:4 Pa s). Temperature at which the stresses generated during forming can be released by viscous relaxation within about 15 min. In order to relieve a glass product from its internal stresses (annealing) the glass has to be heated to just above the annealing point and subsequently cooled down slowly.
During the forming process, the glass is rapidly cooled from a temperature around its working point, to a temperature below its strain point. In addition, the rate of cooling is often not uniform and temperature gradi-
Part E | 36.2
Strain point 14
4
1259
Fig. 36.1 Schematic illustration of a float glass production line. The forming of the glass plates is performed using the float process. Picture courtesy of Asahi Glass Co. Ltd
Refining furnace
Regenerator
36.2 Shaping of Glass at High Temperatures
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ents are generated throughout the article. For example, the surface of the article in contact with the forming medium (e. g., in contact with the molds for the production of containers) will be colder as compared to the inside of the glass. This will lead to the generation of permanent stresses, which need to be removed before the product is put on the market. Therefore, an annealing step is performed after the forming. The glass article is directed through an annealing furnace, or lehr, in which it will undergo a controlled thermal cycle to remove as much as possible of the stresses. It is first heated to a temperature slightly above its annealing point, and kept at this temperature until thermal equilibrium is reached throughout the entire product. It is then cooled down slowly and uniformly until a temperature below its strain point, in order to avoid the generation of new stresses. Once below the strain point, the cooling rate can be increased, as below that point only temporary thermal stresses are generated. In most industrial productions, the annealing step is performed continuously, with the annealing lehr integrated to the production line, as illustrated in Fig. 36.1. The temperature profile within the lehr is adjusted as to allow for a proper annealing within the shortest possible distance [36.8]. The cooling rate between the annealing point and the strain point needs to be carefully selected and adapted to the type of article produced. It is generally calculated based on relations taking into account the properties of the glass itself (its characteristic temperatures) and empirical parameters related to the article shape (e. g., plate, cylinder, . . . ) and dimensions (thickness). Annealing is usually followed by further postprocessing and inspection steps.
36.2.2 Shaping Strategies The type of forming process used differs significantly as a function of the type of article produced. In the following sections, the main forming strategies found in industrial glass making are described, with an emphasis on the main parameters that industrials have to consider when producing these articles. This chapter focuses on the most common industrial processes, i. e., involving mechanized strategies. It has to be kept in mind that other forming strategies may also be found, including more traditional strategies such as artisanal blowing or casting of products. Containers Glass containers are produced using automated pressing and blowing in specifically designed molds. As illustrated in Fig. 36.3, the forehearth at the end of the glass melting tank is equipped with a feeder, compris-
Plunger
Rotating tube
Forehearth
Orifice Shears
Fig. 36.3 Schematic illustration of a feeder: forehearth bringing thermally homogeneous glass to the feeder bowl; reciprocating plunger controlling the flow of glass in the orifice; rotating tube making the glass circulate into the nose of the bowl, maintaining its uniform temperature and helping to control the flow (after [36.9])
ing a plunger, i. e., a cylindrical tube which periodically plunges and pushes a certain amount of the conditioned melt through an orifice, forming a drop of molten glass. This drop is then cut by shears placed just below the feeder, producing a gob that is then delivered to the forming machines placed underneath. The size of the orifice and the frequency of the plunger and shears are adjusted to adapt the weight, temperature, volume, and shape of the gob delivered, critical criteria for the production of containers with high quality. Feeders may be equipped with several plungers, allowing for production of multiple gobs (drops of molten glass with proper weight to form the desired products) simultaneously, and frequencies up to 300 gobs per minute can be achieved. After cutting by the shears, the gobs are conveyed via troughs to the molds, integrated in so-called individual sections (often called IS machines) of typically 612 molds. Depending on the article to be produced, different strategies can be employed: blow–blow or press–blow processes. The blow–blow process is illustrated in Fig. 36.4. The gob falls into a first mold called the parison mold, or blank mold. At the bottom of this blank mold, a socalled neckring allows the neck of the product to be formed. Compressed air is sent though the neckring, blowing the glass against the mold walls to form a parison (or blank). The parison is then released from this first mold and, still held by the neckring, is transferred to a second mold called the finishing mold. A second
Glass Shaping
36.2 Shaping of Glass at High Temperatures
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Fig. 36.4 The blow–blow process. © Emhart Glass
Part E | 36.2
Fig. 36.5 The press–blow process. © Emhart Glass
Fig. 36.6 The narrow-neck press–blow (NNPB) process. © Emhart Glass
blowing step is performed, during which the parison will be blown to take the final product shape. The article is then released from the finishing mold and neckring, before being conveyed by moving belts to the annealing and coating steps. The blow–blow process is used for the shaping of articles with narrow-necks, such as bottles. For widermouth articles such as jars, the press–blow process is used. The press–blow process, illustrated in Fig. 36.5, differs from the blow–blow process mainly at the parison-forming stage. Instead of being blown, the gob is pressed against the walls of the blank mold by a plunger. The parison is then transferred to the finishing mold and blown to give the article its final shape, before being released and conveyed to annealing and coating processes.
More recently, the narrow-neck press–blow process has been developed for the production of bottles, allowing for production of light-weight articles. This process, illustrated in Fig. 36.6, is similar to the press–blow process described above, but uses a narrower neckring and plungers. The blank and finishing molds used for these forming processes are made of two parts in order to allow for the release of the article after the forming process. This construction leads to the formation of so-called mold marks on the containers produced. From the gob of molten glass at relatively high temperature and low viscosity, to the formed article at lower temperature and high viscosity right after release from the molds, heat transfers are crucial in the good performance of the forming process [36.10]. Indeed, the glass
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should be cooled in such a way that the product will retain its shape after release. Typically, the glass gob enters the mold at a viscosity of about 103 104 Pa s (D 104 105 poise), and is released when viscosity is higher than the softening point, i. e., at a viscosity of about 107 Pa s (108 poise). The mold should not be too cold to avoid fracture of the glass surface by thermal shock. Conversely, the mold should not be too hot, to avoid chemical reactions between the mold material and the glass which would lead to a sticking of the glass to the mold. For molding of soda-lime-silicate (SLS) glasses, the mold temperatures are typically in the 400600 ı C range. Temperature control of the molds, contact surface between the glass and the mold, and contact time also play a crucial role in the quality of the forming process. Optimization of the mold geometry, surface quality, distribution of the glass in the mold, and heat transfers from the glass to the mold, are key challenges in the glass industry. It has to be noted that lubrication of the molds is commonly applied in industrial production lines to facilitate the process and reduce contact damages (however leading to increased labor work for the frequent application of the lubricant). Lubricants used are typically oil or graphite-based and applied to the mold by swabbing or cracking. In order to increase their mechanical resistance and to facilitate the application of labels, coatings are applied on the containers produced. The coating of a container is typically a two-step process, with a first coating applied right before the annealing, the hot end coating, and one after the annealing, the cold end coating. The hot end coating is generally made of tin oxide, formed by deposition of a SnCl4 layer on top of the hot article. This hot end coating promotes the adhesion of the cold end coating, which generally consists of a polymer layer sprayed on the surface of the article. The coatings protect the bottles from scratching during their transport and life cycle, ensuring their mechanical performance. The polymer layer also promotes adhesion of the paints or glues used for decoration and deposition of labels on the bottles. Pressed Articles Glass articles such as tableware (e. g., plates, some cups and glasses) are produced by pressing. The process a)
is similar to the first step of the press–blow forming method (Fig. 36.5), without transfer to a second mold. A gob of glass drops inside the forming mold and a plunger presses the glass against the walls. The evolution of the viscosity of the glass during this process is similar to the containers forming process, with the glass entering the mold at relatively low viscosity (104 105 Pa s range) and released when the viscosity is higher than the softening point (> 107 Pa s). The shape and design of the final article is dictated by those of the mold and plunger. After release of the article, it is conveyed to further processing of annealing and coating, similar to those found in the production of glass containers. Pressing can also be used for the production of optical lenses. In this process, illustrated in Fig. 36.7, a piece of cold glass is placed inside a mold and reheated to a temperature above its glass transition temperature, but below the melting point. A pressure in then applied on the mold. The softened glass adopts the shape of the mold, before being cooled down. The choice of the material, temperatures involved, design, and surface quality of the mold are crucial parameters in order to obtain articles with satisfying quality. The molding process can be used for the preparation of products with different geometries, such as aspherical or diffractive lenses, such as those illustrated in Fig. 36.7b for chalcogenide lenses [36.11]. Glass Fibers Several types of glass fibers are commercially produced [36.12, 13]. This includes continuous fibers for reinforcement (e. g., textile E-glass fibers in composite thermoplastic materials), discontinuous fibers for insulation (glass wool, or C-glass), or optical fibers for telecommunications. The shaping processes employed for the forming of these types of fibers differ greatly from one to another. Continuous fibers such as E-glass are produced by tensile drawing while discontinuous fibers are produced by centrifugal spinning. Both types of processes consist of shaping of a molten glass at high temperature. Conversely, optical fibers are obtained using a radically different process, where the glass preforms are produced by chemical vapor reactions instead of melting, before being drawn as a single fiber. More details on optical fibers are found in Chap. 41
b) Glass
Mold Set up
Pressing
Fig. 36.7 (a) Illustration of the molding of glass lenses; (b) examples of aspherical and diffractive lenses made out of chalcogenide glass. Reprinted from [36.11], Copyright (2003) with permission from Elsevier
Glass Shaping
Trough
Binder spray
Melt Spinning wheels
Fibers
Fig. 36.8 Spinning of fibers by cascade process drawing. © 1999 ILO Publications
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Glass stream Blower Spinner Emerging primary filaments Production fibers
Collection of fibers
Fig. 36.9 The rotary process for centrifugal fiber drawing.
© 1999 ILO Publications
of the perforations. Blowers located near the drum promote the elongation of fibers are well as participating in their cooling. Binders are sprayed on the fibers produced downstream of the centrifugal drawing. The quality of the fibers produced by the rotary process is usually higher than those produced by the cascade process. However, this process is more energy intensive, and allows for slightly lower throughput. The diameter of the fibers produced is relatively similar, with an average of 1:58 m for the rotary process, and 310 m for the cascade process. The size distribution for the fibers produced by discontinuous processes is usually nonuniform and difficult to characterize. The key parameter controlled by the fiber producers is fiber diameter. For the production of fibers with lower diameters, the flame attenuation process is usually employed (Fig. 36.10). In this process, the molten glass is poured into heated pots (or bushings), which present holes at the bottom. A continuous stream of molten glass falls from the holes and is pulled downstream by pull rolls, whose function is to control both the pull and the diameter of the fibers. Burners placed underneath the pull are directed at the glass streams, leading to the formation of discontinuous fibers. The flames from the burners attenuate the fibers and entrain them onto rolling mats, before further postprocessing. During their entrainment, a binder is sprayed on the fibers. Fiber diameters ranging from 0:1 to 6 m, and with high quality, can be produced with this method. It has to be noted that the flame attenuation process usually uses glass marbles as starting material. These marbles, previously molten in another furnace, are remelted in a feeder placed upstream of the bushings. Downstream of the fiber-forming process, the fibers are collected in so-called collection boxes, equipped with moving chains or drums. The collection boxes are
Part E | 36.2
Discontinuous Fibers. Discontinuous fibers such as in glass wool are produced by centrifugal spinning. A variant of the centrifugal method is the cascade process, in which the hot molten glass is directed from the furnace via a trough and poured at low viscosity (around 102 Pa s, or 103 poise) over elements rotating at high speeds, as illustrated in Fig. 36.8. Upon effect of the centrifugal force, glass droplets are projected at high speeds from one spinning wheel to another, leading to the formation of fibers. During the process, a binder (often referred to as size or sizing) is sprayed on the fibers to increase their mechanical performance. The cascade process is generally used for glasses with high liquidus temperatures, for which the risk of devitrification is high. For soft glasses, with lower liquidus temperatures, the rotary process, illustrated in Fig. 36.9, is typically used. In this process, a stream of hot molten glass is poured at the center of a hollow drum, or spinner, whose wall is perforated with several thousand holes uniformly distributed around the circumference. The centrifugal force applied on the melt, arising from the spinning at high velocities of the hollow drum (several thousands of rotations per minute), leads to the formation of single glass filaments at each
36.2 Shaping of Glass at High Temperatures
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Fig. 36.10 Schematic of the flame Pellets
attenuation process to produce fibers. The fibers formed by the action of the burners on the molten stream of glass are entrained on a collecting belt (rolling mat). Illustration courtesy of Woltz GmbH
Pellet dosing system Collecting belt
Remelt bushing Attenuation
Glass fiber primaries Burner
Part E | 36.2 equipped with an aspiration system to discard remaining glass drops which would not have formed fibers. The mat of discontinuous fibers can be either transferred to milling, for production of loose-fill fibers, or transferred to an oven, where the binder is cured (the curing oven). The cured fibers are then transferred to further postprocesses, which can include slitting or winding, before packaging. Continuous Filaments. Continuous fibers typically require higher quality than discontinuous fibers. In order to maintain the continuity of the filaments, a great amount of effort is made in order to ensure a good homogeneity and temperature distribution of the glass melt in the forehearth, before the fiber-drawing process. For continuous filament fibers, the hot molten glass is conducted to heated forming plates containing a large number of holes, or nozzles (illustrated in Figs. 36.11 and 36.12). These plates, called bushings, are generally made of platinum or platinum alloys and can contain several hundreds to several thousand nozzles (4008000, typically). The diameter of the nozzles is typically in the 12 mm range. The hot molten glass flows through the nozzles to form a multitude of filaments (diameters of some microns), which are drawn downwards at high speed (1050 m s1 ). A picture of the glass fibers coming out of the nozzles at the bottom of a bushing plate is shown in Fig. 36.11. The fiber-drawing process involves very high forming speeds, and the glass must undergo very rapid changes in temperature and viscosity in short times. Indeed, while low viscosities are required at the bushing for a good forming of the fibers (typically 102 Pa s or lower), the fibers must cool down very fast after the
Fig. 36.11 Continuous filament fibers coming out of the
nozzles at the bottom of a bushing plate. A typical bushing plate can contain 400800 of such nozzles. © 2017 Owens Corning
Glass in forehearth
Bushing
Fig. 36.12 Illustration of a bushing with several nozzles
employed for fiber drawing. © 1999 ILO Publications
nozzles in order to be pulled efficiently. After solidification, the filaments cool down to room temperature very rapidly. Cooling fins or water sprays are placed un-
Glass Shaping
der the bushings to cool and solidify the fibers rapidly (Fig. 36.13). Before the filaments are collated into strands and collected on the rotating drum, antiabrading coatings (also called binders or sizing) are applied on the fibers via an applicator that continuously rotates through a bath of the sizing material. The binder, or size, is applied to ensure three main functions:
The coatings usually contain organic polymers (film formers), coupling agents (e. g., silane compounds for good polymer adhesion), and lubricants. These elements are usually dissolved or emulsified in the binder
liquid, which consists mainly of water. Water also plays a role in the cooling of the fibers. The coating applied plays a significant role in the final properties of the fibers produced, and coating technology has assumed a major role in the development of new glass fiber products. After the sizing applicator, the gathering shoe collects the multitude of single filaments to form one single strand of fibers (sometimes referred to as the sliver). Downstream from the gathering of the single filaments into strands, the further processing of the continuous filament differs, depending on the type of product to be manufactured. Some examples are shown in Fig. 36.13. The fiber strand can be gathered at the bottom of the forming equipment by a rotating drum (the collet), rotating at a constant velocity. The drum velocities range typically from 500 to 5000 m s1 . Spirals, traverse, or stand guides are used to guide the strand on the drum as it increases in diameter, en-
Forehearth Bushing Filaments Water spray Applicator
Gathering shoe Strand or sliver Spiral
Collet
Forming winder or
Traverse Direct-draw winder
Strand guide Collet or
Direct chopper Direct chopped strand
Fig. 36.13 Continuous
fiber-drawing process. The glass flows out of the bushings to form filaments, which are cooled with water spraying before a coating/size is applied by an applicator. The filaments are then gathered into a strand via a gathering shoe, and collected further down the process. Different fiber-collection strategies (winder, chopper) are illustrated. Reprinted with permission of ASM International. All rights reserved. http://www. asminternational.org
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1. To prevent the filaments damaging each other (preserving the mechanical properties of the fibers) 2. Optimal adhesion of the polymer matrix to the glass surface for composite materials 3. Preventing the individual filaments being damaged by the strand guides during further processing.
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suring an even distribution. Several strands can also be drawn in parallel and gathered into bundles, called fiber rovings, which can then be further woven into fabrics. The rovings can be further winded (assembled rovings), milled, chopped (chopped strand mats), or woven into fabrics, depending on the final application of the fiberglass. Single strands can also be directly chopped at the bottom of the process using direct choppers (Fig. 36.13). The length of the chopped strands typically ranges from 3:2 to 12:7 mm (1=81=2 in). Rovings or chopped strands can further be formed into mats (the continuous or chopped strands are sent randomly on continuous belts and bound using binders, often thermoplastic materials). Fiber strands can also be milled using hammer milling systems into smaller sizes, typically 0:80:64 mm (1=321=4 in). Continuous rovings and mats are used mainly for reinforcement applications for e. g., pipes and tanks. Chopped strands are largely used for reinforcement of polymers for injection molding and thermoplastics, while milled fibers are used for providing stiffness and dimensional stability to plastics (while not improving significantly the strength of the material) [36.12]. It has to be noted that the design of the nozzle (height, internal diameter), the viscosity of the glass at the bushing, the surface tension of the glass, the height of the glass above the bushing (hydrostatic pressure), and the drawing speed, all play a role in the process. These parameters are accurately controlled and strict specifications are required in the design and operation of the bushing plates and in the glass melting process. In particular, the temperature in the forehearth is crucial. It should be noted that this process is more challenging for glasses with high liquidus temperatures. Devitrification of the glass in the forehearth should be avoided, as the formation of crystals, even small, would lead to a blockage of the nozzles in the bushing and thus loss of production.
Glass Tubes and Rods Most tubes and rods currently commercialized are produced using either the Danner or the Vello process [36.14]. Both processes are continuous and allow for the production of up to several tens to several hundreds of meters of tube/rod per minute (depending on the tube dimensions). Danner Process. In the Danner process, illustrated in Fig. 36.14, the glass melt (viscosity of 24 102 Pa s) from a feeder falls, via an opening, on top of a so-called mandrel, a hollow rotating cylindrical blowpipe with a downward slope. With the combined effect of glass viscosity and rotation (typically 510 rpm), the glass will cover the cylinder and flow downward on the mandrel. At the end of the mandrel, the so-called onion, the glass is released from the cylinder in the form of a tube (the viscosity of the glass at the onion is typically in the 0:5 104 105 Pa s range). A compressed air flow is sent through the mandrel to maintain the core of the tube hollow. The outer and inner diameters of the tube can be controlled by appropriate choice of the diameter of the mandrel, control of the glass flow, drawing speed, and control of the pressure of the air flow sent inside the mandrel during the process. In case no air is sent through the mandrel, plain rods can be produced. The continuous tube (or rod) will then be transported downstream on rollers, where it is further cooled down, then cut to the desired dimensions. The mandrels, however, have a relatively limited lifetime, and must often be replaced. Vello Process. The Vello process is based on vertical drawing of the glass (Fig. 36.15). In this process, a cone (or bell) is placed underneath a hole at the bottom of the feeder, and is connected to a compressed air supply. The hot molten glass (at a viscosity in the range of 104 105 Pa s) flows on top of the cone, forming a so-called onion, then a tube. The height and
Mandrel Onion Compressed air
Glass tube
Fig. 36.14 The Danner process for production of glass tubes
Glass Shaping
36.2 Shaping of Glass at High Temperatures
Glass Plates and Sheets Early Forming Processes. Modern lifestyle revolves around the availability of glass plates with good flatness, a key factor that enables more and more daring architectural designs. Windows and mirrors are an essential element of our environment, and it would appear difficult to picture our life without them. However, the
The Float Process. The introduction of the float process constituted a real revolution in the production of flat glass. This method, for which the glass melt is poured over a bath of molten tin placed at the end of the melting tank (Fig. 36.1), enables the continuous production of flat glass with very high surface quality, tight thickness control, and in large quantities (typically
Cone Onion
Glass tube
Fig. 36.15 The Vello process for production of glass tubes
Part E | 36.2
dimension of the cone, drawing speed, temperature, and pressure of the air sent through the pipe control the tube dimensions. The tubes are first drawn downwards, in a vertical direction. A few meters below the cone, a series of rollers are used to orientate the tube to a horizontal direction, where it is pulled by a drawing machine, often placed more than 100 m from the feeder. The glass tubes or rods are then cut to the desired dimensions. For both the Danner and Vello process, the ends of the cut tubes are usually smoothed by fire polishing. The Vello process typically allows for higher production throughput than the Danner process. However, its flexibility is limited in terms of manufacturing of tubes with different dimensions. It also requires higher control of the glass melt temperature at the orifice.
possibility to produce large quantities of glass with a high level of flatness, high product control, and relatively low cost is only recent and dates back to the 1950s with the invention of the float glass process by Sir Alastair Pilkington [36.15, 16]. Prior to that era, windows and panes were produced using different methods which resulted in glass with lower optical and/or mechanical properties [36.17]. Until the beginning of the twentieth century, the production of glass windows was mostly based on manual processes, such as casting of molten glass on a metal table (method used by the Verreries Royales de Saint Gobain to produce the mirrors for the Gallerie des Glaces in Versailles). Another popular method, the so-called crown process, involved the preparation of a large glass sphere at the end of a blow pipe by a master glass-blower. That sphere was later opened and spun, forming a crown of glass. The crown was then cut to produce glass panels. However, this method did not allow for a good control of the flatness, smoothness, and thickness of the pieces of glass prepared. The size of the panels was also very limited [36.18]. Another method consisted of the blowing (manual at first, then automatized in the early twentieth century) of large cylinders. A notch was engraved on the length of the cylinder, which was then opened and flattened in a specifically designed oven. Though allowing for production of larger glass panels, the surface quality and the flatness remained relatively poor. In the 1910s and 1920s, continuous processes were developed, in which a glass ribbon was directly pulled from the hot glass melt and drawn into a sheet of glass [36.17, 19]. One of these processes, the Fourcault process, is illustrated in Fig. 36.16. The melt is drawn upwards via a die called the debiteuse, then further conveyed by metallic rollers and cooled down with rollers. The glass sheets are subsequently cut and further processed. These processes enabled a major improvement of the production rates and thickness homogeneity. However, the contact of the rollers with the glass ribbons limits the optical quality and mechanical strength of the windows produced, and polishing of the plates is still necessary in most cases. These processes remained the major technologies for the production of flat glass until the introduction of the float process by A. Pilkington [36.15, 16].
Compressed air
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Glass sheets
Debiteuse
Part E | 36.2
Rollers
cess. In addition, molten tin does not wet the glass. It presents a low vapor pressure (2 103 mmHg at 1100 ı C), limiting its evaporation [36.20]. However, tin reacts strongly with oxygen. To prevent oxidation of the tin and evaporation of SnO, the tin bath is covered by a roof structure and placed under a reductive atmosphere composed of hydrogen and nitrogen (typically 95% N2 C 5% H2 ). The glass flows onto the tin bath with an initial thickness of 5 cm, before spreading on the molten tin to form a sheet with an equilibrium thickness of 6:9 mm (for typical float soda-lime-silicate glass). This equilibrium thickness heq results from the balance of the gravitational force g and the interfacial tensions between the tin and the glass, the glass and air, and tin and air (respectively Stg D 0:528 N m1 , Sga D 0:318 N m1 , and Sta D 0:497 N m1 ), according to (36.1) g h2eq g 2
Coolers Debiteuse Glass melt
Fig. 36.16 The Fourcault process
500700 t=day per production line, up to 1000 t=day in certain cases). In float glass furnaces, at the end of the refiner, the conditioned and homogeneous glass melt at about 1100 ı C is poured over a tin bath, illustrated in Fig. 36.17. The glass melt enters the float bath by the so-called spout and the lipstone. A tweel separates the tin bath chamber from ambient air in the working end, and also controls the amount of glass entering the tin chamber (i. e., the pull). The tin bath (the float) section is a metal container 5075 m long, 78 m wide, and 0:5 m deep (typical float glass melting tanks are 812 m wide, 3045 m long, and produce between 500 and 1000 t of glass per day). The depth of the molten tin bath itself is about 510 cm. Tin is the material of choice for the float process due to the different advantages it offers as compared to other metals. Indeed, molten tin is denser than molten glass, and due to its low melting point (232 ı C) and high boiling point (2602 ı C), it is present in liquid form (at a low viscosity of 102 poise) over the entire range of temperatures involved in the float pro-
g D Stg C Sga C Sta ; 1 tb
(36.1)
with g the density of the glass (g 2500 kg m3 for soda-lime-silicate float glass) and tb the density of the molten tin bath (tb 6500 kg m3 ). In the absence of other applied forces, the molten glass would always tend to achieve this equilibrium thickness. Rolls located on the side of the tin bath are used to either stretch the glass ribbon to produce a thinner sheet, or to contract it and produce a thicker glass sheet. Typical thicknesses achieved by this technique range from 2 to 20 mm. Pulled at the other side of the float line, the glass ribbon is lifted off the tin bath at a temperature of approximately 600 ı C, at which the viscosity is high enough to allow its extraction without deformation. The sides of the ribbon, which have been in contact with the rolls in the tin bath, are removed by cutting (the cut-out glass can be reintroduced in the glass furnace as cullet in the batch). The central, high-quality ribbon is then conveyed on rollers to the annealing lehr, where it is progressively cooled down to room temperature, before further processing (e. g., cutting, tempering, coating, removing of the parts containing defects, . . . ). In applications such as glass for automotive, buildings and structures, or cooking, the flat glass produced is often thermally toughened in order to increase its mechanical and thermal resistance. This process, also known as tempering, consists in creating in a controlled manner permanent stresses in the glass. After annealing, the glass plates are reheated to a temperature slightly above its strain point, but below its deformation point. The surfaces of the glass article are then cooled down very rapidly by ventilators or compressors injecting cold air though nozzles. The surfaces of the glass will then cool down much faster than the core of the
Glass Shaping
N2 +
a)
36.2 Shaping of Glass at High Temperatures
H2
Steel casing
Heater Gas chamber
Tweel
Refractory
Lip
Refractory
Steel shell
Molten tin
Lehr roll
Top speck
b)
Glass ribbon
a)
Fig. 36.18 (a) Profile of
b) Compression 0.21h
Thickness (h)
0.58h
Compression
Tension
a thermally toughened (tempered) glass plate and (b) stress profile within the article
Tension
0.21h
glass, still at a higher temperature. Upon further cooling of the glass, this difference in cooling rates will lead to the formation of permanent stresses. The surfaces of the article are in compression, while the core of the article is in tension. The stress profile generated, illustrated in Fig. 36.18, can multiply the practical strength of the tempered article by 4 or 5 as compared to an annealed, but not tempered article. These stress profiles are also responsible for the characteristic failure behavior of tempered products, which shatter in a multitude of small pieces. These glasses are often referred to as safety glass.
It has to be noted that the stresses generated inside the tempered glass do not allow for further cutting of the articles, which would release the stresses and lead to the critical failure of the glass. The articles must thus be cut and shaped to the desired dimensions before the thermal toughening. In addition, the tempering process requires uniform cooling of the surfaces, which make the process complicated to apply for products with complex shapes such as containers. Moreover, the generation of the stresses relies on the formation of temporary temperature gradients within the article. Therefore, the magnitude of the strengthening obtained (i. e., the gradient of stresses generated in the article) decreases for
Part E | 36.2
Molten glass Top roll
Fig. 36.17a,b The float process for fabrication of glass plates. (a) Side view of the float bath. The glass is poured on top of the tin via the lip (left) and is taken out of the bath (right) by rollers. (b) Top view of the float bath, showing the typical shape of the glass ribbon on top of the molten tin being stretched by rollers to control its thickness. Reprinted from [36.20], Copyright (2004) with permission from Elsevier
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thinner articles, in which the equilibration of the temperature between the core and the surfaces of the article is faster than for thicker articles. Thermal tempering is usually inefficient for glass plates with a thickness below 2 mm (for soda-lime-silicate glasses). For thin glasses, such as glasses for displays, chemical strengthening by ion-exchange process is typically applied. This process is described in Chap. 8.
Part E | 36.2
Bent Glass. While buildings use a significant amount of flat glass for windows or glass facades, architects are using more and more bent glass in more daring structures. In the same manner, the automotive industry requires windshields with specific shapes and curvatures. While these applications rely on the flat glass industry, the flat glass as produced at the end of the tin bath must undergo an additional step to obtain the desired shape. The bending of the glass panes can be done using mostly the processes of hot pressing or hot bending by sagging. Both involve reheating the glass pane above the softening point (typically 580 ı C or higher for sodalime-silicate glasses), after cutting the glass piece to the right dimensions from the ribbon of flat glass produced (thus after a step of glass shaping at low temperature). In hot pressing, the flat glass pane is placed in a specific mold composed of two parts with matching shape, and in which the glass is heated and pressed into the desired shape. The hot-pressed glass piece is then released from the mold, as illustrated in Fig. 36.19. This process can also be combined with tempering and laminating, and is often used for the production of windshields. For hot bending by sagging, the flat glass piece is placed on top of a mold comprising only one part, having the shape of the desired final product. The glass is heated to a temperature that will allow it to sag under its own weight to fit onto the mold (in the case of SLS glass, the sheets are heated up to a temperature of 600640 ı C, corresponding to a viscosity of 108 109 Pa s). This process is illustrated in Fig. 36.20.
Fig. 36.20 Hot bending of a glass plate by sagging. © Glaston Corporation
This process does not allow for simultaneous tempering of the glass. In these processes, the surface of the glass at relatively high temperature comes in contact with the molding material. Good mold surface quality and control of the process is thus of utmost importance to avoid damaging the surface of the glass articles produced. It has to be noted that both these processes require an additional heating step, thus additional energy, to obtain the bent glass. Recently, strategies for cold bending have been developed to reduce energy costs. This process relies on the on-site bending (without heating) of toughened float glass laminates and their fixation to a curved frame [36.21], and is generally limited to bent glass for architectural applications. Rolled Glass. An alternative method employed for the production of glass plates consist in rolling the molten glass between cooled rollers, as illustrated in Fig. 36.21. The spacing between the rollers, placed at the end of the forehearth, as well as the pull, determine the thickness of the plate produced. As for the float process, the glass
Fig. 36.19 Molds used for hot
pressing of different shapes of bent glass. © Glaston Corporation
Glass Shaping
36.2 Shaping of Glass at High Temperatures
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Fig. 36.21 Illustration of glass rolling. The molten glass
Part E | 36.2
passes in between two rollers which determine the thickness and pattern of the final glass sheet produced. © Ducatt
ribbon produced is then conveyed to an annealing lehr and to further postprocessing. This method allows for the production of flat glass as well as patterned glass. In this case, the rolls are engraved with a pattern to be applied on the glass. Thin Film Glass. The need for thin and extrathin glass for LCD screens (TVs, cell phones, tablets, . . . ) has drastically increased since the beginning of the twentyfirst century. These applications require pristine and defect-free surfaces, with high uniformity and thickness consistency. LCD glass substrates can be produced by the float process described in the previous section. In this case, the melting and forming processes have to be adapted, as LCD glass (typically boro-aluminosilicate glasses) usually requires higher process temperatures as compared to float soda-lime-silicate glass. Thin film glass substrates can also be produced by the so-called overflow downward process, or overflow fusion draw, illustrated in Fig. 36.22, developed by Corning in the 1960s [36.22, 23]. In this process, the refined molten glass is fed into an isopipe, or trough, typically made out of zircon or zircon- or alumina-coated platinum [36.24]. The molten glass flows laterally on both sides of the trough and flows downward, following the outer surface of the isopipe. At the bottom of the trough, the two separate flows converge and combine to form a single sheet of molten glass. The surfaces of the glass that have been in direct contact with the trough are now found on the inner side of the formed sheet, while the external surfaces have not been in contact with any other element, leaving (near) pristine, undamaged surfaces. Typical thicknesses produced with the fusion draw process range from 100 m to 1 mm. Below the trough, rolls pull the glass sheet downward, the rolling rate determining the thickness of the sheet produced. As it flows and is pulled downwards,
Fig. 36.22 Overflow fusion draw process. © Corning Inc
the glass cools down to form a solid thin glass substrate, that can be further processed (cutting, strengthening, . . . ). No polishing is required, given the excellent quality of both glass surfaces. An alternative to float and overflow fusion draw processes for the production of thin film glass is the down-draw process (Fig. 36.23). In this process, the refined glass melt is drawn from an orifice placed at the bottom of the furnace, delivering a horizontal sheet of glass. The glass sheet is then drawn downwards by rollers, before being annealed and further processed. The dimensions of the orifice and rollers, rollers pull, and spacing between the rollers, can be used to control the thickness of the glass sheet produced. Sheets as thin as 25 m can be obtained, with typical thicknesses produced with this technique ranging from some tens or micrometers to 1:1 mm. Sintered Products A limited range of glass products are produced by sintering. Sintering implies the use of a glass powder, i. e., starting from a glass product which has previously
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Down-draw Molten glass
Roller Inspection
Bead cutting rolling
Packaging
Annealing furnace
Part E | 36.2
Roller
Glass on roll or cut-to-size sheets
Glass ribbon
Defect mapping
Fig. 36.23 The down-draw process. © Schott AG
been produced and processed into a powder with the desired properties. Such glass powder may have been prepared by conventional melting, followed by quenching or casting to produce a frit that is then milled into a powder. The starting powder may also be prepared by alternative methods such as sol–gel (see Chap. 38 or mechanosynthesis [36.25]).
ing surface curvature and by decreasing the surfacearea-to-volume ratio. This surface energy per unit volume is inversely proportional to the particle diameter. The isothermal neck growth in the case of sintering by viscous flow is measured by the neck size ratio X=D, and is described by (36.2)
Principle. Sintering is the bonding together of particles at high temperatures without melting [36.26]. According to Frenkel’s theory, sintering of glasses occurs by viscous flow under the influence of surface stress. Sintering is a two-stage process, with the two stages possibly overlapping in some cases. In the first stage, bridges, or necks, are formed between adjacent particles of powder, with little or no change in density. The second stage corresponds to the densification of the material by reduction of the porosity, and can lead to large volume changes. The driving force for densification by sintering is the reduction of surface tension. Studies of sintering processes are based on theoretical models assuming a spherical shape of the particles with equal diameters. In most cases, these conditions are not achieved, with particles varying in both sizes and shapes. However, the fundamentals principles remain valid. Particles sinter by atomic motions that eliminate the high surface energy associated with powder, by reduc-
(36.2)
2 X 3 D t; D 2D2
where X is the neck diameter, D is the particle diameter, t is the isothermal sintering time, is the surface energy, and is the viscosity. The initial sintering stage of neck growth between two adjacent particles relies on the motion of atoms by diffusion at the grain boundaries. The diffusion is a thermally activated process, thus diffusion rates are higher at high temperatures. Figure 36.24a–c illustrates neck growth during the sintering of two spherical particles of diameter D. Prolonged sintering causes the two particles to coalesce into a single sphere with a final diameter equal to 1:26 times the original diameter. The neck growth stage may induce the formation of porosity inside the material. Porosity is divided into open pores (connected to the surface) and closed pores (enclosed in the bulk material) as illustrated in Fig. 36.24d. The second stage of the sintering process, the densification, is the elimination of this porosity to
Glass Shaping
a)
b)
c)
D
Neck
36.2 Shaping of Glass at High Temperatures
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d)
1.26D
X
Grain boundary
Open pore
Closed pore
Fig. 36.24 (a–c) represent successive steps of sintering, with neck growth between two particles leading to formation of a single, larger particle; (d) illustration of closed and open porosities
a)
Pressure control
b)
c)
Part E | 36.2
P
Vacuum chamber Power supply
Powder
P
Fig. 36.25 (a) Illustration of the principle of spark plasma sintering (SPS); (b) chalcogenide glass lenses prepared by SPS of a glass powder; (c) infrared image of the lenses showing their transparency in the infrared. Reprinted with permission from [36.27]
obtain a dense material. In most cases, densification comes with shrinkage. The elimination of the pores occurs via diffusion through the material and is therefore thermally activated. The elimination of the closed porosity is a slow process wherein isolated, spherical pores shrink by a bulk diffusion mechanism and is critical to achieve full density. Sintered Glass Products. Sintering allows for the production of articles with complex shapes such as lenses, as the glass powder can adopt relatively easily the form of complex mold designs. Great care must be taken to avoid the presence of air and other inclusions. Sintering can be performed under the action of pressure, or in pressureless processes. Pressureless sintering is commonly applied for sealing applications, when glass is used for a glass-to-metal seal [36.5] or in battery/solid oxide fuel cell applications (Chap. 50). Note that in many cases, binders and/or fillers are added to the powder before sintering to make handling of the product easier or to confer specific properties to the system. An additional heat treatment such as an additional heating stage at higher temperature
is sometimes applied to obtain sintered glass-ceramic sealants. In the case of sintering under application of a pressure, different strategies can be found. The pressure applied to the mold containing the powder can be either uniaxial, or from all directions. The sintering methods are in such cases referred to as hot uniaxial pressing (HUP) or hot isostatic pressing (HIP), respectively. More recently, the possibility to use spark plasma sintering (SPS) for the sintering of glass powders has been demonstrated. This method, in which an electrical current is applied through the mold during sintering (with or without application of uniaxial pressing, as illustrated in Fig. 36.25a), allows for the production of articles in reduced sintering time as compared to HUP [36.25, 27]. For glasses with low resistance to crystallization, such as some chalcogenide glasses, it also offers the advantage of allowing production of products with larger dimensions as compared to those prepared by conventional melting and quenching techniques. Examples of infrared transparent chalcogenide glass lenses prepared by SPS of a glass powder prepared by mechanosynthesis are shown in Fig. 36.25b,c.
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36.2.3 Towards New Glass-Shaping Strategies
Part E | 36.2
Three-dimensional (3-D) printing, or additive manufacturing, which has assumed increasing importance in the manufacturing of a large number of materials such as polymers and alloys, allows for the production of a wide variety of articles with complex geometries, which are difficult to obtain via the more conventional shaping methods such as casting, molding, or sintering. 3-D printing is also successfully employed for the manufacture of bioactive glass and ceramic scaffolds [36.28, 29], allowing for the printing of scaffolds with complex geometries designed to promote bone generation and wound healing. One of the main challenges of the 3-D printing of glass is to obtain a final material with good optical transparency, one of the properties which make glass so attractive in many aspects. This challenge has recently been overcome by a team in crosscollaboration between the MIT (Massachusetts Institute of Technology) Department of Materials Science and Engineering, the Department of Mechanical Engineering, and MIT Media Lab. The team developed and patented a method enabling the 3-D printing of optically transparent glass objects, G3DP [36.30–32]. The printer, schematically illustrated in Fig. 36.26, is based on a dual-heated chamber concept. The upper chamber acts as a kiln cartridge while the lower chamber serves to anneal the structures (annealing chamber in Fig. 36.26). The kiln cartridge operates at approximately 1050 ı C and can contain sufficient material to build a single architectural component. The molten material is funneled through an alumina nozzle, as illustrated in Fig. 36.27. The print annealer avoids ther-
Upper chamber Nozzle Annealing chamber Moving platform
Fig. 36.26 Schematic illustration of the glass 3-D printer
developed at MIT. The upper chamber contains the molten glass, which is printed down in the bottom chamber (printer annealer). Courtesy of Peter Houk (MIT)
Fig. 36.27 Picture of the molten glass flowing from the nozzle during 3-D printing of the glass. Photo courtesy of John Klein
mal shock in the printed components. The platform in the annealer (initially positioned high in the annealing chamber) is progressively lowered during the printing of the glass article. Examples of optically transparent glass structures produced with the printer are shown in Fig. 36.28. These objects illustrate the possibilities offered by 3-D printing in terms of production of objects with complex shapes and geometries. 3-D printing of optically transparent glass could therefore represent a major breakthrough in the shaping of glass articles, thus opening a new era of glass manufacturing allowing for production of articles of complex structures which cannot be obtained by the more conventional glass-forming techniques.
36.2.4 From High- to Low-Temperature Processes Shaping at high temperatures includes a large variety of processes, which may vary depending on the type of article to be produced. Indeed, while starting from a hot glass melt, the process involved for the production of flat glass differs significantly from that of fiber glass or container glass. The product obtained right after the hot-shaping stage may correspond to the final product, yet on many occasions subsequent shaping steps are required. For instance, the product obtained at the end of the tin bath in flat glass production is a continuous ribbon of glass with a given thickness, which cannot be used as such. Further steps are required to shape this ribbon into the final product (e. g., windows with given dimensions). Glass shaping thus also includes a large variety of processes at low temperatures, such as cutting, grinding, polishing, or pocketing. They complete hot processes that give the global form, to shape functional surfaces with specific geometry, location, and roughness
Glass Shaping
36.3 Glass Shaping at Low Temperatures
and without modifying the rest of the work-piece. Depending on the work-piece, the fabrication process can even include a series of hot- and low-temperature processes, followed by subsequent processes at high temperatures. This is for instance the case of car windshields, for which a flat glass ribbon is first produced (hot shaping), cut to the desired dimensions (cold shaping), and then reheated again for shaping by hot pressing.
While viscosity appears to be the most critical parameter in the processes of shaping at high temperatures as described in the previous sections, the mechanical properties of the glass in its brittle regime, such as strength or toughness, become critical in the processes at low temperatures. Therefore, in the next section, specific attention is given to mechanical behavior of glass during shaping at low temperatures.
36.3 Glass Shaping at Low Temperatures This section deals with shaping processes in a lowtemperature regime which does not allow the glass material to flow. The material-removal mechanisms thus involve fragile behavior including a large range of crack networks. We propose to explain the theoretical aspect of the low-temperature glass removal mechanism before exploring the main industrial processes such as grinding and water jet cutting.
36.3.1 Material Removal in Glass at Low Temperatures Shaping a glass work-piece at low temperatures requires damaging the material in its brittle regime. Different material-removal processes are used to shape this material: cutting glass using a scratch or cut-off wheel, drilling of glass, grinding [36.33] and polishing of glass, abrasive air jet or water jet shaping [36.34], etc. All these processes share the same principle. The tool impacts the free surface of the work-piece in its specific environment; the dynamic load develops a crack network big enough to separate some debris from the bulk. Depending on the process, we can distinguish two kinds of elemental loading mechanism:
Particle normal impact, commonly found in typical processes based on force boundary conditions such as abrasive air jet or water jet Scratching, which appears in other processes imposing displacement boundary conditions.
It is worth mentioning that erosion may also appear in some specific processes [36.35], such as the abrasive water jet. Particle impacting and scratching are repeated until the desired shape is achieved. Both impact and scratching are related to indentation of glass. The first is associated with dynamic compression waves which propagate cracks initiated by the penetrator; the second is coupled with a tangential displacement which translates initial damage along the scratch trajectory. The created crack network also depends on several conditions such as the material mechanical behavior [36.36], the penetrator geometry, and the ambient conditions. The different cracks that occur during an indentation test can be seen in Fig. 36.29. They all appear during the loading step except for the lateral cracks, which are generated by the unloading step. For some processes, the nature of these cracks is sometimes intended. For example, glass cutters try to favor median crack formation
Part E | 36.3
Fig. 36.28 Examples of 3-D printed glass structures. Photo courtesy of Chikara Inamura
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a)
b)
Radial
d)
Lateral
c)
Median
e)
Cone
Half-penny
Fig. 36.29a–e Isometric sections of idealized crack morphologies observed at indentation contacts: (a) radial crack and associated contact impression and plastic deformation zone, (b) median crack, (c) halfpenny crack, (d) lateral crack, (e) cone cracks and associative nucleating ring crack (after [36.37])
Part E | 36.3 along the prescratch before breaking their glass plates. This is definitely not the case for the grinding process, which tries to generate a functional surface while minimizing subsurface damage. Processes involving particle normal impacts work with weak cutting forces because of the small size of abrasive particles. Each material removal depends on the kinetic energy of a single particle, its trajectory, its geometry, the material behavior, the surface condition, and the damage of the targeted material. All these parameters being quite difficult to provide explains the lack of a deterministic model for brittle material removal associated with projected particle processes. In the literature, several models for ductile materials [36.38, 39] and some erosion models which can be applied to brittle materials [36.40–42] can be found, but none related to abrasion debris of glass. A contrary process involving scratches imposes strain on the work-piece and thus increases interaction forces and vibrations. The trajectory and geometry of the penetrator are known and depend on the tool used. Grinding is seen as a multiple scratching process. To be efficient, all these single scratches have to work in the microabrasive regime. The different damage regimes can be seen in Fig. 36.30. Three are distinguished:
Regime I—Microductile regime; for light load, this involves anelastic strain with mainly radial cracks Regime II—Microcracking regime; as the indentor slides with heavier load, some lateral and radial cracks emerge at the free surface Regime III—Microabrasive regime; as the load increases, a three-body wear system appears and gen-
erates much debris and a complex crack network including lateral cracks. Even if the microcracking regime may come with chips, only the microabrasive regime involves significant material removal allowing the shaping of a workpiece. Scratching of brittle material depends on many parameters: material composition, ambient conditions, and interface conditions. The most common machined glass system is Na2 O-CaO-SiO2 also known as sodalime-silica; this includes commercial window glasses. The scratchability is greatly affected by the glass composition as shown in Fig. 36.31. A representative scratch groove is shown for six different silica glasses after a normal load monotonically increasing up to 4 N. The different regimes do not appear at the same time. Focusing on the microabrasive regime, it appears in the low-load domain for the fused silica and soda-limesilica glasses with low silica contents, whereas lateral chipping occurs for higher silica amounts. The SLS 2 composition has the weakest toughness, while an increase in silica leads to the disappearance of chipping. In this case, the rearrangement of matter at the atomic or molecular scale is difficult and the glass responds to the high contact stress by allowing cracks to form and propagate. To summarize, glasses from the devitrite phase field, which include crystal nucleations, are sensitive to chipping and glasses with silica-like networks appear to be much more resistant to both crack propagation and chipping during scratch experiments. Moreover, the higher the silica amount is, the earlier the abrasive regime appears; except for the fused silica glass which behaves like an anomalous glass.
Glass Shaping
36.3 Glass Shaping at Low Temperatures
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Indenter
Direction of scratching
Radial (Chevron) cracks
Debris
Subsurface lateral crack Microabrasive regime Chips Microcracking regime Microductile regime
III
II
I Sliding distance
Part E | 36.3
Normal load Fn
200 μm
Fig. 36.30 Typical scratch pattern obtained on the surface of soda-lime-silica glass when scratched by an indentor during a monotonic loading cycle and micrograph of a scratch performed on a glass. Definition of damage regime I, II, and III [36.43] Transition SiO2 Na2O CaO II → III (N) Kc (MPa m½) Fused silica glass
100
SLS 4
71
SLS 3
0.5
1.47–0.77
17.5 11.5
0.9
0.82
74
15.7 10.3
1.1
0.76
SLS 2
77
13.9
9.1
1.6
0.70
SLS 1
80
12.1
7.9
2
0.71
1.2
0.72
Commercial float glass
0 0
1
–
–
70.9 12.8 10.1
2 1
3
4N 2 mm
Fig. 36.31 Evolution of scratch resistance for the five soda-lime-silica glasses and the fused silica glass. Compositions are given in mol%, the microabrasive transition is given in N and toughness Kc in MPa m1=2 . Reprinted from [36.44], Copyright 2003, with permission from Elsevier
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Glass Processing
Part E | 36.3
The humidity level is also considered as one of the most important ambient condition parameters. Indeed, its influence on the scratch patterns is strong as shown in Fig. 36.32. All regime transitions tend to develop at lower loads as the moisture increases. In the particular level of 0% humidity, large subsurface lateral cracks appear during the load process. This phenomenon decreases with the humidity level; the same tendency occurs in lower proportion during indentation tests for several humidity levels. The dynamical scratching effect emphasizes it. The sharp or smooth indentor geometry at the interface along the scratch trajectory may also modify its morphology. The evolution of the transition loads of the three scratching regimes are plotted in Fig. 36.33 for two different indentor shapes. Transition force (N) 2.5
II→III
Fig. 36.32
I→II 0
0
100 Humidity (%)
Transition load with regard to humidity level for a Vickers scratching test (after [36.43]). The gap is related to different load and unload data
36.3.2 Glass Grinding
Transition force (N) 2.5 II→III
Fig. 36.33 II→III I→II I→II
Cone
0
A sharp penetrator shape, such as Vickers, Berkovich or cube corner, introduces an opening crack separation mode, with a tensile stress normal to the plane of the crack. The apparent friction coefficient is quite stable during a monotonic load and the regime transitions appear earlier. Conversely, a smooth penetrator shape involves high contact pressure at the interface associated with an unstable apparent friction coefficient. The shear mechanism is privileged and leads to a high-loaded abrasive regime. The load to unload gap is related to the local state of the material. On one hand, the transition load appears from weak to strong crack networks, and on the other hand the transition unload appears from strong to weak crack networks; they are consequently different. Not all damage that occurs during a scratch test is at the surface. Much damage remains under the free surface of the samples like cone cracks, median cracks, and lateral cracks; this entire hidden crack network is known as subsurface damage or SSD. In most cases they can be highlighted by indirect methods built on surface topography analysis. Direct observation methods are more destructive, like acid etching, traverse polishing, or dynamic shear opening as shown in Figs. 36.34 and 36.35. They allow one to measure SSD depth under the free surface as well as damage morphology. However, the results given by these methods have to be analyzed with great care because of the stress relaxations which may involve uncontrolled crack propagation. SSD knowledge represents a major concern. Such damage is considered as the origin of weakness of glass work-pieces leading to limited in-service life. It should be noted that in many cases polishing or annealing processes are carried out to avoid the SSD effect.
Vickers
Transition load with regard to a penetrator for a 65% humidity scratching test (after [36.43]). The gap is related to different load and unload data
Abrasive machining, and grinding in particular, is the most common material-removing manufacturing process for glass and brittle materials. It can be seen as a multi-indentation [36.46] or scratching process [36.47]. Whereas indentation and scratching involve a single indentation tool, abrasive machining relies on multiple contact interactions. Depending on the process parameters these multiple loading contacts generate lateral and radial cracking resulting in material removal. Figure 36.36 illustrates the grinding principle: the abrasive grains of the grinding wheel moving with a speed vs and a feed rate vw penetrate the material at the depth of cut ap . Depending on the depth of the cut, roughing, finishing, or polishing operations can be achieved. Grinding parameters can be classified into three main categories:
Glass Shaping
36.3 Glass Shaping at Low Temperatures
1279
υs
υw
ap
Fig. 36.36 The grinding principle and parameters
glass sample shaped by an abrasive water jet; the plane view corresponds to a lateral polished cut face [36.34]
h = 0.7 μm n = 2780 rpm v = 40 mm s –1
Grinding direction
Machined surface
Cross section Subsurface damage 2 μm
Fig. 36.35 Typical subsurface damage image of a ma-
chined specimen of glass obtained by an impact cut method. Reprinted from [36.45] with permission of Springer
Machining parameters: feed rate vw , depth of cut ap , wheel speed vs , and manufacturing strategy Tool parameters: wheel dimension and shape, bond material, nature and size of abrasive grains Contact parameters: lubricant type and flow, temperature.
These numerous parameters make this process difficult to master. If the kinematics aspect of the tool displacement is rather simple, the interactions between the abrasive particles and the work-piece are much more difficult to model. The randomness of the abrasive particles’ distribution and of their shapes and sizes lead the grinding process model to be considered as a statistical problem involving probability laws by St˛epie´n [36.48], or Chang [36.49]. Bigerelle has also modeled the tool and the surface finish using fractals [36.50]. These stud-
ies were, however, carried out on nonbrittle materials for which the expected surface finish is more difficult to predict. The following paragraphs present glass surface finish characteristics and the influence of the tool and machining parameters. Surface Finish of Ground Surfaces Grinding brittle material induces scratches, cracks, and even SSD under specific conditions. Characterization of the surface must be made with appropriate parameters. While arithmetic average roughness Ra is the standard parameter used in the manufacturing industry and, to an extent, in the literature, it is also the least relevant parameter when it comes to characterizing surfaces. Ra is the arithmetical mean of the absolute values of the profile deviations (Zi ) from the mean line of the roughness profile. Roughness profiles with different peak spacing or shapes can have the same Ra values. Four roughness profiles are shown in (Fig. 36.37). They share the same Ra value. However, their asymmetry (characterized by Rsk ) and their peakedness (characterized by Rku ) differ. Positive Rsk values correspond to high peak spread on a regular surface, while negative Rsk correspond to a surface with scratches and pores. If Rku D 3 the roughness profile has a Gaussian height distribution. Bumpier surfaces have Rku < 3, while Rku > 3 characterize surfaces with many spikes. A ground-glass-typical roughness profile is shown in Fig. 36.38. The profile shows a large number of valleys and, at a smaller scale, peaks. Parameters obtained from the Abbott–Firestone curve are particularly appropriate to characterize such roughness. The Abbott–Firestone curve can be expressed as a percentage of the evaluation length at a predefined depth below the highest peak [36.51]. This curve can be split into three by means of drawing a secant to the region at the point of inflexion corresponding to a 40% material ratio which is then drawn to intercept the axes [36.52]. From the interceptions with the axes, two horizontal
Part E | 36.3
Fig. 36.34 Subsurface damage micrography of a float
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Rsk > 0
Rku > 3
Rsk < 0
Rku < 3
Fig. 36.37
Amplitude distribution curve about the mean line for two surfaces showing similar Ra values but different values of Rsk or Rku
Part E | 36.3
0.01 Height (mm) 0.01
Fig. 36.38 Roughness profile of a ground glass
0.005
0.005 0
0 –0.005
–0.005
–0.01 –0.015
–0.01 –0.02 4 3 Distance (mm)
2
2
1
4 3 Distance (mm)
–0.015
–0.02
1 0 0
Height (mm) 5 0 –5
0
0.5
1
1.5
2
2.5
lines are drawn such as shown in Fig. 36.39. The resulting central region corresponds to the core roughness Rk . The side of the triangular area equivalent to the area respectively above and below the central region is Rpk , respectively Rvk , and its basis is Mr1, respectively 100 Mr2. Figure 36.39 shows an Abbott–Firestone
3
3.5 4 Distance (mm)
curve representative of a ground glass sample. Rough abrasive machining leads to surface finishes with low Rpk values and similar Rk and Rvk . Brittle peaks generated are broken during the machining process, because of cutting forces and vibrations. SSD can also be related to surface parameters [36.53]. Further work by
Glass Shaping
36.3 Glass Shaping at Low Temperatures
Profile height (μm) 10
5
Rpk
Rk
1281
Fig. 36.39 Abbott– Firestone curve of a ground glass sample. Adapted from [36.33] with the permission of American Society of Mechanical Engineers (ASME)
0
–5
Rvk
Part E | 36.3
–10
–15
–20
0
Mr1
20
40
60
Laheurte has established that Abbott–Firestone parameters are particularly relevant to characterizing SSD without use of a surface-destructive process such as acid etching [36.54]. Influence of Tool Parameters The nature of the tool has a major influence on the ground surface. Grinding wheels are composed of abrasive grains retained by a bond material which acts as a toolholder. When bond wear occurs, abrasive grains are liberated and replaced by newer and sharper cutting edges [36.55]. Increasing the grain size tends to increase surface roughness [36.56]. Grain renewal depends on the wheel bond material which has therefore also a strong influence on the surface finish [36.57]. To avoid grain-renewal issues and bond wear, wheels with a metal bond and an electrolytic grain deposition are commonly used. These tools have a high density of grains on a single layer which limits grain pullout. Influence of the Machining Parameters Many studies have been carried out to model the surface finish of ground surfaces. Some are based on chip formation and material-removal mechanisms [36.58]. Zhang also proposed to define the surface finish using fractals [36.59]. But, in order to predict the surface finish, most of the studies focus on the rela-
80
100 Mr2 Material ratio (%)
tionships between machining parameters and surface roughness [36.60]. These studies are somewhat difficult to apply in a manufacturing context since they require good knowledge of the tool topography and of the material-removal mechanisms. Tool manufacturers usually propose machining parameters based on empirical data studies. They are mostly based on a Design of Experiments methodology and provide information on the feed rate, depth of cut and wheel speed influence on roughness [36.33, 61], geometric error [36.62], or cutting forces. Feed rate is the most influential parameter. Increasing feed rate leads to an increase of the core roughness as well as the depth of the valleys. Conversely, increasing depth of cut decreases both core roughness and valley depth. A grinding strategy with a low feed rate and a high depth of cut seems reasonably appropriate in terms of surface finish and is also suitable in a productivity context. Investigating machining parameters’ influence on material ratio Mr2 has shown that the proportion of valleys decreases when a high wheel speed is set together with a low feed rate and a high depth of cut. Such a parameter setup corresponds to a polishing operation. Fracture Modes Depending on the machining parameters, four different grinding modes for horizontal surface grinding can
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Glass Processing
occur [36.63]. They are defined with respect to the grinding surface plane which is defined in Fig. 36.40:
Brittle mode: lateral cracking occurs and extends below the grinding surface plane Semibrittle mode: lateral cracking occurs and extends near the grinding surface plane Semiductile mode: lateral cracking occurs and does not extend below the grinding surface plane Ductile mode: lateral cracking does not occur.
Part E | 36.3
Lateral cracking occurs when the maximum penetration depth hm is greater than the critical depth to initiate cracking dc . Shaw [36.64] proposed the following expression of hm "
4 vw hm D Cr vs
ap de
12 # 12
;
(36.3)
where ap is the depth of cut, de is the equivalent diameter of the wheel, vs is the speed of the wheel, vw is the feed rate, r is the chip width-to-thickness ratio, and C is the grit surface density which is defined as the number of active points per unit area of the wheel surface. Bifano et al. [36.65] defined dc as dc /
E H
Kc H
2 :
(36.4)
Where E is Young’s modulus, H is the hardness, and Kc is the fracture toughness. From (36.3), increasing depth of cut or feed rate increases the maximum penetration depth and leads to brittle modes and rougher surface finishes. However, as Gu et al. [36.63] observed, the depth of cut influence is weaker since increasing its value also increases the distance between lateral cracks and the grinding plane. Therefore, the grinding modes and the surface finish roughness are mainly driven by the vw =vs ratio. a)
36.3.3 Abrasive Water Jet Cutting The current glass-cutting process for a glass product involves several steps. The glass surface is first scratched with a diamond roller; a fast flexion movement is then applied to the work-piece and the median crack, which is located along the scratch, propagates. A clean cutting profile is obtained and a shaping phase is then carried out using preformed grindstones. The shaping phase is performed in two steps. The first step is a rough machining which consists in grinding 23 mm of material, while the second step is a finishing operation that provides the desired geometry and surface condition. This efficient method has some limitations. The parts must usually be manipulated to move from one production unit to another, increasing the risk of surface scratching, thus degrading the quality of the final product. In addition, this method generates large volumes of very expensive cutting waste for businesses. In this context, new cutting methods that overcome these limitations need to be developed, and water jet cutting is an interesting alternative (Fig. 36.49a). This means of production allows multiple operations in one single phase: cutting, shaping, and finishing while limiting cutting waste which means cutting several parts in one phase. The surface condition obtained depends not only on machining parameters like traverse speed, distance nozzle to part, flow of water etc., but also on the abrasive used, i. e., particle size, density, hardness, and form factor. The abrasive water jet can be defined as a means of cutting using erosion at high speed. The jet is a mixture of water and abrasive particles (Sect. 36.3.3, The abrasives) propelled at supersonic speed in the air. When the jet meets the work-piece it causes damage which results in material removal. Abrasive water-jet cutting technology differs from the pure water jet only in a few aspects. In water jet cutting, the supersonic flow causes erosion of the material. In the abrasive water jet, the flow accelerates abrasive particles which induce erosion of the material. The three-phase jet, a mixture of water, air, and abrasive allows the cutting of materials with high
Penetration depth of a single grain
b)
Lateral cracking
ap
Grinding plane
Fig. 36.40a,b Grinding plane: (a) grinding principle scheme, (b) glass grinding test
Glass Shaping
a)
a diameter < 1:2 mm [36.66, 69]. The impact at a supersonic velocity of about 500 m s1 [36.66] of the jet on a work-piece, causes damage which results in material removal. This material removal is optimal for a diameter ratio of jewel to mixing tube of 0:3 [36.69]. This unconventional technology has several advantages:
The process is extremely versatile. It can cut thin or thick samples up to 300 mm and stacked materials. There is no heat-affected zone and little mechanical effort. Accurate geometries can be obtained and material waste can be minimized. The process is easy to set up and program. Cutting forces are less than 0:454 kg. Secondary operations are reduced or even unnecessary.
The abrasive water-jet’s cutting power is hundreds, even thousands of times greater than just the water jet’s cutting power. While the pure water jet cut mainly soft materials, hard materials such as metals, stone, composites, glass, and ceramics can be cut with the abrasive water jet. The abrasive water jet’s cutting principle implies that the cutting power decreases along the jet’s axis. This means that the highest cutting power is obtained at the work-piece’s first interface. The cutting power decrease together with the nozzle displacement provides a typical surface finish on the cut flank of the work-piece. It is characterized by a curvature and b)
High-pressure water inlet mm –0.06
Jewel (ruby or diamond)
–0.08 y: 7.1 mm
x: 8.0 mm
(Abrasive) garnet μm 85.7 50.0 40.0 30.0 20.0 10.0 0.0 –10.0 –20.0 –30.0 –40.0 –50.0 –60.0 –70.0
Mixing tube Guard Cutting water jet
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y: 7.1 mm
Cut material x: 8.0 mm
–84.2
Fig. 36.41 (a) Diagram of a water jet cutter and (b) topography of a transverse cut glass surface obtained with the noncontact surface metrology machine Altisurf 500
Part E | 36.3
mechanical properties such as stainless steel, titanium, and glass. The efficiency of the jet increases with the energy transmitted to the abrasive particles. The water system is compressed at a high pressure using a high-pressure pump unit. It passes through a pressure intensifier composed of a reciprocating piston with two sections whose area ratio is of the order of 20 [36.66]. An oleo-hydraulic unit allows pressures of 300500 MPa to be obtained in each cycle [36.67]. The pressurized water is collected in a cavity to smooth pressure fluctuations generated by the alternating operation of the pistons. The water is then propelled at supersonic velocity through a jewel orifice (such as ruby or diamond), with a calibrated diameter of 0:080:3 mm [36.66]. This work-piece needs to resist very high pressures and is consequently made of hard material to optimize its service life. The mixing chamber and the mixing tube placed after the jewel, as shown in Fig. 36.41, allows one to obtain a triphasic mixture of water, abrasive particles, and air. This improves the efficiency of the jet for cutting hard materials. At the jewel outlet, the jet whose speed is around 800 m s1 [36.66, 68] then enters the mixing chamber connected to an abrasive tank. The friction between jet and air in this chamber creates a depression zone close to the jet which allows suction of the abrasive. The potential energy of the pressurized jet is converted into kinetic energy as it passes through the jewel. It is transmitted to the abrasive particles during acceleration and focusing of the water air abrasive mixture through a mixing tube with
36.3 Glass Shaping at Low Temperatures
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Part E
Glass Processing
a retardation of the trace of the cut behind the end of the mixing tube during the course of deepening the cut [36.70–72]. According to some authors the topography of the surfaces created by this process on relatively thick material consists of a smooth upper zone and a striated, wavy lower zone [36.71]. Some authors defined an initial zone which is located at the beginning of the cut [36.70, 72]. Hloch et al. defined a transition zone between the smooth zone and the rough zone [36.71].
Part E | 36.3
The Main Influential Parameters Water Pressure. Selvan et al. have shown that increasing the water pressure increases the ability of the jet to suck the abrasive into the mixing chamber and therefore into the mixing tube [36.73]. The abrasive jet can cut greater thicknesses (Fig. 36.42). To equal thickness, the roughness of the cut edge will be better (Fig. 36.43). Cutting performance is improved, provided one does not exceed a pressure threshold, which varies by working configuration. Hashish [36.74] gives a maximum pressure of 320 MPa for a 0:3 mm jewel, a 1:1 mm mixing tube, and an abrasive flow of 7:3 g s1 . Excessive pressure, above 350 MPa, associated with a high flow rate, limit hydraulic efficiency by increasing friction between jet and air in the mixing chamber. The hydraulic efficiency decreases by 5% for an increase in pressure of 150450 MPa [36.66]. The increase in pressure can also prematurely damage the mixing tube. Its service life can be halved when the pressure goes from 170 to 310 MPa [36.66]. Finally, in some cases, one can observe a wetting of the abrasive leading to a plugging of the mixing tube. When increasing the shooting distance, the material removal rate is reduced. This phenomenon can be
Mean surface roughness (μm) 4
3.5
3
2.5
300
350
400 Pressure (MPa)
Fig. 36.43 Influence of water pressure on the ceramic sur-
face roughness Ra . (Abrasive flow rate: 4 g s1 , traverse speed: 4:6 mm s1 , stand-off distance: 1:8 mm) [36.75]
explained by a reduction of the jet energy intensity during impact. Fowler et al. showed that the shape of the cutting profile was sensitive to the distance from the end of the mixing tube to the work-piece, as shown in Fig. 36.44. Laurinat et al. [36.76] showed that this influence is less strong with a distance of 25 mm. Selvan et al. [36.73] showed that the greater the distance between the work-piece and the end of the mixing tube is the less deeply the abrasive water jet can cut (Fig. 36.45). Selvan et al. [36.75] also showed that the greater the distance between the part and the end of the mixing tube, the greater the increase in roughness of the side cut (Fig. 36.46). Comier [36.68] showed that this distance influences the quality of the cut surface; the roughness increases as the distance increases. The Traverse Speed. Much study concluded that an increase in traverse speed causes an increase of the roughness of the cut surface, as shown in Fig. 36.47, and a reduction of the machined depth [36.68, 69, 77– 79] (Fig. 36.48). The experimental results of Fowler
Depth of cut (mm) 48
46
44
42 250
300
350
400 Pressure (MPa)
Fig. 36.42 Influence of water pressure on the depth of
cut for a steel application. (Abrasive flow rate: 8 g s1 , traverse speed: 0:42 mm s1 , stand-off distance: 5 mm) (after [36.73])
Fig. 36.44 Influence of the distance of the end of the mix-
ing tube to the work-piece on cut morphology
Glass Shaping
Depth of cut (mm)
36.3 Glass Shaping at Low Temperatures
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Mean surface roughness (μm) 5
5 4
4.5
3 4 2 1 42.7
42.8
42.9
43 43.1 43.2 Stand-off distance (mm)
5
5.5
6 6.5 Traverse speed (mm s–1)
Fig. 36.47 Influence of the traverse speed on the ceramic
cut surface roughness (abrasive flow rate: 4 g s1 , pressure: 275 MPa, stand-off distance: 1:8 mm); (after [36.75]) Depth of cut (mm)
Mean surface roughness (μm) 5
42 40
4.5
38 36
4 34 0.5 3.5
2
3
4 5 Stand-off distance (mm)
Fig. 36.46 Ceramic surface roughness according to the
distance from the end of the mixing tube to the work-piece (abrasive flow rate: 4 g s1 , pressure: 275 MPa, traverse speed: 4:6 mm s1 ); (after [36.75])
et al. [36.77, 78] showed that the removal rate was the highest for the slower traverse speed, and it rapidly decreases as the traverse speed increases. Moreover, the surface roughness increases by 2040% with a traverse speed increase of 0:030:166 mm s1 . The Abrasives The abrasives used are characterized by their hardness, size, material composition, and shape. Particle material usually determines the mechanical properties and the shape. Depending on the origin of the abrasives they may have angular or relatively round grains. Round grains have poor efficiency in abrading materials that have a high elongation, such as aluminum or copper. Fowler et al. advocate using abrasive angular grains for metals [36.77]. The sizes of these abra-
1
1.5
2 2.5 Traverse speed (mm s–1)
Fig. 36.48 Depth of cut decrease according to the traverse speed (abrasive flow rate: 8 g s1 , pressure: 270 MPa, stand-off distance: 5 mm); (after [36.73])
sives are generally expressed in terms of MESH. This American standard defines the smallest screen mesh to pass an abrasive grain. Consequently, MESH matches the number of screen mesh by inch. In addition, the thiner abrasives particles are (not over 40 MESH), the more efficient the abrasive water-jet is. Thus, the global kinetic energy is higher. Thinner abrasives produce slower cuts and smoother surfaces. In [36.69] Fowler notes that the effective abrasive size is 5500 m. If this value is greater than 100 m the material-removal rate is constant. In the converse case, it decreases rapidly. The higher the form factor, the slower the removal rate according to [36.77]. a low-density abrasive such as olivine limits the volume of air in the jet and occupies more space thus reducing the effectiveness of acceleration of the jet. A high-hardness abrasive generates efficient cutting. Nevertheless, the depth of cut depends on the
Part E | 36.3
Fig. 36.45 Depth of cut in steel according to the distance from the end of the mixing tube to the work-piece (abrasive flow rate: 8 g s1 , pressure: 270 MPa, traverse speed: 0:42 mm s1 ); (after [36.73])
3.5 4.5
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a)
b)
Fig. 36.49 (a) Example
of a twodimensional (2-D) spiral soft structure of soda-silicate glass shaped by an abrasive water jet; (b) glass pockets achieved by the abrasive water jet
Part E | 36.3
relationship between the hardness of the material and that of the abrasive [36.80]. Fowler et al. showed that an increase in the hardness of the abrasive gave an increase in roughness of the cut surface [36.77]. In addition, the work of Khan and Haque [36.80] showed that garnet creates a glass cutting profile wider than Al2 O3 and SiC. The machined depth depends not only on particle size but also on the abrasive flow rate [36.68]. An increase in the abrasive flow improves cutting performance and reduces the roughness obtained [36.68]. However, an excessive increase limits the effectiveness of the mixture: the cut width increases and machine grooves appear on the cutting faces. The machined depth, for a selected particle size, increases to a critical value. Beyond this threshold, the speed of the mixture at the mixing tube output is not homogeneous; the depth of cut is reduced [36.69, 78]. For a pressure of the order of 200 MPa and a jewel of 0:46 mm diameter, the optimal abrasive flow for a garnet type is 15 g s1 [36.66, 74]. Nonthrough Machining: Pocket Milling The abrasive water jet manufacturing process is used to achieve the cutting of various materials. If the abrasive water jet can cut samples with a thickness of several tens of millimeters, it can also and paradoxically, achieve nonthrough machining, also known as pocket milling (Fig. 36.49b), by defining appropriate machining parameters that would allow the material not to be pierced through. The manufacturing strategy as well as the cutting head speed are obviously key parameters to achieve pocketing but many other parameters also influence the quality of the surface finish [36.81, 82]. Brient et al. [36.34] studied the evolution of the roughness and waviness in regard to traverse speed.
When speed increases, material volumes of peaks, Vmp , and core roughness, Vmc , as well as void volumes of valleys, Vvv , and core roughness, Vvc , tend to decrease. Interestingly, the decrease of the four parameters is very similar, and the ratio between material and void remains roughly the same. Waviness amplitude is assessed by summing Spk , Sk , and Svk . These parameters are calculated from the Abbott–Firestone curve of the surface, similarly to the way Rpk , Rk , and Rvk are calculated from the Abbott–Firestone curve of a profile. Using the reduced peak and valley height (heights of the triangles defined in Sect. 36.3.2, Surface Finish of Ground Surfaces) instead of the total height of the surface Sz allow one to filter outliers. It also tends to decrease with traverse speed. Overall, this shows that the surface waviness amplitude decreases with traverse speed while keeping its craters and mounts aspect (Fig. 36.50). This preliminary study of water jet pocketing of glass has enlightened part of the influence of the machining parameters on the surface finish of the pocket bottom. It is characterized by several scales of damage. At the roughness scale, Sk , Svk , Spk give relevant information on the surface characteristics. Cracks, peaks, and core roughness tend to increase in the same proportions when traverse speed increases. At the waviness scale, the increase of traverse speed limits material removal and therefore the amplitude of the waviness. The material and void volume ratio remains the same despite the waviness amplitude decrease. Abrasive water jet cutting has been well studied by many research teams. The influence of the parameters has been studied for different materials such as aluminium, titanium, ceramics, and glass. The machine used for this process often offered the possibility of having an angular jet, but the influence of this parameter was less reported [36.83].
Glass Shaping
Roughness parameters (μm) 25
Sk
20
15
Spk
10
Svk 1000
2000
3000
Fig. 36.50 Evolution of roughness parameters Sk , Spk , Svk and waviness parameters Vmp , Vmc , Vvc , Vvv , amplitude D P .Sk I Spk I Svk /, according to traverse speed [36.34]. Those results are extracted from two different Abbott–Firestone curves of the filtered roughness and waviness surface, respectively
Waviness amplitude (μm) 160 Vvc
30
Vmc
150
140
20 ∑(Sk, Spk, Svk) 10 0
Vmp 1000
2000
3000
130 Vvv
120 4000 –1 Traverse speed (mm min )
36.4 Conclusions Glass is a unique material in terms of the wide range of options that can be used to shape it into various forms, for all types of applications in our everyday life. The shaping of a glass article usually relies on a series of different processes, starting with shaping at high temperature, during the cooling down of a glass melt, followed by steps of shaping at low temperature, such as cutting, grinding, polishing, or pocketing. Depending on the type of article to be produced, the nature of the hot-shaping process can vary significantly. Over the past centuries, industrials have been developing forming tools allowing for mass production of glass articles of various shapes (containers, fibers, plate glass, . . . ) adapted to each type of production, as described in this chapter, and new shaping strate-
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gies such as 3-D printing may open the door to new possibilities. While the viscosity–temperature profile of the glass is the most important parameter when considering the high-temperatures steps, mechanical properties of brittle materials, such as strength or toughness, are the most important for the low-temperature shaping processes. A good knowledge of the mechanical behavior of the material and the influence of the different machining parameters involved is thus critical. For the fabrication of a glass article requiring a combination of several steps and processes at various temperatures, whatever its shape or final application, the good performance of each of these steps is a necessity in glass production.
Part E | 36.4
Waviness parameters (μm) 40
4000 Traverse speed (mm min–1)
36.4 Conclusions
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References 36.1
36.2 36.3 36.4 36.5 36.6
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36.7
36.8
36.9 36.10
36.11
36.12
36.13
36.14
36.15
36.16 36.17
36.18
36.19
36.20
36.21
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36.39
36.40 36.41 36.42 36.43
36.44
36.46
36.47
36.48
36.49
36.50
36.51 36.52 36.53
36.54
36.55 36.56
36.57
36.58
36.59
36.60
36.61
36.62
36.63
36.64 36.65
36.66
36.67
36.68
36.69
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36.72 36.73
36.74 36.75
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M. Hashish: A modeling study of metal cutting with abrasive water-jets, J. Eng. Mater. Technol. 106(1), 88–100 (1984) J.G.A. Bitter: A study of erosion phenomena part I, Wear 6(1), 5–21 (1963) J.G.A. Bitter: A study of erosion phenomena, Wear 6(3), 169–190 (1963) J.H. Neilson, A. Gilchrist: Erosion by a stream of solid particles, Wear 11(2), 111–122 (1968) V. Le Houérou: Scratchability of Soda-Lime Silica Glasses, Ph.D. Thesis (Universite de Rennes, Rennes 2005) V. Le Houérou, J.C. Sangleboeuf, S. Deriano, T. Rouxel, G. Duisit: Surface damage of soda–lime– silica glasses: indentation scratch behavior, J. NonCryst. Solids 316(1), 54–63 (2003) T. Yu, H. Li, W. Wang: Experimental investigation on grinding characteristics of optical glass BK7: With special emphasis on the effects of machining parameters, Int. J. Adv. Manuf. Technol. 82(5), 1405–1419 (2016) R.L. Hecker, I.M. Ramoneda, S.Y. Liang: Analysis of wheel topography and grit force for grinding process modeling, J. Manuf. Process. 5(1), 13–23 (2003) M. Barge, J. Rech, H. Hamdi, J.-M. Bergheau: Experimental study of abrasive process, Wear 264(5/6), 382–388 (2008) P. Stępień: A probabilistic model of the grinding process, Appl. Math. Model. 33(10), 3863–3884 (2009) H.-C. Chang, J.J.J. Wang: A stochastic grinding force model considering random grit distribution, Int. J. Mach. Tools Manuf. 48(12/13), 1335–1344 (2008) M. Bigerelle, D. Najjar, A. Iost: Multiscale functional analysis of wear: A fractal model of the grinding process, Wear 258(1–4), 232–239 (2005) G.T. Smith: Industrial Metrology: Surfaces and Roundness (Springer, London 2002) D.J. Whitehouse: Handbook of Surface Metrology (CRC, Boca Raton 1994) T. Suratwala, L. Wong, P. Miller, M.D. Feit, J. Menapace, R. Steele, P. Davis, D. Walmer: Sub-surface mechanical damage distributions during grinding of fused silica, J. Non-Cryst. Solids 352(52–54), 5601–5617 (2006) R. Laheurte, P. Darnis, N. Darbois, O. Cahuc, J. Neauport: Subsurface damage distribution characterization of ground surfaces using Abbott– Firestone curves, Opt. Express 20(12), 13551–13559 (2012) D.A. Stephenson, J.S. Agapiou: Metal Cutting Theory and Practice, 3rd edn. (CRC, Boca Raton 1994) H. Demir, A. Gullu, I. Ciftci, U. Seker: An investigation into the influences of grain size and grinding parameters on surface roughness and grinding forces when grinding, Strojniski Vestnik/J. Mech. Eng. 56(7/8), 447–454 (2010) S. Tong, S.M. Gracewski, P.D. Funkenbusch: Measurement of the preston coefficient of resin and bronze bond tools for deterministic microgrinding of glass, Precis. Eng. 30(2), 115–122 (2006)
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36.77
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experimental investigation, Int. J. Adv. Sci. Eng. Technol. Res. 1(3), 52–59 (2012) A. Laurinat, H. Louis, G. Meier-Wiechert: A model for milling with abrasive water-jet. In: Proc. 7th Am. Water-Jet Conf., Water Jet Tech. Assoc., Saint Louis (1993) G. Fowler, I.R. Pashby, P.H. Shipway: The effect of particle hardness and shape when abrasive water jet milling titanium alloy Ti6 Al4 V, Wear 266(7/8), 613–620 (2009) G. Fowler, P.H. Shipway, I.R. Pashby: Abrasive water-jet controlled depth milling of Ti6 Al4 V alloy—An investigation of the role of jet–work piece traverse speed and abrasive grit size on the characteristics of the milled material, J. Mater. Process. Technol. 161(3), 407–414 (2005) Y. Petit: Découpe du verre plat de silicate sodocalcique. In: Techniques de l’ingénieur Sciences et technologies du verre (2012) n4401
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A.A. Khan, M.M. Haque: Performance of different abrasive materials during abrasive water jet machining of glass, J. Mater. Proc. Technol. 191(1–3), 404–407 (2007) L.M. Hlaváč, I.M. Hlaváčová, L. Gembalová, J. Kaličinský, S. Fabian, J. Měšt’ánek, J. Kmec, V. Mádr: Experimental method for the investigation of the abrasive water jet cutting quality, J. Mater. Process. Technol. 209(20), 6190–6195 (2009) M.C. Kong, D. Axinte, W. Voice: An innovative method to perform maskless plain waterjet milling for pocket generation: A case study in Ti-based superalloys, Int. J. Mach. Tools Manuf. 51(7/8), 642–648 (2011) J. Wang: Abrasive water-jet machining of polymer matrix composites–cutting performance, erosive process and predictive models, Int. J. Adv. Manuf. Technol. 15(10), 757–768 (1999)
Romain Laniel Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France [email protected]
Romain Laniel received his PhD from the University Montpellier 2, France, in 2007. He worked at the LMGC in the framework of contact mechanics and discrete elements simulations, before joining the Institut de Physique de Rennes at the University of Rennes 1, France. His research focuses on multi-body simulations of manufacturing process and surface generation.
Mathieu Hubert Dept. of Corning Glass Technologies Corning Research & Development Corporation Painted Post, USA [email protected]
Mathieu Hubert received his PhD from the Universities of Rennes 1, France, and Arizona, USA, in 2012. He joined CelSian Glass & Solar in 2013 as a Glass Scientist/Technologist, performing consulting and contract R&D for the glass industry worldwide. In 2016, he joined Corning as a Development Scientist, working on new display glasses and specialty materials.
Mathieu Miroir Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France [email protected]
Mathieu Miroir received his PhD from the University Paris 6, France, in 2009. He worked at the UMR-S 867 team of the Institut National de la Santé et de la Recherche Médicale at Paris, France. He currently works at the Institut de Physique de Rennes at the University of Rennes 1, France. His research area is the design of mechatronic systems, in particular the command scheme and the human-machine interface.
Antoine Brient Institute of Physics – Rennes (IPR), UMR CNRS 6251 University of Rennes 1 Rennes, France [email protected]
Antoine Brient received his PhD from the Ecole Centrale de Nantes and Nantes University in 2004. He has worked at IRENav in Brest and at IRCCyN in Nantes. He currently works in the Mechanics and Glasses Department of the Institute of Physics of Rennes . His research focuses on the influence of machining processes on the surface functionalities of glasses.
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Amorphous T 37. Amorphous Thin Film Deposition
Virginie Nazabal
, Petr Němec 37.1 37.1.1 37.1.2 37.1.3 37.2 37.2.1 37.2.2 37.2.3
Amorphous Film Processing and Coatings on Glass ....................... Film Nucleation and Growth ............... Thin Film Microstructure..................... Thin Layer Characterization Methods ... Physical Vapor Deposition.................. Plasma in PVD ................................... Vapor Techniques .............................. Ion Plating and Ion Beam-Assisted Deposition ........................................
1291 1293 1294 1296 1297 1298 1314 1315
37.3 37.3.1
Chemical Vapor Deposition ................ 1317 Vapor-Based Film Fabrication ............. 1317
37.4
Comparison of PVD and CVD Techniques .......................... 1318
37.5
Liquid-Based Film Fabrication ........... 1320
37.6
Contribution of Amorphous Thin Films and Coatings on Glass to 21st Century Development .................................... 1322
References................................................... 1324
37.1 Amorphous Film Processing and Coatings on Glass First of all, it is important to define the concept of amorphous material or amorphous thin film as a noncrystalline solid without long-range order which may include the more specific and sometimes reductive notion of a glassy thin film demonstrating a glass transition temperature domain. The amorphous thin films, possibly obtained from bulk glass targets, open up innumerable prospects for functional materials by enabling specifically sought-after physical/chemical properties, definite and controlled small dimensions or design conformability that cannot be attained if we use its solid glass counterpart. It is possible to combine the properties of two or more materials including the substrate to form a heterostructure or a composite material whose
characteristics are not readily or economically available with solid materials. For more than 60 years, amorphous or crystallized thin films have been contributing to the industrial manufacture of electronic devices, optical coatings, protecting coatings, and creative arts. Thin films are still at the heart of the high-technology developments to create new functional materials that can meet many of the new needs and desires of our 21st century society like metal and insulating multilayers in microelectronics, ceramic layers in hard and thermal barrier coatings, dielectric layer stacks for optical coatings, semiconductor films in optoelectronics, dielectric films for integrated photonics, multilayers for microbatteries, etc.
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_37
Part E | 37.1
This chapter is devoted to the description of available experimental methods which are used for the fabrication of glassy and amorphous thin films or coatings on glass. Current deposition techniques offer great flexibility for the fabrication of such thin films with specific chemistry and microstructure leading to films and coatings with distinctive properties. After a brief introduction to amorphous thin films’ processing, general information regarding film nucleation and growth, its microstructure and films’ characterization techniques, the main focus is on physical vapor deposition techniques, with special emphasis on plasma processing techniques, i. e., sputter deposition and pulsed laser deposition. The classical vapor deposition techniques as well as ion plating and ion beamassisted deposition are also briefly described. The chapter then describes the exploitation of chemical vapor deposition, after which a comparison of physical vapor deposition processes with chemical vapor deposition is given. Amorphous thin film fabrication via liquids is shortly reviewed, and finally an outlook regarding the contribution of amorphous thin films and coatings to societal development in the 21st century closes the chapter.
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The amorphous film materials can be formed by direct deposition of a glassy material, by deposition at low temperatures leading to a reduced mobility of the adatoms on the substrate preventing crystalline structure formation (high rate of thermal quenching), by ion bombardment of high-modulus materials during deposition, by deposition of materials with bonds partially saturated by hydrogen, like amorphous films a-Si:H, a-C:H, and a-B:H, by ion bombardment of films after deposition, which may lead to their amorphization [37.1]. There are numerous techniques for producing amorphous films of varying thickness on the surface of a substrate which may be of a quite different nature from the deposited layer. In essence, deposition technologies use three main elements:
Part E | 37.1
1. The source corresponding to where the material to be deposited, or one of its components, is concentrated (crucible, metal plate, gas bottle, etc.) and where basic physical phenomena take place like the dispersion of the material in the form of atoms, ions, molecules, clusters (group of atoms or molecules). 2. The medium between the source and the substrate where material transfer phenomena essentially appear. It may also be the location of chemical reactions occurring between the atoms of the material to be deposited and a reactive gas for example. 3. The substrate where a condensation phenomenon occurs. The material from the source, pure or recombined, is then fixed to form seeds, islands that will develop
until the formation of the desired layer. Wet deposition techniques require the use of a liquid such as spin- and dip-coating from sol–gel. For the other type of film deposition processes in which material is vaporized from a solid or liquid source in the form of atoms or molecules, they are commonly divided into two main categories—physical vapor deposition (PVD) and chemical vapor deposition (CVD) techniques even if some links between physical and chemical methods exist (Fig. 37.1). The quenching speed (K=s) from vapor must be superior to 109 K=s for vacuum deposition, CVD and 1016 K=s for sputtering. Compared to air, water quenching or even roll quenching, it is easy to understand that the glassy domain of the thin films is much more extensive in terms of chemical composition than conventional melting/quenching fabrication opening a vast field of investigation. The background pressure in the deposition chamber, the kinetic energy of the incident particles, the nature of the target and the substrate, the deposition rate, the temperature and surface preparation of the substrate are some of the many deposition parameters which influence the characteristics of the film forming on the surface of the substrate [37.2, 3]. These deposition techniques are widely used in order to produce functional or decorative coatings on various glasses in order to control their optical, electrical, and chemical properties. Coatings with their design flexibility may be essential when it is required to confer on a glass substrate distinctive optical and electrical properties, thermal insulation, mechanical strengthening, chemical or solar protection, weight reduction, creative packaging, or specific characteristics for the construction industry, for example. More infor-
Vapor deposition Chemical vapor deposition (CVD)
Physical vapor deposition (PVD)
Vacuum evaporation
Electron beam evaporation
Sputtering
Molecular beam epitaxy
DC sputtering
Ion plating Ion Assisted deposition
Thermal evaporation
RF sputtering
Metalorganic chemical vapor depositionMOCVD
Atomic layer deposition ALD
Low pressure & ultrahigh vacuum LP/UHCVD
Plasma enhanced PECVD REPCVD, MPCVD
Pulsed laser deposition
HiPIMS HPPMS
Fig. 37.1 A nonexhaustive list of various vapor deposition techniques including physical and chemical methods (PVD and CVD)
Amorphous Thin Film Deposition
mation on glass coating are available in two reference books [37.4, 5]. Several stages are constitutive of the formation of the thin film on a substrate defining its microstructure; this goes from the formation of the vapor phase, the transport of the atoms, fragments, or molecules from the vapor source to the substrate, to the deposition of these atoms or molecules and their possible rearrangement on the substrate. We will thus briefly discuss these different stages, which may be specific according to the deposition techniques used or can be approached in a globalized way. A virtuous circle of scientific knowledge must be established between thin film manufacturing, material characterization and causal identification between the characteristics and properties of thin films in order to optimize their functionality. The main methods of amorphous thin film characterization will also be concisely stated in this introductory part.
37.1.1 Film Nucleation and Growth
per unit of time and surface, the energies of activation, adsorption, desorption, thermal diffusion, the temperature, topography, and chemical nature of the substrate. The next step is coalescence for which the islands begin to aggregate to another by reducing the surface of the uncoated substrate. Coalescence can be accelerated by increasing the temperature of the substrate. Gradually a continuous layer is formed when the holes and channels are filled. Conversely, if the atoms that condense react strongly with the surface, the mobility of the atoms will be weak and a monolayer rapidly forms on the surface. If there is a chemical reaction or diffusion, the condensed atoms will react with the surface to form layers that will extend parallel and perpendicular to the surface. This mode of growth will tend to reduce the interfacial porosity. It is worth noting the crucial importance of the process of cleaning the substrate before film deposition because these mechanisms can be extinguished by the presence of a contaminant layer on the substrate surface. Generally, three modes of film nucleation and growth are recognized (Fig. 37.2a–c) [37.8–11]: 1. Three-dimensional (3-D) island growth (Volmer– Weber mode) 2. Two-dimensional (2-D) full monolayer growth (Frank–van der Merwe mode) 3. Two-dimensional growth of full monolayers followed by nucleation and growth of three-dimensional islands (Stranski–Krastanov mode). It is generally believed that the selection of one of the above-listed modes in a substrate–film system Island structure
a)
b)
c)
Uniform film
Island structure
Uniform film
Fig. 37.2a–c Three main film growth processes occurring on substrates: island type/Volmer–Weber mode (a), layer type/Frank–van der Merwe mode (b), mixed type/Stranski–Krastanov mode (c)
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We will begin with the principles of film formation on the substrate which can be described in a relatively general approach considering film nucleation and growth. The condensation phenomena on substrates are treated comprehensively in different references and will be described concisely here and not repeated in great detail [37.1–3, 5–7]. The behavior of an atom that condenses on a substrate surface is determined by its interaction with that surface. At the moment of impact on the substrate, the deposited atoms lose their displacement velocity component and are physically adsorbed on the surface of the substrate insofar as the energy of these atoms is not too high. They are not in thermal equilibrium with the substrate and therefore move on its surface. If there is no bond between the adatom and the surface, the atoms will take the opportunity to interact with each other as the atom will diffuse on this surface until it adheres to an island or contributes to the creation of a new island. These islands are thermodynamically unstable and naturally tend to desorb. When they reach a certain size, they become stable, crossing the nucleation threshold and a nonreactive nucleation mode with disparate islands will emerge. The islands then continue to grow in number and size until reaching the so-called saturation nucleation density. This means that we will have the beginning of continuous layer formation only after the islands have already reached appreciable thickness with the growth type islands/channels. The lateral growth rate is typically much greater than the perpendicular growth rate. The nucleation density and the average size of the islands depend on several parameters such as the energy of the incident species, their quantity
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depends on the thermodynamics relating the surface energies of the film and the substrate and on the film– substrate interface energy. The nucleation of atomic clusters on the substrate is a complex statistical process involving different phenomena illustrated in Fig. 37.3. First, one considers bare substrate areas or already-deposited atomic clusters. Atoms being deposited arrive at the substrate surface with a rate that depends on the experimental conditions of the deposition technique. The atoms at the substrate surface diffuse, form mobile or immobile clusters, bind to already-formed clusters, are desorbed (from the substrate or from the cluster), or are separated from the cluster staying on the substrate surface (Fig. 37.3). The equilibrium between the process of cluster growth and dissociation is driven by the total free energy of the cluster, relative to the group of individual atoms. In Volmer–Weber mode (Fig. 37.2a) [37.8], small clusters are nucleated directly on the substrate surface and then grow into islands of the condensed phase. This may happen when the atoms are more strongly bound to each other than to the substrate. This mode is valid for many systems of metals growing on insulators, including many metals on alkali halides, graphite, and other layer compounds such as mica. Conversely, in Frank– van der Merwe mode (Fig. 37.2b) [37.9] the atoms are more strongly bound to the substrate than to each other. Because of this behavior, the first deposited atoms form a complete monolayer on the surface, which becomes covered with a somewhat less tightly bound second layer. As a result, the layer growth mode is obtained. The depicted growth mode is observed in the case of adsorbed gases, such as several rare gases on graphite and on several metals, in some metal–metal systems, and in semiconductor growth on semiconductors. In an intermediate case, the layer plus island Stranski–Krastanov growth mode (Fig. 37.2c) [37.10], the basic sequence is that the atoms first form a complete monolayer or a few monolayers (typically 15), while subsequent layer growth is unfavorable and islands are formed on top of this layer. This growth mode occurs in metal– Atom deposition on substrate
37.1.2 Thin Film Microstructure Materials deposited in thin layers have properties and behaviors that differ, often neatly, from those of massive materials. Among these properties and different behaviors, we can mention the high defect content, the strong internal constraints, the metastable phase composition, etc. In order to understand the influence of the elaboration conditions on the final properties of the thin film, the study of the reaction phenomena leading to the formation of the interface and to the growth of the film is therefore essential. The morphology of a deposited layer depends on how adatoms are incorporated into the film growth process. The preferential growth of one surface area relative to another can come from the different mobility of the deposited atoms according to the orientation of grains or the islands’ shape. Preferential growth will involve a dominant grain orientation or preferential island shape in the case of amorphous film and a surface will become rougher as the layer becomes thicker. When the surface becomes rougher, shading phenomena will lead to preferential growth on the top of islands, leading to the deposition of a columnar structure. A higher substrate temperature will have effects on the layer’s structure by increasing surface mobility, diffusion phenomena, and permitting recrystallizations. The deposition rate and substrate temperature are two important parameters that determine the microstructure of the thin film. The model of structure zone (MD model) was first proposed in 1969 by Movchan and Demchishin [37.12] who deposited by evaporation thick metal layers on substrates with temperature gradients. This earlier model represents three
Atom deposition on cluster Re-evaporation from substrate
Cluster nucleation
metal, metal–semiconductor, gas–metal, and gas–layer compound systems. It should be mentioned that all of the nucleation and growth modes depicted above postulated homogeneous, random nucleation on the substrate surface. However, a real substrate surface contains many defects (point, line defects, ledges, . . . ) at which, due to their lower energy, heterogeneous nucleation will preferably proceed.
Diffusion to cluster
Re-evaporation from cluster Dissociation of cluster
Fig. 37.3 Nucleation and growth processes involved in film fabrication
Amorphous Thin Film Deposition
zones depending on the ratio of the substrate surface temperature T to the melting point of the deposited material Tm . The homologous temperature Th is defined as the T=Tm ratio:
At low homologous temperature, shadowing effects dominate leading to columns surrounded by shadowed regions, often forming a network of low-density material. The column size generally increases with T with a)
increased mobility and the column density may reflect the nucleation density, especially in the thinnest films. For oblique incidence deposition, the columns are inclined at an angle lying between the film normal and the direction of the incident flux (Fig. 37.4). The film microstructure depends on ballistic shadowing and formation of columnar microstructures during deposition. The glancing angle deposition (GLAD) is an extension to oblique angle deposition where the substrate position is manipulated during film deposition. The GLAD principally occurs in zone I of Movchan and Demchishin’s structure zone model, where Th 0:3 limits surface diffusion, leading to the formation of a columnar structure which can be amorphous [37.15]. Applications of GLAD include active and passive optical devices using numerous materials, providing design flexibility and creating characteristics useful in retarding elements, circular polarizers and polarized light emitters, among others; sensor devices (pressure sensors, optical resonators, humidity sensors, nanomotors); energy devices (electrochemical supercapacitors, microbattery charge storage, fuel cells, solar energy conversion). The concept of a surface zone model (SZM) evolved over the years as deposition technology expanded from evaporation to sputtering and ion beam-assisted deposition. As a function of deposition parameters, the model of structure zone was improved by several authors [37.16–20] and classifies self-organized structural
b)
α
c)
d)
β≠α
Incident vapor
e)
Deposition time = 1 min
500 nm
Deposition time = 10 min
500 nm
Deposition time = 25 min
500 nm
Deposition time = 60 min
500 nm
Fig. 37.4a–e Schematic view of GLAD growth: (a) initial arrival of vapor flux at an angle ˛, producing a random distribution of nuclei on the substrate surface; (b) nuclei grow, casting shadows across the substrate; (c) columns develop, partially shadowing smaller neighbors and suppressing their growth; (d) columns grow at an inclined angle (after [37.13]). (e) SEM images of highaspect-ratio patterns on polydimethylsiloxane (PDMS) surface after carbon amorphous film deposition at 75ı incident angle for four different deposition durations. Reproduced from [37.14] with permission of The Royal Society of Chemistry
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Zone I (Th 0:3): This zone consists of very small crystallites with high defect densities surrounded by low-density, voided boundaries. It occurs when the diffusion of the adatoms is insufficient to compensate the effects. A columnar structure with low density zone between the columns is then obtained. The shaded individual columns are amorphous or polycrystalline with high defect densities. The grain size is small and the topography is rounded. Zone II (0:3 < Th < 0:5): This occurs when the diffusion of the adatoms dominates, so the columnar structure has fewer defects and larger grains, with the zone between the columns of higher density. The topography of the surface here is more angular. Zone III (Th 0:5): This zone exhibits phenomena of diffusion in the mass of the layer and also of recrystallization. The material is formed of coarse grains with high density.
37.1 Amorphous Film Processing and Coatings on Glass
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37.1.3 Thin Layer Characterization Methods
Part E | 37.1
growth during PVD (similar or related diagrams can be formulated for CVD). The SZM, built by the compilation of the experimental results, presents an important guideline to classify the dependence of the structures on the deposition temperature taking into account the homologous temperature, T=Tm . It is generally agreed that the surface and bulk diffusion are the most determinant atomic processes of structure evolution. Then, Barna and Adamik reported on the role of impurities (additives) which can promote or inhibit the operation of the structure-forming phenomena [37.20, 21]. An extended structure zone diagram was later proposed by A. Anders that includes energetic deposition, characterized by a large flux of ions typical for deposition by filtered cathodic arcs and high-power impulse magnetron sputtering [37.22] (Fig. 37.5). The axes are comprised of a generalized homologous temperature, the normalized kinetic energy flux, and the net film thickness, which can be negative due to ion etching. Microstructural and nanostructural engineering can be monitored by controlling the film growth to design a material for specific technological applications. According to these structure zone models defining the morphology of the amorphous and polycrystalline thin films, the homologous temperature has to be between 0:1 and 0:4 depending on chemical composition (Tm ), deposition parameters, and deposition method used (energy flux) in order to avoid zone 3 completely. The thickness t will also play an important role in amorphous thin film microstructure by changing the topography of the film when the film roughness increases.
It is worth stating that the notion of thin film used most of the time in the case of a deposited layer corresponds to a low-dimensional material created by condensing atoms, molecules, or ions with thickness of the order of a few atomic layers to a few micrometers. The term thin film typically refers to a layer presenting different properties from the bulk, strongly affected by its specific surface and interface properties. The thin films are often not as dense as the bulk glass counterpart, frequently under mechanical stress depending on the deposition conditions, with microstructure of different topography and morphology. Thus, the quasisystematic deviation of the chemical and physical properties and the structure of the thin film compared to those of the bulk sample having a nominally identical composition require the combination of complementary techniques, especially for the amorphous layers, in order to characterize all their properties which make thin layers so unique for the different applications envisaged. The purpose of this chapter is not to review the different tools suitable for thin film characterization such as electron microscopy, XPS, AFM, Raman and IR spectroscopy, EXAFS and many others, but to highlight their absolute necessity when one wants to understand and control films’ properties after the essential step represented by the thin film deposition. These characterization techniques and their use can be found in the various chapters of Part C in this book and therefore will not be described here. In addition, it is important to note that the small amount of material available for analysis
Zone 3
Recrystallized grain structure
Zone 2
t*
Zone 1
Columnar grains
1
Zone T Region not accessible
T*
Cutout to show structure Fine-grained, nanocrystalline, with preferred orientation
0.5
0.2
0.1 Porous, tapered crystallites separated by voids, 10 –3 tensile stress Densely packed fibrous grains
Ion etching zone
1
Transition from tensile (low E*) to compressive stress (high E*) Region of possible low-temperature low-energy ion-assisted epitaxial growth
10
Region not accessible 102 103 Region of max. compressive stress
Reduction of deposition by sputtering, dense film, amorphous for some materials
E*
Line separating net deposition and net etching
Fig. 37.5 Struc-
ture zone diagram applicable to energetic deposition; with the generalized temperature T , the normalized energy flux E , and t represents the net thickness. Reprinted from [37.22], with permission from Elsevier
Amorphous Thin Film Deposition
37.2 Physical Vapor Deposition
1297
Table 37.1 Nonexhaustive list of methods for the ex situ characterization of amorphous thin films Pkroperties/characteristics Chemical composition, oxidation states
Thickness
Morphology/topography
Glass network structure
Mechanical properties
Conductivity and electrochemistry properties
and its strong interaction with the environment due to the large surface-area-to-volume ratio require a specific methodology to provide reliable information about thin films, generally mentioned by the authors in their pub-
lications concerning thin film characterizations [37.23]. For the reasons mentioned above, we present in Table 37.1 only a brief review of methods applicable for the ex situ characterization of amorphous thin films.
37.2 Physical Vapor Deposition Physical vapor deposition (PVD) is a family of thin film deposition processes for which it is typical that material is vaporized from a solid or liquid source in the form of atoms, molecules, or clusters (Fig. 37.1). Then the vapor is transported to the substrate in a chamber under (partial) vacuum. The mechanism involved in film formation is a pure physical condensation or involves chemical reactions. The whole process proceeds under vacuum or under low gas pressure.
Using a PVD system, as illustrated by Fig. 37.6, the films can be fabricated in the crystalline or amorphous state with broad thickness range from a few nanometers to micrometers. The physical vapor deposition is useful for the preparation of multilayered structures, graded films, free-standing structures, etc. For instance, PVD has become widespread for coating tools for the improvement of wear resistance, oxidation resistance, lubricity, surface roughness, cutting tools, and sliding characteristics.
Part E | 37.2
Density Optical properties (band-gap, refractive index)
Characterization techniques Energy dispersive x-ray analysis (EDX) Rutherford backscattering spectrometry (RBS) X-ray photoelectron spectroscopy (XPS) Inductively coupled plasma optical emission spectrometry (ICP-OES) Secondary-ion mass spectrometry (SIMS) Auger electron spectroscopy (AES) X-ray absorption near-edge structure (XANES) Profilometry X-ray reflectometry Ellipsometry M-lines Spectrophotometry (R&T) Optical microscopy Scanning electron microscopy (SEM) Transmission electron microscopy (TEM) Scanning probe microscopies: scanning tunneling microscopy (STM), atomic force microscopy (AFM) Glancing incidence x-ray diffraction X-ray photoelectron spectroscopy (XPS) Fourier-transform infrared spectroscopy (FTIR) and Raman scattering spectroscopy Nuclear magnetic resonance (NMR) Extended x-ray absorption fine structure (EXAFS), . . . X-ray reflectometry Ellipsometry M-lines Spectrophotometry (R&T) Stress curvature measurements Adhesion tests Nanoindentation, . . . Complex impedance spectroscopy Cyclic voltammetry and galvanostatic cycling
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Fig. 37.6 PVD cluster including PLD,
Pulsed laser deposition
Sputtering • 2'' target face to face • 3'' target face to face • Cosputtering (three 2'' targets)
RF sputtering and cosputtering, ebeam and thermal evaporation system. Courtesy of University of Pardubice, Czech Republic
Vacuum evaporation • E-beam evaporation • Thermal evaporation
37.2.1 Plasma in PVD
Part E | 37.2
Processes exploiting plasma form one of the most important groups of PVD techniques. Typical plasma processing techniques are sputter deposition, pulsed laser deposition (PLD), arc vapor deposition, and ion plating. Plasma can also be used to enhance some other deposition processes such as chemical vapor deposition. In this chapter, attention will mainly be paid to sputtering and pulsed laser depositions, techniques that are heavily applied for the growth of amorphous and glassy thin films. Sputtering Deposition Principles The main principles of the sputtering deposition method will be concisely described in this chapter and further details are available in cited references [37.6, 7, 24]. Sputtering is a method involving the physical—and nonthermal—vaporization of atoms from the target material to be deposited. Since the material to be deposited passes into the vapor phase as a result of a mechanical process (energy transfer from the incident ion to the surface atom at the moment of collision), virtually all the inorganic materials can be deposited with good adhesion and covering, and low porosity. The sputtering occurs each time an incident ion/particle strikes a surface with sufficient energy to break the bonds and dislodge an atom from the target surface. The source of the incident particles might either be a local plasma (diode or magnetron sputtering) or a separate ion beam source (ion beam deposition). The condition under which sputtering is performed may involve a reactive sputtering or a bias sputtering. During the last decade, the DC (direct current), RF, and pulsed sputtering techniques have been used extensively eventually with the magnetron system to increase deposition rate. This physical process takes place in a working vacuum ranging from 104 to 101 mbar where the mean free path for collision is considered as a middle to short path (102 101 cm) transitioning from molecu-
lar to viscous flow. The system must be able to reach a high vacuum with a molecular flow type and mean free path around 104 106 cm (limit vacuum range: 106 108 mbar) characterized by the mean free path of the residual gas molecules and the type of gas streaming. Hydrogen is the predominant contaminant even in the ultrahigh vacuum system as it permeates practically all materials. The conductance of the pumping is often reduced allowing the control of working pressure with suitable gas flow guaranteeing plasma stability or reactive reaction during deposition. Like the power density applied to the target, the pressure and gas flow of inert and reactive gases can clearly influence the target sputtering rate, deposition rate, and composition of sputter-deposited materials. The main parameters governing the sputtering deposition of thin layers can be summarized as follows: 1. 2. 3. 4. 5. 6. 7.
Partial gas pressure Composition of the gas Power applied to the target Polarization voltage of the substrate holder Current density Angle of incidence of the bombardment particles Presence or absence of magnetic fields.
The interactions between the incident ion and the target atoms correspond to a sum of simple mechanisms if taken into account individually but in reality, forming a relatively complex system with intricate mechanisms. In first approximation, we can estimate an elastic collision as the main motion transfer mechanism within the target material to be sputtered with conservation of kinetic energy and momentum. The ratio between the weight of atoms of the target and that of the incident ions is a prime factor influencing the transmission and distribution of energy into the target. For heavy incident ions, the energy loss is mainly due to nuclear collisions; such collisions are thus quasielastic with two main schemes: the regime of simple impact (501000 eV) and the cascade regime (1100 keV).
Amorphous Thin Film Deposition
Plasma Processing. The plasma, an essential part of the processing in the case of sputtering deposition, is a state of matter which is defined as an ionized medium composed of free particles charged positively or negatively forming a neutral set with collective behavior. In a PVD processing plasma, the plasma is created un-
Ar+ incident ion
der low pressure by electron–atom collisions and the ionization rate of the gas medium is relatively low with a predominance of neutrals. The uniformity of the plasma will play a decisive role in the quality and the characteristics of the sputtered films depending on how the plasma is generated, on the geometry of the system—in particular the electrodes—and on the injected gas fluidic inside the chamber. The plasma is characterized according to different physical quantities and parameters like: 1. Ion and electron density which is defined as the number of ions or electrons present in the plasma per unit volume 2. Ratio of neutrals to ions 3. Neutrals, ion, and electron temperatures. In the case of thin film deposition, the electron density of the plasma can be 1 109 1 1012 cm3 . Electron temperature is also an important parameter defining the plasma. Thus, in cold plasma, during the creation of new species, the ionized medium is no longer in thermodynamic equilibrium, the temperature Te of the energetic primary electron (> 15 eV) is very high with respect to the temperature of the neutral species Tn and ions Ti . Cold plasmas are said to have no thermodynamic equilibrium (unlike hot plasmas in thermodynamic equilibrium), i. e., Te
Tn Ti . Contamination during the development process is often a concern in PVD plasma treatment. It is even more worrying if the conductance of the pumping system is reduced to minimize the flow of Ar gases in the system thereby reducing the possibility of eliminating the contaminants generated during the treatment.
Ar+ incident ion
Sputtered atom Back scattered atom
Reflected neutral/ions Secondary electron
Surface
Altered region (≈ 10 Å?)
Fig. 37.7 Simpli-
Displaced atom
Cascade collision
1299
Implanted Ar+
fied principle of the major events taking place during sputtering
Part E | 37.2
These collisions will hence enable ejection of atoms from the surface of the solid (the target) by bombardment by energetic ions, generally ArC ions accelerated in an electric field. The application of a potential difference between the cathode (target) and the anode (substrate) in a rarefied atmosphere (argon) allows the creation of plasma composed of electrons, ions, photons and neutral species. Under the effect of an electric field, the positive species of the plasma (ArC ) are attracted to the cathode. The ArC ions acquire energy which they will release on impact with the surface of the material and pass to the target atoms by momentum transfer. Schematically, Fig. 37.7 displays some phenomena likely to occur during the interaction between the charged particles arriving on the surface of the material and the latter. This effect will spread by degrees to the atoms in the vicinity of the initial impact until the energy of the incident particle is low enough that network cohesive forces immobilize it. Redistribution of this energy to a portion of the target volume will depend primarily on the energy and mass of the incident ion, the mass of the atoms constituting the target, the nature of the chemical bonds, the network density, and the angle of particle incidence. Some atoms near the surface will therefore acquire enough energy to be ejected from the target with a speed and direction dependent on collision mechanisms in the target.
37.2 Physical Vapor Deposition
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Part E
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Part E | 37.2
Collision Regime and Sputtering Yield. There is a threshold energy below which sputtering does not occur, even if the bombardment flow is high. This energy mainly depends on the ratio between the atom mass of the target and that of the incident ion, the binding energy of the atom within the material (which is the minimum required energy to move an atom from the target), and the surface potential that will control the probability of the atom extracting itself out of the material. The minimal energy of the incident ions causing the sputtering process is often related to the binding energy of surface target atoms which are the weakest bounded (3040 eV). Within the incident energy range between 40 and 1000 eV, the incident particle has enough energy to take out tens of atoms by moving only a few atoms. This energy range corresponds to the knock-on mode which involves only a limited number of atoms and which is in practice the energy conventionally used for the sputtering process [37.6, 24, 25]. This collision regime occurs when the energy of the incident ion is greater than the binding energy of the atoms of the target. The collision sequence is relatively unstable and depends essentially on the bombardment conditions and the impact point of the incident particle. After this first collision, the incident particle and the impacted atom shift causing the movement of the surrounding atoms. Finally, these collisions will cause the ejection of an atom at the solid material surface or its close vicinity. Thus, surface atoms can be emitted either directly by the impact of the primary knock-on or by the impact of an atom that had previously been moved by the incident ion considering secondary knock-on effects. The transition between these two mechanisms lies in the energy range between a few 100 and 1000 eV. The erosion of a material is quantified by the sputtering yield which indicates how many surface atoms are removed per incident ion. In other words, the sputtering yield corresponds to the ratio between the sputtered atoms and the number of incident particles or ions with sufficiently high energy [37.26]. Wehner and coworkers initially carried out a number of experiments that established general trends of the sputtering process [37.27, 28]. It depends on the mass of the incident particle (atom or ion) as well as on its energy and on the characteristics of the target material. The crystallinity, the density, and the crystal orientation of the target for instance influence the sputtering yield. The impact energy of the incident ion is an important parameter that will control the quantity of atoms moving near the surface and the quantity of emitted target atoms (Fig. 37.7). Within optimum energy range, generally between 200 and 800 eV, the sputtering efficiency increases practically linearly with the energy of the incident ions. An increase in the flux of the in-
cident particles also results in a linear increase in the number of sputtered atoms. Moreover, the sputtering efficiency is sensitive to the angle of incidence of the incident particle. In order to determine the sputter yield, the incident particles fluency should be measured accurately and the quantity of sputtered particles must be defined by means of appropriate diagnostic tools, including weight loss, optical emission spectroscopy (OES), quartz crystal microbalance (QCM), or Rutherford backscattering (RBS) [37.24, 25]. Experimental results have been gathered for amorphous or polycrystalline targets but less often for single crystal targets taking into account the required small energy width and angular divergence of incident particles, low target impurities, knowledge of texture target, or high vacuum conditions [37.26]. Nevertheless, the sputtering yield distribution of such measurements remains large mostly due to the variety and complexity of sputtering experiments. Absolute sputtering yields of monoatomic elemental targets were calculated considering Sigmund’s theory [37.26], further improvements by Matsunami et al. [37.29] and finally, the complementary approach of Seah et al. [37.30, 31]. Using a semiempirical equation for Ar, Ne, or Xe incident particles, at 0ı or 45ı incidence from 250 to 10 000 eV, the scatter between the prediction at normal incidence and the experimental data for ArC is 9% [37.32]. The energy transferred by the physical collision between hard spheres corresponding to the incident particles and target atoms can be first approximately described as respecting the conservation law of energy and momentum. The increase of incident angle , from the normal incidence to about 70ı from normal can considerably increase sputtering efficiency, up to 3 times in the case of argon, for most materials. Indeed, a greater amount of energy will be deposited near the surface. The highest sputtering yields occur for the best match between the mass of the incident particles and those of the target atoms. Consequently, a preferential sputtering of these atoms can occur preponderantly for the low energies and for the incident angles deviating from the normal. This preferential sputtering also affects, as we have already mentioned, the atoms exhibiting the lowest binding energies. As we mentioned, the sputtering efficiency will be affected by the nature of the target, its density, crystallinity, surface roughness, porosity, and target temperature. Indeed, when the target is bombarded, the composition and the morphology, topography of its surface will vary, thereby affecting the sputtering efficiency. The sputtering yields of multicomponent systems show even more complex behavior than monoatomic elemental targets and were recently calculated for some oxide targets or alloys by Seah and Nunney [37.32]. The sputtering yields, which
Amorphous Thin Film Deposition
Starting composition Target surface
Equilibrium composition Target surface
Fig. 37.8 Modification of surface target chemical composition depending on the sputtering yields of individual elements
1301
their energy away from the target surface. This can cause substantial damage below the surface over a few microns leading to an inefficient sputtering and in addition, the incident particle is often implanted more deeply within the sample (Fig. 37.7). Emission of Sputtered Atoms. Many sputtered atoms have kinetic energies much higher than those of thermally evaporated atoms. The electrons of the outer electron shells of the atoms of the target are first emitted during ion bombardment because they require less energy and allow maintenance of the plasma by ionizing the argon atoms in turn. However, most of the atoms, molecules, and aggregates from the first atomic layers of the surface (46 Å) are neutral. Fragmentation will depend on the energy density per unit area. The angular emission distribution of sputtered atoms in an energy range between 50 and 1000 keV is still poorly understood, although in the literature it is most often described as a cosine distribution. This means that the relative amount of material sputtered at any angle can be compared to the product of the amount sputtered at the normal incidence and the cosine of that angle. In three dimensions, the overall distribution is often represented as a sphere which is the relative amount emitted at a particular angle centered on the point of impact. However, depending on the energy of the incident ions, this spherical distribution will be modified. Low energies cause subcutaneous packed emission with more emission for angles separated from the normal whose emitted ions preferentially come from the first atomic layer. Conversely, the more energetic incident ions trigger a more elliptical emission in the super-cosine direction pointing towards the normal at the surface associated with ions coming from deeper atomic layers. If the incident ion is lighter than the atoms of the target, the emitted atoms will rather poke on the normal at the surface. Conversely, if the masses are comparable, the atoms will be emitted in the opposite direction to the incident ion beam. Finally, if the incident ion is heavier, the ion and the atom will be projected forward and several collisions will be necessary to emit an atom, with an emission rather to the normal to the surface. Preferential sputtering will also play a role with possible enrichment in the extreme surface of one of the elements causing an emission thereof in sub-cosine, in contrast to the others which may exhibit a rather overcosine emission. Transport of Sputtered Atoms to the Substrate. The sputtered particles must then pass through the plasma to reach the substrate. These particles can then modify their kinetic energy and their velocity because of the collisions with the atoms of the gas. Thus, a thermal-
Part E | 37.2
are different for each atom of a complex target, will lead to a modification of the equilibrium composition of the target surface under the sputtering process [37.24]. A variation in the concentration of each element is expected during sputtering, but this phenomenon is compensated by the fact that the concentration of the elements preferentially sputtered will decrease on the target surface until a so-called equilibrium composition is reached (Fig. 37.8). The amount of incident ions required to achieve equilibrium depends on the sputtering efficiencies of the target: the smaller they are, the greater the amount of required ion is. When the equilibrium composition at the target surface of a complex material is reached the atoms sputtered are deposited in the ratio of the initial bulk composition of the target. However, in some cases, some of the lighter and more volatile species are lost during transport between the target and the substrate, or the probability of reaction with the more condensable species on the surface of the deposition material is lower. This leads to a loss of stoichiometry of these lighter species in the deposited thin layer with respect to the target; often compensated to some extent by reactive deposition. In the case of a target composed of elements with very different electronegativities, such as oxides, negative ions can be sputtered and strongly accelerated away from the cathode. They will then cause a bombardment of the layer being deposited on the substrate which can greatly reduce the growth rate of the film or modify its composition. Incident ions of energy from about 1000 eV to about 50 keV have sufficient energy to break all interatomic bonds in a spherical region around the impact site. The collision cascade regime, from 1 keV to a few tens of keV, involves the movement of a large number of atoms of the target on a region near the impact. In this case, however, the increase in sputtering efficiency is less pronounced. For even higher energies, the sputtering yields decrease. As the incident particles can penetrate the target material more deeply, they release much of
37.2 Physical Vapor Deposition
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Part E
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ization of the atomized species as well as an increase in the mean temperature of the gas results from these collisions. The mean free path pm , i. e., the distance between two collisions, can be used to express the collision probability depending on the gas pressure (pg ), the atomic diameter and weight of the gas atom, and the atomic diameter and weight of the sputtered atom. It can be noted that the probability of collision logically increases with the pressure of the gas. Moreover, it is also influenced by the distance d between the target and the substrate. Thus, the product dpg is used to define the deposition and transport of the sputtered particles to the substrate:
Part E | 37.2
If pm > d, the sputtered particles do not undergo a collision before reaching the substrate, and thus maintain their kinetic energy and their initial direction after sputtering. This system is described as ballistic. It is a directional regime where the product dpg is low (< 5 Pa cm). The deposited material will be dense. If pm < d, the sputtered particles undergo collisions with the neutral atoms of the gas. After about ten collisions, the particles are thermalized, their energy is comparable to the thermal energy of the gas atoms ( 0:04 eV), and they lose their initial direction. This deposition regime is called a thermal regime. It is a diffusive regime where dpg is high, (> 35 Pa cm). The deposited material will tend to be porous.
The thermalization of the sputtered particles, influenced by the gas pressure, thus controls the tension of the film: if the pressure is low, the deposited film may have a high compressive stress, whereas if the pressure is higher, the film may present a stress of traction. Layer Growth and Microstructure of Sputtered Films. It is well known that the growth of thin layers takes place in successive stages characterized by specific processes of evolution of the structure:
Nucleation Insular growth Island coalescence Polycrystalline island and channel formation Continuous structure development Thickness growth.
The evolution of the structure in polycrystalline thin films is a very complex phenomenon and has different characteristics in the different stages of film growth. In 1975, Thornton expanded the structure zone model by introducing the pressure parameter on one of the axes to
account for the effect of pressure on the microstructure characteristics of sputter-deposited films [37.33]. Later taking into account the effect of gas pressure on ion bombardment of the growing film surface during sputter deposition, Messier proposed a fifth morphology zone M consisting of parallel columns with a dome-shaped surface (Fig. 37.9). This structure zone model illustrates the relationship between the coating morphology, the deposition temperature, and the pressure. This zone structure model highlights a transition zone, called zone T, between zones 1 and 2. For the amorphous layers, it can be only roughly predicted that the morphology of amorphous layers would rather lie in the zone 1 and zone T in a small area of the SZM in the case that the temperature of the substrates does not exceed the crystallization temperature of the thin film allowing recrystallization like especially in zone 3, usually the homologous temperature T=Tm must be limited below 0:30:4 as already mentioned in Sect. 37.1.2. As proposed in the SZM, the morphology and topography of the amorphous thin film will be strongly dependent on Ar pressure (Fig. 37.10) [37.34]. Different Sputtering Systems. The phenomenon of sputtering was observed for the first time in 1852 by W.R. Grove with the establishment of an electric discharge under reduced pressure of inert gas thus forming on the surface of an anode a thin layer of the metal constituting the cathode. Since this first experiment, many advances have been made, both in understanding the phenomenon and technological advances, making sputtering a technology widely used in different fields of application such as nanosciences, surface treatments (metallurgy, automotive, . . . ), optics, and since the 1970s in the microelectronics industry. Thus, in order to meet the requirements of these technological applications in industry, various sputtering systems are used: DC, RF, magnetron, high-power impulse magnetron sputtering (HiPIMS), ion beam sputtering (the particularity of which is that the ions are not generated from or around the target but within an ion gun), or high target utilization sputtering (HiTUS) where the plasma is generated remotely (outside the main chamber), which allows in particular a more optimal use of the target and a better deposition rate [37.7, 24, 35]. Sputtering deposition began to be widely used in industry only with the arrival of stable, reproducible sources and the appearance of various types of magnetrons. Magnetron sputtering is a powerful and flexible technique, which uses a magnetic field to confine the motion of secondary electrons near the surface of the planar target, and is currently the most widely used sputtering pattern in production. It is able to deposit a wide
Amorphous Thin Film Deposition
1303
Fig. 37.9 Messier’s model based
1
10 Zone 3
Ion energy (eV/atom) 100
Zone 2
Zone M
37.2 Physical Vapor Deposition
on Thornton’s structure zone model exhibiting the influence of temperature and pressure on the structure of films deposited by sputtering. Reprinted with permission from [37.17]. Copyright 1984, American Vacuum Society
1.0 0.9
Zone 1
Zone T 0.7
30 Ar pressure (mTorr)
0.6 0.5
0.8 Substrate temperature (T/Tm)
0.4
20
0.3 0.2
10 0.1 1
RMS: 0.4 nm
nm
μm
nm 20
RMS: 2.1 nm
1.8
4.0
1.8
1.6
3.5
1.6
1.4
3.0
1.4
14
1.2
2.5
1.2
12
1.0
10
0.8
8
0.6
6
1.0
2.0
0.8 0.5
0.6
18 16
0.4
1.0
0.4
4
0.2
0.5
0.2
2
0
0
0
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 μm
PAr = 5 ×10 –3 mbar
1 μm
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 μm
PAr = 5 ×10 –2 mbar
0
100 nm
Fig. 37.10 AFM (top) and SEM (bottom) images of the crosssection of selenide films illustrating topography and morphology of amorphous thin films depending on Ar pressure: lower Ar pressure (left), higher Ar pressure (right)
Part E | 37.2
μm
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Part E | 37.2
variety of metals, insulators, alloys, composites, and a variety of compounds. The development of advanced vacuum technologies, the design of various sputtering systems, combined with highly sensitive analytical microtechniques, have favored the development of sputtering to obtain high quality thin films with reduced contamination. Depending on the conditions used (reactive sputtering, bias sputtering, cosputtering, etc.) or the chosen configurations (ion beam sputtering, DC sputtering, RF sputtering, magnetron sputtering, highpower pulse sputtering), nucleation and growth kinetics of the thin films will fluctuate noticeably. Consequently, the sputtering method employed will be selected according to the characteristics of the target materials and the properties of the desired films. The classical or balanced magnetron sputtering was introduced in the early 1970s [37.36], followed by the development of unbalanced systems in the late 1980s [37.37]. Lastly, the deposition rate and ions energy can be improved by using a high-power impulse of low frequency and low duty cycle to the cathode target (high-power impulse magnetron sputtering (HiPIMS) or high-power pulsed magnetron sputtering (HPPMS)). HiPIMS utilizes a very high voltage, short duration of the energy (high power densities of the order of kW cm2 in short pulses (impulses) of tens of microseconds at low duty cycle on/off time ratio) focused on the target to generate a high-density plasma that results in a high degree of ionization of the sputtered particles in the plasma. The implementation of these high-power impulse magnetron sputtering deposition technologies brings improvements in the physical properties of the material deposited in thin film form. The main advantages of HiPIMS coatings include a denser coating morphology and an increased ratio of hardness to Young’s modulus compared to conventional PVD coatings. As described briefly above, there are two main sputtering methods of deposition: the DC (diode and triode) and the radiofrequency (RF) sputtering operation [37.7]. DC Sputtering. DC sputtering remains the simplest and most widely used sputtering technology. The cathode electrode is the sputtering target and the substrate is placed on the anode, which is often at ground potential [37.38]. An electrical discharge generating a plasma is initiated, at low pressure, by applying a DC voltage between the two electrodes. The discharge current is transported to the cathode mainly by ArC positive ions from the plasma and to the anode by electrons also coming from the plasma. The difference in mobility between the ions and the electrons of the plasma makes the majority of the applied voltage in the cathode sheath
(space around the cathode). The ArC ions formed in the plasma are accelerated by the electric field of the sheath of the cathode and bombard the surface of the target ejecting surface atoms and secondary electrons of the material. Indeed, the sputtered particles are essentially neutral atoms in the ground state, although ions and clusters of atoms have also been reported in the emitted flux [37.39]. Secondary electrons are in turn accelerated by the potential of the sheath and penetrate into the plasma where they collide with plasma atoms, ionize them, thereby maintaining the plasma. The surface atoms of the target are projected into the sputtering chamber, are directed at high velocity towards the substrate where they will condense forming the thin layer. An advantage of DC sputtering is that the plasma can be established uniformly over a large area. The cathode in DC discharge must be an electrical conductor, since an insulating surface will develop a surface charge that will prevent ion bombardment of the surface. This condition implies that DC sputtering must be used to sputter simple electrically conductive materials such as metals, although the process is rather slow and expensive compared to vacuum deposition. If the target material is dielectric this process rapidly causes a charge build-up at the surface until argon ions are no longer attracted, electrons are no longer released, and the plasma extinguishes. To sputter nonconducting materials it is therefore necessary to apply high frequency or pulsed power to the target. Because the power supply is only negative half the time, rates are lower than for DC sputtering. To make amorphous thin films in the conventional diode sputtering system, the substrates are cooled by water, liquid nitrogen, or He depending on composition as the substrate temperature usually rises during deposition (200500 ı C) [37.7]. RF Sputtering. In high-frequency sputtering, working at frequencies below about 50 kHz, the potential on the target is periodically reversed and the ions have enough mobility so that a DC diode-like discharge, where the total potential drop is near the cathode, can be formed alternately on each electrode. The substrate chamber walls can be used as the counter-electrode. At frequencies above 50 kHz, the ions do not have enough mobility to allow a DC diode-like discharge to be established and the applied potential is felt throughout the space between the electrodes. At 13:56 MHz frequency, the ions are practically insensitive to the RF field and the electrons oscillate in this field. Thus, the number of electrons arriving at the target during a positive alternation is greater than the number of ions which arrive during the negative half-cycle. There is therefore a negative static charge on the target creating a negative DC
Amorphous Thin Film Deposition
Magnetron System. The magnetron effect can be defined as a device in which magnetic fields are used to form electron traps (Fig. 37.11). The magnetron device consists of concentric magnets of opposite polarities located beneath the cathode. A magnetic field is concentrated in the vicinity of the target and oriented so that the field lines are parallel to the surface bombarded by the ions. The magnetic field added to the DC or a)
RF sputtering system will deflect the secondary electrons so that they will move within a closed path on the target surface. Indeed, the electrons emitted by the impact of the incident ions are trapped in front of the target, which increases their probability of encountering an argon ion. This confinement increases the ionization rate of argon atoms. This high current of electrons creates high-density plasma from which Ar ions can be extracted to sputter the target material and therefore increases the sputter rate. Thus, a dense plasma can be formed near the low-pressure cathode such that the ions can be accelerated from the plasma to the cathode without loss of energy due to collisions. The electrons follow helical paths around the magnetic field lines undergoing more ionizing collisions with gaseous neutrals near the target surface than would otherwise occur. An increase in the deposition rate and a decrease in the electron bombardment of the growing layer is then observed while decreasing the power applied to the target. A disadvantage of the planar magnetron configuration is that the plasma is nonuniform on the surface of the target. The extra argon ions created as a result of these collisions leads to a higher deposition rate. Deposition rates are considerably increased and can reach several m=min. This also means that the plasma can be sustained at a lower pressure. Consequently, the variation in thickness of the deposit on the substrate is a function of the position of the substrate with respect to the target. Plasma nonuniformity also means that wear of the target is nonuniform, sometimes with only 1030% of the target material being useable (Fig. 37.11). Different magnet and cathode designs may reduce this problem. The magnetron target is advantageous for amorphous thin film fabrication as it moderates the substrate’s temperature increase. In sputtering deposition, the adatoms’ energy is of the order of 110 eV thus their quenching time is estimated to be higher than 1016 K=s. It is estimated considering that they will lose their energy in 1012 s, which corresponds to the fre-
Ar+
b)
Ar+
c)
Sputtered atoms
S
N
S
N
S
N
Fig. 37.11a–c Photograph of a selenide chalcogenide glass 2 00 target before (a) and after (c) several hours of deposition using the magnetron RF sputtering system (b)
1305
Part E | 37.2
potential called a self-polarization potential. This continuous field makes it possible to accelerate the argon ions formed in the plasma which acquire an energy sufficient to sputter the target material. During part of each half-cycle, the potential is such that ions are accelerated to the surface with enough energy to cause sputtering, while in alternate half-cycles, electrons reach the surface and prevent any charge build-up. Moreover, the increased electron movement in such an RF field increases the probability of an ionizing collision for a given secondary electron. This leads to an increase in plasma density compared to a DC diode resulting in a relatively rapid sputtering process. RF sputtering can be used to sputter insulating material, although the sputtering rate is low. The RF diode system requires an impedance matching circuit consisting of variable capacitances and an inductance. This circuit makes it possible to transfer the power to the target as much as possible by minimizing the reflected power. The use of RF diode systems can lead to intense bombardment of the growing layer, due to high-energy secondary electrons, leading to low deposition rates. It is important to mention that the target and the substrate were facing in an on-axis sputtering configuration. Off-axis sputtering reduces the effects of high-energy particle irradiation to the growing film surface. In off-axis sputtering, the substrates are settled at the outside of the discharge plasma. A rotating substrate holder with a metal shadow mask can be used for the reduction of the thickness distribution of the off-axis sputtering [37.40].
37.2 Physical Vapor Deposition
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quency of thermal lattice vibration of the substrate surface atoms [37.7]. The expected quenching rate in sputtering deposition is much higher than the value obtained in classical quenching from melts suggesting that original structures and compositions can be synthesized.
Part E | 37.2
Reactive Gas Sputtering. Reactive gas sputtering (pressure of about 103 Pa) is often used for the deposition of compounds such as nitrides, carbides, oxides, and sulfides. The reactive sputtering is a process where a target of one elemental chemical composition is sputtered in the presence of a reactive gas or a mixture of gases (oxygen, nitrogen, hydrogen sulfide, acetylene, methane, etc.) added under controlled partial pressure to argon gas (Fig. 37.12). The reactive gas will react during the deposition process to form a coating of a different chemical composition compared to the initial target permitting the deposition of oxide films that can potentially be amorphous (Al2 O3 , SiO2 , TiO2 , HfO2 , ZrO2 , Nb2 O5 , AZO, ITO) or nitride films (e. g., TiN, ZrN, CrN, AlN, Si3 N4 , AlCrN, TiAlN), for instance [37.41–43]. Once reactive gas is introduced into a process chamber it reacts with the unpassivated surfaces, such as chamber walls and the sputtering target. Intensive erosion due to sputtering delays complete poisoning of the target surface. Poisoning proceeds through different target states as a function of partial pressure of reactive gas (critical flow) and time: a clean metallic target N Cathode
S Target
N
(metal sputtering mode), a transition mode, and the final stage, a fully reacted surface (fully poisoned sputtering mode). The rate of erosion is greater than the rate of oxidation thus the surface of the target retains a metallic character. If the rate of erosion is lower than the rate of oxidation the surface of the target will be oxidized and it is poisoned. Technical limitations of reactive magnetron sputtering are related to a significant decrease in deposition speed, phenomena of hysteresis for different discharge parameters, and arc creation if the formed compound is an electrical insulator. A disadvantage of the magnetron sputtering configuration is that the plasma is confined close to the cathode and is not available to active reactive gases in the plasma near the substrate. This difficulty was overcome using an unbalanced magnetron configuration, where some electrons can escape from the cathode region [37.37]. A disadvantage of the unbalanced magnetron is that the current of escaping electrons is not homogeneous inducing a nonuniform plasma. Reactive sputter deposition at high deposition rates requires operation in the transition region. Operating in the transition region allows a fine tuning of coating chemical composition and the ability to optimize and improve film properties substantially. Nowadays, reactive sputtering deposition is a well-established technique used for industrial coating deposition as well as for research and development. Reactive cathode sputtering is used for the production of thin films for high-value-added products, such as optical components (multilayer oxide antireflective coatings), flat screens, organic light-emitting diode (OLED) device encapsulation, oxy-nitride coatings for the solar absorber layer in a thermal solar cell, creative design products etc.
Target poisoning Reactive gas
Plasma Pump
Anode
Substrate
Fig. 37.12 Scheme of reactive magnetron sputtering during
the deposition process
Ion Beam Deposition and Electron Cyclotron Resonance (ECR) Sputtering. Alternatively, if the source of ions is not local to the target but is rather a neutralized beam, the electrical characteristics of the target are no longer of importance. In this technique, known as ion beam deposition (IBD) ions are extracted from a separate ion source to which the argon is fed directly. The vacuum chamber pressure is therefore lower than that in the ion source allowing very low deposition pressures. IBD is often used in ultrahigh vacuum (UHV) systems and for ultraclean applications. It also has the advantage that the energy with which the ions impact the target can be varied independently of other system characteristics such as ion density—both energy and rate can affect the characteristics of the film grown. The disadvantages of this technique may include: the small area bombarded by the ion beam and the relatively high cost.
Amorphous Thin Film Deposition
In the late 1980s, deposition technologies saw the advent of high-density plasmas such as ECR plasmas. The ECR microwave-based plasma was first developed for reactive etching or plasma CVD deposition. By varying the source, it can also be used for sputtering deposition and reactive sputtering deposition. The ECR discharge is sustained under an RF electric field and with a static magnetic field (frequency D 2:45 GHz and B D 874 G). For a typical ECR, the system comprises a negatively biased ring system target settled at the outlet of the discharged chamber. The target bias is 0:41 keV. If the system uses a chemically stable cold cathode, a reactive gas could also be used for the sputtering. However, ECR systems operate better in low pressure regions which have weak gas scattering effects on the sputtered flux and were advantageously replaced by inductively coupled plasma.
Plasma Diagnostics. The study of plasma parameters determining thin film growth remains a crucial and difficult field of investigation. Information about plasma characteristics (gas phase composition, electron and ion densities, energy distributions, and temperatures) and thin film growth (thickness and deposition rate) can be obtained by means of in situ
plasma diagnostics. To preserve thin film performance, several methods with their own advantages and limitations can be used and located inside or outside the deposition chamber. They can be implemented in order to characterize plasma parameters influencing thin film growth and consequently, the properties of the resulting thin films. The plasma diagnostic techniques for sputtering systems usually include optical spectroscopy and electrostatic probes, since these methods are relatively easy to implement and effective for such plasmas. Among the plasma diagnostics proven to be useful for investigations of thin film growth are optical emission spectroscopy, laser-induced fluorescence, Fourier-transform infrared spectroscopy, tunable diode laser absorption spectroscopy, quadrupole mass spectrometry (nature and concentration of plasma particles), Langmuir probes for the detection of low-energy species, electrostatic analyzer for detection of high-energy species within the plasma, temperature-sensitive probes for energy-flux measurements. The most commonly used methods for the characterization of thin films during deposition employ quartz crystal microbalances (mass variation per unit area giving film thickness), mass spectroscopy (nature and concentration of deposited particles), x-ray emission by electron impact (surface analysis of light elements B, C, N, and O), x-ray photoelectron spectroscopy (XPS, surface analysis of elemental identity, chemical state, and quantity of a detected element), atomic absorption spectroscopy (relative atomic species concentrations), ellipsometry (film thickness, refractive index, extinction coefficient), multiple wavelength pyrometric interferometry (simultaneous film thickness and temperature measurements), laser reflectometry (reflectance, film thickness, extinction coefficient, refractive index), x-ray reflectivity (surface and interface roughness, film thickness, film density), and x-ray fluorescence (thickness and composition of layers and coatings). Invasive monitoring tools localized inside the deposition chamber can disturb or contaminate the thin film fabrication process [37.47]. Optical-based tools, mostly nonintrusive, which measure through the optical path between the source and substrate or directly on the substrate, present the disadvantage of the viewport becoming coated over time. Some plasma diagnostic tools will also be described in Sect. 37.2.1, Plasma Plume Diagnostics. Table 37.2 summarizes the operating parameters of typical sputtering systems excluding information for HiPIMS which can be found in specific literature. HiPIMS generates a high-density plasma of the order of 1013 ions=cm3 containing high fractions of sputtered ions [37.44].
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High-Power Impulse Magnetron Sputtering. Highpower impulse magnetron sputtering or HiPIMS is a fairly recent innovation in sputtering technology which combines a powerful power supply with a conventional planar magnetron [37.44]. HiPIMS represents an important development for the thin-film coating industry. This technique, first reported and patented in 1999 by V. Kouznetsov, uses very high power and short duration pulses of power to generate a plasma and ionize a large percentage of the sputtered atoms [37.45]. These sputtered atoms have much higher energies than in conventional magnetron sputtering. Power densities can reach levels of a few kW=cm2 (compared to a few W=cm2 for conventional magnetron systems), which produces energetic deposition ions with energies in the range of 50100 eV (compared to only about 110 eV in conventional sputtering). Pulsing the high voltage energy prevents overheating of the target, which can cool down during the predominant off time resulting in low average cathode power. Thus, higher deposition rates than conventional sputtering methods can be reached without incurring damage through target temperature increase. The high voltage levels for short durations of time and the increased velocity of ionization of the target gives rise to improved film adhesion and more uniform films presenting very high density with no voids [37.46].
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Table 37.2 Operating parameters of sputtering systems [37.7] Operating parameters Operating pressure (Pa) Ionization degree Electron temperature (K) Ion temperature (K) Gas temperature (K) Plasma density (cm3 ) Particle adatoms energy (eV) Energy secondary electron bombarding Ionization degree of adatoms
DC, RF diode sputtering 0:1100 105 104 104 105 103 103 108 1010 110 Large 103 102
Part E | 37.2
Examples of Sputtered Amorphous Thin Films. The applications of sputtered deposition are extremely varied and affect a lot of areas like aerospace and defense (heads-up cockpit displays, jet turbine engines, mirrors for optical and x-ray telescopes, night vision equipment), coating tools (wear coatings, anticorrosion coatings, antiseize coatings, dies and molds, sewing needles, tool and drill bit hardening), microelectronics (sensors, surface acoustic wave (SAW) devices), automotive (car headlights and tail-lights, trim components, drive train bearings and components), wheels and rims optics (antireflective/antiglare coatings, cable communications, laser lenses, optical filters for achromatic lenses, spectroscopy), data storage (DVDs, microelectronic flash memory, read/write heads), medicine (antirejection coatings, dental implants, drug delivery). Many of these thin films or coatings composed of multilayers may be crystallized but for many of these applications, films are also produced in amorphous state. Indeed, the amorphous Si in solar cells or the amorphous C for hard wear-resistant coatings are well known; only a few examples can be cited below for different and representative types of amorphous or glassy materials obtained by sputtering methods. Indium-tin-oxide (ITO) thin films can be deposited on glass substrates using DC magnetron reactive sputtering at different bias voltages and substrate temperatures. Some improvements were obtained in terms of film properties, microstructure, and other physical characteristics for different conditions. Amorphous and polycrystalline films can be obtained for various deposition conditions exhibiting suitable optical transmittance and conductivity for electrochromic applications [37.48]. Investigation of sputtered HfF4 films and application to interference filters for thermophotovoltaics were performed [37.49]. Amorphous ABO3 thin-film-type ferroelectric materials are interesting because of specific physical properties. The amorphous LiNbO3 and LiTaO3 materials exhibit dielectric anomalies near the crystallization temperature ("r > 105 ), ferroelectricity, and high ionic conductivity. Smooth,
Planar magnetron sputtering 0:0110 105 102 104 105 103 103 109 1012 110 Small 103 101
Ion beam sputtering
ECR sputtering
0:0010:1
0:0010:1 103 101 5 104 106 103 104 103 109 1012 110 Small 102 101
110 103 102
transparent, and colorless thin films were obtained by RF magnetron sputtering [37.50]. The dielectric anomalies are observed at 200300 ı C lower than in the bulk counterparts obtained by roller-quenching. PbTiO3 is also obtained by RF sputtering presenting a high surface electrical conductivity of around 10 1 cm1 due to electrons hopping between the Pb metal crystallites [37.51]. An amorphous indium gallium zinc oxide (IGZO)-based electrolyte-gated field-effect transistor (IGZO-EGFET) was fabricated and its feasibility as a biological sensing platform was evaluated [37.52]. Amorphous SiC thin films were obtained via reactive sputtering of a Si target in a C2 H2 or CH4 gas [37.53]. The inclusion of hydrogen in sputtered SiC films stabilizes the amorphous phase. Moreover, thin films of amorphous Si were also deposited by sputtering methods [37.54–57]. Since such amorphous thin films produced by a sputtering process often include nanocrystallites (NCs) that do not predominantly affect optical losses, they are promising materials in photonics with specific optical properties related to amorphous and crystalline phases. The sputtering method allows relatively easy synthesis of rare earth-doped films dedicated to active devices directly from a rare earth-doped target or from several targets by cosputtering allowing better flexibility. More specifically, Er-doped waveguide amplifiers (EDWAs) are extensively studied in integrated optical (IO) circuits at standard telecommunications wavelength. Advantages of erbium-doped amplifiers are the linear gain response, temperature and polarization insensitivity, and low noise [37.58]. Beneficial for low-cost amplifiers, short-pulse amplification, or compensation of optical loss in integrated optics devices, for instance, appropriate thin films are fabricated using sputtering. We can find the nanocrystallite containing thin films (Er3C :SiO2 ) with Si nanocrystallites for which photoluminescence (PL) was studied by several authors [37.59]. Recently, thin films were also obtained by RF cosputtering of Er2 O3 and Si targets in the plasma of an Ar-diluted 1% O2 atmosphere. The
Amorphous Thin Film Deposition
a)
Second Bragg reflector Defect layer
First Bragg reflector
1 μm
b)
10 μm
Fig. 37.13a,b SEM micrograph of the one-dimensional (1-D) microcavity cross-section. The bright and the dark areas correspond to TiO2 and SiO2 layers, respectively. The substrate is located at the bottom of the images and the air at the top. (a) Image for a section of the sample of about 16 m in length. (b) Image for a section of the sample of about 60 m in length. Reprinted with permission from [37.62], The Optical Society of America
IR [37.65–68]. An original set-up for the deposition of Tb3C :SiO2 film was also recently realized using electron cyclotron resonance plasma-enhanced chemical vapor deposition (ECR-PECVD) and magnetron sputtering systems [37.69]. Tellurite glasses can be promising for optical amplification or light sources because of their high photoluminescence emission efficiency and high erbium solubility. Thus, peak internal gains of up to 14 dB have been achieved in 5 cm long rib waveguides (2:8 dB=cm) fabricated by cosputtering of tellurium and erbium in an oxygen ambient using reactive ion etching [37.70]. Broadband and anisotropic light emission from rare-earth-doped tellurite thin films was demonstrated using Er3C :TeO2 photonic crystals [37.71]. Moreover, a hybrid waveguide was fabricated with a strip-loaded structure made from an Er-doped TeO2 slab and an etched As2 S3 strip. Almost complete loss compensation is demonstrated with 1480 nm pumping and a fully lossless waveguide with high nonlinear coefficient can be achieved with higher 1480 nm pump power [37.72]. High rare earth-doping concentrations are usually required for IO circuits where rare-earth clustering effects become important leading to a low luminescence efficiency. The low solubility of rare earth in silica or chalcogenide glasses due to the mismatch in size, valence, or ion covalency between the rare earth ions and the constituents of the glass network remains an issue to overcome. The addition of other elements into such a glass matrix (Al2 O3 , P2 O5 , and HfO2 to silica glass [37.73] or Ga, In, P, and I to chalcogenide glasses [37.74]) was studied to improve rare earth solubility and their optical properties flexibility. Still concerning the doping of rare earths, chalcogenide films are mainly sought for their luminescence properties in the mid-IR [37.66–68]. In photonics, they are of significant interest for optical nonlinear devices or photosensitive properties [37.75–80]. Considering sensor applications, an interesting review was presented by Schöning and Kloock about technological aspects of fabrication and of silicon-based thin film sensors with chalcogenide glass materials for heavy metal analysis [37.81]. Pulsed Laser Deposition Fundamentals. Pulsed laser deposition (PLD) is one of PVD techniques that exploits plasma. To produce plasma, this deposition technique typically uses pulsed lasers. The basic principle of the common PLD system is illustrated in Fig. 37.14. The laser beam, which is characterized by its wavelength, pulse duration, repetition rate, and spot size (among its main characteristics), is focused onto a target material mounted in a vacuum chamber. When the laser pulse hits the target, it inter-
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effect of microstructure evolution of Si NCs on the Errelated luminescence in erbium-doped SiO2 amorphous films was studied. The coalescence of Si NCs in microstructures would reduce the luminescence of Si NCs and further quench the luminescence of Er3C [37.60]. Optical waveguides were also envisaged based on such materials doped with Er3C or Nd3C [37.61]. Other types of amorphous materials that do not necessarily include nanocrystallites are currently being studied for active optics like microcavity or waveguide fabrication (Fig. 37.13). Rare earth-doped amorphous aluminum oxide (Al2 O3 :RE3C ) thin films are attractive materials for near-IR amplifiers and lasers that can be integrated with silicon-on-insulator waveguides or deposited onto complementary metal-oxide-semiconductor (CMOS) integrated optical structures [37.58, 63, 64]. In the case of oxide materials for which the glassforming region is well-known such as silica, silicate, tellurite, phosphate, or chalcogenide materials like arsenic or germanium-based glasses, thin films were deposited by RF magnetron sputtering mainly for their optical/luminescence properties from visible to mid-
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Rotating target
Incident laser beam Mirror
Vacuum gauge
Target holder Substrate holder Gas inlet Substrate
Fig. 37.14 Basic principle of the common PLD system
Part E | 37.2
acts with solid or liquid state material. As a result of this interaction (under the condition of sufficiently high laser energy density), each laser pulse ablates a small part of the target material and the material is ejected from the target surface forming a plasma plume. Material contained in the plasma plume is directed towards substrates, where it condenses and the thin film is created. The plume is the source of material flux necessary for thin film growth. The initial research activities in the field of PLD were performed in the 1960s after the discovery of the laser. Then, in the 1970s and 1980s, the interest in PLD became limited. PLD began to rise in popularity in the late 1980s and 1990s and this was connected to the application of PLD for growth of high-temperature superconducting thin films. The last twenty years of PLD can be characterized as the age where it became a mature deposition method that has been significantly improved and been massively applied in research on thin film growth. Nowadays, PLD is used for thin film or multilayered structure fabrication of diverse materials such as metals, semiconductors, insulators, polymers, or biological layers [37.82], as illustrated in Fig. 37.15. In comparison with other thin-film deposition techniques, PLD offers several good reasons to be used. First, PLD is very flexible from the point of view of energy density and laser wavelength to reach the ablation threshold for any material. The flexibility of PLD resides also in good geometrical versatility which is caused by the fact that the laser is placed outside the vacuum chamber. One of the most attractive characteristics of PLD is its capability for stoichiometric material transfer from the multicomponent target to the film. When the energy fluence reaches the ablation threshold, which is basically wavelength dependent,
500 nm
Fig. 37.15 TEM micrograph (cross-section) of PLD multilayered structure: a microcavity consisting of Ga5 Ge20 Sb10 S65 (doped with 5000 ppm of Er3C ) spacer surrounded by two 10-layer As40 Se60 -Ge25 Sb5 S70 reflectors. Reprinted from [37.84], with permission from Elsevier
the deposition process transforms from simple thermal evaporation to laser ablation. This means that the energy absorbed by the target material is larger than the energy that is required for the evaporation. Exceeding the ablation threshold results in energy absorption by the ablated species. Consequently, plasma is formed at the target surface. The key point is that the process is independent of vapor pressures of the individual components constituting the target material which leads to the stoichiometric transfer of the material from the target to the film. Another advantage of PLD is the good control of the growth rate which is given by easy control of the pulsed laser parameters. Finally, the kinetic energy of the ablated species can be moderated in order to control the growth of the films [37.82, 83]. Mechanism of Laser Ablation (Plus Angular Distribution of Ablated Material). The process of laser ablation includes the ejection of the species from the target surface which is a consequence of absorption of a high-energy laser pulse and the formation of a plasma plume moving quickly away from the target. The plasma plume typically contains neutrals (ground state or excited), ions, electrons, eventually particulates. The plume is often visible to the naked eye due to the fluorescence from the excited atoms. However, generally plasma plume means an expanding visible or nonvisible cloud of material originating from the ablation. The plasma plume grows in all directions, but preferably along the target normal. The shape of the plume drastically influences the thickness distribution of the films being deposited.
Amorphous Thin Film Deposition
The process of laser ablation employing nanosecond or longer pulses is described in five steps (which can partially overlap in time) as follows: 1. Absorption of light in the target material 2. One-dimensional expansion of the plasma plume during laser irradiation 3. Three-dimensional adiabatic plasma plume expansion into vacuum or background gas 4. Slowing/stopping of the plasma plume in the presence of background gas 5. Condensation of plume species on substrate and thin film growth.
Further, the presence of background gas may increase the quantity of chemical reactions between the plasma species and gas. The type of gas and its pressure dominate the plume dynamics. When the gas pressure is low, i. e., below 1 Pa, the behavior of the plume is close to the plume expansion in the vacuum. When the gas pressure ranges from 10 to 100 Pa, the plume induces a compression of the gas/plume leading to the reduction of mean free path of the plume species, formation of a shock wave, and finally plume pressure equilibrates the background pressure [37.88]. Using pressure > 100 Pa, short stopping distances of the plume due to its strong confinement are observed. The final step of the ablation process covers plume arrival at the substrate surface followed by thin film growth. The film may grow in different modes which depend on the energy of arriving species and energy of the atoms/aggregates on the substrate surface. When plume species arrive at a substrate surface, the first arriving pulse causes the nucleation of high numbers of smaller clusters. These subcritical clusters tend to dissociate into mobile species that will nucleate new clusters of a different size during the time of no vapor arrival. The next pulse will initiate the same process again, with the difference that some of the mobile atoms will reach previously formed clusters. Under typical PLD conditions, the deposition rate per laser pulse can range from 0:001 to 1 Å=pulse. The amount of material grown per laser pulse will depend on multiple factors, including target-to-substrate distance, background gas pressure, laser spot size, and laser energy density [37.82, 85]. Plasma Plume Diagnostics. In order to efficiently correlate plasma conditions with the properties of thin films grown by PLD, fast, in situ plasma diagnostics at nanosecond speed are required. Among all possible plasma plume parameters, of main interest are: the shape and velocity of the plume time dependences, spatial distribution of density and temperature in the plume and their time dependences, and spatial variations of the plume [37.86]. Unfortunately, the physics of laser ablation plasmas limits the applicability of individual diagnostic techniques. Commonly used experimental methods are as follows:
Mass spectrometry: Time-of-flight mass spectrometry is widely used to estimate the distribution of the velocities of ions, atoms, and molecules present in the plasma plume. Generally, mass spectrometry represents probably the most applied method for the characterization of charged species in the plasma plume. Time-offlight mass spectrometry permits mass identification and energy analysis after each laser shot. This tech-
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During the first step, the photons of the laser pulse are absorbed in the solid material. The absorption depends on the material itself; it is determined by the electronic band structure. The laser energy is absorbed by electrons of the target. After tens of picoseconds, the electrons and atoms of the material equilibrate at very high temperature. Consequently, high temperature results in explosive evaporation of neutrals, ions, and electrons. The ejection of the species from the target is not determined only by absorption of the material, but also by its reflection and cohesive energy. An important parameter describing the ablation process is ablation yield, which is driven by the cohesive energy. Lowest ablation yields of the order of 0:1 1015 atoms/pulse were reported for W, Mo, or Ta. Conversely, the largest ablation yield values (10 1015 atom=pulse) were observed for Bi, Sn, and In [37.85]. During the second step of the laser ablation process, the photons of a laser pulse are absorbed by the plume (but also by the target). Direct photoexcitation and inverse bremsstrahlung phenomena contribute to the absorption of plume atoms/ions. Within this step, partly ionized plasma is formed and the plume is luminescent due to the radiative de-excitation of excited neutrals/ions [37.85, 86]. In the third stage, the plume expansion in vacuum after the termination of the laser pulse is considered as adiabatic, because there is no mass and energy transfer to the ablation plume and hence the plume expansion is expected to be almost collision free. The plume expansion, driven by the pressure gradients of the plume, is described as an ellipsoid, if one accepts the theoretical description of adiabatic expansion proposed by Anisimov [37.87]. On the basis of equations for the plume expansion derived by Anisimov, some common effects of plume dynamics such as plume sharpening in forward direction, forward peak from a broad beam spot on the target, or flip-over effect are explained. A background gas can be used for the reduction of the kinetic energy of the species in the plasma plume.
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nique also provides direct observation of the species arriving at the substrate forming the film, when analyzing at the position of the film substrate. This could be important to clarify the kinetics of thin film growth. Last but not least mass spectrometry can also be used for the analysis of the neutrals contained in the plume if an appropriate method for ionization is performed. Generally, a temporally resolved mass analysis of the plasma plume as well as spatial distribution of charged species in the plume can be studied. Time-of-flight mass spectrometry is carried out in different experimental set-ups: linear arrangement, reflectron or quadrupole mass spectrometry. The development of reflectron mass spectrometers has resulted in an improved mass resolution of time-of-flight instruments. Quadrupole mass spectrometry brings very high mass resolution with high efficiency. Conversely, this type of mass spectrometer has the disadvantage that only a single charged species per laser shot is analyzed [37.88]. Optical methods: To record images of the selfemission of the plasma plume with a time resolution of a (few) nanoseconds, gated intensified chargecoupled devices (ICCD) can be employed. Plume dynamics can be successfully observed through varying the time delay between the laser and ICCD gating pulse. An identification of electronically excited species in the plume is possible on the basis of optical emission spectra measurements. The electron temperature and density in the plume can be derived from the emission spectra as well. In detail, using the intensity ratio of two spectral lines originating in two excited states in the same atom or ion, the electron temperature can be obtained. By analyzing several spectral lines one can calculate so-called Boltzmann plots; the electron temperature is then given by the slope of the linear dependences which intersperse experimental data for individual atoms/ions. When recording time- and space-resolved (at various distances from the target) emission spectra, the velocities of individual excited species can be calculated. Other optical methods applicable for plasma plume characterization are based on Thomson scattering and the interferometric method. Thomson scattering is the most direct and least theory-dependent among optical methods. However, due to the very low cross-section of the underlying process the experiments are very difficult to perform. The laser interferometric method analyses the fringe structures originated by a probe beam crossing the plasma cloud in the vicinity of the target surface. It allows accurate determination of the electron density and is particularly used in the first moments of
the plasma plume expansion, when the strong continuum associated with bremsstrahlung and recombination emissions does not permit a clear detection of the emission lineshape via optical emission spectroscopy [37.88]. Apart from the self-emission of the plasma plume, laser-induced fluorescence technique exploiting other laser for the excitation of a specific transition can be used to study the atoms and molecules present in the plume in the ground state [37.86]. Electrical methods: The plasma plume is often investigated through electrostatic ion probes (or Langmuir probes) giving a possibility to estimate the electron temperature, plasma density, and angular distribution of the ion production. The advantage of Langmuir probes is not only their simplicity but they also provide local information contrary to most spectroscopic or imaging techniques which show average information along the line of sight. Another advantage is that they can work in dense plasmas and with higher background pressures when compared with other diagnostic techniques (mass spectrometry). The Langmuir probe works in such a way that a metal probe with variable bias voltage is inserted directly into the plasma. Electrostatic ion probes are realized as wires, plane discs, parallel plate probes, or multigrid retarding-potential probes. At negative biases, a positive current pulse is collected which corresponds to the flux of ions arriving at the probe [37.89].
PLD Equipment. The first attempts of using laser ablation for thin film growth exploited ruby lasers emitting at 694 nm. Nowadays, PLD systems employ mostly excimer or Nd:YAG lasers providing high pulse energies in UV. This is favorable due to the fact that most of the materials being deposited exhibit strong absorption in the range 200400 nm, which brings the benefit of reduced penetration depth into the target material leading to thinner ablated layers of the material. Both, excimer or Nd:YAG lasers differ particularly not only in price or maintenance but mainly in laser beam characteristics. Nd:YAG lasers are common solid-state systems with Gaussian or super-Gaussian beam profiles (Fig. 37.16). The fundamental lasing wavelength of Nd:YAG lasers lies in the near-infrared spectral region at 1064 nm. Using a nonlinear crystal, frequency conversion (doubling, tripling, quadrupling, and quintupling) of the fundamental 1064 nm beam permits exploitation of 532, 355, 266, and 213 nm wavelengths. The energy of Q-switched Nd:YAG lasers which are commercially available may reach several tens of J/pulse for fundamental wavelength with pulse durations from a few to tens of nanoseconds. At present,
Amorphous Thin Film Deposition
Intensity (arb. u.) 2.0 1.5
Gaussian profile Super-Gaussian profile (n = 10) Flat-top profile
1.0 0.5 0 –200 –150 –100
–50
0
50
100 150 200 Radial position (μm)
Fig. 37.16 Output laser beam profiles of lasers used in the
PLD systems
is lower (for example at the edges of the beam), simple evaporation proceeds. Conversely, in the center of the beam, where the intensity is higher, a pure ablation process is taking place. This is why it is, in principle, advantageous to exploit laser beams with flat-top intensity distribution (Fig. 37.16) as provided by excimer lasers. Between the laser output and the target installed in a vacuum chamber, several optical elements are placed. These optical elements (apertures, mirrors, lenses, beam splitters, and eventually laser windows) drive and focus the laser beam on the target. Among the mentioned optical elements, lenses are probably the most important ones. Material choice for the lenses/laser windows depends primarily on the laser wavelength. Commonly used lens/laser window materials are UV-grade fused silica, sapphire, calcium or magnesium fluoride, borosilicate glass, zinc sulfide or zinc selenide. The mirrors for PLD are dielectric multilayered structures optimized for a very narrow spectral range. Beam splitters serve different purposes in PLD: to monitor the laser energy (unequal beam splitting) or to perform dual-beam PLD (equal beam splitting). The deposition system can be aimed at only PLD or can combine various deposition techniques (PLD, magnetron sputtering, etc.) as shown in Fig. 37.6. Two approaches are basically available: one can use a commercial PLD system or a home-built one. In any case, a versatile PLD system contains a vacuum chamber, subsystem for target(s) manipulation, substrate(s) holder/heater, pumps subsystem, gas(es) flow, and vacuum gauging [37.82, 83, 89]. Some Applications of PLD for Amorphous Films Fabrication. During the last two decades, PLD has been widely studied as a deposition technique for many different amorphous thin films. Apart from the deposition of amorphous elements, such as carbon [37.91], silicon [37.92, 93], germanium [37.92], phosphorus [37.94], binary amorphous materials were fabricated by PLD too, for example nitrides (boron nitride [37.95], carbon nitride [37.96], etc.), silicon carbide [37.97], aluminum oxide [37.98, 99], titanium oxide [37.100, 101], and many others. Regarding ternary, quaternary, and generally multicomponent oxide-based amorphous thin films, PLD was often employed for the growth of glass thin films for optics [37.84, 102–105], optoelectronics [37.106, 107], or focused on bioglass layers [37.108, 109]. Less frequent are studies of PLD amorphous fluoride films [37.110, 111]. Significant attention was recently paid also to fabrication and characterization of chalcogenide-based amorphous thin films, e. g., sulfides [37.112–114], selenides [37.115, 116], and tellurides [37.117, 118].
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picosecond Nd:YAG lasers are also affordable. However, because of the limited efficiency of nonlinear processes, the energies at 532, 355, and 266 nm are about 50, 20, and 15% of the fundamental one. Excimer lasers discovered in 1970 are gas lasers delivering high output energy exceeding 1 J=pulse at a timescale of tens of nanoseconds with flat-top intensity distribution (Fig. 37.16) operating at different wavelengths in UV which depends on the used gas composition. Among the available excimer laser wavelengths, those at 351, 308, 248, 222, 193, and 157 nm correspond with XeF, XeCl, KrF, KrCl, ArF, and F2 active excimer molecules, respectively. Probably the most popular excimer laser for PLD is the KrF one offering the highest gain [37.82, 83]. It has to be mentioned that apart from excimer or Nd:YAG lasers, for PLD one can also exploit femtosecond lasers. Femtosecond pulses provide short interaction time with light in a solid leading to a rapidly heated impact zone without energy loss by heat conduction during the laser pulse. The plasma plume is generated after the termination of the pulse. Moreover, in contrast with ns PLD, there is no absorption (scattering) of the laser pulse in the plume. Because of the fact that the laser intensity is typically sufficient for multiphoton processes, it is possible to prepare thin films of (dielectric) materials with a sub-band gap photon energy. It should be taken into account that the deposition rate per pulse will be, due to low pulse energy, lower for fs PLD. However, this disadvantage can be compensated with high repetition rates resulting in competitive average power of fs lasers [37.90]. It is important to note that a homogeneous and uniform output beam is crucial for PLD. Poor laser beam quality (nonuniformity, hot spots, etc.) results in the deposition of nonstoichiometric films (when working with multicomponent materials) and formation of defects (droplets). When the intensity of the laser beam
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Advantages and Disadvantages of Plasma Processing for Amorphous Films The major advantage of sputtering technology is the ability to make thin films from a wide variety of metals, insulators, alloys, and composites. In situ cleaning before film deposition by reversing the potential on the electrodes is useful. Depending on configuration and system operation, stoichiometric films with large area uniformity, dense, with small grain size and good adhesion can be obtained. Low-temperature deposition is possible enabling a gentle deposition process for delicate substrates. To obtain high-quality thin films at high deposition rates, closed-loop process control systems are used to provide stable operation by means of basic feedback signals during deposition. The disadvantage can be related to the quite low deposition rate of some materials compared to thermal evaporation or PLD. The substrate and the growing film can undergo low-energy bombardment of host species, dopants, or accelerated gaseous ions. As we have seen previously, they can play a decisive role in determining the nucleation and growth kinetics and the probabilities of dopant incorporation. The design of sputtering systems utilizing the latest developments in advanced vacuum technology and highly sensitive analytical techniques has helped the development of sputtering technology to obtain high-quality films with reduced contamination. Concerning the sputtering target, often expensive, it is required to use large area targets for uniform thickness over large substrates. The sputtering targets, particularly those of insulators, can be easily fragmented during handling or by nonuniform heating. Moreover, an erosion track in the target is observed for magnetron sputtering. It is also difficult to deposit uniformly on complex shapes and highperformance thick coatings are hard to produce due to high internal residual stress levels. As partially discussed above, the advantages and the drawbacks of PLD caused by the high energy densities are as follows. The deposited films may contain macroscopic and microscopic particles which were ejected from the target. The presence of micrometer-sized particles in PLD films is frequently found when the laser penetration depth in the target material is large. Further, large kinetic energy of plume species may lead to a resputtering effect. Apart from resputtering effects, highly energetic plume species may induce a compressive stress in deposited films. In the plume, light elements have different expansion velocities and angular distributions when compared with heavier ones. That is why the content of light elements in the films should be moderated (background gas or designed target composition). Other problems of PLD are connected with the angular energy distribution in the plasma plume which
is highly focused. Therefore, particular changes of deposition rates on dimensions of a few centimeters are typical. Different solutions may be used to produce uniform film thicknesses over larger substrate sizes such as a combination of substrate rotation with rastering of the laser beam over the target material.
37.2.2 Vapor Techniques The main difference between the previous thin-film deposition methods and vapor techniques is that no plasma is used during the process. Generally, in vapor techniques, material is thermally vaporized from a solid (sublimation) or liquid (evaporation) source in the form of atoms or molecules. Then, vapor is transported under vacuum or low-pressure gas environment to the substrates. On the substrates, vapor condenses and thin film grows. The rate of evaporation can be very high. It is important to note that the vapor composition of mixtures, alloys, or multicomponent materials (which is the case of glassy materials, except of a few exceptions, such as amorphous selenium) is proportional to individual vapor pressures. Because of this behavior, a component with high vapor pressure vaporizes faster than a component with low vapor pressure. In a positive way, this effect is used for the purification of the materials (selective vaporization and condensation). A negative effect of this phenomenon is different composition of the thin films when compared with the starting material or a gradient of film composition. In the case of compounds, vapor contains different species (atoms, molecules, clusters). Molecules can also be dissociated; apart from compositional dependence, the degree of their dissociation depends mainly on the temperature of evaporation. The problem of nonstoichiometric or gradient transfer of the multicomponent material from the source to the film may be solved by using flash evaporation techniques. Here, only a small amount of the material to be deposited is completely evaporated in a periodical manner. Another approach for the deposition of multicomponent material by vapor techniques is coevaporation, where the vapor flux is produced simultaneously from multiple sources. The composition of the deposited film is controlled by adjusting the evaporation rate of the respective elements. Two schemes of deposition systems exploiting evaporation process are shown in Fig. 37.17a,b. The left and right panel present the use of a resistively heated source and electron beam (e-beam), respectively. Thermal evaporation can be performed with resistively heated sources (most common for materials which evaporate below 1500 ı C) or heating can be provided via the energy of an electron beam (for
Amorphous Thin Film Deposition
a)
b)
Substrates
Substrates
37.2 Physical Vapor Deposition
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Vaporized material Target material Heater
Target Cooling system
Vacuum system
Power supply
Electron beam gun Vacuum system
Power supply
Fig. 37.17a,b Evaporation systems: (a) resistively heated source and (b) electron beam heating
vantage of a large substrate to source distance is that it allows fixture motion and shutters installation above the source. To overcome cosine angle-dependent distribution of atoms evaporated from a point source, the position and angle (with respect to the direction of the vapor flux) of the substrates are randomized; they are often rotated [37.1]. In the field of fabrication of glassy and amorphous thin films via thermal evaporation, the focus is often on materials with lower evaporation temperatures, for example amorphous chalcogenides [37.114, 119–122].
37.2.3 Ion Plating and Ion Beam-Assisted Deposition The ion plating method is a term used to define a film deposition process in which the surface of the substrate and the growing film, throughout deposition, are subjected to continuous or periodic bombardment by a flow of particles whose energy is sufficient to cause changes in the interfacial region and modify the properties of the layer compared to the same deposition performed without ion bombardment. That is, the morphology and topography of the layer, the density of the layer, the internal stresses of the film, the adhesion of the layer on the substrate, the homogeneity and the uniformity of the layer, and the modification of physical properties. The technique was initially used in 1964 for the improvement of adhesion, recovery, and uniformity as well as densification of PVD layers. It was used also to improve chemical reactions in the development of composite deposition. Later, ionic deposition proved useful for controlling the properties of CVD layers such as density and residual stresses. In most installations, the source placed in a vacuum chamber is a Joule-heated crucible or an electron gun. The substrate is bombarded by ions, usually argon, cre-
Part E | 37.2
temperatures above 1500 ı C). Sometimes, inductive radio-frequency heating is used. In the case of resistive heating, the material to be evaporated is heated through contact with a hot surface; heating is provided by a current going through a suitable material (W, Ta, Mo, C, or conductive composite ceramics such as BN=TiB2 ) in the form of a wire, basket, boat, etc. The material to be evaporated is stored in a container (crucible); the evaporated material and the container should not react. An important point is that there should be good thermal contact between the evaporated material and the container. Good thermal contact is assured by good wetting when evaporation from melt takes place. Resistance and induction heating makes it possible to obtain coatings at a high deposition rate. Conversely, their main weak point is the need to use sufficient power to evaporate the most refractory compounds. In addition, the energy of the evaporated adatoms is relatively weak, resulting in poor adhesion [37.1]. For the materials that evaporate above 1500 ı C (typically ceramics, glasses, carbon, etc.) or for evaporation of a large quantity of material, a focused e-beam is needed. E-beam-heated sources usually evaporate material in a vertical configuration (Fig. 37.17). To generate electrons in an electron gun, a thermionic emitting filament is used. The emitted electrons are accelerated with high voltage. The electron beam is focused and deflected onto the deposited material by an electric or magnetic field. Both metals and dielectrics can also be deposited (Ni, Pt, Ir, Rh, Ti, V, Zr, W, Ta, Mo, Al2 O3 , SiO, SiO2 , SnO2 , TiO2 , ZrO2 ) by e-beam evaporation allowing various fabrications of heterostructure or multilayer coatings on glass substrates at high deposition rates that can in some cases reach 50 m=s. In order to particularly reduce radiant heating of the substrates by the evaporation source, the distance of the substrates from the source is large. Another ad-
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Part E
Glass Processing
Substrate
Pump Ion beam Evaporated material Ion source E-beam evaporation
Part E | 37.2
Fig. 37.18 Combination of e-beam evaporation source with ion source
ated in a plasma according to the same mechanisms as those of sputtering. It is also possible to use ions from an ion source commonly referred to as an ion gun (Fig. 37.18). The essential difference to a sputtering apparatus is that it is the substrate that is polarized negatively (cathode) and is therefore bombarded by the energetic particles. The substrate is bombarded with ions of inert gas for a time sufficient to modify its surface, and the layer deposition is started without interrupting the ion bombardment. For a layer to form, it must be understood that the deposition rate is higher than the sputtering speed. Argon ions bombardment may continue after establishment of the interfacial zone or it may be interrupted. Of course, the continuous diode plating ion technique can only be used with conductive substrates. If the substrate is insulating as in the case of a glass substrate, it will accumulate electrical charges on its surface which will quickly prevent any bombardment by particles with a positive charge. It is then necessary to use an ion plating HF system, where the plasma of ions and electrons is generated by a high-frequency discharge. The glass substrate on which it is required to deposit a thin layer is placed on a metal electrode close to the plasma. Thus, the insulating surface will be polarized positively and negatively alternately. As the electrons are more mobile than the ions, the surface will keep a significant negative polarization which will be sufficient to accelerate the ions of the plasma to sputter the surface of the substrate and the layer formed. This technique is used in the case we are inter-
ested in, namely to deposit layers on a glass substrate or an insulator material on conductive substrates. The presence of contaminants in the deposition chamber is even more crucial in the case of the ion plating technique. The reactive species are activated in the plasma and can contaminate the substrate and the deposited layer. The evaporation source and the source of energetic ions for bombardment can be separated. The advantage of using an ion gun with respect to a plasma is the ability to separately control the parameters of the bombarding ions. This process is often called ion beamassisted deposition (IBAD). Frequently, the ion beam is neutralized by the addition of electrons. The beam is neutral or a mixed ion/electron plasma is generated in the source preventing Coulomb repulsion in the beam as well as charge buildup on the bombarded surface. The bombardment must be continuous from the preparation of the surface until the formation of the interface to obtain good adhesion. It can be easily understood that to modify the composition, morphology, topography, and physical properties of the growing layer, the bombardment is also continuous during this period. The effect of bombardment on the surface of the substrate will make it possible to eliminate oxide residues by sputtering, and to obtain in situ a clean and reactive surface for deposition. The reactive surface is created by the generation of reactive sites and defects. Reactive ions, such as oxygen, can react with a contaminant layer, like hydrocarbons, to produce volatile species. If the defects produced by the ion bombardment are sufficiently immobilized, the superficial crystallography will be modified and can be transformed into an amorphous structure. The bombardment increases the surface roughness via normal incident bombardment. As a general rule, amorphous materials trap more gas than crystalline materials, which can lead to Ar concentrations of several percent, significantly influencing the internal stresses of the layer. An increase in the surface temperature and a modification of the surface composition under the effect of the bombardment are also to be expected. Surface cleaning, formation of defects and reactive sites on the surface, implantation of species, surface temperature and composition change of the interface compared to the bulk substrate with acceleration of diffusion or pseudodiffusion are all processes that will influence the formation of the interface when the film is deposited. The effect of bombardment on the formation of the interface will start with the modification of the nucleation process of atoms on the surface previously modified by energetic particle bombardment increasing the nucleation density leading to better adhesion.
Amorphous Thin Film Deposition
37.3 Chemical Vapor Deposition
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37.3 Chemical Vapor Deposition 37.3.1 Vapor-Based Film Fabrication
SiH4 .g/ ! Si(s) C 2H2 .g/
a)
Reactants
1. Thermal decomposition reactions (or pyrolytic reactions) that are characterized by dissociation of a gaseous compound into a solid material and a gaseous by-product.
Substrate
Exhaust
2. Reduction reactions, where hydrogen acts as a reducing agent. SiCl4 .g/ C 2H2 .g/ ! Si(s) C 4HCl(g)
Furnace
3. Exchange reactions in which an element replaces another element. Zn(g) C H2 S.g/ ! ZnS(s) C H2 .g/
b) Reactants
Exhaust Heated substrate
Fig. 37.19a,b The two main CVD reactor types: a hot-wall reactor (a) and a cold-wall reactor (b)
4. Disproportionation reactions (rare in CVD) that occur when the oxidation number of an element both increases and decreases; as a result, two new species are formed. 2TiCl2 .g/ ! Ti(s) C TiCl4 .g/
Part E | 37.3
Chemical vapor deposition (CVD) is a technique in which a solid material is deposited from a vapor by a chemical reaction occurring on or in the vicinity of a normally heated substrate surface [37.123, 124]. By varying the experimental conditions such as substrate material, substrate temperature, composition of the reaction gas mixture, total pressure gas flows, etc. solid materials with different properties can be fabricated. A characteristic feature of the CVD technique is its excellent throwing power, enabling the production of coatings of uniform thickness and properties with a low porosity even on substrates of complicated shape. Another important feature is the capability of localized, or selective deposition, on patterned substrates. The CVD process has many variants, for example atmospheric pressure, low pressure, ultrahigh vacuum CVD, direct liquid injection CVD, aerosol-assisted, microwave plasma-assisted, remote plasma-enhanced, atomic layer, hot wire or metal-organic CVD, just to mention a few. CVD reactions can be activated and maintained by heat, photons, electrons, ions, or plasma. Nevertheless, in each CVD process, gaseous reactants are introduced into a reactor (Fig. 37.19). CVD reactors are characterized by many parameters. However, two main CVD reactor types are a hot-wall reactor (Fig. 37.19a) and a cold-wall reactor (Fig. 37.19b). When using the hot-wall CVD reactor, the substrates and walls have the same temperature. This leads
to film growth not only on the substrates, but also on the inner surface of the reactor walls. The disadvantage of the hot-wall reactor is possible contamination, if the wall material reacts with the gas(es) in the system. The second problem of this reactor type is the formation of defects on the surface of deposited films originating from particle downfall from the reactor walls above the substrates. Conversely, the walls of a cold-wall reactor are unheated and no material deposition occurs on the walls, which eliminates the above-mentioned risk of film defects. Low wall temperature also reduces the risk of contamination due to vapor–wall reactions. The choice of substrate heating depends on its electrical conductivity. Both resistive or inductive radio-frequency heating are used for conductive substrates. Electrically nonconductive substrates are typically heated optically (tungsten lamps, lasers), by thermal radiation techniques, or by susceptors and inductive radio-frequency heating. If the substrates are in a form of a large number of small pieces, fluidized bed technique may be applied. Key aspect to obtain high-quality thin films by CVD is gas flow dynamics (rate and arrangement of gas flows). Reactions proceeding during a CVD process may be classified as follows:
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Glass Processing
5. Coupled reactions, for instance reduction coupled to an exchange reaction: CO2 .g/ C H2 .g/ ! CO(g) C H2 O.g/ 2AlCl3 .g/ C 3H2 O.g/ ! Al2 O3 .s/ C 6 HCl(g)
produce a very compliant deposition. The other difference, when comparing ALD with CVD, is that CVD is generally temperature dependent while ALD has weak temperature dependence. One ALD cycle consists usually of four steps (Fig. 37.20):
which give overall reaction 2AlCl3 .g/ C 3CO2 .g/ C 3H2 .g/ ! Al2 O3 .s/ C 3CO(g) C 6HCl(g)
Part E | 37.4
CVD is widely used to produce thin films for different fields, for example in microelectronics, solar energy conversion, optical fibers, semiconductor lasers, heat-/erosion-/corrosion-/wear-resistant coatings, hightemperature superconductors, etc. Among the mentioned applications, fabrication of amorphous and glassy CVD thin films was reported for instance for aluminum oxide, silicon, germanium, carbon, boron, BN, Si-Ge, Si-C, C-N, TiO2 , SiOx , Ge-(Sb)-Te, phosphosilicates, and borophosphosilicates [37.125]. Atomic layer deposition (ALD) is considered to be one of the CVD techniques, where film growth proceeds by exposure of the substrate surface to a chemical reaction (gas–solid) of at least two compounds (precursors) in a cyclic manner [37.126]. The advantage of ALD is accurate thickness control at the monolayer level. Contrary to CVD, the precursors are never present simultaneously in the deposition chamber. The basic requirement for uniform film growth on large area/complex shape substrates is that the proceeding reactions are irreversible and self-terminating [37.127]. The selfterminating aspect of ALD leads to excellent coverage and conformal deposition on high-aspect-ratio structures. During the reaction and because of the different precursor gas flows, the precursors will adsorb and subsequently desorb the surfaces where the reaction has come to an end. Also the desorbed precursors will then react with other areas that have not yet reacted and
1. First gas–solid reaction (chemisorption reaction of the first reactant, which is typically a metal) 2. Purge or evacuation (to remove gaseous byproducts and unreacted precursor) 3. Second gas–solid reaction (chemisorption reaction of the second reactant, which is typically a nonmetal) 4. Purge or evacuation. Outside of the semiconductor industry, ALD is a really attractive deposition method for example for low electron leakage dielectrics for magnetic read/write heads and diffusion barrier coatings with low gas permeability [37.128]. During the past decades, many different chemical paths have been studied for the application of ALD to thin film growth. The self-terminating nature of the surface reactions produces a nonstatistical deposition because the randomness of the precursor flux is removed. As a result, ALD films remain extremely smooth and conformal to the original substrate because the reactions are driven to completion during every reaction cycle. Because no surface sites are left behind during film growth, the films tend to be very continuous and pinhole-free. This factor is extremely important for the deposition of excellent dielectric films. Depending on the used precursors, substrates, and ALD experimental conditions, deposited films can be of amorphous or crystalline nature as described in detail in comprehensive reviews by Miikkulainen et al. and other authors for elements, oxides, nitrides, fluorides, sulfides, selenides, tellurides, and other materials [37.127, 129].
37.4 Comparison of PVD and CVD Techniques Each thin-film deposition technique has its advantages and its limitations leading to different fields of application. Their advantages and disadvantages are summarized and presented in Table 37.3. Thickness control and coating of large-area films can be realized in PVD, which has become the main film-coating technique
(especially the sputtering method) in the fields of electronics, electricity, and optics due to its high production efficiency, high film purity, and low production cost. In CVD processes, films can be deposited on substrates with much more complex profiles and adhesion between films and substrates is generally strong.
Amorphous Thin Film Deposition
37.4 Comparison of PVD and CVD Techniques
1319
Purge or evacuation
By-product Chemisorption Reaction B Reactant B
Purge or evacuation
Part E | 37.4
Chemisorption Reaction A Reactant A
Substrate before ALD process
Fig. 37.20 Scheme of the atomic layer deposition reaction cycle (adapted after [37.127]) Table 37.3 Comparison of classical PVD and CVD techniques Process
Material
Deposition rate (Å=s)
Sputtering
Metal and dielectrics
Metal: 100 Dielectric: 110
PLD
Metal and dielectrics
10
Thermal evaporation
Metal Low melting-point materials
120
E-beam evaporation
Metal and dielectrics
10100
LPCVD
Mainly dielectrics
10100
PECVD
Mainly dielectrics
10100
Stoichiometry
Impurity
Density
Uniformity for industrial process
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37.5 Liquid-Based Film Fabrication In this section, thin film deposition techniques that use liquids are briefly described:
Part E | 37.5
Electroplating: Some metallic elements (Ag, Au, Rh, Cr, Ni, Zn, etc.) or alloys (Cu-Zn, Pb-Sn, NiFe, etc.) can be deposited by electrolysis from solutions. Also, a few conductive oxides (PbO2 or Cr2 O3 ) can be coated via electroplating. For the electrodeposition, usually an electrolytic cell consisting of two electrodes, electrolyte, and external source of current is used. The possibility of electroless plating also exists, where a current source is not necessary. Electrophoretic deposition: Electrophoretic deposition exploits electrophoresis which is a process of electric field-governed migration of charged colloidal particles suspended in a liquid medium. As a result of migration of colloidal particles, their deposition onto an electrode proceeds. Both aqueous and nonaqueous electrophoretic deposition are known and used. Chemical reduction: In some cases, thin films are deposited from solutions at low temperatures. The solution is commonly composed of two or more components which react together. A typical example is chemical silvering where silver is deposited by a reaction of an aldehyde with an ammonia complex of silver in a basic aqueous solution. Another example is Cu2 O deposition from a solution of CuSO4 , Na2 S2 O3 , and NaOH. Sometimes, metallic layers are deposited through thermal decomposition of a solution. Spray pyrolysis: This technique employs spraying a precursor solution onto a heated substrate.
Droplets impact on the substrate surface, spread into disk-shaped structures, and undergo thermal decomposition. The film is usually composed of overlapping disks of metal compound being converted into the desired material (often a crystalline oxide layer) on the heated substrate. Spray pyrolysis represents a very simple and relatively costeffective thin-film deposition method. Typical spray pyrolysis equipment consists of only an atomizer, precursor solution, substrate heater, and temperature controller. Sol–gel (dip coating, spin coating): Sol–gel process means the formation of solid materials, mainly inorganic, from solutions. This can be a solution of monomeric, oligomeric, polymeric, or colloidal precursors. The sol–gel process generally consists of several steps. First, a homogeneous solution of easily purified precursors is prepared. Second, the solution is converted to the sol form via treatment with a suitable reagent. Third, the sol is transformed into a gel by a condensation process. Fourth, the gel or viscous sol is shaped to the final form (thin film, fiber, etc.). Finally, the shaped gel (or sol) is converted to the solid state material at temperatures that are much lower than those required in conventional PVD or CVD techniques. Another advantage of the sol–gel method is easy coating of large areas.
For the fabrication of thin films by applying the sol–gel process, different coating techniques can be used. The most important are dip and spin coating. Dip coating, as illustrated in Fig. 37.21, is a process where the substrate is immersed in a liquid and then withdrawn with a defined speed under controlled
a)
b)
Fig. 37.21a,b Spin-coating (a) and dip-coating process scheme (b)
Amorphous Thin Film Deposition
1321
achieving high performance and reducing costs for next-generation displays. In this research, amorphous hafnium silicon oxide (HfSiOx ) was fabricated by a simple spin-coating method [37.141]. Rare earth oxides as dielectric films in electronic devices were elaborated by a sol–gel method [37.142]. Conversely, the use of spin-coating techniques for amorphous halogenidebased films is very limited [37.143]. The use of dip coating for the growth of amorphous films seems to be less frequent. For instance, silica glass films were coated on polypropylene microporous membrane separators by a dip-coating method, in which polysilazane diluted with xylene was used as the precursor material for the silica glass [37.144], or As2 S3 layers were prepared by using spin- or dip-coating techniques with As2 S3 solutions in ethylenediamine and n-propylamine as solvents [37.145]:
Printing techniques (inkjet, screen-printing): Finally, printing techniques for the fabrication of thin films using a liquid phase should be mentioned. Among the printing techniques, inkjet and screenprinting seem to be favorable for the fabrication of thin films applicable in modern industrial fields such as biosensors, microelectronics, micro-optics, etc. Inkjet printing is considered to be one of the most versatile methods allowing fast deposition of very low liquid volumes (picoliters), high resolution, and great reproducibility. Screen-printing is widely used because of its robustness, simplicity, high throughput, and low cost for mass production. In the field of amorphous and glassy thin films, printing techniques were studied e. g., for inkjet-printed amorphous zinc-tin-oxide TFTs and simple inverter circuits [37.146], for the fabrication of chalcogenide glass microlenses [37.147], for spatially varying effective refractive index gradient using chalcogenide glass layers printed on a silicon wafer using an optimized electrospray deposition process. Using solution-derived glass precursors, IR-transparent Ge23 Sb7 S70 and As40 S60 glass films of programmed thickness are fabricated to yield a bilayer structure, resulting in an effective gradient refractive index film [37.148].
Part E | 37.5
conditions (temperature, atmosphere). The atmosphere governs the evaporation of the solvent which leads to the destabilization of the sol. Consequently, the gelation process starts and a film is formed. The resulting film is densified by thermal treatment. The main parameters defining the thickness of the coating is withdrawal speed, the content of solid material, and viscosity of the liquid. In the spin-coating process, the substrate is rotated around an axis that is perpendicular to the surface of the substrate. The different stages of a spin-coating process (deposition of the sol, spin-up, spin-off, and solvent evaporation causing gelation) are illustrated in Fig. 37.21. The final step of the process is again thermal treatment. Spin coating has been employed for the deposition of amorphous chalcogenides films such as AsSe [37.130], As-S [37.131, 132], and Ge-Sb-S [37.133]. Recently, spin coating was successfully used for the fabrication of amorphous oxide films. Using Al.NO3 /3 9H2 O as a precursor, optically transparent Al2 O3 amorphous thin films have been successfully synthesized by a sol–gel spin-coating process and annealing [37.134]. Amorphous ZrO2 films were also synthesized [37.135]. Using inorganic sol–gel with V2 O5 powder and hydrogen peroxide (H2 O2 ) as precursors in spin-coating, V2 O5 thin films deposited on glass substrates were found to be amorphous with smooth surfaces, whereas films deposited on quartz, silicon, and alumina substrates exhibited a polycrystalline nature [37.136]. ITO layers were obtained by the sol–gel process as well [37.137]. Amorphous TiO2 films were deposited using a low-temperature (< 250 ı C) sol–gel process fully compatible with monolithic integration on plastic substrates. High-index-contrast flexible optical waveguides and resonators were fabricated using the sol–gel TiO2 material, and resonator quality factors up to 20 000 were measured [37.138]. Amorphous oxide semiconductor In-Si-O was fabricated via solution processing [37.139]. Amorphous SrTiO3 thin films were fabricated by sol–gel and spin-coating technology [37.140]. Novel solution-processed amorphous high-k dielectrics for thin film transistors (TFTs) have been systemically studied with the objective of
37.5 Liquid-Based Film Fabrication
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Glass Processing
37.6 Contribution of Amorphous Thin Films and Coatings on Glass to 21st Century Development
Part E | 37.6
In recent years, the development of amorphous thin films and glass coatings has made great strides in the fields of renewable energy sources, environment, aerospace, security, health, and biology. Materials science is the keystone of these new developments, not only in terms of process but also in terms of new concepts and therefore new applications. As an illustration, some of these high-tech developments will be presented below. The glass material in its use as glazing in housing has today moved away from bulk glass. Modified by various forms of thin film deposition, chosen to meet functional specifications, it has evolved into a high-tech material. If we can adapt the aesthetics of the glass by coloring it or by applying an antireflection treatment to make attractive commercial windows, we can also adapt glass via the deposition of more or less complex thin layer stacks on its surface to photovoltaic applications by making it electrically conductive, produce glass materials for the new screen types required by progress in communications, make it self-cleaning, improve its mechanical properties, make it resistant to scratches, or improve its thermal performance (glazing with reinforced thermal insulation, solar control glazing). A further refinement of adding a thin layer on the surface of the glass to reflect the far infrared produces so-called high-tech glass material. On conventional float glass, a so-called low-emissive layer is deposited which allows the visible spectrum to pass, thus preserving the property of transparency, but reflects the thermal infrared with great efficiency. Glass always absorbs thermal radiation, does not re-emit it outwards and only re-emits inwards under the effect of the low emissive layer that reflects it. The radiant heat transfer is thus considerably attenuated with values of the order of 1:1 W=.m2 K/ compared to 2:6 W=.m2 K/. In order to regulate the temperature in houses or buildings, it is necessary to design technical glasses able to circumvent the fact that the radiations of the sun bring an excess of heat. Thus, it is necessary to control not only the thermal infrared but also the near-infrared, allowing only visible light. Specific reflective metal or oxide-metallic layers have been designed for this purpose. Nowadays, it is electrochromic glazing that presents the most modern technical possibilities to promote active or smart glazing designs. The inorganic technology implements the successive deposition of a series of thin layers (current supply electrodes for the transparent conducting oxides, active layers for the electrochromic layer and for the associated counter-electrode, electrolyte for ionic conduction) [37.149].
The photovoltaic effect was discovered by Edmond Becquerel in 1839. It then took 115 years to make the first efficient solar cell, with a few watts produced, about 50 years to deploy 3 GW of production capacity worldwide, and only 13 years to reach 300 GW in 2016. 500 GW are expected in 2020, and the TW within the next decade [37.150]. Photovoltaics should continue to grow very well and will quickly become an essential feature of house and building and beyond that, a major component of the energy industry. The well-established silicon industrial sector represented in 2016 about 94% (single crystalline and polycrystalline solar cells) of the annual production capacity of solar cells, with the remaining 6% shared by thin film technologies (CdTe, Cu(In,Ga)(S,Se)2 (CIGS), . . . ). CdTe and CIGS thin film pathways are currently in full development, with efficiencies of up to 22:1 and 22:6% respectively, beyond that of polycrystalline silicon [37.150]. These thin layer stacks are deposited on glass substrates to form a few microns-thick device: solar cells based on amorphous silicon, based on cadmium telluride (CdTe), and finally those based on a Cu.In;Ga/.S;Se/2 alloy. The development of the use of glass in architecture probably explains the current development of thin film technologies on glass for photovoltaics. Recently very large modules, nearly 6 m2 were made in one piece. The interest in this technology—and what explains its success—is that CdTe deposition processes are extremely fast (from a few seconds to a few minutes), which allows important production rates to be reached thus reducing production costs. The arrival of this technology marked a real break in the competitiveness of photovoltaics. There are many examples of integration of these thin film cells on large-scale glass installations on buildings. This sector is expected to continue to develop as cells based on the Cu.In;Ga/.S;Se/2 thin film system achieve laboratory efficiencies of more than 22% [37.151, 152]. Connectivity is at the heart of our modern world with systems that occupy a smaller and smaller volume of a few cubic millimeters to be widely dispersed in our environment to make it more and more smart and interactive. These miniaturized devices are and will increasingly be able to collect information, act accordingly, and communicate. Applications related to these connected objects are numerous: monitoring of the natural environment, industrial or urban, industrial activities, connected housing, smart clothing, monitoring or medical diagnosis and drug delivery directly into the human body. These systems involve the diversification of functions and integrated technologies dependent
Amorphous Thin Film Deposition
high precision in manufacturing processes. In addition, in order to meet consumer demands, manufacturers are investing heavily because of the growing popularity of microsensors consuming less energy and also being less cumbersome. The growth of the microsensor market can be understood by taking into account its beneficial characteristics based on their low cost, accuracy, and sensitivity. On the basis of the input signal, the microsensors can be classified into optic, magnetic, biological, thermal, mechanical, and chemical ones. Types of microsensors include biochips, environmental microcells, microelectromechanical systems or nanosensors developed for manufacturing, robotics, automotive, aircraft and aerospace, consumer electronics, medicine, food, and are found in many other aspects of our daily lives. As in the case of energy source and storage, amorphous thin films can play a major role in the development of microsensors, especially in the case of optical sensors. Integrated optics and nanotechnologies are highly innovative technologies that are expected to be high growth markets in the future. The micro and nanophotonic structures are elementary building blocks offering a large number of functionalities such as optical filtering, laser sources and light-emitting diodes or detectors being able to result in obtaining optical sensors. The fabrication of such photonic structures is feasible with a variety of different deposition techniques, such as spin coating, sputtering, evaporation, pulsed laser deposition or CVD methods allowing easy integration into many types of IO devices. Photonics technology is driving many of the major end markets, including advanced manufacturing, communications/information technology, energy, defense, healthcare and medicine. Among the different integrated optical sensors, mid-IR sensors and notably generic integration platforms should be developed in the next decade [37.161]
Analytical e-beam 10 μm AES SEM
Mica Pi LiCoO2 LiPON Li Mica
Fig. 37.22 Scheme of solid-state Microbattery stacking
Sputtering beam for ion milling cross-section
microbattery stack with AES and SEM images. Reprinted with permission from [37.153], copyright 2017 American Chemical Society
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on the development of thin films to meet all of these functionalities. Thus, new energy sources and new energy storage devices must be developed with the same degree of miniaturization. At the microscopic scale, research on the recovery of solar, mechanical, and thermal energy is in full rise. The development of microsystems for electrochemical storage is at the center of this issue. Microbatteries require the use of specific active materials [37.153] (Fig. 37.22). The main specificity comes from the nature of the electrolyte. Indeed, in order to achieve a monolithic system, a vitreous inorganic electrolyte is generally used. However, it limits the performance of the microbattery at low temperature because of its low ionic conductivity ( 106 S=cm) (about 1000 times lower than that of liquid electrolytes) and its high activation energy ( 0:5 eV). Nevertheless, it allows energy storage over a long period thanks to its low selfdischarge resulting from its low electronic conductivity (1013 1014 S=cm). In addition, its good electrochemical stability (often greater than 5 V versus Li=LiC ) allows a large number of cycles. The use of a solid electrolyte is an undeniable gain in terms of safety and environmental gain compared to the use of a liquid electrolyte. Interesting conductivities are obtained with thin layers of sulfide glasses (B2 S3 -Li2 S-LiI, Li2 S-Ga2 S3 P2 S5 , Li2 S-GeS2 -Ga2 S3 , and LiI-Li2 S-P2 S5 -P2 O5 fabricated by PLD or RF-sputtering). Nevertheless, thin layers of sulfides are hygroscopic and therefore difficult to use from an industrial point of view. An interesting solid electrolyte in microbatteries is the LiPON amorphous layer, prepared by sputtering and also films from the vitreous domain of the B2 O3 -Li2 O-Li2 SO4 system with deposition performed under nitrogen plasma to improve ionic conductivity [37.154–159]. In the same spirit of connectivity research, the deployment of microsensors in industries, whether medical or chemical, can be explained by the requirement for
37.6 21st century development
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Microfluidic channel
Waveguide integrated Si-Ge detector
Fig. 37.23 Design of integrated onchip photonic sensor device. Reprinted with permission from [37.160]
Doped glass ring laser
Ultrahigh-Q ChG resonator
Part E | 37
(Fig. 37.23). Mid-infrared photonic integrated circuits for detection in a gas medium or liquid phase are a quasi-unexplored research field that has huge potential for applications such as food analysis, environmental monitoring (pesticides, NOx , CH4 , CO, . . . ), health (diagnosis), toxicology (illicit drug, sport doping), and safety (warfare agents, . . . ). For instance, the detection of specific contaminants in food quality control is of primary importance to improve consumer safety. The only remediation is to detect the contamination before it reaches the regulatory threshold and to carry out the analysis directly at the production site. It requires a very sensitive, fast, easy, and low-cost assaying system as well as a compact and easily usable detection device.
CMOS circuitry
Some new technological solutions like an optical integrated spectrometer in the mid-infrared wavelength range could provide new breakthroughs in the detection field. For more details on the use of amorphous films as integrated waveguides, please refer to Chap. 42 on integrated optics in this book. Acknowledgments. The financial support of the French National Agency of Research (ANR) for the LOUISE project (Nı ANR-15-CE04-0001-01) and the Czech Science Foundation under project No. 1617921S is acknowledged. We dedicate this chapter to the memory of Patrick Smutek of the Plassys company.
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References
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Virginie Nazabal Institute of Chemical Sciences ISCR, UMR CNRS 6226 University of Rennes 1 Rennes, France [email protected]
Virginie Nazabal received her PhD in Solid State Chemistry from Bordeaux University, after an ENS graduate degree at Paris VI University. In 2000, she joined the NIMS in Tsukuba, Japan. In 2001, she joined the CNRS at Rennes University, becoming a CNRS Senior Researcher in 2015. Her research is devoted to glass for photonics.
Petr Němec Faculty of Chemical Technology University of Pardubice Pardubice, Czech Republic [email protected]
Petr Nˇemec received his PhD in Chemistry and Technology of Inorganic Materials from the University of Pardubice (2002). Since 2006, he has worked as an Associate Professor at the Faculty of Chemical Technology, University of Pardubice. He became a full Professor in 2015. His expertise includes inorganic glasses and amorphous thin films.
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Sol-Gel Glass 38. Sol-Gel Glasses
Lisa C. Klein 38.1
The Role of Sol–Gel Processing in Glass Technology .......................... 1331
38.2 Sol–Gel Processing ............................ 38.2.1 Precursors, Metal Alkoxides, Salts and Colloidal Suspensions .................. 38.2.2 Hydrolysis and Condensation Polymerization Reactions ................... 38.2.3 Acid Versus Base Conditions................ 38.2.4 Complete or Partial Hydrolysis ............ 38.3
1333 1333 1334 1334 1336
Gelation, Percolation and Syneresis ... 1337
38.4
Drying and Removal of Solvent and Water ........................ 38.4.1 Xerogels............................................ 38.4.2 Aerogels ........................................... 38.4.3 Porous Gels and Their Uses ................. 38.5 38.6
Consolidation and Sintering .............. Sol–Gel Fibers, Thin Films and Other Applications ..................... 38.6.1 Thin Films by Dipping or Spinning ...... 38.6.2 Optical Applications and Other Surface Treatments .............
1338 1338 1339 1339 1340 1342 1342 1344
38.7
Organic–Inorganic Hybrid Sol–Gel Glasses ............................................. 1345
38.8
Summary and Future Prospects ......... 1347
References................................................... 1348
38.1 The Role of Sol–Gel Processing in Glass Technology Of all of the alternative methods for glass formation, principally oxide glasses, why has sol–gel processing maintained its appeal, despite having no chance of replacing conventional glass melting? Sol–gel processing emerged about 30 years ago. At first, it was a laboratory curiosity, mostly for making shaped objects. The cost of the precursors, in comparison to glass sands and carbonates, was considered prohibitive. Nevertheless, here it is 30 years later, and there is no sign that interest in the sol–gel process is decreasing. Perhaps one of the reasons is that there are many applications for sol–gel processing, where conventional processing does not meet the requirements for purity and chemical
uniformity. Certainly, among optical materials, porous materials and thin and thick coatings, there are many outstanding examples of successful use of the sol–gel process [38.1–3]. The sol–gel process broadly includes roomtemperature solution routes for preparing oxide materials [38.4, 5]. In most cases, the process involves the hydrolysis and polymerization of metal alkoxide precursors of alumina, silica, titania, zirconia, as well as other oxides [38.6, 7]. The solutions of precursors are reacted to form irreversible gels that dry and shrink to rigid oxide shapes. A schematic of the overall process is shown in Fig. 38.1. As an example of a truly
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_38
Part E | 38.1
Sol–gel processing is a nonmelting path to forming primarily silicate glasses. The most widely used precursors for the sol–gel process are metal alkoxides that undergo hydrolysis and condensation polymerization. Pure silica, binary compositions and multicomponent compositions are reacted to generate oxide polymers in the presence of water and alcohols. The oxide polymers grow and crosslink to produce a gel network at the sol–gel transition. After gelation, the solvents are removed, leaving behind a microporous skeleton that can be collapsed to a chemical and physical duplicate of a melted glass. The sol–gel process also refers to solution routes that involve soluble salts and colloidal routes that involve metastable suspensions of oxide nanoparticles. Combinations of alkoxides, salts and colloids are all considered sol–gel routes. The advantage of the sol–gel process, compared to melting and quenching, is that the process is carried out largely at room temperature. The low temperature makes the sol–gel process compatible with organic polymers, which enables formation of organic–inorganic hybrids. Also, when it is not necessary to remove the porosity, the sol–gel process is a means to form microporous and macroporous glasses.
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Solution/sol
2 3
Solution
Sol
Alcogel
Hydrogel
Xerogel
Aerogel
Cake
Powder 1
Fig. 38.1 Schematic of overall sol–gel process
Part E | 38.1
bottom-up process, the building block is the metal alkoxide molecule, which is smaller than a nanometer [38.8, 9]. The process begins with the formulation of the alkoxide-water-solvent mixture, proceeds to the shaping of the gel by dipping, drawing or casting, is followed by drying and removal of byproducts, and finishes with some treatment that establishes the integrity of the gel. This final step may involve consolidation or reinforcing with a second component. Thirty years ago, when there was a revival of interest in the sol–gel process, the emphasis was on the duplication of existing commercial glasses and their properties typically achieved by melting. Trying the sol–gel process was motivated by claims of the purity of the starting materials and potentially lower temperatures. Relative to high-temperature melting of sand and carbonates, the sol–gel process takes less time to reach a homogeneous chemical composition. At room temperature, there is little reaction between the components and their container, where refractory corrosion is a serious problem at high temperature [38.10] or the need for platinum crucibles adds cost. Issues with crystallization or phase separation during cooling are avoided, although transformations during consolidation are a concern [38.11, 12]. For the sake of argument, using industry figures, say that the cost of a glass made by conventional melting and quenching is 75 cent per kg, of which 4 cent is raw materials. If the popular metal alkoxide, tetraethylorthosilicate (TEOS), is $ 25 per kg, then a replacement glass from the sol–gel process is not commercially viable. On the other hand, estimates of
5
6
4
Fig. 38.2 Assortment of sol–gel processed silicates, including (1) capped and inverted wet gel undergoing syneresis, (2) spin coating on silicon wafer, (3) aerogel in 2:54 diameter test tube, (4) rod-shaped rigid silica monolith, (5) silica monolith infiltrated with methyl methacrylate monomer and polymerized, and (6) silica gel shape doped with Rhodamine 6G
the material cost in fiber-optic waveguides are as high as $ 50 000 per kg, taking into account equipment costs, so there must be some middle ground for sol–gel processed glasses [38.13, 14]. In the end, glasses made by the sol–gel process are finding niche applications. Sol–gel processing has been successful in a number of forms. In some cases, the process is used to mold a shape, referred to as a monolith, which preserves the shape and miniaturizes the features of the mold. Alternatively, while the sol–gel process is underway and the precursors are in liquid form, coatings can be applied to substrates in spinning and dipping operations. When shapes are formed and the solvent is removed by supercritical evacuation, the ultralightweight structure that remains is an aerogel. When shapes are allowed to shrink but remain porous, the porosity can be infiltrated with an organic monomer, such as methyl methacrylate, or doped with organic dyes. All of these forms are illustrated in Fig. 38.2. The rest of this chapter elaborates on these processes and forms.
Sol-Gel Glasses
38.2 Sol–Gel Processing
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38.2 Sol–Gel Processing In the current terminology, sol–gel processing is a bottom-up process on the nanometer scale [38.8]. Initially, the sol–gel process begins with a nanosized unit, a molecule. The molecules participate in reactions on the nanometer scale, resulting in a material with nanometer features. In its simplest manifestation, the sol–gel process is a combination of chemical reactions turning a solution of reactants into an infinite molecular weight oxide polymer. This oxide polymer is a threedimensional (3-D) skeleton surrounding interconnected pores. Ideally the polymer is isotropic, and uniform in its nanostructure. On the microscale, it replicates its mold. Since it is isotropic, the gel miniaturizes the texture of its mold without distortion during shrinkage. In many cases, it is the nanophase porosity, rather than the oxide skeleton itself, that is the feature of interest, both scientifically and technologically.
38.2.1 Precursors, Metal Alkoxides, Salts and Colloidal Suspensions
a)
Fig. 38.3a,b Molecular
b) O
O O
O
Si O
O
Si O
O
structure of tetraethyl orthosilicate (TEOS) (a) and tetramethyl orthosilicate (TMOS) (b)
Table 38.1 Chemical formulas and properties of two common silica precursors Chemical name
Formula
Tetraethoxy orthosilicate C8 H20 O4 Si Tetraethoxysilane (TEOS) Tetramethoxy orthosilicate C4 H12 O4 Si Tetramethoxysilane (TMOS)
Molecular weight Melting point (ı C) 208:33 77
Boiling point (ı C) 169
Specific gravity 0:9335
% SiO2
152:22
121
1:032
39:5
4
28:8
Part E | 38.2
The sol–gel process starts out as a solution of one or more selected alkoxides. Alkoxides are the organometallic precursors for alumina, silica, titania, and zirconia, among others [38.6, 7]. An alkoxide is an alcohol derivative or metal hydroxide derivative, with the bonding between the metal ion and the alkoxy group polarized in the direction of the alkoxy group, depending on the electronegativity of the metal ion. On the one hand, with an electronegative element like Si, alkoxides are covalent volatile monomers. On the other hand, with electropositive elements like Mg, alkoxides are polymeric solids. By far the most common glass-forming system starts with tetraethyl orthosilicate (TEOS: Si.OC2 H5 /4 water-alcohol) [38.15]. The clear TEOS liquid is the product of the reaction of SiCl4 with ethanol. While tetramethyl orthosilicate (TMOS) contains more SiO2 by weight, it is harder to work with because of its rapid hydrolysis and the hazards associated with methanol [38.16]. A simple representation of the TEOS molecule is given in Fig. 38.3. The central Si is bonded to four equivalent ethoxy groups through the Si–O bond.
The characteristics of the starting materials TEOS and TMOS are compared in Table 38.1. Alkoxides react at different rates depending on the electronegativity of the cation and the length of the hydrocarbon chain in the alkoxy group [38.17]. This means that TMOS reacts more quickly than TEOS. Both are liquids at room temperature. They are stable in air, and show no sign of condensing to higher molecular weight at room temperature in a closed container. Another difference between them is the silica content of the precursor. On a weight basis, TMOS contains more silica (39:5% versus 28:8%), meaning less weight loss between the starting formulation and the final gel. However, the faster reaction rate and higher silica content of TMOS are balanced by the fact that TEOS has less tendency to fully hydrolyze and this makes it easier to work with TEOS in multicomponent systems. Both TEOS and TMOS, along with other alkoxides, release alcohols and require proper ventilation when using. Another approach to sol–gel processing is aqueous colloidal sols. The mechanism for bringing about the sol–gel transition in colloidal sols is quite different from the mechanism in alkoxide solutions [38.5, 18]. In sols such as Ludox™ , the aggregation of colloidal particles occurs as a consequence of changing the pH or changing the concentration. In fact, the colloidal particles can be gelled in such a way that the structure is a continuous linking of sol particles. What is different about the linking of sol particles, as opposed to the polymerization of hydrolyzed alkoxides, is that these are discrete, dense particles that make up the 3-D skeleton. Another feature that distinguishes colloidal gels from alkoxide-derived gels is that there are pores within secondary particles and pores between secondary particles. The chemical and structural differences between nonaqueous alkoxide precursors and aqueous sol precursors
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become harder to distinguish at later stages of the sol– gel process.
38.2.2 Hydrolysis and Condensation Polymerization Reactions Many studies of the sol–gel process deal with a single alkoxide. Each alkoxide has its own reaction rate, which varies with temperature, and complicated interdependences of pH, concentration and solvent. Even in the relatively straightforward case of alumina, using aluminum-sec-butoxide (ASB: Al.OC4 H9 /3 ), the expected reactions (38.1)–(38.4) are Al.OC4 H9 /3 C H2 O (38.1) ! Al.OC4 H9 /2 .OH/ C C4 H9 OH ; 2Al.OC4 H9 /2 .OH/ ! 2AlO.OH/ C C4 H9 OH ; (38.2)
2Al.OC4 H9 /2 .OH/ C 2H2 O ! 2Al.OH/3 C 2C4 H9 OH ;
(38.3)
AlO.OH/ or Al.OH/3 ! Al2 O3 C zH2 O :
(38.4)
Part E | 38.2
The pH is controlled by acid or base additions, typically referred to as catalyst additions. The first reaction is hydrolysis to make the solution active (38.1). This is followed by condensation polymerization (38.2), which releases an alcohol molecule. Polymerization continues simultaneously with further hydrolysis. These reactions increase the molecular weight of the oxide polymer (38.3) and (38.4) resulting in either the monohydroxide AlO(OH) (boehmite) or the trihydroxide Al.OH/3 (bayerite) [38.19, 20]. Mixing as a first step applies to the single alkoxide, multiple alkoxide and colloidal sol processes. Since the formulation has at a minimum the selected alkoxide, water, and solvent, the reaction needs to proceed uniformly throughout the volume of the mixture. Typically, the acid or base conditions are established by setting the pH with an aqueous solution. If the acid or base needs to be introduced into the mixture, it is undesirable for there to be pockets of high or low pH. To prevent this, the solution is usually mixed continuously with a magnetic stirrer and the acid or base is added dropwise. Between drops, the solution is mixed thoroughly. Absence of light scattering is a good indication of uniform mixing. This can be judged by eye, basically looking for the presence or absence of cloudiness. At this point, the building blocks are nanometer in size, and smaller than the wavelength of visible light. If the system remains in the nanometer range, gelation occurs and remains transparent through the sol–gel transition. It is easy to follow, in a qualitative way, the progress of the linking of building blocks by measuring viscos-
ity. Gelling is often determined empirically as the time when the solution shows no flow. For example, a vial containing a solution will show no flow when the vial is inverted, if the solution has gelled. The gel then occupies the volume that was once fluid. The time when this happens is referred to as the time-to-gel. At this point, it is observed that the viscosity increases sharply [38.21].
38.2.3 Acid Versus Base Conditions The chemical reactions in sol–gel processing have been described in detail in the comprehensive volume by Brinker and Scherer [38.4] and using nuclear magnetic resonance (NMR) spectroscopy [38.22]. Taking as a common example the monomer TEOS under acid conditions, or more generally, SiOR4 , where R is an alkyl group, the monomer undergoes electrophilic substitution, with the leaving group on the same side as the protonated water molecule. The net result is that an OR group is replaced by a hydroxyl (OH group). The byproduct of the reaction is an alcohol molecule ROH. In contrast, under base conditions the monomer undergoes nucleophilic substitution, with the leaving group on the opposite side from the –OH group, making the leaving group –OR. Under acid conditions, the monomer tends to link with other monomers in a linear fashion, meaning that a monomer is hydrolyzed at one location before it undergoes condensation with another monomer. Under base conditions the monomer branches, creating clusters, meaning that a monomer may undergo hydrolysis of several OR groups before it participates in condensation with another monomer or oligomer [38.23]. This progression is shown very roughly in Fig. 38.4, to show the expected behavior during hydrolysis and condensation-polymerization. The time sequence is given in reduced time, the actual time divided by timeto-gel .tgel /. At around 60% of tgel , small molecular weight polymers are detected by photon correlation spectroscopy, for example, and the polymers are highly mobile. At around 90% of the tgel , the oligomers or polysiloxanes have grown. Their mobility has decreased more in the base conditions than in the acid conditions. The viscosity increases gradually in the base conditions, while the viscosity increases abruptly in the acid conditions, at around 95% tgel . The time dependence of the viscosity is shown schematically in Fig. 38.5, with the time-to-gel marked as t=tgel D 1. Before tgel , the material behaves as a viscous fluid. At tgel , the material becomes viscoelastic. The structure becomes irreversible, that is, when the structure is disrupted by high shear, the structure cannot recover.
Sol-Gel Glasses
a)
38.2 Sol–Gel Processing
1335
Fig. 38.4a,b Schematic of the linking of monomers that (a) leads to tangled spaghetti under acid conditions and (b) leads to linked clusters under basic conditions
b)
t/tgel = 0.6
t/tgel = 0.9
t/tgel = 0.95
100 000 10 000 1000 Base catalyst
100 10 1
Acid catalyst 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 t/tgel
Fig. 38.5 Time dependence of viscosity for solutions under acid conditions (triangles) and base conditions (circles)
While colloidal gels do not follow the behavior of alkoxide gels, which undergo hydrolysis and condensation polymerization, they do show some of the characteristics with respect to acid and base [38.24]. Take for example colloidal silica sols from commercial sources with particle size around 30 nm, as shown in Fig. 38.6. When the colloids are aggregated under
acid conditions, the particles are still visible and their individual outlines can be seen. Addition of aqueous HCl while stirring turns a translucent sol into an opalescent gel in about 20 min. After drying for two days, the gel breaks into shiny white chunks. Under the scanning electron microscope (SEM), the microstructure looks uniform throughout Fig. 38.6a. In contrast, addition of aqueous NH4 OH while stirring turns the sol into chalklike clumps in about 20 min. After drying, the gel is friable. In the SEM micrograph, the colloids are aggregated under basic conditions, the texture looks more like cauliflower, and the structure is variable, as seen in Fig. 38.6b. Returning to behavior in alkoxide gels, the solution eventually reacts to a point where the molecular structure is no longer reversible. This point is known as the sol–gel transition. In the case of acid conditions, bonds form between the linear molecules, while in the case of base conditions, bonds form among the clusters. In either case, the gel corresponds to a condition of no flow. If the gel is in a container, then the container can be tilted or inverted, and the gel does not move. The gel is an elastic solid filling the same volume as the solution. Figure 38.7 shows a plastic container on its side. The gel is seen through the plastic as a right cylinder surrounded by water and alcohol.
Part E | 38.2
η (10 –3 Pa s) 1 000 000
1336
Part E
Glass Processing
a)
b)
100 nm
100 nm
Fig. 38.6a,b Contrasting appearance of colloidal gels aggregated (a) under acid conditions and (b) under basic condi-
tions
Part E | 38.2
Fig. 38.7 Container with gel inside, on its side showing
replication of right cylinder shape and surrounding liquid
38.2.4 Complete or Partial Hydrolysis For multicomponent gels or gels that are used in coatings and fibers, it is common to only partially hydrolyze the precursor. This allows for more reaction among the components in a solution, and subsequent hydrolysis during a coating application. Since the rates of hydrolysis for different precursors vary, the order of addition of the components can make a difference to the homogeneity. In terms of formulating a gel, there are many factors to consider, such as choice of alkoxide, choice of acid or base, ratio of water to alkoxide, choice of solvent, degree of dilution, and temperature [38.25–28]. Simply put, to practice the sol–gel process means selecting a formulation based on the oxide composition desired in the final glass. The molar ratios of alcohol and water are established empirically to allow mixing of all components in the cosolvent alcohol and to achieve the degree of hydrolysis needed to form the oxide skeleton. The water may be added all at once or added gradually. The alkoxides are introduced in reverse order of their reactivity, which usually means TEOS first, followed by the rest. The viscosity of the mixture is initially low. Continuous stirring is recommended, and the
solution should be clear and generally colorless. The viscosity increases as more oxygen linkages form between metal ions. Characteristics of the oxides, such as their isoelectric point (IEP), are good indicators of the proper pH, either to avoid or to promote gelling, or to find the order of addition to delay gelling until everything is mixed. In fact, the behavior of aqueous oxides as a function of pH is well known. The chemistry of silica has been covered by Iler [38.18] in a comprehensive way. The isoelectric point of silica in water is around pH D 2, where the surface charges change, as indicated by the ratio of SiO =SiOH decreasing and the ratio of SiOHC 2 =SiOH increasing. The time-to-gel is a maximum at pH D 2. If the idea is to promote gelling, in the case of silica, this is accomplished by beginning the process in acid conditions and ending the process with an addition of a base. By increasing the pH above 2, the time-to-gel can be decreased. In Table 38.2 are examples of three compositions indicating stoichiometric water (4 mol) to an excess of water (8 and 16 mol) [38.15, 29, 30]. The formulations are given by weight, then by volume taking into account densities. Also the ratios of water and alcohol are calculated on the basis of 1 mol of the oxide. The last column gives the calculated oxide content of the formulation based on the molecular weights of the precursors. According to the simplest chemical reaction for total hydrolysis, it would take 4 mol of water to hydrolyze 1 mol of TEOS. However, this is misleading, since hydrolysis and condensation polymerization occur simultaneously. Consider the hydrolysis and condensations reactions Hydrolysis .RO/3SiOR C H2 O ! .RO/3 SiOH C ROH (38.5)
Sol-Gel Glasses
38.3 Gelation, Percolation and Syneresis
1337
Table 38.2 Typical formulations for sol–gel processing Glass Content in 100 g solution Content in 100 ml solution Oxide composition (wt%) (vol:%) (mol) Sia Tib Alc Lid H2 O Alcohol Sia Tib Alc Lid H2 O Alcohol Total H2 O oxide 100%SiO2 45 – – – 16 40e 43 – – – 14 43e 1 16 90%SiO2 47 5 – – 17 31f 45 5 – – 15 35f 1 4 10%TiO2 82%SiO2 35 – 1 3 33 29e 34 – 1 1 30 34e 1 8 15%Li2 O3%Al2 O3
Total oxide content in 100 ml solution (g) Alcohol – 4 2
11:3 13:5
4
10:6
Si D Si.OC2 H5 /4 .MW D 208, 20 ı C D 0:936 g=cm3 / Ti D Ti.OC3 H7 /4 .MW D 284, 20 ı C D 0:955 g=cm3 / c Al D Al.OC H / .MW D 246, ı D 0:967 g=cm3 / 4 9 3 20 C d Li D LiNO .MW D 69, ı D 2:380 g=cm3 / 3 20 C e E D C H OH .MW D 46, ı D 0:786 g=cm3 / 2 5 20 C f P D .CH / CHOH .MW D 60, ı D 0:783 g=cm3 / 3 2 20 C H2 O .MW D 18, 20 ı C D 1:000 g=cm3 / a
b
Condensation 1 2.RO/3SiOH ! .RO/3 SiOSi.OR/3 C H2 O (38.6)
Condensation 2 .RO/3 SiOH C .RO/3SiOR ! .RO/3 SiOSi.OR/3 C ROH
(38.7)
38.3 Gelation, Percolation and Syneresis When the solution has reached the condition of no flow, it is called an alcogel, an oxide network condensed in the presence of alcohol. Percolation is a convenient way to think of the structure [38.34, 35]. The last link has been connected so that what was previously oxide oligomers is now an infinite spanning molecule. The gelation is irreversible. What previously behaved
as a viscous fluid is now an elastic solid. The solid is undoubtedly weak, but is now a skeleton surrounding pores that are filled with water and alcohol. In Fig. 38.8, a simple bond percolation model is shown. Imagine a grid of molecules. The object of the percolation process is to find the shortest path from top to bottom by connecting the dots [38.35].
Part E | 38.3
The hydrolysis reaction releases alcohol. Condensation 1, on the other hand, releases water, which is available for hydrolysis. The hydrolysis reaction does not have to go to completion before the condensation reactions begin to generate Si–O–Si linkages. Therefore, it does not necessarily take 4 mol for the complete hydrolysis. The role of the water is not only as a reactant but as a diluent. Some alkoxides do not mix with water unless there is a cosolvent. Generally, what is observed is that the water and alkoxide become more miscible with time, so that any initial cloudiness in the solution disappears. The hydrolysis reaction is exothermic, and it is noticeable that the solution becomes warm when it is mixed. The formulations in Table 38.2 are often referred to as
recipes, and in a way, they are. By trial and error, it is possible to make most glass compositions. Sol–gel processing is not as random as this might seem, because there are some underlying principles, but there is still some art to successful formulations. Some of the underlying principles can be summed up in these three ideas. In preparing a multicomponent solution, start with the component that has the slowest hydrolysis rate. Second, to slow down the rate, increase the length of the alcohol chain on the alkoxide, and use the longer-chain alcohol as the cosolvent. Finally, in most multicomponent systems, begin with less than stoichiometric water, and add water after all components are mixed. Other techniques have been designed to increase the degree of hydrolysis. These include mixing solutions under reflux conditions [38.31]. Solvent extraction under vacuum can also alter pore structures [38.32]. Addition of small amounts (a few %) of substituted alkoxides, for example vinyl triethoxy silane, can change the surface tension of the gel [38.33]. Lastly, some solutions are exposed to atmospheric moisture, and that is used to complete hydrolysis.
1338
Part E
Glass Processing
The molecules are located in a random pattern. For bond percolation, there is a bond formed between sites, presumably monomers or polymers. Each bond has a certain probability, p. When a path is found, the socalled percolation threshold is reached. The threshold is surprisingly low in gels, which explains the low density of aerogels. The percolation model is analogous to reaching the time-to-gel. When the skeleton is affected by the surface energy between the solid network and the surrounding liquid, the skeleton will begin to age. The process of syneresis takes place, and causes some shrinkage of the gel, even before drying begins. Syneresis is observed when a mold containing a gel is inverted (Fig. 38.7) and the gel freely slides in the mold with a thin layer of liquid surrounding it. During syneresis, there is some adjustment of the structure to decrease the overall surface energy. For cases where large shapes are being formed
Fig. 38.8 Square lattice used to demonstrate percolation from top to bottom
using gels, it is recommended that as much shrinkage be allowed to occur while the pore liquid is present. This decreases the tendency to crack when the gel is dried [38.36–38].
38.4 Drying and Removal of Solvent and Water
Part E | 38.4
The sol–gel process can be used to make bulk objects using a mold. The solution is cast into a shaped mold, allowed to gel, and then dried to give a microporous preform that is near-net shape. This preform is called a monolith to refer to its continuity. Monolithic gels can be formed from a colloidal sol or from an alkoxide solution [38.24]. As mentioned above, an important difference between colloidal gels and alkoxide gels is their pore structures. In general, alkoxide gels have small pores .< 10 nm/, while colloidal gels have bigger pores or voids between particles. Producing defect-free monoliths is the most challenging demonstration of the sol–gel process, because of the tendency for monoliths to crack during drying. At the beginning of drying, the pores are filled with a mixture of water and alcohol. With evaporation, a meniscus appears. The factors involved in drying are shown roughly in Fig. 38.9. If the gel is soft, the gel can relax. If the gel is stiff, the surface tension of the solH 2O/C2H5OH
vent may be higher than the strength of the gel, and the gel will crack. At the same time that solvent is escaping, further condensation reactions occur that in effect strengthen the gel. If the evaporation from all surfaces is uneven, the gel can warp and distort. It is also possible that nonuniform pores empty at different rates and the composition of the pore liquid is changing. All of these factors can lead to cracking and the failure of the gel to dry in one piece. Needless to say, the drying of gels is a complex process.
38.4.1 Xerogels Whether the selected geometry is a monolith, film or fiber, all sol–gel processed materials experience a drying step. For monoliths, drying is more difficult than for films and fibers, because of the longer path for removal of water and solvents [38.39, 40]. Keeping in mind the nanoscale structure of the material, several
H 2O
HO– –OH
Fluid evaporating while capillary stresses act on pore walls
Further condensation polymerization
Differential stresses from pores of different sizes and different heights of fluid filling
Fig. 38.9 Schematic of factors involved in drying gels, with composition of fluid varying during syneresis and drying between ethanol ( Š 0:024 N=m, Tboil Š 78 ı C) and water ( Š 0:072 N=m; Tboil D 100 ı C)
Sol-Gel Glasses
Fig. 38.10 Evidence of 70 vol:% shrinkage during preparation of xerogel
1339
pore volume, average pore size 1:5 nm and bulk density of 1:52 g=cm3 [38.42].
38.4.2 Aerogels Alternatively, the solvent can be removed from wet gels under supercritical conditions [38.43]. By simultaneously heating and pressurizing wet gels, it is possible to reach the critical point where the gas and liquid become indistinguishable. That way the solvent can be evacuated without imposing capillary stresses on the gel skeleton. It is also possible to exchange the solvent for a lower surface tension solvent [38.44] or replace it with CO2 [38.45, 46]. The conditions for extracting CO2 are milder than removing water-alcohol mixtures, so CO2 exchanged gels are being commercialized. Once the solvent is removed, the remaining skeleton is an aerogel. The surface area can be 1000 m2 =g and higher, and the bulk density can be around 0:1 g=cm3. The skeleton experiences no shrinkage, which is consistent with the low bulk density and the very high surface area. Extremely low-density silica aerogels are used for thermal insulation. They have many characteristics of silica glass, but they have the density of a cotton puff. Aerogels are translucent to transparent, despite being 85% pores or more. This is because the pores are smaller than the wavelength of visible light.
38.4.3 Porous Gels and Their Uses Following mixing, reacting, forming, gelling and drying, gel materials have many of the characteristics of the corresponding ceramic oxide, but they are more or less porous [38.47]. Interconnected pores allow the water and solvent to escape. In most oxides, the pores remain open at the surface until the gels are fired to temperatures well above 600 ı C. Since the sol–gel process results in a porous material, and the porosity is open, interconnected and controllable, an opportunity presents itself to exploit the porosity. While the sol–gel process may be used ultimately to form a dense glass, there are many cases where a glassy material with interconnected porosity is the desirable form. Porous materials can be used to perform separations. Filters are porous materials that separate by physical processes or by size. Membranes are a class of filters that separate by physical and chemical processes [38.48]. The concept of thirsty glass has been around since the discovery of the Vycor process. In this process, an alkali-borosilicate glass is phase separated into a silica-rich glass and an alkali borate-rich glass. The alkali borate-rich glass is removed in an acidic medium, and the sponge-structured silica-rich glass remains. The porous, unconsolidated silica-rich
Part E | 38.4
drying treatments have been developed. One route is aerogels that are dried in an autoclave by hypercritical techniques. More commonly, there are xerogels that are dried by natural evaporation. Xerogels are 60% dense and have 40 to 70% reductions in volume. This is seen in Fig. 38.10. The sample on the left (which contains Rhodamine 6B dye to make it easy to see) has gelled, synerized, and is beginning to shrink. The shrinkage has been arrested by sealing the container. If the container is opened and the sample is allowed to shrink and dry slowly for about one month, the miniature rigid sample on the right is the result. The dried sample is hard and stable, and does not shrink further. During natural evaporation, the gel skeleton experiences high capillary stress from the surface tension of the solvent. If the skeleton has experienced syneresis and aging, it may be able to withstand the stresses of removing the solvent. Of course, the shorter the distance the solvent has to travel, the easier the drying, so thin films and fibers can be dried with relative ease. However, monoliths are challenging. The pore size is typically a few nanometers, which contributes to the capillary stresses being extremely high. Also, if the porosity is not uniform, the differential pressure is a problem. Nevertheless, xerogel monoliths have been dried, but it can take weeks. For example, pure silica xerogels 5 cm in diameter and 0:3 cm thick can be dried crack-free when they are prepared from a high water, diluted ethanol-TEOS solution under acid conditions, in loose covered plastic Petri dishes in about one month [38.41]. These dried monoliths have continuous porosity, surface area of about 640 m2 =g, 36%
38.4 Drying and Removal of Solvent and Water
1340
Part E
Glass Processing
glass has the ability to adsorb various molecules on its surface, and fibers of thirsty glass are used in chromatography [38.49]. Similarly, sol–gel-derived porous materials are suitable for selective adsorption applications [38.50]. The porosity in sol–gel processed materials ranges from nm to submicrometer, making these materials useful in water filtration, juice clarification, and sterilization. More recently, the process has played an important role in membranes used for protonexchange membrane fuel cells [38.51]. Among the available oxide membranes, alumina membranes are the best developed and characterized [38.52]. Sol–gel-derived pure zirconia membranes have been investigated [38.53], along with porous sil-
ica layers [38.54] and silica-zirconia layers [38.55]. The sol–gel method has an advantage in that a thin layer with very fine pores can be prepared by deposition onto a ceramic tube to be the active membrane layer and repeated dip-coating can be used to form graded porosity [38.56]. Zirconia and alumina are most often crystalline in structure, but sol–gel-derived silica forms a porous network, which remains amorphous over a wide temperature range. Silica-zirconia is relatively inert and therefore safe to use, for example, for filtration of juices or beverages. A mixture of silica-zirconia forms an amorphous structure, which is stable during heating, providing an isotropic, porous structure.
38.5 Consolidation and Sintering
Part E | 38.5
After processing, gelling and drying, it is fair to ask if the material at this stage is a glass. Is it x-ray amorphous? Does it have a random network? Are there no stoichiometric limits on composition, as expected for glass? The answer would be yes, in terms of being noncrystalline, but the material is not yet equivalent to the conventional melted glass of its same composition. In order to match the physical properties of the equivalent melted glass, the gel has to be consolidated [38.57– 59]. Consider the flow chart in Fig. 38.11. At the stage of xerogel for the gel containing erbium in an yttrium sili-
TEOS + EtOH + H 2O 1 : 1 : 1 Partial hydrolysis 45 min
HCl, catalyst
Y(NO3)3 + Er(ac)3 4 : 1 H 2O + EtOH
Clear solution Hydrolysis Condensation
cate gel, the monolith is transparent, crack-free, and flat with a diameter of about 5 cm [38.60]. This composition was investigated because Er3C -containing glasses have optical properties that are useful in telecommunications. The solubility of Er3C in silica glasses is limited, so yttria is added to increase its solubility. While this can be accomplished readily in the solution formulation with addition of rare-earth salts, it is important that the subsequent steps are carried out carefully to maintain the optical properties and activity of the rare-earth ions. By following the steps in the flow chart, sufficient activity was achieved [38.61]. The process can be
HNO3 45 min ∆ = 70 °C
H 2O + EtOH
Stable sol 1–2 days
Gelation
Transparent wet-gel Drying
Aging: 60 °C 2 weeks
Xerogel
Densification
Monoliths
Milling Powders 4+
3+
3+
4+
3+
3+
[Si + Y + Er ] : [EtOH] = 1 : 5 and [Si + Y + Er ] : [H 2O] = 1 : 10
Fig. 38.11 Flow chart of complete sol–gel process to prepare codoped erbium-yttrium silicate glass
Sol-Gel Glasses
L 3 t ; D L0 2d
(38.8)
where L is the change in length, L0 is the original length, is the surface tension (liquid–vapor), is the viscosity, and d is the diameter of the particle. The vis1000 °C
600 °C
10 h
60 °C/h 10 h
60 °C/h
30 °C/h 250 °C
10 h
15 °C/h Xerogel
Room temperature
Fig. 38.12 Heat treatment schedule used to consolidate
codoped erbium-yttrium silicate glass
1341
cosity is calculated according to [38.67] D . Kl0 /
s 0
1=3 ;
(38.9)
where is the surface tension, is the viscosity, K is the so-called sintering parameter, l0 is the cylinder length in the framework model, s is the skeletal density, and 0 is the initial bulk density. The calculated viscosity agreed well with the measured viscosity in an experiment using beam-bending viscometry, where the viscosity was determined from the deformation rate .dy=dt/ in cm=s [38.67] .Wl3 / dy D dt 144I
r 3 2r
;
(38.10)
where is viscosity, W is a central load, l is the distance between supports, I is the moment of inertia for a beam, and r is the relative density. For pure SiO2 , the skeletal density is approximately 2:202 g=cm3 . The bulk density starts at about 50%, with both open porosity and excess free volume. The surface area initially increases as the hydroxyls in pores condense and evaporate. By 700 ı C, the surface area decreases and pores begin to close. By 1000 ı C, the skeleton is dense and the porosity is removed. This temperature, when compared to 1800 ı C where conventional fused silica is usually formed, is certainly a large reduction. In optical waveguides, this may be straightforward because the water content of the preform is small. However, sol–gel processed glasses tend to have high water content. The internal surface is covered with hydroxyls, typically 4:6 OH=nm2 , and the surface area can be several hundred m2 =g [38.68]. The heat treatment schedule shown in Fig. 38.12 that was determined empirically takes more than one day. The reason for several steps in the schedule is to allow the structure to relax and dehydrate. A delicate balance is struck between holding on too long for full dehydration and heating too fast, which traps water [38.69]. It is possible to take advantage of the reduced viscosity of the gel while it is wet to speed up viscous sintering. At a given temperature, the viscosity may be depressed by an order of magnitude. At the same time, it is necessary to allow the water to escape before the connected porosity becomes isolated. If the water is not removed, the glass will bloat, meaning the glass will expand like popcorn. The time dependence of the viscosity and the time dependence of the surface energy have to be factored into the sintering schedule for gels. The surface energy of hydroxylated silica is around 0:13 J=m2 , while the surface energy of dry silica is closer to 0:25 J=m2 . Nev-
Part E | 38.5
generalized to other rare-earth additions [38.62]. Notice that this process takes over two weeks. At this point, there is a choice. Is the goal to make a powder or to sinter the monolith? If the choice is a monolith, then the heat treatment schedule in Fig. 38.12 is required. The schedule has three isothermal holds of 10 h each. The reasons for the holds are explained in the description of viscous flow sintering. Including the isothermal holds, the heating steps and the cool down, the cycle is a total of about 31 h. When achieving a nonporous, dense oxide is the goal, the final stage of sol–gel processing is sintering, same as it would be in conventional powder processing. The high surface area in the gel-derived material contributes to a high driving force for sintering, so sintering in gel-derived materials tends to occur at lower temperatures than in conventional powder compacts. Sintering to full density results in a material equivalent to conventionally sintered materials. The only difference is that the gel-derived material arrives at the fully dense condition at lower temperature or shorter time. The mechanisms for densification in glassy porous gels are relaxation, dehydration and viscous flow [38.57, 63]. This behavior has been modeled for porous preforms for optical waveguide fibers, and the principles apply reasonably well [38.64, 65]. The structure is taken to be a framework of cylinders surrounding pores [38.58]. The elimination of the porosity is driven by the exchange of energy from reducing surface area for energy to drive viscous flow. In the viscous flow (Frenkel) model for sintering, the shrinkage is usually related to the viscosity [38.66]
38.5 Consolidation and Sintering
1342
Part E
Glass Processing
ertheless, it is possible to achieve pore-free materials, generally at temperatures well below the temperature used in conventional melting for that composition. The three-step process in Fig. 38.12 takes into account relaxation, depressed viscosity, and finally surface energy.
It has been shown that it is possible to reach full density, the physical equivalent of conventional fused silica, by 1000 ı C, reproducing physical properties such as index of refraction, dielectric constant, and optical transmission [38.16, 70].
38.6 Sol–Gel Fibers, Thin Films and Other Applications
Part E | 38.6
Table 38.3 is a summary of the shapes possible via the sol–gel process. The examples are more or less porous materials. The form of the material is described as onedimensional (1-D), such as a fiber, two-dimensional (2-D), such as a thin or thick film, or 3-D, such as bulk monoliths. Bulk or 3-D materials show isotropic shrinkage, with near equal shrinkage in x, y, and zdimensions. Thin films on substrates show highly anisotropic shrinkage with most of the shrinkage occurring in the thickness or z-dimension. High aspect ratio fibers also show anisotropic shrinkage, where the shrinkage occurs primarily in the radial dimension. Thin films are remarkably simple to prepare. A solution containing the desired oxide precursors is applied to a substrate by spinning or dipping. The dipping process is able to apply a coating to the inside and outside of complex shapes simultaneously. The time-to-gel is short, in some cases just a few minutes. When it comes to dip coatings, submicron coatings are typical for single dips, and multiple dip coatings are common. Similarly, fibers can be drawn out of low water content solutions. The sol–gel process allows one to bait and draw a string of gel about the same diameter as the desired fiber directly from the solution [38.74].
The thickness of the wet film is controlled by balancing two forces. As the substrate is withdrawn from the liquid at a fixed speed, there is a viscous drag that pulls liquid upward. This is balanced by the pull of gravity. The thickness .h/ is estimated from (38.11) hD
u g
1=2 ;
(38.11)
where is the liquid viscosity, u is the withdrawal speed, is the density of the liquid, and g is the gravity constant. Basically, an increase in the withdrawal speed increases the film thickness. In the coating operation, the solution goes through its sol–gel transition when the coating is on the suba)
b)
Substrate
c)
d)
H 2O H 2O H 2O H 2O H 2O
38.6.1 Thin Films by Dipping or Spinning
H 2O
At this time, the majority of commercial sol–gel coatings are applied by dipping [38.75]. This is an approach that allows the intrinsic properties of the fluid solution to control the deposition. A substrate is lowered into a vessel containing the solution. A meniscus develops at the contact of the liquid and the substrate. While the substrate is withdrawn at a controlled rate, the meniscus generates a continuous film on the substrate. The process is able to apply a coating to both sides as shown in Fig. 38.13.
H 2O Sol
H 2O
Fig. 38.13a–d Schematic of the dipping process: (a) dip substrate into solution; (b) withdraw substrate at controlled rate; (c) expose coated substrate to humid atmosphere to complete reactions; (d) dry and heat coated substrate to achieve adhesion and dense film
Table 38.3 Common shapes of sol–gel materials, with commercial applications Shape Thin film Fiber Bulk xerogel Bulk aerogel
Composition Titania-silica Alumina-zirconia-silica Silica Silica
Typical application Interference filter mirror Reinforcement Nextel® GRIN lens (gradient refractive index) Thermal insulation Cryogel® , Spaceloft®
Reference [38.71] [38.72] [38.73] [38.45, 46]
Sol-Gel Glasses
h D h0 .1 C 4Kh20 t/1=2 ;
equation predicts the thickness. If the evaporation rate of the solvent in ml=.s cm2 / becomes an important contribution, other calculations result in a power law dependence closer to 1=3. These factors have been treated in detail, especially with regard to preventing striation [38.81, 82]. As with dip coatings, a film around 1 m results. An example of a spin coating is shown in Fig. 38.15. Here a 10 cm silicon wafer has been patterned by photolithography. A borosilicate solution has been spun onto the wafer in preparation for electrostatic bonding with another wafer. If the coating were prepared properly, the coating would not be visible. As seen in the reflection of the overhead lights, this coating is not uniform, and interference rainbows are observed. Further development of the coating needs to take into account spin speed, both spin up and spin down. The first step in all examples for thin films, whether for dipping or spinning, is choosing the right precursors and solvents. Once again, silica is the model system. Of the available silicon alkoxides, tetraethyl orthosilicate (TEOS) is used most often. TEOS reacts more slowly with water than TMOS. TEOS comes to equilibrium as a complex silanol rather than hydrolyzing to completion as silicic acid .Si.OH/4 /. In a partially hydrolyzed state, TEOS has a shelf life of about six months. The colorless liquid has a density of about 0:9 g=cm3 , is easy to handle safely and is very pure when distilled. The vast majority of sol–gel coating formulations are for oxides. A comprehensive volume has been assembled of investigated thin film compositions [38.78]. For example, silica is used as an amorphous coating, for passivating a surface or improving surface perfec-
(38.12)
where K D ! 2 =3, is density, ! is the rotation rate in rad=s, is the viscosity, t is time, and h0 is the initial layer thickness. As long as K is a constant, this
Syringe
Material to be deposited
Uniform layer of material
Wafer Vacuum chuck
Fig. 38.14 Spin coating setup, where you fasten the sub-
Fig. 38.15 Photograph of a nonuniform spin-coated sili-
strate to a turntable and spin at 6001000 rpm to achieve 100500 nm film
con wafer, showing reflection of ceiling lights and interference fringes
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Part E | 38.6
strate. Once the liquid film is attached to the substrate, the solution undergoes a sharp increase in viscosity. If the substrate has been handled properly, a tacky gel covers the entire surface. This is shown as Fig. 38.13b,c, where atmospheric moisture is used to complete the reactions. In comparison to chemical vapor deposition (CVD), physical vapor deposition (PVD), sputtering or any deposition technique that involves vacuum or protective atmosphere processing, sol–gel dip coating requires equipment that is inexpensive to assemble and operate. Basically, the equipment is a bath to hold the solution and a screw-drive mechanism to lower and raise the substrate into and out of the bath. See, for example, the turnkey solutions such as ACE dip 2.0 [38.76]. Coatings can be applied to metals, plastics, glasses, cements and ceramics. Typically, the coatings are applied at room temperature. Then the coatings need to be dried and, in some cases, densified with heating. Dip films are typically less than 1 m, uniform over large areas and adherent. The time-to-gel is especially important for coatings because film formation, drying and creation of pores occur quickly. Optimum film formulations correspond to those solutions that lose tackiness in a matter of minutes [38.77, 78]. For one side coating, it is possible to use spin coating [38.79, 80]. In this case, the substrate is placed on a turntable, usually with a vacuum holder, and rotated at perhaps 200 rpm while solution is dripped on the center of the substrate. The spin coating process is shown schematically in Fig. 38.14. The solution is dripped onto a spinning substrate. The thickness of the layer .h/ is estimated from (38.12)
38.6 Sol–Gel Fibers, Thin Films and Other Applications
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tion. Titania is an example of both an amorphous or crystalline coating that is used for its high index of refraction or its semiconductor properties. Alumina is generally a crystalline coating that finds use in abrasive environments. Of course, there are other specialized applications that call for multicomponent oxides. Increasingly, there are formulations for nonoxides. For example, silicon oxycarbides and oxynitrides have been formed by treating silica gels with reactive gases [38.83]. Fluoride compositions such as zirconium barium lanthanum aluminum and sodium (ZBLAN) have been prepared with gels that can be fluorided [38.84]. In addition, nanoparticle-containing coatings have been prepared that exhibit plasmonic effects [38.85]. Finally, there are many organic–inorganic coatings, which are discussed in more detail later in Sect. 38.7 [38.86]. Considering (38.11) and (38.12), the effect of the viscosity is stronger than the effect of the surface tension. Two simple correlations are: 1. That the film thickness increases with increasing withdrawal rate. 2. That the film thickness increases with an increase in oxide content, for a given withdrawal speed.
Part E | 38.6
On the bench scale, the process is a batch process. However, the batch process can be scaled up, and repeated dipping leads to thicker films. The expressions relating film thickness, withdrawal rate or spin speed have been derived with all of the necessary assumptions. Details of the fluid mechanics that support these expressions are readily available [38.87].
38.6.2 Optical Applications and Other Surface Treatments Where are sol–gel coatings finding use? Several broad areas come to mind. These are optical coatings, electronic coatings, protective coatings, porous coatings, anticorrosion coatings, and composite coatings. A few examples of sol–gel thin films and optical hosts are listed in Table 38.4. One of the first applications was rear-view mirrors for cars, to replace conventional metallizing. These coatings consist of titania-silica-titania interference filters that give the effect of total reflectance [38.88]. Another early use of sol–gel processing was solar reflecting films for windows [38.89]. These coatings contain Pd nanoparticles in titania films, which display selective absorption. Soon after, antireflective coatings of several types were developed. Both borosilicates and titania silicates were developed for this application [38.90]. Broadband antireflection coatings were developed for
laser optics, using silica broadband antireflective coatings with reduced ultraviolet (UV) scattering [38.91]. Thin films have been applied from solution for numerous conductive, semiconducting, insulating and magnetic applications. Notably, indium tin oxides (ITOs) were developed for transparent conducting films for displays [38.92]. In another widespread application, silica thin films with low dielectric constants were used to lower the resistance and capacitance signal delay in back-end-of-the-line interconnects in integrated circuits [38.93]. Tungstate, niobate and NiO-TiO2 films have been prepared for electrochromic displays [38.94]. Reactionformed silicon oxynitride films were used for oxidation masks in microelectronic device fabrication [38.95]. In porous and dense conditions, a layer of alumina on the surface of plastics has been used to provide scuff resistance, especially polycarbonate windows [38.96]. Phosphate coatings were applied to silicate glass panels to improve their chemical resistance to attack by water. This improvement was accomplished in 0:2 m. This pointed out one of the primary advantages of sol– gel processed films: the material use is efficient. Any excess solution that did not stick to the substrate was recovered and could be used again. Even relatively costly components such as zirconia and gold nanoparticles have been considered [38.97]. This is not meant to be an exhaustive list, but it is meant to highlight the range of applications. A few of the general themes in sol–gel coating chemistry and mechanical behavior, which may or may not be obvious, are repeated for emphasis. First, gels are amorphous, meaning no stoichiometric rules. This means that any amount of a metal oxide can be added to a multicomponent composition. Second, being thin, sol–gel films do not delaminate when the substrate is bent. Finally, gel coatings are more or less porous, and, if desired, they can be undetectable when a cover coat is applied on top. While the coatings are initially porous, fully dense coatings can be obtained from gels with appropriate heat treatment, for example laser treatment [38.98]. On the other hand, microporous films find unique applications modifying a physical property such as thermal conductivity or in performing as a selective membrane [38.99]. Porous gels can be infiltrated with organic monomers and polymers to form organic–inorganic coatings, classified as hybrid coatings. The low temperature of the sol–gel process allows the combination of organic and inorganic components in ways not possible with conventional coating methods, such as enameling. In addition, the porosity can be infiltrated with organic phosphors and quantum dots [38.100].
Sol-Gel Glasses
38.7 Organic–Inorganic Hybrid Sol–Gel Glasses
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Table 38.4 Selected sol–gel thin films and hosts and their optical applications Optical application Color filters Mirrors Antiglare films Antireflection—narrow Antireflection—broadband Antireflection—broadband IR reflectors Pick-up lens Tunable lasers Nonlinear optics
Mechanism Selective absorption Interference Absorption Graded porosity Interference 1/4 wavelength Interference Gradient refractive index (GRIN) Rare-earth scintillator Semiconductor quantum dots
Typical composition Cr2 O3 -SiO2 14-layer TiO2 :SiO2 CoO-SiO2 SiO2 3-layer SiO2 -TiO2 :ZrO2 :SiO2 3-layer TiO2 :Ag:TiO2 PbO-B2 O3 -SiO2 Er3C -Y2 O3 -SiO2 (CdS,PbS)-SiO2
38.7 Organic–Inorganic Hybrid Sol–Gel Glasses
R0 Si.OR/3 C Si.OR/4 C H2 O OR j ! R0 Si OSi.OR/3 C ROH ; j OR
where OR is OC2 H5 and R0 is CH3 in the case of methyltriethoxysilane (MTES). During the hydrolysis and condensation polymerization processes, the Si–C bonds are not disrupted, meaning that Si–C bonds persist in the final hybrid materials [38.105, 106]. The presence of the organic modifier groups R0 decreases the degree of crosslinking. Undoubtedly, the sol–gel processes involving functionalized silanes are more complex than those with TEOS or TMOS. Organic–inorganic sol–gel processing involves competition among different reactions including hydrolysis, condensation polymerization, re-esterification, depolymerization, and transesterification [38.102]. Organic–inorganic hybrid materials are often classified by the nature of the interaction between the organic and inorganic components. One class requires that there is direct covalent bonding between the organic and inorganic parts. Another class of hybrids does not have direct linking by covalent bonds, but instead has hydrogen bonding between organic and inorganic parts, with anywhere from weak to relatively strong interactions [38.107]. Another way of classifying hybrids is to call them physical hybrids or chemical hybrids. In chemical hybrids, the assumption is that the organic and inorganic components are covalently bonded, and both are involved in the polymerization. In physical hybrids, the organic polymer and the inorganic polymer can form simultaneously or sequentially. In either case, the intera)
b) O Si O O
Fig. 38.16a,b Molecular O Si
O O
(38.13)
structures of functionalized silanes, methyl triethoxysilane (a) and phenyl triethoxysilane (b)
Part E | 38.7
When the sol–gel process is carried out with a precursor containing all identical alkoxy groups, for example four ethoxy groups in EOTS, the hydrolysis and condensation polymerization reactions generate an inorganic polymer with Si–O–Si links. In contrast, a sol–gel process with a precursor such as methyltriethoxysilane (MTES) .CH3 /Si.OC2 H5 /3 or phenyl triethoxysilane (PhTES) .C6 H5 /Si.OC2 H5 /3 , has only three equivalent groups. In such a precursor, there is a direct link between Si and C that cannot undergo hydrolysis. The molecular structures are shown in Fig. 38.16. The presence of the Si–C bond decreases the functionality of the precursor and leads to the formation of linear molecular chains. By selecting precursors containing hydrolytically stable Si–C bonds, the product of the sol–gel process is an organic–inorganic hybrid. The number of silica-based precursors with one, two or three nonhydrolytically active functional groups that are commercially available is easily hundreds. These precursors have been developed for specialty coatings, catalyst applications and paints [38.101, 102]. Some precursors have reactive sites capable of undergoing UV polymerization or thermally induced crosslinking [38.103, 104]. The main reactions of hydrolysis and condensation polymerization in the sol–gel process occur with modification. For example, with the organically modified alkoxides, where R and R0 are used to indicate different functional groups, the reaction would be
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Part E | 38.7
action between the organic polymer and the inorganic polymer is through hydrogen bonding, whether the polymer starts as a monomer that polymerizes at the same time the alkoxide hydrolyzes and polymerizes, or that the monomer requires thermal initiation or UVinitiation for polymerization after the alkoxide reacts. Categorizing physical hybrids is approximate at best, because of the processing factors that influence their structures, for example phase separation [38.108, 109], solubility as a function of molecular weight [38.110], and relative speeds of hydrolysis, polymerization and gelling [38.111]. Poly(methyl methacrylate) (PMMA)/SiO2 hybrids have been synthesized by sol–gel processes that are considered simultaneous and sequential [38.107, 112]. They have been prepared by mixing a methyl methacrylate monomer with tetraethylorthosilicate (TEOS), so that their polymerization processes occur simultaneously. Alternatively, TEOS has been polymerized first and then infiltrated with MMA monomer. In the sequential hybrids, electrostatic attraction between organic and inorganic groups influences the behavior of the composite, along with hydrogen bonding. In comparison to the sol–gel approach of using alkoxysilyl-containing organic precursors or coupling agents, PMMA/SiO2 hybrids are straightforward to prepare. Figure 38.17 shows three types of composites that are possible by the sol–gel process. In the first case, a porous preform of inorganic gel is infiltrated with a monomer, and the monomer is polymerized in situ [38.112–114]. This composite is sequential polymerization, because the organic is polymerized after the inorganic. In the second case, the inorganic precursor and the organic monomer are mixed in the same solvent. The polymerization occurs simultaneously. The result is interpenetrating networks with generally weak van der Waals bonds between the components [38.108]. In the Sequential
UV irradiation to cure PMMA
1. Softening 2. Becoming stiff 3. Resoftening, which can be repeated countless times, even after sitting in closed vials at ambient temperature for several years.
Simultaneous
TEOS
Encapsulated in gel
PVAc
Methyl methacrylate monomer with UV initiator Preformed monolith of SiO2 50% porous
last case, the organic component is particulate or molecular, and the organic component is intended as a host or encapsulant. The organic could be a dye molecule or enzyme that needs to be suspended in a rigid host [38.115, 116]. Other examples of organic–inorganic hybrids include sol–gel processes with functionalized siloxanes added to TEOS or TMOS. For example, reactions of TEOS and MTES by a sol–gel process lead to hydrophobic coatings. When this combination was deposited onto a commercial ionomer Surlyn® , the contact angle of the Surlyn® with respect to a drop of water increased dramatically. Chemical interaction between the sol–gel coating and Surlyn® was confirmed by Raman spectroscopy, where it was found that the methyl groups were concentrated at the surface of the films, leading to the increase of the contact angle [38.117]. The effect of hydrophobic groups on the surface can be quite dramatic. When an aerogel was processed with methyl-substituted siloxanes, MTES, with only a 5% substitution, the dried aerogel repelled water. Figure 38.18 shows an aerogel monolith, where water droplets are being dropped onto it from an eye dropper. Not only does the water not spread, it actually bounces on the aerogel and rolls off. A special category of hybrid gels constitutes the so-called melting gels [38.106, 118–120]. Melting gels are organic–inorganic silica gels that are stiff at room temperature, soften and flow at temperature T1 and irreversibly consolidate at temperature T2 (T2 > T1 ), when cross-linking is complete. The process consists of:
Add nanoparticles to solution
Fig. 38.17
Mixed in acidified water
Schematic of three possible methods to prepare organic– inorganic hybrid composites
Sol-Gel Glasses
Fig. 38.18 Photograph of water being dripped onto an aerogel that is hydrophobic, where the water bounces and rolls off
ysis with hydrochloric acid, followed by a second step to encourage condensation with ammonia. It has been confirmed with infrared and NMR spectroscopy that the resulting molecular structure is 3-D, with the organic groups having weak bonds between molecular chains [38.121]. PhTES-DPhDES hybrids have been formed with or without ethanol, and the glass transition temperatures varied with ratio of PhTES and DPhDES [38.118]. In general, melting gel behavior is observed in polysiloxane polymers that contain cross-links between disubstituted and monosubstituted siloxanes. The reversible behavior of becoming stiff at room temperature and then softening at about 110 ı C can be repeated many times. Before consolidation, the melting gels exhibit glass transition behavior at temperatures around room temperature or below, according to differential scanning calorimetry. However, once the gel is heated to its consolidation temperature, it no longer softens and no longer shows a glass transition behavior at low temperature. The temperature needed for consolidation increases with an increase in the number of nonhydrolytic groups, meaning the number of direct Si–C bonds. At the consolidation temperature, further crosslinking of the polysiloxane network is facilitated. Related to melting gels, an exciting new area for hybrid gels is patterning. Many optical and chemical effects are achieved on the surface of glass through texturing. The ability to impart lotus leaf effects on glass to improve self-cleaning or patterning for light concentrating surfaces is an active area [38.122–124].
38.8 Summary and Future Prospects When considering where sol–gel glasses were 30 years ago, most of the applications were substitutions of a sol–gel material for a glass or ceramic obtainable by other means. Nowadays, sol–gel processing is a mainstream method for glass preparation, and is included in the leading textbook on glass [38.125]. A newer way of thinking about this is that there are some applications that are unique to sol–gel processing, such as porous glasses and organic–inorganic hybrid glasses. As a low-temperature process, energy costs in processing are decreased. Also, there is a reduction in volatilization of high-vapor-pressure species, such as Zn, or oxidation of sensitive metals, such as Mg. In fact, this low-temperature process can handle some compositions that cannot be made by conventional means due to tendencies to phase separate or devitrify. A creative way of looking at the sol–gel process is to imagine that it creates an amorphous material that is porous. The
porosity is continuous, meaning that there is a pathway to the nanostructure. This pathway opens up opportunities to design new host materials and nanocomposites. A major advantage of the sol–gel process as a lowtemperature process is its capacity to incorporate organic material. Whether this is accomplished by infiltrating a previously formed oxide gel host with monomers, creating an organic–inorganic copolymer with a functionalized alkoxide, or simultaneously polymerizing monomers and metal alkoxides, the number of combinations is huge. A defining characteristic of these hybrids is the scale of the mixing of the organic and inorganic phases, which is truly on the nanoscale. The trademarks of the sol–gel process that have been touted from the start are the high purity and ease of mixing. In addition, the process involves simple processing steps, flexibility of solution chemistry, low processing temperatures and a small investment in
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Originally, so-called melting gels were investigated to replace low-melting-temperature sealing glasses, such as those used in thick film pastes. Most of these sealing glasses are loaded with borates and phosphates and melt around 600 ı C. This temperature is too high for most electronic packaging, especially newer devices such as organic light-emitting diodes (OLED). Finding a glass that gives a hermetic seal at 200 ı C is technologically urgent. In addition to forming melting gels from methylsubstituted siloxanes, it is also possible to form them with PhTES and DPhDES (diphenyl-diethoxysilane). Using phenyl-substituted siloxanes, polysilsesquioxanes are obtained that show a very low softening point. To prepare melting gels, the first step involves hydrol-
38.8 Summary and Future Prospects
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PDMS pattern
Melting gel warmed to its softening point
Melting gel poured into o-ring with inverted pattern
Melting gel after removing PDMS pattern
Melting gel with pattern reproduced in gel after consolidation heat treatment
Fig. 38.19 Photograph of melting gel that has been imprinted using a soft silicone rubber stamp, demonstrating the
ability to reproduce the pattern with fidelity and high aspect ratio
Part E | 38
equipment. Now, the challenge of the sol–gel process is to exploit the nanostructure aspects of the process. The continued use of the sol–gel process is dependent on finding innovative ways to assemble new functional glasses. Acknowledgments. Over the years, I have had the privilege of working with many excellent undergraduates, graduate students, postdoctoral fellows, research associates and colleagues at Rutgers University, and I thank them all. For specific figures that have not been published previously, I want to thank Varadh Ranganathan (Figs. 38.11 and 38.12), Max Freedman
(Fig. 38.18) and Brooke McClarren and James Davanzo (Fig. 38.19). One impetus to put this information together was the course offered through the Lehigh University–Penn State University International Materials Institute for new functionality in glass (IMI-NFG) on glass processing in spring 2015. Currently, my research is supported by NSF Award 1313544 Materials World Network-SusChEM, in collaboration with M. Aparicio, Instituto de Ceramica y Vidrio Consejo Superior de Investigaciones Cientaficas (CSIC), Madrid, Spain and Andrei Jitianu, Lehman College-CUNY and The Graduate Center, The City University of New York.
References 38.1
38.2 38.3
38.4 38.5 38.6
L.C. Klein: Sol–Gel Technology: For Thin Films, Fibers, Preforms, Electronics and Specialty Shapes (Noyes, Park Ridge 1988) L.C. Klein: Sol–Gel Optics: Processing and Applications (Kluwer Academic, Boston 1994) M. Aparicio, A. Jitianu, L.C. Klein: Sol–Gel Processing for Conventional and Alternative Energy (Springer, New York 2012) C.J. Brinker, G.W. Scherer: Sol–Gel Science (Academic, Boston 1990) A.C. Pierre: Introduction to Sol–Gel Processing (Kluwer Academic, Boston 1998) D.C. Bradley, R.C. Mehrotra, D.P. Gaur: Metal Alkoxides (Academic, London 1978)
38.7
38.8
38.9
38.10 38.11
N.Y. Turova, E.P. Turevskaya, V.G. Kessler, M.I. Yanovskaya: The Chemistry of Metal Alkoxides (Kluwer Academic, Boston 2002) L.C. Klein: Processing of nanostructured sol–gel oxide materials. In: Processing of Nanostructured Materials, ed. by A. Edelstein, R.C. Cammarata (Institute of Physics, Bristol 1996) pp. 147–164 L.C. Klein: Advanced ceramics processing. In: Handbook of Materials Selection, ed. by M. Kutz (Wiley, New York 2002) pp. 1113–1128 R.A. McCauley: Corrosion of Ceramic Materials, 3rd edn. (Taylor Francis, Boca Raton 2013) D.R. Uhlmann, M.C. Weinberg, G. Teowee: Crystallization of gel-derived glasses, J. Non-Cryst. Solids 100, 154–161 (1988)
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38.12
38.13
38.14
38.15 38.16 38.17
38.18
38.19
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38.21 38.22
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Series, Vol. 194, ed. by J.S. Falcore Jr. (ACS, Washington 1982) pp. 293–304 D. Gallagher, L.C. Klein: Silica membranes by the sol–gel process, J. Colloid Interface Sci. 109, 40– 45 (1986) S. Yacoub, S. Calas-Etienne, J. Jabbour, R. Courson, R. Tauk, A. Khoury, A. Mehdi, P. Etienne: Synthesis of new vinyl ether functionalized silica for UV-patterning, J. Sol–Gel Sci. Technol. 67, 384–393 (2013) I.A. David, G.W. Scherer: An organic/inorganic single-phase composite, Chem. Mater. 7, 1957– 1967 (1995) D. Stauffer, A. Aharony: Introduction to Percolation Theory, revised 2 edn. (Taylor Francis, Philadelphia 1994) J. Zarzycki, M. Prassas, J. Phalippou: Synthesis of glasses from gels: The problem of monolithic gels, J. Mater. Sci. 17, 3371–3379 (1982) G.W. Scherer: Recent progress in drying of gels, J. Non-Cryst. Solids 147/148, 363–374 (1992) G.W. Scherer: Effect of drying on properties of silica gel, J. Non-Cryst. Solids 215, 155–168 (1997) D.M. Smith, G.W. Scherer, J.M. Anderson: Shrinkage during drying of silica gel, J. Non-Cryst. Solids 188, 191–206 (1995) G.W. Scherer, S. Haereid, E. Nilsen, M.-A. Einarsrud: Shrinkage of silica gels aged in TEOS, J. NonCryst. Solids 202, 42–52 (1996) L.C. Klein, G.J. Garvey: Monolithic dried gels, J. Non-Cryst. Solids 48, 97–104 (1982) T.A. Gallo, L.C. Klein: Apparent viscosity of sol–gel processed silica, J. Non-Cryst. Solids 82, 198–204 (1986) M.A. Aegerter, N. Leventis, M.M. Koebel: Aerogels Handbook (Springer, New York 2011) A.V. Rao, G.M. Pajonk, N.N. Parvathy: Influence of molar ratios of precursor, catalyst, solvent and water on monolithicity and physical properties of TMOS silica aerogels, J. Sol–Gel Sci. Technol. 3, 205–217 (1994) Aspen Aerogels: Cryogel Z, https://www.aerogel. com/products-and-solutions/cryogel-z Aspen Aerogels: Spaceloft Aerogel Insulation, https://gryphon4.environdec.com/system/data/ files/6/11160/epd725%20Spaceloft%20Aerogel %20Insulation.pdf (2015) C.J. Brinker, R. Sehgal, S.L. Hietala, R. Deshpande, D.M. Smith, D. Loy, C.S. Ashley: Sol–gel strategies for controlled porosity inorganic materials, J. Membr. Sci. 94, 85–102 (1994) D.M. Liu: Porous Ceramic Materials: Fabrication, Characterization, Applications (Trans Tech, Zurich 1996) T.H. Elmer: Flow of air, nitrogen and hydrogen through porous glass tubes, Sep. Sci. Technol. 27, 2041–2054 (1992) M.M. Collinson: Sol–gel strategies for the preparation of selective materials for chemical analysis, Crit. Rev. Anal. Chem. 29, 289–311 (1999) E. Bakangura, L. Wu, L. Ge, Z. Yang, T. Xu: Mixed matrix proton exchange membranes for fuel cells:
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38.24
R.M. Almeida, M.C. Goncalves: Crystallization of solgel-derived glasses, Int. J. Appl. Glass Sci. 5, 114–125 (2014) G.C. Righini, A. Chiappini: Glass optical waveguides: A review of fabrication techniques, Opt. Eng. 53, 071819-1-15 (2014) A.B. Seddon: Applicability of sol–gel processing in production of silica based optical fibres, Mater. Sci. Technol. 9, 729–736 (1993) L.C. Klein: Sol–gel processing of silicates, Ann. Rev. Mater. Sci. 15, 227–248 (1985) L.L. Hench: Sol–Gel Silica: Properties, Processing and Technology Transfer (Noyes, Westwood 1998) T.W. Zerda, G. Hoang: Effect of solvents on the hydrolysis reaction of tetramethyl orthosilicate, Chem. Mater. 2, 372–376 (1990) R.K. Iler: The Chemistry of Silica: Solubility, Polymerization, Colloid and Surface Properties and Biochemistry of Silica (Wiley, Hoboken 1979) B.E. Yoldas: Hydrolysis of aluminum alkoxides and bayerite conversion, J. Appl. Chem. Biotechnol. 23, 803–809 (1973) L.F. Nazar, L.C. Klein: Early stages of alumina sol– gel in acidic formation media: An 27 Al NMR investigation, J. Am. Ceram. Soc. 71, C85–C87 (1988) R. Roy: Ceramics by the solution-sol–gel route, Science 238, 1664–1669 (1987) R.A. Assink, B.D. Kay: Study of sol–gel chemical reaction kinetics by NMR, Annu. Rev. Mater. Sci. 21, 491–513 (1991) T. Katagiri, T. Maekawa: Influence of solvents on the structure of SiO2 gel from hydrolysis of tetramethylorthosilicate, J. Non-Cryst. Solids 134, 181–190 (1991) D.P. Partlow, B.E. Yoldas: Colloidal versus polymer gels and monolithic transformations in glassforming systems, J. Non-Cryst. Solids 46, 153–161 (1981) M. Yamane, S. Aso, T. Sakaino: Preparation of a gel from metal alkoxide and its properties as a precursor of oxide glass, J. Mater. Sci. 13, 865–870 (1978) S. Sakka, K. Kamiya: The sol–gel transition in the hydrolysis of metal alkoxides in relation to the formation of glass fibers and films, J. Non-Cryst. Solids 48, 31–46 (1982) S.-P. Szu, L.C. Klein, M. Greenblatt: Effect of precursors on the structure of phosphosilicate gels: 29 Si and 31 P MAS NMR study, J. Non-Cryst. Solids 143, 21–30 (1992) M. Aparicio, L.C. Klein: Synthesis and characterization of SiO2 -P2 O5 -ZrO2 , J. Sol–Gel Sci. Technol. 28, 199–204 (2003) L.C. Klein, N. Giszpenc: Preparation of crack-free titania-silica gels, Adv. Mater. Manuf. Process. 4, 439–448 (1989) H. de Lambilly, L.C. Klein: Crystallization of lithium alumino silicate gels, J. Non-Cryst. Solids 102, 269–274 (1988) L.C. Klein, G.J. Garvey: Silicon alkoxides in glass technology. In: Soluble Silicates, ACS Symposium
References
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State of the art and perspectives, Prog. Polym. Sci. 57, 103–152 (2016) R.R. Bhave: Inorganic Membranes: Synthesis Characteristics, and Applications (Van Nostrand Reinhold, New York 1991) B.E. Yoldas: Zirconium oxides formed by hydrolytic condensation of alkoxides and parameters that affect their morphology, J. Mater. Sci. 21, 1080–1086 (1986) T. Jin, Y. Ma, W. Masuda, M. Nakajima, K. Ninomiya, T. Hiraoka, J.-Y. Fukunaga, Y. Daiko, T. Yazawa: Preparation of surface-modified mesoporous silica membranes and separation mechanism of their pervaporation properties, Desalination 280, 139–145 (2011) M. Eriksson, L.C. Klein, E. Liden, K. Lindqvist: Preparation of nano-porous silica-zirconia layers by an in-situ sol–gel method, J. Mater. Sci. Technol. 22, 611–614 (2006) Y.S. Lin, A.J. Burggraaf: Experimental studies on pore size change of porous ceramic membranes after modification, J. Membr. Sci. 79, 65–82 (1993) G.W. Scherer, C.J. Brinker, E.P. Roth: Sol!Gel!Glass. 3. Viscous sintering, J. NonCryst. Solids 72, 369–389 (1985) G.W. Scherer: Cell models for viscous sintering, J. Am. Ceram. Soc. 74, 1523–1531 (1991) G.W. Scherer, S. Calas, R. Sempere: Densification kinetics and structural evolution during sintering of silica aerogel, J. Non-Cryst. Solids 240, 118–130 (1998) V. Ranganathan, L.C. Klein: Sol–gel synthesis of erbium-doped yttrium silicate glass-ceramics, J. Non-Cryst. Solids 354, 3567–3571 (2008) N. Yao, K. Hou, C.D. Haines, N. Etessami, V. Ranganathan, S.B. Halpern, B.H. Kear, L.C. Klein, G.H. Sigel: Nanostructure of Er+3 doped silicates, J. Electron Microsc. 54, 309–315 (2005) I.M. Azzouz, L.C. Klein: Red, violet and up conversion luminescence of Eu/Sm codoped SiO2 -TiO2 , Opt. Mater. 35, 292–296 (2012) L.C. Klein, T.A. Gallo: Densification of sol–gel silica: Constant rate heating, isothermal and step heat treatments, J. Non-Cryst. Solids 121, 119–123 (1990) G.W. Scherer, D.L. Bachman: Sintering of lowdensity glasses: I. Theory, J. Am. Ceram. Soc. 60, 236–239 (1977) G.W. Scherer: Sintering of low-density glasses: II. Experimental study, J. Am. Ceram. Soc. 60, 239– 246 (1977) L.F. Francis: Materials Processing: A Unified Approach to Processing of Metals, Ceramics and Polymers (Academic, London 2016) T. Gallo, C.J. Brinker, L.C. Klein, G.W. Scherer: The role of water in densification of gels. In: MRS Better Ceramics Through Chemistry, Vol. 32, ed. by C.J. Brinker, D.E. Clark, D.R. Ulrich (Elsevier, New York 1984) pp. 85–90 S. Wallace, L.L. Hench: Structural analysis of water adsorbed in silica gel, J. Sol–Gel Sci. Technol. 1, 153–168 (1994)
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T.A. Gallo, L.C. Klein: Dehydration effect on the viscosity of sol–gel processed silica, J. Non-Cryst. Solids 100, 429–434 (1988) L.C. Klein, T.A. Gallo, G.J. Garvey: Densification of monolithic silica gels below 1000 °C, J. Non-Cryst. Solids 63, 23–33 (1984) MAGNA: Interior Mirrors, https://www.magna. com/products/power-vision/product/interiormirrors 3M: 3M™ Nextel™ Ceramic Fibers and Textiles: Technical Reference Guide, http://multimedia. 3m.com/mws/media/1327055O/3m-nexteltechnical-reference-guide.pdf (2018) Canon Global: Optical technologies that consistently produce new value, http://www.canon. com/technology/approach/history/op-tech.html S. Sakka: Sol–gel process and applications. In: Handbook of Advanced Ceramics: Materials Applications, Processing and Properties, 2nd edn., ed. by S. Somiya (Elsevier, San Diego 2013) pp. 883–910 C.J. Brinker, C.S. Ashley, R.A. Cairncross, K.S. Chen, A.J. Hurd, S.T. Reed, J. Samuel, P.R. Shunk, R.T. Schwartz, C.S. Scotto: Sol–gel derived ceramic films—Fundamentals and applications. In: Metallurgical and Ceramic Protective Coatings, ed. by K.H. Stern (Chapman Hall, London 1996) pp. 112– 151 SolGel Way: ACEdip 2.0 Accurate Environmental Dip-coater, http://www.solgelway.com/ downloads/ACEdip%202.0%20Specification %20Sheet%2028082015.pdf T. Minami: Advanced sol–gel coatings for practical applications, J. Sol–Gel Sci. Technol. 65, 4–11 (2013) M.A. Aegerter, M. Mennig: Sol–Gel Technologies for Glass Producers and Users (Kluwer Academic, Norwell 2004) D.P. Birnie: A model for drying control cosolvent selection for spin-coating uniformity: The thin film limit, Langmuir 29, 9072–9078 (2013) D.P. Birnie, D.M. Kaz, D.J. Taylor: Surface tension evolution during early stages of drying of sol– gel coatings, J. Sol–Gel Sci. Technol. 49, 233–237 (2009) D.P. Birnie, S.K. Hau, D.S. Kamber, D.M. Kaz: Effect of ramping-up rate on film thickness for spin-on processing, J. Mater. Sci. Mater. Electron. 16, 715– 720 (2005) D.P. Birnie: Combined flow and evaporation during spin coating of complex solutions, J. NonCryst. Solids 218, 174–178 (1997) P.M. Glaser, C.G. Pantano: Effect of H2 O/TEOS ratio upon the preparation and nitridation of silica sol–gel films, J. Non-Cryst. Solids 63, 209–221 (1984) J. Eamsiri, A. Elyamani, R.E. Riman: Sol–gel synthesis of amorphous 5-component oxide systems using crown-ether complexation-ZBLAN gels, J. Non-Cryst. Solids 163, 133–147 (1994) H. Lunden, A. Liotta, D. Chateau, F. Lerouge, F. Chaput, S. Parola, C. Brannlund, Z. Ghadyani,
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B. Dunn, J.I. Zink: Optical properties of sol–gel glasses doped with organic molecules, J. Mater. Chem. 1, 903–913 (1991) D. Avnir, L.C. Klein, D. Levy, U. Schubert, A.B. Wojcik: Organo-silica sol–gel materials. In: The Chemistry of Organosilicon Compounds, Vol. 2, ed. by Z. Rappoport, Y. Apeloig (Wiley, London 1998) pp. 2317–2362 C. Sanchez, F. Ribot: Chemical design of hybrid organic–inorganic materials synthesized via sol– gel, New J. Chem. 10, 1007–1040 (1994) A.B. Wojcik, L.C. Klein: Organic–inorganic gels based on silica and multifunctional acrylates, J. Sol–Gel Sci. Technol. 2, 115–120 (1994) A.B. Wojcik, L.C. Klein: Transparent inorganic/organic copolymers by the sol–gel process: Thermal behavior of copolymers of tetraethyl orthosilicate (TEOS), vinyl triethoxysilane (VTES) and (meth) acrylate monomers, J. Sol–Gel Sci. Technol. 5, 77– 82 (1995) A.B. Wojcik, L.C. Klein: Organic/inorganic hybrids by the sol–gel process: Classification of synthesis methods, Appl. Organomet. Chem. 11, 129–135 (1997) L.C. Klein, A. Jitianu: Organic–inorganic hybrid melting gels, J. Sol–Gel Sci. Technol. 55, 86–93 (2010) J. Sun, E.K. Akdogan, L.C. Klein, A. Safari: Characterization and optical properties of sol–gel processed PMMA/SiO2 hybrid monoliths, J. Non-Cryst. Solids 353, 2807–2812 (2007) K. Nakanishi, N. Soga: Phase separation in silica sol–gel system containing polyacrylic acid. I. Gel formation behavior and effect of solvent composition, J. Non-Cryst. Solids 139, 1–13 (1992) H. Kaji, K. Nakanishi, N. Soga: Formation of porous gel morphology by phase separation in gelling alkoxy-derived silica. phenomenological study, J. Non-Cryst. Solids 185, 18–30 (1995) S. Wang, D.K. Wang, S. Smart, J.C.D. da Costa: Ternary phase-separation investigation of sol–gel derived silica from ethyl silicate 40, Sci. Rep. 5, 14560 (2015) C.L. Beaudry, L.C. Klein, R.A. McCauley: Thermal weight loss of silica-poly(vinyl acetate) (PVAc) sol–gel composites, J. Therm. Anal. 46, 55–65 (1996) E.J.A. Pope, M. Asami, J.D. Mackenzie: Transparent silica gel-PMMA composites, J. Mater. Res. 4, 1018–1026 (1989) B. Abramoff, L.C. Klein: Thermal properties of PMMA-impregnated silica gels. In: Chemical Processing of Advanced Materials, ed. by L.L. Hench, J.K. West (Wiley, New York 1992) pp. 815–821 B. Abramoff, L.C. Klein: Mechanical behavior of PMMA impregnated silica gels. In: Ultrastructure Processing of Advanced Materials, ed. by D.R. Uhlmann, D.R. Ulrich (Wiley, New York 1992) pp. 401–407 D. Avnir, T. Coradin, O. Lev, J. Livage: Recent bioapplications of sol–gel materials, J. Mater. Chem. 16, 1013–1030 (2006)
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M. Kildemo, M. Lindgren, C. Lopes: Dispersion and self-orientation of gold nanoparticles in sol– gel hybrid silica–optical transmission properties, J. Mater. Chem. C 3, 1026–1034 (2015) R.B. Figuiera, I.R. Fontinha, C.J.R. Silva, E.V. Pereira: Hybrid sol–gel coatings: Smart and green materials for corrosion mitigation, Coatings 6, 1–19 (2016) R.A. Cairncross, L.F. Francis, L.E. Scriven: Competing drying and reaction mechanisms in the formation of sol-to-gel films, fibers, and spheres, Dry. Technol. 10, 893–923 (1992) M.N. Ghazzal, O. Deparis, A. Errachid, H. Kebali, P. Simonis, P. Eloy, J.P. Vigneron, J. DeConnick, E.M. Gaigneaux: Porosity control and surface sensitivity of titania/silica mesoporous multilayer coatings: Applications to optical Bragg resonance tuning and molecular sensing, J. Mater. Chem. 22, 25302–25310 (2012) B. Yoldas, T. O’Keefe: Deposition of optically transparent IR reflective coatings on glass, Appl. Opt. 23, 3638–3643 (1984) C.J. Brinker, M.S. Harrington: Sol–gel derived antireflective coatings for silicon, Sol. Energy Mater. 5, 159–172 (1981) B.D. Fabes, D.P. Birnie, B.J.J. Zelinski: Porosity and composition effects in sol–gel derived interference filters, Thin Solid Films 254, 175–180 (1995) N.J. Arfsten: Sol–gel derived transparent IR-reflecting ITO semiconductor coatings, properties and technical possibilities, J. Non-Cryst. Solids 63, 243–249 (1984) L. Gambino, A. Jitianu, L.C. Klein: Dielectric properties of organically modified siloxane melting gels, J. Non-Cryst. Solids 358, 3501–3504 (2011) K. Zhang, X.Q. Zhang, C.X. Zhang, S.J. Zhang, X.C. Wang, D.L. Sun, M.A. Aegerter: Electrochromic behavior of NiO–TiO2 films prepared with sodium dodecyl sulfonate added to the sol, Sol. Energy Mater. Sol. Cells 114, 192–198 (2013) C.J. Brinker, D.M. Haaland, R.E. Loehman: Oxynitride glasses prepared from gels and melts, J. Non-Cryst. Solids 56, 179–184 (1983) Y.X. Chen, W.M. Liu: Characterization and investigation of the tribological properties of sol–gel zirconia thin films, J. Am. Ceram. Soc. 85, 2367– 2369 (2002) D. Chateau, A. Liotta, D. Gregori, F. Lerouge, F. Chaput, A. Desert, S. Parola: Controlled surface modification of gold nanostructures with functionalized silicon polymers, J. Sol–Gel Sci. Technol. 81, 147–153 (2017) D.J. Taylor, B.D. Fabes: Laser processing of sol– gel coatings, J. Non-Cryst. Solids 147/148, 457–462 (1992) Y. Lu, G. Cao, R.P. Kale, S. Prabakar, G.P. Lopez, C.J. Brinker: Microporous silica prepared by organic templating: Relationship between the molecular template and pore structure, Chem. Mater. 11, 1223–1229 (1999)
References
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C. Rottman, A. Turniansky, D. Avnir: Sol–gel physical and covalent entrapment of three methyl red indicators: A comparative study, J. Sol–Gel Sci. Technol. 13, 17–25 (1998) A. Jitianu, G. Amatucci, L.C. Klein: Organic– inorganic sol–gel thick films for humidity barriers, J. Mater. Res. 23, 2084–2090 (2008) A. Jitianu, G. Amatucci, L.C. Klein: Phenyl-substituted siloxane hybrid gels that soften below 140 °C, J. Am. Ceram. Soc. 92, 36–40 (2008) A. Jitianu, J. Doyle, G. Amatucci, L.C. Klein: Methyl modified siloxane melting gels for hydrophobic films, J. Sol–Gel Sci. Technol. 53, 272–279 (2010) A. Jitianu, G. Gonzalez, L.C. Klein: Hybrid sol–gel glasses with glass transition temperatures below room Temperature, J. Am. Ceram. Soc. 98, 3673– 3679 (2015) A. Jitianu, S. Cadars, F. Zhang, G. Rodriguez, Q. Picard, M. Aparicio, J. Mosa, L.C. Klein: 29 Si NMR
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and SAXS investigation of the hybrid organic– inorganic glasses obtained by consolidation of the melting gels, Dalton Trans. 46, 3729–3741 (2017) S. Jeong, S.-J. Ahn, J. Moon: Fabrication of patterned inorganic-organic hybrid film for the optical waveguide by microfluidic lithography, J. Am. Ceram. Soc. 88, 1003–1036 (2005) A. Matsuda, Y. Matsuno, M. Tatsumisago, T. Minami: Fine patterning and characterization of gel films derived from methyltriethoxysilane and tetraethoxysilane, J. Am. Ceram. Soc. 81, 2849– 2852 (1998) F. Back, M. Bockmeyer, E. Rudigier-Voigt, P. Lobmann: Hybrid polymer sol–gel material for UVnanoimprint: Microstructure and thermal densification, J. Sol–Gel Sci. Technol. 66, 73–83 (2013) A.K. Varshneya: Fundamentals of Inorganic Glasses (Academic Press, San Diego 1994)
Lisa C. Klein Dept. of Materials Science & Engineering Rutgers University Piscataway, NJ, USA [email protected]
Lisa C. Klein received a BS in 1973 and PhD in 1977 from the Material Science and Engineering Department of the Massachusetts Institute of Technology. In 1977, she was the first woman hired to a tenure-track position in the School of Engineering, Rutgers University. The focus of her research is the synthesis and processing of ceramics and glasses using the sol-gel process.
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Glass Recyclin 39. Glass Recycling
Ronan Lebullenger
, François O. Mear
The main objective of this chapter is to give the reader a general overview of glass recycling activity. Industrial and academic results are presented, which are useful to open new possibilities of economic activities using glass waste for environmental benefits for the society. The greatest answer to master the environmental effect of glass wastes is to reuse them. Recycling of these wastes principally from glass bottles and flat glasses will benefit in safeguarding the earth’s natural resources, diminishing landfill places, and saving energy and money. With a number of TV sets and computers attaining their end-of-life, electronic production is also challenged with the main difficulty of dealing with used devices.
39.1 39.1.1 39.1.2 39.1.3 39.1.4 39.1.5
Why Recycle Glass?............................ Glass Recyclability ............................. Glass Waste Management................... Benefits of Recycling Glass ................. Glass Recycling in the Roman Period ... Research on Glass Recycling................
39.2
Recycling Methods for Glass Products ............................. Recovery of Glass Containers, Bottles, and Jars............................................ Glass Container Cullet Treatment ......... Flat Glass .......................................... Glass Fiber Reinforced Plastics (GRFP) .. Other Recycling Methods ....................
39.2.1 39.2.2 39.2.3 39.2.4 39.2.5 39.3
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39.3.4 39.3.5
Waste Cathode Ray-Tube Glass Recycling: A Case Study ..................... Cathode Ray-Tube Design ................... Chemical Composition of CRT Glasses ... Status of Waste CRT Recycling (Closed and Open-Loop Cycles) ........... Foam Glass Products .......................... Conclusions.......................................
39.4
Summary.......................................... 1372
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References................................................... 1373
39.1.1 Glass Recyclability The proper nature of glass materials prepared by cooling a liquid and presenting the reversible glass transition phenomenon allows their infinite recyclability. Glass is one of the oldest synthetic materials; one can cite ancient Egypt production evidence reports from the third millenium BC. A glass free of pollutants can be recycled indefinitely without losing any of its qualities. Requirement of recycling industrial wastes is nowadays an environmental and economic priority. Glass is identified as an eternal recyclable solid. Mostly, glass cullet is re-injected into container and window glass furnaces. The state of the art of glass recycling is pre-
sented in this chapter. Academic and industrial results are detailed for different kinds of glasses and the valorization of end-consumer glass wastes.
39.1.2 Glass Waste Management The 3Rs Approach It is difficult to define the exact origin of the theory of the 3Rs (reduce, reuse, recycle) but for many, its creation would come from the establishment of Earth day in 1970. During the celebrations, the aim was to sensitize communities to safeguarding the planet. Subsequently, many acts of laws introduced the concepts of recycling and re-sourcing. The 3Rs propose ecological choices to deal with rising generation of wastes and its
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_39
Part E | 39.1
39.1 Why Recycle Glass?
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associated influence on human health, economy, and the natural ecosystem. The 3Rs (Fig. 39.1) represent a strategy for the management of end-of-life products and the resulting waste, to:
Reduce the amount of products that arrive at the end of life Reuse products or parts thereof that would otherwise become waste Recycle raw materials.
Part E | 39.1
End-of-life products that cannot fit into this scheme are considered ultimate waste; they can only be stored, eventually waiting for a way to be found to return them to the circuit. Voices of youth (VOY) has been in existence since 1995 and is a United Nations Children’s Fund’s (UNICEF) online place for young people to study more about questions disturbing their ecosphere. Even if recycling occupies the third place in the waste queue, it displays a prime role. For example, the European Commission (EC) asks for that the EU progress towards a recycling society. In other places on the planet (the Americas, Asia, . . . ) governments are implementing specific programs encouraging industries and citizens to care about glass waste management. Frequently in waste organization, only the classical routes, namely recycling, incineration, and landfill, are engaged (Fig. 39.2). Figures reporting the amount of waste materials that are recycled, incinerated, or landfilled can be found in various papers [39.1]. The extended producer responsibility (EPR) was initiated in Europe in 1990 by the Swedish academic Thomas Lindhqvist. Since then, the massive majority of EU member states have familiarized EPR for packaging, while the form of application varies from one country to the next, oscillating from mandatory principles to voluntary covenants between administration and production to deliberate industry initiatives. For North America, the Glass Packaging Institute (GPI) reveals that in the function of the implantation of volunteer collection points in various states, the efficiency of glass
Reduce
Reuse
Fig. 39.1 The 3Rs logo from VOY
Recycle
waste treatment varies. This means, if each government state invests, citizens’ behavior improves. In the domain of waste supervision, EPR is a policy planned to encourage the integration of environmental charges linked with goods during their life cycles into the market price of the products. The EPR regulation is an impulse for the adoption of remanufacturing initiatives as it focuses on the end-of-use treatment of consumer products and has the primary aim to increase the amount and degree of product recovery and to minimize the environmental impact of waste materials. [39.3]
EPR could take place such as in a reuse, buy-back, or recycling program. The producer may also choose to depute this charge to a third party, a so-called producer responsibility organization (PRO), which is remunerated by the manufacturer for used-product control. In this way, EPR moves the obligation for waste management from administration to private industry, willing producers, importers and/or sellers to assume waste management costs in their product charges and certify the safe treatment of their products. Within the Organization for Economic Cooperation and Development (OECD) the tendency is towards the extension of EPR to novel goods, product groups, and waste streams, such as electrical machines and electronics. Definition of Glass from Environmental Agencies Commonly, glass (silicate based) is considered an inorganic material with the Chemical Abstracts Service (CAS) number 65997-17-3, hereafter, the complete definition made by the United States Environmental Protection Agency (US EPA) [39.4]: CAS number for glass: 65997-17-3 Glass, oxide, chemicals CAS number: 65997-17-3 EPA registry name: Glass, oxide, chemicals Molecular formula: Unspecified
This category includes the different chemical ingredients manufactured in the fabrication of inorganic glasses. Glass is defined as an amorphous, inorganic, transparent, translucent, or opaque solid, usually fashioned by the fusion of sources of silica with a flux, such as an alkali-metal carbonate, boron oxide, etc., and a stabilizer into a mass that is cooled to a rigid condition without crystallization in the case of transparent or
Glass Recycling
Reduction of fuel oil used for incineration
Reduction of necessary production volume
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Fig. 39.2 The 3Rs approach and its impact on greenhouse gas (GHG) emission. After [39.2]
Reduction of waste Restraints on waste generation (reduce)
39.1 Why Recycle Glass?
Reduction of energy consumption
Change to production process
Reduction of GHG emission
Reduction of fossil fuel consumption
Reuse Alternative energy
Reduction of methane generated at landfill sites
Reduction of waste for landfill
Increase the amount of carbon stored in soil
Recycling Return to the environment
describe the different families of industrials glasses that are potential waste candidates for the recycling process. Common Silicate-Based Glasses The main types of silicate glasses, conferring to physicochemical composition, are soda-lime glass, lead crystal and crystal glass, borosilicate glass, and electric glass, also called E-glass, which is used as a reinforcement in composites in printed circuit boards and aerospace products, for example. The first three groups account for more than 95% of all glass manufactured and are summarized in Table 39.1. One has to keep in mind that a glass product is not only an addition of the different oxide compounds as described in Table 39.1, but glass is a complex network where metal (Si, Na, B, etc.) atoms are connected to each other by oxygen anions. This aspect is very important for the legislation aspect for glass waste treatment. It means that these silicate glass wastes are not concerned with the exposure of workers to respirable crystalline silica (RCS). According to Unicem’s Guide to Good Practice [39.6],
Table 39.1 Major constituents of soda-lime glass, lead crystal glass, borosilicate glass, and E-glass [39.5] Siliceous dioxide (SiO2 ) Boron trioxide (B2 O3 ) Lead oxide (PbO) Soda (Na2 O) or potassium oxide (K2 O) Lime (CaO) Aluminum trioxide (Al2 O3 )
Soda-lime glass 7175%
Lead crystal glass 5465%
Borosilicate glass 7080% 715%
E-glass 5256% 010%
2530% 1216% 1315%
48%
1015% 7%
02% 1625% 1216%
Part E | 39.1
liquid-phase separated glass or with controlled crystallization in the case of glass-ceramics. All glasses contain one or more of these ingredients. The elements listed below are principally present as components of oxide systems, but some may also be present as halides or chalcogenides, in multiple oxidation states, or in more complex compounds. Trace amounts of other oxides or chemical compounds may be present. Oxides of the first seven elements listed comprise more than 95%, by weight, of the glass produced: aluminum; boron; calcium; magnesium; potassium; silicon; sodium; antimony; arsenic; barium; bismuth; cadmium; carbon; cerium; cesium; chromium; cobalt; copper; germanium; gold; holmium; iron; lanthanum; lead; lithium; manganese; molybdenum; neodymium; nickel; niobium; nitrogen; phosphorous; praseodymium; rubidium; selenium; silver; strontium; sulfur; tellurium; tin; titanium; tungsten; uranium; vanadium; zinc; zirconium (from EPA Substance Registry Services (SRS)). More than 90% of the world’s glass production is based on soda lime silicate oxide glasses. Hereafter, we
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three of the various forms of crystalline silica are considered: quartz, cristobalite, and tridymite. It does not cover amorphous silica, fused silica, or other silicate minerals or silicate-based glasses. So, another manner to represent the glass is the molecular aspect (or chemical formulation Ma M0b Oc with a C b C c D 1) as presented hereafter by an extract from the Glass Alliance Europe document. Glass Under the REACH Registration. The REACH (registration, evaluation, authorization and restriction of chemicals) regulation (regulation EC No. 1907/2006) is the EU’s controlling structure on chemicals and their not dangerous use. It came into vigor on 1st June, 2007. It rationalizes and expands the former legislative framework on chemicals of the EU. REACH makes the industry accountable for evaluating and managing the risks posed by chemicals and for providing suitable safety information to their users. In parallel, the EU can take other measures on very hazardous ingredients where there is a need for complementary action at EU level [39.7]. Glass is an inorganic material achieved from different inorganic raw materials that react at high temperature to form a new random network, where different elements are connected, typically by oxygen bridges. For the REACH regulation, glass is considered a UVCB (substance of unknown or variable composition, complex reaction products, or biological materials). The general chemical formation for silicate sodalime glass can be clarified by the following simplified reaction equation
Part E | 39.1
aSiO2 (sand) C bNa2 CO3 (soda) C cCaCO3 (lime) C dCaMg.CO3 /2 (dolomite) C eNa2 SO4 (sodium sulfate) C : : : ! xSim Nan Cao Mgp : : : Os (glass) C yCO2 " CzSO2 " C : : : Raw materials used in a glass formulation suffer physical (melting) and chemical (formation of the network) processes. During the chemical reaction to form glass (synthesis), different crystalline substances (a; b; c; d; e, etc.) are transformed into a non-crystalline vitreous substance (x). The physicochemical properties of the new substance glass (chemical resistance, mechanical resistance, transmittance, color, etc.) are a function of the network formed. Different compositions lead to different glass chemical structures and, consequently, to different physicochemical properties of the final material.
For borosilicate glass, silica and boron are the network formers of the glass structure, and the simplified formula is aSiO2 (sand) C bNa2 B4 O7 (borax) C cNa2 CO3 (soda) C dAl2 O3 (alumina) C : : : ! xSim Bn Nao Alp : : : Os (glass) C yCO2 " C : : : Glass is a substance of variable composition, which by convention is expressed as oxides of the constituent elements (SiO2 , Na2 O, K2 O, PbO, etc.). While conventionally glass compositions are stated as oxides of the different elements, it is important to be aware that glass is not a mixture of the different oxides or raw materials, but a substance that does not contain these oxides as such. Glass can better be identified by its chemical formula Sim Nan Cao Mgp . . . Os (glass). In Europe (EU-28), in view of annual production volumes, the potential deposit of glass waste is in the region of 30 Mt=year. The repartition of the glass production volume of the EU ( 30 Mt=year during the 2006–2015 period), within the 28 EU member countries (including the UK) is presented in Fig. 39.3. This produced volume keeps the EU as the major glass manufacturer in the world with a market portion of about one-third of the total world market. Germany remains the EU’s biggest producer with about one-fifth of the volume, closely followed by France, Spain, Italy, and the UK. For other world countries where glass manufactures are well implanted, we can observe equivalent proportions for these different glass types, with the major volume produced for container glasses and the second for flat glasses. Container Glass The container glass industry offers an extensive range of glass packaging products for food and beverages, as well flacons for perfumery, cosmetics, and pharmacy to a European and world-wide customer base. The production volume is about 20 Mt=year [39.8]. Flat Glass The dominant markets for flat glass are the building (windows and facades) and automotive industries (windscreens, side and rear-side glazing, backlights, and sunroofs). Flat glass is also used in solar-energy applications (photovoltaic and solar thermal panels), as well as in urban and domestic furniture, appliances, mirrors, and greenhouses. The production volume is about 810 Mt=year [39.9].
Glass Recycling
39.1 Why Recycle Glass?
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Fig. 39.3 35
European UE28 glass production (million tons). After [39.8]
30 25 20 15 10
Others Reinforcement GF Domestic Container Flat glass
5 0
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2007
2008
2009
2010
2011
2012
2013
Domestic Glass The domestic glass part represents about 2% of the total glass production. This sector includes the trade of glass tableware, cookware, and decorative items, such as drinking glasses, bowls, plates, cookware, vases, and ornaments. Domestic glass is mainly manufactured by SME (small and medium-sized enterprise) facilities. Special Glass Special glasses for silicate-based ones signify about 1% of glass production in Europe. These merchandises have a high added-value related to their strong technological content. This sector includes a great variety of products, such as lighting glass, glass tubes, laboratory glassware (borosilicate glasses), glass ceramics, heatresistant glass, optical and ophthalmic glass, extra thin glass for the electronics industry (e. g., liquid-crystal
2015
display (LCD) panels, photovoltaics), and radiation protection glasses. Other industrial glasses such as phosphates for optical or laser applications (Kigre, Hoya companies), fluorides (Le Verre Fluoré, FiberLabs, Thorlabs), or chalcogenides (Umicore, IRradiance, Schott) for infrared optical devices are produced in a very discrete volume (kg or a few t=year). So, the waste management of end-consumer objects have not yet been established with a valuable economic schema. These special glasses could include the WEEE (waste of electrical and electronic equipment) recycling sector. Glass Reuse Since the first glass production, the reuse of pristine glass object containers was routine. However, nowadays, the one-shot use bottle is a problem for environment considerations. Historically, Owens-Illinois introduced, a one-way bottle called the stubby in 1935. With the increase of the one-way container and a hotend coating to recover flaw resistance, producers began the process of light weighting containers by at least 30%. Companies continue to work on improving the strength of glass in order to be more competitive. However, depending on the laws in each country, in Europe, there is a consciousness for reusable glass containers for food and beverages. For example, in France, hotel and restaurant enterprises use an internal schema to collect glass bottles to return to the refilling companies. However, this consignment for re-use now concerns marginal quantities for a few beverages (beer, wine) at the level of certain regional distribution channels. Even if the step of cleaning containers before reuse is expensive, the global CO2 aspect has to be considered.
Part E | 39.1
Reinforcement Glass Fiber The manufacture of continuous filament glass fiber (CFCG) is one of the smallest sectors of the glass industry in terms of tonnage (23%, 1 Mt). Continuous filament glass fiber uses are known as fiber-reinforced polymers or glass-reinforced plastics. Glass fiber is formed when thin strands of silica-based or other formulation glass are extruded into many fibers with small diameters suitable for textile processing. The modern method for producing glass wool is the invention of Games Slayter working at the Owens-Illinois Glass Co. (Toledo, Ohio). In 1938, the Owens-Illinois Glass Company and Corning Glass Works joined to form the Owens-Corning Fiberglas Corporation, which is still the major glass-fiber producer in the market today. The most common type of glass fiber used in fiberglass is E-glass [39.10–12].
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Part E | 39.1
Reducing Glass The second R item relating to glass life cycle, is to limit the quantity of material making up these final objects. The packaging sector is an industrial example of continuous progress in limiting weight or volume to what is strictly necessary; the European directive 94/62/EC lays down these requirements. In the glass industry, many efforts were made, for example, to reduce the weight of bottles (as shown Fig. 39.4) and jars conserving the same optical and mechanical qualities and properties. Further to finding technical solutions for reducing containers weight, a main industry-wide initiative called Container Lite (UK) has better understood of how clients react to lightweight glass bottles in regard of strength or quality of new products. Studies display that users have a positive opinion of light weighting when the ecofriendly benefits are emphasized. Light weighting can profit both major brand and high-volume stock containers [39.14]. Companies involved in these initiatives worked with glass manufacturers and managed to reduce the Burgundy bottle weight from 480 to 420 g (12:5 wt% reduction) and its Bordeaux bottle weight from 420 to 385 g (8 wt% gain). This gain provides a reduction around 2395 t of CO2 emissions. Also, Saint Gobain has announced a lightweight range named Ecova, decreasing bottle masses and the carbon emanated during manufacture by up to 15%, while Consol Glass, South Africa’s primary glass manufacturer, has presented a screw cap, 75 cl wine bottle that weighs 350 g. Other major achievements were observed in light weighting Champagne and sparkling wine bottles, which are required to endure important internal pressure and frequently weigh between 800 and 900 g. The Comité Interprofessionnel du Vin de Champagne (CIVC), for example, has confirmed that 65 g of mass can be removed from typical Champagne bottles without impacting flacon strength, merchandise quality, or consumer awareness. Whilst for glass packaging, industry efforts and technical solutions were achieved in the last decades
with the aim to reduce container weight, for the flat (float) glass industry producing objects for civil engineering, the drastic mechanical resistance requirements do not allow huge weight (thickness) reduction. Nevertheless, flat glass surface treatment by coating or atmosphere control could reduce defects, the origin of fragility for civil or automotive applications. Glass Recycling The third R step in the 3Rs approach of glass endconsumer life is recycling. Two ways are possible; on the one hand, closed-loop recycling, where glass waste (cullet or internal cullet) is considered as secondary raw materials and, on the other hand, the open-loop process where glass waste is considered as an additive or a matter to transform before re-using. Recycling covers a set of routes that can be categorized conferring to diverse aspects. First, the grade of processing that occurs leads to the subsequent categories [39.1]:
Product recycling: Any method in which the chemical and physical composition of a product is preserved but the product is not used for the original purpose (using glass flasks as construction material). Material recycling: Any method in which the physical but not the chemical composition is destroyed (melting and reprocessing glasses). Feedstock recycling (also raw material recycling or chemical recycling): Any route in which the physical as well as the chemical structure of a material is reprocessed into its original constituents.
Secondly, the allocation technique for recycling comprises the following two situations [39.15]:
A closed-loop practice applies to closed-loop product schemes. It also applies to open-loop product classifications where no changes occur in the intrinsic properties of the recycled material. In such cases, the need for allocation is avoided, since the
a) Unit weight (g)
b) Unit weight (g)
600
500
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400
400
300
300
200
200
100
100 0
Fig. 39.4a,b
1994
1997
2000
2003
2006
2009 Year
0 1970s
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Example of glass weight reduction for consumer products: (a) A 75 ml bottle of alimental oil, (b) a 275 ml beer bottle. After [39.13]
Glass Recycling
use of secondary material displaces the use of virgin materials. An open-loop route applies to open-loop product schemes where the material is recycled into other manufactured goods, and the material undergoes a change to its characteristics.
39.1.3 Benefits of Recycling Glass
Energy savings: An increase of 10% of recycled glass in place of virgin raw materials allows a 3% energy saving; as an example, increasing the cullet percentage in the batch of an efficient end-port fired regenerative container glass furnace from 65 up to 75% decreases the specific energy consumption from 3:95 MJ=kg molten glass to 3:8 MJ=kg. The use of cullet also aids in reducing the batch-free time by both reducing the amount of refractory material in the batch and by providing additional liquid throughout the melting process.
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Limiting the release of CO2 : 1 t of recycled glass saves more than 500 kg of CO2 . Decreasing the removal of natural resources: For each kg of cullet used in replacement of the raw material, there is a saving of 1:2 kg of virgin materials. Optimizing logistics and, thus, minimizing the carbon footprint linked to transportation: Recycled glass comes from local collections, close to the glass production plants. Avoiding landfilling or incineration.
39.1.4 Glass Recycling in the Roman Period Carthage was an essential place in maritime interchange networks during the Roman and late antique periods. Meticulous bivariate and multivariate data studies identified diverse primary glass groups and confirmed extensive recycling. Roman mixed antimony and manganese glasses with MnO contents in excess of 250 ppm were clearly the product of recycling, while iron, potassium, and phosphorus oxides were regular impurities. Primary glass sources were categorized using TiO2 as a proxy for heavy minerals (ilmenite/spinel), Al2 O3 for feldspar, and SiO2 for quartz in glassmaking sands. It was, therefore, possible to draw suppositions about the chronological and geographical provenances of the primary glass types [39.17, 18]. In these papers, the authors first checked the chemical composition of archaeological glasses and the different ratios of oxides. Also, optical studies were carried out on color or colorless glass pieces and correlations with the use of Mn, Mo, or other redox elements such as Sb were achieved. They indicated the localization of glass manufactures or mineral raw materials source. Founded principally on variances in the alumina, lime, and iron oxide contents, a number of natron-type glasses was recognized that controlled the archaeological record in the Mediterranean and Europe for most of the first millennium and that are thought to have been produced on the Levantine coast. Roman glass was mass-produced in large installations and then merchandised as raw glass. The above papers reveal the problem of transport between the local production site and the reuse or recycling site.
39.1.5 Research on Glass Recycling Recycling of glass is also an important subject in the field of academic research. Research from academic laboratories thus supports the economic and industrial sector. The graph in Fig. 39.5 shows that the number of specific publications on glass recycling has grown significantly since the early 1990s and continues to grow
Part E | 39.1
Recycling processes include a vast number of actions, which can be more or less efficient. End-of-waste (EoW) criteria specify when certain waste ceases to be waste and obtains a status of a product (or a secondary raw material). The quantity of inorganic wastes (derived from construction and demolition and mining and quarrying activities) in Europe is valued to be more than 1:5 Gt. The amount of glass material concerns common silicate-based glasses. The incessant rise of waste amount necessitates not only actions that reduce its generation, but also recycling and recovery. For this reason, the European directives concerning waste, directive 2006/12/CE and directive 2008/98/CE, are focused on converting the EU into a recycling society that challenges engendering waste and that uses its waste as a resource. Usually, non-hazardous inorganic wastes are disposed of in landfills and are frequently discarded directly into ecosystems without acceptable treatment, but potential recovery or recycling choices should be explored and applied [39.16]. Conferring to Article 6 of the Waste Framework Directive 2008/98/EC (WFD), certain identified waste shall stop being waste when it has suffered a recovery process and obeys the detailed criteria to be developed in line with a sum of legal situations, especially when there is a present market or request for the material, and the use is lawful and will not lead to environmental or human health impacts. This EoW criteria mechanism was announced to further inspire recycling in the EU [39.5].
39.1 Why Recycle Glass?
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Published items 240 220 200 180 160 140 120 100 80 60 40 20 0 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Year
exponentially. Today, according to the consultation of the website of Science, almost one scientific article per working day deals with the recycling of glass. The low rate of publications for the period 1970–1990 can be ex-
Fig. 39.5 Glass and recycling papers per year according to Web of Science (consulted [39.19])
plained by the fact that the citizenry, in general, was not aware of the necessity to preserve the planet. We recall the beginning of awareness initiated with Earth day in 1970.
39.2 Recycling Methods for Glass Products
Part E | 39.2
In the second part of this chapter, we will present the different steps in the glass recycling process. As previously indicated, glass is a copiously recyclable solid that can be recycled in a closed-loop procedure (Fig. 39.6). This is mainly true for glass bottles, which have a recycling frequency varying from 50 to 80%. Glass recycling also aids in saving energy as cullets melt at a lower temperature than raw materials. Large efforts are made to recycle glass after use, even though each subdivision has its own specificities and quality necessities. The quantity of solid waste created by glass manufacture is extremely low, as almost all glass waste (cullet) are directly recycled and put back into furnaces [39.7]. The residual glass is then joined with soda ash, limestone, and sand to make new glass products.
Glass waste
Collection
Purification
End products
Glass
Fining
Forming
Cullet melting
Purification
Fig. 39.6 Schema process for glass recycling in a closed-
loop procedure. After [39.20]
39.2.1 Recovery of Glass Containers, Bottles, and Jars Volunteer Contribution Points In the UK and Germany, citizens are accustomed to sorting glass bottles by color. Different containers are available to separate the white (clear), green, and amber (brown) glass (Fig. 39.7). In France in the 1990s, glass companies (BSN Danone, Saint Gobain) in partnership with local authorities, established areas to collect all glass bottles and alimentary containers (VAP). Since 2010, the EcoEmballages organization has been collecting around 2 Mt of mixed glass bottles and containers every year. However, about three out of ten bottles and jars are still disposed of with household garbage. So, to improve the collection, citizens have to become more informed and conscious about the benefits of glass recycling. In France and Spain, mixed colors are accepted in VAP. However, for all European countries, infographs explain to the citizens which glass products are acceptable and which ones are forbidden (Fig. 39.8). The greatest problems nowadays are linked to the existence of glass ceramics in post-consumer waste glass and the movable quantity of different colors in the glass cullet or changing pollution by organics. For ex-
Glass Recycling
39.2 Recycling Methods for Glass Products
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Fig. 39.7 Volunteer contribution points (UK, France, Germany)
YES
NO
Jars, large and small bottles
Glasses, light bulbs, ceramic, lids and bottle tops
Fig. 39.8 Infograph on VAP. After [39.21]
ample, small pieces of porcelain or glass ceramics in the cullet, with sizes less than 5 mm, will possibly end as glass imperfections in glass products. Bigger pieces of glass ceramics could lead to drastic disturbances in the gob formation process, due to difficulties with cutting of the gobs with high viscous inclusions. In recent cullet treatment factories most ferro and non-ferro metals are quite efficiently removed. In the European area, the ratio of collected waste container glass versus consumed glass is about 70% (Fig. 39.9).
39.2.2 Glass Container Cullet Treatment
Glass quality troubles: inclusions or color changes Glass melting inconveniences by foaming or limited heat transfer into melt Shorter lifetime of glass furnace by downward drilling of melts of metals present in the cullet.
Even if suggested for restraining the consumption of energy and natural raw materials, the usage of cullet in the engineering of new glass articles is not effortless. Actually, only glass cullet with well-controlled composition is usually received in conventional (flat glass, glass containers) products. Table 39.3 summarizes the specified contaminant limits of the treated cullet before being re-introduced in glass furnaces of manufacturers. Regarding the last item (grain size cullet) in Table 39.3, some comments are necessary. While fine particles melt more rapidly, they can also agglomerate to form larger,
Part E | 39.2
Processing facilities use various sorting equipments to recycle waste glass jars and bottles into secondary raw materials (Fig. 39.10 and Table 39.2). Glass sorting apparatus is required to separate the glass objects according to color, since tinted glass cannot be mixed together when creating new controlled colored glass objects. Brown glass can only be recycled into brown containers, and green glass can only be used to make green bottles. Nevertheless, certain chemicals can be employed to eliminate any dye before combining clear, green, and brown glass. The first sorting step includes eliminating all labels and lids and cleaning off any future unmelted particles and extraneous matter that would deteriorate the recycled product. A machine then grinds the glass into small pieces, called cullet. This substance is subjected to a screening and detection process to detect any metal, paper, and plastic substances. A powerful vacuum takes away these components, since they would weaken the strength of the new glass product.
Ceramic elements are also detected by an x-ray fluorescence set-up and removed from glass pieces by an air flow ejection set-up at the end of the belt used to transport the treated solid wastes. Unfortunately, this process leaves only very fine ceramic dust that is very difficult to eliminate from the product. If left in the mix, the melting process may dissolve the dust, but some defects and imperfections can greatly affect the recycled glass. Recycling glass bottles and jars using glass sorting equipment induces less energy and time to produce new glass products. The environment is also spared, since waste glass does not decay like other products in landfills. Pollution of the cullet may lead to:
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Fig. 39.9
Recycling rates for glass containers in EU28 in 2014. After [39.22] Finland 81%
Norway 94% Sweden 102%
Estonia 73% Latvia 55% Lithuana 55%
Denmark 85% Ireland 77%
Portugal 55%
United Kingdom 67%
The Netherlands Poland 80% 59% Germany Belgium 89% 94% Czech Republic Luxembourg 72% Slovak Republic 95% 39% Austria 89% Hungary Switzerland 36% Slovenia France 96% Romania 86% 74% 40% Croatia 53% Italy Bulgaria 77% 63%
Spain 69%
Greece 21%
Turkey 14%
Malta 49%
Cyprus 32%
Fig. 39.10
Part E | 39.2
Sorting by color
Silo Waste cullet
Opto-mechanical sorting
Sieve
White Green Amber
Silo Treatment by color separated cullet
Separate silos for each color or fine cullet
Stock Suction system
Silo
For larger pieces, optional: sorting on color
Glass cullet sorting plant. After [39.23]
Iron Iron Crusher/mill Magnet separation Air filtering
Separation of ceramics, stones, china
Metal detection Mixed colors
One glass color
+ – – + Eddy-current Clean fraction < 8 mm
Waste
Glass Recycling
Table 39.2 Technology used for glass container waste
sorting [39.24] Sorting task Separation from Ceramics, stones, porcelain (CSP) Metal (ferrous and non-ferrous) Lead glass Glass ceramics
Plastics, acrylic glass, laminated glass Sorting according to color Other sorting tasks Treatment of CRT glass Input sample analysis and/or output quality control
Technology Camera with light transmitter All-metal sensor X-ray fluorescence X-ray fluorescence, x-ray absorption, hyper-spectral imaging, UV techniques Near-infrared spectroscopy Camera with light transmitter X-ray fluorescence Sample analysis system
Table 39.3 Specifications for sorted and processed cullet to be accepted for secondary raw materials [39.22] Acceptable content < 2535 g=t < 25 g=t Size lower than 34 mm < 5 g=t < 5 g=t < 1 g=t < 5 g=t < 7 g=t < 200 or 500 g=t < 12001500 mg O2 /l < 60 g=t < 23 wt% < 1500 g=t < 100 g=t No cullet pieces > 7 cm Cullet pieces < 0:5 cm: max 12%
porous particles, which effectively prevent penetration of the viscous liquid to the particle surfaces. Since these agglomerations have a low bulk density, they can float to the surface of the melt, which significantly slows the dissolution process. Escape of gases is inhibited when very fine particles are used, since the channels between the particles are reduced in size. The use of very fine particles can result in the blockage of these channels in the early stages of the melting process, which can suppress decomposition reactions.
Economic Aspect: Glass Cullet Secondary Raw-Materials Market EU-28 trade in glass waste shows a growth from about 250 000 t=month in the year 2002 to approximately 350 000 t=month in 2007 and further to 430 000 t=month in 2013. The data displays that the extra EU-28 export of 84 000 t in 2013 for approximately 1% of glass waste separately collected in EU-28 according to the waste statistics regulation data (approximately 9 Mt in EU-28 for 2010). The cross-border trade capacity is controlled by intra EU-28 trade. Extra EU-28 export commerce is minor for glass (4% of the exported volume). So, when comparing the European glass production volume ( 30 Mt=year) and the European glass cullet market ( 9 Mt=year), one can predict that a third of the total glass production is potentially reusable as cullet when the initial glass product is in end of life. With respect to the price of glass waste, fluctuations are observed, but it remains at a level between 40 and 50 £=t [39.25]. For the covering and sorting steps some average price will be presented. Cullet market prices differ according to the color of the glass. Figure 39.11 presents the cullet price observed in the UK but differentiated with respect to glass color. As one can note, clear recovered glass presents the higher price, whilst the mixed recovered glass can in the function of market demand presents a negative price. The recovered glass container price does not include the sorting and cullet treatment process. Another point to take into account to understand the price differences is the recovery system implemented in the UK or in Germany, compared with those in other European country such as France or Spain. In the UK and Germany, citizens sort packaging glass by color before placing it in the receptacles provided for collection (VAP). Recovered glass container prices (£/t) 30 20 10
Clear Amber Green
0 –10
Mixed
–20 Apr 15 Jun 15 Aug 15 Oct 15 Dec 15 Feb 16 Apr 16
Fig. 39.11 Recovered glass container price according to color. After [39.26]
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Part E | 39.2
Cullet contaminant Stones, ceramics, chinaware, pottery (excluding glass-ceramics) Glass ceramics Glass ceramics pieces if present Magnetic metals Non-magnetic metals Lead (Pb) Aluminum (Al) All metals Organic material Chemical oxygen demand (COD) of washing water from cullet Plastics Moisture Paper/cork/wood Opal glass Grain size cullet
39.2 Recycling Methods for Glass Products
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39.2.3 Flat Glass
Part E | 39.2
Automotive Glass Currently, according to data of the EC, among 89 Mt of end-of-life vehicle (ELV) waste is created each year in the EU. Some instructions enforce a objective to recycle certain percentage of vehicle waste, for example, the reuse and recovery at a rate of 95% of the ELV weight. Automotive glass is around 3 wt% of the total structure of a car. For automotive glass waste, two kinds of glass are present in the vehicle. Firstly, the rear and lateral windows, which are generally toughened glass and partially coated by ceramic enamels, and secondly, the laminated windshield front glass. Enamel contaminants are a problem for closed-loop glass recycling, because of the source of the coloring and/or infusible agents. Every windshield encloses about 1 kg of PVB (polyvinyl butyral) sheet, which can be raw materials for recycling for the polymer industry, but for the glass industry [39.27], the organic nature of PVB will change the redox behavior of the batch introduced in the melting furnace. Recuperating and separating automotive glass is a multifaceted and, therefore, lengthy process (Fig. 39.12). If the glass is recyclable, it needs to be appropriately dismantled from cars and sorted from other scrap to eliminate antennas, connectors, and solders. Then, it needs to be treated in special facilities before it can be melted again as glass, or alternatively used as a secondary aggregate material to produce materials and products such as fiber glass and abrasives in the open-loop recycling process. An interesting study on finding the best practices for automotive glazing recycling conclude that while the current glazing recycling situation is not economically viable, a national glazing recycling network could actually become beneficial for all stakeholders (collecting, dismantling, storage, treatment, cullet market) under certain conditions that are likely to appear in the near future [39.28]. Flat Glass from Construction and Demolition Waste (C&D) Directive 2008/98/EC (WFD) and directive 1999/31 /EC (Landfill Directive) need to be reviewed to effec-
Fig. 39.12 Safety glasses and windshields with PVB
tively eliminate landfill deposits of recyclable glass, develop collection of building glass waste, and raise recycling rates. The WFD sets a general 70% goal for reuse and recycling of C&D waste. As glass is less than 1% of C&D waste, this objective does not serve as a motivation to set up flat glass collection organization. Construction and demolition debris (C&D) is defined as all non-hazardous solid waste. Despite its recyclability, end-of-life building glass is practically never recycled into new glass products. As an alternative it is crushed together with other building materials and put into landfills. This is enabled by its inert characteristics. It presently has a low market value because there is a lack of organized collection systems to generate a secondary raw material. Often, landfill costs are cheaper than the cost of separately collecting and treating building glass, particularly in countries with low landfill taxes/fees in place. Building glass cullet that cannot be recycled technically and cost effectively in the flat glass sector could be recycled in other sectors of the glass industries, such as in the container and fiber glass sectors. Glass for Europe and Their Flat Glass Recycling Initiatives Glass for Europe is the trade association for Europe’s manufacturers of flat glass. Glass for Europe has four members: AGC Glass Europe, NSG-Group, SaintGobain Glass, and Sisecam-Trakya Cam and works in association with Guardian. Altogether, these five companies represent 90% of Europe’s flat glass production [39.9]. Nevertheless, flat glass producers initiated some projects named REVALO (in France) and VRN (in the Netherlands), where a strategy is developed to optimize flat glass recycling efficiency [39.29–31]. The EC participates to these projects via funding Life projects [39.32]. LIFE is the EU’s financial instrument supporting environmental, nature conservation, and climate action projects throughout the EU. In 2000, Dutch sheet glass manufacturers launched an initiative to set up a voluntary recycling scheme in order to meet their responsibilities as producers of sheet glass. Three organizations participated in the initiative: the Manufacturers of Double Glazing in the Netherlands (FIGIN), wholesalers and importers of sheet glass, who were collectively represented by the Glass Branch Organization (GBO) and the Dutch Glass Federation (NGF). Even if the collected and treated flat glass volume is not yet optimized, hereafter the repartition of the cullet for the VRN project in the three main glass manufacturers is: the sheet-glass industry (15%), insulation products (13%), and the packaging glass industry (72%).
Glass Recycling
39.2.4 Glass Fiber Reinforced Plastics (GRFP)
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fly-ash and slag. Boron oxide, which is an E-glass constituent, can lead to a reduction in the initial strength of cement, but in low concentration, this is not a problem [39.37].
39.2.5 Other Recycling Methods Non-Sorted Glass Cullet for Road Structure There is, however, the potential to use non-sorted or rejected glass from VAPs or construction and demolition civil glass treatment as a sub-base material for road pavement construction. Research done for geotechnical engineering proposes to use recycled glass as a roadway sub-base is cost effective, and thus excludes costly sorting. However, there is the necessity to program additional studies on the potential short and long-term toxicity, health hazards, and/or environmental pollution of the mixed glass cullet used as an aggregate, considering conditions during stockpiled storage and after placement. The results of test centers on recycled glass vis-à-vis its potential to discharge contaminants to the environment via leaching are now controlled. For example, in Melbourne, Australia, five random samples of crushed glasses were collected from a recycling company. The limitations tested for each sample were total organic matter, heavy metals, sulfates, chlorides, conductivity, pH, and surfactant levels. The conclusion was that contamination levels were within the State of Victoria’s Environmental Protection Agency specified limits for manual handling, thus indicating that recycled glass could probably be safely used in pavement sub-bases [39.38]. Recycled glass can be introduced as substitute aggregate in concrete and asphalt and as a boundless aggregate auxiliary for roadway sub-base and base layers. When recycled glass is used as a bound material in concrete or asphalt, it is named glascrete and glasphalt, respectively. Based on the study, different recycled glass types were considered: fine recycled glass (FRG), medium recycled glass (MRG), and coarse recycled glass (CRG) with maximum particle sizes of 4:75, 9:5, and 19 mm, respectively. Another example, in the United States, is that the Federal Highway Administration (FHWA) suggests maximum percentages of 15 and 30% of recycled glass by weight used in base and sub-base courses. Also, crushed glass (CG) among 20 and 80% by weight mixed with dredged materials (DM) can offer the designer the flexibility to increase some design factors. The different investigation groups settled that using recycled glass particles with other materials usually leads to improvement of the performance of blends. The engineering properties of recycled glass are mostly comparable to natural aggregates [39.39].
Part E | 39.2
E-glass fibers represent the greatest reinforcement in polymer matrix composites. Almost 9095% of composite merchandises enclose E-glass, typically in the form of continuous fibers, cut strands, or whiskers. The annual manufacture of glass fibers touched 5 Mt, and it is probable that fabrication will grow in the coming years [39.33, 34]. A challenge is their recycling at the end of product life. Environmental pressure to ban or limit the disposal of waste composites via land fill-in is a fact. Several routes are used for recycling thermoset matrix composites, with mechanical grinding, addition to cement kilns, and chemical or thermal recycling [39.35]. Mechanical grinding into powder to granular units (between 0:1 and 20 mm) for use as a filler material is a current technique, but the fibers are not recovered for reuse. Also, the use of glass fiber reinforced plastic (GFRP) as feedstock to cement saves material and energy, but, again, the glass fibers are not retrieved. Chemical and thermal recycling are the processes for recuperating fibers for reuse in new composite materials or other applications. Chemical processes dissolve the polymer matrix at elevated temperature and leave the fibers ready for re-use; however, this process consumes chemicals such as acids, bases, solvents, and washing liquids to remove residues on fibers. Even with moderate temperature treatment of < 350 ı C, chemical recycling reduces the fiber strength by over 50% during the recycling process (2:2 GPa to lower than 1 GPa), liable on solvents, catalysts, temperature, exposure time, and the extent of resin removal [39.36]. Moreover, some thermal recycling processes based on burning off the polymer matrix to recover the glass fibers, include fluidized beds, pyrolysis, and thermal fluid methods. Energy can be recuperated from the exothermic decomposition of the polymer matrix knowing that polymers present a high calorific value. The recovered fibers can possibly be recycled as reinforcement in new composite materials. Another way to recycle GFRP is co-processing in cement kilns, when mixed with other waste to feed into the kilns. When introduced into a cement kiln, the organic resin burns providing energy (about 12 MJ=kg of waste, decreasing the carbon footprint of cement business by up to 16%, EuCIA reports), and the mineral constituents such as alumino borosilicate E-glass fiber and calcium carbonate filler provide feedstock for cement clinkers. Any calcium carbonate calcines (releasing carbon dioxide) to calcium oxide, a crucial component of Portland cement. Aluminum and silicon oxides present cementitious properties and are classically present in Portland cement at about 25%, and in much higher proportions in cement alternatives from
39.2 Recycling Methods for Glass Products
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Glass Cullet as Mortar (Concrete) Ingredient Concrete is a common construction material. The cement industry is in front of various defies such as growing cost in energy supply, the necessity to diminish CO2 emanations, and the access to raw materials in adequate qualities and quantities. With the exception of Al2 O3 and CaO, the fractions of the foremost ingredients of different kinds of glass are similar. So, silicate-based glass can be considered a pozzolanic-cementitious material conferring to the chemical requests in ASTM (American Society for Testing and Materials) C 618 if the alkali concentration is ignored. Alkalis can originate alkali-silica reaction (ASR) and expansion when aggregates are alkali reactive. Consequently, high alkali content of glass is a typical concern for its use in concrete, but research has demonstrated that finely ground glass does not contribute to ASR. The pozzolanic properties of glass are sensitive to particle sizes lower than 300 m. Under 100 m, glass presents a pozzolanic reactivity that is greater than that of fly ash at low percentage cement replacement levels and after 90 days of curing [39.40, 41]. Other studies exposed that green particles of 1:18 and 2:36 mm exhibited the highest reactivity, while further sizes caused small ASR expansions. Brown glass of less than 2:36 mm did not cause great ASR expansion. Also, different ASR inhibitors were studied and found to destroy ASR development. These included supplementary cementitious materials, steel fiber reinforcement, and lithium compounds [39.42].
Part E | 39.3
Conversion of Cullet into Sodium Silicate Solutions or Silicate Products Sodium silicate solutions have various applications such as detergents and washing compounds, pulp and paper manufacturing, adhesives, metal cleaning, petroleum treating, water management, building products, or textile fabrication. The usual way to formulate sodium silicates is an alkali attack of sand, by direct melt of accurately measured percentages of pure silica sand (SiO2 ) and soda ash (Na2 CO3 ) or sodium sulfate (Na2 SO4 ) in furnaces fired at temperatures above 1000 ı C. Regarding the chemical composition of industrialized sodium silicates, the weight proportion SiO2 =Na2 O fluctuates from 3:75 to 1:6. Grades with ratios under 2:85 are
called alkaline, whilst those with an upper SiO2 =Na2 O quotient are labeled as neutral. Depending on chemical purity requirements, the use of glass cullet as a SiO2 source decreases the final price and contributes to waste management. Hydrothermal and fusion procedures are employed to formulate sodium silicate from waste glasses. Three different colors of waste glasses (white, green, and brown) are used to produce sodium silicate solution. The best situation for sodium silicate solution fabrication by fusion is using waste bottle glass with 90 wt% NaOH at 650 ı C for 60 min [39.43]. A large range of silicate compounds such as zeolite can also be manufactured by using hydrothermal reaction of cullet glasses in high pH conditions [39.44, 45]. Recycled Glass as Water Filtration Media The UK’s Waste and Resources Action Programme (WRAP) has supported a series of experiments that indicate that using recycled glass could diminish the cost of water filtration and reduce environmental complications. For example, UK-based water treatment professionals Aqua Enviro, revealed that recycled glass filtration media (RGFM) can enhance the quality of effluents when paralleled to traditional sand. Current trials show that a two-stage filter practice with different grades of glass in each can offer a better filter performance [39.46]. Glass Beads Various methods have been developed for the production of glass beads from finely divided glass cullet. One is the flame furnace, where a mixture of fuel and air is proportioned so as to insure that the flame temperature is sufficiently high that the glass particles soften or melt in the flame and assume a spherical shape. The glass beads produced after sieving for size separation have different applications. Using beaded lines on roads for night time reflectivity is now accepted worldwide. For beads with large diameters, applications such as support for fluidized beds for temperatures lower than glass temperature (< 500 ı C) are developed. Also, one can cite the support for distillation column in the chemical industry.
39.3 Waste Cathode Ray-Tube Glass Recycling: A Case Study The quantity of waste electrical and electronic equipment (WEEE), or e-waste, created in the world is increasing quickly. The content of dangerous constituents in electrical and electronic equipment (EEE) is a main concern. Preferably, the resources in electronic merchandises would be re-used when the goods reach
the end of their lifetime. In the EU, WEEE signifies about 7:5 Mt=year [39.47], where computer monitors and TV sets containing cathode-ray tubes (CRTs) represent about 80% of the total electronic waste [39.48]. In the United States, it is valued that 300 000 t of e-waste finished in landfills in 2000 [39.49] and as described by
Glass Recycling
Townsend et al. [39.50], CRTs are about one-third of the electronics waste weight. The three types of glass presented in CRT monitors enclose hazardous and heavy chemicals (lead, strontium, antimony, barium, europium, selenium, etc.) and weigh between 50 and 85% of the total weight [39.48, 51–53]. Presently, collected monitors are ripped to pieces and treated, and CRT glass usually ends up in a distinct landfill certified for hazardous waste. Therefore, in Europe, practically all of these are in landfills. As the lead content in these waste products represents as much as 80% of the toxic metals in discarded electronics, CRTs clearly represent a potential pollution danger to the environment [39.53]. To explore the possible applications of waste CRT glass, descriptions of these materials need to be carried out. Waste CRT glass can be categorized as being part of either color or black-and-white monitors, and by their producer. Much research has been carried out to explore how waste CRT glass could be re-used [39.55–58]. CRT glass should be recycled in a closed-loop system (i. e., in the manufacture of new CRT glass) or an open-loop system (i. e., the glass is used in other outlets).
39.3.1 Cathode Ray-Tube Design There are two kinds of CRTs: black-and-white (monochrome) and color. The monochrome CRT involves a front panel used as the screen, a neck that covers the electron gun, and a funnel that attaches the Non-glass parts
panel and the neck. The panel and the funnel are produced by pressing and sealing together. A color CRT contains a panel, a shadow mask, a glass funnel, and an electronic gun. The shadow mask is the tiny sheet metal positioned behind the glass panel. The glass funnel is linked to the back of the glass panel, both coupled using a solder glass frit. It is estimated that CRT represents around 65% of the weight of a television or a computer monitor and is composed of 85% glass where the front panel contributes 65%, the funnel 30%, and the neck glass 5% [39.59]. The front panel is a barium-strontium silicate glass (up to 12% barium oxide and up to 12% strontium oxide), while the funnel is a lead silicate glass (up to 25% lead oxide). The neck of the CRT consists of a glass with a very high lead content (up to 40% lead oxide), while the frit is made of a low melting lead glass (up to 85% lead) [39.54, 57]. The quantity of lead oxide existing in CRTs fluctuates from 0:5 kg for a 1200 CRT to 3 kg for a 3200 CRT [39.57]. In addition, the inside of the CRT panel is layered with coats of phosphor, which contain cadmium and other metals. The outer section of the funnel section is coated with graphite, and the inner section with iron oxide [39.60]. A quick representation of a CRT is shown in Fig. 39.13 to demonstrate the components used.
39.3.2 Chemical Composition of CRT Glasses Cathode-ray tube glass encloses heavy metals, so in order to identify its possible re-use, it is imperative to
Glass parts Panel glass Ba and Sr glass containing two thirds of the total mass
Frit Shadow mask Iron oxide layer
Funnel glass Pb glass containing one third of the total mass
Graphite layer
Electron gun
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Part E | 39.3
Conductive material, layers of phosphors
39.3 Waste Cathode Ray-Tube Glass Recycling: A Case Study
Neck glass 25 wt% PbO glass containing very low mass, less than 1%
Fig. 39.13 Representation of CRT
constituents. After [39.54]
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Glass Processing
Table 39.4 Chemical composition ranges (in oxide weight percent) of the CRT glass types found in the literature [39.54] Oxide Network formers SiO2 Sb2 O3 As2 O3 Network intermediates Al2 O3 PbO ZnO TiO2 Network modifiers Na2 O K2 O Li2 O CaO MgO Fe2 O3 SrO BaO CeO2 ZrO2
Black and white Range Standard content
Color panel Range Standard content
Color tunnel Range Standard content
6466 0:30:6 00:3
65 0:45 0:01
6063 0:250:5 00:2
62 0:35 0:02
5256 0:10:3 00:1
52 0:25 0:01
35 2:84:4 00:1 0:10:2
3 4 0:05 0:15
23:5 03 00:6 0:40:6
2:2 – 0:3 0:5
3:55 1923 00:1 00:1
4 22 – 0:05
6:58 67:5 00:6 01 – 0:050:2 02 912 0:10:2 00:5
7 7 0:3 0:5 – 0:12 1 11 0:18 0:25
7:89 67:5 00:5 02 01 0:070:12 610 911 020:3 02:5
8 7:5 0:2 0:5 0:2 0:08 8:5 10 0:25 1:5
68 7:58:5 00:1 24 1:22 0:050:07 01 02 – –
6:8 7:8 – 3:8 1:8 0:06 0:5 1 – –
define their chemical composition. Waste CRT glass composition varies from producer to producer. Table 39.4 recapitulates the oxide composition of the diverse glass, as well as the usual content for every glass used in CRT glass engineering found in the literature. CRT glass contains silicate glass with a complex formulation, including several components incorporated into the glassy network in several ways. They are categorized into three groups, and the characteristics are summarized as follows:
Part E | 39.3
Network formers are oxides that naturally form a glassy edifice (SiO2 , B2 O3 , P2 O5 , for example) Network modifiers terminate networks by needing fewer oxygens to balance the valency (MgO, CaO, Na2 O, K2 O, for example) Network intermediates can join in glassy networks but cannot themselves form glass (Al2 O3 , PbO, for example).
39.3.3 Status of Waste CRT Recycling (Closed and Open-Loop Cycles) When recycling waste CRTs, recovered glass can be used in the further manufacture of CRTs (closed-loop recycling) or in other products (open-loop recycling). Recycling of waste CRTs consists of three broad technologies: glass-to-glass, glass-to-lead, and glass-toproducts recycling.
Glass-to-glass recycling is a closed-loop process involving various steps [39.61]:
Removing the CRT from plastic casing Releasing the vacuum in the tube Removing various metals and non-glass metals including the electron gun Sorting panel glass from funnel glass with x-ray fluorescence set-up Removing the phosphor coatings from the panel glass.
Glass-to-glass recycling of CRT glass enables replacement of the virgin raw materials with recycled cullet at equal or lower cost. But nowadays, the production of new CRT is almost zero around the planet. Glass-to-lead recycling resolves the problem of CRT funnel glass, reduces the environmental menace of lead leaching, and recuperates the lead tripped in glass matrix. This is certain to achieve separation of lead from leaded glass. The development tendency for lead-glass disposal is to achieve the extraction of metallic lead. Advanced technologies have been planned in lead extraction from waste CRT funnel glass, which has roughly been divided into high temperature separation and pretreatment and hydrometallurgical leaching [39.62–64]. Glass-to-products recycling is not easy, since it is against the law to introduce hazardous elements (such
Glass Recycling
as lead, arsenic, and cadmium) into products like glass containers, tableware, or glass fibers. In this situation, the glass industry is a possible consumer only for glasses without the above-mentioned elements. In the ceramics industry, the restriction is not so limiting, and both glass from screens and cones are in theory suitable as secondary raw materials, even if they must be provided with specific characteristics of homogeneity, cleanness, etc. Some examples of the end use of CRT glass in these and other industries are shown in Fig. 39.14. Ceramic products: In the ceramics industry, it is possible to use both panel and funnel glass from CRTs, as the restrictions are much lower. Research work by Andreola et al. [39.59] studied the use of CRT glass (panels and funnels) as secondary raw material alternatives for common ceramic frits used in the manufacture of glazes. The investigation was undertaken in the research laboratory as well as in production plants and established that glazes achieved using CRT glass have similar aesthetic and mechanical properties to standard glazes. The investigators also conducted a life cycle assessment (LCA) on standard industrial glaze and CRT glass glaze. The results indicated that the fabrication of glaze with CRT glass leads to a global decrease of environmental damage of 36%.
b)
c)
d)
1369
Moreover, Andreola et al. [39.66] considered the potential of using CRT glass in glass-ceramics manufacturing. Glass-ceramics have the properties of both glass and traditional crystalline ceramics and are used very commonly for cook tops. The results obtained indicate that CRT glass is very versatile for this purpose, because if it is mixed with suitable raw materials such as dolomite or alumina and subjected to adequate thermal treatments, it can be used in glass-ceramics manufacturing.
39.3.4 Foam Glass Products Foam glass has an exceptional mix of properties such as being lightweight, rigid, compression resistant, thermally insulating, freeze tolerant, noninflammable, chemically inert and nontoxic, rodent and insect resistant, and water and steam resistant. Moreover, foam glass enables fast assembly and has low transport expenses. This mix of properties generates foam glass that is practically unique both in the construction (e. g., for the insulation of roofs, walls, floors, and ceilings under hot or cold conditions) and in many other fields [39.67]. The production of glass foam dates back to the 1930s, when major research activity was managed throughout the developed countries. The patented de-
Part E | 39.3
a)
39.3 Waste Cathode Ray-Tube Glass Recycling: A Case Study
Control
5% glass
10% glass
Fig. 39.14a–d
Several kinds of typical construction materials that use lead glass: (a) foam glass (b) glass ceramics (c) brickworks (d) paving bricks. Reprinted from [39.65] with permission from Elsevier
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velopments can be separated into two fundamental types: engineering of foam glass by the above-described sintering of finally ground glass powders with a suitable foaming agent (e. g., ISOVER (), France; CERNIX, France; MISAPOR, Switzerland), and the direct introduction of gas (air, CO2 , water vapor) into the molten glass (e. g., Saint-Gobain, France; Pittsburgh Plate Glass and Corning Glass Works, USA). Foam Glass Products from Recycled CRT Foam glass is currently a relatively small market but it does have many uses, which include, but are not limited to, cold and hot insulation works, waterproofing, and noise mitigation works. It is commonly valued for having good general insulating properties and also doubling as a useful structural component. An interesting aspect of glass foam is that it is very reasonable to manufacture from entirely recycled materials. This makes it a potentially cheap and environmentally friendly product. Glass foam can be made from many different compositions of glass and can utilize different recycled foaming agents. The main producers of foam glass in Europe are Foamglas (www.foamglas.de), GeoCell (www.geocell-schaumglas.eu), TECHNOpor (http:// www.technopor.com), EcoGlas (ecoglas.de), Misapor (http://www.misapor.ch), and Foamit (www.foamit.fi).
Part E | 39.3
The Foaming Process Foam glass is mostly obtained by the reaction of a gasgenerating agent with the initial finely divided powder glass. The mixture of glass powder and foaming agent is heated to a temperature between 700 and 900 ı C, at which the gas from the foaming agent occurs within a pyroplastic mass of the softened glass particles undergoing viscous flow sintering. Figure 39.15 shows images of foam glass obtained after the expansion processing function of a foaming agent used. Most glass foams are only made out of two raw materials: the glass and the foaming agent. The raw glass can be remarkably different and yet obtain similar goals, however it can have some unintended consequences. This is on a case-by-case basis, depending on
a)
b)
the composition, as different foaming agents can provide drastically different results. There are two main types of foaming agents. The first types are foaming agents that decompose and release gas under heat, due to thermal decomposition. These include compounds like CaCO3 and other oxides. The chemical reaction for calcium carbonate to calcium oxide and carbon dioxide is shown as (39.1). CaCO3 (s) ! CaO(s) C CO2 (g)
(39.1)
Degassing foaming agents like this will usually result in open porosity foam. Thermal decomposition reactions are preferable for glasses containing high amounts of heavy metals, since they do not present the risk of oxidation reactions by the reduction of easily reducible oxides, like those of some heavy metals. The other type of foaming agents used to make foam glass involve redox reactions that effectively use the oxygen available from the oxides in the glass structure to form CO2 or some other gas, which can include CO and O2 . A very common form of this method involves SiC. This process depends on more than one reaction. One of these reactions is shown in (39.2). SiC(s) C 2O2 (g) ! SiO2 (s) C CO2 (g)
(39.2)
This reaction, however, is slow, even at 900 ı C, and is not likely to be the cause of most of the foaming. It is much more likely to form carbon monoxide (CO) than carbon dioxide (CO2 ). The resulting CO is reactive with other oxides in the glass, especially those that are easily reducible, like heavy metal oxides. The CO strips them of their oxygen to form CO2 and leaves only the heavy metal behind. Table 39.5 summarizes the different categories of foaming agents used for the elaboration of foam glass and shows the mechanism of expansion. Foam Glass Properties The ability of a glass melt to foam through the sintering approach is controlled by many factors, e. g., the glass composition, particle size, temperature, and type and
c)
d)
60 mm
Fig. 39.15a–d Images of the glass foam composition function. (a,b) CRT and SiC, (a) CRT and CaCO3 , (b) CRT and
TiN
Glass Recycling
39.3 Waste Cathode Ray-Tube Glass Recycling: A Case Study
1371
Table 39.5 Summary of foaming agents used for the elaboration of glass foam Category Metal carbonates/sulfates Metal oxides Nitrides Carbonaceous
Foaming agent Na2 CO3 =CaCO3 =MgCa.CO3 /2 (dolomite)/Na2 SO4 =CaSO4 Mnx Oy =Fex Oy =Crx Oy =PbO AlN=TiN=Si3 N4 SiC Carbon Water glass Virgin glass
concentration of the foaming agent. Optimizing all the parameters is extensive, and a good starting point is essential to reach optimal conditions within a reasonable time. The foaming temperature is easy to control and is perhaps one of the most studied parameters. An accurate temperature control is important, since it affects properties such as the melt viscosity, bubble pressure, rate of bubble coalescence, crystallization, and gas formation. Table 39.6 summarizes the typical properties of commercial glass foam products. The glass foam quality is determined by an optimal balance of properties. The most important ones are density, closed porosity, compression, and flexural strength and thermal conductivity. The density is strongly correlated to the thermal conductivity and the mechanical strength, as is shown in Fig. 39.16. It is challenging to obtain closed pores in a low density glass foam (< 0:18 g=cm3 ) but very easy in high density glass foam. Hence, there is a strong connection between density and closed porosity. The density is, therefore, the most important property of glass foams, and it is accordingly meaningful in a first attempt to relate density with melt viscosity. If the viscosity is the dominant factor controlling the foaming process, the foaming could proceed at a sim-
Table 39.6 Typical properties of commercial glass foam products [39.68] Density (g=cm3 ) Porosity (%) Crushing strength (MPa) Flexural strength (MPa) Flexural modulus of elasticity (GPa) Coefficient of thermal expansion (K1 ) Thermal conductivity (W=.m K/) Specific heat (kJ=.kg K/) Thermal diffusivity at 0 ı C (m2 =s) Sound transmission loss at normal frequency (dB/100 mm)
1.4 1.2 1.0
90 250
80 70
200
Compressive strength
100 1
0.2
0
0.0 0.2
0.4
0.6
0.8
–1 1.0 ρ*/ρs
60 50
Flexural strength
2
0.4
Flexural strength (MPa) 100
300
150
0.8
0.0
b) Compressive strength (MPa)
3
0.6
0:10:3 8595 0:46 0:31 0:61:5 8:9 106 0:040:08 0:84 .3:54:9/ 107 28
ilar viscosity independently of the glass composition. The majority of the reported glasses are soda-lime-silica glasses, due to their importance in the glass foam industry. Figure 39.17 shows that the foaming preferably occurs between 103 and 107 Pa s. It is observed that the viscosity window is dependent on the type of foaming agent. Metal carbonates (CaCO3 , Na2 CO3 , MgCO3 , SrCO3 , dolomite), and MnO2 should preferably be used in the range of 104 106 Pa s. Using SiC to foam soda-lime-silica glasses and CRT panel glasses requires higher treatment temperatures (900950 ı C)
K (GPa) 6 K (SiC) K (TiN) 5 E (SiC) E (TiN) 4
1.6
Redox reaction
40 30 20
50
10 0
0 0
20
40
60
80 100 Porosity (%)
Fig. 39.16 (a) Variation of Young’s modulus E and compressive modulus K with relative density p =ps . (b) Variation of the compressive and flexural strengths versus porosity. After [39.69]
Part E | 39.3
a) E (GPa)
Mechanism Reactive/thermal decomposition Redox reaction in melt Redox reaction Surface reaction Solid–gas reaction
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Glass
Foaming agent
Bottle SLS E-glass Labware CRT panel CRT panel CRT panel
Dolomite CaCO3 CaCO3 CaCO3 CaCO3 MnO2 Na2CO3
Float Float/bottle Bottle CAS Bottle Float/bottle SLS CRT panel
CaCO3 CaCO3, MgCO3, SrCO3 N/A SnO + SiC SiC SiC SiC Fe2O3/Co3O4 + SiC
Fig. 39.17 Viscosity window for
Metal carbonates, SiC MnO2
2
4
and, hence, the melt must have a lower viscosity (103:3 104:0 Pa s). The viscosity windows given here provide a guideline to optimize the glass foam production process. In the future it would be worth establishing the viscosity windows of the foaming processes for mixtures containing other types of foaming agents and glasses.
39.3.5 Conclusions Part E | 39.4
Recycling waste CRT glass is not easy due to the presence of four different types of glasses: panel, fun-
obtaining a low density glass foam. The viscosity () ranges are reported for bubble and crystal-free glass melts. After [39.70]
6
8 log η (Pa s)
nel, neck, and frit, with varying material compositions. Closed-loop and open-loop recycling are two principal ways of recycling CRT glass. For closed-loop recycling, varying material composition of CRT glass with the different manufacturers, costs of dismantling the CRT, and cheap and ready obtainability of other recycled glass costs form major barriers to overcome. For more than 70 years, glass foam production has been recognized as a valid method both to obtain products with a unique combination of properties and for open-loop recycling of the growing quantities of CRT glass.
39.4 Summary Waste glass recycling in a closed loop is a sustainable practice, but various barriers exist. Strict specifications concerning the maximum levels of impurities that can be tolerated in glass waste to be re-introduced into glass furnaces are the main hindrance. High technologies used in cullet treatment plants need to be more efficient to produce clean secondary raw materials. The open-loop strategy should be the appropriate way to valorize the rebut cullet coming from the glass container or for complex glassy materials, such as glass
fibers, building and automotive glasses, or CRT glass. Concrete and mortar solutions seem to be more adapted for the moment, these industries using a large volume of matter. A more discrete solution such as foam glass production is an alternative way. Moreover, to achieve waste legislation recommendations, in particular on glass waste, financial aid is necessary to develop academic research and viable industrial solutions. Citizens have to be aware that protecting the planet is not a simple subject.
Glass Recycling
References
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References 39.1
39.2
39.3
39.4
39.5
39.6 39.7
39.8 39.9 39.10 39.11
39.12
39.14
39.15
39.16
39.17
39.18
39.19
39.20
39.21 39.22 39.23 39.24
39.25
39.26 39.27
39.28
39.29
39.30 39.31 39.32
39.33
39.34
39.35
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39.13
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39.36
39.37
39.38
39.39
39.40
39.41
39.42
39.43
39.44
39.45
39.46 39.47
39.48
Part E | 39
39.49
39.50
39.51
39.52
39.53
G. Oliveux, J.L. Bailleul, E.L. La Salle: Chemical recycling of glass fiber reinforced composites using subcritical water, Composites A 43, 1809–1818 (2012) S. Job: Recycling glass fibre reinforced composites—history and progress, J. Reinf. Plast. Compos. 33(16), 1542–1556 (2014) M.A. Imteaz, M.M.Y. Ali, A. Arulrajah: Possible environmental impacts of recycled glass used as a pavement base material, Waste Manag. Res. 30(9), 917–921 (2012) S. Mohsenian: Current state of the art practice of use of glass in pavement structures. In: Proc. Innov. Pavement Mater. Surf. Technol. Conf. Transp. Assoc. Can., Charlottetown (2015) Y. Jani, W. Hogland: Waste glass in the production of cement and concrete—A review, J. Environ. Chem. Eng. 2(3), 1767–1775 (2014) A.M. Matos, J. Sousa-Coutinho: Durability of mortar using waste glass powder as cement replacement, Constr. Build. Mater. 36, 205–215 (2012) H. Du, K.H. Tan: Effect of particle size on alkali– silica reaction in recycled glass mortars, Constr. Build. Mater. 66, 275–285 (2014) M. Keawthun, S. Krachodnok, A. Chiasena: Conversion of waste glasses into sodium silicate solutions, Int. J. Chem. Sci. 12(1), 83–91 (2014) Z.M. Veloza, K. Yanagizawa, N. Yamasaki: Recycling waste glass by means of the hydrothermal hot pressing method, J. Mater. Sci. Lett. 18, 1811–1813 (1999) N.J. Coleman: 11 Å tobermorite ion exchanger from recycled container glass, Int. J. Environ. Waste Manag. 8, 366–382 (2011) P. Lavender: Filter media: Treating chemical wastewaters, Filtr. Sep. 45(4), 16–18 (2008) M. Marshall, J. Henderson: New approaches to the challenge of CRT recycling. In: Recycling and Reuse of Glass Cullet, ed. by T. Telford (2001) pp. 75–83 F. Andreola, L. Barbieri, A. Corradi, I. Lancellotti, R. Falcone, S. Hreglich: Class-ceramics obtained by the recycling of end of life cathode ray tubes glass, Waste Manag. 25, 183–189 (2005) C. Gable, B. Shireman: Computer and electronic product stewardship: Are we ready for the challenge?, Environ. Qual. Manag. 11(1), 35–45 (2001) S.E. Musson, Y.-C. Jang, T.G. Townsend, I.-H. Chung: Characterization of lead leachability from cathode ray tubes using the toxicity characteristic leaching procedure, Environ. Sci. Technol. 34, 4376–4381 (2000) J.P. Desgeorges: Objective Concerning the Re-use of End of Life Electric and Electronic Products, Report for the French Ministère de l’environnement (Paris 1992) V. Palm: Environmental Hazards Connected to the Composition of Cathode-Ray Tubes and Cabinets, Report Swedish Environmental Research Institute (Stockholm 1995) N. Menad: Cathode-ray tube recycling, Res. Conserv. Recycl. 26, 143–154 (1999)
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39.55
39.56
39.57
39.58
39.59
39.60
39.61
39.62
39.63
39.64
39.65
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39.67 39.68
39.69
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F.O. Mear, P. Yot, M. Cambon, M. Ribes: The characterization of waste cathode-ray tube glass, Waste Manag. 26, 1468–1476 (2006) Commission Européenne: Recycling of end-of-life cathode ray tube glass, https://cordis.europa.eu/ project/rcn/34576/factsheet/fr (1996) E. Döring: TV glass recycling in Europe—description of the situation and possibilities, http://www. viah.fi/klo/research/kimokela/TV_glass_summarypdf (2002) Industry Council for Electronics Equipment Recycling: Material Recovery from Waste Cathode Ray Tubes (CRTs) (WRAP, Banbury 2004) A.S. Smith: Recycled CRT Panel Glass as an Energy Reducing Fluxing Body Additive in Heavy Clay Construction Products (WRAP, Banbury 2004) F. Andreola, L. Barbieri, A. Corradi, I. Lancellotti: CRT glass state of the art—A case study: Recycling in ceramic glazes, J. Eur. Ceram. Soc. 27(2–3), 1623–1629 (2007) Industry Council for Electronics Equipment Recycling: New Approach to Cathode Ray Tube (CRT) Recycling (Department of Trade and Industry, London 2003) D.H. Weitzman: Is CRT glass-to-lead recycling safe and environmentally friendly? In: IEEE Int. Symp. Electron. Environ (2003) pp. 329–334 M. Chen, F.S. Zhang, J. Zhu: Lead recovery and the feasibility of foam glass production from funnel glass of dismantled cathode ray tube through pyrovacuum process, J. Hazard. Mater. 161, 1109–1113 (2009) T. Okada: Energy-efficient modification of reduction-melting for lead recovery from cathode ray tube funnel glass, Waste Manag. 33, 1758–1763 (2013) H. Inano: Effect of alkali metal oxide on Pb recovery from the waste CRT glass by reduction melting method. In: Design for Innovative Value Towards a Sustainable Society, ed. by M. Matsumoto, Y. Umeda, K. Masui, S. Fukushige (Springer, Dordrecht 2012) W. Meng, X. Wang, W. Yuan, J. Wang, G. Song: The recycling of leaded glass in cathode ray tube (CRT), Procedia Environ. Sci. 31, 954–960 (2016) F. Andreola, L. Barbieri, A. Corradi, I. Lancellotti: Cathode ray tube glass recycling: An example of clean technology, Waste Manag. Res. 23, 314–321 (2005) G.W. Mc Lellan, E.B. Shand: Glass Engineering Handbook (McGraw-Hill, New York 1984) G. Scarini, G. Brusatin, E. Bernardo: Glass Foams. In: Cellular Ceramics: Structure, Manufacturing, Properties and Applications, ed. by M. Scheffler, P. Colombo (Wiley, Weinheim 2006) F.O. Méar, P. Yot, R. Viennois, M. Ribes: Mechanical behaviour and thermal and electrical properties of foam glass, Ceram. Int. 33, 543–550 (2007) R.R. Petersen, J. König, Y. Yue: The viscosity window of the silicate glass foam production, J. Non-Cryst. Solids 456, 49–54 (2017)
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References
1375
Ronan Lebullenger Institute of Physics – Rennes (IPR), UMR CNRS 6251 Institute of Chemical Sciences Rennes (ISCR) UMR CNRS 6226 University of Rennes 1 Rennes, France [email protected]
Ronan Lebullenger received his PhD from Rennes University in 1994. He spent six years in Brazilian scientific institutions investigating rare-earth-doped glasses and ceramic materials. After industrial experience with Alcatel France, he joined Rennes University as an Associate Professor. His research focus are glasses and ceramics for optical or environmental applications.
François O. Mear Lille University Lille, France [email protected]
Francois O. Méar received a PhD from Montpellier II University. After Postdoctoral assignments at Cambridge and Tohoku University, he became an Assistant Professor at Lille I University for Catalysis and Solid State Chemistry. He develops glass matrices for unconventional applications and investigates the synthesis of self-healing glassy matrices.
Part E | 39
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Optical a Part F Optical and Photonic Glass Applications
40 Laser Glasses Simi A. George, Duryea, PA, USA Joseph S. Hayden, Duryea, PA, USA
45 Display Glass Matt Dejneka, Corning, NY, USA T. J. Kiczenski, Corning, NY, USA
41 Optical Fibers Thierry Chartier, Lannion, France
46 Scintillator Glasses Russell Lee Leonard, Tullahoma, TN, USA Jacqueline A. Johnson, Tullahoma, TN, USA
42 Glass in Integrated Photonics Juejun Hu, Cambridge, MA, USA Lan Yang, St. Louis, MO, USA 43 Amorphous Silicon in Microphotonics Anuradha M. Agarwal, Cambridge, MA, USA Jurgen Michel, Cambridge, MA, USA
47 Mid-Infrared Molecular Sensing Angela B. Seddon, Nottingham, UK
44 Phase-Change Memory and Optical Data Storage Xiang Shen, Ningbo, China Yimin Chen, Ningbo City, China Guoxiang Wang, Ningbo, China Yegang Lv, Ningbo, China
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_39
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Bulk solid-state lasers (SSLs) are a preferred class of lasers for high peak power and high average power generation due to their technological simplicity and economical power scaling. At the heart of a bulk SSL is a crystalline or amorphous material doped with transition metal ions or rare-earth elements. The focus of this chapter is a special subset of gain materials used for bulk solid-state laser emission, namely multicomponent glasses. A broad discussion on why glass is ideally suited for many laser applications along with methods used for assessing the many optical, thermal, mechanical and laser properties is presented. A detailed survey of spectroscopic methods used for the firstorder approximation of laser performance from Er3C - and Nd3C -doped glasses is given. A few critical considerations for high-quality laser glass and components manufacturing is given in the final sections.
40.5
Commercially Available Er3C -Doped Glasses ......................... 1387
40.6
Estimating Refractive Index ............. 1388
40.7
Glass Melting and Measurements for Bulk Material Properties Characterization .............................. Calculation of the Nonlinear Refractive Index at Emission Wavelength.................... Measuring Temperature-Dependent Refractive Index Change, dn=dT ........ Determination of the Hydroxyl Content in Glass ............................... Composition and Active-Ion Concentration Analysis......................
40.7.1
40.7.2 40.7.3 40.7.4 40.8 40.8.1 40.8.2
40.1 40.1.1 40.1.2 40.1.3
Short Introduction to Lasers ............. Rare-Earth Elements for Laser Emission ............................ Glasses versus Crystals ...................... What Is a Laser Glass? .......................
1380 1380 1382 1383
40.2
Commonly Used Lanthanide Elements in Glasses for Lasers ........................ 1384
40.3
Specification of Laser Glass Doping Level .............. 1385
40.4
Rules of Thumb in Glass Selection for Performance .............................. 1386 The Laser Performance Figure of Merit 1386 Thermal and Mechanical Performance Figure of Merit ................................. 1387
40.4.1 40.4.2
40.9 40.9.1 40.9.2 40.9.3 40.9.4 40.9.5
1389 1390 1390 1390 1391
Derivation of Laser Performance Related Properties ........................... 1391 Fluorescence Lifetime Measurements ................................. 1391 Deriving Laser Properties for Laser Glasses............................... 1392 Laser Damage Testing ...................... Transient Thermal Effects .................. Surface Damage ............................... Self-Focusing Damage ...................... Multiphoton Induced Damage ........... Point Defect Laser Damage ................
1396 1396 1397 1397 1398 1398
40.10
Storage and Handling of Laser Glass .................................. 1399 40.10.1 Methods to Enhance Component Strength......................... 1399 40.10.2 Liquid Cooling of Laser Glasses .......... 1399 40.11
Summary ........................................ 1399
References................................................... 1400
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_40
Part F | 40
Laser Glasses 40. Laser Glasses
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Part F | 40.1
40.1 Short Introduction to Lasers At the time of its discovery in 1960 [40.1], the laser was a “solution looking for a problem”. It has since become one of the most significant inventions of the 20th century. At present, laser-based technologies are ubiquitous and essential to all areas of modern life. Unlike sunlight or lamplight, laser beams typically exhibit a high degree of spatial and temporal coherence, that is, narrow bandwidths and low divergence. As a result, laser radiation can traverse long distances and can focus to the diffraction limit for producing large irradiance intensities. Laser light can be continuous or can be delivered as a pulse of short durations (nanoseconds, picoseconds and femtoseconds) at various repetition rates. Numerous applications take advantage of these coherent, intense light fields for advancing science, medicine, communications, manufacturing and other technologies. The term laser, first coined by Gordon Gould [40.2], is an acronym for light amplification by stimulated emission of radiation. A laser is very much analogous to an electronic oscillator, where an amplifier is excited to oscillations by feedback coupling. In the case of the laser, the laser-active atoms in a gain medium are excited using a pump light source to achieve population inversion. Population inversion means that more atoms of the laser medium occupy the upper excited states than the lower or ground states. This is a necessary condition for laser oscillation to begin and amplify to gain saturation (gain equals losses). Thus, a laser is also an oscillator or a resonator. A laser oscillator consists of three basic components. First is a laser medium capable of producing amplification or laser gain. Second is a mechanism for generating excited states within the gain medium to reach population inversion. This is often a light source such as a flashlamp or diode. Finally, mirrors select the frequency for oscillations, gain amplification, and outcoupling. One of the mirrors is a total reflector and one is a partial reflector for outcoupling. Figure 40.1 is a simple schematic of a laser resonator. For the interested reader, references [40.3–5] provide detailed, theoretical treatment on lasers physics and related technologies. Pump light source (flash lamp or diode)
Laser beam
Laser medium Full reflector
Output coupler or partial reflector
Fig. 40.1 Components of a typical laser
The first demonstrated laser used a ruby crystal (Al2 O3 :Cr) as the laser gain material [40.1]. Since then, scientists have produced laser emission from a variety of gain configurations. Today, the most common types of lasers are bulk solid-state, fiber, semiconductor and gas-based. Of these, bulk solid-state lasers (SSLs) are a preferred class, especially for high peak power and high average power generation due to technological simplicity and economical power scaling. At the heart of a bulk SSL is a crystalline or amorphous material doped with transition metal ions or rare-earth elements. The focus of this chapter is a special subset of gain materials used for bulk solid-state laser emission, namely multicomponent glasses. Fiber lasers may be considered a subset of solidstate laser; however, the material and manufacturing properties required to enable gain fibers differ significantly from that of the solid components. As a result, a treatise on the materials for fiber lasers is not included. References [40.3–11] provide a deeper overview of fiber laser technology, materials, and current state of the art in the fiber laser and materials arena.
40.1.1 Rare-Earth Elements for Laser Emission Solid host materials doped with elements from the lanthanide (Ln) series in the periodic table remain the most heavily utilized method for laser gain in solid-state lasers. The lanthanides are thirteen elements following lanthanum in the periodic table and are the rare-earth ions for their unusual electronic configuration [Xe] 4fn with n D 1 13. In most host materials, Ln ions exist as trivalent ions. The 4f electrons contribute strongly to the optical emissions and couple weakly to the host structure. By LS coupling and Hund’s rules, the large number of electrons contribute to orbital angular momentum, producing numerous fine-structure states with many energy levels. Dieke [40.12] completed the original calculations of the Ln energy levels with finestructure splitting and Carnall et al. [40.13] refined it further. Figure 40.2 [40.14], adapted from the early works of Dieke and Carnall, shows the multitude levels possible from Ln ions and illustrates the difficulty in populating a single energy level. Energy separation is comparable to thermal energy and the electron population is distributed among levels with similar energy. The electric dipole transitions or vibronic coupling within the unique Ln 4f orbitals give rise to f–f transitions, which are symmetry forbidden (selection by the Laporte rule). Electrons can transition from low-energy state to a high-energy state as a result, a necessary con-
Laser Glasses
G
7/2
D 5/2
9/2
1
S
2
2
1/2
0 2
2
40
I 13/2 3/2 3/2 17/2 11/2
F 7/2 9/2
7/2 5/2
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6
I
2
2 7/2
P 3/2
0
5/2
5/2 7/2
17/2
30
11/2 3/2 2
2 3
P2
1/2
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F 3/2 G 5/2
K6 F5
G
2
4
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15/2 9/2
4
2
F
6
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6
3
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F5/2 Ce
H4 Pr
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6
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5
9/2 7/2
13/2
5
3
7
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4
I9/2 Nd
5 I4 Pm
6
H5/2 Sm
H 11/2 3/2
4
5
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3
4
3
F2 3
5
I
3/2 5/2
4
7/2
5
H
I 9/2
H 5/2
4 5/2
11/2 3
H5
6
7/2 5/2
8
15/2
G4
7/2
↑4S
6
1
5/2 3
9/2
2 6
G 9/2
5
4
3
D2
5
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3/2
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1
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5
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P 3/2
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4 2 3 2 1
7/2
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2
1 0 6
2
1
5
F 9/2
1
D
4 3
4
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G
7/2
4
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5 10 3
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11/2
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3/2
5
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3
0
D
↑5D
6 3
1 2
1/2
1
2
1
P2
5/2 7/2
5
7/2
P 3/2
↑2P
4
6
3/2 9/2
3
H 9/2
3 4
11/2 7/2
0 1 2 3 4
6 5 4 3 2 1 7
F0 Eu
3
13/2
11/2
F4
7 13/2
5
8 S Gd
7
F6 Tb
6
H15/2 Dy
5 I8 Ho
4
I15/2 Er
3
H6 Tm
2
F7/2 Yb
Fig. 40.2 Dieke diagram showing the energy levels of the trivalent rare-earth element (REE) ions arising from their 4fn
electron configurations [40.12, 13]. The bars represent closely packed transition levels
dition for population inversion. Photon pumping can activate the f–f transitions in the trivalent Ln ions enabling electrons to populate higher energy states. The decay of electrons from these excited states to the
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Energy (×103 cm –1) 50
40.1 Short Introduction to Lasers
ground state is comparatively slow, which makes it possible to achieve the population inversion required for gain saturation. In recent years, Nd- and Er-doped glasses have been prevalent in solid-state lasers. In this
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Part F | 40.1
chapter, an overview of these multicomponent glasses from the scientific and manufacturing perspective is given.
40.1.2 Glasses versus Crystals By definition, glass is an amorphous solid. Long-range periodicity does not exist in the atomic structure of a glass [40.15]. In contrast to glass, crystalline materials exhibit symmetric and repeating atomic structures. Figure 40.3 shows the atomic arrangement of SiO2 as an amorphous solid (fused silica) and as a crystalline solid (quartz). Atomic arrangement variations of the same elements, as shown, result in vastly different material properties. Table 40.1 provides a comparison of a few well-known material properties of crystalline SiO2 and glassy SiO2 , along with the N-BK7 multicomponent borosilicate glass from SCHOTT. Chapter 33 of the Handbook of Optics (Vol. IV) gives a more detailed treatment on the properties of glasses and crystals [40.16]. As shown, the crystalline order brings about higher thermal strength (high thermal conductivity) because of the strong bonds, which is very attractive for many applications that require it. A disadvantage is that some of these properties vary with the plane of symmetry, such as the coefficient for thermal expansion, which causes optical distortions requiring spatial filtering. The hardness properties may make crystalline materials brittle, which is challenging for machining and processing. Finally, crystal growth is a slow process where large-scale manufacturing can be difficult and expensive. Doping crystalline materials (adding impurities into the crystal structure) is one way to produce desirable properties for technical applications. Unfortunately, the achievable doping concentrations are typically low due to the strong bond strengths of the crystal lattice. Doped a)
Table 40.1 Common material properties of crystalline SiO2 , fused SiO2 , and N-BK7 glass Material property Refractive index (at 633 nm) Coefficient of thermal expansion (106 =ı C) Thermal conductivity (W=.m K/) dn=dT (106 =ı C) Density (g=cm3 )
Crystalline Fused silica quartz .SiO2 / .SiO2 / 1:5 1:45
N-BK7 glass 1:5
7:1
0:56
8:3
10:7
1:4
1:1
5:5
C12:9
1:86
2:6
2:2
2:5
crystals often exhibit concentration gradients, which can be a disadvantage when homogeneity of ionic distribution is a requirement for high-power solid-state laser gain components. Lanthanide-doped crystals are typically used in laser applications that need high repetition rates. Ndand Er-doped yttrium aluminum garnet (YAG) crystals are the most commonly used SSL gain materials in the world. The high thermal conductivity of the YAG, coupled with ease of manufacturing and handling, make it possible for high-energy laser outputs and high repetition rates. One limitation is thermal lensing during laser operations, which often leads to beam quality issues needing secondary filtering. For Ln ions, the crystal field or the chemical environment within which the ions occupy affects the f–f transitions. Observed emission bands for Ln3C in glass compared to the Ln3C in YAG or other crystals exhibit differences in emission peaks, widths, and decay times, all of which matter to the production of lasers [40.17]. When compared to crystals, the thermal and mechanical strength of glass is lower, as shown in Ta-
b)
Fig. 40.3a,b Two-
O Si
dimensional (2-D) comparison of the chemical structures of (a) an amorphous solid made of silicon dioxide glass and (b) a crystal of silicon dioxide quartz. After [40.15]
Laser Glasses
40.1.3 What Is a Laser Glass? Laser glass is a subset of transparent glasses, which exhibits the ability to amplify light by stimulated emission of radiation in the solid-state laser class. In its most common form, it is a multicomponent oxide glass doped with a lanthanide ion such as neodymium (Nd), erbium (Er), ytterbium (Yb), holmium (Ho) or thulium (Tm). In the past, the dominant application for laser glass was in large laser systems for inertial confinement fusion research and weapons physics [40.20, 21]. Today, these materials have found their way into a number of commercial, medical and defense applications. Leading examples involve the field of laser shock peening [40.22], cosmetic skin treatments [40.23] and laser rangefinding [40.24]. Laser glass manufacturing and development is a mature field that has evolved over the last decades. Many glass compositions and/or processing details have already been identified, enabling customization of properties for many situations [40.25]. For example, high peak power lasers require specific properties tailored to produce the highest possible stored energy and extraction efficiency resulting in high peak powers in single shots separated in time. Repetition rates of such systems are at most a few Hz or one to several laser shots per day. High average power (HAP) applications, on the other hand, require repetition rates in the range of
120 Hz from glasses. Generally, such laser systems require aggressive cooling to remove heat deposited into the glass during repeated optical pumping. In addition to good laser properties, glasses designed for HAP lasers possess enhanced thermomechanical properties where high thermal loading is a requirement. Since compositions matter significantly to laser emission from lanthanide-doped glasses, categorizing compositions is a need. Lawrence Livermore National Laboratory (LLNL) established a catalog for Nd-doped glasses in the 1980s, which serves as a reference for the laser community for Nd-glass laser designs [40.26]. This catalog provides the laser, optical, physical, thermal, mechanical properties and compositions of all known laser glasses including an overview of measurement methods utilized. The main glass former (largest amount of chemical compound) in a glass recipe categorizes the numerous laser glass compositions identified to date. Most common glass formers are oxides such as SiO2 , B2 O3 , GeO2 , or P2 O5 , which form continuous random networks [40.15] in a given glass structure. The first laser glass to be identified was a glass based on silica (SiO2 , commonly called a silicate glass) [40.27]. There are glasses based on other glass-forming systems, as well as glasses that contain in addition, or in place of oxygen, other anions such as fluorine, chlorine or bromine [40.26]. Today, the multicomponent glasses of greatest commercial value for lasers are phosphate based .P2 O5 /. These compositions are essentially free of any silica .SiO2 / and glasses are available in high optical quality from a number of commercial vendors with a wide range of dopants and doping levels. Phosphate laser glasses demonstrate superior laser performance and resistance to laser damage when operated in high fluence applications [40.28]. For the development of the LLNL National Ignition Facility (NIF), one of the key requirements was the development of platinum-free Nd-doped phosphate glass [40.29]. Platinum (Pt) inclusions arriving into the glass during manufacturing can significantly alter the laser damage threshold of the final component. Removing these Pt particles from phosphate systems required significant research focus. Efforts here resulted in processing methods that demonstrated ten-times improvement in damage thresholds with Pt-free manufacturing [40.30]. To date, phosphate glasses are the only systems demonstrated for Pt-free glass manufacturing for continuous and discrete melting. Through the selection of various dopant ions, either alone or in combination, a wide range of laser wavelengths are possible from lanthanide-doped glasses. Many Ln ions do not have absorption bands in the visi-
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ble 40.1. Regardless, it is extremely durable under most environmental conditions. Lacking in grain boundaries that result in scattering losses, glass is highly transparent. Glass properties are a function of composition and/or processing conditions. One can use any element in the periodic table to modify its optical and physical properties. Index homogeneities to the sixth decimal place with better than 99:0% transmittance is achievable with process control for certain glasses in the ultraviolet to visible part of the electromagnetic spectrum [40.18, 19]. For optics manufacturing, glass softens when heated above its transition point making forming and shaping easy. Manufacturing techniques such as grinding, polishing, and coating can produce even higher transparencies in a glass component when compared to bulk glass. Glass catalogs available from major manufacturers often contain more than 120 types of glasses. The variety, durability, and flexibility resulting from the amorphous nature of glass makes it possible for its widespread use in all sectors of life. Up to 90% of the optical materials in systems are glass. In comparison, crystals are mainly optical windows rather than optical elements in many systems.
40.1 Short Introduction to Lasers
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Part F | 40.2
Table 40.2 Laser wavelengths from selected active ions in
glass
Energy 4
Active Approximate emission ion wavelength ( m) Nd3C 0:93, 1:06, 1:35 Er3C Yb3C Dy3C Sm3C Ho3C Tm3C Tb3C Pr3C
1:30, 1:54, 1:72, 2:75 1:03 1:32 0:65 0:55, 1:38, 2:05 0:80, 1:47, 1:95, 2:25 0:54 0:89, 1:04, 1:34
G11/2
Sensitizing ions
2
T1 (t22g e1g)
Cr3C , Mn2C , Ce3C , Eu3C , Tb3C , U3C , Bi3C Cr3C , Yb3C , Nd3C Nd3C , Cr3C – – Er3C , Yb3C Er3C , Yb3C Ce3C , CuC –
H9/2
F3/2, 4F5/2 4 F7/2 2 H11/2 4 S3/2
4
4
4
T2
4
F9/2
4
I9/2
2
F5/2
4
I11/2
4
I13/2
1.54 μm
ble region, which makes laser pumping with flashlamps difficult. One way to mitigate the low absorption is by adding other elements (Ln or transition metal elements) into the glass composition as sensitizers. Sensitizing ions have the ability to absorb pump radiation and transfer the absorbed pump energy to the lasing ion, which increases the efficiency for gain saturation and increases laser output. Table 40.2 lists typical laser wavelengths available from common glass hosts along with common sensitizing ions. As previously stated, emission wavelength is a function of glass composition, thus the values in the table serve as a rough guide only. In glasses with multiple laser-active ions, generally one or more ions take the role of sensitizer where they transfer absorbed energy to the primary lasing ion. It is possible to incorporate sensitizers in large concentrations for improving laser output efficiencies in glasses (up to 60% of the
2
4
A2
Cr
3+
Fig. 40.4 Er
Yb
3+
4
F7/2
I15/2
Yb
3+
Er
3+
3C
emission at 1540 nm, sensitizing with Cr3C and Yb3C to improve laser efficiency since Er has very few absorption bands in the visible region for pump light absorption. Yb3C can be included in large amounts (10s of wt%), has large absorption cross-section at 980 nm for diode pumping, and adds energy storage capacity for the laser pulse, and Cr3C has broad visible absorption for capturing flashlamp energy
glass composition in some cases). Solubility to rareearth limits the concentrations in a given glass structure, where the glass stability is impacted and devitrification is observed beyond a given amount. The classical case is the codoping of Er with Yb and Cr, where Cr and Yb transfers energy to Er for 1540 nm emission (Fig. 40.4).
40.2 Commonly Used Lanthanide Elements in Glasses for Lasers A significant number of applications today use laser glasses doped with Nd and Er in a phosphate or a silicate matrix. As such, the scope of the discussion in this chapter is limited to these two lanthanide ions. As discussed previously, phosphate laser glasses can be manufactured platinum free. Moreover, the highest laser efficiencies are demonstrated for Ln ions incorporated into a phosphate matrix when compared to any other glass systems, which makes phosphate glasses the most common in glass lasers. In the past, the need for high optical quality gain materials in large formats for high-power, high-energy research lasers ensured Nd was the most common dopant and lasing ion; with flashlamp pumping as the most economical. Today, retina-safe wavelengths from
Er-Yb codoped glasses are widely used in the medical (laser hair removal, tattoo removal, wrinkle removal) and in the defense sector for rangefinding, sensing, and light detection and ranging (LIDAR). Either flashlamp or laser diodes are used as pumps in Er-Yb glass lasers. For medical and defense applications, high efficiency from lasers in the retina-safe region (called eye-safe) in the range between 1400 and 1800 nm is of high importance. This wavelength region coincides with the low loss window of fused silica fibers used for optical fiber communications (S and C bands) near 1500 nm. For lasers in medicine, laser wavelengths need to overlap the absorption bands from hemoglobin, melanin, and water in the tissues. High absorption of laser wavelengths above 1400 nm makes rapid thermal
Laser Glasses
Fig. 40.5a,b Laser glasses: (a) Nd-doped phosphate glasses, (b) ErYb-Cr-doped glasses. Courtesy of SCHOTT Advanced Optics
b)
heating below the skin possible (without much damage to the skin itself), which is useful for aesthetic and surgical treatments with lasers. Figure 40.5 shows representative laser glass components with the largest being a slab of more than 1 m on its diagonal axis as used in high peak-power laser fusion research. Also shown in Fig. 40.5b are the erbium-
doped glasses for cosmetic and defense applications. In comparison to Nd-doped glass components, the Er laser components are a fraction of the size. The formats of components shown in Fig. 40.5 are not in any way comprehensive. The sizes, shapes and concentrations required for each component is as varied as the number of laser designs that exist.
40.3 Specification of Laser Glass Doping Level A common problem in the identification of the optimal laser glass composition is the selection of doping level of the lasing species or other sensitizing ions. Laser-active ion concentrations are largely driven by two factors: the requirement for pump uniformity over the entire laser glass volume while avoiding the phenomenon called concentration quenching. Concentration quenching occurs when two neighboring ions in the glass can exchange energy between them resulting in a reduction in laser level population. There are two mechanisms by which concentration quenching occurs. The first mechanism is the migration of excitation energy from one ion to the next. The second is cross-relaxation where one ion shares its energy with the nearest neighbor [40.31–33]. Figure 40.6 shows the effect of concentration quenching for neodymium where the lifetime of the excited state used in the laser transition decreases with dopant level for some representative neodymium-doped laser glasses. An estimate of the effect of concentration quenching is 0 n i ; Dh 1 C NQ
(40.1)
where is the lifetime at neodymium concentration level N (in units of 1020 ions per cm3 ), 0 is the effective lifetime for a negligible doping level in the glass and Q is a concentration quenching factor that correFluorescence lifetime (ms) 600 550
Silicate
500 450 400 350
Phosphate
300 250 200 0.10
1 10 Nd ion concentration (1020 cm –3)
Fig. 40.6 Typical concentration quenching curves
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Part F | 40.3
a)
40.3 Specification of Laser Glass Doping Level
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Optical and Photonic Glass Applications
Part F | 40.4
Table 40.3 Guidelines for neodymium dopant level for
Table 40.4 Rare-earth active-ion content conversion fac-
various rod diameters
tors
Rod diameter (mm) 5 57 610 913 1216 1520 2026 27
Nd concentration in phosphate laser glass (wt% Nd2 O3 ) 8:0 6:0 4:0 3:0 2:5 2:0 1:5 1:0
Nd concentration in silicate laser glass (wt% Nd2 O3 ) 3:5 3:0 3:0 3:0 3:0 2:0 2:0 2:0
sponds to the doping level at which the lifetime value falls to 1=2 of 0 . The value of n is generally equal to 1 or 2, and depends more on the amount of data available to determine the fit to (40.1) than on material considerations [40.31]. For Nd-laser glasses, Table 40.3 provides a rough guideline for dealing with pump uniformity, which lists typical doping levels as a function of laser rod diameter for flashlamp pumped Nd-laser systems. Nominally, uniform excitation of the complete active volume in a laser occurs in these cases. The concentration quenching effect also varies with glass type where it is less prominent in phosphate compositions than in silicate glasses. Table 40.3 also lists different optimal doping levels for both the silicate and phosphate glass types. The data in Table 40.3 is from laser performance data collected over a number of years. Rare-earth ion concentrations in laser glasses are reported in a number of ways. The most common spec-
Rare earth cation Nd Er Yb Tm Ho Pr
F 0:358 0:315 0:306 0:313 0:319 0:402
ification is expressed as ions per cubic centimeter. It is straightforward to convert between these two values if one knows the density of the glass. For the case of various lanthanide cations, the following conversion formulae between lanthanide ion density, in units of 1020 cm3 , and weight percent of the lanthanide oxide is used Ln3C ion density D F.wt% Ln2 O3 / (40.2) wt% Ln2 O3 D Ln3C ion density=.F/ ; (40.3) where is the glass density in g=cm3 and the value of F for a number of common rare-earth elements is given in Table 40.4. For laser ions other than Nd, the tables and data may roughly hold true. To date, detailed analyses are not completed. Note that Table 40.3 only deals with the flashlamp pump cases. When you pump gain materials with diode lasers, the concentrations needed may be different. In the case of Er-Yb glasses, the pump schemes and q-switch methods significantly influence laser thresholds and efficiencies [40.34].
40.4 Rules of Thumb in Glass Selection for Performance Laser designers select glasses based on a defined material property space. Glasses need to meet many requirements beyond laser properties to be suitable for applications. Entire system-level considerations are necessary because active laser properties and stress management at the glass cladding interface drive laser performance. A set of predictive tools called figure of merits (FOMs) exist for quick identification of appropriate glasses from material and laser properties. These FOMs aided material scientists in identifying the best glasses during product development cycles. Most laser systems require a best balance of the two FOMs.
40.4.1 The Laser Performance Figure of Merit Figure of merits are determined from measured and calculated properties of a glass. Detailed discussion on these measurements and spectroscopy is presented in the following sections. For each laser glass, laser performance is a function of emission bandwidth, the potential for high population inversion, and the decay time of the laser level. Then, having a large value of the following laser figure of merit, FOMlaser , FOMlaser D
Q ; n2
(40.4)
40.5 Commercially Available Er3C -Doped Glasses
Laser Glasses
Cross-section for stimulated emission (1020 cm2 ) Concentration quenching factor (1020 cm3 ) (n D 2 in (40.1)) Nonlinear refractive index (1013 esu) Fracture toughness (MPa m1=2 ) Thermal conductivity (W=.m K/) Poisson’s ratio Thermal expansion (106 K1 ) Young’s modulus (GPa) Refractive index at 1060 nm dn=dT2040 ı C at 1060 nm
SCHOTT LG-760 4:5
SCHOTT LG-770 3:9
SCHOTT LG-750 3:7
HOYA LHG-80 4:2
HOYA LHG-8 3:6
KIGRE Q-88 4:0
10:0
8:8
7:4
10:1
8:4
6:6
1:02 0:47 0:60 0:27 15:0 53:7 1:508 6:8
1:01 0:48 0:57 0:25 13:4 47:3 1:499 4:7
1:08 0:48 0:60 0:26 13:2 50:1 1:518 5:1
1:24 0:46 0:59 0:27 13:0 50:0 1:534 3:8
1:12 – 0:58 0:26 12:7 50:1 1:521 5:3
1:14 – 0:84 0:24 10:4 69:8 1:536 0:5
HOYA HAP-4 3:6 – 1:21 0:83 1:02 0:24 7:2 70 1:534 1:8
KIGRE QX-Nd 3:34 – 1:17 – 0:85 0:24 8:4 71 1:530 1:0
Table 40.6 Properties of laser glasses capable of rep-rated operation, Nd3C
Cross-section for stimulated emission (1020 cm2 ) Concentration quenching factor (1020 cm3 ) (n D 1 in (40.1)) Nonlinear refractive index (1013 esu) Fracture toughness (MPa m1=2 ) Thermal conductivity (W=.m K/) Poisson’s ratio Thermal expansion (106 K1 ) Young’s modulus (GPa) Refractive index at 1060 nm dn=dT2040 ı C at 1060 nm
implies a higher laser performance where is the cross-section for stimulated emission and Q is the concentration quenching factor (40.1), which together are a measure of the laser gain available in the glass. n2 is the nonlinear index, which is a measure of glass weakness to resist damage when transmitting a high-intensity pulse of laser light. Expected values for these, for a few commercial laser glasses, are in Table 40.5.
40.4.2 Thermal and Mechanical Performance Figure of Merit Multiple shots per second (repetition rate) operation of glass laser systems necessitate increased thermal and mechanical strength along with good laser perfor-
SCHOTT APG-1 3:35 16:7 1:13 0:60 0:83 0:24 7:6 71 1:529 1:2
SCHOTT APG-2 2:39 10:6 1:02 0:67 0:86 0:24 6:4 64 1:503 4:0
mance. Having a large value for the FOMlaser and the thermal and mechanical figure of merit, FOMTM , is necessary. The FOMTM is defined as FOMTM D
K1C .1 / ; ˛E
(40.5)
where K1C is the fracture toughness, is the thermal conductivity, is the Poisson’s ratio, ˛ is the thermal expansion and E is the Young’s modulus of the glass. Table 40.6 gives thermal and mechanical properties for typical high average power commercial laser glasses, along with their laser properties as discussed previously. For the preparation of fiber lasers and amplifiers, fiber drawing is possible for the glasses described.
40.5 Commercially Available Er3C -Doped Glasses Erbium-ytterbium (Er-Yb) glasses, with and without Cr and Ce, are available commercially. Cr3C has broad emission bands in the visible spectrum, and is a sensitizer for Er, as described previously. Ce3C is in-
corporated in small amounts to prevent solarization (or browning) during high-power flashlamp pumping. Some formats of these glasses used in lasers are in small rod form, where they are less than 6 mm in diameter
Part F | 40.5
Table 40.5 Properties of laser glasses utilized for high peak powers, Nd3C
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Optical and Photonic Glass Applications
Part F | 40.6
Table 40.7 Commercialized Er-Yb laser glasses
Glass former Emission cross-section (1020 cm2 ) Peak emission wavelength (nm) Fluorescence lifetime (ms) Refractive index at 587 nm Dispersion Density (g=cm3 ) Linear coefficient of thermal expansion (106 K1 ) Glass transition temperature (ı C) Thermal conductivity (W=.m K/) Young’s modulus (GPa) Poisson’s ratio Indentation fracture toughness (MPa m1=2 ) Knoop hardness number
SCHOTT LG-940 P 2 O5 0:77 1535:1 9:4 1:54 61:84 3:1 12:0 456 0:6 58 0:26 0:61 380
and 100 mm in length. Typical sizes for the eye-safe laser components are square rods below 5 mm, which are sometimes 100 m in thickness. Planar waveguide structures are fabricated from integrated optic glass (IOG) glasses using ion exchange in a molted KNO3 or AgNO3 salt bath [40.35]. The ion exchange struc-
SCHOTT LG-960 P 2 O5 0:67 1535:4 9:8 1:54 62:62 3:1 9:3 503 0:7 65 0:25 0:68 431
SCHOTT IOG-10 SiO2 0:58 1536 17:8 1:53 56:6 2:7 9:3 569 0:92 71 0:24 0:71 520
SCHOTT IOG-2 P 2 O5 0:8 1533 9:0 1:52 66:8 2:7 12:5 375 0:6 54 0:27 0:47 340
KIGRE QX-Er P 2 O5 0:8 1535 7:9 1:53 63:7 2:7 – 470 – 67 0:24 – 435
KIGRE MM-2 P 2 O5 0:8 1535 7:9 1:54 – 2:7 – 506 – – 0:24 – 435
turing technique uses initiation temperatures below the transformation point of the glass, which is the temperature at which glass deforms under its own weight. Table 40.7 contains other associated properties for ErYb-containing glasses.
40.6 Estimating Refractive Index Glass manufacturers typically report refractive index and dispersion as measured at wavelengths near 587:6 nm. It is a common requirement to estimate the refractive index of laser glass at additional wavelengths, for example for purposes of coating design at a pump or lasing wavelength. In addition, refractive index is a function of doping identity and content, so that catalog index values and those listed here in Tables 40.5, 40.6 and 40.7 are only rough guides. For this, a useful relationship for the refractive index at different wavelengths, n./, is [40.26] n./ D nD
nD 1 1:5079 5:2364 105 2 VD 2
;
(40.6)
where nD is the refractive index at 589:3 nm. The optical dispersion or the Abbe number, VD is given by VD D
nD 1 ; nF nC
(40.7)
and nF is the index at 486:1 nm, nC is the index at 656:3 nm, and is in nm [40.36]. The accuracy of (40.6) is ˙ 0:001 when glass index measurement accuracy is better than ˙ 0:0001. High optical quality,
high-homogeneity glasses are often in this range. There is no applicable wavelength range provided [40.26]. Alternatively, a similar equation based on index data measured at the Helium d-line at 587:6 nm is the following nd 1 1:5079 523640 n./ D nd (40.8) ; Vd 2 where nd is the refractive index at 587:6 nm, Vd is given by .nd 1/=.nF nC /, nF is the index at 486:1 nm, nC is the index at 656:3 nm, and is again in nm. Equation (40.8) is expected to be accurate to ˙ 0:003 for IR wavelengths up to 2:3 m in the cases where index measurements are accurate to ˙ 0:00002. The v-block refractometer and the spectral goniometer are two methods for measuring refractive indices. Figure 40.7 shows the principle of the v-block measurement. Glass samples about 20 20 5 mm are placed in a v-shaped block prism where the refractive index of this prism is known to high precision. The refraction of an incoming light beam depends on the refractive index difference between the sample and the v-block prism. The advantage of this method is that up to ten samples can be glued together into one v-block stack and many samples can be measured
Laser Glasses
Optical axis
Immersion oil Sample nsample
θ
Sample with lower refractive index
nv-block
Fig. 40.7 v-block refractometer principle (after [40.36])
J
nair
Incident light ray at wavelength λ
v-block-prism with precisely known index of refraction
in a very short time with a high relative measurement accuracy. Standard measurement temperature is 22 ı C [40.36].
The highest accuracy index measurement is the spectral goniometric method [40.36], where the angle of minimum refraction in a prism-shaped sample is measured. With the automated spectral goniometer, the ultraviolet to infrared refractive index measurement system (URIS), the refractive index of optical glasses are measured to an accuracy of ˙ 0:4 105 . The measurement accuracy for the dispersion .nF nC / is ˙ 2 106 . These measurement accuracies are independent of the glass type and over the complete wavelength range from 185 to 2325 nm. The samples are prismshaped with dimensions of about 353525 mm3 . The standard measurement temperature is 22 ı C.
40.7 Glass Melting and Measurements for Bulk Material Properties Characterization The highest quality raw glass needs to be qualified for performance before the fabrication of all precision laser components. Thus, a critical part of the components fabrication requires characterization of the laser glasses for all of the optical, mechanical, physical, and laser properties required. The next sections outline how this is typically accomplished. Standard glass production first involves liquefying powdered oxide raw materials in a refractory crucible. This process is called melting. The selection of the crucible material depends on the reactivity of the liquid melt to the crucible, both at high temperatures above 1000 ı C and at various points in the process. Phosphate batches used for laser glasses are highly reactive during the initial stages of melting, which leads to strong incorporation of platinum particles and other ions into the melt. The use of fused silica crucibles circumvents this problem to a degree. Unfortunately, liquid glass reacts with fused silica and quartz. Resulting dissolution of the crucible into the melt causes inhomogeneities (striae patterns) leading to low transmitted wavefront quality in a component fabricated from such a glass. Moreover, the material properties may change depending on the amount of SiO2 incorporation. Figure 40.8 shows a shadowgraph picture of striae within N-LAK8 exhibiting a frozen convection pattern [40.37]. Controlling material properties, then, is essential to guaranteeing required performance of a material in an optical system. Optical system designs require that optical parameters do not vary beyond a given criterion. Besides optical properties, many other properties are
also collected to monitor glass as a standard practice. The following paragraphs provide a brief overview of these properties and the methods used to collect them. Most of these measurements are common to the glass industry and detailed descriptions are available in many literature examples. Refractive index from each glass is determined using a standard v-block method described previously. This index is used to calculate values for dispersion, Vd , refractive index at the lasing wavelength and the nonlinear refractive index, n2 . Other characterizing optical metrologies include a transmission spectrum, Fourier-
Fig. 40.8 Shadowgraph picture of striae within N-LAK8 exhibiting a frozen convection pattern. From [40.37], courtesy of SCHOTT Advanced Optics
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Part F | 40.7
Sample with higher refractive nair index
40.7 Glass Melting and Measurements for Bulk Material Properties Characterization
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Optical and Photonic Glass Applications
Part F | 40.7
transform infrared (FTIR) spectrum for gaging the hydroxyl content in the glass, and the temperaturedependent refractive index difference, dn=dT. Typically, an ultraviolet-visible spectrophotometer records absorption in the region from 400 to 2500 nm. Detailed descriptions of both hydroxyl absorption and dn=dT measurements are in the next section. Thermal and physical properties are measured for every glass manufactured in order to monitor compositional stability along with the optical index and dispersion. These include density, coefficient of thermal expansion, and glass transition temperature. Additionally, thermal conductivity, Poisson’s ratio, Knoop hardness, Young’s modulus, indentation fracture toughness, weight loss in water, and softening points etc. can also be monitored as needed. Density is determined using the well-known Archimedes method with a standard accuracy of ˙ 0:003 g=cm3 . Coefficients of thermal expansion and the glass transformation point (Tg ) are determined using dilatometric analysis. Dilatometric beam bending (three-point) and softening-point methods are used to determine the temperature corresponding to particular viscosities, including annealing point (3:16 1015 Pa s), strain point (1 1014 Pa s) and softening point (3:98 108 Pa s). During glass developments, high-temperature rheometry defines the melt viscosity around the working point of the glass (1 105 Pa s). Many individual points have been collected and fitted to the well-known Vogel–Fulcher–Tammann (VFT) model to produce the viscosity curve [40.38–40]. Differential thermal analysis (DTA) determines the relative devitrification stability of each composition. The Vickers indentation method determines the hardness and fracture toughness. Young’s modulus is determined using an impulse excitation technique. Once the glass characterization measurements are completed, the next step is to assess laser-related performance parameters. This starts with emission spectroscopy and fluorescence lifetime determination.
40.7.1 Calculation of the Nonlinear Refractive Index at Emission Wavelength The nonlinear refractive index correlates to the maximum laser fluence through an optical material before damage by self-focusing of the laser beam. The effective refractive index, neff , increases with the electric field intensity, E, of the applied laser beam in a material, according to the equation neff D n C n2 hE2 i ;
(40.9)
where n2 is the nonlinear refractive index. In order to estimate the nonlinear refractive index, the following equation, as referenced from [40.26], is used 2 68.nd 1/ n2d C 2 n2 D h i1=2 ; Vd nVd 1:52 C n2d C 2 .nd C 1/ 6n d (40.10)
where nd is the refractive index at 587:6 nm, Vd is the dispersion, n is the refractive index at 1060 nm, and n2 is in units of 1013 esu.
40.7.2 Measuring Temperature-Dependent Refractive Index Change, dn=dT Temperature-dependent refractive index change is assessed with high accuracy using the index and dispersion measurement methods already described [40.36]. During laser glass developments, high-quality glasses are not often available, thus high precision is not a requirement and an alternative method is used. For a given laser wavelength of interest, dn=dT of a glass over a temperature range from 2530 ı C is measured at that wavelength. A typical method from literature is a solid etalon method, where etalons are prepared from the manufactured glasses [40.41]. Data on the temperature-dependent shift in wavelength of the interference fringe ./ as the temperature is cycled up and down through the temperature range is collected. From this data, the dn=dT of the sample over the temperature interval is calculated using the following equation dn 1 D ˛ n ; dT T
(40.11)
where is the measurement wavelength, T is the temperature (ı C), ˛ is the coefficient of thermal expansion in the temperature region and n is the refractive index at the respective wavelengths. The results of the measurement are reported in units of ppm=ıC with measurement uncertainty less than 0:1 ppm=ıC.
40.7.3 Determination of the Hydroxyl Content in Glass Solid-state laser glasses doped with rare-earth ions producing transitions in the near infrared (near-IR) are influenced by residual hydroxyl (O–H) groups within the glass structure introduced by conventional melt quenching techniques. These groups can nonradiatively quench the laser-excited state. It is well established
Laser Glasses
40.7.4 Composition and Active-Ion Concentration Analysis A significant source of error in the derived laser properties results from the inaccurate active ion concentrations input into the determination of the absorption cross-section. Typically, an input wt%-based concentration is used for derivations. During the glass-making process, high temperatures, volatile components, and other process parameters considerably influence the retained Nd3C content in the glass structure. Thus, it is not appropriate to assume that input concentration is retained in the final glass produced. Compositional changes during manufacturing may shift glass properties as well, as some of these properties are used for the computations. Analytical standards for a given glass type are typically established by dissolving powdered glass in a solvent and then analyzing the solution using an inductively coupled plasma-atomic emission spectroscopy (ICP-AES) instrument. Simultaneous analysis of multiple elements is possible with this method. The detection limit range is in the 0:1 to 10 ppm range. Reliable statistics also require repeated analysis. Once a composition standard is established, subsequent measurements collected use an energy dispersive x-ray fluorescence (XRF) spectrometer. Signal levels are compared relative to this established glass standard in XRF, since this method is precise and fast. Even at ppm-level elemental concentrations, it has been shown that the detected values have uncertainties below ˙5% with XRF analysis, when used relative to the analyzed standard.
40.8 Derivation of Laser Performance Related Properties 40.8.1 Fluorescence Lifetime Measurements Nd3C fluorescence emission lifetime is determined by exciting a 10 mm cube sample with a pulsed laser diode of nominal output at any of the absorbing wavelengths. The sample is prepared with two orthogonal surfaces polished for excitation and off-axis collection of emission and the other six surfaces given a fine ground (60 grit) finish to reduce the tendency of the sample to self-pump by its own emission. Emission signal is recorded with a filtered and amplified InGaAs fast photodetector. Typical values are on the order of several 100 s. Analysis of the raw data can proceed by a variety of paths. First, the data can be screened to identify the time required for the emission intensity to fall to 1=e of its initial peak value, often referred to in the literature as the first e-folding time [40.26]. A second analysis
path is to fit the entire dataset to a best-fit exponential decay. In contrast to crystals, in glasses the two results are not exactly equivalent. Because of the amorphous nature of glass, neodymium sites and nearest neighbors chemically differ from location to location leading to a departure from pure exponential decay. For Er/Yb-doped glasses, sample preparation is identical to the Nd-doped glasses, where 10 mm cube samples are prepared from each melt with two adjacent sides polished and the remaining six sides being finely ground. The samples are excited through one polished face at nominally 980 nm with a laser diode, and emission is collected through the orthogonal polished face. The emission wavelength is not known exactly; it is specified to be between 970 and 990 nm and is a function of electrical power provided to the device. The fluorescence lifetimes of erbium and ytterbium are
1391
Part F | 40.8
that residual hydroxyl in glass has a noticeable impact on the emission lifetime of the upper laser level in Nd3C -doped glasses. This is a direct result of the O–H fundamental vibrational energy being about a quarter of the energy in the 4 F3=2 state, which increases the probability of nonradiative transfer of energy from excited Nd3C to O–H vibrational modes in the glass (i. e., as heat). This is detectable as a reduction in emission lifetime from the expected radiative lifetime. The energy of two O–H stretching vibrations can bridge the energy gap (overlap) of about 6500 cm1 between the ground state, 4 I15=2 , and the first excited state, 4 I13=2 , of the Er3C ion [40.42]. Thus, the presence of hydroxyl impurities in the glass can nonradiatively quench the laser excited state, which will then affect the fluorescence decay of Er3C ions at 1:5 m, resulting in reduced quantum efficiencies of the 4 I13=2 Er level [40.42]. Due to these effects, the residual hydroxyl content is monitored for all glasses produced by utilizing the O–H absorption bands near 3333 cm1 (3:0 m) and 3000 cm1 (3:333 m) that are detectable in an FTIR spectrum. The method assumes proportionality between the concentration of the O–H species and the measured absorption. The amplitude of the hydroxyl absorption at the two previously mentioned wavelengths allows for the estimation of concentration by the Beer–Lambert law. Normally, the ppm-level concentrations in the glass are not explicitly calculated, rather, a value is set for maximum tolerable level for absorption. For a laser-grade glass, the absorption must be less than 2:0 cm1 and preferably less than 1:8 cm1 at the wavelength of 3000 nm regardless of the active ion present [40.26].
40.8 Derivation of Laser Performance Related Properties
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Part F | 40.8
measured separately by selecting 1550 and 1000 nm emitted light with 10 nm full width at half maximum (FWHM) interference filters. Careful analysis of the temporal emission from ytterbium allows for the determination of energy transfer efficiency for glasses doped with both erbium and ytterbium. After the pulse has been absorbed and the excitation pulse removed (defined as t D 0) the 1550 nm emission (assigned to the 4 I13=2 to 4 I11=2 transition in erbium) is observed to decay. The fluorescence lifetime, designated as , is calculated by fitting the data from t D 0 to a point where the intensity has fallen to less than 1=e of its initial value using I.t/ D I0 exp
t
;
(40.12)
where I.t/ is the emission intensity with time, t, and I0 is the maximum emission intensity (at t D 0) [40.34, 43].
40.8.2 Deriving Laser Properties for Laser Glasses Calculations of laser performance-related properties utilizes the appropriate theoretical considerations for the active ion of interest. A short description of the methodologies for deriving laser performance-related properties from doped glasses follows. Most methods originate from cross-section theories and utilize the energy level information known for the given laser ion of interest. Calculation of absorption and emission crosssection, bandwidth, and radiative lifetimes requires measured glass transmission and fluorescence emission from the material of interest. Several mathematical treatments exist for determining laser properties from materials. Judd–Ofelt theory [40.44–47] is the most commonly used method for establishing a first-order approximation of laser action from materials. A brief overview of methods used for deriving laser properties from glasses is given. Deriving Laser Properties for Nd3C Trivalent Nd-doped materials are by far the most commonly used in solid-state lasers. Nd3C has a number of transitions in the visible spectrum enabling broadspectrum pump light absorption. These transitions arise from the three optically active electrons in the partially filled 4f shell. The chemical environment does not affect these transitions as the optically inactive Xe shell of the Nd3C shields the 4f3 shell. As a result, Nd3C is shown to lase in many different types of hosts, whether solid or otherwise.
The Nd configuration is written as [Xe] 4f3 . Even though the three electrons in the 4f shell drive the optical transitions, configuration interactions also have a role in the spectral line strengths. Calculations typically use the Russell–Sanders coupling to determine the electronic terms. Spin–orbit and Coulombic interactions are applied as perturbations before the chemicalfield splitting, which is weak field interaction. Then, the spectroscopic terms for the spin and orbital quantum numbers are found by applying Pauli’s exclusion principle [40.45], and by using Hund’s rule the energies of the upper levels with respect to the ground state are determined. For Nd3C , the ground electronic state is defined by electron orbital angular momentum .l/ and spin angular momentum .s/, totals of these (L and S respectively), and the total angular momentum .J D L C S/. Observed room-temperature spectra of Nd-doped glass is the result of the total spin angular momentum .S/ and total angular momentum .J/ taking on different orientations with respect to the electromagnetic field of the ion (called spin-orbit splitting and Stark splitting). The total number of such an orientation is given by 2S C 1 and 2J C 1, respectively. The term symbols for an electronic state are given by 2SC1 LJ , where a letter is used to denote the value of L (S, P, D, F, G, H, and I for L D 0, 1, 2, 3, 4, 5 and 6). Thus, Nd3C 4f3 vector sums result in L D 6, S D 3=2 and J D 9=2 producing the electronic state term symbol 4 I9=2 , where the multiplicity of the LJ state is 2SC1 D 4. The Nd3C ion ground state is spin-orbit split into four discreet states, each with its own value of total angular momentum, J, of 9=2; 11=2; 13=2 and 15=2 since the sum of L C S is a vector addition. The next energetic electronic state has the term symbol 4 F3=2 . These five electronic states, shown in Fig. 40.9, are responsible for the energy absorption and for the primary emission of the Nd3C ion. Figure 40.9 also illustrate the transitions from the energetic state to the ground state, the energy of which is somewhat modified by the chemical environment of the ion. The most utilized Nd-laser transition is that which terminates to the 4 I11=2 lower state with emission near 1064 nm in crystals and near 1054 nm in multicomponent glasses. The upper and lower electronic states can further split into 2J C 1 levels by Stark splitting, though these are not typically resolved in glasses at room temperature. In glasses, the splitting of the various Stark states along with the chemical environment of Nd3C contribute to the observed emission bandwidth of the laser transition. The electronic states that are higher in energy than the 4 F3=2 state are responsible for the absorption features seen in a typical ultraviolet to visible (UVVis) absorption spectrum (Fig. 40.10). Note that the
Laser Glasses
k=1
f0
2
r 2 f0
3
r 3 f0
4
H9/2 + 4F5/2
4
F3/2
r4 f 0 4
I15/2
4
I13/2
4
I11/2
4
I9/2
Fig. 40.9 Representation of the branching ratios for Nd3C
laser transitions from the same excited state to the terminal state. After [40.44]. k notates emission transitions from a given excited level, f0 represents the terminal level, and ri f0 is the oscillator strength of each transition, where r is the ratio of the oscillator strengths of two transitions Energy (×103 cm –1) H H-like 25
Hcoul
Hso 2
2
D, 2P
2
P1/2
S.aJ W bJ 0 / D
X
˝ t jhaJkU .t/ kbJ 0 ij2 ;
(40.13)
tD2;4;6
Nd absorpion spectrum (phosphate glass)
Hcf
Energy (×103 cm –1) 25
D5/2
4
G11/2
2
D3/2 G 9/2
spectral shape of the emission from lanthanide ions in glasses are additionally influenced by different linebroadening mechanisms [40.25, 26, 45–47]. Thermally activated vibration is the strongest known broadening in glasses. When developing Nd-doped glasses for specific applications, required laser performance modeling requires knowledge of the stimulated emission crosssection. The emission cross-section is directly related to many characteristics of a laser, such as the gain, lasing threshold, output energy, pulse duration and so on. Many methods are available for deriving the stimulated emission cross-section of a gain material. For small sample volumes, the absorption and fluorescence spectra coupled with the Judd–Ofelt treatment is the most widely used [40.45–49] for its elegance and simplicity. The Judd–Ofelt theory for forced electric dipole transitions relates the line strength, S, of a transition between two electronic states as a sum over three terms [40.25, 26, 45–47]
4 4
G
20
2
K
2
G 7/2 2G 9/2 K15/2
4
2
G
2
G 7/2
2
15
2 4
H
H11/2
20
2
G5/2 K13/2
4
4f3
4
F9/2 F7/2, 4S3/2
15
4
4
F, S
2
H9/2
4
F5/2 F3/2
4
10
10
4
I15/2
5
4
I
5
4
I13/2
4
I11/2
4
0
I9/2
0
1
2 3 Absorption cross section (×10 –20 cm 2)
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2
40.8 Derivation of Laser Performance Related Properties
0
Fig. 40.10 The absorption bands from transitions between various electronic states of the Nd3C in the glass (after [40.26]). H-like denotes hydrogen-like single electron, coul notates Coulombic interactions, so denotes spin–orbit interactions, and cf denotes the weak chemical field interactions
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Part F | 40.8
where a and b are the various quantum numbers (S, L, and others) that specify the coupled eigenstates (4f3 states). U .t/ is the irreducible unit tensor operator and the three doubly reduced matrix elements, haJkU .t/ kbJ 0 i, for each transition have been calculated using an intermediate coupling approximation for many transitions of interest and are tabulated in the literature [40.26, 48]. The three ˝2;4;6 coefficients (called the Judd–Ofelt coefficients or the Judd–Ofelt parameters) are found by experiment. Since the matrix elements are a constant for the Nd3C absorption and emission transitions of interest, cross-section calculation uses the absorption bands in a measured ultraviolet-visible spectrum to generate and solve a set of equations (with the three ˝ values as unknowns) [40.26]. Specifically, for the mechanics of the cross-section, abs/em ./, calculations involve measured transmission data covering a wavelength range from 250 to 1200 nm. For Nd3C , there are several bands in the wavelength range of interest (Fig. 40.10). This transmission data is corrected for reflection and absorption cross-sections are calculated using the well-known relationship abs ./ D ln Tc =.d Nd /. The relationship between the line strength and the integrated absorbance of an electric dipole transition is given by Z abs ./d D
8 e N .n C 2/ S ; (40.14) 3ch.2J 0 C 1/ 9n 3 2
2
2
band
where is the center wavelength of the transition, J 0 is the total angular momentum quantum number of the lower state (i. e., 9=2), n is the refractive index, e is the electronic charge (4:803 1010 esu), c is the speed of light in vacuum (2:998 1010 cm=s), and h is Plank’s constant (6:626 1027 erg s). Each of the well-resolved bands in the measured spectrum are integrated and combined with the neodymium input concentration, N , to give line strength values, S, for each transition per (40.14). Combining (40.13) and (40.14) produces a series of equations for the unknown ˝ coefficients (three per transition). The Judd–Ofelt parameters, ˝2 , ˝4 , and ˝6 are solved for by minimizing the standard deviation between the calculated and measured line strength values (least squares fit). Once solved, these Judd–Ofelt coefficients for a given laser glass are used to calculate individual transition probabilities, A.aJ W bJ 0 /, between the upper 4 F3=2 state and the lower four 4 I states using A.aJ W bJ 0 / D
n.n2 C 2/2 64 4 e2 3 3h.2J C 1/ 9 X .t/ ˝ t jhaJkU kbJ 0 ij2 : t
(40.15)
These transition probabilities are then summed over all terminal states to derive the radiative lifetime, RAD , of the 4 F3=2 state and the branching ratios .ˇ/ to the four terminal states X 1 D ŒA .F3=2 W 4 IJ 0 / I ˇ .4 F3=2 W 4 IJ 0 / RAD 0 J
D RAD A .4 F3=2 W 4 IJ 0 / : (40.16)
The next part of the calculations requires a recorded fluorescence emission spectrum, I./, from the material of interest. For Nd emission near 1060 nm, emission is specific to the 4 F3=2 to 4 I9=2 laser transition. Thus, the wavelength range from 1000 to 1200 nm is recorded for glassy materials to cover the entire emission band. This data is used to calculate the line-shape function, g./, by dividing each data point by the integral of the entire emission curve g.i / D R
I.i / : I./d
(40.17)
The line-shape function is related to the emission crosssection values using emm ./ D
4 g./AR ; 8 n2 c
(40.18)
where AR is the relevant transition probability, that is inversely proportional to the radiative lifetime, for the 1060 nm transition. Once emission cross-section is determined, the final step is the determination of the bandwidth of the laser transition. The effective bandwidth, eff , is defined as the integral of the fluorescence intensity curve divided by the intensity at the peak wavelength, Imax , R I./d : (40.19) eff D Imax ./ Note that eff is just the inverse of the peak value of the lineshape function. The bandwidth at full width half maximum .FWHM / is often reported in the literature, which is found by locating the points on the emission cross-section curve where the value is onehalf the peak value and identifying the corresponding wavelength difference. It is worth mentioning that the accuracy of the procedure also depends on the accuracy of the Nd concentration and of the Judd–Ofelt fitting routine. Moreover, note that there are assumptions implicit to the theory and its application that limit the accuracy of the method in amorphous materials [40.49]. Nevertheless, for relative comparisons of spectral intensities within a compositional space, the Judd–Ofelt method is the best approach.
Laser Glasses
6
4
F7/2
5 4
2
3
4
2
4
1
4
H11/2 S3/2
4
F9/2
Phonons 2
e
F5/2
I11/2
I13/2
670 nm
Pump 1.064 μm
550 nm 530 nm 2
g Yb3+-sensitizer
F7/2
4
I15/2
0 Er 3+-acceptor
Fig. 40.11 Energy levels and pathways for energy exchange in a glass doped with Er and Yb
calculations for estimating laser properties ignore many of these interactions [40.50, 51]. Two different methods compute radiative lifetime and cross-sections for stimulated absorption and emission as a function of wavelength for Er- and Yb-doped glasses: the McCumber theory [40.43] and a simplification of Judd–Ofelt theory often referred to in the literature as the Fuchtbauer–Ladenburg relation [40.52–54]. Both techniques allow for a first-order estimation of laser performance from these glasses. A brief description of both techniques is in the following paragraphs. The Miniscalco simplification of McCumber theory uses raw transmission data for the erbium transition (can be used without emission spectrum). Details of the method are found in the reference by Miniscalco and Quimby [40.51]. McCumber theory when applied to an erbium-ytterbium codoped glass is identical to that for an erbium only material—the ytterbium or other sensitizers play no role in the analysis. A calculation method that accounts for the sensitizer contributions to the Er emission is not currently available. The McCumber theory provides an estimate of emission cross-section, emm , as a function of wavelength from the measured absorption cross-section, abs , by the relation ." h / ; (40.20) emm . / D abs . / exp kB T where is the frequency of interest, kB is Boltzmann’s constant, T is the temperature in units of Kelvin, and " is a temperature-dependent excitation energy described as that required to excite one Er3C ion from the 4 I15=2 ground state to the 4 I13=2 excited state at temperature T. Since the ground state manifold width exceeds kB T at room temperature, the higher energy portion of the manifold is not highly populated and does not contribute to the measured absorption curve. However, these energy states do contribute to the emission curve, resulting in the emission and absorption curves being offset from one another with the emission curve extending to lower energy (longer wavelength). To use the McCumber method, analysis begins with a transmission curve, typically between 1400 and 1700 nm in 0:1 nm increments. Transmission values are corrected for reflection losses using the appropriate baseline extracted from fitting the data where there are no erbium absorption features present; for example, near 1400 and 1700 nm of the measured curve. The corrected transmission data, Tc , are then converted to absorption cross-sections abs ./ as a function of wavelength by the formula abs . / D
ln Tc ; d NEr
(40.21)
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Part F | 40.8
Deriving Laser Properties for the Erand Yb-Doped Laser Glasses Er3C has 11 electrons in the 4f orbitals, the vector sums of which give L D 6, S D 3=2, and J D 15=2. By convention, the term symbol for L D 6 is the letter I. The value of 2S C 1 D 4 is the multiplicity of the LJ state, and Stark splitting into .2J C 1/=2 levels is small but will be visible in the measured data. Similarly, Yb3C has 13 electrons in the 4f orbitals, the vector sums of which give L D 3, S D 1=2, and J D 7=2. By convention, the term symbol for L D 3 is the letter F. The value of 2S C 1 D 2 is again the multiplicity of the LJ state and the Stark splitting into .2J C 1/=2 levels is small but observable. Figure 40.11 illustrates potential pathways for energy exchange between Er and Yb in glasses. In an active material doped with both erbium and ytterbium, there is opportunity for energy exchange between the two rare-earth ions. Yb3C has a high absorption cross-section (higher than Er3C ) in the pump band near 1000 nm, which can efficiently absorb pump energy and then can transfer energy to the 4 I11=2 state of Er3C . The laser transition is a fast nonradiative transition in Er3C from the 4 I11=2 to the 4 I13=2 followed by emission to the ground state. There are also opportunities for upconversion in Er3C . All of this makes for rather complicated physics if accounted fully. Present
40.8 Derivation of Laser Performance Related Properties
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Part F | 40.9
where NEr is the number density of Er3C input to the glass in ions/cm3 and d is the sample thickness in cm. To calculate emission cross-section values, it is necessary to arrive at a value for ", which is the excitation energy for erbium in the host being measured. To a first approximation, " can be estimated as the energy corresponding to the peak absorption cross-section (i. e., D hc=abs,max). This has been shown to be the energy separation between the lowest Stark levels in the upper excited 4 I13=2 state and the ground 4 I15=2 state [40.49, 50]. Integral of the emission curve is used to calculate the radiative lifetime of the excited 4 I13=2 state using the relationship 1 rad
Z D 8 cn2
emm ./ d ; 4
(40.22)
where n is the refractive index at 1:54 m and c is the speed of light. Since there are contributions from multiple ions in the visible absorption spectrum of the Er- and Ybdoped glasses, it is difficult to derive laser properties using pure Judd–Ofelt theory. Regardless, spectroscopy is simplified because the lower state is the same as the ground state of Er3C . The calculation routine again starts with the spectrophotometer transmission spectrum collected from 1400 to 1700 nm with 0:1 nm steps. From this data, an absorption curve, ˛./ D ln Tc =d, is generated and integrated across the transition of interest for arriving at the radiative lifetime, 1 rad
D 8 cn2
.2J 0 C 1/ 4 abs;max .2J C 1/
Z ˛./d ; (40.23)
where J 0 and J are the total momentum of the lower and upper levels, in the case of erbium 15/2 and 13/2, respectively, and the integration is taken from 1400 to 1700 nm. The emission cross-section is then emm ./ D
4 g./ ; 8 cn2 rad
(40.24)
where g./ is the line-shape function obtained from the emission data, I./, collected and integrated from 1400 to 1700 nm g./ D R
I./ : I./d
(40.25)
This simplification of the Judd–Ofelt theory is almost the same as the Fuchtbauer–Ladenburg equation. The difference in the two methods is that the Fuchtbauer– Ladenburg equation uses measured fluorescence lifetime for the derivations, while the method as described above uses the radiative lifetime calculated from the absorption curve to arrive at the laser properties. In the case of Er3C =Yb3C -doped glasses, there is high interest in calculating the net gain possible . / for a given population inversion (a typical inversion value is 50%). The calculation looks for the best gain-to-loss ratio in the emission cross-section data, ./ D N2 em ./ N1 abs ./ ;
(40.26)
where N2 and N1 are the number of Er3C ions in the upper and lower laser levels, respectively. The ytterbium amount in the glass does not seem to change the net gain result; the ytterbium contributions are thus not accounted for in the calculations.
40.9 Laser Damage Testing Advances in high-power and high-energy laser systems have made available power densities on optics in excess of 109 W=cm2 . At these levels, a number of different damage mechanisms come into play that can lead to temporary or even permanent changes in the optical quality of optical materials including laser glass. Such changes may occur at a surface or within bulk material, and can both render an optic unusable and/or alter the transmitted beam profile, which may lead to damage of the downstream components in an optical system.
40.9.1 Transient Thermal Effects Since the refractive index is generally a function of temperature, thermal gradients within laser glass parts can
lead to optical distortion of propagating light through inhomogeneous changes in optical path length. For some applications, it is possible to have laser glasses that behave essentially as athermal components having the thermal expansion of the glass offset the change in optical path length due to the variation of index with temperature. For a laser glass component within a cavity of an otherwise fixed length (for example as defined by a frame constructed from near zero expansion materials such as Zerodur® or Invar® ), the variation in optical path length with temperature, dS=dT, is given by dS dn D ˛.n 1/ C ; dT dT
(40.27)
Laser Glasses
dS dn D n˛ C : dT dT
(40.28)
Typical values for ˛, n, and dn=dT are included with other laser glass properties in Tables 40.5–40.7.
40.9.2 Surface Damage Surface damage on active (and also passive) optical materials in high-intensity laser systems normally appears as circular elevations (pustules) or depressions (pits) on transmission surfaces. The number density and size of these features is somewhat determined by the laser energy density and pulse length, respectively. Laser glass surfaces are vulnerable to laser damage since they typically become contaminated through routine storage and handling as well as the gradual accumulation over time of airborne particles. Surface contamination serves as a nucleation point for damage. The initial preparation of the surface can potentially play a critical role in determining the likelihood of experiencing laser damage. After polishing of a surface is completed, there can still exist residual scratches, defects, and subsurface flaws that can retain contaminants of polishing compounds and cleaning materials. Such sites on optical material surfaces serve as additional nucleation points for laser damage. Induced damage on beam exit surfaces is often correlated with absorption of laser energy at such surface defect sites, followed by formation of a plasma, which in turn can enhance reflection of the laser light back on itself, further increasing the local electric field intensity associated with the laser beam. Finishing vendors for high damage threshold optics need to avoid leaving a residue of polishing compounds that absorb strongly at the intended wavelength of exposure. Surface damage threshold is also clearly improved by proper cleaning of optical surfaces and subsequent protection from atmospheric contaminants, including water, which can alter surface properties through condensation and diffusion.
40.9.3 Self-Focusing Damage Self-focusing occurs due to the dielectric breakdown of an optical material from localized focusing of a propagating laser beam by increasing the refractive index with the applied light intensity. This effect leads to one or more thread-like damage sites oriented along the main optical axis that are often referred to by a number of different terms including tracks or angel hair [40.34]. The damage event often begins as a localized hot spot within a laser beam that causes an increase in local refractive index within the glass. Since the optical path length is increased at such a hot spot, and drops towards the original value away from the high-intensity region, this portion of the laser glass essentially acts as a positive lens. This artificial lens further converges the laser beam, compounding the effect. This convergence continues until the electric field associated with the laser increases to a point that atoms are ionized and a plasma is produced within the glass. An example of such selffocusing damage is shown in Fig. 40.12. The phenomena of self-focusing is driven by the laser glass nonlinear refractive index, n2 , the accumulated optical path length, and the presence/absence of localized hot spots in the laser beam. Internal optical quality of laser glass has improved over time to the point that meter-class sections are available that are essentially free of all bubbles and inclusions that can cause localized fluctuations in beam intensity through diffraction effects, so the nonlinear index plays a prominent role in determining if laser damage of this type will occur. It is for this reason that n2 appears in Table 40.5 for a FOMlaser . In addition to selection of a laser glass with low n2 , laser cavity and beamline designs need to
Fig. 40.12 Self-focusing damage in a 50 mm diameter
laser glass
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Part F | 40.9
where the glass is characterized by a thermal expansion value of ˛, refractive index of n, and temperature change of refractive index, relative to air, with temperature of dn=dT. An alternative situation occurs if the laser glass is coated in such a way as to define the length of the optical cavity, as in the case where the end mirrors of a laser oscillator cavity are directly applied to the ends of a laser rod. In this case, the cavity length variation with temperature is given by
40.9 Laser Damage Testing
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Part F | 40.9
minimize the possibilities for high fluence locations in beams passing through laser glass components, i. e., the laser energy should be spread out over as large an area as practically possible.
40.9.4 Multiphoton Induced Damage Multiphoton transitions involve two or more photons whose energies are combined to a value sufficient to excite a real transition in a material. High-fluence laser sources provide high photon flux levels that make these low-probability multiphoton transitions in glass observable. Damage from multiphoton absorption can occur when electrons are excited into an optical material’s effective conduction band, where they then migrate to stable traps in the material and induce structure and property changes. Damage takes two principle forms: as a localized discoloration and/or as a permanent change in the refractive index of the damaged region. This type of laser damage is almost always viewed as problematic and the observed absorption characteristics as a function of wavelength are generally similar to that observed with high-energy radiation damage, such as that found with UV, x-ray, or particle (proton, electron, etc.) exposure. For a particular laser design, the extent of multiphoton damage is determined by the number of laser photons required to achieve a combined energy sufficient to lead to damage. As a rough guide, one can use an effective bandgap of the laser glass, as calculated from the onset of absorption in the high-energy end of the electromagnetic spectrum, compared to the energy available from a single photon at the laser wavelength.
produced within pots and crucibles made of precious metals and their alloys. Subsequent particulate-related damage from these inclusions appears as isolated damage sites within a bulk optic. Figure 40.13 shows a magnified image of such a damage site that measures 0:25 mm in diameter. The damage mechanism is believed to be direct absorption of laser radiation by the dielectric or conducting defect site, followed by heating of the particle to above its boiling point, with subsequent crack nucleation and growth from both the vaporization-related shock wave and localized thermalinduced stress occurring. In the case of metallic Pt inclusions, the boiling temperatures are near 3800 ı C. Since the initial discovery of the laser in 1960, the largest single improvement in laser glass damage threshold performance has been the development of manufacturing technologies capable of producing meter-class phosphate laser glass components completely free of all inclusions or internal defects capable of becoming particulate damage sites [40.55–57]. The specification of such platinum-particle-free glass should be made when laser fluence levels approach the damage threshold, a condition approximated for pulsed, nanosecond, 1:064 m laser exposure by 0:3 EDamage D 2:5 ns :
(40.29)
Although laser damage is an extensively studied field, there is no comprehensive database of the enormous amount of accumulated experimental data on this subject making it possible to predict laser damage level for a particular situation. Interested readers are referred to several textbooks that deal exclusively with this field of investigation [40.55–57].
40.9.5 Point Defect Laser Damage Nearly all optical materials, including laser glass, contain some level of localized microscopic bulk defects including bubbles, dielectric inclusions, and precious metal particles. All such defects have some relationship to the original manufacturing process. Most inclusions and metal particles represent either unmelted compounds from the original glass melt or portions of the manufacturing equipment that were incorporated into the final laser glass component. Bubbles by themselves are not typically linked with the creation of localized damage sites, however they can cause diffraction of a propagating laser beam with associated small spatial scale high-intensity power spikes that can then damage other optical elements in a laser system through nonlinear effects. Metal particles, chiefly platinum, remain in laser glass since for optical quality reasons these glasses are
Fig. 40.13 Particulate damage in laser glass due to a plat-
inum particle (initial size of the inclusion was near 5 m, which grew to five times that after laser irradiation)
Laser Glasses
40.11 Summary
Laser glasses are typically brittle materials easily chipped or broken upon thermal or mechanical loading. As a result, heating and cooling of glass parts should be at rates not exceeding 2030 ı C=h. Laser glasses with good laser properties are generally of compositions that also exhibit low chemical durability. The low durability can sometimes be used to an advantage, since deliberate chemical etching [40.58] or chemical ion exchange processes [40.59] can be used to enhance mechanical strength. There exists no universal method for evaluating all possible chemical attack paths to available laser glass compositions. As a rule, the presence of water is nearly always a prerequisite for the chemical attack of glass. Consequently, long-term storage of sensitive glasses is best within a closed, and preferably evacuated, environment containing a desiccant material such as in a glovebox.
40.10.1 Methods to Enhance Component Strength Laser glasses can be strengthened by techniques such as acid etching and ion exchange. In the former, surface removal by etching is accompanied by blunting of crack tips left following fabrication or mechanical handling. Blunted crack tips require a higher energy level to propagate into cracks or fractures, effectively increasing the resistance of the glass part to breakage. Ion exchange involves the substitution of a smaller cation within the glass structure by a larger cation, effectively placing the surface of the glass under compression [40.60, 61]. To experience fracture, the applied stress must exceed not only the initial strength level of the glass but the compressive surface stress as well. Both processes involve some level of chemical attack of glass surfaces
and are not suitable for polished optical surfaces. The exit and entrance surface for the laser beam is polished to necessary quality and is protected from the chemical treatment if it is completed after polishing.
40.10.2 Liquid Cooling of Laser Glasses Solid-state laser systems employing laser glass as the gain medium are typically cooled by a recirculating liquid coolant system. Chemical attack by the coolant solution is a variable to be considered, in particular when phosphate laser glasses are employed and the component is to be left in contact with coolant during periods of no operation. In these cases water or a similar liquid circulates within the cavity and around the laser component to remove excess heat from the laser component. Addition of ethylene glycol to water can provide improved protection to chemical attack, as seen in Fig. 40.14. Weight loss (mg/(cm2 day)) 0.050 LG-770 LG-760 0.040 LG-750 APG-1 0.030 0.020 0.010 0.000 0
25
50
75 100 Water content (%)
Fig. 40.14 Chemical durability in EtOH/water mixtures: weight loss after storage at 50 ı C for 24 h
40.11 Summary Solid-state lasers need gain materials that are sufficiently transparent and homogeneous in order to absorb pump radiation and emit laser radiation. Most often these materials take advantage of the forbidden f–f transitions of the lanthanide ion 4f configuration for laser emissions. Commonly available lanthanide hosts for solid-state lasers are crystals and glasses. Of these two classes of materials, multicomponent laser glasses are unique for cost, size, shape and engineerability in laser systems. The ability for direct pumping results in proven and elegant laser architectures for high peak
power and high average power lasers. Phosphate laser glasses dominate the utility in laser systems compared to any other glass hosts due to the availability of a volume manufacturing method in meter-class formats with zero inclusions and high optical quality. At present, phosphate glasses doped with Er and Yb are finding their way to commercial applications involving sensing for autonomy and medicine. Once thought to be obsolete, the glass laser materials field continues to evolve and flourish in novel ways due to the material flexibility.
Part F | 40.11
40.10 Storage and Handling of Laser Glass
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Part F | 40
Acknowledgments. This chapter builds on a previous publication, namely the section Laser Glass within the following chapter: M. Brinkmann, J. Hayden, M. Letz, S. Reichel, C. Click, W. Mannstadt, B. Schreder, S. Wolff, S. Ritter, M.J. Davis, T.E. Bauer, H. Ren, Y.-H. Fan, Y. Menke, S.-T. Wu, K. Bonrad,
E. Krätzig, K. Buse, R.A. Paquin: Optical materials and their properties, In: F. Träger (ed.): Springer Handbook of Lasers and Optics, 2nd edn. (Springer, Heidelberg 2012) pp. 253–399. It has been thoroughly revised and updated.
References 40.1 40.2
40.3 40.4 40.5 40.6
40.7
40.8
40.9
40.10
40.11
40.12 40.13
40.14
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40.15 40.16
40.17
40.18 40.19
40.20
40.21
40.22 40.23
40.24
40.25
40.26
40.27 40.28
40.29
W.H. Zachariasen: The atomic arrangement in glass, J. Am. Chem. Soc. 54(10), 3841–3851 (1932) M. Bass: Properties of Crystals and Optics. In: Handbook of Optics: Volume IV – Optical Properties of Materials, Nonlinear Optics, Quantum Optics, 3rd edn., ed. by M. Bass (McGraw-Hill, New York 2010) R. Paschotta (Ed.): Encyclopedia of Laser Physics and Technology, 1st edn. (Wiley-VCH, Weinheim 2008) P. Hartmann: Optical Glass (SPIE, Bellingham 2014) P. Hartmann, R. Jedamzik, S. Reichel, B. Schreder, M. Fokine: Optical glass and glass ceramic historical aspects and recent developments: A Schott view, Appl. Opt. 49, D157–D176 (2010) J.H. Campbell, M.J. McLean, R.A. Hawley-Fedder, I.T. Suratwala, G. Ficini-Dorn, J.-H. Trombest: Development of continuous glass melting for production of Nd-doped phosphate glasses for the NIF and LMJ laser systems, Proc. SPIE (1999), https://doi.org/10.1117/12.354192 J.L. Emmett, W.F. Krupke, J.B. Trenholme: The Future Development of High-Power Solid State Laser Systems (Lawrence Livermore National Laboratory, Livermore 1982), UCRL-53344 A.H. Clauer: New Life for Laser Shock Processing, Ind. Laser Rev. 1996(March), 7–9 (1996) J.H. Kunishige, D.M. Friedman: Nonablative laser and light sources. In: Cosmetic Dermatology, ed. by A. Musad, H.B. Gladstone, R.C. Tung (Elsevier, Amsterdam 2009) pp. 139–141 M. Silver, S.T. Lee, A. Borthwick, I. McRae, D. Jackson, W. Alexander: Compact, diode-pumped, solid-state lasers for next generation defence and security sensors, J. Phys. Conf. Ser. 619, 012022 (2015) J.S. Hayden, Y.T. Hayden, J.H. Campbell: Effect of composition on the thermal, mechanical, and optical properties of phosphate laser glasses, Proc. SPIE (1990), https://doi.org/10.1117/12.20590 S.E. Stokowski, R.A. Saroyan, M.J. Weber: Laser glass: Nd-doped glass spectroscopic and physical properties, Vol. M-95, Rev. 2 (Lawrence Livermore National Laboratory, Livermore 1981) pp. 1–9 E. Snitzer: Optical laser action of Nd3+ in a barium crown glass, Phys. Rev. Lett. 7, 444–446 (1961) J.H. Campbell, T.I. Suratwala: Nd-doped phosphate glasses for high-energy/high-peak-power lasers, J. Non-Cryst. Solids 263/264, 318–341 (2000) J.H. Pitts: Modeling laser damage caused by platinum inclusions in laser glass. In: Proc. Laser Induc. Damage Opti. Mater., Boulder Damage Symp., Boulder, USA (1985) pp. 537–542
Laser Glasses
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40.34 40.35
40.36 40.37 40.38 40.39
40.40
40.41 40.42
40.43 40.44
40.45
40.46 40.47
J.H. Campbell, E.P. Wallerstein, J.S. Hayden, D.L. Sapak, D.E. Warrington, A.J. Marker III, H. Toratani, H. Meissner, S. Nakajima, T. Izumitani: Elimination of Platinum Inclusions in Phosphate Laser Glasses (Lawrence Livermore National Laboratory, Livermore 1989), UCRL-53932 J.H. Campbell: Recent advances in phosphate laser glasses for high-power applications, Proc. SPIE 10286, 1028602 (1996) A. Caird, A.J. Ramponi, P.R. Staver: Quantum efficiency and excited-state relaxation dynamics in neodymium-doped phosphate laser glasses, J. Opt. Soc. Am. B 8, 1391–1403 (1991) D. Pugliese, N.G. Boetti, J. Lousteau, E. Ceci-Ginistrelli, E. Bertone, F. Geobaldo, D. Milanese: Concentration quenching in an Er-doped phosphate glass for compact optical lasers and amplifiers, J. Alloy. Comp. 657, 678–683 (2016) W. Koechner: Solid-State Laser Engineering, 6th edn. (Springer, New York 2006) D.L. Veasey, D.S. Funk, N.A. Sanford, J.S. Hayden: Arrays of distributed Bragg-reflector waveguide lasers at 1536 nm in Yb/Er codoped phosphate glass, Appl. Phys. Lett. 74(6), 789–791 (1999) Advanced Optics SCHOTT AG: Refractive Index and Dispersion: TIE 29 – Technical information (2016) Advanced Optics SCHOTT AG: Striae in Optical Glass: TIE 25 – Technical information (2006) H. Vogel: Das Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten, Z. Phys. 22, 645 (1921) G. Tammann, G. Hesse: Die Abhängigkeit des Viskosität von der Temperatur bei unterkühlten Flüssigkeiten, Z. Anorg. Allg. Chem. 156, 245 (1926) G.S. Fulcher: Analysis of recent measurements of the viscosity of glasses, J. Am. Ceram. Soc. 8, 339 (1925) L. Pavesi, D.J. Lockwood (Eds.): Silicon Photonics, Vol. 1 (Springer, Berlin 2004) pp. 369–371 G.C. Righini, M. Ferrari: Photoluminescence of rareearth doped glasses, Riv. Nuovo Cimento 28(12), 1– 53 (2005) D.E. McCumber: Theory of phonon-terminated optical lasers, Phys. Rev. 134, A299 (1964) R.M. Martin: Reciprocity between Emission and Absorption for Rare Earth Ions and Glass, Ph.D. Thesis (Worcester Polytechnic Institute, Massachusetts 2006) S.A. George, J.S. Hayden: Spectroscopy of Nd-doped laser materials, Proc. SPIE (2014), https://doi.org/10.1117/12.2040841 B.R. Judd: Optical absorption intensities of rareearth ions, Phys. Rev. 127(3), 750 (1962) G.S. Ofelt: Intensities of crystal spectra of rareearth ions, J. Chem. Phys. 37(3), 511 (1962)
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40.56 40.57
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C.W. Nielson, G.F. Koster: Spectroscopic Coefficients of the pn , dn , and fn Configurations (MIT Press, Cambridge 1963) B.M. Walsh: Judd–Ofelt theory: Principles and practices. In: Advances in Spectroscopy for Lasers and Sensing, ed. by B. Di Bortolo, O. Forte (Springer, Dordrecht 2006) pp. 403–433 E. Desurvire, J.R. Simpson: High-gain erbium doped travelling-wave fiber amplifier, Opt. Lett. 15(10), 547–549 (1990) W.J. Miniscalco, R.S. Quimby: General procedure for the analysis of Er3+ cross sections, Opt. Lett. 16(4), 258–260 (1991) W.B. Fowler, D.L. Dexter: Relation between absorption and emission probabilities in luminescent centers in ionic solids, Phys. Rev. 128(5), 2154 (1962) W.F. Krupke: Induced-emission cross-sections in neodymium laser glasses, IEEE J. Quantum Electron. 10, 450 (1974) B.F. Aull, H.P. Jenssen: Vibronic interactions in Nd:YAG resulting in nonreciprocity of absorption and stimulated emission cross sections, IEEE J. Quantum Electron. 18(5), 925 (1982) L.M. Sheehan, S. Schwartz, C.L. Battersby, R.K. Dickson, R.T. Jennings, J.F. Kimmons, M.R. Kozlowski, S.M. Maricle, R.P. Mouser, M.J. Runkel, C.L. Weinzapfel: Automated damage test facilities for materials development and production optic quality assurance at Lawrence Livermore National Laboratory, Proc. SPIE (1999), https://doi.org/10.1117/12.344447 R. Wood: Laser Damage in Optical Materials (SPIE Optical Engineering, London 1990) D.C. Brown: Damage effects in high peak power Nd:Glass laser systems. In: High-Peak-Power Nd:Glass Laser Systems (Springer, Berlin, Heidelberg, New York 1981) pp. 170–187 D.H. Roach, A.R. Cooper: The effect of etch depth on strength of indented soda lime glass rods. In: Strength of Inorganic Glass, ed. by C.R. Kurkjian (Plenum, New York 1985) pp. 185–195 W.C. LaCourse: The strength of glass. In: Introduction to Glass Science, ed. by L.D. Pye, H.J. Stevens, W.C. LaCourse (Plenum, New York 1972) pp. 451–512 T.M. Gross: Scratch damage in ion-exchanged alkali aluminosilicate glass: Crack evolution and the dependence of lateral cracking threshold on contact geometry. In: Fractography of Glasses and Ceramics VI, ed. by J.R. Varner, M. Wightman (Wiley, Hoboken 2012) pp. 113–122 R. Gardon: Thermal tempering of glass. In: Glass Science and Technology, ed. by D.R. Uhlmann, N.J. Kreidl (Elsevier, New York 1980) pp. 145–216
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Part F | 40
40.30
References
1402
Part F
Optical and Photonic Glass Applications
Simi A. George
Part F | 40
SCHOTT North America, Inc. Duryea, PA, USA [email protected]
Simi George is a physicist with a background in laser plasmas, optics, and the design and manufacturing of optical materials. Currently, she is the Global Laser Product Manager of SCHOTT’s Advanced Optics division. Simi obtained her PhD in Physics from the University of Central Florida, USA. Her early career included Sn-doped droplet laser-produced plasma sources for EUV lithography.
Joseph S. Hayden SCHOTT North America, Inc. Duryea, PA, USA [email protected]
Joseph Hayden has a BS from Saint Joseph’s University and a PhD in Chemical Physics from Brown University. He joined SCHOTT in 1985, where he has worked in glass composition and process development with an emphasis on laser, nonlinear and technical glasses. He is a Research Fellow at SCHOTT’s North American Research and Technology Department.
1403
Optical Fibers 41. Optical Fibers
Thierry Chartier 41.1 41.1.1 41.1.2 41.1.3 41.1.4
Theory of Light Guiding .................... Introduction ..................................... Ray Optics Approach .......................... Wave Optics Approach ........................ Mode Properties ................................
1403 1403 1404 1405 1408
41.2 41.2.1 41.2.2 41.2.3 41.2.4 41.2.5
Fiber Properties ................................ Fabrication of Optical Fibers ............... Attenuation ...................................... Dispersion ........................................ Polarization Effects ............................ Nonlinearities ...................................
1413 1413 1415 1416 1418 1419
41.3 41.3.1 41.3.2 41.3.3 41.3.4 41.4 41.4.1 41.4.2 41.4.3
Specialty Optical Fibers ..................... Rare-Earth-Doped Fibers ................... Photonic Crystal Fibers ....................... Nonsilica Fibers ................................. Fiber Bragg Gratings .......................... Applications of Optical Fibers............. Optical Communications..................... Amplifiers and Lasers......................... Fiber-Optic Sensors............................
1424 1424 1425 1427 1429 1431 1431 1432 1434
References................................................... 1436
41.1 Theory of Light Guiding After a short introduction, basic concepts about light guiding will be given in this section, based on a ray optics approach. A more precise theory will be presented afterwards and some properties of the guided solutions will then be examined.
41.1.1 Introduction An optical fiber is a dielectric waveguide with a circular symmetry. It is usually made of a core with refractive index n1 surrounded by a cladding with refractive index n2 . The guiding of light is only possible in the core if n1 > n2 [41.1].
Figure 41.1 shows an example of silica fiber with the typical dimensions of a single-mode telecommunication fiber. The cladding diameter is usually 125 m and is made of silica with a refractive index n2 of the order of 1.46. The core has a diameter 2a of a few micrometers (typically in the range 510 m) and a refractive index n1 , slightly higher than the cladding, due for example to the presence of dopants in the silica matrix (usually germanium). The fiber is generally coated with an external polymer cladding to isolate silica from the external medium because of corrosion. It also helps enhance mechanical properties. This polymer cladding does not play any role
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_41
Part F | 41.1
Optical fibers are dielectric waveguides that transport light between two points. They are usually made of high-purity glasses. It is well known that light travels in a straight line in free space but when light is trapped in an optical fiber, it can propagate with bends and can carry information anywhere from a few meters to thousands of kilometers. This property of optical fibers has driven the fabrication of low-loss optical fibers for telecommunication applications. Nowadays, optical fibers are used in many other fields such as lasers, amplifiers, and sensing. This chapter is organized as follows: In the first part, fundamentals of light guiding in optical fibers will be given. In the second part, after a brief presentation of the fabrication process of optical fibers, some properties of optical fibers such as attenuation, dispersion, polarization effects, and nonlinearities will be presented. In the third part, some types of specialty optical fibers will be described, in particular rare-earth-doped fibers, photonic crystal fibers, nonsilica fibers, and fiber Bragg gratings. Finally, in the fourth part, a focus will be put on some usual applications of optical fibers, in particular for telecommunications, amplifiers, lasers, and sensing.
1404
Part F
Optical and Photonic Glass Applications
y
Cladding (125 μm)
z –a
r
n2
Part F | 41.1
φ a
Core (few μm)
x n1
41.1.2 Ray Optics Approach
2a
Fig. 41.1 Schematic representation of an optical fiber with
the typical dimensions of a single-mode telecommunication fiber
in the guiding mechanism and will be ignored in the following. In this fiber, light is confined in the vicinity of the core and propagates along the z direction. In the transverse plane .x; y/ of the fiber, it is usually convenient to use the polar coordinates .r; '/ as illustrated in Fig. 41.1. For a perfectly circular fiber, the refractive index is '-independent while its variation along r is generally referred to as the refractive-index profile. For the step-index fiber represented in Fig. 41.1 the refractive-index profile can be defined as follows ( n1 if r < a ; n.r/ D (41.1) n2 if r > a ; where a is the core radius. Note that the refractive-index profile is not necessarily a step-like profile but can be a parabolic graded-index profile, for example. Figure 41.2a shows the refractive-index profile of a step-index fiber and Fig. 41.2b shows the refractive-index profile of a graded-index fiber. Graded-index fibers are essentially used for data transmission in local-area networks while step-index fibers are present in most applications including highdata-rate transmissions, lasers, amplifiers, and fiberoptic sensors. Let us define the profile height parameter by [41.2] D
n21 n22 : 2n21
The parameter is generally referred to as the refractive-index difference between the core and the cladding. In the following theoretical approach, step-index fibers will only be considered for the sake of simplicity. Basics of light guiding in step-index fibers can be given using a geometrical optics, or ray optics, approach. This will be the aim of the next section. However, in order to have a more complete description of how light is guided in optical fibers, it is preferable to use the electromagnetic wave approach presented in Sect. 41.1.3.
(41.2)
Because n1 is generally close to n2 , is of the order of 0:11% and can be approximated by n1 n2 : (41.3) n1
Figure 41.3 represents a cross-section of a step-index fiber in the plane .r; z/. Due to Snell’s law [41.3], an optical ray can experience a series of total internal reflections if n1 > n2 and if the angle between its direction and the interface (Fig. 41.3) remains lower than the critical angle c defined by [41.3] cos c D
n2 : n1
(41.4)
From Fig. 41.3, we can then define the acceptance cone into which external rays can be guided in the fiber core. Using Snell’s law, the maximum angle i0 , defined in Fig. 41.3, must satisfy p sin i0 D n1 sin c D n1 1 cos2 c :
(41.5)
Using (41.4) in (41.5), we find sin i0 D
q n21 n22 D NA ;
(41.6)
where we have introduced a useful parameter called the numerical aperture (NA) of the fiber. Using (41.2), NA can be expressed as p NA D n1 2 :
(41.7)
The acceptance cone is then related to the angle ˛ given by ˛ D 2i0 D 2 arcsin NA :
(41.8)
The numerical aperture is a dimensionless quantity related to the maximum incidence angle i0 for an external ray to be guided in the fiber. This angle is also the maximum angle of the output rays exiting the fiber. The numerical aperture only depends on the refractive indices of the fiber. Let us take for example an optical fiber with n1 D 1:46 and D 0:005. We find NA D 0:15 and ˛ D 17ı . These values are typical for telecommunication fibers.
Optical Fibers
n(r)
a)
n1
n1
n2 Core a
r
−a
Cladding a
r
Fig. 41.3 Cross-section of a step-
r Refraction
index fiber in the .r; z/ plane and trajectories of optical rays
Cladding n2
θ α
Total reflection
Core n1
i0
Air
z
α
Cladding n2
An optical ray that would enter the fiber with an incidence angle outside the acceptance cone would undergo a series of refractions at the core-cladding interface and would not be guided in the fiber core. In contrast with the guided rays (or bound rays), refractive rays lead to energy radiation outside the core. Far from the input end of the fiber only the guided rays remain. They can be considered as the steady-state solution of the waveguide [41.2]. Ray optics is a first approach to understanding the principle of light guiding in optical fibers and to introducing useful parameters such as the refractive index difference or the numerical aperture. However, to more precisely describe the steady-state distribution of light in the core, a more complete approach, based on the wave equation, must be used. This will give rise to the concept of propagation modes.
41.1.3 Wave Optics Approach The most rigorous method to calculate the transverse distributions of light in an optical fiber is to start from the wave equation for the electric field E of an electromagnetic wave. This equation is written, in a homogeneous medium with refractive index n, as [41.3] @2 E 1 @E 1 @2 E @2 E n2 @2 E C C D 0 ; (41.9) C @r2 r @r r2 @' 2 @z2 c2 @t2 where r, ' and z are the spatial coordinates defined in Fig. 41.1, t is the time, and c is the speed of light in vacuum (c 2:998 108 m=s). The fiber is not a ho-
mogeneous medium but is composed of two different media with refractive indices n1 and n2 . We have to assume that the electric field exists in both media and that the part of the electric field in the core obeys (41.9) with n D n1 and the part of the electric field in the cladding obeys (41.9) with n D n2 . At the interface between the two dielectric media, we use the boundary conditions for the electric fields. These conditions stipulate that the tangential component of the electric field and the normal and tangential components of the magnetic field must be continuous at the interface [41.3]. The Weakly Guiding Approximation Usually, the refractive-index difference of optical fibers is weak (of the order of 0:11%) and it is convenient to use the weakly guiding approximation [41.4, 5]. Under this assumption, the longitudinal component Ez of the electric field approaches zero. The electric field E is then essentially in the transverse plane .r; '/ and can be decomposed into two linear and orthogonal polarizations Ex and Ey . Each polarization component is assumed to have the same transverse distribution E.r; '/ and the same propagation constant ˇ. Assuming a monochromatic wave of angular frequency !, the vectors Ex and Ey can be written as Ex;y D E.r; '/ei.!tˇz/ ux;y ;
(41.10)
where ux;y are unitary vectors along arbitrary axes x and y. In the framework of the weakly guiding approximation, two linearly polarized (LP) solutions have to be found.
Part F | 41.1
−a
index fiber
n2
Core
Cladding
1405
Fig. 41.2a,b Refractive-index profiles for (a) a step-index fiber (b) a graded-
n(r)
b)
41.1 Theory of Light Guiding
1406
Part F
Optical and Photonic Glass Applications
At this stage of the study, to describe the propagation of light in an optical fiber, the unknowns are the transverse field distribution E.r; '/ and the propagation constant ˇ. Introducing (41.10) in (41.9), the following scalar wave equation is found
Part F | 41.1
@2 E 1 @E 1 @2 E C 2 2 C k02 n2 ˇ 2 E D 0 ; C 2 @r r @r r @' (41.11)
where k0 D !=c D 2 =0 is the propagation constant of light in vacuum and 0 is the free-space wavelength. We have to mention here that the boundary conditions, presented earlier for vectorial fields, turn out to be equivalent, in the weakly guiding approximation, to the conditions that the scalar function E.r; '/ must be continuous and must have a continuous derivative at r D a. Solutions of the Scalar Wave Equation To solve this equation we decompose E.r; '/ as the product of a radial profile R.r/ and an azimuthal profile .'/ E.r; '/ D R.r/ .'/ :
(41.12)
It can be shown [41.1] that each part of E.r; '/ satisfies the following equations @2 C l2 D 0 ; @' 2 @2 R 1 @R l2 2 2 2 C k0 n ˇ 2 R D 0 ; C @r2 r @r r
(41.13)
(41.14)
where l is a constant. The solutions of (41.13) must be periodic in the angle '. This gives harmonic solutions for .'/ and l as an integer (l D 0; 1; 2; : : :). We decompose as odd (sine) and even (cosine) functions ( cos.l'/ ; (41.15) .'/ D sin.l'/ : Equation (41.14) is a well-known differential equation whose solutions are the family of Bessel functions. Among the different solutions of this equation, we must exclude functions that approach 1 in the core at r D 0 and in the cladding for r ! 1 [41.1]. This leads to the following distinct solutions for R.r/ in the core (r < a and n D n1 ) and in the cladding (r > a and n D n2 ) ( R.r/ D
AJl . r/; r < a (core) ; BKl . r/; r > a (cladding) ;
(41.16)
where A and B are constants of integration, Jl .x/ is the Bessel function of the first kind and order l, and Kl .x/ is the modified Bessel function of the second kind and order l. Figure 41.4 shows the first orders of these two Bessel functions. The oscillating behavior of Jl .x/ and the exponential-like decay of Kl .x/ indicate that the field is confined in the vicinity of the fiber core. The new parameters and are real and positive quantities defined as follows
2 D n21 k02 ˇ 2 ; Dˇ 2
2
n22 k02
:
(41.17) (41.18)
Since and are positive, we immediately note that n2 k0 < ˇ < n1 k0 :
(41.19)
This relation indicates that the value of the propagation constant lies between the value n2 k0 of a wave propagating in a homogeneous medium with refractive index n2 and n1 k0 of a wave propagating in a homogeneous medium with refractive index n1 . This indicates that, as the field solution takes place both in the core and in the cladding, its propagation constant has an intermediate value between n2 k0 and n1 k0 . Boundary Conditions At this stage, even if the analytic expressions of both the radial part R.r/ and the azimuthal part .'/ of E.r; '/ have been derived, many unknowns remain to fully describe the guided wave: l, A, B, ˇ, , and . Fortunately, some of these unknowns are not independent (ˇ, , and ) and one constant of integration does not need to be determined. We have now to consider the boundary conditions. The function R.r/ must be continuous and must have a continuous derivative at r D a. This leads to the two following conditions [41.1] Jl . a/ ; Kl . a/ Kl1 . a/
Jl1 . a/ D : Jl . a/ Kl . a/ BDA
(41.20) (41.21)
Equation (41.20) links the two constants of integration in order that the function R.r/ is continuous at the corecladding interface. The absolute value of one constant of integration cannot be determined and will remain arbitrary in the following. Equation (41.21) ensures that the derivative of the function R.r/ is continuous at r D a. This equation is used to find ˇ and, consequently,
and . To do that, the normalized frequency V (or V number) and the normalized propagation constant b are
Optical Fibers
a) 1
J0(x)
0.8 J1(x)
0.6
J2(x) J3(x)
0.4
0
2
4
6
8
10 x
–0.2 –0.4
b)
5 4 3 2 K1(x) 1
K2(x)
K3(x)
K0(x)
0 0.5
1
1.5
2
2.5
3
x
Fig. 41.4 (a) The four first orders of the Bessel functions of the first kind Jl .x/; and (b) the four first orders of the modified Bessel functions of the second kind Kl .x/
introduced as follows [41.1] q 2 a NA ; V D ak0 n21 n22 D 0 ˇ 2 n2 k 2 b D 2 2 2 02 : k0 n1 n2
of l, several values of b exist, they are numbered with an integer m and the solutions are denoted blm . The guided solutions are called the LPlm modes of the fiber. Once blm is found, (41.23), (41.17) and (41.18) allow us to determine ˇlm , lm , and lm , and then the transverse distributions Elm .r; '/ of all the LPlm modes of the fiber. Equation (41.24) does not admit analytic solution and has to be solved numerically or graphically. The graph of Fig. 41.5 represents the left- and righthand sides of (41.24) as a function of b for the case l D 0 and V D 8. Three solutions are found, leading to three distinct modes LP01 , LP02 , and LP03 . It is possible to use a numerical routine that systematically finds all the solutions for b. The results can be summarized on a unique graph representing the values of b for each mode as a function of V. This graph is shown in Fig. 41.6. For a given value of V, it immediately shows how many LPlm modes can propagate in the fiber and gives the values of blm . Fiber Modes Let us now summarize the wave optics approach by writing the field amplitude of the LPlm modes and their propagation constant Elm .r; '/ D 8 ( ˆ cos.l'/; ˆ ˆ r a (core); ˆAJl . lm r/ < sin.l'/; ( ˆ cos.l'/; ˆ Jl . lm a/ ˆ r a (cladding) : ˆ :A Kl .lm a/ Kl . lm r/ sin.l'/;
(41.22) (41.23)
As we shall see shortly, the normalized frequency V is an important quantity depending on the three parameters that fully describe a fiber (a, n1 , and n2 ) and the free-space wavelength 0 of the wave. With the parameters V and b, (41.21) is rewritten as p p Jl1 V 1 b p Kl1 V b D V b p : V 1b p Jl V 1 b Kl V b p
(41.24)
In (41.24), for a given fiber and at a given wavelength, V is known and the only unknowns are l and b. Since l is supposed to be a positive integer, discrete values of l are tested, starting with l D 0, and the values of b satisfying (41.24) are determined, if they exist. If, for a given value
(41.25)
Using (41.23) the expression of ˇlm is q ˇlm D k0 n22 C blm n21 n22 :
(41.26)
We have to mention here that modes with the same propagation constant are known as degenerate modes. It appears from the analysis that modes with l 1 are fourfold degenerate (odd and even azimuthal distributions, x and y polarizations) while modes with l D 0 are only twofold degenerate (x and y polarizations) since they cannot support any odd solution (the sine function vanishes in (41.25)). Let us take the example of a fiber with the following parameters: a D 16 m, n2 D 1:45, and D 0:36%. At the wavelength 0 D 1550 nm, the normalized frequency V is equal to 8. For this value, ten LPlm modes exist, from the LP01 to the LP51 , as seen in Fig. 41.6. Actually, due to the degeneracy of modes, 34 modes can be identified. Figure 41.7a shows the amplitude distri-
1407
Part F | 41.1
0.2
41.1 Theory of Light Guiding
1408
Part F
Optical and Photonic Glass Applications
Fig. 41.5 Evolution of
10 8 6 4
Part F | 41.1
2 0
b 03
b 01
b 02
0.1
0.2
0.3
0.4
0.6
0.5
0.7
0.8
1 b
0.9
the left-hand side (dashed line) and the right-hand side (solid line) of (41.24) as a function of b for l D 0 and V D 8. Three solutions are possible in this case, named LP01 , LP02 , and LP03
–2 –4
LP03
–6 LP02
–8
LP01
–10
1
b 01
0.9
11
0.8
21 02
0.7
Fig. 41.6 Normalized propagation constant b as a function of the normalized frequency V
31
0.6
12 41
0.5
22 03 51
0.4 0.3
32 61 13
0.2 0.1
42 0
0
1
2
3
4
5
6
7
8
9
10 V
2.405
bution E01 .r; '/ of the LP01 mode along one radial axis of the fiber (x axis for example). We note that the field is essentially present in the core of the fiber (between a and Ca) but also extends, to a lesser degree, into the cladding. Figure 41.7b represents the intensity distribution jE01 .r; '/j2 of the LP01 mode in the transverse plane of the fiber. Another example is given in Fig. 41.8, which represents the LP22 mode. For this mode the odd/even degeneracy exists as shown in Fig. 41.8b. Figure 41.9 represents the intensity distribution, calculated from (41.25), of the first ten even LP modes of a stepindex fiber.
41.1.4 Mode Properties Equations (41.25) and (41.26) give the mathematical expressions of the possible guided modes in step-index fibers under the weakly guided (or LP-mode) approximation. In this section some properties of the fiber modes will be pointed out. Number of Modes It is obvious from Fig. 41.6 that the number of modes increases with the value of the normalized frequency V. Except for the LP01 mode, each mode has a cut-
Optical Fibers
a)
b)
Normalized amplitude (arb. u.) 1.2 Cladding
1
Core
0.8
41.1 Theory of Light Guiding
Fig. 41.7 (a) Normalized amplitude of the LP01 mode along the radial coordinate x; and (b) intensity distribution of the LP01 mode
Part F | 41.1
0.6 0.4 0.2 0
−a
–40
a)
–30
–20
+a –10
0
10
20 30 40 Radial coordinate (μm)
b)
Normalized amplitude (arb. u.) 1.2 1
Cladding
Core
0.8 Even
Fig. 41.8 (a) Normalized amplitude of the LP22 mode along the radial coordinate x; and (b) intensity distribution of both even and odd LP22 modes
0.6 0.4 0.2 −a
0
+a
–0.2 Odd –0.2 –0.2 –0.2 –40
–30
–20
–10
0
10
20 30 40 Radial coordinate (μm)
off frequency below which the mode does not exist. For large V the number M of modes grows rapidly and an approximate relation directly gives the number of modes (including degeneracy). This relation is written as [41.3] M
1409
4 2 V 2
for V 1 :
(41.27)
For example, a typical silica multimode fiber has the following parameters: a D 25 m, n1 D 1:47, and D
1%. At the wavelength 0 D 850 nm, the normalized frequency V is about 38 and the number of modes is approximately 600. When a large number of modes is not detrimental, a multimode fiber offers the advantage of a large core diameter and a large NA. This facilitates fiber-to-fiber coupling or optical power delivery, for example. However, in some applications (long-haul fiber-optic communications, laser sources, or sensing applications for example), single-mode fibers (SMFs) are required.
1410
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Optical and Photonic Glass Applications
βlm (×105 rad/m ) 5 01 11 21 02 31 12
4.5 LP01
LP11
4 3.5
Part F | 41.1
3
n1k0
2.5 2 n 2k 0
1.5 LP21
LP02
1 0.5 0
0
1
2
3
4
5
6 V
Fig. 41.10 Propagation constant ˇlm as a function of V for the first modes of an optical fiber LP31
LP41
LP12
LP22
and a normalized frequency V D 1:9 at 0 D 1550 nm. The fiber is then single-mode at this wavelength. However, there exists a wavelength below which V is greater than 2:405 and the LP11 mode appears. We define the cutoff wavelength of a SMF as the wavelength above which the single-mode operation is ensured. Using (41.22), the cutoff wavelength must satisfy c D
LP03
LP51
Fig. 41.9 Intensity distribution of the first ten even LP modes of a step-index fiber
According to Fig. 41.6 an optical fiber can support one single LP mode if V is smaller than the cutoff frequency of the LP11 mode. This occurs for V < 2:405 :
(41.28)
In this case, the remaining mode is the LP01 mode and is called the fundamental mode of the fiber. The other modes are referred to as the higher-order modes. Let us take the example of a conventional silica SMF with the following parameters: a D 4:1 m, n1 D 1:47, and D 0:3%. This fiber has a numerical aperture NA D 0:11
2 a NA D 2:613a NA : 2:405
(41.29)
Note that the fundamental mode LP01 is twofold degenerate and can be polarized along two arbitrary axes x and y with the same propagation constant in an ideal fiber. Propagation Constant The propagation constant ˇlm of a LPlm mode is given by (41.26). The knowledge of ˇlm is required to evaluate the phase shift ˇlm L introduced during the propagation over a distance L, the phase velocity !=ˇlm or the group velocity .dˇlm =d!/1 (Sect. 41.2.3). Figure 41.10 shows the evolution of the propagation constant ˇlm of the fundamental mode LP01 and the first higher-order modes of an optical fiber as a function of the normalized frequency V. The propagation constant ˇlm evolves from the asymptote n2 k0 to the asymptote n1 k0 as V increases. Note that the refractive index difference has been voluntarily exaggerated for clarity in Fig. 41.10. The effective refractive index nlm eff is defined as the refractive index experienced by a LPlm mode when propagating in the fiber. It must satisfy ˇlm D nlm eff k0 and,
Optical Fibers
41.1 Theory of Light Guiding
1411
Fig. 41.11 Illustration of the radiation modes and the guided modes in an optical fiber
Radiation modes + Guided modes
Guided modes
using (41.26), nlm eff is written as q n22 C blm n21 n22 : nlm eff D
Part F | 41.1
Source
Normalized amplitude (arb. u.) (41.30) 1
Since blm can only take values between 0 and 1 (according to (41.23)), the effective refractive index nlm eff is between n2 and n1 . We clearly see from Fig. 41.10 that the different modes of a multimode fiber do not have the same propagation constant. We also note that the propagation constant does not evolve linearly with V. These two points lead to the phenomenon of dispersion and will be discussed later in Sect. 41.2.3.
0.8 0.6
Δ = 2 ×10−4
V = 0.5
Δ = 5 ×10−4
V = 0.8
0.4
V = 1.1
Δ = 10−3 0.2 Δ = 5 ×10 –15 –10 −3
Orthogonality of the Modes In the previous analysis, we introduced the concept of modes through the function of two variables Elm .r; '/ describing the distribution of the electric field in the transverse plane of the fiber. Each mode has its own transverse distribution and its own propagation constant. Actually, the set of possible functions Elm .r; '/ of a multimode fiber forms a basis on which any field distribution at the input of the fiber can be decomposed [41.5]. This means that the different functions Elm .r; '/ are orthogonal according to the following definition ZC1Z2 0
Elm El 0 m0 rdrd' D ıll0 ımm0 ;
(41.31)
0
where ıii0 (i D l; m) is the Kronecker delta (ıii0 D 1 if i D i0 and 0 otherwise). However, the set of guided modes does not form a complete basis of decomposition. Indeed, radiation modes can also propagate in the cladding of the fiber, specifically at the beginning of the fiber [41.2]. Already presented in the ray optics approach of Sect. 41.1.2, these modes are the refracted rays propagating through the core-cladding interface. Any external field distribution is then decomposed, at the input of the fiber, on both the basis of the radiation modes and the basis of
0 –20
Δ = 5 ×10−2 V = 7.6 –5
0
V = 2.4 5 10 15 20 Radial coordinate (μm)
Fig. 41.12 Normalized amplitude of the LP01 mode along the radial coordinate x for different values of the refractive index difference
the guided modes. As illustrated in Fig. 41.11, the radiation modes vanish soon after the input end of the fiber and only the guided modes remain after a certain length of fiber. Mode Confinement The LP01 mode represented in Fig. 41.7 is essentially confined in the fiber core, even if a small part of the field extends into the cladding. The part of field in the cladding is an evanescent field and is usually close enough to the core to prevent it from interacting with the outer medium beyond the cladding. It is interesting to study how the fundamental mode remains confined when some fiber parameters vary. Figure 41.12 represents the field distribution of the fundamental LP01 mode along the x radial axis for different values of the refractive index difference (reported in the figure). The other parameters of the fiber are a D 4:1 m, n1 D 1:47, and the wavelength is 0 D 1550 nm. The corresponding values of the normalized frequency V are also reported for each curve.
1412
Part F
Optical and Photonic Glass Applications
Normalized amplitude (arb. u.) a = 2 μm, V = 0.5
1 0.8
Part F | 41.1
a = 4 μm, V = 1.1
0.6
Core External medium
0.4
a = 8 μm, V = 2.1
0.2 0 –20
a = 16 μm, V = 4.3
–15
–10
–5
0
5 10 15 20 Radial coordinate (μm)
Fig. 41.14 Illustration of a tapered fiber used to maximize
the interaction of the field with the external medium
Fig. 41.13 Normalized amplitude of the LP01 mode along
the radial coordinate x for different values of the core radius a
This figure indicates that the mode is increasingly less confined as V becomes smaller. For values of V smaller than 1, the mode extends so far into the cladding that the guiding process cannot be considered as sufficiently robust. Indeed, deconfined modes suffer from excessive loss due to bends or to interaction with the outer medium. Practically, a SMF must have a value of V smaller than 2:405 to ensure single-mode operation and higher than 1:5 to ensure confinement of the fundamental mode. From another point of view, Fig. 41.13 represents the field distribution of the fundamental LP01 mode for different values of the core radius a (reported in the figure for each curve with the corresponding value of V). The other fiber parameters remain constant and equal to n1 D 1:47, D 0:1%, and 0 D 1550 nm. When the core radius a decreases, the fundamental mode width starts to become smaller (for core radius from 16 to 8 m for example) and then becomes larger for smaller values of a. These curves indicate that, when decreasing a, the mode becomes more confined and is finally completely deconfined for core diameters comparable to the wavelength. This explains the principle of a counterintuitive application of tapered fibers. A tapered fiber is a fiber whose transverse dimension reduces adiabatically with length [41.6], as illustrated in Fig. 41.14. In this figure, only the core of the fiber is represented for simplicity. As the core gets thinner, the mode diameter is supposed to decrease too. However, below a certain value, the mode is no longer guided and extends significantly into the external medium. This deconfinement increases the possibility that light will interact with the external
medium and is used for sensing applications for example, as will be seen in Sect. 41.4.3. Figure 41.13 also explains that, to have a good confinement of the fundamental mode in small-core fibers, the refractive index difference should be large enough to keep V in the range 1:52:4. For example, for a D 2 m, should be 2% to have V D 2:4. Small-core fibers are used for nonlinear applications and are usually referred to as highly nonlinear fibers (Sect. 41.2.5). Refractive index differences of about 23% are generally the maximum values achievable in highly germanium-doped silica fibers [41.7]. To reduce more the core size of highly nonlinear fibers, larger values of can be obtained with photonic crystal fibers, as will be seen in Sect. 41.3.2. On the other hand, enlarging the core diameter of optical fibers, while preserving single-mode operation, requires decreasing . Large-core fibers, also called large-mode-area fibers, are of interest in limiting nonlinear effects in high-power applications. Decreasing too much leads, however, to some limitations such as a higher sensitivity of the fiber to bending losses. Due to this difficulty of preserving robust single-mode guidance, diameters of step-index large-mode-area fibers are generally limited to 20 m [41.8]. Larger diameters can be obtained in photonic crystal fibers, as will be seen in Sect. 41.3.2. A convenient way to measure the dimension of the LP01 mode of a SMF is to use the effective mode area Aeff defined by [41.9] R 1 2 jE01 .r/j2rdr Aeff D 2 R0 1 (41.32) : 4 0 jE01 .r/j rdr The effective mode area is a representation of the lightcarrying region of optical fibers and is a useful pa-
Optical Fibers
rameter to evaluate nonlinear effects in optical fibers (Sect. 41.2.5). For example, for a conventional SMF with a D 4:1 m and D 0:36%, the effective mode area Aeff is of the order of 80 m2 at 1550 nm.
Exact LP01 solution Gaussian approximation
E01 .r/ D A e
;
0.4
2w 1/e
(41.33) 0.2
where w is the radius of the mode field pattern (at 1=e of the maximum). The mode radius w may be estimated from the core radius a and the V parameter, using the following (empirical) Marcuse’s equation [41.1] 1:619 2:879 w 0:65 C 3=2 C : a V V6
0.6
Part F | 41.2
r2 =w 2
(41.34)
This equation is accurate within about 1% for 0:8 < V < 2:5. As an example, Fig. 41.15 represents both the exact field distribution of the LP01 mode calculated from (41.25) and the Gaussian fit given by (41.33) for V D 2. A reasonable agreement is found between both functions. The core diameter is 8 m in the example and the mode field diameter 2w is found to be approximately 10:2 m. With the Gaussian approximation, the
0
–15
–10
–5
0
5 10 15 Radial coordinate (μm)
Fig. 41.15 Exact and approximate field distributions of the LP01 mode
effective mode area, defined in (41.32), can be approximated to Aeff D w 2 :
(41.35)
Thanks to the Gaussian approximation, simple analytical expressions for the coupling coefficients between two fibers or between an input Gaussian beam and an optical fiber can be derived [41.1].
41.2 Fiber Properties In the previous section, a theoretical approach to light guiding in step-index optical fibers was presented. In this section a focus is put on some properties of optical fibers that do not appear directly in the theoretical approach. Some physical aspects of optical fibers such as attenuation, dispersion, polarization effects, and nonlinearities are in particular examined. First of all, a brief focus on the fabrication method of optical fibers will be presented.
41.2.1 Fabrication of Optical Fibers All the methods used in the fabrication of low-loss silica optical fibers are based on thermal chemical vapor-phase reactions from starting reagents, all of which present ultralow-level impurities (Fe < 0:1 ppb, OH < 0:1 ppm) necessary to enable the minimal losses of about 0:17 dB=km observed today in telecommunications fibers. Those vapor-phase processes are essentially defined in two categories. The first category is the outside vapor deposition (OVD), first developed by
1413
Normalized amplitude (arb. u.) Cladding Core 1 0.8
Gaussian Approximation The fundamental mode field distribution can be well approximated by a Gaussian function, which may be written in the form
41.2 Fiber Properties
Corning, and its variant the vapor phase axial deposition (VAD) process. The second category is the inside vapor phase deposition (IVPD) process including both the modified chemical vapor deposition (MCVD) and the plasma chemical vapor deposition (PCVD) processes. While the OVD processes are more suited for the fabrication of large-size preforms with deposition rates up to 1020 g=min, the IVPD processes remain the preferred methods for realizing complex refractive-index profiles. The MCVD process involves depositing starting materials on the inner walls of the substrate tube, as illustrated in Fig. 41.16a. The dimensions, such as siding, ovality, cross-sectional area, and uniformity of those tubes are critical to ensure precise dimensional tolerances of the manufactured core rod preform. The tube is then mounted in synchronous rotating chucks of a glassworking lathe so that it is rotating concentrically with respect to the lathe’s rotating axis. An oxyhydrogen torch is the most commonly used heat source. Next, controlled quantities of chemical reactants are entrained
1414
Part F
Optical and Photonic Glass Applications
a)
Deposited glass layer
Substrate silica tube
Gas mixture of reactants
GeCl4 .g/ C O2 .g/ • GeO2 .s/ C 2Cl2 GeO2 .g/ • GeO.g/ C 0:5O2
Soot
Part F | 41.2
Translation Oxyhydrogen torch
b)
dynamic equilibria
Deposited core and cladding
Collapsing
Fig. 41.16a,b MCVD process: (a) glass layer deposition; and (b) collapsing of the preform
in a gas stream by passing a carrier gas such as Ar, He, or O2 though liquid dopant sources such as SiCl4 , GeCl4 , POCl3 , BBr3 , or gases (SF6 , SiF4 ). All these dopants are characterized by the feature that their vapor pressures are orders of magnitude higher than any transition metal impurities that could still be present in the starting material. The chemical gas mixture is injected into the rotating tube in the same direction as it is being heated by the traversing heat source. As the mixture enters the hot zone, a homogeneous gas phase reaction takes place at high temperature to form submicrometer glassy particles, called soot, that deposit downstream of the hot zone. These particles are driven to the cooler glass wall by thermophoresis, where they deposit on the inner surface of the tube. The subsequent heating from the traversing heat source sinters the deposited material to form a high-optical-quality glass film. A basic feature of the MCVD is that the fiber waveguide structure is built up by depositing successive layers of precisely controlled chemical compositions and then collapsing the composite tube to a preform rod, as illustrated in Fig. 41.16b. In order to achieve the desired refractive index profile, considerable understanding of the high-temperature chemistry and mass transport phenomena are particularly important in order to precisely control the incorporation of the desired dopants required. In particular, in contrast to SiCl4 and POCl3 , which are completely oxidized, the oxidation and incorporation of GeCl4 is strongly affected by the unfavorable thermo-
where both the chlorine amount generated by the reactions of the other gas constituents and the higher temperature strongly influence the GeO2 incorporation rate. Similarly with fluorine doping, necessary for cladding compositions that require indexes lower than silica, the effect of fluorine doping on the deposition efficiency and rate has shown that, for high fluorine content, SiF4 could be formed at the expense of SiO2 , thus decreasing the amount of SiO2 available for deposition. The total number of deposited layers, as well as the exact chemical reactant flows for each successive layers forming the cladding and core, is chosen on the basis of the starting tube dimensions, deposition rate, profile complexity, and fiber design to be realized as depicted in Fig. 41.17. Dopants such as GeO2 =P2 O5 or SiF4 are the most commonly used to raise or decrease (respectively) the refractive index of the deposited material relative to silica. As an example, up to 500 layers are required for the fabrication of a commercial multimode preform. The next step in the process of producing optical fibers is to convert the manufactured preform into a hair-thin fiber. The preform is mounted on a downfeed mechanism, which allows the preform tip to be lowered into a high-purity graphite furnace where pure inert gases (such as helium) are injected to provide a clean and conductive atmosphere. In the furnace, tightly controlled temperatures approaching 2000 ı C soften the tip of the preform. Once the softening point of the preform tip is reached, gravity takes over and allows a molten gob to free fall until it has been stretched into a thin strand. The fiber is then fed through a series a)
b)
c)
d)
Fig. 41.17a–d Examples of refractive-index profiles realized using a MCVD process: (a) graded-index fiber; (b) single-mode depressed-clad fiber; (c) dispersion-shifted fiber; and (d) dispersion-flattened fiber
Optical Fibers
41.2.2 Attenuation In the theoretical analysis of Sect. 41.1.3, modes propagate without loss in the fiber. This assumption is true as long as the fiber is short enough. However, in many applications, such as optical communications for example, attenuation is a key parameter since it results in a decay of the optical power transmitted into the fiber. When attenuation of the fiber is taken into account, the power Pout .L/ at the output of a fiber of length L is related to the power Pin at the input of the fiber by the relation Pout .L/ D Pin e˛L ;
(41.36)
where ˛ is the attenuation coefficient. It is customary to use the ratio AdB between the output and input powers after 1 km, defined by [41.10] AdB D 10 log
10
Pout .1 km/ D 4343˛ ; Pin
(41.37)
where ˛ is given in m1 . The fiber-loss parameter AdB depends on the wavelength of the optical signal. Figure 41.18 presents the evolution of AdB as a function of the wavelength for the frequently used silica (SiO2 ) SMF. Three main loss contributions are visible. Rayleigh scattering at short wavelengths is due to random inhomogeneities of the glass that act as scattering centers. The scattered intensity is proportional to 1=40 so that short wavelengths are more strongly scattered than long wavelengths. For wavelengths longer than 1:6 m the main loss contribution is the infrared absorption due to the tails of vibrational resonances of silica in the infrared region. The absorption peak at 1:39 m is a harmonic of a vibrational resonance of the OH bond occurring near 2:73 m. The silica SMF exhibits a minimum value of loss below 0:2 dB=km in the wavelength region near 1:55 m. This explains the choice of this wavelength for long-haul fiber-optic communications. In modern fibers, the OH concentration is considerably reduced and the 1:39 m peak almost disappears. Ultralow losses below 0:15 dB=km have been demonstrated with such dry fibers [41.11]. This value of loss around 0:2 dB=km at 1550 nm is incredibly low if we consider that light can travel 15 km in a solid material and only lose half of its power (3 dB). On the other hand, after 150 km, the attenuation reaches 30 dB and only 0:1% of the power remains in the fiber. This explains why optical amplification is needed for optical transmissions over hundreds of kilometers (typically one optical amplifier every 100150 km). Multimode fibers generally have a higher dopant concentration in order to reach larger numerical apertures. This results in higher Rayleigh scattering loss. Fiber bending and core-cladding interface irregularities are also the cause of extra losses in optical fibers [41.10].
Loss (dB/km)
5
Infrared absorption Rayleigh scattering
2 1 OH absorption
0.5 0.2 dB/km
0.2 0.1 0.6
0.8
1
1.2
1.4
1.6 1.8 Wavelength (μm)
Fig. 41.18 Loss spectrum in a silica
SMF
1415
Part F | 41.2
of coating dies where a two-layer protective UV curable coating is applied to the fiber. This two-part protective jacket provides mechanical protection for handling while also protecting the pristine surface of the fiber from harsh environments. The fiber is pulled by a tractor belt situated at the bottom of the draw tower and then wound on winding drums. During the draw, the preform is heated at the optimum temperature to achieve an ideal drawing tension. Draw speeds up to 40 m=s are not uncommon in the industry. A laser-based diameter gage continuously monitors the fiber diameter where its value is compared to the 125 m target and slight deviations from the target are converted to changes in draw speeds and fed to the tractor mechanism for correction. Typically, 125 m diameter control is achieved with a tolerance of ˙0:25 m or below.
41.2 Fiber Properties
1416
Part F
Optical and Photonic Glass Applications
41.2.3 Dispersion
Part F | 41.2
Dispersion is the fact that the velocity of light depends on its frequency (or wavelength). In optical fibers, we have to distinguish dispersion in multimode fibers (also called intermodal dispersion) and dispersion in SMFs (intramodal dispersion). First of all, let us recall that the phase velocity v' and the group velocity vg are related to the propagation constant ˇ of an optical wave by the following relations [41.3] ! ; ˇ 1 dˇ vg D : d!
v' D
(41.38)
(41.39)
The concept of group velocity appears when an optical signal, composed of a optical pulse train for example, propagates in an optical fiber. A perfect monochromatic wave is composed of one single frequency while the spectrum of an optical pulse contains several frequencies. The phase velocity is the velocity at which each frequency component of the pulse travels while the group velocity is the velocity of the overall envelope of the pulse. Note that group velocity is also the energy propagation speed. Intermodal Dispersion It was shown in Sect. 41.1.3 that the propagation constants ˇlm of the LPlm modes have different values (see Fig. 41.10 for example). A single optical pulse entering a multimode fiber is decomposed on the basis of the different modes and spreads into several pulses. Each pulse travels with a different group velocity and the pulse broadens considerably at the output of the fiber due to different time delays, as illustrated in Fig. 41.19. The broadening can be simply evaluated by considering the shortest and longest ray paths in the ray optics approach of Sect. 41.1.2. It is relatively straightforward to show that the broadening per unit of length is approximately given by [41.1]
n1 : c
(41.40)
∆τ
t
Multimode fiber
t
Fig. 41.19 Illustration of intermodal dispersion in a multi-
mode fiber
For a multimode fiber with n1 D 1:47 and D 1%, the broadening is found to be about 50 ns=km. Let us point out that multimode fibers typically have large core diameters of 50 or 62:5 m but that the diameter value does not appear in the evaluation of . The broadening can be related to the transmission capacity of the fiber, measured through the maximum bit rate B the fiber can support. The bit rate is the number of bits per second in an optical signal (i. e., the number of optical pulses for an on-off keying modulation format for example). The bit time 1=B is the time interval between two adjacent bits or pulses. It is generally agreed that the pulse broadening due to dispersion must not be larger than the bit time, otherwise pulse overlapping may have dramatic consequences on the data recovery. The maximum bit rate in a multimode fiber of length L is therefore Bmax D 1=. L/. In the previous example, the broadening of 50 ns=km leads to a transmission capacity around 20 Mbit=s km. This means that a 1 km-long multimode fiber has a maximum capacity Bmax of 20 Mbit=s and a 10 km-long fiber a maximum capacity Bmax of 2 Mbit=s. These rates are incompatible with high-data-rate long-haul optical communication systems. Multimode fibers are only suitable for local-area networks. It is worth noting that graded-index fibers with nearly parabolic index profile, introduced in Sect. 41.1.1, considerably reduce the modal dispersion. The bandwidth of multimode gradedindex fibers is increased by more than one order of magnitude compared to multimode step-index fibers (typically up to 500 Mbit=s km). Intramodal Dispersion The solution to avoid intermodal dispersion is to use SMFs. These fibers, with a smaller core (typically a D 4 m) and a smaller refractive index difference (typically D 0:4%) compared to multimode fibers, only support the fundamental LP01 mode. However, remembering that the fundamental mode can support two orthogonal polarizations, one could imagine that polarization-mode dispersion, similar to intermodal dispersion, should occur in SMFs. This point will be examined in the next section. In this section a focus is put on another phenomenon, related to group-velocity dispersion. Let us consider an optical pulse traveling in an optical fiber. As mentioned previously, the spectrum of the pulse extends over a certain spectral range. The pulse duration and the spectral width are linked through the Fourier transform. The shorter the pulse, the wider the spectrum is. For example, a Gaussian-shape Fourier-transform-limited pulse with 10 ps duration extends across 0:35 nm [41.9]. As illustrated in Fig. 41.10, which shows the evolution of ˇ01 as a function of the normalized frequency V D !aNA=c, the propagation
Optical Fibers
d.1=vg / : d
DD
D D DM C DW :
(41.41)
The dispersion D is usually given in units of ps=.km nm/ and is closely related to the broadening of a pulse (in ps) per unit of propagation length (in km) and unit of spectral width (in nm). The dispersion D has two distinct causes in an optical fiber: the material dispersion and the waveguide dispersion [41.1]. The material dispersion comes from the fact that the refractive index of the material changes with the optical frequency. This leads to wavelength dependence of the group velocity. Material dispersion is proportional to the second derivative of the refractive index with respect to the wavelength. No light guiding is necessary to have this effect, usually known as chromatic dispersion. The waveguide dispersion is the contribution of the light-guiding mechanism to the wavelength dependence of the group velocity. Let us remember that,
∆τ t
in the wave optics approach presented in Sect. 41.1.3, no wavelength (or frequency) dependence of the indices n1 and n2 was taken into account. However, the propagation constant ˇlm , plotted in Fig. 41.10, shows a nonlinear frequency dependence. This leads to a frequency dependence of the group velocity. A waveguide is therefore intrinsically dispersive and the intramodal dispersion D of a SMF is the sum of the material dispersion DM and the waveguide dispersion DW
t
Single-mode fiber
Fig. 41.20 Illustration of intramodal dispersion in a SMF
(41.42)
Figure 41.21 shows the wavelength dependence of DM , DW , and D for the particular case of a conventional silica SMF used for telecommunications. It turns out that DM vanishes for D 1:276 m. This wavelength is referred to as the zero-dispersion wavelength ZD of fused silica. Below ZD , the dispersion DM is negative and becomes positive above that. Negative dispersion, also referred to as normal dispersion, means that higherfrequency components travel slower than the lower-frequency components. Conversely, positive dispersion is referred to as anomalous dispersion and implies that high-frequency components travel faster than the lower ones. At ZD pulses suffer minimal spreading from dispersion. The waveguide dispersion DW remains negative and contributes to shifting the dispersion D toward lower values. The zero-dispersion wavelength ZD of the fiber shifts to 1:31 m and the total dispersion D is 17 ps=.km nm/ in the telecommunication window around 1:55 m. This value is much lower than the intermodal dispersion calculated previously for multimode fibers (50 ns=km) but is still too high to achieve signal transmission without pulse overlapping over long distances at high bit rates. One possible answer to this problem
Dispersion D (ps/(km nm)) 40 DM 20
0
–20
D 1
1.2
1.4
1.6
1.8 λ (μm) DW
–40
Fig. 41.21 Total dispersion D, material –60
dispersion DM , and waveguide dispersion DW for a conventional SMF
1417
Part F | 41.2
constant ˇ01 of the LP01 mode does not vary linearly with frequency. The group velocity vg , given by (41.39), is therefore frequency-dependent. This means that the different spectral components of the pulse disperse and do not arrive at the fiber output simultaneously. This leads to pulse broadening as illustrated in Fig. 41.20. It is usual to specify the group-velocity dispersion by the parameter D, which measures the wavelength dependence of the inverse of the group velocity, as follows
41.2 Fiber Properties
1418
Part F
Optical and Photonic Glass Applications
Part F | 41.2
could be to send optical signals around the wavelength of 1:3 m where the dispersion falls to zero. However, at this wavelength the light would suffer from more loss than at 1:55 m and would not benefit from efficient optical amplifiers as is the case at 1:55 m (Sect. 41.4.2). Instead, the solution that has been chosen in practice is to compensate for the fiber dispersion at 1:55 m. Since the waveguide dispersion depends on the fiber parameters (in particular a and ), it is possible to design fibers with waveguide dispersion that partially or totally compensates for the material dispersion at 1:55 m. These fibers are called dispersionshifted fibers and can have their zero-dispersion wavelength in the vicinity of 1:55 m. This solution, which is attractive for a single-wavelength transmission, is however detrimental for wavelength division multiplexing (Sect. 41.4.1). It is also possible to tailor the fiber in such a way that the total dispersion is strongly negative at 1:55 m (40 ps=.km nm/ for example). These fibers are called dispersion-compensating fibers (DCFs). Periodically alternating spans of SMF and DCF in long-haul transmission systems minimizes the detrimental effects of fiber dispersion [41.10].
41.2.4 Polarization Effects In a perfectly circular SMF the two orthogonal polarizations of the fundamental mode are degenerate. This means that they have the same propagation constant ˇ01 and the same field distribution E01 . Their directions are arbitrary since the fiber is perfectly circular. However, due to the fabrication process, real fibers are not perfectly circular and exhibit some ellipticity. They may also experience residual intrinsic or extrinsic anisotropic stress. The cylindrical symmetry is then broken and the degeneracy is removed. This results in two polarization axes x and y, also called the polarization eigenstates of the fiber, with two different propagation constants ˇ01x and ˇ01y , respectively. Two different effective indices nx and ny are associated with the linearly polarized modes and the birefringence of the fiber is defined as n D jnx ny j. The birefringence of conventional SMFs is of the order of 107 to 106 . When an arbitrary-polarized wave with wavelength 0 enters the fiber, it is decomposed on the basis of the two x and y polarization states. Each polarization travels at its own velocity and a relative phase shift given by D
2 nL 0
(41.43)
occurs after propagation over a length L of fiber. The polarization state is not preserved in the fiber and evolves periodically, as illustrated in Fig. 41.22. The pe-
Output polarization
ny
nx LB Input polarization
Fig. 41.22 Illustration of polarization evolution in a bire-
fringent SMF
riod LB is the length of fiber that leads to D 2 and is referred to as the beat length, given by LB D
: n
(41.44)
The typical value of the beat length is a few meters for standard SMFs. When the fiber length is not exactly a multiple of the beat length, the wave exits the fiber with an elliptical polarization state. This can be detrimental in applications requiring control of the polarization state. Moreover, in conventional SMFs, for which fabrication anisotropies are relatively low, the birefringence is sensitive, in magnitude and direction, to temperature changes or external stresses such as bends or twists. It results in a random evolution of the polarization state at the fiber output. To avoid these problems, it is possible to make fibers for which a strong anisotropy is intentionally induced during the fabrication process. The birefringence of these fibers is typically a few multiples of 104 and, because of their strong intrinsic anisotropy, they are much less sensitive to external fluctuations. These fibers are called polarization-maintaining (PM) fibers and can preserve a linear polarization state provided that the input polarization is injected along one of the eigenstates of the fiber. Polarization effects in optical fibers are also a source of pulse broadening that could affect lightwave transmission systems. If an input pulse excites both polarization states of the fundamental mode, it propagates at two different group velocities since both polarizations have different propagation constants. This results in a broadening of the pulse at the output of the fiber and even a splitting of the pulse into two pulses. This phenomenon is known as polarization-mode dispersion
Optical Fibers
where vg x and vg y are the group velocities associated with the x and y polarization components respectively. The DGD T is a measure of the PMD and is quite large ( 1 ns=km) for PM fibers while it is much lower for conventional SMFs ( 1 ps=km). Actually, the situation is different for conventional SMFs submitted to random fluctuations of birefringence and the simple estimation considered above is inadequate. A more realistic model must include statistical treatment of the birefringence [41.10] and it can be shown that the average time delay p does not depend on the length L of the fiber but on L. A typical p value of DGD for conventional SMFs is 0:1 ps= km. This relatively low value of PMD only affects long-distance and high-data-rate lightwave communications systems, and to overcome this issue, PMD-compensation schemes have been developed [41.10].
Self-Phase Modulation Self-phase modulation (SPM) is the accumulation of a nonlinear phase delay depending on the intensity, when light propagates in an optical fiber with Kerr effect. If the wave is an optical pulse, the nonlinear phase is time dependent. Knowing that the instantaneous frequency of an optical wave is the time-derivative of the phase, it can be understood that SPM causes a modification of the optical spectrum and, in particular, the creation of new frequencies. The nonlinear phase shift NL , after propagation over a length L, is given by [41.9] NL D PLeff ;
(41.47)
where is the nonlinear coefficient given by
41.2.5 Nonlinearities Any dielectric medium has a nonlinear response when exposed to intense electromagnetic fields. Glasses are not among the most nonlinear materials but when they are drawn into fibers their nonlinearity is enhanced. This enhancement is due to long interaction lengths of light with the medium and the high power density offered by the small cross-section of the fiber. Among the different glasses for fibers, chalcogenide glasses can be up to 1000 times more nonlinear than the usual fused silica glass. The most relevant nonlinear effects occurring in optical fibers are third-order effects such as optical Kerr effect, stimulated Raman scattering, and stimulated Brillouin scattering [41.9]. Because of the amorphous nature of glass, second-order nonlinear effects do not exist in optical fibers. Optical Kerr Effect The third-order nonlinear susceptibility of glass induces an intensity dependence of the refractive index n as n D n0 C n2 I ;
where n0 is the usual linear refractive index considered in the previous sections, n2 is the nonlinear refractive index, and I the optical intensity. The optical intensity is related to the optical power P and the effective mode area Aeff introduced earlier: I D P=Aeff . A typical value of n2 is 2:6 1020 m2 =W for fused silica [41.9]. Due to the optical Kerr effect, an intense light can modify the medium in which it propagates, which in turn modifies the light properties. In optical fibers the transverse mode shape is not affected by index variations, but the propagation constant becomes intensity dependent. This refractive index variation is responsible, in optical fibers, for self-phase modulation, cross-phase modulation and four-wave mixing.
(41.46)
D
2 n2 ; 0 Aeff
(41.48)
and Leff the effective length given by Leff D
1 e˛L : ˛
(41.49)
The nonlinear coefficient is a measure of the strength of the Kerr effect in the fiber. Its value depends on the material parameter n2 and on the waveguide parameter Aeff . The conventional silica SMF has a nonlinear coefficient around 1 W1 km1 at 1550 nm. In silica-based highly nonlinear fibers, with smaller effective mode areas, the nonlinear coefficient is increased to about 20 W1 km1 [41.7]. Chalcogenidebased highly nonlinear fibers with a photonic crystal structure (Sect. 41.3.2), can reach nonlinear coefficients of 46 000 W1 km1 [41.12]. The nonlinear phase shift NL is proportional to the length over which the optical field interacts with the fiber. However, the nonlinearity is no longer efficient if
1419
Part F | 41.2
(PMD). To avoid this problem PM fibers cannot be used because lightwave transmission systems cannot guarantee linear polarizations at the input of optical fibers. The high birefringence of PM fibers is a drawback that prevents them from being used in communications systems. Indeed, the differential group delay (DGD) T per unit of length between the two polarization components can be estimated, in first approximation, by [41.10] ˇ ˇ ˇ 1 1 ˇˇ ; T D ˇˇ (41.45) vg x vg y ˇ
41.2 Fiber Properties
1420
Part F
Optical and Photonic Glass Applications
Part F | 41.2
the optical power is too low because of the fiber losses. This aspect is taken into account through the effective length Leff . This parameter can be approximated to the fiber length L when losses are negligible (˛L 1) and reaches a limit equal to 1=˛ if ˛L 1. This means that the maximum nonlinear phase shift is obtained after propagation over a length Lmax of fiber equal to 1=˛. For conventional SMFs with loss of 0:2 dB=km (˛ D 4:6 105 m1 ), Lmax is equal to 21:7 km. For chalcogenide fibers with 1 dB=m of loss (˛ D 0:23 m1 ), Lmax is equal to 4:3 m. The threshold power Pth above which SPM becomes significant can be estimated as the power required to reach a nonlinear phase shift NL of 1 rad [41.9]. From (41.47), for a conventional SMF of length Lmax D 21:7 km with a nonlinear coefficient of 1 W1 km1 at 1550 nm, Pth is estimated around 50 mW. When an optical pulse undergoes the effect of SPM, new frequencies are created and its spectrum broadens. For strong SPM the optical spectrum can exhibit oscillations. Figure 41.23 shows the spectra of a Gaussian pulse for several values of the nonlinear phase shift NL . Larger broadening can be obtained for higher phase shifts. SPM is an important effect involved in supercontinuum generation [41.13] where spectral broadening can extend over several hundreds of nm, similar to white light. It has been seen in Sect. 41.2.3 that dispersion spreads out in time the spectral components of an optical pulse. In this section, we describe the SPM-induced spectral broadening of a pulse. When dispersion and SPM are present simultaneously in an optical fiber, and if the dispersion D is negative, their combined effects broaden an optical pulse both in time and frequency. If Intensity
Intensity
0
Intensity π/2
Frequency Intensity
Frequency Intensity
3π/2
Frequency
π
Frequency Intensity
5π/2
7π/2
Frequency
Frequency
Fig. 41.23 SPM-broadened spectra of a Gaussian pulse for
several values of the nonlinear phase shift
D is positive, a particular situation can occur because the effects of dispersion and SPM can cancel each other out and give rise to optical solitons [41.9]. Thanks to the precise balance between dispersion and nonlinear effects solitons can propagate in an optical fiber with no change either in time or in frequency. Optical solitons have been extensively studied for their great potential, in particular for long-distance optical fiber communications. Cross-Phase Modulation In SPM, a single wave itself creates a refractive index variation that modifies its spectrum. When two or more waves at different frequencies travel together in a nonlinear fiber, they undergo the refractive index variations caused by themselves and by the other waves. The latter effect is called cross-phase modulation (XPM). The nonlinear phase shift of the j-th wave is [41.9] 0 jNL
D Leff @Pj C 2
N X
1 Pk A ;
(41.50)
k¤j
where N is the number of waves involved in the process and Pq (q D j; k) is the power of each wave. The factor 2 in (41.50) indicates that XPM is twice as effective as SPM for the same power. This is due to the form of the nonlinear susceptibility [41.9]. Similarly to SPM, XPM is responsible for the modifications of the optical spectrum of a wave by another wave. Figure 41.24 represents the spectrum of two waves traveling at different frequencies in an optical fiber for several values of their power ratio P1 =P2 . When wave no. 1 is off (i. e., P1 D 0), the spectrum of wave no. 2 is only broadened by SPM. When wave no. 1 starts growing, it does not affect the spectrum of wave no. 2 as long as its power is too low (typically P1 =P2 < 0:1). The oscillating and asymmetrical spectrum of wave no. 1 at higher power ratios (P1 =P2 > 0:1) indicates that it experiences the influence of wave no. 2. When both waves have equivalent powers, the deformations of their spectra are similar. Compared to SPM, XPM induces an asymmetry and a shift in the broadened spectra. Note that XPM not only occurs between waves at different frequencies but can also be present between the two polarization components of the fiber modes. In optical fiber communications, XPM can lead to problems with channel cross-talk. XPM can however be used to monitor the phase change of a wave by the power of another wave. This finds applications in the field of short-pulse lasers and all-optical signal processing for example. XPM is a nonlinear effect for which only the power (not the phase) of a wave induces phase changes on another wave, according to (41.50). When
Optical Fibers
Wave No. 2
!1 C !2 D !3 C !4 :
(41.51)
P1/P2 = 0.5
ˇ D ˇ3 C ˇ4 ˇ1 ˇ2 ;
(41.52)
the phase also plays a role in the wave coupling, this effect is called four-wave mixing.
where ˇj are the propagation constants of each wave. When ˇ D 0, the FWM process is completely matched and the idler wave can be efficiently generated. Furthermore, if the frequency !4 preexists in the fiber, it can be amplified through the FWM process; in this case it is called parametric amplification. When the FWM process involves four waves, it is called nondegenerate FWM. There is also the possibility of degenerate FWM, where two of the four frequencies coincide. In this case, two waves of frequency !1 and !2 give energy to a third wave whose frequency !3 satisfies 2!1 D !2 C !3 . Figure 41.25 illustrates the generation of a new frequency through both nondegenerate and degenerate FWM processes in an optical fiber. FWM is a phase-sensitive process widely used in optical fibers for many applications such as wavelength conversion [41.15], optical time-domain demultiplexing [41.16], parametric amplification [41.14], or frequency-comb generation [41.17].
Four-Wave Mixing Four-wave mixing (FWM) is observed in nonlinear fibers when resonant coupling occurs between four
Stimulated Scattering The previously presented SPM, XPM, and FWM effects are known as elastic nonlinear processes in the sense
P1/P2 = 0.1
P1/P2 = 0.02
P1/P2 = 0
Frequency
Fig. 41.24 SPM- and XPM-broadened spectra of two waves for several values of their power ratio
a)
ω1 ω2
ω
Fiber
ω3
ω1 ω2
ω4 ω
b)
ω2
ω1
ω
Fiber
ω2
ω1
ω3 ω
Fig. 41.25a,b Illustration of (a) nondegenerate FWM and (b) degenerate
FWM
Part F | 41.2
Practically, this means that if three waves of frequencies !1 , !2 , and !3 copropagate inside a fiber simultaneously, they can generate a fourth wave, called the idler wave, whose frequency !4 satisfies the previous condition. Resonant coupling implies also a condition on the propagation constants of the waves. The phase mismatch ˇ is written as
P1/P2 = 1
ω3
1421
waves of frequencies !1 , !2 , !3 , and !4 . Resonant coupling means that some phase relations between waves are satisfied. A first relation leads to the following condition on the frequencies of the waves [41.14]
Intensity Wave No.1
41.2 Fiber Properties
1422
Part F
Optical and Photonic Glass Applications
Part F | 41.2
that the total optical energy is maintained throughout the process. Waves simply exchange their energy without loss. As will be seen in this section, stimulated Raman scattering and stimulated Brillouin scattering are inelastic nonlinear processes. A certain amount of optical power is lost to (or given by) the host matrix of the fiber. The Raman process is due to the interaction of photons with optical phonons (quanta of the molecular vibrations related to the polarizability fluctuations) while acoustic phonons (quanta of the molecular vibrations related to the density fluctuations) are involved in the Brillouin process. Stimulated Raman Scattering In Raman scattering, photons interact with matter through the vibrational states of the host material as illustrated in Fig. 41.26a. One pump photon gives up a part of its energy to an optical phonon and is converted into one lower-energy photon called the Stokes photon. In principle, it is also possible that an already-existing phonon interacts with a pump photon to generate one higher-energy photon called an anti-Stokes photon. That process, however, is usually weak but can be significant if it is amplified by a phase-matched FWM process. The optical frequency S of the Stokes photon is then generally lower than that of the pump photon p . The frequency difference p s is called the Raman shift R . In silica fibers the Raman shift R is centered at 13 THz with a 3-dB-bandwidth R of about 7 THz.
When the Raman effect is excited in an optical fiber by a pump frequency, a red-shifted broadband spectrum, arising from spontaneous Raman scattering, can be observed at the output of the fiber, as illustrated in Fig. 41.26b. The Raman scattering process becomes stimulated if the pump power exceeds a threshold value. Stimulated Raman scattering (SRS) can occur in both forward and backward directions. A preexisting signal with an optical frequency around S can be amplified by SRS as illustrated in Fig. 41.26c. The threshold power Pth of SRS, defined as the incident power at which half of the pump power is transferred to the Stokes wave, is estimated from [41.9] Pth
16Aeff ; gR Leff
(41.53)
where gR is the peak value of the Raman gain. For silica fiber gR 7 1014 m=W at the wavelength of 1:55 m. For a conventional SMF (Aeff D 80 m2 ) at its maximum effective length Lmax D 21:7 km, Pth is about 840 mW. By transferring an important part of the energy of an incident wave into another wavelength, Raman scattering can limit the peak power achievable in some fiber devices and is, in this case, detrimental. It can, however, be utilized as the stimulated process required in fiber amplifiers or cascaded Raman fiber lasers. Raman scattering is also widely used in spectroscopy to investigate the vibrational modes of materials.
a)
Phonon Stokes or anti-Stokes photon
Pump photon
Pump photon
AntiStokes photon
Stokes photon
Phonon Phonon
b) νR
Pump Raman ∆ν R νp
Fiber
νS
νp
c) Amplified signal Signal
νS
νp
Fiber
νS
νp
Fig. 41.26a–c Illustration of the Raman effect: (a) principle; (b) spontaneous Raman scattering; and (c) stimulated Raman scattering
Optical Fibers
When excited in an optical fiber, Brillouin scattering leads to the generation, in the backward direction, of a red-shifted spectrum as illustrated in Fig. 41.27b. Similarly to the Raman effect, stimulated Brillouin scattering (SBS) can occur above some threshold and can be used to amplify a counterpropagating signal in the fiber, as illustrated in Fig. 41.27c. Because of the small bandwidth of the Brillouin gain, only signals with a spectrum falling in the Brillouin bandwidth are amplified at the peak value of the Brillouin gain. SBS acts as a highly frequency-selective optical amplifying process. For silica fibers, the peak value of the Brillouin gain is gB 5 1011 m=W, which is much higher than the Raman gain. The Brillouin threshold, defined as the incident power at which the power of the Stokes wave is half of the power of the pump wave, can be estimated as [41.9] Pth
21Aeff : gB Leff
(41.54)
a) Index grating induced by the acoustic wave
Pump wave
Stokes wave
b) Pump
νp Fiber
Brillouin νB ∆ν B νS
c) Pump
Signal νp Fiber
νS
νS
Fig. 41.27a–c Illustration of the Brillouin effect: (a) principle; (b) spontaneous Brillouin scattering; and (c) stimulated Brillouin scattering
1423
Part F | 41.2
Stimulated Brillouin Scattering Brillouin scattering is due to the phenomenon of electrostriction. An oscillating electric field at a pump frequency p generates an acoustic wave at some frequency B . The process of spontaneous Brillouin scattering can be seen as the reflection of the pump wave on the longitudinal index grating induced by the acoustic wave. The scattered wave is also called the Stokes wave in this case. The scattering process must conserve both the energy and the momentum. Conservation of energy requires that the Stokes frequency S is downshifted by
B with respect to the pump frequency. Conservation of momentum indicates that the scattered light travels only in the backward direction [41.9]. This process is schematically represented in Fig. 41.27a. For silica fibers the Brillouin shift B is about 11 GHz at the wavelength 1:55 m and its 3-dB-bandwidth B is about 50 MHz. This spectrum is less shifted and much narrower than the Raman spectrum.
41.2 Fiber Properties
1424
Part F
Optical and Photonic Glass Applications
Part F | 41.3
For silica fibers, with the above value of gB and the same fiber parameters as for the Raman threshold estimation (Aeff D 80 m2 and Lmax D 21:7 km), Pth is as low as 1:5 mW. Clearly, SBS limits the launched power to a few milliwatts in silica optical fibers. This estimation is, however, only valid for narrowband signals whose spectrum is less than the Brillouin gain bandwidth of 50 MHz (such as unmodulated continuous-
wave signals for example). For broader signals, the Brillouin threshold is significantly increased. SBS can be used in optical fibers as the amplifying process of Brillouin fiber lasers. Such devices can have a relatively low pump threshold and a very small linewidth. The temperature dependence of the Brillouin shift can be used for temperature and pressure sensing (Sect. 41.4.3).
41.3 Specialty Optical Fibers The optical fibers taken as examples in the previous sections were generally telecommunication SMFs. These fibers are characterized by single-mode operation and ultralow loss at 1:55 m. There exist, however, many other types of fibers different in terms of their geometry or glass composition. Optical fibers that are not directly used for telecommunications are generally referred to as specialty optical fibers [41.18]. In this section the most frequently used specialty optical fibers will be presented, in particular rare-earth-doped fibers, photonic crystal fibers, and nonsilica fibers. Fiber Bragg gratings, which are rather fiber components than specialty fibers, will also be presented due to their wide range of applications.
41.3.1 Rare-Earth-Doped Fibers A major field of interest in which optical fibers offer great opportunities is the domain of all-fiber light sources. Fiber lasers and fiber amplifiers are nearly always based on glass fibers doped with rare-earth ions (of the lanthanide family). Due to their atomic structure, rare-earth ions have quite narrow and highly efficient optical transitions. When incorporated in the core of an optical fiber, these ions absorb pump light at a specific wavelength. This excites some metastable levels and allows for light amplification via stimulated emission. Table 41.1 gives examples of the most common laser-active ions and their typical emission wavelength range [41.19].
Note that the emission range of erbium corresponds to the minimum loss window of silica fibers. This drove extensive research in the 1980s for the development of the erbium-doped fiber amplifier [41.20] for telecommunication applications (Sect. 41.4.2). In fiber amplifiers and fiber lasers, the three fundamental interaction processes between light radiation and atomic transitions are involved. These processes are absorption, spontaneous emission and stimulated emission. Figure 41.28 illustrates the three processes in the case of an erbium-doped fiber pumped with a 980 nm radiation wavelength. In this case, the erbium ion behaves like a three-level system. The fundamental level is the 4 I15=2 level. An incident pump photon at 980 nm can be absorbed from this level and can excite the upper level 4 I11=2 . Due to the fast multiphonon transition from 4 I11=2 to 4 I13=2 the lifetime of the upper state is at most a few microseconds and the transition is nonradiative. The lifetime of the 4 I13=2 level is of the order of 10 ms and this level is referred to as a metastable level. When excited, this level can spontaneously return to the fundamental state by emitting a photon. This spontaneous photon has random direction, polarization and phase. 4
I11/2
Nonradiative transition 4
Table 41.1 Frequently used rare-earth ions and their main emission spectral range Dopant Neodymium (Nd3C ) Ytterbium (Yb3C ) Erbium (Er3C ) Thulium (Tm3C ) Holmium (Ho3C )
Wavelength range ( m) 1:031:1 1:01:1 1:51:6 1:72:1 2:12:9
I13/2
980 nm
1550 nm 4
I15/2
Absorption
Spontaneous emission
Stimulated emission
Fig. 41.28 Interaction of light with erbium ions: absorp-
tion; spontaneous emission; and stimulated emission
Optical Fibers
41.3.2 Photonic Crystal Fibers In contrast with conventional fibers, made of different glass compositions with different indices n1 and n2 , photonic crystal fibers (PCFs) can be made from a single glass composition and an arrangement of air holes [41.22]. Figure 41.29 illustrates the cross-section of a frequently used PCF. It consists of a triangular pattern of air holes with one hole missing in the center. This fiber can be roughly described as a solid core surrounded by an effective cladding composed of glass and air. The effective refractive index of the cladding is then lower than that of the core. The guiding mechanism
Fig. 41.29
Λ Cladding Core
1425
d
Cross-section of a solid-core PCF. The brown area indicates glass and the gray circles air holes
can be understood with the principle of total internal reflection in a higher refractive index area, similar to conventional fibers. The air-hole diameter is usually denoted d and the distance between holes is the pitch #, as depicted in Fig. 41.29. These fibers offer many degrees of freedom in their design and present remarkable properties [41.22]. Similar to conventional fibers, PCFs are fabricated in two steps: first, a preform is fabricated and it is then drawn into a fiber. For the preform fabrication, one of the most frequently used methods consists of stacking glass capillaries and glass rods to achieve the preform design. The obtained preform is then drawn in a drawing tower with pressure-controlled gas flows to avoid holes collapsing. The procedure of drawing can be repeated until the desired structure and dimensions are achieved. One of the most interesting properties of PCFs is the fact that they can be endlessly single-mode, providing that the condition d=# < 0:4 is satisfied. This means that the fiber can always be single-mode whatever the wavelength. Another unusual property that we do not find in conventional fibers is the fact that the waveguide dispersion of PCFs can be positive and can, for example, shift the zero-dispersion wavelength of the fiber below 1:3 m for fused silica fibers. The third interesting property is the possibility of achieving extremely small or extremely large mode areas. A high refractive index difference between the core and the cladding is possible with large values of d=# (larger proportion of air in the cladding than glass). This allows small-core fibers for nonlinear applications or high numerical aperture fibers for power delivery. In contrast, a small refractive index difference allows large mode areas and very weak optical nonlinearities. Note, however, that attenuation in PCFs is very sensitive to structural variations, both in the transverse and longitudinal dimension of the fiber. Losses in PCFs are generally higher than in conventional fibers. However, efforts are made to reduce hole surface imperfections and losses of 0:18 dB=km, comparable to conventional SMF, have already been obtained in PCFs [41.23]. Since their first demonstration in 1996 [41.24], many kinds of PCFs have been studied and fabricated.
Part F | 41.3
Its wavelength is roughly between 1500 and 1600 nm, corresponding to the emission wavelength range of erbium. An incident photon in the range 15001600 nm can be incident on an ion, initially excited at the 4 I13=2 level. In this case, there exists a probability of generating a stimulated photon, with the same properties as the incident one (wavelength, direction, polarization, and phase). Through the stimulated emission process, a pump photon is absorbed and a signal photon is generated. Absorption of a photon at 1550 nm can also occur between levels 4 I15=2 and 4 I13=2 similar to the absorption of a pump photon between 4 I15=2 and 4 I11=2 . The probability of having preferentially stimulated emission between levels 4 I13=2 and 4 I15=2 rather than absorption is related to the ratio between the number of ions N2 at the excited state and the number of ions N1 at the fundamental state. When N2 > N1 , the population inversion is achieved and stimulated emission is the dominant effect. The number of stimulated photons increases with the population difference N2 N1 . The gain of such an amplifying medium increases with the number of absorbed pump photons. Stimulated emission in rare-earth-doped fibers is the physical mechanism at the origin of the development of fiber amplifiers and fiber lasers [41.19], whose principle will be detailed in Sect. 41.4.2. One of the most famous fiber amplifiers is the erbium-doped fiber amplifier [41.20], developed in the 1990s to amplify optical telecommunication signals at 1:55 m. Since then, a large variety of fiber amplifiers and fiber lasers have been proposed. Power scaling of these devices has been enabled by the advent of new optical fibers, in particular double-clad fibers (described in Sect. 41.4.2). New challenges are now the limitation of nonlinear effects occurring in these fibers because of the high power density [41.21]. In this context, large-mode-area fibers are extensively studied and photonic crystal fibers offer promising solutions in this field, and also in many others, as will be seen next.
41.3 Specialty Optical Fibers
1426
Part F
Optical and Photonic Glass Applications
Part F | 41.3
In the following, some examples of frequently used PCFs are given. Many other kinds of PCFs exist but will not be presented in this section. Figure 41.30a represents the cross-section of an endlessly single-mode silica PCF. This fiber is used for power delivery of visible and near-infrared wavelengths [41.25]. It can also be made with other glasses than fused silica for mid-infrared applications (Sect. 41.3.3). Figure 41.30b illustrates a highly nonlinear silica PCF. Compared to the previous fiber, the ratio d=# is larger and the pitch # is smaller. This leads to highindex contrast between the core and the cladding and the possibility of strongly confining the fundamental mode in an extremely small core. Compared to the value of 80 m2 for the effective mode area of a conventional SMF, effective mode areas as small as a few m2 can be reached in such fibers. This significantly enhances the nonlinear coefficient while shifting the zerodispersion wavelength toward the short wavelengths. For example, nonlinear coefficients of 70 W1 km1 (compared to 1 W1 km1 for conventional SMFs) with a zero-dispersion wavelength at 800 nm are commercially available with silica PCFs. To further enhance the nonlinear coefficient, other glasses than silica can be chosen such as heavy oxide glasses or chalcogenide glasses known to be 1001000 times more nonlinear than silica (Sect. 41.3.3). Another design to enhance the nonlinear coefficient of optical fibers is the suspended-core structure represented in Fig. 41.30c. The core area is surrounded by only three large holes. The effective mode area can be as low as a few m2 with a triangular shape. This kind of fiber is, however, usually multimodal. Similar to conventional step-index fibers, polarization-maintaining PCFs can be fabricated to preserve a linear polarization during the propagation. To do that, the symmetry of the structure must be broken to induce a strong birefringence. This can be done by the presence of two larger holes on a transverse axis of the fiber, as illustrated in Fig. 41.30d. High numerical aperture multimode fibers are generally required to transport high power from broadarea lasers with poor beam quality (such as high-power diode bars used for pumping operation for example). Since high-index contrast can be achieved thanks to air holes in PCFs, high numerical apertures of 0:6 or 0:7 can be reached. These multimode PCFs are generally referred to as air-clad fibers and an example is shown in Fig. 41.30e. The core diameter can be typically in the range 100200 m. Note that this air-clad design can be advantageously used to fabricate double-clad fibers for amplifier and laser applications [41.21] as discussed in Sect. 41.4.2.
a)
b)
c)
d)
e)
f)
g)
h)
Fig. 41.30 (a) Endlessly single-mode PCF; (b) highly nonlinear PCF; (c) suspended-core PCF; (d) polarizationmaintaining PCF; (e) air-clad PCF; (f) hollow-core fiber; (g) photonic bandgap fiber; and (h) pixelated Bragg fiber. (a–g) © Photonics Bretagne, (h) courtesy of Laboratoire
de Physique des Lasers, Atomes et Molécules, CNRS/Université de Lille 1, France)
In the previously described PCFs, light guidance is possible in a higher refractive index core, similarly to conventional step-index or graded-index fibers. There also exist certain hole arrangements resulting in
Optical Fibers
41.3.3 Nonsilica Fibers Different materials, other than glasses, can be used to fabricate optical fibers. For example, plastic optical fibers are made out of polymer, traditionally poly(methyl methacrylate). Multimode, with a high numerical aperture, these fibers are usually easy to use and low cost. They find applications in industrial or home networks for example [41.31]. Crystalline fibers, such as sapphire fibers, are also used for their transparency in the infrared region and their capability to support high powers [41.18]. Regarding glass fibers, a large variety of glasses, other than fused silica, can also be used to make optical
1427
fibers. Chalcogenide glasses have already been mentioned for their nonlinear properties. Lead silicate or bismuth oxide optical fibers are also known for their high nonlinearity. In this section, a focus will be put on the two most frequently used nonoxide glass fibers, namely fluoride fibers and chalcogenide fibers. Fluoride Fibers Fluoride fibers are optical fibers made of fluoride glasses such as zirconium fluoride (ZrF4 ), indium fluoride (InF3 ) or aluminum fluoride (AlF3 ) glasses [41.32]. Fluoride fibers are transparent from ultraviolet to midinfrared wavelengths. Zirconium fluoride glass fibers are commonly referred to as ZBLAN fibers, as they are made from ZrF4 , BaF2 , LaF3 , AlF3 , and NaF. They are the most transparent fibers in the 24 m spectral range. Optical losses of ZBLAN fibers can be as low as 0:001 dB=m at 2:56 m and below 0:005 dB=m in the 22:4 m wavelength region. Indium fluoride glass fibers have a broader transparency range than ZBLAN fibers but their attenuation is higher. Attenuation of indium fluoride fibers is below 0:05 dB=m in the 24:1 m range and below 1 dB=m in the 0:35:3 m range. Aluminum fluoride glass fibers are made from AlF3 , ZrF4 , BaF2 , CaF2 , and YF3 and exhibit the largest chemical durability and damage threshold. Their attenuation is below 0:06 dB=m in the 1:73:1 m range and below 1 dB=m in the 0:34 m range. Many types of fluoride fibers can be made (singlemode fibers, multimode fibers, polarization-maintaining fibers). These fibers are exploited for their midinfrared transparency and find applications in spectroscopy, fiber-optic sensors, thermometry, and imaging. They can also deliver power from Er:YAG lasers operating at 2:9 m used for medical applications. Fluoride fibers can also be doped with a number of rare-earth ions for applications in fiber lasers and amplifiers in mid-infrared wavelengths. Due to their low phonon energy, fluoride fibers can be doped with high concentration of rare-earth elements. This makes upconversion processes possible and visible laser lines have also been obtained using different rare-earthdoped fibers. Chalcogenide Fibers Chalcogenide glasses are based on the chalcogen elements sulfur (S), selenium (Se), and tellurium (Te) with the addition of other elements such as germanium (Ge), arsenic (As), and antimony (Sb). Typical glass transition temperatures range from 100 to 400 ı C. Chalcogenide glasses are suitable for fiber drawing pro-
Part F | 41.3
a photonic bandgap mechanism where light guidance is possible in a central area where the refractive index is lower than in the cladding. Guidance in a hollow core is even possible. Such a guiding mechanism is comparable to a two-dimensional (2-D) Bragg mirror effect and only works in a limited wavelength region. Figure 41.30f represents a hollow-core fiber where light is guided in the central air core. Such fibers are interesting for high power delivery [41.26]. The hollow core can also be filled with gas or liquids and such fibers can be exploited for nonlinear applications [41.27] and fiberoptic sensors [41.28]. Figure 41.30g illustrates an all-solid photonic bandgap fiber. Instead of containing air holes, the cladding consists of an arrangement of high-index circular rods embedded in a lower-index glass. The lowerindex glass is usually pure silica while rods can be made of germanium-doped silica. The central part exhibits a lower refractive index than the cladding and the guidance mechanism is also possible through the photonic bandgap mechanism. This kind of design can be used for creating large-mode-area fibers that only support the fundamental mode [41.29]. They are less sensitive to nonlinear effects and thus allow power scaling of fiber amplifiers and fiber lasers when they are doped with active ions. The last example is the fiber illustrated in Fig. 41.30h. It represents a pixelated Bragg fiber [41.30]. This fiber consists of a pure-silica matrix with highindex inclusions (germanium-doped silica) arranged in two concentric circles with some missing inclusions. Guidance in this fiber is obtained through the antiresonant reflecting optical waveguide mechanism. Extremely large mode areas can be achieved and single-mode operation is possible thanks to a well-chosen symmetry of heterostructuration together with an optimized distance between the two high-index circles. Effective mode area of about 3700 m2 at 1:035 m has been demonstrated in such a fiber.
41.3 Specialty Optical Fibers
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Part F
Optical and Photonic Glass Applications
Part F | 41.3
cesses. In particular, both all-solid step-index fibers and photonic crystal fibers can be fabricated from chalcogenide glasses [41.33]. Chalcogenide fibers can be transparent from the visible region (sulfur-based glass) up to the mid-infrared (25 m for telluride glasses), which offers great interest for mid-infrared applications. Furthermore, the nonlinear refractive index n2 of chalcogenide glasses is 1001000 times higher than that of silica glass at 1:55 m, which makes them useful for nonlinear applications. Recently, chalcogenide fibers have generated a great interest in leading-edge research fields such as optical sensing, mid-infrared beam delivery, supercontinuum generation, and Brillouin fiber lasers. Figure 41.31 illustrates two achievements of chalcogenide PCFs. Figure 41.31a shows the attenuation curve of a wide-bandwidth chalcogenide PCF. The glass composition is AsSe and the microstructure is composed of a solid core surrounded by three rings of air holes (see inset of Fig. 41.31a). The fiber is endlessly single-mode and the mode-field diameter is 10 m. The attenuation curve shows that the propagation window of the a) Attenuation (dB/m) 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0
3
3.5
b)
4
4.5
Single mode fiber
5
5.5
6
3-ring
φinput = 13 μm
fiber extends from 5 to 9 m where losses are around 0:5 dB=m. This fiber is used for mid-infrared beam delivery, especially from quantum cascade lasers or optical parametric oscillators [41.36]. A highly nonlinear chalcogenide fiber is illustrated in Fig. 41.31b. The glass composition can be AsSe or GeAsSe and the microstructure can be a three-ring arrangement or a suspended-core structure, as illustrated in Fig. 41.31b. The nonlinear refractive index n2 of AsSe or GeAsSe is about 400500 times higher than in silica at 1:55 m. Moreover, the nonlinearity is exacerbated by an extreme reduction of the effective mode area of the fiber. This is achieved by a tapered section as illustrated in Fig. 41.31b. The core diameter can be as low as 2 m in the thinnest part of the taper. Nonlinear coefficients as high as 46 000 W1 km1 have been obtained with this kind of fiber [41.12], which has been successfully used for applications in nonlinear all-optical signal processing [41.37], supercontinuum generation [41.38], and Brillouin fiber lasers [41.39]. A record nonlinear coefficient of 133 000 W1 km1 has even been reached in a 7 cm-long AsSe microtaper [41.40].
6.5
7
7.5
8
8.5 9 9.5 10 Wavelength (μm) Suspended-core
φoutput = 13 μm φc = 2–8 μm
Fig. 41.31 (a) Chalcogenide PCF for mid-infrared beam delivery; (b) highly ≈ 20–50 cm
Lwaist ≈ 15–100 cm
≈ 20–50 cm
nonlinear chalcogenide PCF [41.34, 35] (reproduced with permission of SelenOptics, France)
Optical Fibers
41.3.4 Fiber Bragg Gratings
B D 2neff # ;
(41.55)
where neff is the effective refractive index of the fundamental mode of the fiber. The inset of Fig. 41.32a represents the typical reflection spectrum of a Bragg grating at B with a full width at half maximum B and a peak reflection Rmax . A phase mask technique can be used instead of the two-wave-interference technique described in Fig. 41.32a. In this case, the intensity modulation is created by the diffraction of the UV beam on a diffractive plate. This technique allows mass production and nonuniform index modulation profiles. There exist various kinds of FBG, depending on the desired application. They differ by their index profile, which can be tailored by the UV beam profile, particularly in the case of the phase mask technique. Figure 41.32b illustrates the basic uniform FBG. This grating reflects light over a narrow bandwidth. The Bragg wavelength is determined by the period # of
the grating. The reflection bandwidth B and the peak reflection Rmax are monitored as a function of the modulation depth and the grating length. Typically, the reflection bandwidth B can be adjusted from less than 0:1 nm to a few nanometers and the peak reflection Rmax from a few % to quasi-100%. These FBGs are used as highly selective filters or in-fiber laser mirrors, as will be seen in Sect. 41.4.2. The transmitted spectrum exhibits a dip around the Bragg wavelength and FBGs can also be used, in transmission, as band-stop filters. Figure 41.32c represents a tilted FBG. In this grating the index modulation makes an angle with the fiber axis. The effect of the angle is to reflect light into the cladding rather than into the fiber core. This FBG can be used in transmission as an optical band-stop filter without the drawback of unwanted back reflections toward the light source. A chirped FBG exhibits a linear variation in the grating period, as illustrated in Fig. 41.32d. This nonuniform grating means Bragg wavelength changes along the grating length and broadens the reflected spectrum. These FBGs can be used for wide-band filtering applications. The nonuniformity of the grating means that longer wavelengths are not reflected in the same position as the shorter wavelengths. This results in strong chromatic dispersion of the grating and chirped FBGs are also used for dispersion compensation in optical fiber communications systems. Another kind of nonuniform FBGs are phaseshifted FBGs. In the case of -shifted FBGs, the cosine index profile exhibits a phase shift of at the center of the grating, as illustrated in Fig. 41.32e. This results in a Fabry–Perot resonance in the central area of the grating. This induces a dip in the reflected spectrum and a peak in the transmitted one. This kind of FBG can be used for ultranarrow optical filters. When the -shifted FBG is directly written in a rare-earth-doped fiber, this results in a distributed feedback fiber laser. These lasers are interesting for their single-frequency operation, compactness, and robustness. The Fourier transform of the longitudinal index profile of FBGs gives a very good idea of their reflection spectrum. Uniform FBGs, described by a longitudinal rectangular function, exhibit a spectrum with side lobes, similar to a cardinal sine function, as depicted in the inset of Fig. 41.32a. Suppression of the side lobes is possible with apodized FBGs represented in Fig. 41.31e. One of the most commonly used functions to apodize a FBG is the Gaussian function. More generally, apodized grating allows tailoring of the shape of the spectrum of FBGs. Due to the strain and temperature dependence of the Bragg wavelength, FBGs are also widely used as sensors as will be seen in Sect. 41.4.3.
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Part F | 41.3
Fiber Bragg gratings (FBGs) have had a major impact on optical fiber communication systems, fiber lasers, and optical fiber sensors since the late 1980s. These optical elements are photowritten into a silica fiber and act as wavelength-selective reflectors. Reflection of light is possible in FBG because of the periodic modulation of the refractive index of the fiber core caused by the photoinscription process. Figure 41.32a shows the method of fabrication of FBGs [41.41]. The fiber core is transversely illuminated by two coherent ultraviolet (UV) beams, usually coming from a high-power excimer laser. This results in an interference pattern that consists of a periodic modulation of the light intensity along the longitudinal direction of the fiber. The fiber core, which is usually doped with germanium, is photosensitive, which means that its refractive index changes with exposure to UV light. This process allows the photoinscription of a periodic and permanent modulation of the refractive index into the fiber core. The period # of the modulation is the fringe spacing. It is related to the angle between the two UV beams and can easily be adjusted. The depth of the modulation depends on the intensity and duration of the exposure. The length of the Bragg grating is the length of fiber exposed to the UV interference pattern. Light that travels longitudinally in a FBG experiences multiple reflections on the different interfaces caused by the refractive index changes. It can be shown that there exists a wavelength for which these reflections constructively interfere [41.42]. The Bragg wavelength B for which the reflection is maximum satisfies the following relation
41.3 Specialty Optical Fibers
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Optical and Photonic Glass Applications
a)
Reflexion coefficient 1 0.9
Rmax
λB
0.8 UV beams
0.7 0.6
Part F | 41.3
∆λB
0.5 0.4
Interference pattern
0.3 0.2 0.1 Photo-induced grating
0
1549.9
Fiber core
1550
1550.1 1550.2 1550.3 1550.4 1550.5 1550.6
Wavelength (nm)
Period Λ
b)
c)
d)
e)
π
f)
Fig. 41.32 (a) Photoinscription process; (b) uniform Bragg grating; (c) tilted Bragg grating; (d) chirped Bragg grating; (e) -shifted Bragg grating; and (f) apodized Bragg grating
Optical Fibers
41.4 Applications of Optical Fibers
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41.4 Applications of Optical Fibers By the beginning of the 1990s, optics had become the unique technology in backbone networks. The advent of EDFAs paved the way for worldwide networks mainly used for Internet traffic. The capacity of backbone networks is continuously increasing as well as the amount of Internet traffic. The basic principle of fiber-optic communication is the following [41.10]. The information to transmit is digitized and modulates a laser source, generally a semiconductor laser in the near-infrared region. The laser light travels in an optical fiber over kilometers, or even thousands of kilometers for long-haul systems. At the end of the transmission link, light is demodulated by the receiver and the information is recovered. Light has an enormous potential for data transmission compared to microwave or electrical communication systems. The high carrier frequency of light ( 100 THz) allows modulation at high bit rates and the small wavelength of light ( 1 m) allows compact devices like semiconductor lasers or waveguides. The bit rate (number of bits per second) is the unit of measure of the capacity of a digital optical link. One important parameter is the bit error rate (BER) defined as the number of received bit errors divided by the total number of transmitted bits during a studied time interval. The errors usually originate from noise, interference, or distortion. With the exponential growth in data transmission, a major challenge for lightwave communication systems is to increase the capacity of optical links while preserving acceptable BERs. In the early 1990s, the bit rate was about 2:5 Gbit=s per fiber. The invention of EDFAs gave rise to wavelength division multiplexing (WDM) allowing an efficient use of the enormous fiber bandwidth. The principle of WDM technology is illustrated in Fig. 41.33. It consists of modulating several optical carriers and launching them in the same fiber through an optical multiplexer (Mux in Fig. 41.33). Due to fiber loss, the signals need to be reamplified by EDFAs every 100150 km approximately. The bandwidth on which the WDM channels extend is limited by the EDFA bandwidth, typically 15251565 nm for the C-band and 15701610 nm for the L-band. At each reamplifying span, a DCF module allows dispersion compensation.
41.4.1 Optical Communications A lightwave communication system can transmit information from one place to another by sending light through an optical fiber. Lightwave technology has played a major role in the advent of the information society. Optical fibers are used to transmit Internet communications, telephone signals, and cable television signals. The rise of optical communications has benefited from several breakthroughs since the 1960s, summarized with the following key dates [41.43]:
1960: Invention of the first laser by Theodore H. Maiman from Hughes Research Laboratories, USA [41.44]. 1962: First semiconductor laser by Robert N. Hall from General Electric, USA [41.45]. 1966: Suggestion by Charles K. Kao (from International Telephone and Telegraph Co, UK) that loss of silica fibers can be reduced under the limit of 20 dB=km [41.46]. Kao received the Nobel Prize in Physics in 2009 for his pioneering works. 1970: First optical fiber with loss below 20 dB=km in the wavelength region near 1 m by Corning, USA [41.47]. 1978: First single-mode fiber with loss below 0:2 dB=km in the wavelength region near 1:55 m by Nippon Telegraph and Telephone, Japan [41.48]. 1986: First demonstration of erbium-doped fiber amplifiers (EDFAs) at the University of Southampton, UK [41.49]. SMF
Mux EDFA
λ1 λ2 λ3 λn
DCF Emission
SMF EDFA
DCF Propagation
Demux EDFA
DCF
λ1 λ2 λ3 λn Reception
Fig. 41.33 Schematic representation
of an amplified WDM lightwave communication system
Part F | 41.4
Fiber-optic communications is the first application presented in this section. Research and industrial developments in this field contributed to the advent of low-loss single-mode optical fibers in the early 1970s and have given birth to modern telecommunications systems. Fiber-based communications is clearly the most important fiber application in terms of global fiber sales. Progress in this field has also had a positive impact on other technologies. In this section two other major applications of optical fibers will be presented: fiber amplifiers and fiber lasers, and fiber-optic sensors.
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Part F
Optical and Photonic Glass Applications
Part F | 41.4
At the end of the transmission link an optical demultiplexer (Demux in Fig. 41.33) is used to separate the different channels in order to detect them separately and recover the information on each channel individually. The first WDM systems, installed in 1995, provided a capacity of 10 Gbit=s (four channels at 2:5 Gbit=s). The bit rate per channel as well as the number of channels increased rapidly and systems transporting up to 80 10 Gbit=s channels in the C-band were deployed in the first half of the 2000s in terrestrial networks and over undersea lightwave cables. Around 2010, advances in electronics and signal processing made the implementation of coherent receivers possible and 8 Tbit=s (80 100 Gbit=s) could be transported over one fiber in the C-band. It must be noted that practically all the fibers deployed in backbone networks in the world are SMFs, i. e., fibers that were designed many years before the advent of WDM, for a transmission capacity totally negligible compared to what can be reached today. New schemes such as space-division multiplexing are explored in multimode and multicore fibers to provide the next step change in transmission capacity [41.50]. The scheme proposed in Fig. 41.33 concerns long-distance communication systems. For fiber-to-thehome or mobile fronthaul networks where distances are below 100 km for example, no amplifier is necessary and the wavelength region around 1:3 m can be exploited. Moreover, the transmission capacity of the fiber does not need to be as high as long-haul systems and coarse WDM (channel spacing of 20 nm) can be used. For smaller distances or local-area networks, silica or polymer multimode fibers can be used. Optical fibers (single-mode and multimode) are also frequently deployed in data centers to address the needs of increasing the bandwidth and reducing the power consumption.
41.4.2 Amplifiers and Lasers If optical fibers are most often used to transmit information between two points, as seen in the previous section, they can also be used as an active medium for amplification purposes and laser development. In these cases, rare-earth-doped fibers are used for their light-emission properties.
Fiber Amplifiers Fiber amplifiers are based on the stimulated emission process in rare-earth-doped fibers (Sect. 41.3.1). Demonstrated in the 1980s, the EDFA is a key component of fiber-optic communication systems [41.20]. EDFAs are also used in many other domains when optical power near the 1:55 m region needs to be amplified. Another commonly used fiber amplifier is the ytterbium-doped fiber amplifier operating near the 1 m region. This amplifier is used to boost powers up to several kilowatts, mainly for industrial applications. Figure 41.34 illustrates the principle of a simple EDFA but can be generalized to other kinds of fiber amplifiers. In this example a laser diode at 980 nm provides the pump power for the erbium-doped fiber. Thanks to stimulated emission, a weak input signal at 1550 nm can be amplified throughout its propagation inside the doped fiber. Two optical isolators reduce the sensitivity of the device to back-reflections and prevent it from a lasing effect. Due to the possible long length of the doped fiber (a few tens of meters for example), high small-signal gain can be achieved with moderate pump power (typically 4050 dB of gain). For example, a 40 dB-gain EDFA with 100 mW of pump power can amplify an input signal from 1 W to 10 mW. The gain, however, decreases dramatically if the input power becomes too high. This saturation effect is simply due to the fact that the amplified power cannot exceed the pump power. In addition to the small-signal gain, the maximum output power is then an important parameter to take into account in fiber amplifiers. Another important parameter in fiber amplifiers is the noise due to amplified spontaneous emission (ASE). In doped fibers, randomly emitted photons from spontaneous emission are also amplified by stimulated emission. This effect becomes relevant for gains roughly exceeding 40 dB and for weak input signals. It limits the power transferred to the signal and adds random fluctuations to the signal. In the field of optical communications the excess noise degrades the optical signal-to-noise ratio by a factor of at least two. When high power levels have to be reached through an amplifying process for industrial applications (typically
Laser diode 980 nm Er-doped fiber Input signal 1550 nm
Amplified signal 1550 nm Isolator
Mux
Isolator
Fig. 41.34 Setup of a simple erbiumdoped fiber amplifier
Optical Fibers
Fiber Lasers Principle. To make a laser, two ingredients are necessary: an amplifying medium and a resonant cavity [41.3]. The amplifying medium acts as a photon reservoir in a spectral band determined by the spectroscopic properties of the gain medium. The cavity provides the required optical feedback to amplify light along one precise direction (ensuring high spatial coherence of the laser light) and at one or several precise frequency(ies) (ensuring high temporal coherence). A fiber laser is made by inserting an optically pumped rare-earth-doped fiber inside an optical cavity [41.19]. Figure 41.35 illustrates two possible setups for an erbium-doped fiber laser. The setup of Fig. 41.35a is a Fabry–Perot laser. The cavity is formed by two FBGs. As seen in Sect. 41.3.4, these components are wavelength-selective reflectors directly made in a fiber spliced to the doped fiber. Reflection bandwidths of FBGs are typically in the range of 0:11 nm. One FBG has a peak reflection Rmax approaching 100%. The second FBG is the output reflector of the laser and has a)
a reflection coefficient Rout < 100% allowing light to exit the cavity. For high-gain media Rout can be as low as a few percent. In this case, the output power of the laser is maximized. In Fig. 41.35b, a ring cavity is presented. No reflector is used; the cavity is simply obtained by connecting the output end of the doped fiber to its input end. A fiber coupler is used to extract light from the cavity. For example, the 10% output of a 90=10 fiber coupler can be used. In free-space lasers (gas lasers for example), the geometrical properties of the laser beam (size and divergence) are essentially governed by the mirror curvatures and the cavity length. In fiber lasers, the spatial properties of the laser beam are determined by the fiber. Doped single-mode fibers are generally preferred because the output laser beam is a pure LP01 mode approaching an ideal Gaussian beam. The possibility of generating high-quality beams is one of the major advantages of fiber lasers. Another major interest of fiber lasers is the fact that no alignment is required when the cavity is made of all-fiber components, generally spliced or connected together (as illustrated in Fig. 41.35). This also leads to less maintenance for these devices. Adding the fact that fiber lasers dissipate heat more efficiently, are generally more compact, and less expensive than other solid-state lasers, they potentially offer many advantages. However, one major issue was not addressed before the 1990s: the possibility of reaching high output powers with single-mode fibers. Powers were limited to a few tens of milliwatts and that has restricted the use of fiber lasers in many applications.
Laser diode 980 nm Er-doped fiber Amplified signal 1550 nm
Bragg grating (Rmax)
Bragg grating (Rout)
Mux
b) Mux
Er-doped fiber
Laser diode 980 nm
Isolator
Coupler
Laser output 1550 nm
Fig. 41.35a,b Setup of an erbiumdoped fiber laser in (a) a Fabry–Perot cavity; and (b) a ring cavity
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Part F | 41.4
from several tens of watts to hundreds of watts), several amplifying stages, with moderate gain on each, are cascaded to limit the impact of ASE noise. The last stage, supplying the major part of the power, is called the booster stage [41.21]. When no input optical signal enters a fiber amplifier, all the available gain is used to amplify the spontaneous emission and the device acts as a broadband ASE source.
41.4 Applications of Optical Fibers
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Optical and Photonic Glass Applications
Part F | 41.4
The reason is quite simple. The maximum output power of a fiber laser is limited by the injected power of the pump laser and only single-mode laser diodes can be efficiently coupled in single-mode doped fibers. Unfortunately, single-mode laser diodes have limited optical powers (typical maximum around 1 W). Multimode laser diodes (like high-power diode bars for example) can deliver power levels up to hundreds of watts but they can only be efficiently injected in multimode fibers from which light exits with poor beam quality. This dilemma has been resolved with the invention of double-clad fibers [41.51].
lasers or can be directly used, with no external signal, as the gain medium of a fiber laser. Some double-clad fibers, among the most efficient ones, exhibit a photonic crystal structure with an active core for the single-mode operation and an air cladding structure for the multimode guidance of the pump (Sect. 41.3.2). With the recent advent of double-clad fibers, fiber laser technology now rivals other high-power laser technologies such as solid-state lasers. Fiber laser technology is also frequently used for narrow-linewidth fiber lasers, Q-switched fiber lasers, or mode-locked fiber lasers [41.19].
Double-Clad Fiber Lasers. Figure 41.36 illustrates the principle of a double-clad fiber. Compared to simple single-mode fibers, this fiber exhibits an additional low-index layer around the first cladding of the fiber, as represented in Fig. 41.36a. The three refractive indices satisfy n1 > n2 > n3 . This fiber has the properties of both an active single-mode fiber (core and inner cladding) and a passive multimode fiber (inner cladding and outer cladding). Highly multimode beams of highpower laser diodes can easily be injected in the large inner cladding. The pump light also partly propagates in the single-mode core where it is absorbed by the active ions. The gain medium can then amplify a signal injected in the fiber core, as illustrated in Fig. 41.36b. The amplified signal is single-mode. Its power is comparable to the absorbed pump power and can reach hundreds of watts, even sometimes several kilowatts [41.21]. Double-clad fibers are used to amplify low-power seed
41.4.3 Fiber-Optic Sensors Another major application of optical fibers is the domain of sensing. Fiber-optic sensors are divided into two categories: extrinsic and intrinsic sensors [41.41]. An intrinsic fiber sensor uses the fiber as the sensing element while an extrinsic fiber sensor uses the fiber just to carry light from a remote sensor to the signal processing station. The advantages of optical fibers for extrinsic sensors is their small size and small weight, their immunity to electromagnetic interference, and the possibility to multiplex many sensors along the fiber. For intrinsic sensors, the fiber can be used in many different ways depending on the measured quantity. Intrinsic fiber sensors can typically measure temperature, mechanical strain, displacements, pressure, acceleration, or concentrations of chemical species. In the following, four types of intrinsic sensors will be presented: interferometric
Radial coordinate
a)
Index profile Outer cladding Core Inner cladding n1 Inner cladding
b)
n 2 n3 Outer cladding
Pump
Amplified signal Signal
Lens
Doped single-mode core
Fig. 41.36 (a) Index profile of a double-clad fiber; and (b) principle
of operation of a double-clad fiber
Optical Fibers
the measurement. This kind of sensor array can be embedded into the materials of huge buildings, bridges, or dams for example. This allows one to monitor the conditions of these structures, sometimes called smart structures. Other kinds of distributed fiber-optic sensors do not use discrete FBGs as sensors, but rather the fiber itself. The principle of sensing is based on Rayleigh scattering, Raman scattering, or Brillouin scattering. For example, optical time-domain reflectometry, based on Rayleigh scattering, is a method to localize weak reflections along an optical fiber. Methods based on inelastic scattering (such as Raman or Brillouin scattering) exploit the dependence of the frequency shift of the scattered light on external parameters. For example the frequency shift of Brillouin scattering, which is about 11 GHz at 1:55 m in fused silica (Sect. 41.2.5), has a linear dependence on strain ( 40 kHz= ") and temperature ( 1 MHz=K). Currently, Brillouin-based fiber-optic sensors are widely used for distributed temperature and strain sensing in long transducers (hundreds of kilometers) made of standard single-mode telecommunication optical fibers. Pipeline protection is one of the most popular fields of interest for these sensors. The last kind of fiber-optic sensor is based on evanescent field interaction. It has been seen in Sect. 41.1.3 that a part of the electromagnetic field of the guided mode of an optical fiber extends into the cladding and is called the evanescent field. This field exponentially decreases but can extend far from the core if the V parameter of the fiber is relatively low. In Fig. 41.14 we described the example of tapered fibers, which can enhance the part of the evanescent field in the medium surrounding the fiber. In such devices the mode can efficiently interact with the external medium, which can contain chemical species. When the wavelength of the field corresponds to an absorption wavelength of the molecules, the presence of these molecules strongly attenuates the amount of optical power transmitted through the device [41.55]. This technique is used to measure concentrations for biological and chemical sensing. Gas detection of CO2 , O2 , NH3 , or SO2 is particularly developed for industrial pollutant monitoring and control. Acknowledgments. The author is grateful to Margaux Barbier, Claire Le Page, Michel Joindot (University of Rennes 1, Enssat, France), and Irène Joindot for stimulating discussions and critical reading of the manuscript. The author would also like to thank Thierry Taunay (Photonics Bretagne, France) for his collaboration for writing Sect. 41.2.1 on the fabrication of optical fibers.
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Part F | 41.4
sensors, fiber Bragg grating sensors, distributed sensors, and evanescent sensors. The use of interferometers in optical measurement is a well-established technique. Simple two-wave interferometers, such as Mach–Zehnder, Michelson, or Sagnac interferometers, allow precise measurements of displacements, or pressure or temperature changes for example. Phase shifts between the two arms of the interferometers lead to intensity variations that can be easily detected by conventional detectors. The interest of interferometers is their sensitivity to small displacements. Variations of a fraction of the wavelength are generally accessible. One of the great advantages of allfiber interferometers is that they have extremely flexible geometries and high sensitivity [41.52]. This is due to the nature of optical fibers, which can be very long and offer a large surface of interaction with the external medium. Among the most popular interferometric fiberoptic sensors is the fiber-optic gyroscope (FOG) based on the Sagnac interferometer [41.53]. The principle is to use a coil of optical fiber, which can be several kilometers long. Two beams from a same laser are injected in the fiber in opposite directions. When the coil rotates the two beams experience a slightly different path delay. The resulting phase shift is measured by recombining the two beams through interferometry. FOGs provide extremely precise rotation rate measurement (their sensitivity can be less than 0:01 deg=h) and are widely used in inertial navigation systems. Fiber Bragg gratings (FBGs) were presented in Sect. 41.3.4. We recall that they can be considered as infiber highly selective reflectors at a precise wavelength called the Bragg wavelength. It appears that the Bragg wavelength is highly sensitive to mechanical strain and temperature changes [41.54]. The typical sensitivities of a conventional FBG are 10 pm=K for the temperature dependence and 1 pm= " for the strain dependence. We recall that the strain " D L=L is a measure of the deformation L of a piece of material of length L. The principle of FBG-based sensors is to illuminate the FBG, with a broadband source for example, and to measure the shift of the Bragg wavelength. With this technique resolutions of 0:01 K and 0:1 " are achievable. The effects of strain and temperature can be distinguished with various techniques (by using reference gratings that are not subject to the strain for example). FBGs give access to local measurement of temperature or strain. An interesting feature of this technique is the possibility of implementing WDM schemes for multipoint measurements. In this case, FBGs that slightly differ in their Bragg wavelength are distributed along a single fiber. A scheme to interrogate each FBG separately allows spatial distribution of
41.4 Applications of Optical Fibers
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Optical and Photonic Glass Applications
References 41.1 41.2 41.3
Part F | 41
41.4 41.5 41.6 41.7
41.8
41.9 41.10 41.11
41.12
41.13 41.14
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Optical Fibers
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F.P. Kapron, D.B. Keck, R.D. Maurer: Radiation losses in glass optical waveguides, Appl. Phys. Lett. 17, 423 (1970) T. Miya, Y. Terunuma, T. Hosaka, T. Miyashita: Ultimate low-loss single-mode fiber at 1.55 m, Electron. Lett. 15, 106 (1979) R.J. Mears, L. Reekie, M. Jauncey, D.N. Payne: Lownoise erbium-doped fiber amplifier operating at 1.54 m, Electron. Lett. 26, 1026 (1987) D.J. Richardson, J.M. Fini, L.E. Nelson: Space-division multiplexing in optical fibres, Nat. Photonics 7, 354 (2013) E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, B.C. McCollum: Double-clad, offset-core Nd fiber laser. In: Optical Fiber Sensors, OSA Technical Digest Series, PD 5, Vol. 2 (Optical Society of America, New Orleans 1988) S. Yin, P.B. Ruffin, F.T.S. Yu (Eds.): Fiber Optic Sensors, 2nd edn. (CRC Press, Boca Raton 2008) H.C. Lefèvre: The Fiber-Optic Gyroscope, 2nd edn. (Artech House, Norwood 2014) A. Cusano, A. Cutolo, J. Albert (Eds.): Fiber Bragg Grating Sensors: Recent Advancements, Industrial Applications and Market Exploitation (Bentham Science, Sharjah 2011) F. Charpentier, J. Trolès, Q. Coulombier, L. Brilland, P. Houizot, F. Smektala, C. Boussard-Plédel, V. Nazabal, N. Thibaud, K. Le Pierres, G. Renversez, B. Bureau: CO2 detection using microstructured chalcogenide fibers, Sens. Lett. 7(5), 745 (2009)
Thierry Chartier CNRS, Institute Foton University of Rennes 1 Lannion, France [email protected]
Thierry Chartier received his PhD degree in Physics from the University of Rennes 1 (France) in 1997. In 1998, he joined the laboratory Coria of the University of Rouen (France) to study short-pulse fiber lasers. Since 2003, he is Professor of Photonics at the Institut Foton of Univ Rennes, where his research interests concern highly nonlinear optical fibers and fiber lasers.
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References
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Glass in Integ 42. Glass in Integrated Photonics
Juejun Hu, Lan Yang
Ever since the invention of clear glass back in the Roman ages, transparency—perhaps the most striking property of glass—has made glass the material of choice for optical applications. Given the close connection between glass and optics, it comes as no surprise that when the need for optical data communications first arose in the 1960s, great efforts were devoted to reducing optical attenuation in glass in the hope that glass could be used as the medium for longhaul optical signal transmission. It is now well recognized that these pioneering efforts culminated in the invention of low-loss silica glass optical fibers, which laid the foundation for the internet age [42.1]. What is lesser known is that investigations into planar glass optical waveguides for optical communication applications commenced at almost the same time. In 1969, a landmark paper entitled Integrated optics: An introduction by S. Miller proposed a laser beam circuitry where miniaturized optical sources, modulators,
42.1
Processing of Planar Glass Photonic Components ....................... 1441 42.1.1 Photonic Device Fabrication Processes . 1441 42.1.2 Post-Fabrication Reflow Processing ..... 1446 42.2 42.2.1 42.2.2 42.2.3 42.2.4 42.2.5 42.3
Integrated Photonics Platforms Based on Glass Materials ................... Silica and Silicate Glass ...................... Non-Silicate Oxide Glass .................... Chalcogenide Glass (ChG).................... Halide Glass ...................................... Glass Ceramics and Phase Change Materials ...............
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Summary and Outlook ...................... 1464
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addresses the key facets of glassy materials in the context of integrated photonics, including material characteristics and processing technologies with specific application examples based on different glass composition families.
and detectors were interconnected via lithographically defined optical waveguides on a single planar glass substrate [42.2]. While photolithography at that time was unable to provide the required resolution to realize waveguides with sufficiently low loss for practical applications, the visionary proposal from almost half a century ago clearly heralds on-chip photonic integration, a transformative paradigm shift in optics and photonics analogous to integrated circuits revolutionizing the electronic industry. Throughout the history of integrated photonics, glass has always been a foundational optical material. Early embodiments of integrated optical components primarily made use of the low-loss light transmission characteristics in silica glass thin films [42.3–5], but glass materials certainly have many other attractive attributes to offer. The useful optical and processing properties of glass materials that account for their prevalence include:
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_42
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Integrated photonics, which generically refers to the technology of combining multiple optical components on a chip-scale platform to form a functional photonic circuit, is often hailed as the optical equivalent of electronic integrated circuits, which holds the potential to revolutionize communications, computing, sensing, and imaging. Similar to microelectronic integrated circuits, which assimilate more than half the Mendeleev periodic table into the manufacturing process, integrated photonics necessarily involves many classes of materials to enable different photonic functionalities essential to photonic circuit operation. Glassy materials, with their exceptional optical and structural properties, constitute critical building blocks in state-of-the-art integrated photonic systems. The progress in these materials will help diversify the choices of materials for novel devices and components and will, therefore, push forward the development of integrated photonics with advanced functionalities. This chapter
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1. Low optical attenuation: Glasses are among the man-made materials with the lowest optical attenuation. Generally speaking, the trade-off between Rayleigh scattering, which scales with 4 (where denotes the wavelength), and phonon absorption, which dominates long-wave infrared absorption, defines the minimum-loss window in glass materials. From a technical perspective, while growing large-size single crystals is costly and sometimes challenging, glasses can be prepared in a fiber or thin film form with excellent uniformity over large length scales with relative ease and low cost. In silica glass, the minimum-loss window coincides with the 1550 nm telecommunication band, where a low intrinsic loss of 0:2 dB=km has been experimentally attained in optical fibers. Even lower optical losses have been projected theoretically based on extrapolated attenuation values in infrared glasses, such as chalcogenides and multicomponent halides [42.6] (even though such predicted loss values have not yet been realized experimentally due to the presence of impurity and the so-called concentration scattering effect [42.7, 8]). 2. Diversity in chemical composition: Stable glass can be formed in a wide variety of composition groups including oxides, chalcogenides, halides, etc., as well as alloys between them. Taking advantage of this composition agility, a broad range of optical, structural, and chemical attributes can be realized in glasses to meet diverse application needs. 3. Precise refractive index control: The refractive indices of glass can be precisely tuned via doping or alloying. For instance, GeO2 , P2 O5 , and Al2 O3 are commonly used to raise the refractive index of silica glass, whereas B2 O3 doping or fluorine substitution of oxygen suppresses the silica glass index. The dopants can either be incorporated during thin film preparation (e. g., by changing reactant composition in a chemical deposition process or codeposition in physical vapor deposition) or be introduced post-deposition using ion exchange or ion implantation. These techniques enable precise control of the spatial distribution of dopants and, hence, refractive index profiles in photonic components. 4. Post-deposition property modification: The structural and optical properties of glass thin films can be modified post-deposition making use of their photosensitive or phase change properties. Most glasses are thermodynamically metastable and exhibit photosensitive structural changes upon exposure to photons with energy comparable to or larger than their optical band gap. Although the refractive index modification accompanying the structural change is, in general, relatively small
(n 0:001 or less), much larger photo-induced index change (n 0:1) has been reported in select glass compositions [42.9–11]. Phase transition from the amorphous to the crystalline phase is another means to induce optical property change in glass thin films. The property modification associated with the amorphous–crystalline phase transition is particularly pronounced in some chalcogenide alloys (e. g., Ge2 Sb2 Te5 ) with a large index change n > 2 [42.12]. Various applications have benefited from the post-processing modification, such as waveguide and grating writing [42.13, 14], post-fabrication trimming [42.15], and photonic reconfiguration [42.16]. 5. Low-cost, substrate-agnostic film deposition: Unlike single crystals, which generally require epitaxial growth, glass thin films can be deposited on a large number of technically relevant substrates without being limited by the lattice-matching constraint. Viable substrates for glass film deposition include, but are not limited to, semiconductors, glass, polymers, optical crystals, and ceramics. In addition, since glasses are inherently in a thermodynamically non-equilibrium state, deposition of glass thin films can be performed at reduced temperatures to lower the processing thermal budget or at higher deposition rate to improve processing throughput. Therefore, glasses can be deposited using not only the classical vacuum vapor deposition techniques, such as sputtering and pulsed laser deposition (PLD), but also cost-effective, highthroughput methods, which normally do not apply to crystal growth, such as solution processing and thermal evaporation. 6. Glass-transition-enabled device processing: Glasses exhibit a gradual change of viscosity during glass transition, a unique characteristic that enables direct nanoimprint fabrication and postfabrication reflow treatment. In the nanoimprint process, a patterned master stamp (or mold) is pressed against a heated glass thin film to drive viscous flow of the glass and fill the groove patterns on the stamp. Subsequently, a negative pattern of the master stamps is formed in the glass film [42.17–19]. Afterwards, during a reflow process, as-fabricated glass photonic components are heated to above the glass transition temperature .Tg / using an oven or a laser such that the residual surface roughness can be spontaneously removed under the action of surface tension. The reflow process is the key to achieve record low-loss onchip photonic components [42.20]. An optimal viscosity window exists for both processes where the glass is viscous enough to retain its overall ge-
Glass in Integrated Photonics
to the fourth power [42.22]. Therefore, high-refractive-index glasses, such as Hydex® (the trade name of a doped silica glass) and chalcogenides often claim high Kerr nonlinearity, and applications including ultrafast optical signal processing and frequency comb generation have been demonstrated in planar photonic systems based on these materials [42.23, 24]. We further note that while, in general, second-order nonlinearity is absent in glasses, it can be induced through the poling process and surface/interface-induced symmetry breaking [42.25–27]. Chapter 6 in this book presents a comprehensive review of optical nonlinear phenomena in glass materials. Besides their optical functionalities, glasses are also widely deployed in photonic integrated circuits to serve non-optical purposes functioning as interlayer dielectrics, surface passivation coatings, planarizing agents, doping sources, sacrificial layers, etc. This chapter will primarily focus on optical applications of glassy and amorphous materials in integrated photonics. The rest of this chapter is organized as follows. Section 42.1 provides an overview on the processing techniques for glass-based integrated photonic device fabrication, and Sect. 42.2 elaborates on several common material systems and their respective photonic application. We note that glass, following the most widely accepted definition, refers to amorphous solids exhibiting a glass transition. State-of-the-art integrated photonics also make use of amorphous thin film materials that do not exhibit glass transition behavior under normal circumstances, such as amorphous silicon [42.28], silicon nitride (SiNx ), and certain transition metal oxides. These amorphous non-glass materials, while presenting optical and processing characteristics similar to classical glasses in many aspects, are outside the scope of this chapter. Amorphous silicon photonics is addressed separately in Chap. 43.
42.1 Processing of Planar Glass Photonic Components Processing flow of glass photonic devices, in general, consists of three steps: thin film deposition, device patterning, and post-fabrication treatment. Almost all known physical and chemical thin film preparation methods can be applied to glass film deposition, and we refer the readers to Chap. 37 for detailed discussions on glass thin film processing. The latter two steps determine the pattern fidelity, which is correlated with the deviation from the designed operation wavelength, as well as the surface roughness, which is linked to op-
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tical scattering loss. In the following, we review the patterning and post-fabrication treatment processes for integrated glass photonic devices.
42.1.1 Photonic Device Fabrication Processes Standard Lithographic Fabrication Glass photonic device fabrication leveraging standard semiconductor microfabrication techniques date back to the early 1960s, when D. Anderson described the
Part F | 42.1
ometry, and yet microscopic flow driven by applied pressure or surface tension (stamp pattern filling or roughness removal) is still kinetically permissible. Access to this optimal viscosity window is possible in glass materials given their continuous viscositytemperature behavior. 7. Optical gain: Glasses can be doped with active light emitters, such as quantum dots, dyes, transition metal ions, or rare earth (RE) ions to function as optical gain media [42.21], which have played important roles in a broad range of applications from lasing to light amplification and sensing. Erbium doping is of particular interest for integrated photonics, since the transition wavelength of trivalent Er3C ion overlaps with the telecommunication C-band. Other dopants such as neodymium, praseodymium, holmium, and thulium offer a wide range of emission wavelength choices for on-chip sources and waveguide amplifiers. In addition to generating gain by various dopants in the glass, nonlinear gain has been utilized in glasses. Parametric gain has been exploited to achieve on-chip frequency combs. With Raman gain in silica, an ultra-low-threshold on-chip lasers has been demonstrated. The optical Raman gain spectrum is frequency downshifted from the pump wave by an amount determined by molecular vibrations in the materials. As a result, the Raman gain spectra vary from one molecular composition to another. Stimulated Brillouin scattering (SBS) also provides a nonlinear process to generate optical gain in glasses. 8. Optical nonlinearity: The lack of long-range structural order in glasses means that glasses usually do not exhibit second-order optical nonlinearity, and therefore, the third-order Kerr effect is the dominant source of optical nonlinearity in glasses. According to the semi-empirical generalized Miller’s rule, the third-order nonlinear susceptibility .3/ of a glass scales with its linear susceptibility .1/
42.1 Processing of Planar Glass Photonic Components
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fabrication of linear waveguides and junctions in thermal oxides on silicon wafers using photolithographic patterning [42.29, 30]. Two archetypal fabrication processes, etching and lift-off, are illustrated in Fig. 42.1. Lithographic patterning (by UV lithography or electron beam lithography) coupled with plasma-based dry etching is probably the most common processing route and has been widely applied to device fabrication in silica, silicates, chalcogenide glasses, and transition metal oxides. Highly anisotropic dry etching producing vertical sidewalls on etched patterns and superior feature resolution can be obtained by controlling the sidewall passivation, gas pressure, and substrate bias [42.31]. In such an anisotropic etching process, line edge roughness on device sidewalls is usually the dominant source of optical scattering. Such roughness-induced loss can be mitigated by a post-fabrication reflow process (e. g., in silica and silicate glasses [42.32, 33]) or performing a resist reflow step prior to dry etching. Propagation losses as low as 0:85 and 0:3 dB=m near 1550 nm wavelength have been reported in single-mode and multimode silica waveguides patterned using reactive ion etching (RIE) [42.34, 35]. These impressive low losses, however, are still far from the intrinsic silica material attenuation, and, therefore, roughness scattering is considered the culprit for the excess optical loss. Wet etching as a low-cost alternative to dry etching has also been used for glass photonic device patterning, although often at the expense of compromised pattern fidelity and feature resolution due to undercut underneath the resist mask. Interestingly, by utilizing specific designs, researchers have found ways to mitigate optical losses in wet etched structures. For example, a wedge-shaped sidewall profile in silica waveguides resulting from hydrofluoric acid wet etching was shown to reduce the waveguide modal overlap with sidewall roughness, and a low optical loss of 0:08 dB=m was measured in these waveguides (Fig. 42.2) [42.36]. The same approach was also adopted for microdisk resonator fabrication and a quality factor (Q-factor) up
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Fig. 42.2 (a) Tilted view of spiral silicon dioxide waveguides supported on silicon pillars fabricated using hydrofluoric acid (HF) wet etching followed by a XeF2 isotropic silicon etch to suspend the silica structure. Guided optical modes are supported at the outer edge of the silica structure. (b) Close-up view of oxide edge formed using a non-optimized wet etch with significant surface roughening. (c) Close-up view of oxide edge that is formed using an optimized etch, showing the wedged sidewall profile with a smooth surface. (d) Finite element simulation of the fundamental optical mode propagating inside the waveguide. From [42.36]
to 5 107 [42.37]. The same group has recently enhanced the Q-factor of these wedge-shaped resonators to 8:8 108 via optimized silicon oxide growth and wet etching procedures [42.38]. Unlike etching, lift-off first lithographically defines a resist pattern that is the negative replica of the final design prior to glass film deposition. The resist is then dissolved to lift off the undesired parts of the glass
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Glass in Integrated Photonics
film. The main advantage of lift-off is its versatility: it can be adapted to different glass compositions with minimal process development, and, therefore, it is particularly suited for rapid prototyping or patterning of glass compositions not readily amenable to etching. For lift-off patterning, the glass should be deposited at a relatively low temperature compatible with the polymer resist mask, in most cases using evaporation or sputtering. Lift-off has been employed for photonic device fabrication in chalcogenide glasses [42.39–44], fluoride glasses [42.45, 46], and amorphous transition metal oxide thin films [42.47–49].
glass layer. One major advantage of NIL is its superior resolution: dense patterns with 4 nm half-pitch have been demonstrated [42.50], whereas isolated structures with feature sizes down to 2 nm have been transferred to polymers by NIL [42.51]. In the standard thermal NIL process depicted in Fig. 42.3a, the intermediate pattern transfer step entails using a thermoplastic polymer as an imprint resist. Successful pattern transfer to the resist during the stamping process generally requires an optimal resist viscosity in the 103 107 Pa s range [42.52]. Coincidentally, this viscosity window almost exactly overlaps the working range in glass (between the working point D 103 Pa s and the softening point D 106:65 Pa s), as shaping a glass gob and filling a nanoimprint stamp both involve deforming a viscous fluid. The continuous dependence of viscosity on temperature in glasses, similar to that of thermoplastic polymers, therefore allows direct thermal nanoimprint on glass thin films without the intermediate pattern transfer step (Fig. 42.3b). For oxide glasses such as fused silica (Tg 1300 ı C) and Pyrex borosilicate glass (Tg 560 ı C), glassy carbon was used as the mold material to withstand elevated imprint temperatures [42.17]. Direct nanoimprint is particularly suited for glasses with a relatively low glass transition temperature, as the reduced processing temperature improves )RUFH
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1443
Part F | 42.1
Replication-Based Fabrication: Nanoimprint, Molding, and Others Replication-based techniques start with fabrication of a master mold or stamp, and the patterns on the mold are subsequently transferred to a glass layer via stamping or molding. The mold can be made from rigid materials (e. g., Si, silica, or SiC) or elastomers as in the case of soft lithography. Figure 42.3a illustrates the standard nanoimprint lithography (NIL) process, where the pattern on the mold is first embossed onto a polymer resist layer in a UV or thermal nanoimprint process, followed by a subsequent etching step to transfer the pattern to the
42.1 Processing of Planar Glass Photonic Components
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Optical and Photonic Glass Applications
Part F | 42.1
the mold longevity and also allows the use of soft molds to enhance contact conformality and to accommodate possible substrate warping. Direct nanoimprint has been implemented to fabricate optical waveguides, resonators, gratings, and wire grid polarizers in chalcogenide glasses whose Tg are significantly lower than their oxide counterparts [42.19, 53–56]. The other way to reduce Tg involves the addition of organic chemicals as plasticizers [42.18, 57–59]. In addition to the simplified process, direct imprint also enables the replication of non-binary structures such as microlenses [42.60]. The similarity between the rheological properties of glasses and thermoplastic polymers suggests that in addition to nanoimprint, many other soft lithography techniques, which have been widely used for polymer device fabrication, are equally applicable to these lowTg glasses. As an example, Tsay et al. fabricated chalcogenide glass waveguides using microtransfer printing and demonstrated hybrid integration of chalcogenide glass waveguides with quantum cascade lasers using micromolding in capillaries (MIMIC) [42.61, 62]. Soft lithography-based replication methods are also routinely applied to the molding of sol–gel derived materials with sub-micrometer resolution [42.63–67]. The soft lithography techniques described above use molds made of elastomers, e. g., polydimethylsiloxane (PDMS). An alternative replication scheme named wet stamping makes use of hydrogel stamps soaked with etchant solutions. When a glass substrate is placed on the stamp, the etching reaction takes place only at locations where the stamp is in conformal contact with the substrate. As the etching process proceeds, the glass substrate eventually adopts a shape complementary to the stamp geometry [42.68, 69]. Laser or Particle Beam Direct Writing Direct beam writing techniques have been exploited to create photonic structures either through refractive ina)
dex modification induced by a focused laser beam or subatomic particles (protons, electrons, or ions) or by tailoring the material compositions and shaping the geometries via a focused ion beam. Figure 42.4a schematically depicts the typical laser direct writing (LDW) process. Laser light is focused onto a glass sample via a high numerical aperture (NA) microscope objective to induce refractive index increase or depression at the laser focal spot. The sample stage is translated during the writing process to create desirable index patterns. For materials exhibiting an index increase upon laser irradiation, the exposed region naturally forms the light guiding core; whereas for materials whose refractive indices decrease after laser exposure, a so-called depressed cladding geometry is adopted, where laser writing defines a cladding region with lower index surrounding an unmodified waveguide core. In LDW, the femtosecond laser is a preferred light source for direct writing, which can generate modification in materials without the collateral damage observed for pulses longer than a few picoseconds [42.71, 72]. Alternatively, continuous wave (CW) sources can be used to trigger photosensitive properties in glass materials, including photo-induced refractive index change [42.73–79], photoexpansion [42.80], and photo-diffusion [42.81]. The LDW technique is highly versatile and is capable of device fabrication in glass thin films or inside a bulk sample [42.82]; one such example is the recent demonstration of the integration of photonic components in the cover glass of a smart phone by LDW to perform sensing functions [42.83, 84]. A large body of literature is dedicated to the LDW technique, and we refer interested readers to several comprehensive reviews in this field [42.85–90]. Focused proton [42.91–95] and electron [42.96, 97] beams can also be used for glass optical device fabrication. In addition to direct writing of photonic components, electron beam writing in high-energy beam
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Glass in Integrated Photonics
Ion Exchange Ion exchange is a mature technology for glass waveguide fabrication with a history dating back to the early days of integrated optics [42.114, 115]. The basic process involves substitution of mobile ions in the glass with other ions of different polarizability to locally modify the refractive index. In oxide glasses, the process is usually based on cation exchange of alkaline or group 11 metal (silver and copper) ions due to their high mobility. In fluoride glasses, the fluorine ion is highly mobile, and thus anion exchange processes have been devised taking advantage of this unique property [42.116, 117].
There are a number of variants in the ion exchange process. In general, an ion exchange process comprises one or several steps, illustrated in Fig. 42.5 using the silver-sodium ion exchange pair as an example. Figure 42.5a–c depict configurations used to introduce ions into the glass. Ion exchange can either entirely rely on thermally activated ion diffusion (Fig. 42.5a) or be facilitated by an applied electric field in a fieldassisted process (Fig. 42.5b). The waveguide geometry is defined by a lithographically defined thin film metal or dielectric mask that serves as a diffusion barrier. The molten salt bath usually contains nitrates with a relatively low melting point [42.118]. In Fig. 42.5c, a deposited metal thin film is used as the ion source in place of the molten salt bath. Once the ions are incorporated in glass, the spatial distribution of ions can be further modified to engineer the refractive index profile of the resulting waveguide. Figure 42.5e shows a simple thermal annealing step to drive in the ions by diffusion. In Fig. 42.5f,g, the waveguide formed in the initial ion exchange step is buried through a second thermal (Fig. 42.5f) or electric field-assisted (Fig. 42.5g) ion exchange treatment in a salt bath containing the ions originally in the glass. Figure 42.5d shows the waveguide formation and burial processes combined in a single step; the field-assisted burial process occurs as soon as the metal thin film source is depleted. Ion exchange has been applied to both passive and active photonic device fabrication. Examples of passive components fabricated using ion exchange include waveguide splitters [42.120], multi-mode interferometers [42.121], Mach–Zehnder interferometers [42.122], and arrayed waveguide grating (AWG) multiplexers [42.123]. These passive components can be further integrated with III-V semiconductor membrane optoelectronic devices via layer transfer [42.124, 125]. Waveguide lasers and amplifiers have also been demonstrated via ion exchange in glasses doped with transition metals or RE ions [42.126–129]. Ion Implantation Ion implantation is a standard technology widely used in integrated circuit fabrication to introduce dopant atoms in semiconductors through high-energy (from tens of keV up to several MeV) ion bombardment. Interaction of implanted ions with solids is a complicated process, and we direct the interested reader to dedicated monographs for detailed reviews on this topic [42.130, 131]. The most important effect relevant to optical fabrication is refractive index modification. When ions travel through a solid, they gradually lose energy through Coulombic interactions with the electrons and elastic collision with the atomic nuclei, where the latter results in material damage in the form of
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sensitive (HEBS) glass is a standard protocol for grayscale photomask fabrication. HEBS glass is a low expansion zinc-borosilicate glass, a white crown glass doped with silver-alkali-halide nanocrystals and photo inhibitors [42.98]. The photo inhibitors (typically TiO2 , Nb2 O5 , or Y2 O3 ) increase the optical band gap of the base glass so that it becomes inert to UV light. Upon exposure of the glass to high-energy electron beams (10 kV and above), silver in the nanocrystals is reduced, forming coloring specks. The optical density of the glass can be adjusted by changing the electron beam exposure dose. The technique is capable of producing nonbinary photomasks for gray-scale photolithography. The laser or particle beam direct writing methods generally yield photonic structures with a small index contrast (n 0:001). One approach to obtain higher index contrast structures involves preferential etching of glass following laser or particle beam writing, where the glass essentially functions as an inorganic resist material. A prominent example is hydrogen silsesquioxane (HSQ), a widely used high-resolution negative-tone electron beam resist. Electron beam exposure cleaves the Si–H bonds to form an inorganic glass network crosslinked by bridging oxygen (Si–O–Si), which is insoluble in standard potassium hydroxide (KOH) or tetramethylammonium hydroxide (TMAH) developer [42.99]. Several other amorphous oxides [42.100–103] and chalcogenide glasses [42.104–110] have also been investigated as inorganic UV, x-ray, ion beam, and electron beam resist materials. Compared to polymer resists, these glassy resists generally feature superior resolution and contrast due to their smaller structural unit size. Focused ion beam (FIB) milling is another related technology to sculpt high-index-contrast nanoscale photonic structures, which, as its name implies, uses a FIB to induce site-specific sputtering of materials. Its applications in nanophotonic fabrication span a wide range of materials including glass. Readers may refer to references herein for more information about the technology [42.111–113].
42.1 Processing of Planar Glass Photonic Components
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Optical and Photonic Glass Applications
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Fig. 42.5a–g Ion exchange process configurations. (a) Thermal exchange from a molten salt bath; (b) fieldassisted exchange from a molten salt bath; (c) field-assisted exchange from a deposited metal thin film source; (d) field-
assisted exchange and burial from a deposited thin film source with molten slat; (e) thermal diffusion; (f) thermal burial of a waveguide; and (g) field-assisted burial of a waveguide. Adapted from [42.119]
atomic defects. The material damage is usually most pronounced towards the end of the ion track, where the generation of atomic defects leads to volume expansion and refractive index depression. The resulting low index region, i. e., the optical barrier, constitutes an optical cladding to confine the waveguide mode. In some materials, a well region with an increased refractive index is formed near the sample surface, which further enhances optical confinement [42.132, 133]. When a broad area ion beam source is used, selective implantation through a photoresist or metal thin film mask is used to modulate the in-plane index profile to provide lateral (in-plane) optical confinement [42.134]. Compared to ion exchange, an important advantage of ion implantation is that virtually any type of ions, including RE and transition metal ions, can be embedded into a glass substrate using implantation. For example, planar waveguide amplifiers and microcavity lasers with ultra-low threshold have been demonstrated by erbium implantation in silica glass followed by annealing to activate the erbium ions [42.135–137]. Inkjet Printing Inkjet printing is an additive microfabrication technology increasingly adopted in biotechnology, medicine, and electronics manufacturing [42.138]. As a microfabrication technology, inkjet printing claims the advantages of extreme versatility, reduced material wastage, low cost, and large-area roll-to-roll compatibility. Solution-processed glassy and amorphous materials, such as hybrid organic–inorganic silicates [42.139, 140], sol– gel derived oxides [42.141, 142], and chalcogenide glasses dissolved in organic amines [42.143] can be formulated as inks compatible with inkjet printing technologies. A major limitation of inkjet printing is its spatial resolution, which is typically 20 m (1200 dots-per-inch) and above, limited by the ink droplet size, spreading of the droplet on substrates, as well as droplet placement accuracy. Further improvement of the printing resolution requires specialized print head design [42.144] or substrate pre-patterning [42.145], both of which complicate the fabrication process. Consequently, inkjet printing is better suited for microoptical fabrication (e. g., microlens printing) than for guided-wave optical device processing where sub-micrometer feature size is often necessary.
42.1.2 Post-Fabrication Reflow Processing In a reflow process, fabricated glass devices are heated using an oven (thermal reflow) or laser light (laser reflow) to reduce the viscosity of the glass such that viscous flow takes place under the action of surface
Glass in Integrated Photonics
42.1 Processing of Planar Glass Photonic Components
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Fig. 42.6 Reflow
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cally studied the roughness evolution kinetics in surface tension driven flow [42.153–155]. In a structurally homogeneous glass sheet, where surface tension is the only driving force for surface morphology evolution, amplitudes of the Fourier components of roughness on a free surface decay exponentially over time, and the components with a smaller wavelength (i. e., higher spatial frequency) decay more rapidly [42.154]. The ultimate roughness limit is set forth by energy equipartition in the surface capillary wave (SCW) modes. In hollow-core silica glass fibers, the SCW limit corresponds to a low roughness-scattering-induced loss of 0:1 dB=km in the near-infrared (near-IR) [42.155], which is even lower than the intrinsic material attenuation of silica glass. This ultimate limit of roughness, however, is difficult to reproduce experimentally. Atomic force microscopy (AFM) measurements on silica microspheres fabricated by re-melting fiber tips (which closely resembles the thermal reflow process) yield a root-mean-square (RMS) surface roughness of .1:7 ˙ 0:5/ nm, much higher than the thermodynamic limit due to frozen-in SCW modes [42.156]. The residual roughness observed is likely a consequence of surface inhomogeneity. Carefully optimized laser reflow processing has led to the demonstration of ultra-high-Q silica microtoroid resonators with Q-factors exceeding 108 [42.20, 157, 158]. Figure 42.7 illustrates the microtoroid fabrication process. Detailed descriptions of the fabrication protocols (along with video demonstrations) are also available through [42.159]. The process involves litho(WFK6L2FLUFXODUSDG
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Part F | 42.1
tension. The surface tension of solids is a manifestation of the cohesive force between constituent atoms. Existing data compiled from a large number of silicate glass compositions [42.146] suggest that surface tension of glass is a relatively weak function of temperature. On the other hand, the viscosity of glass critically depends on temperature, which is evident from either the classical Vogel–Fulcher–Tammann (VFT) equation or the more recent Mauro, Yue, Ellison, Gupta, and Allan (MYEGA) model [42.147]. Therefore, although the surface tension of fused silica changes only by 3% from 1100 to 1300 ı C [42.148], the viscosity of silica glass changes by over two orders of magnitude over the same temperature range. As a result, kinetics of the reflow process are largely dictated by the glass viscosity, which is critically controlled by the processing temperature. For photonic applications, reflow processing is implemented either to shape the glass structure or to remove surface roughness on the glass. The former application is exemplified by thermal reflow fabrication of microlenses, whereas the latter process contributes to optical scattering loss suppression in glass photonic devices. Figure 42.6 shows a typical reflow fabrication process for microlens arrays. First, a glass layer deposited or bonded onto a supporting substrate is lithographically patterned into an array of cylinders. Subsequently, the glass is reflowed by an annealing process such that the cylinders transform into a meniscus shape. The resulting geometry (and, hence, the lens’ focal length and NA) of the microlens is determined by the starting diameter and thickness of the cylinder, the contact angle between the glass and the substrate, and in some cases, volume loss due to glass evaporation during the reflow process [42.149]. The reflow process provides a simple and high-throughput fabrication of microlens arrays. The approach has been adopted in a number of glass systems, including soda-lime glass [42.150], borosilicate glass [42.151], and chalcogenide glass [42.152]. In addition to shaping optical elements, reflow post-treatment is also an effective means to eliminate surface roughness from lithographically defined glass photonic devices. The roughness removal process is thermodynamically driven by surface energy minimization. Several research papers have theoreti-
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Fig. 42.8a–c Surface morphology of an As2 S3 glass waveguide measured by AFM. (a) As-patterned; (b) reflowed at 230 ı C for 15 s; and (c) reflowed at 245 ı C for 15 s. From [42.154]
Part F | 42.2
graphic patterning of thermal oxide on a silicon wafer to a microdisk shape, followed by isotropic etching of the underlying Si substrate by XeF2 to suspend the microdisks from the substrate. The microdisks are then heated sequentially using a focused CO2 laser to render a silicon oxide toroid structure with a smooth surface finish. Silica microtoroid resonators represent an ideal platform for investigating enhanced light-matter interactions given their ultra-high Q-factors. Their applications in non-linear optics, sensing, optomechanics, and quantum optics are discussed in Sect. 42.2.1.
For on-chip waveguides, the efficacy of roughness reduction via reflow is further limited by substrate nonuniformity and contamination, which incur excess line edge roughness due to contact angle variation and defect pinning [42.160]. Figure 42.8 presents an example of reflow postprocessing, where the surface roughness of an As2 S3 chalcogenide glass waveguide is significantly reduced after annealing [42.154]. It is noted that the roughness removal process is always accompanied by a change in the waveguide’s cross-sectional geometry.
42.2 Integrated Photonics Platforms Based on Glass Materials 42.2.1 Silica and Silicate Glass The invention of optical fibers made mainly of silica for communication systems has boosted the applications of silica and silicate glass in optics, including integrated photonics. Various on-chip photonic components, ranging from lasers, filters, modulators, and sensors, have been fabricated from silica on a silicon substrate. A number of methods have been used to prepare silica films on a silicon substrate, such as flame hydrolysis deposition, chemical vapor deposition (CVD), and thermal oxidation. An alternative route to fabricate silica films is the sol–gel technique, a wet chemical synthesis in which only solvents are involved in the beginning of the fabrication process. Sol–gel processing is a relatively mild chemical method to fabricate porous materials and relies on converting precursors to colloidal dispersion and then further to a highly open gel network. The sol–gel method has several advantages: first, it is a versatile technique that involves wet chemical synthesis, therefore the chemical composition of the materials can be stoichiometrically controlled, and the distributions of dopants are homogeneous. Sec-
ondly, it is cost effective due to reaction at room temperature without using expensive and delicate vacuum systems. Various optical devices, such as erbiumdoped waveguide amplifiers, one-dimensional photonics crystal devices, and size-tunable silica nanocubes have been fabricated by sol–gel methods. As implied by the name, a transition from a liquid sol (colloidal solution) into a gel phase in involved in a sol–gel process [42.161]. Initially, metal alkoxide precursors undergo hydrolysis and condensation reactions to form a colloidal system composed of solid particles (with sizes ranging from 1 to 1000 nm). As the chemical and physical changes proceed in the sol–gel solution, a three-dimensional (3-D) cross-linked network structure of metal oxide glass is formed. The hydrolysis of tetraethoxysilane (TEOS) has been used in industrial applications as a convenient process to obtain thin silica films. Sol–gel processing does have its limitations. In most systems, the pore size and the interconnected pore size are difficult to manipulate. The size of the interconnected pores usually affects the optical quality of the sol–gel coating, since the pore size close to the
Glass in Integrated Photonics
a)
the silica Raman gain spectrum. Figure 42.10b shows a laser emission spectrum for a microtoroid laser fabricated from Er3C -doped sol–gel silica film. The pump wavelength is at 1442 nm, and the lasing wavelength is at 1553 nm. The laser output as a function of absorbed pump power is shown in the inset of Fig. 42.10b. Owing to both the high quality factor and the small mode volume of the cavity, a threshold pump power of 3 W was measured in the given data. Optimization of the coupling condition and doping level achieved a record low threshold of 660 nW. Figure 42.10c,d presents side and top images of an Er3C -doped sol–gel silica microtoroid, respectively. The green rings are due to upconversion of Er3C in the materials. In addition to improving the quality of sol–gel silica, the CO2 laser reflow technique has been utilized to improve the optical quality of on-chip photonic devices with loss initially limited by the surface roughness introduced by various etching processes during device fabrication.
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Fig. 42.9 (a) A sol–gel silica film before CO2 laser reflow; (b) after CO2 laser reflow. The CO2 laser reflow technique smooth out the surface roughness and increase the optical quality of the film
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Fig. 42.10 (a) Raman emission spectrum of an undoped sol–gel silica microtoroid with a principal diameter of 49 m. The pump wavelength is at 1561 nm, and Raman oscillation occurs at 1679 nm. The inset shows the measured Raman laser output power (in W) versus the absorbed pump power (in W). (b) A typical laser spectrum of an Er3C -doped sol–gel silica microtoroid laser. The pump wavelength is at 1442 nm, and the laser line appears at 1553 nm. The inset shows the measured laser output power (in W) plotted versus the absorbed pump power (in W). (c) Side image of an Er3C -doped sol–gel silica microtoroid coupled by a fiber taper waveguide. (d) Top image of an Er3C -doped sol–gel silica microtoroid with diameter of 30 m. Reprinted from [42.162], with the permission of AIP Publishing
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light’s wavelength is capable of scattering light leading, to scattering loss in a photonic device. Controlling the sol–gel film porosity and the average size of the interconnected pores is difficult, yet critical, for highquality photonic device fabrication. A study by Yang et al. successfully improved the optical quality of sol– gel silica films by a post-processing laser treatment (Fig. 42.9). Following the fabrication process as described in Fig. 42.7, ultra-high-quality (> 107 ) on-chip resonators have been processed from sol–gel silica film deposited on a silicon wafer. Figure 42.10a presents a lasing spectrum due to stimulated Raman scattering (SRS) in an undoped sol–gel silica microtoroid resonator. The Raman shift corresponds to the frequency of the vibration mode of the silica at 460 cm1 . The inset of Fig. 42.10a presents the Raman laser output power as a function of absorbed pump power and shows a sub-milliwatt threshold. The offset of the Raman lasing signal around 15:7 THz is within the peak area of
42.2 Integrated Photonics Platforms Based on Glass Materials
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Different from crystalline materials for which the device fabrication is limited by lattice-matching constraints, glass could easily be shaped in different structures with either planar or curved surfaces. This unique feature is critical to the recent progress of whispering-gallery mode (WGM) microresonators, a class of devices that play a special role in modern photonics. The WGM microresonators have turned out to be the ideal tools to store and manipulate light for a whole variety of applications, ranging from cavity quantum electrodynamics (QED) and optomechanics to ultra-low threshold microlasers, frequency combs, and high-performance sensors. Much effort has, therefore, been invested into providing these versatile devices with new functionalities, each of which was greeted with enormous excitement by the community. Fabrication of ultra-high-quality crystalline WGM microresonators is largely limited to mechanical polishing methods [42.163]. In contrast, it is far more straightforward to process glass materials as described a),QWHQVLW\ G%P
in Sect. 42.1. Various nonlinear processes, including SRS for lasing [42.162, 164, 167], third harmonic generation [42.165, 168], SBS for lasing [42.38, 169], fourwave mixing, and soliton generation [42.166, 170–173], have been demonstrated in high-quality silica glass microresonators. Figure 42.11 shows different nonlinear processes observed in high-quality WGM resonators. The high flexibility and low optical loss in silica and silicates also qualify them as excellent candidates to form specific geometries to trap light fields and achieve enhanced light–matter interactions. For example, in an optical resonator, photons circulate in a confined volume and interact with the surrounding materials on their optical pathway multiple times. This is in stark contrast to single-pass photonic devices, such as waveguide and optical interferometers, where enhancing the interaction between light and matters necessarily involves increased physical length of the devices. There has been a strong need for miniature sensors for a wide range of applications from environmental monitoring to medical
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Fig. 42.11a–d Nonlinear effects in glass microresonators. (a) Raman laser spectrum of a microsphere. Inset: A microsphere coupled with a fiber taper. From [42.164]. (b) Third-harmonic generation spectrum of a microtoroid. The x-axis is interrupted to show two spectra in different bands. The inset shows a photo of the third-harmonic generation in the 500 nm band, as well as the corresponding energy level diagram. Reprinted from [42.165]. (c) Brillouin laser spectrum of a millimeter sized disk resonator. After [42.38]. (d) Frequency comb from a monolithic toroidal microresonator. After [42.166]
Glass in Integrated Photonics
the first. The concept was then extended to more complicated structures and configurations involving many coupled optical waveguides with varying numbers of PT-symmetric unit cells. Figure 42.13 demonstrated experimentally the first PT-symmetric optical microcavities and showed clearly PT-symmetry breaking in such a system composed of two coupled WGM microresonators with balanced gain and loss [42.181]. Non-reciprocal behavior requires time-reversal-symmetry breaking, and is traditionally achieved using magneto-optics [42.182, 183]. According to the principle of Lorentz non-reciprocity, a linear static dielectric system cannot support non-reciprocity; however, a system with nonlinearity can. Thus, there have been efforts in building non-magneto-optical systems for non-reciprocal light transmission, based on nonlinear processes or spatial-temporal refractive index modulations. Figure 42.13 shows nonlinearity-based non-reciprocal light transmission in the broken-PT phase where the nonlinearity is significantly enhanced due to field localization. The experiments showed a complete absence of transmission in one direction and resonantly-enhanced trans-
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Fig. 42.12 (a) Schematic setup of the single nanoparticle detection using a microsphere. Reprinted from [42.176]. Copyright 2008 National Academy of Sciences, USA. (b) Mode shift of streptavidin binding to previously surface immobilized bovine serum albumin (BSA) biotin. After [42.177] with permission of AIP Publishing. (c) Mode splitting induced by individual single potassium chloride (KCl) nanoparticles. The spectra are offset vertically for clarity. After [42.178]. (d) Mode broadening when single polystyrene (PS) particles with a radius of 70 nm bind to the cavity surface. Adapted with permission from [42.179]
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diagnosis and security. Given the significantly enhanced light–matter interactions in resonant structures, optical microresonators have been the frontrunners for sensing applications [42.174, 175]. A single molecule attaching on high-quality microresonators can interact with the light over a million times, which helps to detect such a trace amount of sensing targets. Figure 42.12 illustrates different schemes adopted by optical microresonators for ultra-sensitive detection of small objects including virions, proteins, and nanoparticles. The versatile schemes available to introduce optical gain in glass materials have made them an excellent candidate for parity-time symmetry and non-Hermitian photonics. The physics around parity-time (PT) symmetry [42.180] has helped the development of new strategies to achieve novel functionalities in photonic systems. It is worth noting that PT-symmetric optical structures can be realized in systems with balanced absorption (loss) and amplification (gain). This can, in principle, be realized in a unit cell of two coupled optical structures, one of which has passive optical loss and the second one has optical gain balancing the loss of
42.2 Integrated Photonics Platforms Based on Glass Materials
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Part F | 42.2
mission in the other direction with power levels as small as a few microwatts, providing an elegant solution to the long-standing power budget and loss problems in nonlinearity-based non-reciprocity. The applications of silica glass in photonics are certainly well beyond what is reviewed here. High-quality silica microresonators have been exploited as an excellent platform to explore optomechanics [42.184– 188], through which mechanical oscillation is coupled with light fields. Such an interaction enables innovative concepts to control light flow in photonic structures [42.189–192] and creates new strategies for optical cooling [42.187]. Non-Hermitian physics has been explored recently in silica microresonators. Examples including chiral modes, direction lasing, and enhanced sensing leveraging on topological features of the silica microresonators around exceptional points have been demonstrated [42.193–195].
42.2.2 Non-Silicate Oxide Glass Non-silicate oxide glasses include germanates, phosphates, tellurites, gallates, borates, heavy metal oxide (HMO) glasses, etc. These glasses are usually introduced into planar photonic platforms to utilize their enhanced optical nonlinearity compared to silicates or to use them as RE host materials. The enhanced Kerr optical nonlinearity in selected non-silicate glass compositions can be accounted for using a simplistic two-level bond orbital model derived by Lines [42.196], which correlates the nonlinear index n2 of oxide glass with its material parameters. According to the model, glass with a high linear index, a large nearest neighbor bond length, and a small Sellmeier energy gap is associated with a large nonlinear index n2 . This conclusion is also in agreement with the generalized Miller’s rule [42.22]. The model suggests two candidate glass composition groups for nonlinear optical application in the near-IR wave band. Both groups are based on tellurite, gallate, or germanate glass formers, alloyed with either high-valency empty d-band transition metals (such as W, Ta, Nb, and Mo) or heavy metal oxides containing Bi, Pb, Tl, or Cd. The Lines model has been validated by experimental measurements of n2 in transition metal-doped tellurite glasses, which show that addition of the oxides of Nb, Ta, W, and Ti significantly increases the nonlinear susceptibility of the base TeO2 composition [42.197–199]. Similar trends of nonlinearity increase were identified in heavy metal-doped germanates and gallates [42.200]. Investigations into non-silicate RE hosts are mainly motivated by two reasons. First of all, several nonsilicate glass compositions are known for their exceptionally high RE solubility, which helps minimize
clustering of RE ions at high RE concentrations and, thereby, suppresses luminescence quenching due to cross-relaxation between RE ions. Large optical gains per unit device length can, therefore, be attained in these glasses, a critical advantage for on-chip integration, where the accessible optical path length is limited. For example, tellurite and phosphate glasses are known to exhibit RE solubility exceeding several percent by weight [42.201–204]. In contrast, erbium segregation occurs in silica glass at concentrations as low as 0:01 at:% upon annealing [42.205]. Secondly, the Si–O bond has a relatively high phonon energy of 1100 cm1 (in wave number), which exacerbates nonradiative transitions due to multiphonon relaxation in silicate glasses. The high phonon energy also imposes a long wavelength cut-off for the RE emission [42.206]. Substitution of silicon with heavier elements, for instance in the cases of germanates, tellurites, and HMOs, reduces phonon energy and helps improve luminescent efficiency. Planar waveguide amplifiers and lasers based on RE doped non-silicate oxide glasses have been fabricated following a number of technical routes, such as ion exchange [42.207, 208], LDW[42.209, 210], or ion implantation [42.211] in bulk glass, and photolithography followed by plasma etching of the deposited thin films [42.212, 213]. They open up doors for light source integration in a planar photonic circuit platform. Nevertheless, non-silicate oxide glass photonics is still much less advanced to date compared to devices based on silica—the incumbent oxide glass material for on-chip integration.
42.2.3 Chalcogenide Glass (ChG) Chalcogenide glasses (ChG) refer to amorphous compounds containing S, Se, and/or Te. The heavier constituent atoms of chalcogenides account for their larger electronic polarizability compared to oxides and, hence, higher linear refractive indices, usually between 2 to 3:5. High-index-contrast, compact on-chip photonic devices such as sub-micrometer single-mode waveguides and photonic crystals can, therefore, be fabricated in ChGs to tightly confine optical modes. In addition, it has been predicted by both the Lines model [42.196] and the more generalized Miller’s rule [42.22] that high linear indices are correlated with large optical nonlinearity: as expected, ChGs exhibit nonlinear indices n2 two to three orders of magnitude higher than that of silica glass [42.214–216]. ChGs’ extraordinary Kerr nonlinearity has been exploited for a variety of nonlinear optical applications, including ultrafast all-optical signal processing, supercontinuum generation, and Raman amplification [42.217].
Glass in Integrated Photonics
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Fig. 42.13 (a) PT-symmetric resonator system consisting of two directly coupled microresonators, one with gain (R1 ) and the other with loss (R2 ). (b) A coupled PT-symmetric WGM silica microresonator system. Each resonator is also coupled with a tapered silica fiber through which light is coupled in and out of the resonator. (c) Experimentally observed unidirectional transmission for symmetric microresonators with balanced gain and loss elements. When the gain and loss is above some critical value, and the system is in the broken symmetry region, transmission becomes unidirectional. Reprinted with permission from [42.181]
The heavy constituent elements and weaker chemical bonds in ChGs relative to oxides also give rise to their low phonon energy and long-wavelength cut-off extended deep into the infrared: sulfide glasses transmit light from visible to about 10 m wavelength, selenides up to about 15 m, and the transparency window of telluride glasses extends beyond 20 m [42.218, 219]. ChGs are, thus, regarded as a promising optical material for mid-infrared (mid-IR) integrated photonics, an emerging device platform for spectroscopic sensing, astronomical optics, and infrared imaging [42.220– 224]. Another salient feature of ChGs compared to oxide glasses is their low deposition and processing temperature. For instance, the substrate can be maintained near room temperature without active substrate cooling during thermal evaporation deposition of ChGs [42.225]. The negligible substrate heating effect is a direct consequence of the relatively weak chemical bonds in ChGs. Take the archetypal As2 S3 ChG as an example, its vapor pressure is approximately 6 Pa at 560 K [42.226]. In comparison, silica has to be heated to 2000 K to reach the same vapor pressure [42.227]. The much higher crucible temperature required for silica vaporization, therefore, significantly increases radiative heating of the
receiving substrate. The post-deposition annealing temperatures of ChGs are also generally much lower than those of oxide glasses given ChGs’ lower Tg . The low deposition and processing temperature, coupled with the amorphous nature of ChGs, enable the integration of the photonic components of ChGs on virtually all types of technically important substrate materials, such as semiconductors, dielectrics, polymers, optical crystals, metals, and ceramics. In this section, we first review ChG thin film deposition and device fabrication techniques and then proceed to discuss three main applications of chalcogenide photonics in nonlinear optics, sensing, and substrateagnostic photonic integration, all of which leverage the aforementioned optical and processing properties of ChGs. While outside the scope of this section, it is worth mentioning that besides their utility as an optical material for passive photonic components, ChGs are amorphous semiconductors, and, thus, they can play a role in active optoelectronic devices by functioning as carrier transport layers [42.228, 229] or rectifying p-n junctions [42.230]. ChGs are also known for the threshold switching behavior, which is important to their applications in ovonic switching devices and phase change memories [42.231].
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Deposition and Processing of Thin Film Chalcogenide Glasses ChG thin films can be prepared using physical vapor deposition methods (thermal evaporation, electron beam evaporation, flash evaporation, sputtering, PLD, etc.), CVD [42.232–234], as well as solution processing using organic amine solvents [42.62, 235, 236]. The films are usually formed under conditions far from thermal equilibrium, and, consequently, films prepared using different methods can yield rather different structural, optical, and thermal properties (which are also different from those of bulk glasses) [42.225, 237, 238]. In several cases, post-deposition annealing has been shown to relax the thin film structure to a more stable structure closer to the bulk glass state [42.239]. One such example is As2 S3 films deposited using thermal evaporation or PLD. In both cases, the resulting films contain a significant fraction of homopolar As–As and S–S bonds in the forms of As4 S4 units and S chains/rings as a result of the following vaporization reactions [42.226] As2 S3 (s) ! As2 S3 (g) 1 1 As2 S3 (s) ! As4 S4 (g) C S2 (g) 2 2 Vapor condensation onto a substrate occurs at a high effective cooling rate (up to 1014 K=s), and, therefore, these non-equilibrium structural moieties, present only in small quantities in bulk glasses [42.240, 241], are frozen in the resulting films. X-ray-absorption fine structure (EXAFS) and Raman spectroscopy measurements reveal that post-deposition annealing converts the homopolar bonds back to heteropolar As–S bonds [42.242, 243]. It is, however, unlikely that annealing can fully restore the bulk glass structure in thin films [42.243]. A study by Choi et al. also shows that properly annealed As2 S3 films exhibit reduced optical loss compared to as-deposited films due to annihilation of the structural defects [42.244]. Photonic device fabrication in ChGs generally follows three schemes: 1. Photosensitive patterning using LDW or masked light exposure 2. Standard lithography coupled with plasma etching or lift-off 3. Replication from molds (nanoimprint, MIMIC, microtransfer printing, etc.) [42.245]. The first approach, which capitalizes on the photosensitivity of ChGs to visible or UV light, produces low-index-contrast (n < 0:1) waveguides with optical losses down to 0:2 dB=cm at 1550 nm wavelength [42.246] and 0:5 dB=cm at 8:4 m mid-IR wave-
length [42.247]. Similar low-loss values (0:13 dB=cm at 1550 nm) were recently reported in femtosecond laser inscribed single-mode ChG waveguides [42.248]. The versatile LDW technique has also been adopted for 3-D waveguide circuit fabrication in bulk ChGs [42.249]. Photodoping of silver metal offers an alternative photosensitive patterning method to create waveguides with higher index contrast (n 0:3) [42.250, 251]. Besides waveguide and Bragg grating writing, photosensitivity in ChGs was also harnessed for post-fabrication photonic device trimming [42.15, 43, 252–254] as well as double-heterostructure photonic crystal cavity fabrication [42.255]. High-index-contrast (HIC) ChG photonic devices including waveguides, resonators, and photonic crystals have been fabricated using lithographic patterning or nanoimprint. There is one caveat when applying standard UV photolithography to ChG patterning: commercial alkali-based photoresist developers (usually formulated based on TMAH) can attack chalcogenides and, thus, special care needs to be taken [42.256]. Large-core rib waveguides with an impressive low loss of 0:05 dB=cm [42.257], submicrometer single-mode waveguides with a loss of 0:5 dB=cm [42.258], photonic crystal cavities with a Qfactor of 750 000 [42.259], and microdisk resonators with an intrinsic Q-factor of 1:2 106 [42.258] represent state-of-the-art performance in lithographically patterned planar ChG devices near 1550 nm telecommunication wavelength. In these HIC devices, optical scattering induced by surface roughness is often the dominant source of measured optical loss. In the mid-IR band, low-loss waveguides (0:3 dB=cm at 5 m), highQ optical resonators (Q D 4 105 ), and photonic crystal nanobeam cavities have been demonstrated [42.260– 264]. Several groups have developed direct nanoimprint patterning of ChG devices, including optical waveguides, resonators, gratings, and wire grid polarizers taking advantage of the lower Tg of ChGs compared to oxide glasses [42.19, 53–56, 265–267]. ChG melt or solution filling of pre-patterned substrates has also been explored for HIC ChG waveguide device fabrication [42.268, 269]. Compared to their low-indexcontrast counterparts, HIC ChG waveguide devices claim much smaller optical mode field areas in the order of 108 cm2 and can tolerate tight bends with radii down to 10 m without suffering from excessive radiative loss, which are attractive features for on-chip integration and the applications to be discussed in the succeeding sections, which demand strong light–matter interactions. Last but not least, it is worth mentioning that while significant efforts are still being devoted to perfecting processing of passive ChG photonics, which is far
Glass in Integrated Photonics
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Fig. 42.14a–h QCL–ChG waveguide integration process. (a) The QCL chip was soldered onto a Cu heat sink; (b) a precleaved glass coverslip was glued onto the Cu block to serve as the waveguide substrate; (c) a PDMS elastomer mold attached to the coverslip; (d) amine solution of As2 S3 glass filled the mold by capillary action; (e) the mold was removed after post-baking to solidified the As2 S3 waveguide; (f) the pre-cleaved coverslip piece was removed to form an optical output facet; (g,h) tilted-view SEM images of the integrated QCL-waveguide structure. Reprinted with permission from [42.270]
less mature compared to the well-established silica-onsilicon platform, on-chip integration of ChG components with active optoelectronic devices was pioneered in a few recent reports describing hybrid integration of quantum cascade lasers (QCL) with solution processed ChG waveguides (Fig. 42.14) [42.270], on-chip integration of mid-IR ChG waveguides with PbTe photodetectors [42.271, 272], as well as ChG waveguide integration with III-V semiconductor nanomembrane detectors on flexible substrates [42.273, 274]. These initial demonstrations represent the first step towards realization of a ChG photonic integrated circuit. Chalcogenide Photonics for Nonlinear Optics ChGs’ large Kerr nonlinearity, in conjunction with low two-photon absorption (TPA) reported in many compositions at the telecommunication wave band and negligible free carrier absorption make them promising material candidates for nonlinear optical applications [42.275]. Another advantage of ChGs is their high linear refractive indices, which enables strong optical confinement in HIC ChG waveguides to boost the nonlinear interactions. The combination of large Kerr nonlinearity and tight optical confinement leads to ChG waveguide devices with an exceptional nonlinear parameter , conventionally defined as D
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modal area. A nonlinear parameter of 136 W1 m1 was realized in sub-micrometer single-mode ChG channel waveguides [42.276], and an even higher effective nonlinear parameter up to 6:3 104 W1 m1 was demonstrated in ChG photonic crystal waveguides taking advantage of the slow light effect [42.277]. The large Kerr nonlinearity in ChGs is dominated by electronic contributions (anharmonic oscillation of an electron cloud driven by the electric field of light) with a response time of the order of 10 fs [42.278]. The slower nuclear contribution (anharmonic bond length modulation), which is related to Raman scattering, accounts for 15% of the third-order nonlinearity observed and has a response time of 500 fs [42.168]. This ultrafast nonlinear response allows all-optical signal processing with large bandwidth in the THz regime, well beyond the speed of existing electronic circuits. As an example of ultrafast all-optical signal processing using Kerr nonlinear interactions in ChG devices, Fig. 42.15a illustrates a terabaud optical transmitter–receiver system built around ChG waveguide chips for both optical performance monitoring and signal demultiplexing [42.279]. The ChG chips each contain a dispersion-engineered As2 S3 rib waveguide of 7 cm in length with a bandwidth exceeding 2:5 THz (Fig. 42.15c). On the transmitter side, a singlewavelength optical signal at 1:28 TBd is produced by interleaving 128 channels each at a base bit rate of 10 GBd. The optical signal to be monitored from the terabaud channel is combined with a CW probe light
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and coupled into a ChG waveguide chip. As the signal and the probe light co-propagate in the ChG waveguide, sidebands are generated around the probe’s light frequency due to cross-phase modulation (XPM). These sidebands, monitored in real time by an optical spectrum analyzer (OSA), correspond to the radio frequency (RF) spectrum of the optical signal. The autocorrelation wave form of the signal is then extracted by performing an inverse Fourier transform (IFT) on the RF spectrum to provide real-time information about optical signal impairment (Fig. 42.15b). On the receiver end, the terabaud signal is optically demultiplexed using another ChG waveguide chip to the 10 GBd base rate, such that it can be converted back to the electronic domain using a photodetector. The optical demultiplexing process operates based on degenerate four-wave mixing (FWM). The high bit-rate terabaud signal co-propagates with control pulses (the pump) at the base rate in the second ChG waveguide chip. By adjusting the time-domain delay between the pulses and the signal, the pulses can be aligned to a target channel within the high bit-rate signal. The target channel is converted to the idler wavelength via FWM and can be readily detected after passing through a band pass filter (BPF) to remove the pump and signal wavelengths (Fig. 42.15d). ChGs’ large optical nonlinearity coupled with their broadband optical transparency also spur considerable interests in their applications for nonlinear frequency generation and conversion. On-chip coherent broad-
band sources based on ChG photonics for the midIR wavelength regime, such as supercontinuum (SC) and frequency comb sources, are of particular interest for spectroscopy applications [42.280]. Although spectral broadening in ChG thin film waveguides induced by self-phase modulation was reported around the turn of the millennium [42.281–283], broadband SC generation in ChG waveguides was only realized in laser written 79GeS2 -15Ga2 S3 -6CsI ChG waveguides several years later, in the 13201920 nm nearIR band [42.284]. Broadband supercontinuum spanning over two octaves from 1:8 to 7:5 m wavelengths was generated using a Ge11:5 As24 Se64:5 ChG core rib waveguide on a Ge11:5 As24 S64:5 cladding pumped by a 4 m optical parametric amplifier (OPA) [42.285]. The waveguide dimensions were chosen to obtain a flattened dispersion profile. Compared to an earlier demonstration in As2 S3 rib waveguides on a silicon oxide cladding [42.286], the combination of ChG waveguide core and cladding materials, as well as the use of a mid-IR pump source, significantly extend SC spectral coverage in the mid-IR. A mid-IR Kerr frequency comb source based on dispersion-engineered ChG microresonators has also been proposed [42.287, 288], although so far no experimental demonstration of comb generation in on-chip ChG cavities has been reported to the best of the authors’ knowledge. In a recent instance illustrating the utility of on-chip supercontinuum sources in sensing, a ChG waveguide was used simulta-
Glass in Integrated Photonics
neously as a supercontinuum source and an evanescent wave sensor to perform spectroscopic chemical detection over a broad spectral band [42.289].
42.2 Integrated Photonics Platforms Based on Glass Materials
Optical Sensing The operation wavelengths of traditional integrated photonics platforms based on LiNbO3 , silica-on-silicon, and a silicon-on-insulator are largely limited to the near-IR due to phonon absorption in the oxide materials. In contrast, the broad infrared transparency window of ChGs (up to 25 m) in telluride glasses [42.219] presents an intriguing opportunity of extending the operation wavelengths of integrated photonics systems to the mid-IR, simultaneously covering the function group region (4000 to 1450 cm1 in wave number or 2:5 to 6:9 m in wavelength) and the fingerprint region (1450 to 500 cm1 in wave number or 6:9 to 20 m in wavelength). The absorption cross-sections of molecules in the function group region is one to three orders of magnitude higher compared to their near-IR overtone bands, which is conducive to high detection sensitivity; on the other hand, the fingerprint region, as its name suggests, contains absorption spectral patterns unique to each chemical molecule, which can be used for unambiguous identification of target species. This extraordinary broadband transparency, therefore, qualifies ChGs as a compelling material choice for on-chip infrared spectroscopic sensors [42.217]. The most basic ChG optical sensor configuration is an evanescent-wave waveguide, through which the infrared absorption spectra of analytes are inferred from the variation in the optical losses of light passing through a planar ChG waveguide surrounded by the analytes [42.290]. Initial investigations on ChG evanescent-wave waveguide sensors have focused on the nearIR 1550 nm band, since sources emitting in telecommunication wave bands are readily accessible [42.292–
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Part F | 42.2
300]. Catalyzed by recent strides in mid-IR sources, in particular the advent of broadly tunable QCLs and optical parametric sources capable of room-temperature CW operation, in the last decade, the working wave bands of ChG waveguide sensors have been expanded to cover the mid-IR. Ma et al. fabricated ChG rib waveguides with a low propagation loss of < 1 dB=cm over the functional group spectral region and used the device to measure the absorption spectrum of Prussian blue in dimethyl sulphoxide [42.260]. Han et al. demonstrated on-chip methane gas sensing by monitoring the molecule’s absorption band at 3:3 m wavelength using a spiral-shaped ChG waveguide designed to increase the interaction length while maintaining a compact sensor layout (Fig. 42.16). The ChG optical chip is also integrated with gas-flow microchambers to facilitate gas analyte delivery [42.291]. As an alternative to evanescent-wave waveguide sensors, on-chip cavity-enhanced sensing using ChG microresonators has also been demonstrated, first in the near-IR telecommunication band [42.301, 302] and later in the mid-IR [42.220]. In addition to the small footprint of resonant devices, one potential advantage of on-chip cavity-enhanced sensing over waveguide sensors is that resonator structures (with propagation loss even lower than their waveguide counterparts) can be employed to increase the accessible optical path length and, hence, improve detection sensitivity [42.303]. For example, in an optical microdisk cavity with a Q of 106 , a photon (in the mid-IR band) has a lifetime of 3 ns and, therefore, can travel in the cavity for 1 m before it decays. The photons will circulate around the cavity numerous times to greatly increase the length of the optical path far beyond the physical dimension of the cavity. The resonant structure thus provides another strategy to increase the interaction length for ChG optical sensors.
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In both waveguide and resonator sensors, however, the detection sensitivity is bound by the relatively high optical propagation loss in planar ChG photonic components; taking the lowest loss value of 0:3 dB=cm or 0:13 cm1 in on-chip mid-IR ChG devices reported to date [42.260, 261], the effective optical path length in these devices is < 10 cm, several orders of magnitude lower compared to the attainable path length in free-space multipass spectroscopic absorption cells. As a consequence, the detection limit of traditional on-chip spectroscopic sensors is bound to the parts-per-million (ppm) level in the absence of pre-concentration or enrichment coatings. A cavity-enhanced photothermal sensing mechanism was proposed to resolve this limitation, and gas sensing down to the sub-parts-per-billion (sub-ppb) level was predicted taking advantage of the low thermal conductivity in ChGs to enable strong heat localization [42.304–306]. Besides infrared spectroscopy, alternative sensing schemes involving ChG thin films include using photosensitive patterned ChG films as surface-enhanced Raman spectroscopy (SERS) substrates [42.307] and potentiometric sensors based on metal-doped ChG ionic conductor electrodes [42.308]. Photonic Fabrication on Unconventional Substrates Another prominent feature of ChG thin films is their compatibility with numerous deposition substrates. This distinctive attribute comes from both the materials’ amorphous nature, which circumvents lattice-matching constraints, as well as ChG films’ low deposition temperatures, which reduces processing thermal budget and a)
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minimizes detrimental effects due to coefficient of thermal expansion (CTE) mismatch between the film and the substrate. The substrate-agnostic or substrate-blind integration capability, combined with the diverse repertoire of coating techniques for ChG films, open up many useful applications that are not possible with other materials [42.310]. For example, ChG films coated onto semiconductors can function as index-matching adhesives to eliminate Fresnel reflection [42.311]. In the same vein, solution processed ChG films were used as bonding adhesives between stacked multi-junction solar cells to reduce reflection and, thereby, boost energy conversion efficiency [42.312]. Integration of ChG optics with LiNbO3 crystals, a concept dating back to the 1980s [42.313], has garnered renewed interest in recent years to exploit electro-optic activity of LiNbO3 as well as HIC integration capacity of ChGs [42.314, 315]. ChGs can even be conformally coated onto delicate biological samples, such as butterfly wings, to replicate biomimetic structures [42.316] or integrated with twodimensional (2-D) materials to realize a wide variety of photonic components [42.317–319]. Flexible integrated photonics is another emerging field that benefits from the substrate-agnostic integration capability of ChG materials. By imparting mechanical flexibility to planar photonic structures, flexible photonics has enormous application potential for aberration-free optical imaging [42.320], epidermal sensing [42.321], chip-to-chip interconnects [42.322, 323], and broadband photonic tuning [42.324]. ChGs have several unique advantages for photonic integration on flexible substrates: they can be monolithically deposited and fabricated into functional devices (Fig. 42.17a);
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Fig. 42.17 (a) Fabrication process of flexible ChG photonic chips; (b) photo of a flexible ChG photonic chip; (c) loaded Q-factors and extinction ratios of a flexible resonator device after multiple bending cycles at 0:5 mm radius; (d,e) SEM images of (d) a multilayer woodpile photonic crystal where the colors label different ChG layers; and (e) a ChG waveguide integrated photodetector on a flexible substrate. From [42.309]
Glass in Integrated Photonics
42.2.4 Halide Glass The main interest in halide glasses stems from their low phonon energy (e. g., the phonon energy of fluoride glasses is around 500600 cm1 in wave number compared to 1100 cm1 of silica glass [42.328]). The low phonon energy in halides pushes the material optical attenuation minima to longer wavelengths, where Rayleigh scattering, which scales with the inverse fourth power of the wavelength, is much lower. Minimum optical loss down to 0:005 dB=km in the mid-IR was predicted in halide glasses [42.329], although such exceptionally low loss has never been experimentally realized due to transition metal impurity (Fe2C , Cu2C , etc.) contamination, as well as the glasses’ tendency of crystallization as a result of atmospheric oxygen and moisture attack. Therefore, passive photonic applications of halide glasses have largely focused on fiber-based platforms for short or medium-distance infrared light delivery, and several products are already commercially available [42.330]. Laser-inscribed fluoride glass waveguides with a propagation loss of 0:3 dB=cm have also been demonstrated at 4 m mid-IR wavelength [42.331]. On the other hand, reduced multiphonon relaxation as a direct consequence of the low phonon energy along with good RE solubility (> 5 mol% in fluoride glasses) make halides a useful material for light emission and amplification in both near-IR and mid-IR bands for planar photonic applications [42.332]. By far the most attention has been given to multicomponent heavy metal fluoride glasses (HMFGs) such
as ZBLAN (ZrF4 -BaF2 -LaF3 -AlF3 -NaF) glass, which has the distinction of being the most stable HMFG against devitrification and also an excellent host material for RE ions. Planar HMFG photonic devices have been fabricated from thin films as well as bulk glasses. While a wide variety of methods including evaporation [42.333], CVD [42.334], sol–gel [42.335], and hot spin coating [42.336] have been adopted for HMFG film preparation, incorporation of RE ions into fluoride glass films is most conveniently accomplished by either PLD from an RE-doped glass target [42.337–339] or co-evaporation of undoped fluoride glass and RE fluorides [42.340–343]. In the latter case, it is critical that the glass components in the undoped HMFG have similar vapor pressure to ensure congruent vaporization and minimal composition deviation in the resulting film, which places additional constraints on the glass compositions amenable to evaporation deposition. Device fabrication from fluoride thin films can either follow standard lithographic routes [42.45, 46, 336] or leverage LDW [42.338]. The LDW technique can also be applied to waveguide or grating fabrication in bulk glass plates [42.344–346]. Another frequently adopted route for device fabrication in bulk HMFG samples is ion exchange. In HMFGs containing alkaline ions, options of exchanged ion pairs include those routinely encountered in oxide glass ion exchange processing, such as NaC =KC and LiC =NaC [42.328, 347]. Unlike oxygen in oxide glasses, the anion (F ) in HMFG has high mobility, and, therefore, F =Cl anion exchange gives another viable path for waveguide processing [42.117, 348]. The ion exchange techniques are readily applicable to RE-doped fluoride glasses for light emitter and amplifier fabrication. The main motivations for using RE-doped halide glasses for lasers and amplifiers are to extend the spectra coverage both across the entire silica fiber low-loss window at 1:261:625 m (O to L bands) currently not accessible to erbium-doped fiber amplifiers, as well as to the mid-infrared (2 m and above) where severe phonon relaxation in silicates prohibits their use as RE hosts. A series of planar waveguide amplifiers and lasers has been demonstrated, covering a broad optical spectral range. Early attempts of optically pumped RE-doped HMFG waveguides were not successful in obtaining net gain due to the high waveguide losses [42.338, 342, 349]. Net gain at 1:54 m wavelength has been achieved in Er:Ce codoped ZrF4 -BaF2 -AlF3 -CeF3 glass waveguides fabricated by F =Cl ion exchange [42.350], as well as femtosecond laser inscribed waveguide amplifiers made from Er:Yb co-doped oxyfluoride glass [42.351]. Lasing in fluoride glass waveguides was first reported in a Nd-doped fluoroaluminate glass waveguide prepared
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their high refractive indices allow compact HIC device designs; and their compatibility with a wide range of materials facilitates multi-material integration to realize different photonic functionalities. A number of mechanical designs have been implemented to fabricate extremely flexible glass photonic structures despite the mechanical fragility of ChGs [42.325]. As an example, Fig. 42.17b shows a photo of a bendable ChG photonic chip; by using a multi-neutral-axis design, the strain exerted on the ChG device layer is nullified during bending [42.309]. Devices designed following the strategy exhibit extraordinary mechanical robustness and can sustain repeated bending down to sub-millimeter radius without measurable performance degradation (Fig. 42.17c). More recently, a serpentine ChG waveguide geometry was implemented to create mechanically stretchable photonic structures [42.326]. The ability to stack multilayer ChG structures further enables two-and-a-half-dimensional (2.5-D) fabrication of woodpile photonic crystals and integration of ChG waveguides with nanomembrane photodetectors (Fig. 42.17d,e) [42.273, 274, 327].
42.2 Integrated Photonics Platforms Based on Glass Materials
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Table 42.1 Performance characteristics of optically pumped fluoride glass waveguide lasers Glass
Fabrication method
Nd-doped Fluoroaluminate Yb-doped ZBLAN Tm-doped ZBLAN Tm-doped ZBLAN Ho-doped ZBLAN Ho-doped ZBLAN
UV laser writing in hot spin film fs LDW in bulk glass fs LDW in bulk glass fs LDW in bulk glass fs LDW in bulk glass fs LDW in bulk glass
Emission wavelength (nm) 1048/1317
Lasing threshold (mW) 60/32
Slope efficiency (%) 27/2
Reference
1036 1880 1890 2052 2900
25 21 12 20 27
84 50 67 20 19.5
Palmer et al. [42.353] Lancaster et al. [42.354] Lancaster et al. [42.355] Lancaster et al. [42.356] Lancaster et al. [42.357]
Part F | 42.2
by a combination of hot spin coating and direct UV laser writing [42.352]. The past few years have witnessed considerable improvement in the performance and spectral span of HMFG waveguide lasers. Table 42.1 compares the characteristics of several optically pumped fluoride glass waveguide lasers. The best performance so far has been attained in femtosecond laser written waveguide lasers in RE-doped ZBLAN glass with a depressed cladding configuration.
42.2.5 Glass Ceramics and Phase Change Materials Crystallization has long been considered the mortal enemy of glass scientists. In this section, however, we focus on two classes of materials that benefit from the phenomenon of crystallization or devitrification in glasses to acquire useful optical functionalities. Glass Ceramics in Integrated Photonics Glass ceramics (GC) are nanocomposite materials composed of both crystalline and amorphous phases obtained through controlled crystallization from a precursor glass matrix, a process known as ceramming. The most prevalent method of GCs preparation involves a two-step process: 1. Bulk or thin film glass is first produced using any of the standard glass-forming techniques. 2. Then the glass is heat treated via furnace or laser annealing to partially crystallize the glass matrix. Unlike sintered ceramics, GCs exhibit negligible porosity, a prerequisite for optical transparency. Compared to their parent glasses, GCs often offer improved thermal, mechanical, and chemical stability [42.358]. Interests in GCs for optical applications date back to the 1960s when the first transparent ceramics were demonstrated [42.359, 360]. Contrary to the conventional view that GCs suffer from high scattering loss and are not legitimate materials for guided wave optics, Tick projected in his 1998 paper that the ultimate optical loss in GCs can be as low as tens of dB=km, and he pro-
Harwood et al. [42.352]
posed four criteria for obtaining low optical attenuation in GCs [42.361]: 1. Particle (crystallite) size must be less than 15 nm 2. Interparticle spacing must be comparable with the crystal size 3. Particle-size distribution must be narrow 4. There cannot be any clustering of the crystals. Indeed, GC fibers with a minimum propagation loss of about 1 dB=m have been fabricated following the design rules [42.362]. The criteria above are consistent with the condition to minimize Rayleigh scattering in an effective optical medium. It was later discovered that the classical Rayleigh scattering theory, which assumes random spatial distribution of scatterers, overestimated optical attenuation in GCs by almost an order of magnitude [42.363]. To account for the remarkable transparency in GCs, Mattarelli et al. suggested that the discrepancy was a consequence of correlation among the spatial locations of the crystallites, which arises from the non-interpenetrating condition as well as competition between crystallites during coarsening [42.364]. Besides small crystallite size and uniform spatial distribution, other factors contributing to low optical loss include low birefringence in the crystals and reduced index contrast between the crystal and the glassy phases. It has been shown that transparent GCs can be prepared even in highly crystallized (with crystalline phase fraction exceeding 90%) samples by matching the refractive indices of the crystalline and the amorphous phases [42.365, 366]. Transparent GCs are useful to integrated photonics in several aspects. Of particular interest are RE-activated GCs, which have been explored as optical gain media and frequency up-converters [42.367, 368]. The unique advantages of GCs over single-phase glasses or sintered ceramics can be best illustrated through the example of oxyfluoride GCs [42.369]. Precipitation of fluoride nanocrystals in an oxide glass matrix produces composite GC materials that inherit the superior chemical durability and mechanical ruggedness of oxides relative to fluoride glass. In these materials, the RE
Glass in Integrated Photonics
nanocrystal impregnated silica glass thin films prepared by a sol–gel route and subsequent thermal annealing treatment to nucleate the nanocrystals [42.384]. Incorporation of nanocrystals also imparts electrooptical activity to GCs, a property associated with non-centrosymmetric crystals but absent in unpoled glasses [42.385]. In addition to their applications as functional optical materials, GCs are used as substrate materials for photonic devices because of their optical transparency, low thermal expansion, and mechanical and chemical durability [42.386]. Another emerging application of GCs in photonic device manufacturing is to utilize controlled crystallization to locally modulate the refractive index in an initially uniform glass matrix, thereby creating graded-index (GRIN) structures. As a proof-of-concept, a GRIN lens has been fabricated using this method [42.387, 388]. The approach can be readily extended to the processing of arbitrary flat optical elements in GC thin films. Chalcogenide Phase Change Materials Phase change materials (PCMs) generally refer to substances that undergo phase transition when driven by external stimuli (heat, electric fields, optical waves, etc.) and exhibit large optical, electrical, or thermal property changes upon phase transition. Specifically, phase transition in an optical PCM must be accompanied by drastic modifications to the material’s optical properties, i. e., refractive index and/or absorption coefficients. The two most common types of optical PCMs are Mott insulators, exemplified by VO2 and ChGs. In this section, we confine our discussions to the phase change ChGs, which are mainly tellurides such as GeSb-Te (GST) and Ag-In-Sb-Te (AIST) alloys. For instance, a gigantic refractive index change of n 3 occurs along with the amorphous-crystalline (hexagonal phase) transition in the alloy Ge2 Sb2 Te5 (Fig. 42.18a). This is in stark contrast to other optical materials, whose refractive indices can merely be tuned by a small fraction through thermo-optic, electro-optical, or magnetooptical effects. The unique ability of PCMs to create two distinctively different optical states in a reversible, non-volatile manner, a capability that used to be monopolized by optical microelectromechanical systems (MEMS), has triggered a recent surge of interest in their utility in integrated photonics. Optical switching [42.389–393], non-volatile display [42.396], and photonic reconfiguration [42.397–399] are among the first applications where PCMs may challenge the incumbent optical MEMS technologies. In addition to being a rugged solid-state technology without mechanical moving parts, other advantages of chalcogenide PCMs evidenced by their widespread adoption in the phase change memory industry include fast switch-
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Part F | 42.2
ions are preferentially partitioned into the fluoride crystals [42.370]. The preferential partition results in high RE concentrations in the fluoride nanocrystals, and, therefore, the crystals often take the form of RE-containing solid solutions. The RE ions are well dispersed in the crystalline solid solutions, which suppresses concentration quenching [42.371]. The low-phonon energy fluoride crystal environment also reduces multi-phonon quenching and inhomogeneous linewidth broadening of RE emission, leading to enhanced luminescence and up-conversion efficiency, as well as an increased absorption cross-section of RE ions. For these reasons, doubled RE emission quantum efficiency has been measured in oxyfluoride GCs compared to ZBLAN glass [42.372]. Silica-metal oxide GCs (e. g., silica-hafnia and silica-tin oxide GCs [42.373]) are another example of two-phase GCs that combine the mechanical strength of host glass phase and a local crystal environment favoring RE emission. Lasing in RE-doped GC optical fibers has been demonstrated [42.374], and planar optical waveguides have been fabricated in a variety of RE-activated GC compositions [42.375–379], although net gain and lasing in planar integrated photonic devices based on RE-doped GCs have not yet been realized to the best of our knowledge. Energy transfer between RE ions and luminescent nanocrystals offers another pathway to engineer luminescent properties of GC materials. A case in point is erbium-doped silicon-rich silicon oxide (SRSO, SiOx with x < 2). Although often not classified as a GC in the classical sense, the material is commonly synthesized using protocols identical to the preparation of GCs: an off-stoichiometric silica glass film is first deposited, followed by annealing to precipitate Si nanocrystals/nanoclusters and activate the erbium ions [42.380]. The Si nanocrystals serve as effective sensitizers for erbium; the nanocrystals have much larger photon absorption cross-sections compared to Er ions, and the absorbed photon energy can be efficiently transferred via confined excitons to Er ions, which predominantly reside in the glass matrix. It was found that the energy transfer process can boost the emission cross-section of Er ions by up to four orders of magnitude [42.381]. Given its compatibility with standard complementary metaloxide-semiconductor (CMOS) processing, SRSO has attracted significant interest as a potential light source material for Si microphotonics, although more recent work reveals that achieving optical gain in SRSOs is challenging due to large free carrier absorption in the Si nanocrystals and erbium ion clustering [42.382, 383]. Alternatively, light emitters can also be fabricated leveraging luminescent nanocrystals precipitated from a glass matrix without RE doping. As an example, UV light emitting diodes have been processed from SnO2
42.2 Integrated Photonics Platforms Based on Glass Materials
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Fig. 42.18 (a) Refractive indices and (b) extinction coefficients of different phases of Ge2 Sb2 Te5 (GST 225) alloy; graphs were plotted using data from [42.394] (0:755:15 eV) and [42.395] (0:040:5 eV); (c) FOM of the 225 alloy (for hexagonal-amorphous phase transition) defined by (42.1)
ing speed (sub-ns switching time [42.400]), outstanding endurance (> 109 cycles [42.401]), and integration compatibility with standard microphotonic and microelectronic systems. For these binary photonic applications involving two optical states, we define a generic figure of merit (FOM) to quantitatively evaluate the performance of optical PCMs FOM D
k n or : k k
(42.1)
Here, n and k represent the changes of refractive index and extinction coefficient upon phase transition, respectively, and k denotes the material’s extinction coefficient. The FOM is defined as such to account for the desired optical actuation effect (n or k) and optical loss penalty (k). In the case of optical switching, the FOM determines the on/off contrast ratio. Figure 42.18 plots the optical constants and FOM of the classical Ge2 Sb2 Te5 alloy (the so-called GST 225 composition) as an example. The 225 phase change alloy functions by switching between its amorphous and crystalline phases. GST 225 crystals exist in two polymorphs: a thermodynamically stable hexagonal phase and a metastable face-center-cubic (fcc) phase. Apparently, the FOM defined by (42.1) increases in the visible/near-IR range as the photon energy approaches the material absorption edge (Fig. 42.18c). The amorphous phase has a Tauc gap of 0:7 eV, and the hexagonal phase shows a band gap of 0:5 eV [42.394], and therefore GST 225 exhibits a relatively large FOM in the mid-IR wave band. At photon energies below the optical band gap, optical absorption in amorphous GST alloys is characterized by an exponential dependence of photon energy known as the Urbach edge [42.402]. The magnitude of optical absorption in the Urbach edge regime is a sensitive function of the preparation con-
ditions and processing history of the film [42.403]. At energies well below the band gap, optical absorption becomes negligible in the amorphous phase. On the other hand, crystalline GST materials are nearly degenerate p-type semiconductors with high concentrations of charged carriers [42.404]. The drastic rise of optical loss in the crystalline phases at the long wavelength end is attributed to free carrier absorption [42.395]. Therefore, for many photonic applications (especially for guided-wave applications), the optimum operation wave band of a PCM is defined between the material’s band gap and the onset of free carrier absorption. According to Fig. 42.18, the low-loss window of the archetypal GST 225 alloy situates in the mid-IR regime. At the near-IR telecommunication wave bands, the material is highly absorptive; for example, the optical absorption of GST 225 is 10 000 and 135 000 cm1 for the amorphous and hexagonal phases, respectively. To mitigate the large parasitic optical loss induced by GST, the PCM thin film is usually patterned into small patches to limit spatial overlap with optical modes [42.390, 393]. Figure 42.19a illustrates the design of an optical switch based on GST; a short segment (3 m in length) of a racetrack microresonator is covered with a 20 nm thick GST 225 thin film [42.391]. Phase transition in the GST layer is triggered by laser pulses. As shown in Fig. 42.19b, the contrast between the on/off states in this device (corresponding to the crystalline and amorphous phases of the GST material, respectively) is a combined effect of both resonant peak detuning resulting from refractive index change n and peak extinction ratio decrease as a consequence of increased optical absorption k upon crystallization. The contrast ratio ( 13 dB in this device) is ultimately bound by the optical absorption in the GST amorphous phase, which delimits the optical mode overlap with GST and the Q-factor of the resonator (i. e., sharpness of the resonant peak).
Glass in Integrated Photonics
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Fig. 42.19 (a) Top: Schematic layout of a resonant optical switch based on PCM. Bottom: Optical micrograph of two resonators. The one covered with GST 225 film functions as a switch, and the other one is a reference device. (b,c) Evolution of the switch’s transmission spectrum during (b) crystallization and (c) reamorphization of the GST film by laser pulses. Reprinted from [42.391], with the permission of AIP Publishing
To operate PCM devices at near-IR telecommunication bands, alternative compositions with higher FOM are desired. One such example is the recently demonstrated Ge-Sb-Se-Te (GSST), which has been applied to significantly improve the performance of optical switches at the telecommunication band [42.405, 406]. Chalcogenide PCM supports operations not only between the binary fully amorphous and crystalline states, but also between a multitude of intermediate states that are mixtures of the amorphous and crystalline phases with varying fractions. This unique property of ChG PCMs has been utilized in phase change memories for multi-bit (multi-level) storage [42.407]. The concept was transplanted to integrated photonics with the recent demonstration of a multi-level, non-volatile all-optical memory [42.408]. Figure 42.20a–c illustrates the basic photonic memory element consisting of a small GST island sitting on the top of a Si3 N4 ridge waveguide. The structural state of the GST island is controlled by a train of high-power pump optical pulses during the write/erase cycles. When the GST island resides in the amorphous state, optical attenuation in the waveguide is relatively low, corresponding to the on state. The much higher optical absorption of the crystalline phase leads to diminished optical transmittance through the waveguide, which defines the off state (Fig. 42.20d). Information encoded in the transmittance state of the waveguide can be read out using low-power probe pulses. The authors demonstrated that the memory device operated at switching energies as low as 13:4 pJ at an operation speed of 800 MHz. The same device can also be used for multi-level recording based on interme-
diate states in GST. Figure 42.20e plots the waveguide transmittance measured as a function of time, while the GST element is switched between eight structural states, each corresponding to a distinctive transmittance level. The levels can be addressed using varying write pulse energies, as shown in Fig. 42.20f. We note that the number of recording levels in the device is limited by the transmittance contrast between the two fully crystallized and amorphous end-point states, and thus is ultimately dictated by the material’s FOM at the memory’s operation wavelength. Besides amorphous-crystalline phase transition, ionic transport and electrochemical redox reactions in ChG ionic conductors offer a second phase transition mechanism that is potentially of interest to integrated photonics. In this case, metal ions (usually Ag or Cu ions) are transported inside a ChG ionic conductor from an anode to a cathode under the action of an applied electric field. The process leads to metal ion reduction at the cathode and metallic dendrite growth, thereby significantly altering the optical properties in the regions surrounding the cathode. Continuing dendrite growth eventually creates metallic filaments connecting anode and cathode accompanied by a dramatic reduction of electrical resistance between the electrodes. Reversing the electric field direction results in dissolution of the deposited metal back into the ChG solid electrolyte and, therefore, the metallization process is reversible and field switchable. The mechanism has been implemented in non-volatile memories in the form of programable metallization cells (alternatively termed conductive bridging random access memory or
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Fig. 42.20 (a) Schematic structure of the photonic memory. Information is encoded in the structural state of the GST film by using high-power write/erase optical pulses and extracted by measuring the waveguide transmittance using low-power read pulses; (b) SEM micrograph of the photonic memory device showing a GST island on a Si3 N4 waveguide; (c) optical mode profile of the Si3 N4 waveguide; (d) the on/off states of the memory device correspond to the amorphous/crystalline phases of the GST island; (e) 8-level memory operation demonstration: the brown curve is the optical transmittance through the waveguide measured in real time by read pulses, while the memory device is sequentially encoded in different levels using write/erase optical pulses. The black dotted lines denote the write (partial crystallization) steps, and the red dotted lines correspond to the partial erase (partial amorphization) steps. The horizontal color bars correspond to confidence intervals of each level; (f) relation between the pulse energy, addressed level and corresponding change in readout transmission for the write operations used in (e). Error bars show uncertainty in level attainability. From [42.408]
CBRAM) [42.409]. The large optical contrast between the electrochemically deposited metal film and the dielectric ChG matrix also makes the approach appealing
for photonic and plasmonic applications. For example, a programable plasmonic antenna has been theoretically proposed based on this mechanism [42.410].
42.3 Summary and Outlook Glassy materials are indispensable for photonics application because of their versatility in material composition to tailor their optical properties, the ease in introducing optical gain, and compatibility with various substrates. Different from crystalline materials in which the lattice structure makes it challenging to modify the chemical compositions, the amorphous phase in glass can readily accommodate chemical and structural changes, which allows us to precisely control the spectral features of the materials. ChG showcases
such a feature and has been demonstrated to be an excellent material candidate for integrated photonics in mid-IR. Silica glass was selected as the suitable material for optical fibers to guide light for their low loss in the communication band around 1550 nm. It is also worth noting that a hybrid material system combing the features of both crystal and glass, i. e., PCMs, can also be formed. Due to the distinct structures in amorphous and crystalline phases, a gigantic refractive index change could be achieved by control-
Glass in Integrated Photonics
ling the amorphous-crystalline phase transition. The amount of changes in the refractive index induced by the phase change is much higher than what can be achieved by traditional optical materials, whose refractive index is tuned through thermo-optic, electrooptical, or magneto-optical effects. It will significantly enhance the tunability of the optical properties of photonic structures. Moreover, as a typical system in a thermodynamically non-equilibrium state, the synthesis of glass is not limited to stringent conditions, such as vacuum, high temperature, or well-controlled environments. Such a feature allows researchers to
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References
Juejun Hu Dept. of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA, USA [email protected]
Juejun (JJ) Hu is currently the Merton C. Flemings Career Development Associate Professor at MIT’s Department of Materials Science and Engineering. His primary research interest is enhanced photon–matter interactions in nanophotonic structures, with an emphasis on on-chip spectroscopy and chemical sensing applications using novel infrared glasses. He holds degrees in materials science and engineering from MIT and Tsinghua University, China. Prior to joining MIT, he was an Assistant Professor at the University of Delaware. For more information see “About the Editors”.
Lan Yang Dept. of Electrical and Systems Engineering Washington University in St. Louis St. Louis, MO, USA [email protected]
Lan Yang is currently a Professor in the Electrical and Systems Engineering Department of Washington University, St. Louis. Her research focuses on photonic resonators and their applications for sensing, lasing, light harvesting, and optical communication. She received a PhD in Applied Physics from Caltech and a BS in Materials Science and Engineering from the University of Science and Technology of China. She is an OSA Fellow.
Part F | 42
T. Nirschl, J. Philipp, T. Happ, G. Burr, B. Rajendran, M.-H. Lee, A. Schrott, M. Yang, M. Breitwisch, C.-F. Chen: Write strategies for 2 and 4-bit multi-level phase-change memory. In: Proc. 2007 IEEE Int. Electron Devices Meet (2007) pp. 461–464 C. Ríos, M. Stegmaier, P. Hosseini, D. Wang, T. Scherer, C.D. Wright, H. Bhaskaran, W.H. Pernice: Integrated all-photonic non-volatile multilevel memory, Nat. Photonics 9, 725–732 (2015) M.N. Kozicki, P. Dandamudi, H.J. Barnaby, Y. Gonzalez-Velo: Programmable metallization cells in memory and switching applications, ECS Transaction 58, 47–52 (2013) S. Dong, K. Zhang, Z. Yu, J.A. Fan: Electrochemically programmable plasmonic antennas, ACS Nano 10, 6716–6724 (2016)
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Amorphous S 43. Amorphous Silicon in Microphotonics
Anuradha M. Agarwal, Jurgen Michel
In this chapter, we add to the large body of available literature on amorphous silicon for optoelectronics [43.1, 2]. Previous work has demonstrated that hydrogen passivation of dangling bonds within amorphous silicon (a-Si:H) leads to low-defect material, which has typically found application in solar cells. Amorphous Si, like all semiconductors, consists of nonlocalized (extended) band states separated by an energy gap, Eg . In amorphous semiconductors, this energy typically corresponds to an energy for breaking valence bonds. Disorder and defects in amorphous semiconductors create localized states within the energy gap [43.3]. A localized state is defined as one in which probability amplitude decreases exponentially with the distance from the center of localization for a sufficiently large distance. As shown in Fig. 43.1, there is a sharp separation of energy levels between nonlocalized and localized states, an idea first presented by Banyai [43.5], and later refined by Mott et al. [43.6] and Cohen et al. [43.3]. In particular, Cohen et al. suggested that disorder would lead to a distribution of electronic states within the gap,
43.1
Amorphous Silicon as a Photonic Material ...................... 1482
43.2
Amorphous Silicon for Photonic Devices ......................... 43.2.1 Waveguides ...................................... 43.2.2 Passive Photonic Devices .................... 43.2.3 Active Photonic Devices ...................... 43.3
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Summary.......................................... 1489
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Part F | 43
Amorphous silicon (a-Si) is an attractive highrefractive-index material for waveguide applications because of its flexible deposition conditions, which do not rely on the existence of crystalline silicon. However, a-Si can exhibit significant propagation losses due to unsaturated bonds in the silicon. Adding hydrogen will reduce those losses, but hydrogen itself can out-diffuse due to elevated processing temperatures. In this chapter, we describe the progress that has been made in the last 20 years with a-Si waveguides and related passive and active photonic devices. We review the basic mechanisms of loss in a-Si and solutions for reducing propagation losses to an acceptable level. We then discuss passive a-Si devices such as ring resonators and multimode interferometer (MMI) power splitters. In the last section, we focus on active devices that use a-Si-based waveguides.
DOS (cm –3 eV–1) Localized states
1022
Ecμ
Evμ 1021 Extended states
Nc(E)
Nv(E)
1020
Extended states
1019 1018 1017 –0.5
Valence band 0
Conduction band 0.5
1
1.5
2 2.5 Energy (eV)
Fig. 43.1 The valence band and conduction band DOS functions, Nv .E/ and Nc .E/, with the valence Ev and conduction band Ec mobility edge locations. Representative optical transitions between electronic states are shown with arrows. After [43.4]
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_43
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Fig. 43.2 Density-of-states distributions, DOS in cm3 eV1 , for a-Si samples. (Curve a) Glow discharge at 520 K; (curve b) glow discharge at 350 K; (curve c) evaporated. The solid lines indicate results obtained from field-effect experiments, and the arrow on each curve shows the position of the Fermi level. The edges of the graph represent the energy of the valance (Ev ) and the conduction band (Ec ), respectively. Extended states lie outside the graph. After [43.1] I
DOS (cm –3 eV–1) Tail states
Tail states
Gap states
1020 c
1019
Part F | 43.1
coupled with the presence of relatively sharp mobility edges. Several studies [43.7–9] attempted to differentiate between localized states caused by the different types of defects, including translational disorder, impurities, surfaces, interfaces, and dangling bonds. Spear et al. [43.8] performed experiments to probe states within the gap of a-Si using a field-effect configuration that displaced defect states with respect to the Fermi level using small energy steps. An externally applied electric field normal to the surface induced excess charge that modified the surface energy, leading to a measurable change in conductivity, from which energy levels within the gap could be determined. These data and other experimental evidence were used by Mort and Knights [43.1] to attribute deep states within the gap to dangling bonds in a-Si, the results of which are shown in Fig. 43.2. They were also the first to
b 1018 Ev 1017 1.6
Ec
a 1.2
0.8
0.4
0 Ec – E (eV)
show what is accepted knowledge today that defects in amorphous semiconductors behave much like those in crystalline solids in that (a) their creation depends on the method of preparation and the underlying chemical composition, and that (b) defects control several material properties.
43.1 Amorphous Silicon as a Photonic Material Complementary metal-oxide semiconductor (CMOS)compatible amorphous silicon (a-Si) has been employed extensively and successfully in low-cost solar cells [43.10] and in thin-film transistors [43.11]. Two achievements that catapulted a-Si to successful implementation in these application spaces were (a) low-cost and low-temperature Si-CMOS-compatible large-area fabrication processing and (b) hydrogen passivation of dangling bond defects to improve device performance. These advantages were leveraged in the early employment of a-Si for microphotonics [43.12]. Silicon microphotonics, in general, offers lightspeed signal propagation through optical interconnects (waveguides), which minimizes signal propagation delays that dominate over gate delays in the ever-shrinking ultra-large-scale integrated (ULSI) circuits. Channel waveguides consisting of polycrystalline silicon (poly-Si) clad with SiO2 offer excellent optical confinement and ease of fabrication, and are ideal for such interconnect applications. However, one major challenge in using the poly-Si material system for photonics was its high insertion loss of 77 dB=cm.
Just as carrier scattering and recombination contribute to losses in poly-Si electronic devices (e. g., thin-film transistors and solar cells), thereby leading to lower mobility and gain, photon scattering and absorption losses limit the performance of photonic devices such as waveguides. Scattering losses can occur due to scattering at rough surfaces/edges of the patterned waveguide device and/or at grain boundary defects in the bulk. Starting with low-temperature (< 560 ı C) growth yields an a-Si film with a smooth surface and with few nucleated grains. As depicted in Fig. 43.3, when this a-Si film is further crystallized to poly-Si during a highertemperature (600 ı C) anneal, the surfaces maintain their smoothness. The few nucleated sites already present in the a-Si film grow as grains, eventually presenting fewer grain boundaries than if the film had started out as a poly-Si film with several nucleated sites. This pathway for waveguide fabrication in which the film is deposited as a-Si and then annealed to poly-Si leads to fewer surface and bulk scattering sites compared to films deposited directly as poly-Si (625 ı C).
Amorphous Silicon in Microphotonics
a)
43.1 Amorphous Silicon as a Photonic Material
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b)
SiO2
SiO2 0.5 μm
0.5 μm
Fig. 43.3a,b Cross-sectional transmision electron microscope (TEM) images of 625 ı C poly-Si. (a) Smaller grain size of 0:18 m when film is deposited as poly-Si at 625 ı C; (b) larger grain size of 0:40 m when film is deposited as
amorphous Si at 560 ı C and is then recrystallized to poly-Si using a 600 ı C anneal. After [43.12]
1. First to 37 dB=cm by starting with a lowertemperature (560 ı C) a-Si film, which provides a smoother surface than as-deposited poly-Si, thus allowing the formation of only a few seed nuclei, reducing roughness-related surface and bulk scattering losses. 2. Second to 20 dB=cm by using a post-deposition anneal at 600 ı C of the starting a-Si, allowing the growth of only a few seed nuclei, thus creating a polycrystalline material with larger grains and hence fewer grain boundaries (GBs), reducing bulk GB scattering losses. 3. Third to 11 dB=cm after the poly-Si annealed at 600 ı C was subjected to an additional higher-temperature anneal of 1100 ı C, reducing absorption losses due to defects within grains. 4. Fourth to 9 dB=cm upon hydrogen passivation of the poly-Si grain boundary dangling bond defects in the high-temperature (1100 ı C)-treated poly-Si of (3.), further decreasing bulk absorption. In addition to annealing, other work has demonstrated that larger grain size can be obtained in the conversion of a-Si to poly-Si even at room temperature by exposure to either a hydrogen plasma [43.15] or a pulsed laser [43.16].
To reduce losses even more, hydrogenated amorphous silicon (a-Si:H) was introduced for photonics applications [43.17]. As in the poly-Si material, in aSi, hydrogen serves to passivate the dangling bonds that form midgap states which cause increased optical losses. Generally, waveguides have been used to determine the optical losses in a-Si:H; those results will be presented in the next section, since other loss mechanisms such as sidewall roughness scattering also influence optical losses. Harke et al. [43.18] report 0:5 dB=cm losses for 1550 nm light in large multimode waveguides that closely resemble bulk material, since the mode interacts only slightly with the waveguide boundaries. Active photonics based on a-Si have also been investigated. For light emission, the effect of erbium doping on the structural and optical properties of hydrogenated amorphous silicon (a-Si:H) was evaluated by Kim et al. [43.19]. Optical absorption and Raman spectra indicate that erbium doping introduces defect states, and that above a concentration of 0:27 at:%, it induces strong structural disorder. Their photoluminescence measurements show that erbium doping introduces nonradiative decay paths for carriers in a-Si:H, leading to a decrease in both the Er and intrinsic a-Si:H luminescence intensity when the Er concentration is increased to more than 0:04 at:%. The possible excitation mechanisms of Er in a-Si:H are shown in Fig. 43.4. The upper parts of the figure (with the states indicated by smaller dashes, since they reproduce the various localized or band-tail states) represent the relaxation within the a-Si:H material. The bottom shows the states within the Er dopants and how the relaxation in the a-Si:H is reflected in excitations within Er. Post-deposition trimming, photoinduced, thermooptic, and electro-optic effects in a-Si:H have been in-
Part F | 43.1
Bulk losses in passive waveguides are caused predominantly by absorption at dangling bond sites within the grain or at the grain boundary. Hydrogen passivation has been shown to minimize this absorption loss. Applying these ideas to microphotonics for the very first time, waveguide transmission losses in poly-Si waveguides measured at the telecommunication wavelength of 1550 nm were systematically and sequentially decreased from 77 dB=cm [43.12–14] to 9 dB=cm:
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Conduction band
a)
b)
a-Si:H
c)
a-Si:H
Defect state
Fig. 43.4a–c Possible excitation
a-Si:H
Er-related state
Valence band 4
I9/2 I11/2
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4
4
4
4
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Part F | 43.1
vestigated by several researchers and summarized by Della Corte [43.20]. As one example of such studies, the effects of thermal treatment on the propagation loss and refractive index change in photonic devices fabricated in a-Si:H were reported by Selvaraja et al. [43.21]. The authors used dehydrogenation that occurred due to annealing to tune and trim a-Si:H wavelength-selective devices up to 6:6 nm. Low-temperature deposition of a-Si:H is used to enhance the Pockels effect (the linear electro-optic effect), which can be obtained even when using a lowindex-contrast LiNbO3 substrate [43.22]. The a-Si:H provides tight waveguide mode confinement while allowing strong evanescent coupling to the underlying LiNbO3 substrate, which in turn enables efficient electro-optic modulation. a-Si:H material has also been leveraged to achieve faster operation in resonator-enhanced nonlinear devices, as it has a shorter carrier lifetime ( 10 ps) [43.23] owing to its relatively large density of defects (localized states) as recombination centers. Such nonlinear optical effects dominated by free-carrier nonlinearity in a-Si films were measured by Ikeda et al. [43.24] using the z-scan technique, which confirmed that the enhanced nonlinearity is mainly due to the presence of midgap localized states. Wang and Foster [43.25] demonstrated wavelength conversion through nonlinear parametric processes in hydrogenated amorphous silicon (a-Si:H) with maximum conversion
I13/2
mechanism of Er3C (states shown at the bottom by solid lines) in a-Si:H (states shown at the top by dashed lines): (a) Auger excitation of the higher excited states of Er3C by the transitions between band-tail states, (b) defect-related Auger excitation and (c) Auger-excitation of Er3C through the recombination of an electron–hole pair trapped at an Er-related state. After [43.19]
I15/2
efficiency of 13 dB at telecommunication data rates (10 GHz) using only 15 mW of pump peak power. Conversion bandwidths as large as 150 nm (20 THz) were measured in a continuous-wave regime at telecommunication wavelengths. The nonlinear refractive index of the material was determined by fourwave mixing (FWM) to be n2 D 7:43 1013 cm2 =W, approximately an order of magnitude larger than that of single-crystal silicon. Narayanan and Preble [43.26] concluded that the optical nonlinearities of a-Si:H waveguides measured by propagating ultra-short pulses through it yield a nonlinear coefficient which is at least five times that of crystalline silicon, a figure of merit which indicates that a-Si:H can be a promising alternative platform for enabling nonlinear silicon photonics. One must also consider the noninstantaneous nonlinear effects that have been shown by Wathen et al. [43.27], who demonstrate from a series of wellplanned experiments that the a-Si:H waveguide demonstrates essentially zero instantaneous nonlinear absorption, but it does exhibit appreciable noninstantaneous nonlinear absorption and refraction. The amplitude transient scales with applied pump power leading to a third-order nonlinearity rather than a combination of instantaneous two-photon absorption followed by free-carrier absorption. The noninstantaneous nonlinear refraction has the same sign as the instantaneous Kerr refraction, which cannot be attributed to the dispersive effect of free carriers.
Amorphous Silicon in Microphotonics
43.2 Amorphous Silicon for Photonic Devices
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43.2 Amorphous Silicon for Photonic Devices 43.2.1 Waveguides
Propagation loss (dB/cm) TE TM
60 40 20 14 12
Forming gas annealing
10 8 6 4 2 0 RT
200
300
400 500 600 700 Annealing temperature (°C)
Fig. 43.5 The transverse electric (TE) and transverse mag-
netic (TM) propagation losses in 220 nm 500 nm a-Si:H wire waveguides (100 W=400 ı C deposition) as a function of subsequent forming gas anneal at 30 min for each temperature. The initial propagation losses (square symbols), as well as those after the anneal, carried out prior to upper cladding SiO2 deposition (triangles), are also shown. After [43.33]
Part F | 43.2
Optical losses in Si waveguides are typically due to light scattering at rough interfaces, which have been reduced due to the advancement of improved lithography and etching. Si waveguides now show losses well below 1 dB=cm. In a-Si:H, material losses are expected to dominate due to the high concentration of midgap states, as mentioned above. In addition, the stability of the Si–H bond may be compromised during thermal treatment, leading to increased H loss and thus increased optical loss [43.28]. Plasma-enhanced chemical vapor deposition (PECVD) has been used for the deposition of a-Si, given the high hydrogen content that can reduce dangling bonds to levels around 1015 cm3 [43.29]. Lowering of the PECVD deposition power during the deposition of a-Si yields transmission losses of 6:5 dB=cm for a TE single-mode amorphous Si channel waveguide at 1550 nm [43.30]. The kinetic energy used in the dissociation of the SiH4 precursor is reduced, which increases the H content in the a-Si films, passivating the dangling bond defects responsible for absorption [43.12], and thus decreasing bulk loss. In the last decade, losses have been further reduced, with Fedeli et al. reporting 4 dB=cm [43.31], Selvaraja et al. reporting 3:46 dB=cm [43.32], and Zhu et al. reporting 3:2 dB=cm [43.33] for singlemode channel waveguides at 1550 nm. Lower losses of 1:2 dB=cm have been reported for single-mode waveguides, although the cut-back measurement technique used to determine the loss is not reliable for such low losses [43.34]. Lower losses have also been reported for ridge waveguides (1:34 dB=cm at 1550 nm) [43.32] or 800 nm-wide waveguides (< 1 dB=cm at 1300 nm) [43.31]. Much concern has been given to the stability of a-Si:H, because mobile H can out-diffuse and increase the optical loss of the material, thereby decreasing device reliability. Selvaraja et al. tracked the propagation losses in single-mode waveguides for 50 days and found little change in the waveguide loss [43.32]. However, the measurements were performed at room temperature (RT), and no thermal treatment was used in the long-term evaluation. Zhu et al. conducted an extensive study on the thermal stability and the thermal impact on optical loss in a-Si:H waveguides [43.33]. They found that, in agreement with Selvaraja et al., the loss does not change when the samples are stored at room temperature. The waveguides with initial losses of about 4 dB=cm at 1550 nm were then thermally treated at different temperatures for 30 min. Their re-
sults are shown in Fig. 43.5. Below 200 ı C, no change in waveguide loss is observed. Above 200 ı C, however, the loss increases, first slowly, and then very rapidly at temperatures above 350 ı C, reaching values greater than 40 dB=cm at 450 ı C. The authors conclude that the initial loss at exposure to temperatures below 350 ı C had already weakened the Si–H bonds, allowing H to out-diffuse. Even small amounts of outdiffused H, not measurable by other methods [43.35], have been found to cause significant optical losses in waveguides. Since back-end processing temperatures exceed the critical temperature of 200 ı C where optical loss increases, a-Si:H devices have limited application unless H out-diffusion can be prevented. To achieve this goal, Sun et al. developed a process to clad the a-Si:H waveguides with a silicon nitride diffusion barrier [43.36]. A well-passivated a-Si waveguide core and a low-loss PECVD silicon nitride intercladding layer coupled with a top silicon dioxide (SiO2 ) cladding, as shown in Fig. 43.6, was developed to reduce H out-diffusion. The intercladding also works as a hydrogen diffusion bar-
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Optical and Photonic Glass Applications
SiO2
a-Si:H
PECVD SiN
SiO2
Silicon substrate Waveguide cross section
Fig. 43.6 Schematic of the waveguide cross section of an
a-Si:H waveguide with a nitride intercladding layer. The plasma-treated low-loss nitride intercladding serves two functions: it decreases the sidewall refractive index contrast between the a-Si core and the SiO2 cladding, thereby reducing the sidewall roughness scattering loss coefficient, while also serving as a barrier that traps hydrogen within the a-Si core. After [43.36]
Part F | 43.2
rier to preserve hydrogen passivation. While the nitride layer is thin, so there is negligible impact on scattering loss, the nitride layer introduces a trade-off, since N–H bonds, existing in the nitride layer due to the high H content, absorb at 1510 nm and contribute to absorption loss. An in situ nitrogen/argon (N2 =Ar) plasma treatment process at 300 ı C reduces H in the as-deposited nitride film, successfully removing 80% of N–H bonds in the thin nitride intercladding layer, yielding a net reduction in the transmission loss of a-Si channel waveguides with a nitride intercladding. This nitride layer potentially allows a-Si waveguides to maintain their low-loss property at temperatures higher than 400 ı C, when hydrogen can typically out-diffuse. A transmission loss of 2:7˙0:4 dB=cm for TE mode at 1560 nm in a single-mode a-Si channel waveguide was obtained for the silicon nitride-clad waveguides. For 1300 nm light, the additional plasma treatment may not be necessary, since the N–H absorption band does not extend into this wavelength range.
43.2.2 Passive Photonic Devices The development of low-loss a-Si:H waveguides enables the fabrication of other passive devices based on a-Si:H. Since a-Si uses the same processing equipment as Si, the lithography can be seamlessly transferred to a-Si:H. Because passive photonic devices depend mainly on lithographic resolution, they can be copied directly from Si photonics. The main factor determining the quality of those passive devices is waveguide loss. Losses at or below 3 dB enable photonic interconnects without the use of crystalline Si.
Several publications evaluate the performance and fabrication tolerances of racetrack or ring resonators, which can be used as add/drop filters [43.32, 36–38]. Figure 43.7 shows an example of an a-Si:H racetrack resonator. All authors report quality factors Q of lowto mid-104 , comparable to crystalline Si ring resonators with similar lithographic resolution. Lipka et al. explored a range of passive a-Si devices to build an a-Si-based photonics platform [43.37]. They demonstrated fiber-to-waveguide couplers with 3:8 dB loss and 3 dB bandwidth of 60 nm. In addition, a polarization rotator/splitter was demonstrated with a polarization extinction ratio of > 10 dB and an insertion loss of 1 dB. Optical add/drop multiplexers (OADMs) were demonstrated using thermal tuning [43.37]. For this purpose, titanium microheaters were integrated with the individual microrings. Individual heater control allows for precise positioning of the ring resonance. An example is shown in Fig. 43.8. Based on these devices, 4 4 reconfigurable photonic routers based on microring resonator switches were demonstrated, using the a-Si:H platform. If H outdiffusion can be prevented, these results show the potential to realize a low-cost, densely integrated 3-D stacked photonic system with back-end-of-line processes. Zhu and Lo [43.39] recently explored the use of a-Si:H for vertically stacked multilayer photonics. By adding an AlN waveguide layer above the a-Si:H waveguide layer, high-performance multimode interference (MMI) power splitters, ring resonators, arrayed waveguide gratings, and other passive photonic devices were demonstrated. Figure 43.9 shows four-stage cascaded Normalized transmission (dB) 0
–5
–10
–15 5 μm
–20 1500 1510 1520 1530 1540 1550 1560 1570 Wavelength (nm)
Fig. 43.7 Normalized transmission spectrum of an amor-
phous silicon racetrack ring resonator and scanning electron microscope (SEM) image (inset) of the structure. After [43.32]
Amorphous Silicon in Microphotonics
43.2 Amorphous Silicon for Photonic Devices
1487
length with ring radius was observed, indicating good fabrication tolerances.
a)
43.2.3 Active Photonic Devices
100 μm
b) Normalized transmission (dB) 0 –5 –10 –15 –20 –25 1562
1564
1566 1568 Wavelength (nm)
Fig. 43.8a,b Wavelength-trimmed eight-channel multiplexer. (a) Micrograph, (b) through- and drop-port spectra. The through-port response is shown as a solid line, while the drop-port responses are shown as dashed lines. Reprinted with permission from [43.37]
1 2 MMI splitters with very low excess losses of less than 0:1 dB, comparable to MMIs made from crystalline Si. The authors point out that these MMIs have relatively large fabrication tolerances. The same platform was used to fabricate multiple-channel ring filters, as shown in Fig. 43.10. Nine add/drop filters with increasing radii from 2.5 to 2:564 mm were cascaded to address different wavelengths. A near-linear increase in the resonance wavea)
Out-5
Out-4 Out-3 In
b)
LMMI
WMMI
Out-2 Out-1 1 μm
Fig. 43.9 (a) Layout of a four-stage cascaded 1 2 MMI splitter, (b) SEM image of an a-Si:H MMI power splitter. © 2016 IEEE. Reprinted with permission from [43.39]
Part F | 43.2
1560
Active a-Si:H-based devices would enable a wide variety of photonic systems without the need for crystalline Si in back-end-of-line processes. Due to the limited temperature exposure, doping cannot be used to fabricate traditional devices that are based on different dopants for carrier injection or extraction. When doping is not available, only a limited number of effects can be used to actively influence photons in a-Si:H waveguides or passive devices. Photoinduced effects describe the effect of light on the device properties. Photoinduced absorption can be achieved by using light that is absorbed in the a-Si:H devices and generates carriers that change the optical properties of the material. Two parameters are of specific interest: the lifetime of the generated carriers and the free-carrier absorption. Fauchet et al. [43.23] reported that the photogenerated carriers recombined nonradiatively in as short a time as 1 ps, indicating that GHz modulation may be possible. Furthermore, the free-carrier absorption was found to be significantly larger than in Si [43.40]. Based on these parameters, Narayanan et al. demonstrated a-Si:H-based all-optical modulation using a-Si:H. Free carriers generated by a pump wavelength of 405 nm were used to modulate light from a continuous-wave tunable laser diode at D 1550 nm. The time response was limited by surface recombination at the waveguide sidewalls to 400 ps, as shown in Fig. 43.11. From their experiments, the authors concluded that the freecarrier absorption in a-Si:H is at least an order of magnitude higher than in crystalline silicon ( D 1:45 1017 cm2 ). Similar results were reported for an a-Si:H ridge waveguide [43.41]. The carriers were excited by a pump laser at 532 nm wavelength. Figure 43.12
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a)
1 2 3 4 5 6 7 8 9
Fig. 43.10 (a) Nine-cascaded add/-
b)
drop ring resonators fabricated on the a-Si:H layer; the radius ranges from 2.5 to 2:564 m in steps of 0:008 m, (b) SEM image of one of the add/drop WRRs, (c) the measured spectra from the nine output waveguides. © 2016 IEEE. Reprinted with permission from [43.39]
R
c) Transmission (dB) 39th resonance –5
2
4 –10
5
40th resonance 6
1 9 8
3
5
7
41th resonance 9
2 1
4 3
8
7 6
–15 –20 –25
Part F | 43.2
–30 1540
1550
1560
1570
1580
1590
Normalized probe transmission ∆t ≈ 25 ps 1.0
1600 1610 Wavelength (nm)
Transmitted optical intensity (5 mV/div)
0.9 Nonradiative surface recombination of carriers 0.8 Timebase (20 ns/div)
0.7
Fig. 43.12 Photoinduced absorption effect in a 3 m-thick, 0.6 0.5 0.0
Relaxation of carriers from extended states 0.5
1.0
1.5
2.0 Time (ns)
1 mm-long a-Si:H rib waveguide. The electrical signal at the photodiode output is shown in the figure. The pump pulse was a high-energy 532 nm wavelength, 20 ns-long coherent light pulse. The measured rise and fall times (tr , tf ) are 20 ns and the modulation depth (M) is 90%. After [43.41]
Fig. 43.11 All-optical modulation in a-Si:H using a pump-
probe scheme. The carriers undergo rapid thermalization before undergoing nonradiative recombination. The gray line shows an exponential fit with a 400 ps time constant relating to the surface recombination at the sidewalls. After [43.40]
shows the optical response of a 20 ns-long pulse. The modulation depth (M) is 90%, suitable for many applications.
A second approach to changing the optical properties of a-Si:H is to use the temperature dependence of the refractive index. This effect is described by the thermo-optic (TO) coefficient. The local heating of a-Si:H microring resonators, utilizing the thermooptic effect, was applied to generate amplitude-shiftkeying optical signals [43.26]. To achieve localized heating, nickel-chromium heaters were positioned on top of the ring resonators, separated by 600 nm oxide.
Amorphous Silicon in Microphotonics
Applied signal (V)
Normalized transmission 0 mW 2 mW 8 mW 18 mW
1.0 0.8
43.3 Summary
1489
Optical output (arb. u.)
15 0
0.6 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 Time (s)
0.4 0.2 0.0 1594
1595
1596
1597 1598 Wavelength (nm)
Fig. 43.13 Thermal tuning of resonant wavelengths is
achieved by applying heat to the individual rings. After [43.26]
was irreversible. The propagation losses varied by only 0:4 dB=cm up to an annealing temperature of 400 ı C. The third method to actively change the optical properties of a-Si:H is by using an electro-optic effect. Here, an electric bias produces an electric field that can alter the band transitions or cause carrier injection or depletion. Electro-optic absorption has been demonstrated in multilayer waveguides consisting of a-Si:H=a-SiCx Ny layers on a p-type Si wafer for 1:55 m light [43.42]. By applying a bias voltage of up to 35 V, a modulation depth of up to 27% was observed. Figure 43.14 shows the applied electrical bias and the responding optical signal. Improved performance has been demonstrated by altering the layer stack [43.43]. The modulation depth was improved to above 3 dB at 35 V bias. Due to the relatively slow trapping and releasing of carriers in a-Si:H, the modulation frequency was limited to below 1 MHz. A more detailed review of active photonic devices in a-Si:H can be found in [43.20].
43.3 Summary a-Si:H has been shown to be an excellent material for photonic applications with light around 1550 nm. Passive photonic devices using a-Si:H, such as waveguides, resonators, or splitters, show similar performance as those made from crystalline Si. However, since H plays a major role in passivating defects in the amorphous Si, out-diffusion of H at elevated temperatures quickly degrades device performance. Temperatures above 200 ı C cause out-diffusion of H, and
therefore this material cannot be used in back-end-ofline processes without further temperature restrictions or measures to prevent H out-diffusion. Active photonic devices based on a-Si:H are limited due to the absence of activated dopants in the amorphous matrix. Several methods for overcoming this limitation have been suggested, but these active devices cannot reach the performance level of devices based on crystalline Si.
Part F | 43.3
The resonance shift was measured to be 0:14 nm=mW. Figure 43.13 shows the resonance shift for different electrical power. An electrical modulation frequency of 100 Hz was used, since the thermal response is inherently slow. As mentioned above, the stability of a-Si:H is limited when heated. Higher temperatures cause out-diffusion of H and permanently change the refractive index. When used for ring resonators, trimming of the resonance wavelength is possible. Selvaraja et al. [43.21] utilized the resonant frequency response of the ring resonators to temperature to demonstrate trimming at higher temperatures and tuning when using the TO effect at lower temperatures. They determined a critical temperature of 200 ı C below which the resonance shift was reversible, while above this temperature the shift
Fig. 43.14 Output light power and applied voltage for a six-bilayer 1 cm-long waveguide. The modulating signal has Vmin D 0 V, Vmax D 15 V, duty-cycle D 50%, frequency D 10 Hz. After [43.42]
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Optical and Photonic Glass Applications
References 43.1
43.2
43.3
43.4
43.5
43.6 43.7
Part F | 43
43.8
43.9 43.10
43.11
43.12
43.13
43.14
43.15
43.16
43.17
J. Mort, J. Knights: Localization and electronic properties in amorphous semiconductors, Nature 290, 659–663 (1981) F. Gaspari: Optoelectronic properties of amorphous silicon the role of hydrogen: From experiment to modeling. In: Optoelectronics – Materials and Techniques, ed. by P. Pradeep (InTech, London 2011) M.H. Cohen, H. Fritzsche, S.R. Ovshinsky: Simple band model for amorphous semiconducting alloys, Phys. Rev. Lett. 22, 1065 (1969) F. Orapunt, S.K. O’Leary: Optical transitions and the mobility edge in amorphous semiconductors: A joint density of states analysis, J. Appl. Phys. 104, 073513 (2008) L. Banyai: On the theory of electric conduction in amorphous semiconductors. In: Proc. 7th Int. Conf. Phys. Semicond., Paris (1964) p. 417 N.F. Mott: Electrons in disordered structures, Adv. Phys. 16(61), 49–144 (1967) E.A. Davis, N.F. Mott: Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors, Philos. Mag. 22(179), 0903–0922 (1970), https://doi.org/10.1080/14786437008221061 A. Madan, P.G. Le Comber, W.E. Spear: Investigation of the density of localized states in a-Si using the field effect technique, J. Non-Cryst. Solids 20, 239– 257 (1976) N. Mott: The mobility edge since 1967, J. Phys. C Solid State Phys. 20, 3075–3102 (1987) M. Green: Thin-film solar cells: Review of materials, technologies and commercial status, J. Mater. Sci. Mat. Electron. 18(1), 15–19 (2007) Y. Kuo: Thin film transistor technology – Past, present, and future, Electrochem. Soc. Interface 22(1), 55–61 (2013) A.M. Agarwal, L. Liao, J.S. Foresi, M.R. Black, X. Duan, L.C. Kimerling: Low-loss polycrystalline silicon waveguides for silicon photonics, J. Appl. Phys. 80(11), 6120–6123 (1996) L. Liao: Low Loss Polysilicon Waveguides for Silicon Photonics, Ph.D. Thesis (Massachusetts Institute of Technology, Cambridge 1997) L. Liao, D.R. Lim, A.M. Agarwal, X. Duan, K.K. Lee, L.C. Kimerling: Optical transmission losses in polycrystalline silicon strip waveguides: Effects of waveguide dimensions, thermal treatment, hydrogen passivation, and wavelength, J. Electron. Mater. 29(12), 1380–1386 (2000) K. Pangal, J.C. Sturm, S. Wagner, T.H. Büyüklimanli: Hydrogen plasma enhanced crystallization of hydrogenated amorphous silicon films, J. Appl. Phys. 85(3), 1900 (1999) S.J. Fonash, G. Liu: Low temperature crystallization and patterning of amorphous silicon films on electrically insulating substrates, US Patent 527585 (1994) W.B. Jackson: Hydrogen in amorphous silicon, Curr. Opin. Solid State Mater. Sci. 1(4), 562–566 (1996)
43.18
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43.23
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43.29 43.30
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A. Harke, M. Krause, J. Mueller: Low-loss single mode amorphous silicon waveguides, Electron. Lett. 41(25), 1377–1379 (2005) M.-J. Kim, G.K. Mebratu, J.-Y. Sung, J.H. Shin: Erdoped hydrogenated amorphous silicon: Structural and optical properties, J. Non-Cryst. Solids 315(3), 312–320 (2003) F.G. Della Corte, S. Rao: Use of amorphous silicon for active photonic devices, IEEE Trans. Electron Dev. 60(5), 1495–1505 (2013) S.K. Selvaraja, W. Bogaerts, D. Van Thourhout, M. Schaekers: Thermal trimming and tuning of hydrogenated amorphous silicon nanophotonic devices, Appl. Phys. Lett. 97(7), 071120-1–1071120-3 (2010) L. Cao, A. Aboketaf, Z. Wang, S. Preble: Hybrid amorphous silicon (a-Si:H)–LiNbO3 electro-optic modulator, Opt. Commun. 330, 40–44 (2014) P.M. Fauchet, D. Hulin, R. Vanderhaghen, A. Mourchid, W.L. Nighan Jr.: The properties of free carriers in amorphous silicon, J. Non-Cryst. Solids 141, 76–87 (1992) K. Ikeda, Y. Shen, Y. Fainman: Enhanced optical nonlinearity in amorphous silicon and its application to waveguide devices, Opt. Express 15(26), 17761–17771 (2007) K.-Y. Wang, A.C. Foster: Ultralow power continuous-wave frequency conversion in hydrogenated amorphous silicon waveguides, Opt. Lett. 37(8), 1331 (2012) K. Narayanan, S.F. Preble: Optical nonlinearities in hydrogenated amorphous silicon waveguides, Opt. Express 18(9), 8998–9005 (2010) J.J. Wathen, V.R. Pagán, R.J. Suess, K.-Y. Wang, A.C. Foster, T.E. Murphy: Non-instantaneous optical nonlinearity of an a-Si:H nanowire waveguide, Opt. Express 22(19), 22730–22742 (2014) P.K. Lim, W.K. Tam, L.F. Yeung, F.M. Lam: Effect of hydrogen on dangling bond in a-Si thin film, J. Phys. Conf. Ser. 61, 708–712 (2007) K. Tanaka, E. Maruyama, T. Shimada, H. Okamoto: Amorphous Silicon (Wiley, Chichester 1999) D.K. Sparacin, R. Sun, A.M. Agarwal, M.A. Beals, J. Michel, L.C. Kimerling, T.J. Conway, A.T. Pomerene, D.N. Carothers, M.J. Grove, D.M. Gill, M.S. Rasras, S.S. Patel, A.E. White: Low-loss amorphous silicon channel waveguides for integrated photonics. In: 3rd IEEE Int. Conf. Group IV Photonics (2006), https://doi.org/10.1109/ GROUP4.2006.1708231 J.M. Fedeli, L. Di Cioccio, D. Marris-Morini, L. Vivien, R. Orobtchouk, P. Rojo-Romeo, C. Seassal, F. Mandorlo: Development of silicon photonics devices using microelectronic tools for the integration on top of a CMOS wafer, Adv. Opt. Technol. 2008, 412518 (2008), https://doi.org/10.1155/2008/412518 S.K. Selvaraja, E. Sleeckx, M. Schaekers, W. Bogaerts, D. Van Thourhout, P. Dumon, R. Baets: Lowloss amorphous silicon-on-insulator technology
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for photonic integrated circuitry, Opt. Commun. 282, 1767–1770 (2009) S. Zhu, G.Q. Lo, D.L. Kwong: Low-loss amorphous silicon wire waveguide for integrated photonics: Effect of fabrication process and the thermal stability, Opt. Express 18(24), 25283 (2010) K. Furuya, K. Nakanishi, R. Takei, E. Omoda, M. Suzuki, M. Okano, T. Kamei, M. Mori, Y. Sakakibara: Nanometer-scale thickness control of amorphous silicon using isotropic wet-etching and low loss wire waveguide fabrication with the etched material, Appl. Phys. Lett. 100, 251108 (2012) P.K. Lim, W.K. Tam: Local vibrational modes and the optical absorption tail of amorphous silicon, Int. J. Mod. Phys. B 20(25–27), 4261–4266 (2006) R. Sun, K. McComber, J. Cheng, D.K. Sparacin, M. Beals, J. Michel, L.C. Kimerling: Transparent amorphous silicon channel waveguides with silicon nitride intercladding layer, Appl. Phys. Lett. 94, 141108 (2009) T. Lipka, L. Moldenhauer, J. Müller, H.K. Trieu: Photonic integrated circuit components based on amorphous silicon-on-insulator technology, Photonics Res. 4(3), 126 (2016)
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43.41
43.42
43.43
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T. Lipka, J. Müller, H.K. Trieu: Systematic nonuniformity analysis of amorphous silicon-on-insulator photonic microring resonators, J. Lightw. Technol. 34(13), 3163 (2016) S. Zhu, G.Q. Lo: Vertically stacked multilayer photonics on bulk silicon toward three-dimensional integration, J. Lightw. Technol. 34, 386 (2016) K. Narayanan, A.W. Elshaari, S.F. Preble: Broadband all-optical modulation in hydrogenatedamorphous silicon waveguides, Opt. Express 18(10), 9809–9814 (2010) S. Rao, C. D’Addio, F.G. Della Corte: All-optical modulation in a CMOS-compatible amorphous silicon-based device, J. Eur. Opt. Soc. Rapid Publ. 7, 12023-1–12023-7 (2012) F.G. Della Corte, S. Rao, M.A. Nigro, F. Suriano, C. Summonte: Electro-optically induced absorption in a-Si:H/a-SiCN waveguiding multistacks, Opt. Express 16(10), 7540–7550 (2008) S. Rao, F.G. Della Corte, C. Summonte, F. Suriano: Electrooptical modulating device based on a CMOScompatible ’-Si:H/’-SiCN multistack waveguide, IEEE J. Sel. Top. Quantum Electron. 16(1), 173–178 (2010)
Anu Agarwal received her PhD in Electrical Engineering from Boston University. Currently, as a Principal Research Scientist, she develops integrated Si-CMOS compatible linear and non-linear materials for photonic devices, especially in the midIR regime, for hyperspectral imaging and chem-bio sensing, because most chemical and biological toxins have their fingerprints in this range.
Juergen Michel Materials Research Laboratory Massachusetts Institute of Technology Cambridge, MA, USA [email protected]
Jurgen Michel received his PhD from the University of Paderborn in 1988. He worked at AT&T Bell Laboratories prior to joining the Massachusetts Institute of Technology. As a Senior Research Scientist, he leads research projects in siliconbased photonic materials and devices as well as advanced solar cell designs.
Part F | 43
Anuradha M. Agarwal Materials Research Laboratory Massachusetts Institute of Technology Cambridge, MA, USA [email protected]
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44. Phase-Change Memory and Optical Data Storage
Xiang Shen, Yimin Chen
, Guoxiang Wang, Yegang Lv
Over the past decade, the continuous size scaling of complementary metal-oxide-semiconductor (CMOS) technology, along with its cost reduction, has driven the development of nonvolatile memory (NVM) to meet the growing demand for high-density digital information storage. The extent to which NVM has pervaded our day-to-day lives is truly remarkable. From the music on our MP3 players, to the photos on digital cameras, the stored email and text messages on smartphones, the documents we carry on our USB thumb drives, and the program codes that enable everything from our portable electronics to our cars, the NVM known as flash memory is ubiquitous. However, flash memory technology is inevitably approaching its fundamental limits. State-of-the-art NAND devices are restricted to 12 nm node [44.1, 2] in size, where the node number refers to the minimum channel width of the CMOS. The physical scaling of flash memory depends mainly on state-of-the-art photolithography techniques [44.3, 4], which are confined by the diffraction limit. Second, the scaling margin has also been shrinking,
44.1
Conventional Ge-Sb-Te Phase-Change Films.......................... 1495
44.2
Phase-Change Behaviors of Doped Ge2 Sb2 Te5 Films .................. 1498
44.3
Doped Sb-Te Films for Phase-Change Memory Applications ........................ 1500
44.4
Nanocomposite Films for Phase-Change Memory Applications ..................................... 1506
44.5
Crystallization Kinetics Studied by Ultrafast Calorimetry for Phase-Change Materials .............. 1510
44.6
Phase-Change Materials for Applications in Integrated Photonic Memory ............................. 1513
44.7
Summary.......................................... 1514
References................................................... 1515
since the tunnel oxide layer inside flash memory needs to be thicker than 8 nm in order to eliminate possible electron leakage [44.5]. Moreover, the coupling ratio between the floating gate and the control gate must be maintained at a value greater than 0.6 in order to control the conductive channel and prevent gate electron injection [44.6]. This can be achieved by wrapping the control gate around the floating gate to geometrically increase the gate coupling ratio. Obviously, there is not adequate space to contain such a wrapping structure as the downscaling process continues. Furthermore, the crosstalk effect between two adjacent cells will be strongly aggravated with future scaling; the electrons stored in one cell will have higher tunneling probability, which will adversely affect the performance of scaled devices [44.1]. To overcome the scaling limits of flash memory, more advanced storage technologies are being explored, giving rise to a series of new paradigms, including ferroelectric random-access memory (FRAM) [44.7], magnetic random-access memory (MRAM) [44.8],
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_44
Part F | 44
Phase-change memory is regarded as the most appealing of the nonvolatile memory technologies, with attractive properties including scalability, bit alterability, and fast write/erase and read performance. Over the past decade, the technology has experienced rapid growth. Well-known semiconductor manufacturers such as IBM, Infineon, Samsung, and Macronix have spared no effort in the push to commercialize this technology. At the same time, many novel phase-change materials have been developed, such as typical Ge-Sb-Te alloys, Zn-Sb-Te alloys, and ZnO-Sb2 Te3 nanocomposite. New techniques such as ultrafast calorimetry are continuously emerging to better understand the crystallization kinetics of supercooled liquids for phase-change materials. In addition, phasechange materials are ideal functional materials for use in integrated photonic memory, which provides a new paradigm in all-photonic memory.
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Part F | 44
phase-change random-access memory (PRAM) [44.9], and resistive random-access memory (RRAM) [44.10]. Among these, PRAM is arguably the most appealing. PRAM technology has the potential to provide inexpensive, high-speed, high-density, high-volume nonvolatile storage on an unprecedented scale. Working prototypes of PRAM chips have been tested by IBM, Infineon, Samsung, Macronix, and others. PRAM is regarded as a significant advance, and is likely to become one of the mainstream formats for semiconductor memory. PRAM is based on the repeated switching of a phase-change material (PCM) between the amorphous and the crystalline states, inducing a large change in resistance. The amorphous, high-resistance state represents a binary 0, while the crystalline, low-resistance state represents a 1. Information is then stored in the phase of the material and is read by measuring the resistance of the PRAM cell. Programming a PRAM device involves the application of electric current, leading to temperature changes that either SET or RESET the cell, as shown schematically in Fig. 44.1. To SET a PCM cell to its low-resistance state, an electrical pulse is applied to heat the cell above the crystallization temperature Tc (but below the melting temperature Tm ) of the phase-change material. The pulse is sustained for a period of sufficient length for the cell to transition to the crystalline state. On the other hand, to RESET the cell to its high-resistance amorphous state, a much larger electrical current is applied in order to increase the temperature above Tm . After the material in the cell has melted, the pulse is abruptly cut off, causing the melted material to quench into the amorphous state. To READ the current state of a cell, a small current that does not perturb the cell state is applied to measure the resistance. PCM is also the functional material widely used in rewritable optical media, such as CD-RW and DVD-
9ROWDJH 5(6(7SXOVH TP
TF 6(7 SXOVH 5($' 7LPH
Fig. 44.1 Currents and timings (not to scale) for SET, RESET, and READ operations on a PCM cell. After [44.11]
RW. In those instances, the material’s optical properties are manipulated rather than its electrical resistivity, as its refractive index also changes with the state of the material. Generally speaking, several characteristics are important for the operation of the PCM, including rapid switching between the amorphous and crystalline phases, long data retention at high temperature, and a large difference in electrical resistivity or optical reflectivity between the amorphous and crystalline phases. However, trade-offs are necessary to balance each characteristic of PCM—for example, the contradictory relation between rapid phase change and longterm data retention. Long-term retention of data usually requires a material that is very stable in the amorphous state at high temperatures, which in turn implies that fast crystallization speed is not available. Furthermore, if the reliability of the PRAM cell is considered, then a small change in thickness during the amorphousto-crystalline phase transition is needed to avoid the interface separation between the phase-change layer and the electrode. Since the thinner the phase-change layer, the smaller the change in thickness, a thinner phase-change layer is obviously of benefit for cell reliability. However, the thinner phase-change layer leads to a smaller difference in electrical resistivity or optical reflectivity, which will directly degrade the ON/OFF ratio for PRAM. Tracing the development of PCM, it should be mentioned that in 1968, S.R. Ovshinsky of Energy Conversion Devices demonstrated very short reversible electrical switching phenomena in Te81 Ge15 Sb2 S2 chalcogenide glasses as a potential memory technology [44.12]. Although material quality and power consumption issues prevented commercialization of the technology at that time, this work opened a new chapter in phase-change technology. The early phase-change materials used in optical storage comprised simple alloys based primarily on composition in the vicinity of the tellurium-germanium eutectic. In the early 1990s, Ge-Sb-Te alloys were reported as a second generation of high-speed phase-change materials [44.13]. These alloys have a stoichiometric composition along the GeTe-Sb2 Te3 pseudo-binary line of the phase diagram. As indicated in Fig. 44.2, moving down this pseudo-line from Sb2 Te3 to GeTe, the melting point and glass transition temperature of the material increases, crystallization speed decreases, and data retention increases [44.13]. Therefore, when a rapid phase change is required, a material with fast crystallization speed such as Sb2 Te3 will be selected. However, because of its low activation energy, this material is not stable. On the other hand, a material such as GeTe with good amorphous stability has slow crystallization speed because of
Phase-Change Memory and Optical Data Storage
6E
6E7H
7H
*H6E7H *H6E7H 0HOWLQJ *H6E7H SRLQWLQFUHDVH
*H7H
*H
Fig. 44.2 Phase diagram of the Ge-Sb-Te ternary alloy
system. After [44.13]
its high activation energy. Therefore, to balance thermal stability and crystallization speed, most important materials that have been explored, i. e., Ge2 Sb2 Te5 (GST), GeSb2 Te4 , and GeSb4 Te7 , lie along the pseudo-line between Sb2 Te3 and GeTe. These alloys are now also
44.1 Conventional Ge-Sb-Te Phase-Change Films
1495
widely used in phase-change memory as well as for scientific research. In this chapter, we will first discuss the structure and crystallization behavior of ternary Ge-Sb-Te alloys, after which doped GST will be highlighted for the purpose of obtaining PRAM with lower power consumption and better data retention. We will then present the thermal and phase-change behavior for the novel doped Sb-Te alloys and some nanocomposites. The chapter also focuses on the recent hotspot in crystallization kinetics for GST materials by ultrafast calorimetry, which extends the heating rate to more than 4 104 K s1 and can provide more information on crystal growth in supercooled liquids. In addition, in recent years, phasechange materials have also been used in integrated photonic memory. In this case, both reading and writing of the memory can be performed with ultrashort optical pulses, because the guided light transfers the amorphous and crystallization phases of GST via its evanescent field interaction. This provides a pathway towards a new paradigm in all-photonic memory and nonconventional computing.
44.1 Conventional Ge-Sb-Te Phase-Change Films
9DFDQF\ *H6E 7H c
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Fig. 44.3 Schematic image of the crystal structure of the rock-salt-like phase of, e. g., GST or GeSb2 Te4 . Te atoms occupy one sublattice of the crystal, and Ge atoms, Sb atoms, and vacancies randomly occupy the second sublattice. The typical nearest-neighbor spacing is close to 3 Å. After [44.14]
PRAM works in this crystalline state. As shown in the figure, the Te atoms occupy one lattice site, and Ge and Sb atoms randomly occupy the second lattice site of an atomic arrangement that closely resembles the rocksalt structure. There are a few noteworthy differences from an ideal rock-salt structure. In a material such as GeSb2 Te4 or GST, there are a considerable number of vacancies, as schematically depicted in Fig. 44.3. For GeSb2 Te4 , for example, there are 25% vacancies on the Ge/Sb site, whereas the Te site is fully occupied. The commonly studied phase-change alloys GeSb2 Te4 and GST are found on the pseudo-binary GeTe-Sb2 Te3 line, which is commonly believed to locate the most suitable Ge-Sb-Te-based compounds. The as-deposited films, which are deposited by magnetron sputtering, are amorphous, and the crystallization temperature increases along the GeSb2 Te4 -Ge2 Sb2 Te4 line, indicating higher overall stability with increasing a Ge content. The crystallization temperature of Ge2 SbTe4 is similar to that of GST but higher than that of GeSb2 Te4 . According to the resistance–temperature curve, phase-change materials upon amorphization exhibit a change in resistivity of several orders of magnitude. While the resistivity is low in the crystalline state, the amorphous system is highly resistive, as shown in Fig. 44.4. The metastable crystalline phase of all the novel alloys shows the characteristic peaks of the rock-
Part F | 44.1
Crystalline Ge-Sb-Te films have two possible configurations: a metastable face-centered cubic (fcc) and a stable hexagonal close-packed (hcp) lattice. Figure 44.3 depicts the structure of a typical cubic-phase Ge-Sb-Te alloy. The fcc state is preferred for discussion, because
1496
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Optical and Photonic Glass Applications
Fig. 44.4 Temperature dependence of the resistivity of
R ȍ
a sputter-deposited GeSb2 Te4 thin film. The temperatures of the phase transitions from the amorphous to the rocksalt state at 150 ı C, and further transitions to the stable trigonal state, are indicated by the arrows. A significant resistivity change occurs only at the first phase transition. After [44.15] J
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Part F | 44.1
b),QWHQVLW\ FSV c),QWHQVLW\ FSV
salt structure, with lattice parameters of around 6 Å (Fig. 44.5 and Table 44.1) and no evidence of phase separation in the metastable phase. The resistivity contrast of the new alloys is in the same range as the contrast of GeSb2 Te4 and Ge2 Sb2 Te5 . Understanding the mechanism of the rapid reversible phase transition is important for improving the phase change performance. This mechanism has been discussed extensively during recent years. In 2004, for example, an umbrella-flip model was carried out to explain the rapid phase transition, as shown in Fig. 44.6. Kolobov et al. [44.17] used the EXAFS (extended x-ray absorption fine structure) method to study the conventional GST, and concluded that GST does not have a rock-salt structure, but more likely consists of cubic symmetry that is randomly oriented in space. Laserinduced amorphization results in a dramatic shortening of the covalent bonds and obvious decrease in the relative displacement can be detected, which demonstrates a substantial increase in the degree of shortrange ordering. This transition can be considered as an umbrella flip of Ge atoms from an octahedral position into a tetrahedral position without rupture of strong covalent bonds. In 2006, Kohara et al. [44.18], using reverse Monte Carlo simulation with synchrotronradiation x-ray diffraction data, found that the ring statistics of amorphous GST were dominated by fourand sixfold rings, analogous to the crystal phase, as shown in Fig. 44.7. They conclude that such unusual ring statistics for amorphous GST are the key for the
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a)
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Fig. 44.5a–c X-ray diffractograms (XRD) of (a) Ge1:5 Sb2 Te4 , (b) Ge2 Sb2 Te4 and (c) Ge2 SbTe4 .
The diffractograms show a metastable phase after crystallization from the as-deposited amorphous phase. The peaks have been identified and attributed to the metastable rock-salt structure. From [44.16]
Fig. 44.6a,b Fragments of the local structure of GST around Ge atoms in the crystalline (a) and amorphous (b) states. After [44.17]
Phase-Change Memory and Optical Data Storage
44.1 Conventional Ge-Sb-Te Phase-Change Films
1497
Table 44.1 Crystallization temperature Tc , activation energy against crystallization Ea , and the lattice constant a of the rock-salt crystal structure of the metastable phase for the Ge-Sb-Te alloys. The values of the activation energies were determined by Kissinger analysis based on the variation in the transition temperature, with a heating rate of 5 K min1 . All of these measurements were carried out with alloys in the as-deposited state [44.16] GeSb2 Te4 145 2.64˙0.05 6.043
Tc (ı C) Ea (eV) a (Å)
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Ge2 Sb2 Te5 157 2.23˙0.07 6.000˙0.002
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Fig. 44.7 Schematic presentation of the possible ring size transformation in crystal–liquid–amorphous phase change and amorphous–crystal phase change in GST. Adapted from [44.18], with permission of AIP Publishing
a)
fast phase transition speed of the material. In 2007, Akola and Jones [44.19] used density functional theory (DFT) to investigate the structure of GST. As shown in Fig. 44.8, they found a long-range order among Te atoms and note that the crucial structural motif is a fourmembered ring with alternating atoms of types A (Ge and Sb atom) and B (Te atom), which they called an ABAB square. They posit that the rapid amorphous-tocrystalline phase change is a reorientation of such disordered ABAB squares to form an ordered lattice. They determined that the vacancies in the amorphous GST provide the necessary space for the crystallization to take place, noting a vacancy concentration in GST of about 11:8%. Huang and Robertson investigated structural transition for PCMs in five medium-range order [44.20]. They believe that many Ge sites in GeTe are distorted fourfold sites, indicating that the Ge atom is displaced along the (110) direction to complete the transition, as shown in Fig. 44.9. This is different from the um-
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Fig. 44.9 Structural transition from sixfold to fourfold in
GeTe presented by Huang and Robertson in [44.20]
brella-flip model as shown in Fig. 44.6, where the Ge atoms move along the (111) direction corresponding to a change from an octahedral to tetrahedral structure in the crystalline-to-amorphous phase transition. Thus, the Ge atom is octahedrally rather than tetrahedrally coordinated, leading to a local Peierls-like distortion in the amorphous state. They also showed evidence to illustrate a large effect on the optical matrix elements,
Part F | 44.1
Fig. 44.8a,b ABAB squares and cubes in amorphous GST (Ge in red, Sb in blue, and Te in yellow). (a) Simulation box of amorphous GST with atoms and bonds of ABAB squares and cube highlighted. (b) Local environment of ABAB cube. Reprinted with permission from [44.19]. Copyright 2007 by American Physical Society
b)
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Optical and Photonic Glass Applications
which are roughly twice as large for the resonantly bonded p state. Therefore, the large difference in optical contrast between amorphous and crystalline states in GeTe is attributed to the resonant bonds present in
the crystalline phase. The concepts of Peierls-like distortion and resonant bonding in PCMs have become well accepted recently, and were discussed in detail by Jones [44.21].
44.2 Phase-Change Behaviors of Doped Ge2Sb2 Te5 Films
Part F | 44.2
GST alloys have been proposed for use in PRAM due to their excellent properties with respect to thermal stability, cyclability, and crystallization speed. However, with the increasing need for low power consumption and good data retention, and the challenge in reducing the RESET current for PRAM applications, the performance of the commonly adopted GST still needs to be improved. In fact, many efforts have been made to improve performance by doping various elements, including N [44.22], O [44.23], Si [44.24], Bi [44.25], Ag [44.26], and Sn [44.27], into GST. The changes in properties as a function of doping mainly include increased resistivity of the phases, leading to smaller currents to write and erase, and accelerated crystallization speed or improved thermal stability for the amorphous phase due to increased crystallization activation energy. Generally, appropriate doping enhances the thermal stability of the amorphous phase due to the formation of strong bonds in the glass network. For example, in O-doped GST film [44.28], the presence of nonstoichiometric Ge–O bonds and the Sb2 O3 can be attributed to the suppression of crystallization and the enhancement of thermal stability. However, excess doping may deteriorate other phase transition properties, such as the speed of the phase change. For instance, the sheet resistance of W-GST drops more slowly with W doping of more than 18 at:%, which implies that the excess W causes a decrease in the phase transition speed [44.29]. Excess doping can also lead to a phase separation that reduces the thermal stability. For example, crystallization was suppressed in film with 16:8 at:% incorporated oxygen, while the formation of a separate phase of Sb2 Te3 was observed in films with more oxygen doping, indicating that the crystallization temperature was decreased with greater oxygen doping. We know that the GST film shows two types of phase transitions, i. e., metastable fcc and stable hcp. However, with proper doping, the second phase of hcp will always be inhibited. An ideal PCM possesses both high phase transition speed and amorphous thermal stability. However, a trade-off is required to balance these two properties in each PCM system. In the case of Bi- and Sn-doped GST [44.25], the balance of minimum time and maximum temperature for crystallization was obtained in the
component with 5:9 at:% Bi and 17:7 at:% Sn, respectively. Therefore, the newer PCMs should be explored and characterized. Here, the crystallization behaviors, as well as the thermal and electrical properties, of Zndoped GST will be highlighted for potential PRAM application. Figure 44.10a–d shows x-ray diffraction results for the as-deposited films with different Zn doping concentrations annealed at 200, 250, and 350 ı C for 3 min, respectively. There are no diffraction peaks in Fig. 44.10a, confirming that all the as-deposited samples are amorphous. On the other hand, the diffraction peaks in the GST, Zn6:37 .GST/93:63, and Zn8:13 .GST/91:87 films annealed at 200 ı C, as shown in Fig. 44.10b, correspond to fcc phase peaks in (200) and (220) orientations. Nevertheless, there are no fcc (200) and (220) diffraction peaks in Zn15:16 .GST/84:84 or Zn19:78 .GST/80:22 films annealed at 200 ı C. Diffraction peaks do appear with an increase in annealing temperature to 250 ı C in the Zn15:16 .GST/84:84 and Zn19:78 .GST/80:22 films, as shown in Fig. 44.10c. Thus it can be clearly seen that the onset phase transition temperature of GST from the amorphous state to fcc structure increases with increased Zn doping. As shown in Fig. 44.10d, the structures of Zn15:16 .GST/84:84 and Zn19:78 .GST/80:22 thin films are kept at the fcc phase. However, the phase transition of fcc to hcp (hexagonal close-packed) is present in Zn6:37 .GST/93:63 and Zn8:13 .GST/91:87 when the annealing temperature was increased to 350 ı C. This implies that the high Zn dopant concentration in GST film introduces Zn atoms that serve as a center to restrain the fcc-to-hcp phase transition, resulting in a one-step crystallization process. The temperature dependence of the sheet resistance (R–T) for the Zn-doped GST films with a heating rate of 40 K min1 are displayed in Fig. 44.11a. Clearly, the resistance of the films decreases slightly before their respective crystallization temperature (Tc ) that exhibits an abrupt drop in sheet resistance, which implies the phase transition from amorphous to fcc crystalline structure. A second drop in the sheet resistance occurs in GST, Zn6:37 .GST/93:63, and Zn8:13 .GST/91:87 films, indicating the structural transition of fcc to hcp. Moreover, the Tc values increase with more Zn doping, and they are much higher than that of GST, which helps to improve
Phase-Change Memory and Optical Data Storage
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Part F | 44.2
1499
1500
Part F
Optical and Photonic Glass Applications
Fig. 44.12 Raman spectra of GST and
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Part F | 44.3
the thermal stability of the films. An amorphous/crystalline resistance ratio larger than 105 in the doped films provides a good signal-to-noise ratio for the reading operation in PCM applications. High crystalline resistance can also be obtained in these films, which helps to reduce the programming energy in the RESET operation. The data retention ability of GST and Zn-doped GST is shown in Fig. 44.11b. This can be extrapolated by the Arrhenius equation, t D exp.Ea =.kB T//, where is the proportional time coefficient, Ea is the activation energy for crystallization, and kB is the Boltzmann constant. We determined t as the failure time when sheet resistance reaches half of its initial magnitude at a specific isothermal temperature, which is also indicated in Fig. 44.11b. Clearly, the 10-year data retention temperatures and Ea are all much higher than those of GST (88:9 ı C, 2:98 eV), which means that the PCM based on Zn-doped GST can store the data for a longer time than that of GST. This indicates that Zn-doped GST
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(especially with high Zn dopant concentration) is an ideal PCM, with better amorphous stability, larger crystallization activation energy, and better 10-year data retention. Thus, we will focus on the GST film doped with a high Zn concentration, such as Zn15:16 .GST/84:84 , in the following section. Figure 44.12 shows Raman spectra of GST and Zn15:16 .GST/84:84 annealed at 250 and 350 ı C. The vibration bands in 250 ı C-annealed GST at 105 and 155 cm1 are attributed to the A1 mode of GeTe4 corner-sharing tetrahedral and Sb–Te vibrations in SbTe3 units [44.30], respectively. The vibration band at 155 cm1 is significantly influenced by crystallization when the annealing temperature increases to 350 ı C, indicating a structural transformation from fcc to hcp. However, such a transition cannot be found in 350 ı Cannealed Zn15:16 .GST/84:84 film, indicating that the introduction of Zn into GST restrains the transition of fcc to hcp.
44.3 Doped Sb-Te Films for Phase-Change Memory Applications Compared with conventional GST films, another group of Sb-based materials, including Sb-Te, exhibits a fast growth-dominated crystallization process, and the set operation speed is faster. Therefore, Sb-based materials are also called fast-growth materials. While the fast-growth materials are obviously favored for highspeed reading and writing, the drawback of the materials is low amorphous phase stability and high media noise. An innovative approach for solving these problems is thus needed for the application of fast-growth materials in PCM devices. A preliminary investiga-
tion demonstrated that Sb2 Te3 film doped with other metallic elements including Al [44.31, 32], Ag [44.33], and Ti [44.34] exhibits better data retention, higher crystalline resistance, and a larger amorphous/crystalline resistance ratio ( 105 ) during the crystallization process. Sb2 Te alloys doped with Cu [44.35], Ti [44.36], and W [44.37] were reported to exhibit a high crystallization temperature and better data retention. However, the amorphous/crystalline resistance ratio or speed of crystallization in the alloys was found to degrade with increasing dopant concentrations. The
Phase-Change Memory and Optical Data Storage
a) Sheet resistance (Ω/^ ^)
44.3 Doped Sb-Te Films for Phase-Change Memory Applications
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Sb4Te Zn12.22 (Sb4Te)87.78 Zn17.21 (Sb4Te)82.79 Zn20.21 (Sb4Te)79.79 Zn28.63 (Sb4Te)71.37
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Tc (°C)
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Fig. 44.13 (a) Sheet resistance as a function of temperature for undoped and Zn-doped Sb4 Te films. (b) Crystallization temperatures as a function of composition in the Zn-Sb-Te ternary amorphous-phase-forming region
Figure 44.13a shows the R–T curves of undoped and Zn-doped Sb4 Te films. As we can see, the crystallization temperature (Tc ) of the films increases with increasing Zn content. All of these doped films exhibit a higher Tc than Sb4 Te (136 ı C) and GST (168 ı C). The Zn28:6 .Sb4 Te/71:4 film has the highest Tc at 256 ı C and crystalline resistance (Rc ) at 780 =. The amorphousphase-forming region of Zn-doped Sb-Te and other materials reported in the references are displayed in Fig. 44.13b. As we noted, the value of Tc is clearly increased with higher Zn concentration introduced into Sb-Te, including Sb2 Te3 , Sb2 Te, Sb7 Te3 , Sb3 Te, and Sb4 Te. By using the Arrhenius equation, the temperature for 10-year data retention can be extrapolated, and the fitting results are shown in Fig. 44.14. Clearly, the )DLOXUHWLPH V
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Part F | 44.3
doping of Ge [44.38], In [44.39], and Ag [44.40] into Sb7 Te3 has been shown to increase the crystallization temperature, and has been frequently used for rewritable and recordable optical media such as DVDRW and DVD+RW devices. However, these metaldoped Sb7 Te3 materials are not good in all respects. For instance, Ag-doped Sb7 Te3 always faces the problem of phase separation during the crystallization process, which can lead to poor endurance for PRAM applications. In order to increase the phase transition speed, researchers have tried to add the so-called fast-growth material Sb as much as possible to the phase-change material. Thus, Sb-Te alloys with high Sb content, including Sb3 Te and Sb4 Te, have typically been considered for investigation. Doping of impurities such as Al [44.41] and Au [44.42] into Sb3 Te can increase the crystallization temperature, data retention, and crystalline resistance, but other crystalline phases formed by these impurities will separate out during the crystallization process. Studies of Si-doped Sb4 Te showed that Si doping significantly improved thermal stability, refined their grain size, and altered nucleation characteristics with an increase in silicon content. Investigation by in situ transmission electron microscopy (TEM), however, showed that the crystalline phase of Si-Sb4 Te thin films could be indexed as a hexagonal Sb structure, and Si retained an amorphous state [44.43]. The above results have opened up an avenue of applications for metallic element-doped Sb-Te materials that have specific advantages compared with other phase-change materials. Here, Zn-doped Sb-Te films will be highlighted as a fast-transition and highthermal-stability phase-change material for potential PRAM application.
1502
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Optical and Photonic Glass Applications
Table 44.2 Thermal and electrical parameters of various Zn-Sb-Te compositions; the references GST and Ga2 Te3 Sb5
are listed for comparison Ternary system Ge-Sb-Te Ga-Te-Sb Zn-Sb-Te
a Deduced
Composition (at:%) GST [44.44] Ga2 Te3 Sb5 [44.45] Sb2 Te3 Zn33:3 .Sb2 Te3 /66:7 [44.46] Sb2 Te Zn29:7 .Sb2 Te/70:3 [44.47] Sb3 Te Zn26:3 .Sb3 Te/73:7 [44.48] Sb4 Te Zn28:6 .Sb4 Te/71:4 Sb7 Te3 Zn30:2 .Sb7 Te3 /69:8 [44.49]
Tc (ı C) a 168 228 100 221 144 258 135 202 136 256 142 258
Ea (eV) 2.98 4.3 – 3.59 2.03 3.68 2.08 3.28 2.32 4.46 1.58 4.15
T10 year (ı C) 88.9 161 – 139.5 52 161 53 130 41.6 176.6 30.6 170.6
Rc (=) 95 – – 1238 – 251 – 260 – 780 – 379
Ra =Rc
b
5:4 105 – – 1:5 106 – 3:6 105 – 1:2 104 – 2:1 104 – 1:6 105
from R–T curve at heating rate 40 K min1 resistance Ra measured at 35 ı C, crystalline resistance Rc measured at 300 ı C
b Amorphous
Table 44.3 The amorphous-to-crystalline phase transitions of the undoped and Zn-doped Sb-Te films
Part F | 44.3
Composition
As-deposited
Sb2 Te3 Zn-Sb2 Te3 [44.46] Sb2 Te Zn-Sb2 Te [44.47] Sb3 Te Zn-Sb3 Te [44.48] Sb4 Te Zn-Sb4 Te Sb7 Te3 Zn-Sb7 Te3 [44.49]
Partial crystallization Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous Amorphous
Detected phase at 200 ı C 250 ı C Sb2 Te3 Sb2 Te3 Sb2 Te3 Sb2 Te3 Sb2 Te Sb2 Te Sb2 Te Sb2 Te Sb2 Te Sb2 Te Sb2 Te Sb2 Te Sb Sb2 Te3 Sb2 Te Sb2 Te Sb SbCSb2 Te3 Sb2 Te Sb2 Te
Zn28:6 .Sb4 Te/71:4 film has the largest Ea of 4:46 eV and the highest temperature for 10-year data retention of 176:6 ı C, which meets automotive electronics criteria (10-year data retention temperature should be higher than 120 ı C). A summary of the thermal and/or electrical parameters for Ge-Sb-Te, Ga-Sb-Te, and Zn-Sb-Te films and the respective undoped counterparts are listed in Table 44.2, which shows that the introduction of Zn can effectively increase the Tc , Ea , and 10-year data retention temperature. Compared with GST, Ga2 Te3 Sb5 , and other Zn-Sb-Te films, Zn28:6 .Sb4 Te/71:4 possesses the best physical properties in terms of crystallization temperature, crystalline activation energy, and data retention, as well as crystalline resistance. The XRD patterns of the as-deposited and annealed Zn-Sb4 Te films are presented in Fig. 44.15. In Fig. 44.15a, the sharp crystalline diffraction peaks of 150 ı C- and 200 ı C-annealed Sb4 Te films belong
300 ı C Sb2 Te3 Sb2 Te3 Sb2 Te Sb2 Te Sb2 Te Sb2 Te Sb2 Te3 Sb2 Te SbCSb2 Te3 Sb2 Te
350 ı C Sb2 Te3 Sb2 Te3 Sb2 Te Sb2 Te Sb2 Te Sb2 Te Sb2 Te3 Sb2 Te Sb2 Te3 Sb2 Te
to the rhombohedral Sb-phase (JCPDS no. 35-0731). However, a new rhombohedral Sb2 Te3 crystalline phase begins to separate out (JCPDS no. 15-0874) in 250 ı Cannealed Sb4 Te films. When the annealing temperature increases to 350 ı C, it is completely crystallized with the stable rhombohedral Sb2 Te3 crystalline. Interestingly, there is no Sb or Sb2 Te3 crystalline phase in Zndoped Sb4 Te films. As can be seen in Fig. 44.15b–e, only a hexagonal Sb2 Te crystalline phase (JCPDS no. 80-1722) is present in the annealed Zn-Sb4 Te films. In addition, the intensity of the diffraction peaks for the crystalline Sb2 Te phase decreases with increasing Zn concentration, which implies that Zn doping can significantly suppress the growth of Sb2 Te crystalline grains. The crystalline phases of Sb-Te and Zn-Sb-Te films are listed in Table 44.3. It should be noted that the as-deposited Sb2 Te3 is partially crystallized due to its poor thermal stability. Other as-deposited Zn-doped and
Phase-Change Memory and Optical Data Storage
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Fig. 44.15a–e XRD patterns of undoped and Zn-doped Sb4 Te films annealed at different temperatures for 3 min in Ar atmosphere: (a) Sb4 Te, (b) Zn12:2 .Sb4 Te/87:8 , (c) Zn17:2 .Sb4 Te/82:8 , (d) Zn20:2 .Sb4 Te/79:8 and (e) Zn28:6 .Sb4 Te/71:4
undoped Sb-Te films, i. e., Sb2 Te, Sb3 Te, Sb4 Te, and Sb7 Te3 , are amorphous. Different crystalline phases are found in the films annealed at different temperatures. For instance, Sb2 Te and Sb3 Te films show a single
Sb2 Te crystalline phase, but Sb4 Te and Sb7 Te3 separate out Sb and Sb2 Te3 crystalline phases with the increased annealing temperature. When Zn is doped in these SbTe films, however, it restrains the phase separation, and
Part F | 44.3
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Part F
Optical and Photonic Glass Applications
Part F | 44.3
only a single Sb2 Te crystalline phase can be detected in the above doped films (besides Zn-Sb2 Te3 ). Single Sb2 Te3 crystalline phases are separated out from all the undoped and Zn-doped Sb2 Te3 films in the crystallization process. All these results confirm that Zn can be used to stabilize the crystalline structure of Sb-Te and makes these phase-change materials more thermally stable. In order to obtain additional information on the structure of the crystalline film, transmission electron microscopy (TEM) was employed. The brightfield (BF) TEM micrograph and its corresponding selected-area electron diffraction (SAED) pattern of 300 ı C-annealed Zn20:2 .Sb4 Te/79:8 film are shown in Fig. 44.16a,b, and the BF TEM micrograph, corresponding SAED pattern, and dark-field (DF) TEM image of 300 ı C-annealed Zn28:6 .Sb4 Te/71:4 film are shown in Fig. 44.16c–e. The BF TEM micrographs and SAED patterns indicate uniform Sb2 Te crystalline grains, several tens of nanometers in size, distributed in the Zn-Sb4 Te films. In addition, the Zn28:6 .Sb4 Te/71:4 film has smaller crystalline grains and more continuous diffraction rings in the SAED pattern than the Zn20:2 .Sb4 Te/79:8 film. This implies that the crystalline grain size can be decreased with a higher Zn dopant concentration in the film, which is in line with the results estimated from the decreased line width and diffraction peak intensity of the XRD patterns. The DF TEM micrograph shown in Fig. 44.16e clearly demona)
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strates the uniform morphology, with bright areas (crystalline Sb2 Te phase) embedded in dark areas (amorphous phase) in the 300 ı C-annealed Zn28:6 .Sb4 Te/71:4 film. The uniform distribution of the small crystalline grains is very beneficial for enhanced cycling reliability for PCM devices, which suggests that the Zn28:6 .Sb4 Te/71:4 film is the best candidate for PCM devices, with prolonged cyclability. Phase transition speed is a key factor determining the switching speed of PCM devices. Here, a static tester with different laser pulse widths and power was employed to quantitatively obtain the phase transition speed of Zn-doped Sb4 Te films. Figure 44.17a–d depicts the power-time-effect (PTE) diagrams for Zn12:2 .Sb4 Te/87:8 , Zn17:2 .Sb4 Te/82:8 , Zn20:2 .Sb4 Te/79:8 , and Zn28:6 .Sb4 Te/71:4 films, respectively. The optical contrast R is defined as R D .Rafter Rbefore /=Rbefore [44.25, 26], where Rbefore and Rafter are the optical reflectivity before and after irradiation, respectively. This should not be confused with the resistance R. The different colors indicate the magnitude of R in various crystallization processes. Region I in the figures represents the amorphous state, with no change in reflectivity because of the short laser pulse width and/or low laser power, while region II represents the crystalline state, with significant change in reflectivity because of the wide laser pulse and/or high laser power. The maximum R (Rmax ) value differs for each film, as follows: 0.26, 0.23, 0.20, and 0.19 for Zn12:2 .Sb4 Te/87:8 , Zn17:2 .Sb4 Te/82:8 , Zn20:2 .Sb4 Te/79:8 , and Zn28:6 .Sb4 Te/71:4 film, respectively. Figure 44.18a,b shows the normalized reflectivity evolutions induced by nano-laser pulse for Zn12:2 .Sb4 Te/87:8 and Zn28:6 .Sb4 Te/71:4 films. The initial low reflectivity of the curves in Fig. 44.18 indicates the amorphous state in the films. It increases gradually with increasing pulse duration for each curve (besides the lowermost curve in Fig. 44.18a), indicating the crystallization process before achieving a homogeneous crystalline phase. As we can see, Zn28:6 .Sb4 Te/71:4 begin to crystallize very quickly with a short pulse width; however, it is difficult for the Zn12:2 .Sb4 Te/87:8 film because of its high crystallization threshold. For instance, no change can be found in the optical reflectivity for the Zn12:2 .Sb4 Te/87:8 film, while a slight change can be observed in the Zn28:6 .Sb4 Te/71:4 film, with laser power of 15 mW. Increasing the laser power to 30, 50, and 70 mW, onset crystallization times of 85, 60, and 30 ns, respectively, are detected for the Zn12:2 .Sb4 Te/87:8 film, and 5, 15, and 30 ns for the Zn28:6 .Sb4 Te/71:4 film. The ending crystallization times for these two Zn-doped Sb4 Te films with laser power of 70 mW are 190 and 164 ns for the Zn12:2 .Sb4 Te/87:8 and Zn28:6 .Sb4 Te/71:4 films, respectively. Obviously,
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both the onset and ending crystallization times for the Zn28:6 .Sb4 Te/71:4 film are shorter than those for the Zn12:2 .Sb4 Te/87:8 film. In addition, they are shorter than those for the GST (40 and 280 ns) [44.50] and Sb-rich Zn30:2 .Sb7 Te3 /69:8 (10 and 250 ns) films [44.49], indicating that the Zn28:6 .Sb4 Te/71:4 film has the fastest crystallization speed among these reported phasechange materials. As discussed earlier, the uniform distribution of smaller Sb2 Te crystalline grains in Zn-doped Sb4 Te film is beneficial for enhancing cycling reliability. Therefore, here we employed static testing to investigate cycling reliability. Figure 44.19 illustrates the optical switching behavior over 50 cycles between the crystalline and amorphous phases for the Zn28:6 .Sb4 Te/71:4 film. The optical contrast is positive when loaded on a pulse width of 250 ns and laser power of 35 mW (squares), indicating the crystalline state. On the other hand, the optical contrast is negative when loaded on a pulse width of 150 ns and laser power of 70 mW (circles), indicating the amorphous state. The difference in optical contrast between the amorphous and
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crystalline states remains almost constant during continuous laser application, which demonstrates that the Zn28:6 .Sb4 Te/71:4 film has good cycling reliability.
44.4 Nanocomposite Films for Phase-Change Memory Applications Part F | 44.4
ZnO is a direct-band-gap (3:37 eV) semiconductor with excellent physical and chemical properties and thermodynamic stability at room temperature. It is an ideal material to be doped onto Sb2 Te3 for fabrication of nanocomposite materials for potential PCM applications. Figure 44.20 shows the R–T curves for GST, Sb2 Te3 , and ZnO-doped Sb2 Te3 films. As we see, there is no clear resistance drop in the as-deposited 6KHHWUHVLVWDQFH ȍ̸ ̸
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Sb2 Te3 film due to the partial crystallization. The GST film exhibits two abrupt drops in sheet resistance at 168 and 300 ı C, indicating the transition of an amorphous to fcc structure and fcc to hcp structure, respectively. ZnO-doped Sb2 Te3 films show a sudden drop in resistance when the temperature is close to their specific crystallization temperature (Tc ). The value of Tc is 212, 217, 223, 241, and 275 ı C for .ZnO/0:62.Sb2 Te3 /99:38 , .ZnO/0:82.Sb2 Te3 /99:18 , .ZnO/1:69 .Sb2 Te3 /98:31, .ZnO/5:22 .Sb2 Te3 /94:78, and .ZnO/5:5 .Sb2 Te3 /94:5 , respectively. Clearly, the ZnOdoped Sb2 Te3 films have much higher Tc than GST and Sb2 Te3 , which implies that the introduction of ZnO into the Sb2 Te3 film can significantly increase the amorphous thermal stability. However, the decrease in resistance becomes very sluggish in the .ZnO/5:5 .Sb2 Te3 /94:5 film, indicating that the doping of ZnO is excessive and restrains the phase transition process. The XRD patterns of undoped and ZnO-doped Sb2 Te3 films are shown in Fig. 44.21. In Fig. 44.21a, we note that there is one crystalline diffraction peak that corresponds to Te(110) in the XRD pattern of the as-deposited Sb2 Te3 film, implying that it actually contains a crystalline Te phase. A rhombohedral Sb2 Te3 crystalline phase was found in 200 ı C-annealed Sb2 Te3 film, and the corresponding diffraction peak in-
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tensity was stronger when the annealing temperature was increased to 250, 300, and 350 ı C. Interestingly, a sharp diffraction peak located at 2 D 35:3ı , which is attributed to the Sb2 O3 crystalline phase, was found
when the annealing temperature was increased to 300 and 350 ı C. It is believed that the poor thermal stability of the Sb2 Te3 film results in this Sb2 O3 phase separation.
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Figure 44.21b–f shows the XRD patterns of the asdeposited and annealed ZnO-doped Sb2 Te3 films. We can see that the Sb2 Te3 crystalline phases begin to separate out in 200 ı C-annealed 200 ı C-annealed 250 ı C-annealed 250 ı C-annealed 300 ı C-annealed
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1509
Part F | 44.4
Sb2 Te3 phases can be separated out at high temperature. However, peaks D and E are not so obviously detected in these Raman spectra. All these results support the conclusions summarized from XRD, i. e., high ZnO dopant content can significantly restrain the formation of the Sb2 O3 phase and improve the thermal stability for ZnO-doped Sb2 Te3 films. The BF and DF TEM micrographs, SAED patterns, and high-resolution TEM (HRTEM) images for the 300 ı C-annealed .ZnO/5:2 .Sb2Te3 /94:8 film are shown in Fig. 44.23a–d, respectively. From the BF and DF TEM micrographs, the uniform crystalline grains of 1020 nm in size can be found in the annealed films, which is in good agreement with the estimated XRD results. These nanocrystals are surrounded by amorphous ZnO that exists in the dark area in the DF TEM micrograph. The SAED pattern and HRTEM image indicate that these nanocrystals in the .ZnO/5:22 .Sb2 Te3 /94:78 film are Sb2 Te3 phases, and no other crystalline phase exists in the film. This is in line with the results estimated from XRD and Raman spectroscopy. Based on these analyses, we believe that the nanocomposite structure with mixed amorphous ZnO and crystalline Sb2 Te3 phases in the .ZnO/5:22 .Sb2 Te3 /94:78 film results in enhanced thermal stability and reduced operating power. A static tester using pulsed laser irradiation was employed to determine the phase transition speed for optimal .ZnO/5:22.Sb2 Te3 /94:78 film. The phase transition speed can be obtained by observing the change in op-
films. The Sb2 O3 crystalline phase appears at 250 ı C for the .ZnO/0:62.Sb2 Te3 /99:38, annealed .ZnO/0:82.Sb2 Te3 /99:18, and .ZnO/1:69.Sb2 Te3 /98:31 films. However, the Sb2 O3 crystalline phase is almost suppressed in the .ZnO/5:22.Sb2 Te3 /94:78 and .ZnO/5:5.Sb2 Te3 /94:5 films, even with the annealing temperature increased to 350 ı C. This is evidence that the thermal stability can be significantly improved and phase separation suppressed with increased ZnO doping. In addition, broader line width and lower diffraction peak intensity can be found in Fig. 44.21e,f, indicating that the growth of crystalline grains is restrained with increased ZnO doping. We also performed Raman spectroscopy to study the structure of the undoped and ZnO-doped Sb2 Te3 films, and the results are shown in Fig. 44.22. As seen in Fig. 44.22a, three vibration peaks ascribed to the Sb2 Te3 crystalline phase can be found at 65 (peak A), 110 cm1 (peak B), and 165 cm1 (peak C) in the Sb2 Te3 target and films [44.50, 51]. They become sharper with increasing annealing temperature as more of the Sb2 Te3 crystalline phase is separated out. However, two new vibration peaks at 140 cm1 (peak D) and 123 cm1 (peak E) in the Sb2 Te3 films are detected when the annealing temperature is increased to 350 ı C. These two vibration peaks are ascribed to the vibrations of the Sb2 O3 phases [44.52]. The Raman spectra of the as-deposited and annealed .ZnO/0:62.Sb2 Te3 /99:38 and .ZnO/0:82 .Sb2 Te3 /99:18 films are displayed in Fig. 44.22b,c. Peak C can be found in these two films, but it is much weaker than in the undoped Sb2 Te3 film, indicating that the Sb2 Te3 crystalline phase is significantly restrained by a small amount of ZnO doping. Peaks E and D appear in the Raman spectra of the 250 ı C-annealed .ZnO/0:62.Sb2 Te3 /99:38 and .ZnO/0:82.Sb2 Te3 /99:18 films, which confirms that the Sb2 O3 phases were crystallized in the films. As depicted in Fig. 44.22d–f, some common features of Raman spectra for three other ZnO-doped films can be concluded as follows. Peak C appears from the overlapping broad band from 100 to 180 cm1 with increasing annealing temperature, indicating that the crystalline
44.4 Nanocomposite Films for Phase-Change Memory Applications
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Part F | 44.5
tical contrast (R), which is defined as R D .Rafter Rbefore /=Rbefore , where Rbefore and Rafter are the reflectivity before and after irradiation, respectively. Pulsewidth-dependent R with different laser power levels and the PTE diagram for the .ZnO/5:22 .Sb2 Te3 /94:78 film are displayed in Fig. 44.24a,b. R increases with increasing laser pulse width and/or laser power, but it does not change with increasing pulse width when the laser power is 5 mW, as the applied laser energy is not sufficient to induce film crystallization (region I in the
PTE pattern). When laser power is increased, crystallization occurs and R increases (region II in the PTE pattern). Researchers have reported onset crystallization times for GST of 300, 150, 80, and 40 ns with laser power of 10, 30, 50, and 70 mW, respectively [44.49]. For .ZnO/5:22 .Sb2 Te3 /94:78 film, onset of crystallization occurred in 130, 40, 20, and 10 ns with the same power, which would indicate that the crystallization speed of the .ZnO/5:22 .Sb2 Te3 /94:78 film is faster than that of GST.
44.5 Crystallization Kinetics Studied by Ultrafast Calorimetry for Phase-Change Materials Phase-change materials (PCMs) demonstrate promising performance for next-generation memory technology, with fast, reversible switching speeds between amorphous and crystalline phases, and large optical and electrical contrast. However, the kinetics of switching must be better understood for optimization of PCMs and phase-change devices, especially with regard to the crystallization kinetics, which has aroused much interest over the years in the form of experiments [44.53–57] and molecular dynamics simulations [44.58, 59]. In recent decades, due to the limitations in instrumentation, a majority of experimental investigations of the crystallization kinetics of PCMs have focused primarily on the relatively low-temperature region. For real-world PCM applications, however, crystallization always occurs at higher temperatures, with ultrafast optical or electrical pulses. Fortunately, a new type of calorimetry, ultrafast differential scanning calorimetry
(ultrafast DSC), has been introduced, which extends the heating rate to more than 4 104 K s1 . In 2012, Orava et al. first applied ultrafast DSC to the conventional PCM Ge2 Sb2 Te5 [44.62]. As shown in Fig. 44.25a, the crystallization peaks are readily detectable in these DSC traces, and the corresponding temperature, Tp , increases with the increase in the heating rate. According to the Kissinger equation [44.63] ln
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According to classical nucleation theory [44.66], the crystal growth rate G U / D 1 exp ; kB T so there is a relationship between the kinetic coefficient for crystal growth Ukin and diffusivity D that can be written as Ukin / D. A Stokes–Einstein relation between D and viscosity is D / T=. Therefore, the relationship between Ukin and can be obtained and described as Ukin / T=. Thus, the Ukin term can be evaluated based on the Cohen and Grest expression for the viscosity of glass-forming liquids, which is [44.67] log10 Ukin D A
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Part F | 44.5
tallization is generally obtained in a conventional lowheating-rate test. However, as depicted in Fig. 44.25b, the Kissinger plot of GST based on ultrafast DSC is obviously curved, and the effective activation energy Q decreases at higher temperature, as expected for a fragile liquid. The red curve represents the temperature dependence of the crystal growth rate U in GST, related to the dashed line through the data by numerical modeling of DSC curves. The kinetic coefficient or limiting velocity for crystal growth Ukin is related to U. The real crystal growth rate U can be assumed as [44.64]
Part F
Optical and Photonic Glass Applications
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a large m (D 90) can be obtained, which indicates an obvious non-Arrhenius behavior, as shown in Fig. 44.25a. After Ukin is evaluated over the entire temperature range down to Tg , and the thermodynamic effects are incorporated (44.3), the temperature dependence of the crystal growth rate can be represented as shown in Fig. 44.26. As expected for supercooled liquids [44.64, 68], the interplay of kinetics and thermodynamics yields a maximum in U. This maximum is close to Tm , and for GST the maximum is at 0:76Tm . The arrow in this figure indicates that ultrafast DSC extends conventional measurements and can characterize the temperature dependence of the crystallization rate of GST up to at least 0:72Tm (1:70Tg ), where the crystal growth rate approaches its maximum. In 2015, Orava et al. studied the crystallization kinetics for another PCM, Ag-In-Sb2 Te (AIST), based on ultrafast DSC [44.69]. For this material, however, the Cohen and Grest model for viscosity may be not suitable. The authors believed that there was a fragile-to-strong crossover on cooling the liquid, and applied the generalized Mauro–Yue–Ellison– Gupta–Allan (MYEGA) expression to study the crystallization kinetics. The generalized MYEGA equation from metallic glass-forming systems can be described as [44.70]
W1 , W2 , C1 , and C2 are adjusted parameters, and 1 is the viscosity at infinite temperature. Months later, Chen et al. employed this ultrafast DSC to study the crystallization kinetics of a growthdominated PCM, Ge7 Sb93 [44.71]. Two expressions of viscosity fitting have been used in this material: Cohen and Grest, and Salinga and Mauro. The Salinga and Mauro equation is not shown here, but can be obtained from [44.71]. According to the results, the Salinga and Mauro model for viscosity and growth rate appears more appropriate for this Ge7 Sb93 material. This was also confirmed in a GeTe material [44.72]. It may be noted that both nucleation and crystal growth are determinants of crystallization speed, but the role of nucleation has not been discussed here. As described by Sebastian et al. [44.73], nucleation is expected to become less important, and crystallization would govern crystal growth, at the technologically relevant nanometer length scale and nanosecond timescale. This is particularly true in the meltquenched amorphous state, where a large population of nuclei already exist and a crystal/amorphous interface is present [44.74]. Therefore, we have emphasized the crystal growth rather than the nucleation for the crystallization kinetics of PCMs. In summary, we have achieved important progress regarding the crystallization kinetics of PCMs at higher temperatures by employing ultrafast DSC. In this way, a large range of heating rates (from 10 to 40 000 K s1 ) can be applied, whereby crystallization becomes available over a relatively wide temperature range. The decoupling of Ukin and , and their marked nonArrhenius temperature dependence, shows that conventional DSC crystallization measurements near Tg have limited relevance for the fast crystallization oc-
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Phase-Change Memory and Optical Data Storage
44.6 Phase-Change Materials for Applications in Integrated Photonic Memory
curring in PCMs. Nevertheless, the specific model that can be employed for PCM viscosity fitting is not uniform, whether Cohen and Grest, generalized
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44.6 Phase-Change Materials for Applications in Integrated Photonic Memory
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racetrack resonators, Mach–Zehnder interferometers, and balanced splitters. A thin layer of indium tin oxide was capped on top of the GST to prevent oxidation. The transmission spectra of the devices were strongly affected by the complex propagation constant and attenuation coefficient of the waveguide mode, which was dependent on the phase state of the GST. Using racetrack resonators as memory elements, the authors were able to detect optical properties including the Q-factor, central wavelength of the peak resonances, and the extinction ratio, and to track the state of the GST. This work provides a feasibility study for optically tunable photonic circuits that can potentially be switched on in a picosecond timescale. Using optical near-field effects, GST can be employed to realize bit storage of up to eight levels in integrated nonvolatile photonic memory [44.76], as shown in Fig. 44.27b. By precisely controlling the intensity of the writing pulse with power from 372 to 601 pJ, the ratio of crystalline and amorphous states can be modulated in a controlled manner to realize eight different transmittance levels, as shown in Fig. 44.27c. In addition, the transmittance can arbitrary reach any of eight levels in the case of selective erasure of pulse intensity. The 5-m-long GST devices can be erased
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Fig. 44.27 (a) Schematic overview of the proposed memory element, and the cross-sectional view of the coupling region showing the control port and the GST-covered freestanding waveguide section. Reprinted from [44.75], with the permission of AIP Publishing. (b) A scanning electron microscope image of a fabricated GST optical memory device, from [44.76]. (c) Twolevel and eight-level operations realized by precise control of the volume ratio of the amorphous and crystalline phase. From [44.77]
Part F | 44.6
With the large contrast in optical properties such as refractive index between amorphous and crystalline states, the use of phase-change materials opens up a new dimension for integrated photonic memory. Pernice and Bhaskaran [44.75] have theoretically proposed photonic memory devices using phase-change materials, as shown in Fig. 44.27a. A microring resonator was used to coat a short section of GST. The nearby nanophotonic waveguides propagated the visible control light through evanescent coupling to the microring resonator. GST is optically triggered by the transition between the amorphous and crystalline phases, which changes the transmission characteristics of the microring resonator. The phase status can be read by sending a probe beam, which serves as a digital data bit. Numerical analysis indicates that the crystallization of GST can be induced by a 600 fs optical pulse with power of 5:4 pJ, and reversible amorphization can be achieved by an optical pulse with higher power. Moreover, multilevel recording can be realized in such integrated photonic platforms. Rios et al. [44.78] experimentally demonstrated a hybrid nanophotonic circuit for implementing tunable photonic devices based on nanoscale GST junctions. A 10 nm-thick GST layer was deposited on a section of
1514
Part F
Optical and Photonic Glass Applications
Fig. 44.28 (a) Scanning
a)
electron microscope micrograph of the device. Light is coupled in and out of the on-chip circuitry by means of focusing grating couplers at the lower left and right; (b) The changes in transmission for an individual element for write/erase operations. Adapted from [44.76]
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Part F | 44.7
and written under an 100 ns optical pulse with power of 533 pJ. In a more extreme situation with a 1 mlong GST device, a short 10 ns optical pulse is sufficient for operation at a power energy of only 13:4 pJ. GSTbased photonic memory has been found to be comparable to cutting-edge electronic PCM memory in terms of energy and speed [44.77]. To demonstrate multibit access capability, wavelength selectively operated through a single waveguide was coupled to three ring resonators with embedded GST elements (11 m2 ), as shown in Fig. 44.28a. The three ring resonators with different ring radii were separated from the central waveguide by a gap of 300 nm. The bit status was able to be primarily retrieved by the transmittance change of the GST devices. Using three cavity modes with different wavelengths of 1560.1, 1561.5,
:DYHOHQJWK QP
and 1563:35 nm, a single pulse of 10 ns and a train of consecutive 50 ns pulses were employed to complete write and erase operations, respectively, as shown in Fig. 44.28b. In this section, we have summarized recent advances in photonic memory based on phase-change materials. These materials are characterized by high contrast between the crystalline and amorphous phases of optical properties such as refractive index. A striking and functional feature of phase transition is high speed and scalability, and the high thermal stability of two states satisfies a key requirement for truly nonvolatile memory. Compatibility with CMOS technology vastly expands their capability into photonic devices. With these attributes, PCMs are ideal candidates for optical memory.
44.7 Summary PRAM is an appealing memory technology, and its functional material is a key component of the memory cell. Recent decades have seen considerable progress in the development of phase-change materials for mem-
ory devices with lower power consumption and better data retention. However, a challenge remains in understanding a basic set of scientific concepts, i. e., how to understand the rapid structural change when the phase-
Phase-Change Memory and Optical Data Storage
change materials undergo amorphous to crystallization transition. In this chapter, we have presented the current knowledge about the structural and crystallization behavior of ternary Ge-Sb-Te alloys, and highlighted the use of Zn-doped Ge2 Sb2 Te5 to enhance thermal stability in an amorphous state and increase crystalline resistance. The thermal and phase-change behavior for the novel Zn-Sb-Te alloys and ZnO-Sb2 Te3 nanocomposite was further discussed. We also focused on recent scientific research on crystallization kinetics for phase-
References
1515
change materials by ultrafast calorimetry. Based on this new measurement technology, we can extend our knowledge to the process of crystal growth under supercooled liquid for phase-change materials. Finally, we have discussed recent progress involving the use of PCMs in integrated photonic memory, although much additional work is needed to further reduce the power required for writing and erasure. Nevertheless, this provides a pathway towards a new paradigm in all-photonic memory.
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References
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Part F
Optical and Photonic Glass Applications
Xiang Shen Laboratory of Infrared Materials & Devices Ningbo University Ningbo, China [email protected]
Xiang Shen received his PhD from the Shanghai Institute of Technical Physics (Chinese Academy of Sciences) in 2009. He was a Visiting Scientist at the Austrian National University before joining the Laboratory of Infrared Materials and Devices of Ningbo University, China. His research focuses on the structures, crystallization kinetics, electrical and optical behaviours of chalcogenide glasses.
Yimin Chen Dept. of Microelectronic Science and Engineering, Faculty of Science Ningbo University Ningbo City, China [email protected]
Yimin Chen received his PhD from the Ningbo Institute of Industrial Technology, Chinese Academy of Sciences, and worked at Ningbo University. He works on chalcogenide thin films, focusing on the crystallization kinetics, crystallization behaviours, structural, thermal, electrical and optical properties of phase-change materials.
Guoxiang Wang Laboratory of Infrared Materials & Devices Ningbo University Ningbo, China [email protected]
Guoxiang Wang received his PhD from the Shanghai Institute of Technical Physics, Chinese Academy of Sciences. He currently works at the Laboratory of Infrared Material and Devices at Ningbo University. His research focuses on phase-change materials, specifically controllable crystallization, interface interaction and atomic structure imaging.
Yegang Lv Laboratory of Infrared Materials & Devices Ningbo University Ningbo, China [email protected]
Yegang Lv received his PhD from the Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences and worked at Ningbo University. His research interests include optoelectrical materials and devices.
Part F | 44
1519
Display Glass 45. Display Glass
Matt Dejneka, T. J. Kiczenski 45.1 45.1.1 45.1.2 45.1.3 45.1.4 45.1.5
Overview of Display Technologies ..... LCD Displays ..................................... AMLCD ............................................. AMOLED ........................................... Quantum Dot Displays ...................... Active Matrix TFT Technology..............
1520 1520 1521 1522 1522 1523
45.2 45.2.1 45.2.2 45.2.3
Display Glass Properties ................... Basic Compositional Requirements .... Total Pitch Variability ........................ Physical Requirements......................
1524 1524 1524 1528
45.3 45.3.1 45.3.2
Melting and Fining .......................... 1529 Melting ........................................... 1529 Fining ............................................. 1530
45.4 45.4.1 45.4.2 45.4.3
Forming Precision Sheets for Displays ..................................... The Slot Draw Process ....................... Float ............................................... Fusion.............................................
1532 1532 1533 1534
45.5 45.5.1 45.5.2 45.5.3 45.5.4 45.5.5 45.5.6 45.5.7 45.5.8 45.5.9 45.5.10 45.5.11
Glass Composition ........................... Liquidus .......................................... Annealing Point ............................... Softening Point ................................ Thermal Expansion........................... Density............................................ Young’s Modulus.............................. Optical Properties ............................. Durability ........................................ Other Properties ............................... Rare Earth Oxides ............................. Compositional Summary ...................
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Three-Dimensional (3-D) Upconversion Displays...................... 1545
45.7
Electronics on Glass ......................... 1546
45.8
Flexible Glass and Displays............... 1547
45.9
Conclusions ..................................... 1548
References................................................... 1549
© Springer Nature Switzerland AG 2019 J.D. Musgraves, J. Hu, L. Calvez (Eds.), Springer Handbook of Glass, Springer Handbooks, https://doi.org/10.1007/978-3-319-93728-1_45
Part F | 45
Active matrix displays are rapidly making all other display technologies on the market obsolete. They are all around us, from the smart watches on our wrist, to the phones in our pocket, to the TVs in our homes and they provide us with information, entertainment, biometrics, and a connection to the world, all on a thin bright device. The array of thin film transistors in the backplane of all active matrix devices eliminates cross-talk between pixels, provides a larger dynamic range in brightness, and accelerates the response time of the display. Whether it be a liquid crystal display (LCD) or an organic light emitting diode (OLED)-based display, an efficient and responsive active matrix of thin film transistors requires high mobility silicon, which requires high processing temperatures and precise patterning. This puts great demands on the glass substrate that the transistors and the entire display are built upon. The glass must be incredibly flat, smooth, and dimensionally stable at temperatures that would sag common window glass in a heap. This chapter will explore the amazing melting and forming technologies that have been developed to produce precision display glass sheets as well as the glass compositions that are the foundation for glass forming and device fabrication.
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45.1 Overview of Display Technologies Displays have evolved from being a luxury item in the early days of cathode ray tube (CRT) televisions to a virtual necessity in the modern world. Due to the wide breadth of display applications, from televisions to car dashboards to phones and tablets to wearables, current displays employ a range of technologies. While a vast array of display technologies exist, many (such as CRT, passive matrix LCD, electroluminescent and plasma displays) are very mature, and innovation around the glass substrates used in those applications has slowed or ceased. CRTs dominated the display market for 75 years, from their monochrome introduction in 1922 for oscilloscopes and radar, to black-and-white TV in 1931, to color in 1953, to large screens in the 1980s [45.1], until lighter, thinner, and more efficient LCD flat screens started replacing them around the turn of the century and ultimately drove CRTs out of the market in 2007 (2010 in some parts of the world). Plasma displays with their better contrast ratio and darker blacks reached their peak around 2008, but succumbed to LCD displays in 2014 because of their potential screen burn-in issues [45.2] and the improved brightness and efficiency of LCDs [45.3]. Previous articles and books [45.4] have discussed these outdated technologies in more detail, so this chapter will focus on the current battleground technologies in modern displays, which are active matrix liquid crystal display (AMLCD) and OLED, as they continually push the boundaries on attainable resolutions, brightness, speed, and power consumption.
Part F | 45.1
Light
No voltage
45.1.1 LCD Displays To understand the requirements for the glass, we must first understand how these devices work. An LCD works by rotating the polarization of light to turn a pixel on and off, as illustrated in Fig. 45.1. Incoming light from a back light first passes through a polarizer on the outside surface of the LCD backplane substrate glass. On the inside of this glass is a thin layer of polymer with tiny grooves oriented parallel to the polarizer. The opposing parallel piece of glass called the color filter (CF) (the reason for this name will become apparent shortly) also has a grooved polymer layer on the inside aligned to a polarizer on the outside. However, the polarizers and grooves on the CF sheet are rotated 90ı relative to the backplane sheet, so that the polarizers are crossed and no light should be able to get through. Now, if we fill the gap between the backplane and the CF with liquid crystal (LC), we can control the passage of light. The molecules of the nematic liquid crystal are long and polar. Thus, they align with the grooves on the inside surface of the backplane, then twist a little with each successive layer until they are rotated 90ı and oriented with the grooves on the CF on the other side of the gap. Now, when polarized light enters the gap, it will rotate with the twisted nematic liquid crystal and pass through the polarizer on the CF, as shown on the left-hand side of Fig. 45.1. If a voltage is applied across the gap between the backplane and CF, the nematic liquid crystal molecules will orient parallel to the electric field and perpendicular to the glass sheets, Light
Applied voltage Horizontal polarizer Backplane glass substrate
LC molecule
LC molecule Vertical polarizer Color filter glass substrate
Pixel on
Pixel off
Fig. 45.1 Principle of LCD operation showing a bright pixel on the left and a dark pixel on the right
Display Glass
as shown on the right-hand side of Fig. 45.1. In this orientation, there is no rotation of the polarization, so the light will be blocked, and the pixel will be off or black. As the strength of the electric field is varied, so is the degree of light passed through the pixel, and so it is a continuously variable switch. To make an array of pixels, rows of transparent conductor lines are applied to one sheet of glass and columns of conductive lines are applied to the other. Half the switching voltage is applied to the column and half is applied to the row, so that at the intersection point there is enough voltage to switch the state of the LC at the intersection and turn the pixel on or off without switching the state of neighboring pixels. To make a full color display, each pixel is made up of three red, green, and blue subpixels, whose intensities can be independently controlled to achieve the desired color. Thus red, green, and blue filters are printed on the output layer of glass at each pixel, and this explains why it is called the CF layer. These passive matrix devices, whose pixels are addressed by rows and columns of conductors, are relatively simple to make and are inexpensive, but suffer from slow response time because the applied net voltage is barely enough to switch the polarization state. They also suffer from ghosting due to imprecise voltage control, since the half voltage applied to any row or column affects the voltage felt by the whole row or column and neighboring pixels. Horizontal polarizer
Active matrix (AMLCD) devices overcome these shortfalls by incorporating at least one transistor and capacitor at each pixel, as shown in Fig. 45.2. The transistors serve as switches to individually address each pixel without affecting neighboring ones, while the storage capacitor stores enough charge to maintain the pixel in its desired state until the next refresh. The transistors are grown on the glass substrate as thin films and are referred to as thin film transistors (TFTs). The conducting metal layers and semiconducting Si that make up the TFT are shown in the top expanded subpixel crosssection in Fig. 45.2. The rows and columns are made in different layers on the backplane substrate and are connected at each pixel by a transistor whose output is sent to a capacitor connected to the pixel via a transparent electrode, which is usually made of indium tin oxide (ITO). The transistor acts as a switch, so that when the row voltage (gate line) is above threshold for the transistor, it will be on and, then, the charge sent down the column (data line) will pass through the transistor and be stored on the capacitor to keep the pixel at the desired level until the next refresh. The circuitry is the same as that shown for the active matrix OLED in Fig. 45.3. The column charge cannot affect any neighboring pixels, since their transistors are in an off state. Thus, voltages well above the switching voltage for the LC can
Color filter (green)
Black matrix
Common electrode (transparent ITO)
Liquid crystal
Spacer Capacitor
Si
Part F | 45.1
TFT
Gate dielectric
LC alignment layer Pixel electrode (transparent ITO)
TFT substrate Conductor
Vertical polarizer
Fig. 45.2 Horizontal polarizing filter Front plate
Front glass plate Color filter layer Liquid crystal layer Subpixel electrodes
Vertical polarizing filter Fluorescent backlighting
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45.1.2 AMLCD
CF substrate
Seal
45.1 Overview of Display Technologies
Rear glass plate
AMLCD with expanded view of subpixel, showing the cross-section of TFT, storage capacitor, color filter, and glass substrate layers with rotation of the liquid crystal in the on state
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Fig. 45.3 Active Seal glass
–
Cathode
matrix OLED display
Emissive layer
+
Hole transport layer Anode
+ Gate lines Transistor
+
Data lines
+
+
Part F | 45.1
be used in the horizontal gate lines for faster switching without impacting neighboring pixels and higher dynamic range of the display can be achieved, providing faster displays with greater contrast. However, these devices are more complex and require more than 6 million (1080 rows 1920 columns 3 colors) transistors and capacitors for a single 1080p HD TV with 1080 rows and 1920 columns, and more than 26:5 million transistors and capacitors for a 4 K TV with 4096 rows and 2160 columns; 8 K or UHD TV has 7680 rows and 4320 columns requiring 99:5 million transistors and capacitors to be built on a sheet of glass. Thus, there are tough demands on the glass substrate that must remain dimensionally stable during the fabrication process, since even 10 ppm of shrinkage or distortion would result in misregistration between the pixels in the backplane and those in the CF layers, which go through very different thermal processes.
45.1.3 AMOLED Active matrix OLED (AMOLED) devices operate very differently than LCD devices, but as we will soon discover, have a lot in common with them. OLEDs work by emitting light directly, so they have a wider viewing angle, and there is no need for color filters, which absorb two thirds of the light, so they can be more efficient than LCDs. Even though linear polarizers are not necessary for optically switching OLED pixels on and off, they require a circular polarizer for ambient light rejection, so both LCDs and OLEDs lose half their light output via the circular polarizer. OLEDs also require a glass substrate on which to build the device and an array of conductors to address the transistors that switch the pixels on and off, as illustrated in Fig. 45.3. A transparent conductive oxide layer, usually ITO, is deposited as
TFT substrate glass
the anode on the substrate. Then, an organic conductive layer is deposited to transport holes from the anode to the emissive layer. The organic emissive layer controls the color of the pixel, and red, green, and blue emitting organic layers are patterned as subpixels directly on top of the hole transport (injection) layer. The emissive layers are then contacted with a common cathode, usually with a low work function metal like Ca, to inject electrons into the emissive layer. The transistor controls the current flowing through the emissive layer, where the electrons and holes recombine to emit light with nearly 20% efficiency for red and green diodes but only 5% for blue diodes. The light emission is proportional to the current, so darker areas use only 40% of the power of an LCD, but white areas can consume three times the power of an LCD. The light is emitted in all directions, but in the case of a metallic cathode, it will reflect the light back out through the substrate. Nearly transparent displays can also be made with OLED devices with transparent cathodes. OLED displays also put high demands on the glass substrates. The low work function cathodes will oxidize if exposed to oxygen, and the emitting layers are degraded by exposure to water vapor, so the glass substrate and superstrate (seal) must be hermetic and impervious to air and humidity. Since OLEDs are current driven devices, the transistors require high mobility Si in their TFT arrays, which means high process temperatures, so the glass needs to have excellent dimensional stability during processing and a very smooth surface, just like LCDs.
45.1.4 Quantum Dot Displays Quantum-dot light-emitting diodes (QLED)s are an emerging display type, which could be a serious threat for OLEDs. In fact, Samsung, the largest TV maker in
Display Glass
the world, says that it is focusing on QLED instead of OLED [45.5]. There are two architectures for QLEDs. In one scenario, the quantum dots are simply used as phosphors not diodes, and red and green emitting quantum dots replace the red and green color filters in the CF panel, and the blue color filter is left out. Now, when blue LEDs are used as the sole light source, the blue light travels unimpeded through the now missing blue filter and excites the red and green emitting QDs. The LC controls the intensity of each subpixel just like a conventional LCD. In the second architecture, the QDs function as electroluminescent diodes deposited in the clear aperture between the TFTs. This type of display is like an OLED display, where the organic LEDs and conductive layers are replaced with inorganic QDs. When the TFTs are turned on, they pass current through the QLED, and direct red, green, and blue emitting QDs are used to generate light at the pixel. This technology provides deep blacks and high contrast ratio, since the pixels in the off state are extremely black [45.6]. Regardless of the architecture, most QLEDs still rely on active matrix backplanes with TFTs for best performance, so the requirements of the glass are still the same as for AMLCD and AMOLED devices.
45.1.5 Active Matrix TFT Technology
requiring higher mobility semiconductor layers. The LTPS process enables considerably higher electron mobility than a-Si based TFTs (up to 100 times higher), allowing TFTs to be smaller, which enables higher resolution, lower power consumption, or both. TFTs are not transparent and are, generally, hidden under the black matrix between pixels, so the smaller they are, the more area available for the clear aperture to let light through the pixel. The ratio between the light emitting area versus the total area of a pixel, including the black matrix and opaque electronics, is called the aperture ratio. Higher mobility Si enables higher aperture ratio, so either the pixels can be brighter or smaller with LTPS. If they are smaller, then more pixels can fit in the same area, and resolution is increased. While LTPS can clearly enable a better display, there are many downsides as well, such as the higher temperatures required (as high as 600700 ı C) to grow the Si semiconductors, increased complexity of manufacture, higher costs, and the difficulty in scaling to large display sizes. The third technology, oxide TFTs, has, therefore, been getting a lot of attention in recent years, since it offers the scalability of a-Si but with increased electron mobility (although not as high as LTPS), which could enable high resolution and large displays. Currently, oxide TFTs are used mostly in tablets and are just starting to migrate to TV. This technology strikes a balance between a-Si and LTPS and, it will be interesting to see how widely adopted it is in the future amongst the large panel manufacturers [45.7]. Today’s touch screen devices have more than just two pieces of glass. Figure 45.4 compares the components used to make LCD and OLED touch screen devices. Both can utilize four sheets of glass, including a chemically strengthened cover glass that is more scratch and damage resistant than the display glasses to protect them from breakage. They also have a thin touch sensor with an array of transparent electrodes to sense the location of a user’s finger or stylus. Most multitouch sensors use capacitive touch with rows of transparent electrodes on one side of the touch sensor and columns on the other, creating small capacitors at each crossing. When a user’s finger(s) touches the cover glass, it changes the capacitance at the nearby crossing(s) of the rows and columns on the touch sensor and is detected as a touch [45.8]. Some new phones integrate the rows and columns of transparent touch electrodes directly on the cover glass (on-cell touch) or directly on the display glass (in-cell touch) to eliminate the extra touch sensor glass layer for a thinner device [45.9].
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Part F | 45.1
Independent of the display type, active matrix displays offer faster response and better dynamic range than their passive matrix counterparts. Whether it is LCD, OLED, or QD, most active matrix display technologies use one of three primary TFT backplane technologies: amorphous silicon (a-Si), oxide TFT (often called IGZO, short for indium gallium zinc oxide), or low-temperature poly-silicon (LTPS). These different TFT technologies differ somewhat in their designs but are primarily distinguished based on the material used as the semiconductor layer. The most commonly employed technology is the a-Si TFT backplane due to its simplicity, scalability, and low cost compared to the other options. Generally, a-Si based devices utilize lower temperature processes (200300 ı C peak temperature) and are lower resolution displays. The scalability of the a-Si technology, however, makes it very suitable for large displays, which often have lower resolution and less demanding power requirements than mobile devices. Higher performance displays (such as in extremely high resolution televisions or higher end mobile devices) place more demand on the TFTs,
45.1 Overview of Display Technologies
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Optical and Photonic Glass Applications
Cover
LCD components
Protects display from scratches and breakage
OLED components
Touch sensor Detects physical touch
Fig. 45.4 Comparison of LCD and OLED touch screen components. Courtesy Corning Incorporated
Encapsulation Prevents moisture and oxygen from degrading OLED Color filter/ frontplane Supports CF, polarizer, and LC alignment layer Backplane Supports electrode grid and millions of TFTs
45.2 Display Glass Properties 45.2.1 Basic Compositional Requirements
Part F | 45.2
All glasses used in the industry today have to satisfy some basic requirements before they can be considered as display substrates. The first of these is to control alkali contamination, which can poison Si-based devices and cause performance issues in the TFTs. Most display glasses are considered alkali-free, although they all contain a low level ( 100 ppm or less) of alkali in practice from tramp contamination in the raw materials. This residual level of alkali is generally prevented from entering the TFT through the application of a barrier layer of silicon dioxide or silicon nitride on the substrate. Furthermore, the aluminum and boron ions in the glass have a strong affinity for alkalis and prevent them from diffusing out of the glass and into the Si [45.10]. So, while not truly alkali-free, a glass must have a low enough level of mobile alkali ions such that industryaccepted solutions to alkali-diffusion are effective. Another historically pervasive attribute of display glasses is a low density. While not directly related to the performance of the device, a lower density glass would reduce the weight of the device (always critical in today’s mobile devices) and would allow for easier handling of the large sheets in the manufacturing process. It also reduces sag during the manufacturing process. However, more recent glasses have seen their densities increase relative to the glasses used 1020 years ago
as backplanes have become increasingly thinner while putting more stringent requirements on the total pitch variability of the substrates (this will be discussed in the next section). The fact that the substrates are thinned to only a couple of hundred m in thickness means that the density of the glass contributes less weight to the overall device than previous designs. This lower contribution of weight to the article, therefore, reduces some of the value of a low density glass, allowing glass manufacturers to better optimize attributes that would improve display performance at the expense of increased density.
45.2.2 Total Pitch Variability Within the display industry, there is an ever-increasing demand for higher resolution, brighter screens, or lower power consumption for longer battery life in mobile devices. To enable these improvements, perfect registration (or as perfect as possible) of the various layers of the TFT is critical. The TFT fabrication process can be simplified to a series of thin film deposition, photolithographic patterning, etching, and heat treatment steps. Just a few m of shrinkage can cause a pattern error between successive photolithographic exposures if not properly compensated for [45.11]. Total pitch is the distance any given location or feature on a glass substrate moves during processing. If the shrinkage or total
Display Glass
a) Temperature
important distinguishing factor between potential substrate glasses. Translated to glass properties, this means the glass backplane must demonstrate the minimal amount of total pitch variability possible. Historically, this was described by the compaction or shrinkage performance of the glass, which is the dimensional change undergone by the glass under a thermal cycle in the manufacture of the TFT, often at the highest temperatures in the process like the dehydrogenation step in a LTPS process. The bulk of this dimensional change is due to viscous relaxation, which can also be described as the relaxation of the fictive temperature of the glass (defined as the temperature corresponding to the equilibrium state described by the structure trapped in the glass during formation) towards the temperature of the display panel maker’s process. This became known as compaction due to the fact that the fictive temperature set into the glass during manufacture is often above the heat treatment temperature of the glass during the TFT process. Unlike crystalline materials, the density of a glass is dependent on thermal history and can change with heat treatment. If the heat treatment temperature is below the fictive temperature of the glass, relaxation of the glass structure during processing will result in a reduction of fictive temperature, as shown in Fig. 45.5a. A lower fictive temperature glass has a more dense structure and will, therefore, occupy a smaller volume, resulting in compaction or shrinkage of the glass during the heat treatment. Unlike crystalline materials, the final volume and density of glass is dependent on the thermal history of the glass. Figure 45.5b shows the change in volume as it is cooled at different rates. At high temperatures, the glass has a low viscosity, and the structure relaxes quickly and the volume contracts independently of the cooling rate, hence the two curves are coincident at high temperature. However, as the glass becomes more viscous at lower temperatures, the struc-
b) Volume
Tf0 Tf1
Compaction
Fig. 45.5a,b Tf1 Time
Tf0 Temperature
Change in fictive temperature with (a) time and (b) temperature
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Part F | 45.2
pitch is uniform and reproducible from sheet to sheet, it is not a big problem. Reasonably large amounts of total pitch can actually be accounted for by compensation in the TFT process, traditionally up to 2030 ppm. Since the TFTs and conductive paths are patterned photolithographically, the photo mask can be scaled up in size by 2030 ppm, so that after processing, the product shrinks to the target dimensions and feature sizes and locations. If the total pitch is too large to be compensated for, considerable losses for the panel manufacturer due to dead pixels or light leakage due to misalignment of features (such as the TFT and color filter) would result. What is interesting is that, once below the upper limit of pitch change for a given process, further reduction in total pitch change does not necessarily lead to better alignment. Rather, improvements in variability of the total pitch (known in the industry as total pitch variation or TPV) will lead to better and more repeatable alignment. In other words, a larger but less variable total pitch value is preferred to a smaller but more variable value (although it should be noted that the ultimate desire is often minimal total pitch and minimal total pitch variability). This is due to the fact that, once a given amount of total pitch is identified for a given process, the optical compensation can take care of any change in total pitch as long as it is consistent and does not vary. A reduction in total pitch variability can increase the selects of a panel manufacturer’s process, thereby improving their economics. Beyond cost savings, reducing total pitch variability can also allow the panel manufacturer to improve their aperture ratio. A higher aperture ratio would allow for more light to be emitted at a given resolution (enabling better battery life and/or brightness) or higher resolutions at a fixed aperture ratio. However the manufacturer chooses to spend the improved TPV performance of the substrate, the end result is a better and/or less expensive device. Therefore, total pitch variability has become the most
45.2 Display Glass Properties
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Part F
Optical and Photonic Glass Applications
Part F | 45.2
ture cannot equilibrate quickly enough to keep up, and the volume contraction will slow down and follow the upper curve and transition from the volume contraction curve of the liquid melt at high temperatures to the volume contraction of the solid glass at low temperatures and set in a fictive temperature of Tf0 . If the glass is cooled more slowly, the glass has more time to relax and can equilibrate at higher viscosities (lower temperatures) and contract to a denser lower volume state as illustrated by the lower curve and have a lower fictive temperature Tf1 . In practicality, most glasses will lock in a fictive temperature corresponding to a viscosity of between the strain point (1013:7 Pa s) for extremely well-annealed optical glasses and 1010 Pa s for fusion drawn glasses. When heat treatments are made to the glass after forming, its fictive temperature will relax towards the heat treatment temperature. If the heat treatment temperature is below the fictive temperature, the glass will contract, and the lower the temperature, the slower the rate of equilibration and densification. If the heat treatment temperature were instead above the fictive temperature of the glass, the fictive temperature would increase during relaxation, causing an expansion of the glass. It is, therefore, more proper to refer to this phenomenon as dimensional change rather than compaction, since the latter is shaded by empirical experience in the industry and is not reflective of the actual physics in play. While the total pitch of a substrate was historically attributed to the structural relaxation of the glass due to these changes in fictive temperature, total pitch is actually due to a number of factors and not just the change of the average fictive temperature of the glass. In the following sections, we will discuss some of the most important of these factors, each of which have an additive contribution to the TPV: 1. Elastic distortion 2. Stress relaxation 3. Viscous relaxation. Elastic Distortion Perhaps the easiest to understand of the factors contributing to total pitch variation is elastic distortion. During the manufacture of a TFT, various films are deposited on the glass. While efforts are made to minimize stresses in these films, invariably there is residual stress in the films, which then causes a concomitant strain in the glass. The resulting pitch change in the substrate is consequently governed by the elastic modulus of the glass E and the thickness of the substrate h, as seen in the Stoney equation f tf D
Eh2 : 6.1 /R
(45.1)
In (45.1), f is the in-plane stress in the film, tf is the film thickness, E is the Young’s modulus of the substrate, h is the thickness of the substrate, is the Poisson’s ratio of the substrate, and R is the radius of curvature of the substrate after the film deposition [45.12]. When there is no film stress, f D 0, R must go to infinity, and the sheet is perfectly flat. As can be seen from the equation, when a higher stress film (or thicker film) is applied to a glass substrate with a given modulus and thickness, the radius of the curvature must decrease, resulting in decreased R, and increased warp. Similarly, for a given film stress and film thickness, an increase in either the Young’s modulus or the substrate thickness will result in an increase in the radius of curvature of the substrate, resulting in less warp and a flatter sheet. While the most efficient way to reduce distortion due to film stresses is by increasing the thickness of the substrate (varies as thickness squared), the display industry is constantly driving to thinner and thinner substrates. Consequently, a higher modulus glass is one of the only ways one can reduce the pitch change from a given applied stress from the films, thereby reducing the contribution to total pitch from elastic distortion. Similarly, variations in applied film stress will cause variations in the resulting strain in the glass, so a glass with a higher Young’s modulus would also reduce the TPV due to elastic distortion. Stress Relaxation Once films with stresses have been applied to the glass substrate during TFT manufacturing (often during the early steps of the process), subsequent time spent at elevated temperatures can result in the relaxation of both the film and the glass. This can be a source of TPV if the sheet experiences different temperatures during later steps in the manufacturing process or if there are variations in initial film stress, causing varying degrees of relaxation. This stress relaxation happens much faster (roughly 10) [45.13] than the bulk structural relaxation corresponding to the evolution of the fictive temperature of the glass during heat treatments (covered earlier and in the next section) and can, therefore, be a major source of dimensional change in the glass at lower temperatures where bulk structural relaxation has a negligible contribution to dimensional changes. The rate of stress relaxation is governed primarily by the viscosity of the glass at the processing temperature. In fact, the measurement of stress relaxation in a controlled lab environment can be used as a way to directly measure the non-equilibrium viscosity of a glass at an experimental temperature. At high temperatures (well above the glass transition temperature), the glass structure is in virtually instant
Display Glass
equilibrium with any perturbations to temperature. Consequently, the viscosity–temperature relation of a glass at high temperatures can be easily described by a smooth function. At lower temperatures, however, the viscosity of the glass is much more complicated. This low temperature viscosity is not only a function of the composition of the glass (which determines the viscosity– temperature curve) and the temperature of measurement but also of the thermal history of the glass and time. As a glass is cooled through the glass transition region, the structure ceases to evolve and is frozen at the fictive temperature. When the structure ceases to evolve, the viscosity of the glass departs from the smooth equilibrium viscosity curve and begins to follow a different trend with an effective viscosity (solid line in Fig. 45.6) below that which would be predicted exclusively from the equilibrium curve (dashed line in Fig. 45.6). This lower viscosity is due to the more open structure trapped in the glass characteristic of its higher fictive temperature. The degree of the departure of the glass from the extrapolated equilibrium viscosity curve is, further, dependent on the fictive temperature of the glass (and, therefore, on the cooling rate of the glass) with a higher fictive temperature glass having a lower viscosity than the same composition with a lower fictive temperature. Because of this, maximizing the viscosity of a glass through composition design, thermal history manipulation, or a combination of both, is the best way to reduce the amount of stress relaxation a glass undergoes during TFT manufacturing. Assuming a similar thermal history, the amount of stress relaxed in a given time at temperature should scale directly with the annealing point of the glass (which is a good metric for low temperature viscosity as it is the
temperature where the glass viscosity is 1012:2 Pa s). To measure stress relaxation, a load is applied to a beam of glass at temperature to induce a specified amount of deflection. The stress relaxation is then calculated from the decay in the force required to maintain the specified deflection. In Fig. 45.7, several glasses with varying annealing points are held at relevant temperatures for TFT processing, and the expected trend is precisely what is observed—the higher the annealing point of the glass, the less stress relaxation. The less stress relaxation, the lower the TPV, so higher annealing point glasses are desirable for reducing stress relaxation. Viscous Relaxation Also referred to as structural relaxation, viscous relaxation of a glass is governed by the relaxation of the non-equilibrium nature of the structure of a glass towards the structure consistent with the temperature of the process step at hand due to changes in fictive temperature. The time dependence of viscous relaxation is roughly described by the Kohlrausch–Williams–Watts (KWW) equation [45.14] t .T;T
Tf .t/ D T C ŒTf .t D 0/ Te
f/
;
(45.2)
where Tf .t/ is the change in fictive temperature as a function of time, T is the temperature of the thermal cycle in question, Tf .t D 0/ is the initial fictive temperature, and .T; Tf / is the relaxation time, which is proportional to the viscosity of the glass with said fictive temperature at the temperature of the thermal cycle. In simplistic terms, the rate of this relaxation depends on the driving force for the dimensional change and a reStress relaxed (%) 25
20
15 Tf 10
1/T
Fig. 45.6 Equilibrium and non-equilibrium viscosity. Below Tf , the glass structure is locked in, and the effective viscosity (non-equilibrium viscosity) becomes lower than the theoretical viscosity the glass could have if it were allowed to fully equilibrate at a given temperature (illustrated with the dashed line)
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5
0 700 710 720 730 740 750 760 770 780 790 800 Annealing point of glass (°C)
Fig. 45.7 Stress relaxation as a function of glass annealing
point
Part F | 45.2
Log η
45.2 Display Glass Properties
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Part F
Optical and Photonic Glass Applications
sistance to that change. The driving force in this case is the deviation of the fictive temperature of the glass from the temperature of the process step . . . the larger the deviation, the larger the driving force for structural relaxation. The resistance to this change is the exponential term in (45.2) and is proportional to the effective viscosity of the glass, which is a function of the glass composition, its fictive temperature, and the temperature of the process step (as discussed in Sect. 45.2.2, Stress Relaxation). A reduction in the amount of dimensional change due to structural relaxation can be achieved by either reducing the driving force or increasing the resistance to the change. Reducing the driving force for dimensional change can be accomplished by reducing the difference between the fictive temperature of the glass and the temperature of the heat treatment step. This is illustrated in Fig. 45.8 in the comparison of the standard glass with the same glass that has been annealed at the heat treatment temperature for some time. This plot in Fig. 45.8 shows the dimensional change as a function of time at temperature up to 120 min. While the low viscosity glass immediately compacts even at the shortest times, the annealed version does not start showing appreciable compaction until it has been held at temperature for over 15 min. Even at long times, the annealed glass continues to demonstrate considerably reduced dimensional change relative to the composition with the higher fictive temperature. Alternatively, increasing the resistance to a change in fictive temperature can achieve a similar result. In the right image, a higher viscosity glass is compared to the same standard glass as used in a) Compaction (ppm)
the annealing study. This glass also has minimal dimensional change until it has been at temperature of over 15 min and ends up at virtually the same level of dimensional change as the annealed sample, demonstrating the similar efficacy of both approaches. Since annealing or extremely slow cooling a glass can be cost prohibitive, a very attractive way to reduce the dimensional change observed in a given thermal cycle is to maximize the low temperature viscosity of the glass. As can be seen in Fig. 45.9, if an equivalent cooling rate is applied to a series of glasses with increasing annealing point, the compaction continuously decreases in a high temperature test cycle. This strong correlation of the low temperature viscosity of the glass (i. e., the annealing point) with reduced dimensional change is one of the key factors driving the historical increase in the annealing point of display substrates. Furthermore, the temperatures used by display panel manufacturers are not always known and can vary from one manufacturer to another and can even change when different products are being made, so overcoming dimensional change with increasing viscosity is a more robust solution than annealing the glass.
45.2.3 Physical Requirements While we have discussed a number of compositional requirements for a display glass, the physical requirements for use as a display glass are every bit as stringent. The glass must be exceptionally flat, have low stress, and be clean. The TFT performance can b) Compaction (ppm)
Part F | 45.2
0
0
–100
–100
–200
–200
–300
–300
–400
–400
–500
–500
–600
–600
–700 –800
–700
Annealed – Low viscosity As made – Low viscosity 0
50
100
150 t (min)
–800
High viscosity Low viscosity 0
50
100
150 t (min)
Fig. 45.8a,b Dimensional change (compaction) as a function of time for (a) annealed (squares) and as formed (diamonds) glass and (b) low (diamonds) and high (squares) viscosity glasses
Display Glass
Compaction (ppm) –200 –225 –250 –275 –300 –325 –350 –375 –400 780
790
800
810 820 830 840 Annealing point of glass (°C)
Fig. 45.9 Compaction as a function of the glass annealing
point
45.3 Melting and Fining
1529
be detrimentally impacted if the surface has too much roughness (from scratches or even just the general surface texture). Similarly, a glass substrate with too much distortion or shape can cause handling errors in coarse scale or cell gap deviations in smaller scales. The cleanliness of the substrate must be exceptional, with particles on the order of < 1 m causing visual defects in the resulting display. In high performance displays, the monitored particles may be a low as 0:3 m in diameter. If not carefully monitored, particles can cause massive losses in the manufacturing process (as was the case in the early days of AMLCD manufacture). Thus, the glass needs to be transparent, extremely flat, thermally stable, clean, and chemically stable. To achieve these attributes, the glass composition needs to melt well, have a high liquidus viscosity and annealing point while being compatible with a forming process that is capable of making flat precision sheets. The melting and forming processes used to achieve these feats will be explored next.
45.3 Melting and Fining
log η (Pa s) 13 Annealing 12 Soda-lime silicate 11 EagleXG 10 Lotus 9 Rare earth display glass 8 7 6 5 4 Sheet forming 3 2 Melting and fining 1 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
T (°C)
Fig. 45.10 Viscosity curves of exemplary glasses
surate increase in the temperatures required to lower the viscosity of the melt to between 10 and 100 Pa s, where the batch materials quickly dissolve and trapped gas bubbles can rise to the surface in a reasonable amount of time.
45.3.1 Melting When batch enters the melting tank, fluxes such as boric acid and alkaline earth carbonates decompose to oxides and react with some alumina and silica to form fluid melts. These melts become enriched with more alumina and silica as the melting progresses causing the viscosity to increase. To make pristine glass and eliminate solid inclusions such as unmelted batch, the batch must be fully dissolved into the melt before the glass begins to cool. The rate of dissolution of any solid particle will be determined by the solubility of the particle in the surrounding glass melt and the diffusivity of the component ions of the particle in the glass. The solubility is determined by the identity of the particle and the composition and temperature of the glass melt. The diffusivity D is inversely proportional to viscosity as described by the Stokes–Einstein equation [45.15] DD
kB T ; 6 rH
(45.3)
where kB D 1:38 1023 J=K is Boltzmann’s constant, T is the absolute temperature, is the viscosity, and rH is the hydrodynamic radius of the ion [45.16]. Thus, increasing temperature will increase T and decrease ,
Part F | 45.3
Melting is the process of dissolving solid batch materials into a liquid melt, while fining is the process of removing gaseous inclusions or bubbles from the melt. Display glasses need to not only survive the high temperature TFT manufacturing process, but the sheet must remain dimensionally stable so that it does not warp or shrink to maintain pixel alignment between the TFT and CF panels, which requires a high annealing point, as discussed in Sect. 45.2.2. Unfortunately, raising the annealing temperature of the glass also makes it harder to melt and remove bubbles. Figure 45.10 compares the viscosity curves of display glasses to typical sodalime silicate. The display compositions are roughly 200300 ı C higher in annealing point with a commen-
1530
Part F
Optical and Photonic Glass Applications
Part F | 45.3
which will both increase D, as well as the solubility of the particle components, and combined they greatly increase the dissolution rate of any remaining sand grains or other batch materials. However, the glass melting tank walls are made of ceramic refractories similar to the batch materials (primarily SiO2 , Al2 O3 , and ZrO2 ), so increases in temperature will increase the rate of tank corrosion and shorten the usable tank life, causing costly down time and tank rebuilds. In fact, the tank corrosion rate roughly doubles for every 50100 ı C increase in temperature [45.17]. Thus, there must be a balance between the glass melting rate and the tank corrosion rate. For example, very high SiO2 .> 94%/ glasses with annealing points greater than 1000 ı C have long been known [45.18], but they are not economically feasible to melt and must be made by more expensive, lower throughput means. Alkali metal oxides like Li2 O, Na2 O, and K2 O are extremely effective for dissolving SiO2 grains because of their high diffusivity and viscosity lowering power, which improves melting and fining. Hence, they are used in most glasses for windows and containers, but they are forbidden in display glasses because their high mobility quickly poisons Si transistors. Thus, display glasses are considerably more challenging to melt than their alkali-containing counterparts and require higher temperatures and more advanced tank materials. Higher annealing point glasses needed for improved display glass performance also increase the viscosity at melting temperatures, making them even more difficult to melt and fine. Thus, the glass composition should be designed to have a steep viscosity curve, so that it has a high annealing point for good TPV performance and yet a reasonable melting temperature and high batch dissolution rate to enable efficient production of high quality glass. The dissolution rate can also be improved by judicious selection of raw materials and their particle size.
45.3.2 Fining The melting of typical display glass raw materials produces a lot of gas. Alkaline earth carbonates release CO2 , while the trace amounts of nitrates and sulfates liberate N2 , O2 , NOx , and SO2 . There is also a considerable amount of air trapped between melting batch particles, which then expands with increasing temperature and further increases the gas load in the molten glass. Bubbles are lighter than molten glass, so they float to the top at a rate that is determined by the viscosity of the surrounding glass melt [45.19]. The upward terminal velocity v of a bubble of radius r in a glass melt of viscosity , and density is given by
vD
2gr2 ; 9
(45.4)
where g is the acceleration due to gravity [45.20]. While larger bubbles rise fast enough to be eliminated quickly, the smaller bubbles are the most troublesome, since they are impeded by the viscous drag. To observe this speed differential at room temperature, just vigorously shake a half empty bottle of a viscous liquid like liquid soap and watch the large bubbles race past the tiny ones on their ascent. A 0:1 mm diameter bubble will only rise about 10 cm=day in a glass melt of 10 Pa s viscosity, which is far too slow for effective removal. The temperature of the glass can be increased to reduce the viscosity, but the slope of the viscosity curve is relatively shallow in the melting and fining regime of the viscosity curve shown in Fig. 45.10, so lowering the viscosity by a factor of 100 to 0:1 Pa s would require a 400 ı C increase to well above 2000 ı C, which is far beyond the capability of any large scale melter and the materials used to contain the molten glass. However, the upward velocity is proportional to r2 , so if the size of the bubble could be increased by 10, then a 1 mm bubble will rise 100 faster according to (45.4). So, ironically, the key to fining is to generate more gas and make small bubbles larger, so they can be removed quickly [45.19]. As2 O5 is a very powerful fining agent and has been used for centuries, since it tends to reduce at high temperatures (liberating oxygen) and then oxidize at low temperatures according to (45.5) [45.21, 22]. As2 O5 • As2 O3 C O2
(45.5)
To generate a new bubble requires the generation of a new gas–liquid interface creating a nucleation barrier to generating new bubbles. Furthermore, the capillary pressure inside a bubble is inversely proportional to the radius of the bubble, so it takes a lot of pressure to nucleate a tiny bubble. Thus, it is energetically more favorable for the O2 generated by the As2 O5 reduction to preferentially go into existing bubbles during fining, rather than generating new bubbles. So, once the glass is melted and the large bubbles have already risen to the top, the glass laden with residual tiny bubbles (or seeds, as they are called in the glass industry) then enters the fining section of the melter, where the temperature is increased, causing a reduction of the fining agent and the liberation of O2 , which makes the small bubbles larger and increases their upward velocity. The glass depth is also typically shallower in the fining section, so the bubbles have less distance to rise to the surface. As the glass is conditioned in the sections after the finer and cooled for forming, any residual small O2 bubbles will then be resorbed as the As2 O3 is oxidized back to As2 O5 . Since increasing temperature drives (45.5) to the right, decreasing temperature will drive it back to the left and aid O2 resorption as the glass cools. As the temperature decreases, so does the volume of gas (according to the
Display Glass
ideal gas law PV D nRT). Hence, the bubble shrinks, which increases the surface area to volume ratio of the bubble and the capillary pressure inside, both of which aid in the revers