The World Scientific Reference of Amorphous Materials: Structure, Properties, Modeling and Main Applications (Volume 2) 9789811215551, 9789811215568, 9789811215582, 9789811215605

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Materials and Energy Print ISSN: 2335-6596 Online ISSN: 2335-660X Series Editors: Leonard C. Feldman (Rutgers University) Jean-Luc Brédas (King Abdullah University of Science & Technology, Saudi Arabia) Richard A. Haight (IBM Thomas J. Watson Research Ctr, USA) Angus Alexander Rockett (University of Illinois at Urbana-Champaign, USA) Eugene A. Fitzgerald (MIT, USA, Cornell, USA & The Innovation Interface, USA) Gary Brudvig (Yale University, USA) Michael R. Wasielewski (Northwestern University, USA) Energy and sustainability are keywords driving current science and technology. Concerns about the environment and the supply of fossil fuel have driven researchers to explore technological solutions seeking alternative means of energy supply and storage. New materials and material structures are at the very core of this research endeavor. The search for cleaner, cheaper, smaller and more efficient energy technologies is intimately connected to the discovery and the development of new materials. This collection focuses onmaterials-based solutions to the energy problem through a series of case studies illustrating advances in energy-related materials research. The research studies employ creativity, discovery, rationale design and improvement of the physical and chemical properties of materials leading to new paradigms for competitive energy-production. The challenge tests both our fundamental understanding of material and our ability to manipulate and reconfigure materials into practical and useful configurations. Invariably these materials issues arise at the nano-scale! For electricity generation, dramatic breakthroughs are taking place in the fields of solar cells and fuel cells, the former giving rise to entirely new classes of semiconductors; the latter testing our knowledge of the behavior of ionic transport through a solid medium. Inenergy-storage exciting developments are emerging from the fields of rechargeable batteries and hydrogen storage. On the horizon are breakthroughs in thermoelectrics, high temperature superconductivity, and power generation. Still to emerge are the harnessing of systems that mimic nature, ranging from fusion, as in the sun, to photosynthesis, nature's photovoltaic. All of these approaches represent a body of materials–based research employing the most sophisticated experimental and theoretical techniques dedicated to a commongoal. The aim of this series is to capture these advances, through a collection of volumes authored by leading physicists, chemists, biologists and engineers that represent the forefront of energy-related materials research.

Published Vol. 15

The World Scientific Reference of Amorphous Materials Structure, Properties, Modeling and Main Applications (In 3 Volumes) edited by Alexander V. Kolobov (Herzen State Pedagogical University of Russia, Russia), Koichi Shimakawa (Gifu University, Japan), Ivar E. Reimanis (Colorado School of Mines, USA), Nikolas J. Podraza (University of Toledo, USA) and Robert W. Collins (University of Toledo, USA)

For further details, please visit: http://www.worldscientific.com/series/mae (Continued at the end of the book)

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Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Materials and Energy — Vol. 15 THE WORLD SCIENTIFIC REFERENCE OF AMORPHOUS MATERIALS Structure, Properties, Modeling and Main Applications (In 3 Volumes) Volume 1: Structure, Properties, Modeling and Applications of Amorphous Chalcogenides Volume 2: Structure, Properties and Applications of Oxide Glasses Volume 3: Structure, Properties, and Applications of Tetrahedrally Bonded Thin-Film Amorphous Semiconductors Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-121-555-1 (set_hardcover) ISBN 978-981-121-593-3 (set_ebook for institutions) ISBN 978-981-121-594-0 (set_ebook for individuals) ISBN 978-981-121-556-8 (vol. 1_hardcover) ISBN 978-981-121-557-5 (vol. 1_ebook for institutions) ISBN 978-981-121-558-2 (vol. 2_hardcover) ISBN 978-981-121-559-9 (vol. 2_ebook for institutions) ISBN 978-981-121-560-5 (vol. 3_hardcover) ISBN 978-981-121-561-2 (vol. 3_ebook for institutions) For any available supplementary material, please visit https://www.worldscientific.com/worldscibooks/10.1142/11697#t=suppl Desk Editor: Rhaimie Wahap Typeset by Stallion Press Email: [email protected] Printed in Singapore

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Preface by Editor-in-Chief

Amorphous solids (including glassy and non-crystalline solids) are ubiquitous since the vast majority of solids naturally occurring in our world are amorphous.∗,1 Although this field is diverse and complex, the attached three volume set covers the vast majority of the important concepts needed to understand these materials and their principal practical applications. One volume discusses the most important subset of amorphous insulators, namely oxide glasses; the next two volumes discuss the most important subsets of amorphous semiconductors, namely tetrahedrally coordinated amorphous semiconductors and amorphous and glassy chalcogenides. Together these three volumes provide advanced graduate students, postdoctoral research associates, and researchers wishing to change fields or sub-fields a comprehensive set of theoretical concepts and practical information needed to become conversant in the field of amorphous materials.

∗

The term amorphous does not have a universally accepted scientific definition. In the oxide glass community amorphous materials are defined as those disordered materials not undergoing a glass transition. In this case glasses are a class of materials distinct from amorphous materials. Other scientific communities, including the semiconducting glass community, define amorphous materials as those disordered materials that lack long range periodic order. In this case glasses are a subset of amorphous materials. These discrepancies notwithstanding, the distinction is purely semantic. v

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The topics covered in these three volumes include: • concepts for understanding the structures of amorphous materials, • techniques to characterize the structural, electronic, and optical properties of amorphous materials, • the roles of defects in affecting the electronic and optical properties of amorphous materials, and • the concepts for understanding practical devices and other applications of amorphous materials. Applications discussed in these volumes include transistors, solar cells, displays, bolometers, fibers, non-volatile memories, vidicons, photoresists, and optical disks. The editors of these volumes and the authors of each chapter are internationally-recognized experts in their respective fields. Taken together, these experts cover all the essential aspects needed for researchers entering the field of amorphous materials to succeed. As the editor of this three-volume set, I am indebted to them without whom this endeavor would not have been possible. Reference 1. Michael Pollak, European Phys. J. 227, 2221–2240 (2019).

P. Craig Taylor Colorado School of Mines 1 March 2020

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Preface by Volume Editor

Most people grow up with glass all around them, including art, household objects, and technology, but few people understand the complexity of this fascinating material. Oxide glasses such as silicates, phosphates, borates, represent the most widely used glasses with many common applications including windows, displays for phones and computers, containers, sealing, artificial tissue, and optical fibers. This volume addresses the major concepts, theories and technologies related to oxide glass. The introductory and broad approach is meant for engineers and scientists new to the field of glass. For more depth, the reader is encouraged to seek out references provided in the various chapters. Several textbooks on glass provide in-depth coverage on the technology of oxides glasses and scientific aspects and the reader should consult these valuable sources. Additionally, there are compendia on glass properties and now lots of data available online. In recent years, both glass science and technology have advanced substantially, and the present volume attempts to incorporate these advancements, in addition to providing a useful resource for engineers and scientists. The chapters are written by highly prominent and broadly respected researchers. They summarize the state-of-the-art scientific and technological understanding of oxide glasses, based on seminal research performed by established scientists. While major

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topics are covered, alert readers will find topics missing; the volume is not meant to be all-inclusive, but rather covers what are deemed to be most appropriate for an audience of young professionals, senior graduate students, and professionals changing fields.

Ivar Reimanis Colorado School of Mines

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Contents

Preface by Editor-in-Chief

v

Preface by Volume Editor

vii

Chapter 1.

Introduction to Oxide Glasses

1

Ivar Reimanis Chapter 2.

Characterization of Glasses

15

Mario Affatigato Chapter 3.

Nuclear Magnetic Resonance Spectroscopy of Oxide Glasses

55

Randall E. Youngman Chapter 4.

Contact Damage in Oxide Glass

99

Timothy M. Gross Chapter 5.

Aqueous Corrosion of Glass Dien Ngo and Seong H. Kim

ix

165

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Chapter 6.

Electrical Properties of Glass

199

Caio Barco Bragatto Chapter 7.

Glass Fiber Processing and Applications

223

Elam A. Leed Index

267

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CHAPTER 1

Introduction to Oxide Glasses Ivar Reimanis Colorado School of Mines 1500 Illinois St, Golden, CO 80401, USA

This introductory chapter is meant to give the reader a basic concept of what defines an oxide glass, including the key structural and topological descriptors, as well as a brief overview on fabrication. For more detailed information, the reader should consult textbooks on glass that provide in-depth coverage on the technology of oxides glasses [1] and scientific aspects [2, 3].

1.1. Definition of Oxide Glasses Glass is essentially a frozen liquid in the sense that it has a very similar structure to that of a liquid [4]. A glass is distinctly different from an amorphous solid, even though both possess no long-range structure: glass is a non-equilibrium structure, whereas an amorphous solid can exist in a metastable equilibrium state and experiences a discrete phase transition at a specific temperature [2, 5]. As a non-equilibrium state of matter, glass is always relaxing to another state, which in most cases is a super-cooled liquid state that is itself metastable; the super-cooled liquid will ultimately crystallize. At room temperature, the relaxation of an oxide glass has rarely been observed because the rate of relaxation is much smaller than the rate that can be experimentally measured. However, if the temperature is raised to a high enough temperature, specifically, near the glass transition temperature, Tg , the measurement time is on the same 1

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order of magnitude as the relaxation time and therefore relaxation is observed. A plot of enthalpy as a function of temperature illustrates these concepts (Fig. 1.1). As illustrated in Fig. 1.1(b), the glass transition actually represents a range of temperatures, though Tg has a specific value commonly defined as the temperature at which the viscosity of the supercooled liquid is equal to 1012 Pa-s. Tg is independent of the cooling rate, but the glass transition depends on the cooling rate. The dependence of the glass transition on the cooling rate is characterized by the fictive temperature, Tf . Tf , defined in Fig. 1.1(b), has a single value for a particular cooling rate since it is the intersection of the slope of the super-cooled liquid with the glass. While deeper thermodynamic meanings of Tf have been sought in the past, it has been shown that Tf does not connect uniquely to the local structure of glass, and therefore should be used with caution if one seeks to predict the non-equilibrium glass structure based on the thermodynamic liquid structure [6]. Though it is difficult to detect the structural differences for glasses cooled with different Tf , there are frequently property differences. From an engineering perspective, one might try to define oxide glasses in terms of their properties or the characteristics they exhibit. For example, many oxide glasses are brittle, electrically insulating, and transparent. However, these types of definitions are essentially stereotypes of glass and are dangerous in that they do not include all oxide glasses; many technologically important exceptions exist. The following scientific definition was recently developed by Zanotto and Mauro [4]: “Glass is a nonequilibrium, noncrystalline condensed state of matter that exhibits a glass transition. The structure of glasses is similar to that of their parent supercooled liquids (SCL), and they spontaneously relax toward the SCL state. Their ultimate fate, in the limit of infinite time, is to crystallize.” As a result, the glass-forming tendency of a material is dependent on the cooling conditions and the kinetic behavior that would otherwise lead to nucleation and crystal growth. An oxide glass is a glass in which oxygen is a principal component and not only participates in the covalent bonds that comprise the network, but is part of the fundamental structural unit making

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Introduction to Oxide Glasses

3

led oo c r e id sup liqu

glass time

Enthalpy (or Volume)

uid liq

crystal

Tg

Tm

Temperature (a)

Enthalpy (or Volume)

led oo c r d pe ui su liq

ol) fast co glass (

(s glass

ol) low co

Tslow f

Tfast f

Temperature (b)

Fig. 1.1. Enthalpy, which may be equivalently represented as volume, displayed as a function of temperature for a glass-forming liquid. (a) The vertical downward arrows convey the notion that glass is always relaxing toward the super-cooled and then the crystalline state. (b) A more detailed view of the region around Tg , for a glass cooled at two different rates. The fictive temperature, Tf , is defined for two glasses cooled at different rates.

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Fig. 1.2. Schematics of the structural fundamental unit for SiO2 (a SiO4 molecule, top left), a structural configuration showing the intermediate structure of SiO2 glass, and two boroxyl rings which are the fundamental units for B2 O3 . Various B2 O3 units form when network modifiers like alkali oxides are present.

up the structure. The most common oxide glass is silicate glass, based on the formula SiO2 , but there are others. Figure 1.2 provides depictions of fundamental units for SiO2 - and B2 O3 -based glasses. The fundamental unit for silicate glass is a tetrahedron with the chemical formula SiO4− 4 . Compositions of some common engineering oxide glasses are shown in Table 1.1. The compositions of glasses are frequently given in weight percent due to the practicality of formulating batches. However, since the raw ingredients for many glasses include compounds other than simple oxides, such as carbonates and nitrates, the compositions given in Table 1.1 will likely not be the same as the weight of the raw materials used to make the glass. The names of glasses are usually based on the largest mole percent oxide constituent. Silicates, based on the network former SiO2 , are the most

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Type Fused Silica Soda Lime Silicate

Example

SiO2

Al2 O3

B2 O3

Na2 O

K2 O

MgO

CaO

Li2 O

Fe2 O3

Melting crucible

100

—

—

—

—

—

—

—

—

Float (window) Container

71–73 73–74

0.1 1–2

— —

13–15 11–14

0.1–0.5 0.5–2.0

3–4 0–4

7–9 5–12

— 1.0

1.5 —

81 64 55

2 8 11

13 19 —

4 2 —

— 3 —

— — —

— — 21

— 1 —

— — —

54–57 65.0

14–15 24.5

8 —

1 0.1

0–0.3 0.1

1–2.5 9.5

20–21 0.2

— —

0.4 0.1

Borosilicate

E-glass S-glass

5

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Introduction to Oxide Glasses

Aluminosilicate Boro-aluminosilicate

Labware Sealing Display glass

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Table 1.1. Compositions (in weight percent) of several common silicate glasses.

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common. Soda lime silicate (Table 1.1) is the most widely used glass by volume. Fe2 O3 is usually not added intentionally, but is frequently an impurity present in sources of the batch materials. Oxide glasses exhibit a wide variety of properties and behaviors many of which derive directly from the structure and topology, and hence, glasses differ significantly from crystalline solids. While a thorough, unified description of the structure of oxide glasses does not yet exist, and it is debatable whether or not such a description is even possible, concepts of short-range and medium-range order help to explain certain properties and behaviors. 1.1.1. Structural Descriptions of Oxide Glass Glass does not exhibit long-range periodicity, but it does have a short- and intermediate-range structure. The groundwork for modern concepts of the structure of glass is based on the work by Zachariasen who developed a random network model and postulated empirical rules for oxide glass formation [7]. These rules basically state that the short-range structure in glass is the same as that of the corresponding crystal of the same composition. The short range refers to the nearest neighbor bonding and geometry and is generally described by the fundamental structural unit. The reader is encouraged to review his work [7] or consult other references describing this approach in more detail [2, 5]. In this framework, the main glass former is described as having a continuous random network (CRN) that connects the structural units. Intermediate-range structure refers to the interaction between neighboring fundamental units and typically has a length scale up to about 1 nm. Many insights into the structure of glass have been provided by molecular dynamic simulations, but they are currently not able to model realistic time scales for behavior such as melting or even laboratory scale experiments [8]. Instead, as briefly introduced below, topological constraint theory has been useful. SiO2 is termed a network former since it forms units (SiO4 molecules) that comprise the main network of the glass; like most network formers, SiO2 also forms glass by itself, for example, as pure SiO2 . Two other common oxide network formers are B2 O3 and P2 O5 . Figure 1.2 gives examples of the fundamental unit for

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Introduction to Oxide Glasses

7

SiO2 and B2 O3 glasses. Other glass oxide network formers include GeO2 , As2 O3 , Sb2 O3 , SnO2 , TeO2 , and PbO. It is emphasized that whether or not an oxide is termed a network former depends on its kinetic behavior during cooling; if the cooling rate is faster than the time over which diffusion and molecular rearrangements that lead to crystallization occur, then a glass is formed. Whether or not an oxide acts as a network former also depends on the oxygen–metal atomic bond strength: relatively strong bonds are needed to form glass. For oxides in which the oxygen–metal bond strength is weak, the metal cations do not typically participate in the network. Network formers that exhibit intermediate bond strength may enter an existing glass network but not form glass themselves. Al2 O3 is an example of such an intermediate oxide; in silicate-based glasses, aluminum ions enter the glass network, but Al2 O3 does not form glass as pure Al2 O3 . Large changes in properties may be realized when an intermediate oxide is added. For example, when Al2 O3 is added to a silicate to form an aluminosilicate, the use temperature of the glass may be substantially elevated. Various constituents may be added to the network former to modify either the glass melt properties or the physical/engineering properties or both. The constituents in glass are frequently classified into the following broad categories: (i) network (or glass) former, (ii) network modifier, (iii) intermediate, (iv) flux, (v) fining agent, and (vi) colorant. It is useful to make these broad categories, however the role of a particular constituent may be more complex than would be predicted by the broad categorization and there may be synergies. For example, the addition of Na2 O, a classic alkali network modifier, to a pure silicate glass is known to break up the glass, leading to a lowering of viscosity across all temperatures. However, if enough Na2 O is added, the continuous SiO4− 4 network disappears and eventually the viscosity rises with higher additions of Na2 O; such glasses are called invert glasses since the role of the modifier is essentially inverted. As another example, the addition of two network modifiers (e.g., MgO and CaO) has been shown to lead to nonlinearities, meaning deviations from simple additivity predictions, on various properties, most pronounced being transport properties, but

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also manifesting in mechanical properties. The origin of this mixedmodifier effect is still not well understood. Synergistic effects between different constituents may also complicate the role of an additive. For example, the function of Al2 O3 in alkali aluminosilicate glasses depends on the ratio of Al2 O3 to Na2 O. For ratios less than 1, Al2 O3 functions as a network former, but excess Al2 O3 behaves as a network modifier. This interesting behavior is dictated by the relative charge of the various cation constituents (Si4+ , Al3+ , and Na+ ) as well as their relative amounts, and the coordination of the aluminum ion with oxygen. Network modifiers are usually alkali and alkaline earth oxides. Common ones for silicate and borate glasses include Na2 O, K2 O, Li2 O, CaO, BaO, and MgO. The effects of cations on the structural framework of an oxide glass may be described by the modified random network (MRN) [9] in which the modifying ions form percolation channels within the framework. The MRN can predict various properties of glass qualitatively. Variations of the MRN exist; for example, a new modified random network (NMRN) model has been proposed for aluminosilicate glasses [10]. In the case of borate glasses, the addition of a network modifier may lead to an increase in the coordination of the boron atom, and unlike the case for silicates, the increase in coordination number actually leads to an increase in viscosity. As an alkali oxide is added to pure B2 O3 , the coordination number of boron changes from 3 to 4, and fundamental units making up the glass network may be comprised of several different borates, including diborates, triborates, tetraborates, and others, depending on the amount of alkali oxide. This short-range structure impacts various properties of borate glasses and the behaviors may be different from the corresponding effects observed in silicates. 1.1.2. Bridging Oxygens and Qn One of the most useful ways to describe the structural changes induced by changes in chemical formulation, for example, by the addition of a network modifier to a network former, is a methodology that quantifies the oxygen bonding. A bridging oxygen (BO) in SiO2

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Introduction to Oxide Glasses

9

is defined as an oxygen in the fundamental SiO4 tetrahedral unit that is bonded to a Si atom in a neighboring tetrahedron. Two BOs are seen in Fig. 1.2 for the case of silicate glass: they are the oxygens that are each bonded to two silicon atoms. A non-bridging oxygen (NBO) is therefore an oxygen ion that is only bonded to Si within its tetrahedron; it is akin to a dangling bond, though in actuality, since it is charged, it typically forms a weak bond with a cation (when cations are present in the glass, which is the case for most engineering glasses). The properties and behavior of oxide glasses are observed to depend on the fraction of NBOs. Pure SiO2 has virtually no NBOs, and as a result it has a melting point and higher viscosity than other silicates. It is common to describe the fraction of tetrahedra with 0, 1, 2, 3, or 4 BOs. In this approach, a tetrahedron with zero BOs (i.e., an isolated tetrahedron) is called Q0 and that with one BO is called Q1 , and so on, up to Q4 . Or more generally, a tetrahedron with n BOs is called Qn where n is an integer that varies between 0 and 4. Pure SiO2 glass is theoretically comprised of 100% Q4 where essentially every tetrahedron is bonded to another at all four corners. 1.1.3. Topological Constraint Theory The relation between network connectivity and the properties and behavior of glass has been expressed with topological constraint theory which affords a methodology that has particular use for materials with no long-range structure [11–13]. Topological theory offers many more possibilities for property and performance prediction compared to a simple structural description in which only the atomic positions relative to each other are given. In topological constraint theory, the properties are governed by the constraint of the movement of atoms. The constraints for oxide glasses are best described in terms of the linear movement between the network forming cations (M) and the bridging oxygen (O) or by angular movement either in the O–M–O group or the M–O–M group [14]. These constraints dictate properties like elasticity, plasticity, and viscosity, and may be used to determine whether or not a particular composition will form a glass. Quantitative prediction of temperature dependent properties have been recently made possible through major advancements of

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topological constraint theory [14]. A review of topological constraint theory for glass is given in [8]. 1.2. Fabrication Glasses for most applications are made by melting the raw materials. The melt typically exists at a viscosity of 10 Pa-s (100 Poise), and it needs to attain chemical homogeneity; inhomogeneties may facilitate the nucleation of crystals, something that is undesirable unless the goal is to make a glass-ceramic. After melting the glass is typically transferred to a location where it is formed to the desired shape, a process that takes place at a viscosity of about 103 Pa-s (104 Poise), the working point. The glass is then further cooled until the viscosity is high enough that the part does not deform under its own weight; this viscosity is known as the softening point and is defined to occur at 106.6 Pa-s (107.6 Poise), a value that arises from an agreed upon standard for oxide glasses. Figure 1.3 shows some of the key viscosity points for a soda–lime–silicate glass. A significant amount of data exists on the viscosity of glass, and empirical relations have been developed that predict these behaviors well at elevated temperature. Historically, the most commonly used was the Vogel–Fulcher–Tammann (VFT) equation which predicts the viscosity, η, as, a function of composition, x, and temperature, T [15]: log10 η(T, x) = log10 η∞ (x) − A(x)/[T − To (x)]

(1.1)

η∞ , A(x), and T0 (x) are empirical constants determined by fitting data to the equation. More recently, the Mauro–Yue–Ellison–Gupta– Allan (MYEGA) model developed by Mauro and co-workers [15] incorporates three well-established physical parameters, the glass transition temperature, Tg , the viscosity extrapolated to infinite temperature, η∞ , and the glass fragility, m, defined as a function of composition, x, as  ∂ log10 η(T, x)  m(x) = ∂(Tg (x)/T ) T =Tg (x)

(1.2)

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Introduction to Oxide Glasses

11

Fig. 1.3. An example curve showing viscosity as a function of temperature for a soda–lime–silicate glass.

Mauro and co-workers [15] showed the best description of viscosity may be given by log10 η(T ) = log10 η∞ + (12 − log10 η∞ )    m Tg Tg exp −1 . −1 T 12 − log10 η∞ T

(1.3)

While the VFT equation (Eq. 1.1) works well for many common glasses at many temperatures of interest, Eq. (1.3) is more accurate, especially at lower temperatures. 1.3. Future Directions in Research on Oxide Glass Though oxide glass is one of the oldest materials utilized by humans, many fundamental aspects are still unexplained. The lack of longrange order in glass adds a significant challenge in describing the structure of glass, and therefore, processing–structure–property

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relations remain elusive. The so-called materials science triangle, which connects processing, structure, and properties, is inherently more complex for glass compared with crystalline materials. Mauro et al. showed that there are many future challenges in glass research for the next decades [16]. These include quantitative descriptions of glass structure to enable structure–property relations; modeling of the liquidus temperature and viscosity; glass relaxation; glass fracture; chemical durability and surface behavior; acoustic properties; thermal conductivity; optical properties; glass formed under high pressure; heterogenous and nanostructured glass; and melting and processing. Significant advances in the fundamental understanding and engineering of oxide glass are expected to continue in the coming decades.

References 1. Shelby, J. E. (2005). Introduction to Glass Science and Technology, 2nd Ed. (Cambridge, The Royal Society of Chemistry). 2. Varshneya, A. K., and Mauro, J. C. (2019). Fundamentals of Inorganic Glasses, 3rd ed., Elsevier. 3. Doremus, R. H. (1994). Glass Science, 2nd Ed. (New York, NY, John Wiley & Sons, Inc.). 4. Zanotto, E. D., and Mauro, J. C. (2017). The glassy state of matter: Its definition and ultimate fate, Journal of Non-Crystalline Solids, 471, pp. 490–495. 5. Gupta, P. K. (1996). Non-crystalline solids: Glasses and amorphous solids, Journal of Non-Crystalline Solids, 195, pp. 158–164. 6. Mauro, J. C., Loucks, R. L., and Gupta, P. K. (2009). Fictive temperature and the glassy state, Journal of the American Ceramic Society, 92, pp. 75–86. 7. Zachariasen, W. H. (1932). The atomic arrangement in glass, Journal of the American Chemical Society, 54, pp. 3841–3851. 8. Mauro, J. C. (2011). Topological constraint theory of glass, Ceramic Bulletin, 90, pp. 31–37. 9. Greaves, G. N. (1985). EXAFS and the structure of glass, Journal of Non-Crystalline Solids, 71, pp. 203−217. 10. Allu, A. R., et al. (2018). Structure and crystallization of alkaline-earth aluminosilicate glasses: Prevention of the alumina-avoidance principle, Journal of Physical Chemistry B, 122, pp. 4737–4747.

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11. Thorpe, M. F. (1995). Section 4. Dynamics of glassy systems. Bulk and surface floppy modes, Journal of Non-Crystalline Solids, 182, pp. 135–142. 12. Gupta, P. K., and Miracle, D. B. (2007). A topological basis for bulk glass formation, Acta Materialia, 55, pp. 4507–4515. 13. Mauro, J. C. (2018). Decoding the glass genome, Current Opinion in Solid State and Materials Science, 22, pp. 58–64. 14. Wilkinson, C. J., Zheng, Q., Huang, L., and Mauro, J. C. (2019). Topological constraint model for the elasticity of glass-forming systems, Journal of Non-Crystalline Solids, 2, p. 100019. 15. Mauro, J. C., et al. (2009). Viscosity of glass-forming liquids, Proceedings of the National Academies of Science, 106, pp. 19780–19784. doi:10.1073/pnas.0911705106 16. Mauro, J. C., Philp, C. S., Vaughn, D. J., and Pambianchi, M. S. (2014). Glass science in the United States: Current status and future directions, International Journal of Applied Glass Science, 5, pp. 2–15.

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CHAPTER 2

Characterization of Glasses Mario Affatigato Coe College, 5008, 1220 1st Ave NE Cedar Rapids, IA 52402, USA

2.1. Introduction The characterization of glasses can be separated into two categories: the determination of properties and the study of the structure. The determination of properties poses a relatively simple problem where a particular glass is used to measure one or more properties by looking at its interactions with a stimulus. So, for instance, the glass transition temperature can be determined using a differential scanning calorimeter (DSC). This instrument subjects the sample to a source of heat, causing it to increase in temperature. By measuring the power needed to raise the temperature (when compared to a blank), calculations of the enthalpy and of the threshold temperatures can be obtained. In this chapter, we will highlight property measurement techniques that are widely used in the field of glass science. The study of the structure, on the other hand, is significantly more complex. Disordered materials present a difficult challenge in that 15

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a full and complete knowledge of the structure requires knowledge of the location and bonding arrangement of each and every atom in the sample. In crystalline materials, a simple determination of the unit cell allows a researcher to determine — by symmetry — the atomic arrangement of all atoms in the material [1]. Scientists and engineers studying glass networks do not have the luxury of long-range symmetry, creating a far more difficult problem. It is therefore the case that structure measurements rely on either knowledge of short-range order (SRO; at the level of molecules and their nearest neighbors), or averages over billions of atoms and molecules. In this chapter, we will present examples of both approaches. Yet the researcher should remain aware that any measurement of the structure of an amorphous material suffers from a loss of knowledge — always — and thus can never be used as definitive proof of a particular arrangement. The combination of multiple techniques is preferable, though, again, to be interpreted soberly and with skepticism. The field of glass science is a subset of the larger field of materials science, and is continuously evolving. The number of techniques applied to the characterization of materials now easily reaches into the hundreds, and no book chapter can hope to describe them all. We will therefore restrict our content to commonly used methods — of the kind a starting researcher setting up a lab may need — and seek to provide information useful to such students and researchers in the early stages of their careers. As this is a chapter surveying common techniques, we will sacrifice heavy theoretical/mathematical content, and provide more of a physical and practical guide. 2.2. Property Characterization The characterization of the properties of glasses is common, and used for a variety of reasons. It can be carried out as a means of quality control, as a way to attain a specific behavior in a given sample, or even as a way to test a particular structural model. Here we reiterate that a positive test of a model does not guarantee that the model is correct under all circumstances. Rather, it points to the idea that the model is simply consistent with that particular property

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measurement. On the other hand, a negative result — where the data contradicts the predictions of the model — clearly indicates that the model is flawed. Among the most common property measurements carried out in a traditional glass research laboratory we count those that fall in various categories: thermal properties, optical properties, physical and mechanical properties, transport and electrical properties, and, occasionally, chemical and surface properties. For this chapter, we will focus on common thermal properties measured via calorimetry and basic optical properties like the index of refraction. For structural techniques, we will look at Raman and Fourier transform infrared spectroscopy (FTIR) vibrational spectroscopies, as well as X-ray diffraction (XRD). Finally, for surface microstructure characterization, we will describe scanning electron microscopy (SEM). These choices were made based on equipment often available in glass laboratories (or university user facilities) around the world. 2.2.1. Differential Scanning Calorimetry 2.2.1.1. Theory and Background In any glass research laboratory, a student is likely to encounter equipment designed for calorimetric measurements. These commonly include a DSC, a differential thermal analyzer (DTA), and/or, depending on the lab, a thermogravimetric analyzer (TGA), or a simultaneous thermal analyzer (STA). These are often grouped under the heading of a thermal analysis suite, but the author will focus this section on one of the popular characterization tools, differential scanning calorimetry. The key element that distinguishes DSC from the other thermal techniques is that it measures energy or, more correctly, energy differences (hence differential). In one of the more common instrumental setups [2], a heat-flux DSC will have two small chambers. One contains the sample, embedded in a crimped aluminum pan. The other chamber has an empty pan, and serves as a reference. Ideally, both pans would have the same mass, so that the only difference between the chambers is the actual sample. Each chamber tracks

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both the heating power delivered to it, and its temperature. The instrument will then begin to heat up both chambers, attempting to keep the temperature equal in both. At the beginning of a scan, the only difference is the mass of the sample in the sample chamber, which in turn requires more energy for the sample chamber. This creates a discrepancy in the power delivered to the chambers, and this can be tracked from the difference in the two power inputs (viz., sample minus reference). In this arrangement, when the sample chamber “sucks in” more and more power, as happens when the sample undergoes an endothermic phase transition (like at the glass transition temperature Tg ), a graph of the power difference (properly called a thermogram) will show this event. Physically, this simply represents the need for increased energy necessary to break bonds and undergo the phase transition. Conversely, exothermic events (like glass crystallizations) release energy, and diminish the need for more external power to drive up the temperature. The graph also shows this, with the trend line moving in the opposite direction than in the previous case. In most instruments, the user can select whether an exothermic event moves the thermogram line up or down in the software settings. For a glass researcher, the use of a DSC is critical. Thermograms can be used to measure the glass transition (Tg ) and crystallization (Tx ) temperatures for a given sample (assuming that they are within instrumental range). But they can also help identify traces of water in the sample [3] (with an exotherm at 120◦ C–160◦ C); phase separation in a glass (sometimes visible as two different Tg “steps” [4]); thermally unstable glasses (normally shown by a small gap between Tg and Tx ); thermal history effects (shown by the overshoot of the curve after the Tg step [5]); nucleation kinetics [6]; and other thermal subtleties. Much of this can be attained in a single scan, though heat-flux instruments are slower (and offer more sensitivity). DSC can also be used for more advanced analysis. Careful measurement of the sample mass, coupled with the use of the thermogram data (with and without samples, but with pans) and the use of the heating rate can allow for the calculation of the specific

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heat at constant pressure. The specific heat is then given by [2]   1 dH 1 1 dH 1 dH dt = (2.1) = Cp = m dT P m dt dT m dt k where k is the constant heating rate, H is the heat flow (y-axis of thermogram), and m is the mass of the sample. Thus, the specific heat at any point in the thermogram can be calculated from the (baseline subtracted) value of dH/dt at that point, the mass of the sample, and the heating rate. More accurate measurements — which use sapphire calibrations, and are known as three-curve methods — can also be run. 2.2.1.2. Equipment In the heat-flux design, platinum cups sit on top of constantan disks, which are electrically heated (see Fig. 2.1). The aluminum pans inside the platinum cups can then be heated at a constant rate, which in modern instruments can go from 0.01◦ C/minute to 300◦ C/minute or even higher. Oxidation is prevented by the use of a purge gas, and the temperature is measured by chromel–constantan thermocouples. More modern instruments utilize a double-furnace design, ensuring that both the sample and the reference chambers are heated truly

Fig. 2.1. Sketch of the working arrangement for a heat-flux DSC. The reference and sample cups receive energy from heat resistors, and the temperature is measured by the thermocouples. Figure courtesy of Hitachi Corporation.

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independently, and thus the power difference is a direct measurement of the true electrical power being delivered to each chamber. DSC instruments require both referencing and a baseline calibration. Referencing is the use of standards (like indium and zinc metals) to correctly calibrate the temperature axis. The baseline calibration attempts to make the trace as horizontal as possible for the case where the sample is also an empty aluminum pan, thus making both chambers identical. Normally, referencing is only required occasionally (monthly, say), whereas baseline calibrations are done more often. Older instruments benefit from daily baseline checks and calibrations. Finally, when performing specific heat calculations, it is also useful to perform a benchmark run using sapphire spheres or an equivalent standard. 2.2.1.3. Modulated DSC In modulated DSC (MDSC), the physical configuration of the instrument (heat flux) is similar, but the heating operation is quite different. The heating profile differs in that a sinusoidal variation is superimposed on the traditional heating ramp. Thus, as the temperature increases, the sample is subject to a quick series of small rises and drops in temperature, centered around the main heating ramp. This allows for the separation of a heat capacity component (normally associated with reversible phenomena) and a kinetic component (normally associated with irreversible transitions). Thus, crystallizations would appear in the kinetic component, while a change in the specific heat before and after Tg would appear in the heat capacity component. 2.2.1.4. Examples The use of DSC in a glass research laboratory spans many objectives. Aside from quality control measurements — ensuring that the samples does, indeed, have a glass transition temperature — researchers can use it to provide an early test of structural models. Figure 2.2 shows the changes in the glass transition temperature for three different borate glass families, containing barium, sodium, and lithium as modifiers. The x-axis shows R, the molar ratio of modifier

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Fig. 2.2. Glass transition temperatures for three borate families with different modifiers. R is the molar ratio of modifier to boron oxide. Data and figure courtesy of the author.

to boron oxide (viz., mol% Li2 O/mol% B2 O3 ). One can note the rapid increase early on, followed by a peak at approximately R = 0.5, and a slower decrease up to ca. R = 1.6. This can be explained by the increase in the coordination of the boron units, which grows from 3 to 4 before returning to 3, accompanied (after the coordination begins to decrease) by a growing number of non-bridging oxygen anions. In general, the depolymerization of the glass network results in a drop in the Tg values, thus providing a test for structural changes the glass scientist may believe are occurring. For a more advanced example, the reader can turn to Fig. 2.3. In this case [7], the total heat flow (black line) normally measured in standard DSC, yields no indication of a glass transition temperature, an endothermic event. But the use of a MDSC permits the researcher to separate out the reversing heat flow (red line), and pointing to a very clear endothermic Tg event at T = 161◦ C. 2.2.1.5. Advantages, Disadvantages, and Warnings Though the use of DSC (and other thermal techniques) is widespread, care must be taken with the measurements. Among the advantages of DSC is its relatively low cost for instruments that go up to 600◦ C; extremely accurate results; and good software for calculation and analysis. Disadvantages include the relatively high cost of supplies;

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Fig. 2.3. Modulated DSC thermogram of a Ge2Sb2Te5 chalcogenide glass. Figure from [7], used under a CC BY license.

slow rate of data capture; the need for recurring calibration; and a delicate operation. The latter comment refers to the fact that accurate measurements require care, like placing the aluminum pan in the very center of the platinum chamber. But there are other nuances to the operation of a DSC. Young researchers are warned to know the nature of their samples before they run them. A glass sample that foams, for instance, may overflow the aluminum pan and contaminate the chambers and the thermocouples. This, in turn, can affect subsequent measurements in unpredictable and changing ways, even after cleaning. Gas evolution can also lead to contamination. Another often underestimated factor is the heating rate. Faster rates lead to quicker measurements, of course, but comparisons to scientific papers in the literature should only be done for very similar rates. Thought should be given as to the nature of the thermodynamic and kinetic events one is attempting to measure. For glass research, 10◦ C/minute or slower is considered normal, though rates of up to 40◦ C/minute have also been reported in the literature. Equally important is the idea that the researcher must know the thermal history of the sample, as that can affect the result. This can be set (for good glassformers) by running the DSC on a scan up-scan down-scan up cycle, which defines a specific thermal history.

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2.2.2. Index of Refraction 2.2.2.1. Theory and Background Measuring the (linear) index of refraction, n, of a glass remains an important parameter in optical applications, and is often essential for industrial glasses. Traditionally, the index of refraction of traditional glasses can span from 1.4 (for soda–lime–silicates) to 2.2 or higher (for glasses containing heavy metal oxides). To the glass scientist, the index is important for several reasons. A glass with a high index becomes quite reflective (“brilliant”), and is valued by glassware customers. The light-bending ability of a lens is directly proportional to the index, as is the resolution of microscopes. Along the same lines, the index depends on the wavelength of the light probing the material, and thus affects the dispersion of prisms. Scientifically, the index can be used to trace changes in the network, often as a proxy for density changes (though the relationship in glasses is often not linear). Total internal reflection is also dependent on the indices involved. A high index also usually points to a high third-order nonlinearity, useful in some specific optical applications. Returning to light reflection from glasses, the reflectivity can be calculated from Maxwell’s equations (and the proper boundary conditions for fields that are parallel and perpendicular to the plane of incidence, PoI). This analysis [8] yields reflectance coefficients (RT E , RT M ), and they are known as the Fresnel equations: ∗ For TE (transverse electric polarization = light perpendicular to the PoI) 2   cos θ − n2 − sin2 θ  (2.2) RT E = cos θ + n2 − sin2 θ ∗ For TM (transverse magnetic = light parallel to the PoI) 2   −n2 cos θ + n2 − sin2 θ  RT M = n2 cos θ + n2 − sin2 θ

(2.3)

where n is defined as the ratio of the index of the second medium to the index of the first, and θ is the angle of incidence, measured with

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respect to the vertical axis. So, if we are considering light coming in at normal incidence, entering a standard glass from air, we would get n = 1.5/1 = 1.5, and θ = 0◦ . This would yield equal values for RT E and RT M , namely RT E = RT M = (0.5/2.5)2 = 0.04, or 4% of light reflected at the interface between the media. This can of course be altered by the application of anti-reflective coatings. 2.2.2.2. Equipment There are multiple ways in which glass scientists can determine the index of refraction to a high degree of precision. A very inexpensive method involves the Abbe refractometer, shown in Fig. 2.4: In the Abbe arrangement, the glass sample is placed on top of a glass prism, using a high-index fluid to ensure good contact. The shadow boundary is moved until it is centered in the targeting eyepiece. At that moment, the index can be read off a scale typically also shown in the eyepiece. This setup is capable of measuring the index to two decimal figures, in the range 1.47–1.87, and it is easy to operate. Negatives include the use of liquids, and the fact that the

Fig. 2.4. Instrumental sketch of an Abbe refractometer. From www. refractometer.pl/Abbe-refractometer, figure courtesy of ChemBuddy.

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Fig. 2.5. Sketch of the instrumental arrangement for prism coupling. Figure courtesy of Metricon, Inc.

light source is typically a bulb of undefined wavelengths. A sodium source can be used instead. A second method is ellipsometry. This makes use of the Fresnel equations, sending polarized light to strike the sample, and then measuring the polarization state of the outgoing light. More specifically, the change of phase (Δ, in degrees) and of amplitude (expressed as Tan(Ψ), where Ψ can range from 0◦ to 90◦ ), allows for the calculation of a maximum of two simultaneous optical constants, like film thickness and index of refraction. Normally, the results are limited to one-wavelength, but more expensive multi-wavelength tools are available. Drawbacks include the cost, and the need for data analysis with some prior knowledge of the sample. Finally, a modern third method (see Fig. 2.5) involving prism coupling has also arisen. In this method, laser light is coupled to the sample, and the critical angle for total internal reflection is measured. This provides a direct measurement of the index, and multiple laser sources can be used to measure values at various wavelength. Advantages include high accuracy (±0.0005), wide index range, and speed, though the cost is comparable to ellipsometry. The sample must also couple well to the prism, and withstand mechanical stresses that arise during the coupling. 2.2.2.3. Example Figure 2.6 shows the application [9] of an (interferometric) refractive index measurement to a glass spicule made by the deep-sea sponge

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(b)

(c)

Fig. 2.6. Application of a refractive index measurement to a spicule created by a sea sponge. (a) Shows the microscopic image of the spicule in cross section; (b) displays the longitudinal cut; and (c) is a graph of the refractive index as a function of radial position. Figure from [9], with permission from Springer Nature.

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Euplectella. In part (c) of the Figure, it can be seen that the spicule is characterized by a high-index core surrounded by a low-index cladding, identical in design to a standard optical fiber. Interestingly, the lamellar design (best seen in part (b)) makes the fibers quite strong against crack propagation, and the ability of the sponge to make these materials at ambient temperature also permits for the incorporation of sodium ions without devitrification. 2.2.2.4. Advantages, Disadvantages, and Warnings Measurements of the index of refraction (and of similar properties, like density) are often overlooked, even though they represent a powerful and often inexpensive technique. Yet properties like the refractive index remain of great value to groups concerned with fibers and imaging systems [10]. 2.3. Structure and Surface Characterization The characterization of the structure of glasses is clearly one of the key measurements carried out in laboratories across the world today. Often, the researcher is interested in trends — specific changes in the glass network that result in subsequent changes in properties. A clear understanding of the relationship between the structural changes and the property behavior — even if this relationship is empirical — can provide important clues for the scientist or engineer seeking to design glasses for a particular application. At a more fundamental level, a deep insight into the structure (especially at the atomic level) goes to the very heart of the millennia-old question of how glass is constituted. Often times the various characterization techniques can be classified according to the length scale over which the measurements occur. Raman spectroscopy, for instance, looks at the length scales of individual bonds and tightly knit molecules (like rings). Nuclear magnetic resonance (NMR) and neutron scattering can span from SRO to the beginnings of intermediate-range order (IRO), and no technique can determine the long-range order common in crystals as it is non-existent in glass. For the purposes of this chapter, we will

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focus on vibrational spectroscopy (Raman and FTIR), on NMR, and on X-ray techniques at the introductory level. The choice was made based on equipment often available in glass laboratories around the world. 2.3.1. Raman Spectroscopy 2.3.1.1. Theory and Background The Raman technique falls in the category of a vibrational spectroscopy. This means that light is used to probe the vibrations between atoms, and in larger molecular arrangements. It is more properly understood as a scattering phenomenon, making the interaction between the light and the atoms extremely fast. The electric field of the electromagnetic wave (light) interacts with the electron cloud and the natural resonant frequency of the molecule (bond). This interaction creates [11] a dipole moment P which can be expressed as follows: P = α0 E0 cos 2πv0 t   1 ∂α qE0 [cos{2π(v0 + vm )t} + cos{2π(v0 − vm )t}] (2.4) + 2 ∂q 0 In Eq. (2.1), α0 is the polarizability, q is the nuclear displacement (i.e., the oscillating position), and νm is the resonant frequency of the molecule. The light frequency is ν0 . The second and third term show output light with a frequency equal to the sum (or difference) of the two frequencies. By convention, the sum term is labeled the anti-Stokes shift, while the difference term is named the Stokes shift. The researcher need only measure one of the two shifts, and, since the Stokes shift yields larger peaks due to vibrational electron state populations, that is the one normally measured in the laboratory. Equation (2.4) also highlights some of the important actors of Raman spectroscopy. As the derivative of the polarizability (α) is a term, every molecule will have a different response to the light stimulus. In general, vibrational spectroscopy is not quantitative, as different environments in the glass network will impact the strength of the interaction between the light and the molecule. Though a

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careful use of references — and cross comparisons with quantitative techniques — can overcome this, it is rarely done in practice. Finally, selection rules make Raman especially sensitive to symmetric vibrational modes. It is also worthwhile to note that the Raman scattering intensity (IR ) is given by [11] Eq. (2.5). In the equation, ν0 is the laser light frequency, νj is the frequency of the jth mode, Qj the displacement, and αj is the polarizability of that mode. The important factor to remember is the strong dependence of the Raman scattering on the fourth power of the laser frequency. That would seem to indicate that instruments ought to use lasers that produce blue, violet, or even UV light (as these have the shortest wavelengths and longest frequencies), but this is complicated by the fact that these laser sources can also produce the strongest luminescence, a negative outcome. In cases where a glass has a weak Raman response, it might be useful to attempt the measurement with a different, shorter wavelength laser (e.g., going from 785 to 532 nm, two common Raman laser sources). IR = μ(v0 ± vj )4 α2j Q2j

(2.5)

2.3.1.2. Equipment Most Raman instruments can be analyzed in terms of a few simple primary components, exquisitely aligned. These are the laser source, a beam splitter, a lens system (often a microscope’s objective lenses), a notch filter, a spectrometer (often a high-resolution grating), and a light detector (often a CCD array). In operation, the laser light reaches the sample, and some of it is scattered upward (back toward the objective). The scattered light is made up of Rayleigh light of unchanged wavelength, as well as Raman Stokes and anti-Stokes photons. The notch filter cuts out a great portion of the Rayleigh light, and only the Stokes light is permitted to reach the spectrometer and the CCD array. The spectrometer spreads out the light (recall that the wavelength range is extremely narrow), and the different wavelengths hit different pixels in the CCD array. The array integrates the signal over a time interval set by the user, and displays it in the computer screen as a spectrum.

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Fig. 2.7. Sketch of a Raman system. Image from Sciencefacts.net.

Changing the laser source — a common procedure — requires replacing the notch filter and some realignment. Some laboratories may also use FT-Raman, often as an attachment to an IR system, but this type of system uses near IR light, making it less efficient for Raman scattering production (see Eq. (2.5)). 2.3.1.3. Micro-Raman Confocal Spectroscopy The addition of a spatial filter — a pinhole in the optical setup — provides the user with even more capabilities [12]. On top of being able to use the microscope’s focusing abilities, a researcher can also add confocal measurements to the toolkit. In a confocal measurement, only light coming from a particular depth within the sample (± a couple of microns) is allowed to proceed to the spectrometer and CCD. The researcher can then look at a z-slice of the sample, and even produce depth maps of the glass (though depth resolution must be carefully considered [13]). This is especially important in cases where the surface has a film, or where structure and/or composition is also dependent on the depth. Corroded glass, an area of great importance to scientists that study glasses for nuclear waste disposal, can be analyzed [14] to see how far water has penetrated over a period of centuries and millennia. Laserwritten crystal lines also benefit from the spatial resolution [15].

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In the case of films, the technique is even more important, as a misfocused laser spot may sample the substrate instead of the film layer. 2.3.1.4. Examples Figure 2.8 shows the penetration [16] of below-surface water on a Li–K borate glass, down to a depth of ca. 50 μm. Though water is not directly detectable, the conversion of boric oxide to boric acid, which yields a signature peak at 880 cm−1 , can be tracked inside the glass. The ability to determine the penetration depth is important to understanding the durability of the glass. Finally, Fig. 2.9 illustrates the power of micro-Raman. Raman spectra [17] of various sodium borosilicate glasses are shown, and the comparison is drawn between areas that were indented (red lines), and areas that were never indented (gray lines). The authors believe that the shift of the first (350–460 cm−1 ) Raman peak to higher frequencies indicates a decrease of the angle in structural bridges. Indentation in the case of borate-rich glasses yields a faster breakup

Fig. 2.8. Penetration of water (as noted by the presence of boric acid) in a lithium–potassium borate glass. Figure courtesy of the author.

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(a)

(b)

Fig. 2.9. Comparison of Raman shifts of a family of sodium borosilicate glasses before (gray lines) and after (red lines) indentation. (a) Shows silica-rich, while (b) displays borate-rich glasses. Figure from [17], with permission from Elsevier publishing.

of borate rings containing four-coordinated borons than in boroxol rings (which only contain three-coordinated borons). 2.3.1.5. Advantages, Disadvantages, and Warnings The advantages of Raman spectroscopy are many. It provides a reasonably quick and normally inexpensive way to identify molecules and bonding arrangements in glasses. The technique is mostly insensitive to water, making atmospheric humidity less important. Because of its long history, an extensive list of references can be found on the use of Raman in glasses, making peak identification easier. Modern instrumentation allows for microscopic Raman, leading to the identification of species in areas with a diameter of 2 μm or less. The use of polarized light can permit the researcher to measure the depolarization ratio, and thus get insights into molecular symmetry. Finally, the use of laser light also allows for Raman

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(c)

Fig. 2.10. Effect of a temperature correction on the spectrum of a commercial silicate glass. (a) shows the original spectrum; (b) applies a baseline correction; and (c) shows the frequency-temperature correction. Figure from Ref. [21], with permission from Springer Nature.

measurements under extreme conditions [18, 19], like in a highpressure diamond cell. The disadvantages of Raman are few but important. The use of lasers can lead to the appearance of fluorescence, swamping the Raman signal. This is often avoided through the use of instruments with multiple laser sources (wavelengths). A suitable laser color can then be found to minimize the fluorescence emission, normally by moving toward the red region of the spectrum. If the laser power is too high, sample damage can occur, and this is particularly severe for glasses that show strong light absorption. Finally, though the cost of Raman equipment is relatively low when compared to other techniques, it is not small for a research grade instrument. Any researcher ought to be aware of the ways in which an instrument or technique can fool the user into false insights. For Raman, the warnings are several. Samples ought to be checked after the measurement to ensure that they were not damaged (and thus that the spectra were not modified during the actual measurement). When looking at peaks near the low wavenumber end (say, in the region between 50 and 200 cm−1 ), special care should be taken. Temperature corrections should be carried out [20]. Figure 2.10 shows the difference [21] between an uncorrected spectrum and a corrected one. In this region, Rayleigh filters are present, and what appears to be a peak may actually be a rising part of the spectrum suddenly cut off by the filter. Manufacturers, at times, exaggerate the depth resolution of the confocal microscope [13]. Finally, Raman users

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should avoid the temptation of correlating peak sizes with species abundance, though compositional variations are often used to discuss network changes in a qualitative manner. 2.3.2. Fourier Transform Infrared Spectroscopy 2.3.2.1. Theory and Background FTIR is another technique under the common heading of vibrational spectroscopy. Though less used in modern glass research, it can provide a very useful complement to the data obtained from Raman measurements. More specifically, FTIR looks at more asymmetric vibrations in the material. In this chapter, we are focusing on FTIR and not its less-common variant, wavelength-dispersive IR spectroscopy. In the FT setup, IR light over a wide range of frequencies (normally from 100 to 4000 cm−1 ) is combined through the use of an interferometer. This results in a time-pulse (an interferogram pulse) that is sent toward the sample. This pulse is modified after traversing (or reflecting from) the sample, and the new shape of the pulse is deconvoluted by carrying out a reverse FT in the appropriate software. The result is a spectrum of absorption as a function of frequency, where any absorption bands point to molecular interactions with the IR light. Normally, a single scan of the glass sample can be carried out quickly — this is the key advantage of the FT setup — and thus it is often the case that research spectra actually consist of an average of perhaps 256 scans. It is worthy of note that the signal-to-noise ratio (SNR) is proportional [22] to the square root of the number of √ scans N , so SNR ∝ N . A high number of scans is therefore not unwarranted. Maxwell’s equation for an electric field in an absorbing medium gives us a way [23] to express the interactions of IR light (or any light) with matter. x

x

Ey = E0 e−iω[t−n(v) c ] e−ωκ(v) c

(2.6)

Here we assume that light is traveling in the z-direction while the electric field is oscillating in the y-direction. In the equation, ω is the

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angular frequency, n (v) is real part of the index of refraction (as a function of frequency), and κ (v) is the imaginary part of the index. Also, x is the position, c is the speed of light, and t is the time. The first exponential term is oscillatory, and it describes the light being transmitted through the medium. The second exponential term shows a decay in the strength of the electric field, and physically it represents the absorption of the light by the glass. Normally, however, it is the intensity of the light that is measured, and this is calculated from the square of the electric field, yielding I = Ey2  = I0 (v)e−α(v)x

(2.7)

And this in turn gives us an absorption coefficient α equal to 4πvκ(v) = 4π¯ v κ(¯ v) (2.8) c Equation (2.8) shows the coefficient expressed in terms of the usual frequency v and also in terms of the wave number v. It is also common for instruments to give the results of the data acquisition in terms of the absorbance A(v) (or transmittance T (v)) and the sample thickness d, that is, α(v) =

A(v) =

α(v)d 2.303

I(v) = e−α(v)d T (v) = I0 (v)

(2.9)

2.3.2.2. Equipment Though the layout of a FTIR spectrometer may look complicated, the actual measurement is fairly simple. In Fig. 2.11, we can see that the interferometer accepts the light from a broadband IR source and combines the wavelengths into a time-domain package, which is sent toward the sample via a suitable mirror. The laser in the upper left is simply for alignment and has no impact on the measurement. Once the IR light pulse (interferogram) reaches the sample, a couple of experiments are possible. If the sample’s IR absorption is low enough (or the sample is thin enough), the pulse can be simply sent through the glass samples. If, on the other hand, not enough light makes

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Fig. 2.11. Layout of a FTIR spectrometer, courtesy of Thermo Fisher.

it through the material, a reflection setup is advisable. Accessories would then allow for a measurement of the reflected light at a specified (or even variable) angle, and the new, reflected pulse is sent on toward the detector. The detector then measures the input of light as a function of time, essentially recording the new interferogram. The FT of the interferogram — typically carried out within the operating software — results in a plot of absorption versus light frequency. When using a reflection setup, a further mathematical step must be carried out. To attain a comparable absorption graph, one must perform a Kramers–Kronig transformation, which generates nuances we will discuss later.

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2.3.2.3. Example Figure 2.12 shows the use of FTIR spectroscopy on a set of sol– gel derived bioactive glasses that have been “foamed” to produce scaffolds [24] for applications in tissue engineering. Different sintering temperatures (Ts ) were used to attain various mesoporous structures, and the foams were then exposed to simulated body fluid (SBF) at 37◦ C for 8 hours and for three days. In particular, the objective was to monitor for the formation of the hydroxycarbonate apatite (HCA) layer. The signature bands, in this case, are the peaks at 571 and 602 cm−1 , which correspond to P–O bending vibrations present in crystalline HCA. Figure 2.12(a) shows that this happened at Ts = 600◦ C and (somewhat) at Ts = 700◦ C for the 8-hour experiment, while Fig. 2.12(b) shows that HCA formed on all scaffolds. 2.3.2.4. Advantages, Disadvantages, and Warnings FTIR has several advantages. In general, FTIR spectrometers tend to be low cost, and they make individual measurements at a high rate. Data analysis — including peak deconvolution — is reasonably

(a)

(b)

Fig. 2.12. (a) Shows the FTIR spectrum of foams subjected to SBF for 8 h, whereas (b) shows the foams after 3 days of SBF exposure. The foams were kept at 37◦ C and 175 rpm, and sintered at the temperatures shown. Reprinted with permission from Ref. [24], courtesy of Elsevier publishing.

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straightforward. Thus, FTIR has been used for structural studies of glass families [25–29], with a high rate of success. Disadvantages include the aforementioned sensitivity to water; the difficulty in measuring strongly absorbing samples in transmission (and many glasses fall in this unfortunate category); and the inability of doing micro-scale measurements. Though some FTIR instruments now have IR microscopes to address the latter issue, the use of IR light creates a diffraction-limited spot significantly larger than that of a Raman spectrometer, typically 10–15 μm. Nuances are also extremely important. The use of the reflectance accessories requires care in an effort to avoid artifacts in the acquired spectra. Modern instruments can have a very wide range of frequencies (extending from 400 cm−1 to as high as 7000 cm−1 ), and this improves the accuracy of the Kramers–Kronig transformations. Older instruments, though, can only span from 100 to 400 cm−1 , and this can affect the spectral shape. Reflectance measurements are typically done with accessories, which can mean that different researchers use different angles of incidence, and thus create differences in the spectra. Finally, we note that new researchers and students should pay close attention to the condition of the glass being measured, and to sample holders and sample mounting. Anything in the path of the IR light will affect the spectra, and the author has seen glass spectra that also show (organic) traces of Scotch tape. 2.3.3. X-Ray Spectroscopy 2.3.3.1. Theory and Background Standalone lab X-ray equipment is mainly used for the analysis of nano- and micro-crystals in glasses. Researchers normally would like to see the complete absence of Bragg diffraction peaks in the glass samples unless, of course, the goal is to create glassceramics. When the crystalline volume fraction is sufficiently high (normally a few percent), the Bragg peaks will begin to rise above the amorphous, diffuse background. The peaks can then be used to identify the crystal phase(s) present in the glass matrix. A simple integration of the peaks and of the overall spectrum allows for

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the calculation of the crystalline volume fraction. Further analysis of the width of the peaks — done by proper fitting of the peaks from a background-corrected spectrum and the use of the Scherrer equation — can then yield an estimate of the size of the crystallites. For the glass scientist, XRD can help characterize micro-crystals [30] and phases in bioactive glass [31]. The equipment normally used in a glass research lab is a powder diffractometer. This instrument averages over the many crystal orientations present in a crushed and powdered sample. It is ideal to have a large number of grains to attain a good statistical distribution, and thus sample preparation is fairly important. In the author’s experience, the consistency of beach sand grains is too coarse, and it is preferable to get the texture of powdered sugar (confectioners’ sugar). 2.3.3.2. Synchrotron X-Ray Measurements Though synchrotron X-ray measurements are well beyond the scope of a commonly available lab setup, it is critical to note their importance and usefulness. These measurements include structural studies using elastic scattering from X-rays that can span high momentum transfers (Q) and X-ray absorption in various configurations (XAFS, EXAFS, XANES). To the glass scientist, the first set of measurements allow for direct probing of the glass structure [23], and provide a very nice complement to other structural techniques like NMR and neutron scattering. At low Q-values, these experiments can also look into the intermediate range order (IRO). For the case of the X-ray absorption experiments, the glass researcher can attain coordination numbers around an atomic species in the glass [32, 33], look at polyamorphic transformations [34], and even allow for the study of the transition from solid to liquid and of glasses at high pressure. Powerful as these techniques are, one must bear in mind that the analysis (especially for glasses) is complex, and often best left to experts in the area. Beamtime must be applied for, attained, and sometimes paid for; and the number of samples that can be measured is limited.

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2.3.3.3. Equipment Returning now to the standard laboratory X-ray equipment, the reader can discern the main components shown in Fig. 2.13. The monochromatic X-rays are emitted by a Cu K-alpha tube (or, sometimes, tubes with targets made of Cr, Mn, Fe, Co, Mo, or Ag). Given their high energy, steering them is impossible, and thus slits (and occasionally pinholes) are used to shape the beam. The photons then strike the sample at a specific angle of incidence. The detector, which in modern instruments is a wide-area semiconductor strip, can cover a range of output (scattering) angles of approximately 3◦ –4◦ , making faster measurements due to its greater angular width. A separate water cooling system is needed for the source, and care must be taken to avoid calcium deposits in the line. A good, stable, and well-built mechanical base is critical to the smooth motion of all the components, even though this element can add a fair amount of weight to the system. Cameras and He–Ne lasers are also used for alignment, and high-resolution x–y–z stages are also important.

Fig. 2.13. Sketch of the instrumental setup for a powder X-ray diffractometer. Image from U.S. Geological Survey Open-file Report 01-041, in the public domain.

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2.3.3.4. Examples The recent phenomenon of self-powdering [35, 36] has been shown to occur in gadolinium boromolybdate glasses as the samples are heated. This stands in contrast to the more common fracturing behavior that happens when samples are cooled and break due to thermal stresses. Figure 2.14(a) displays [36] the powdering of the sample, while (b) shows the XRD spectra, and helps to identify the phase of β’-Gd2 (MoO4 )3 that forms as the temperature reaches 570◦ C–590◦ C. Ultimately, in a later work [35], the authors explained

(a)

(b)

Fig. 2.14. (a) Displays the phenomenon of self-powdering as the sample (21.25Gd2 O3 –63.75MoO3 –15B2 O3 glass) temperature is increased, while (b) identifies the crystal being formed as β’-Gd2 (MoO4 )3 . The bottom spectra show the standard, expected Bragg peaks from a crystal reference. Reprinted with permission from Ref. [36], with permission from Elsevier publishing.

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Fig. 2.15. Correlation functions (T(r)) of lead silicate samples. In the graph, x is the molar percent of lead oxide in the glass. Reprinted from Ref. [37], with permission from Elsevier publishing.

the phenomenon as being driven by a significant difference in the density between the glass and the crystal. Finally, we show an example of synchrotron X-ray work. Figure 2.15 shows [37] the correlated functions of three different lead silicate glasses. The analysis of the correlation curves can yield a variety of useful structural parameters: coordination numbers around the Si, O, and Pb atoms; distances between the Pb–O, Si–O, and O–O atom pairs; distributions of distances using FWHM; and total coordination numbers. The authors focused on the environments around the lead atoms, which point to a variety of lead polyhedra (not only PbO4 ) in the silicate glasses. The exact shape of the polyhedra appears to be dependent on the actual glassformer present (viz., SiO2 , V2 O5 , P2 O5 ) more than on the lead concentration. 2.3.3.5. Advantages, Disadvantages, and Warnings A key advantage of the XRD technique is the ability to carry out quick routine measurements ensuring the amorphous nature

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of samples, at a relatively low cost. Maintenance is reasonably low, and some updates are possible (e.g., detector upgrades). The amount of sample needed is fairly small (a few grams), and can even be decreased by the use of pinholes on the source exit. To the glass scientist, a powder diffractometer opens up the possibility of studying glass-ceramics or to diversify into novel crystal formation by devitrification. The analysis of spectra is not particularly difficult, and certainly within the abilities of graduate students or starting researchers. As a common materials characterization technique, students will often have had a course on XRD operation, analysis, and interpretation. Disadvantages include the low Q-range, which makes structural studies of the glass network impossible; some complexity in the software used for operation and analysis (depending on the manufacturer); and the need for a reasonably large footprint in the laboratory. Like all instrumental techniques, XRD has some nuances. Procedurally, powdered samples must be ground quite finely, as we have mentioned before. If looking at glass-ceramics, the crystalline volume fraction in the sample must be on the order of a few percent. And, after a good spectrum is attained, a good reference from the literature must exist and be found. In cases where the crystallites inside the glass are subject to stress (say), it might be common to see differences in the peak positions when compared to bulk crystals in the literature. If carrying out micro-crystallite analysis, one must take into account instrumental and micro-strain broadening to be able to separate out the correct peak width. And the shape of the crystallites can also affect the Scherrer constant in the equation. 2.3.4. Scanning Electron Microscopy 2.3.4.1. Theory and Background Although not a perfect fit to the “Structural Characterization” section, a good argument could be made that SEM — or access to it — is an important tool for glass researchers setting up a laboratory. There are two primary reasons for this importance. Use of a SEM can allow a researcher to look for surface features like surface

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crystallization [38], adsorbents, glass-ceramics [39, 40], fracture [41], and even phase separation [42]. Equally important is the ability of the microscope, through the use of attachments like X-ray fluorescence (XRF), to determine the chemical composition of glass samples. In many laboratories, SEM–XRF has replaced more cumbersome wet-chemistry techniques or standalone XRF tools as the instrument of choice for compositional quality control. This is not only due to ease of use, but also because the combination of SEM and XRF allows the researcher to pinpoint particulates or phases and then determine their composition. This strategy then leads to better identification of the sources of contamination. In another application, SEM–XRF can analyze surface crystals or phases with sufficient accuracy as to aid in the determination of the crystal structure and the phase stoichiometry. Unfortunately, SEM is not always used routinely, occasionally leading to samples of mistaken compositions. 2.3.4.2. Equipment Modern SEM has gained significantly from advances in computer control and software [43]. Physically, however, the mechanisms behind the microscope are quite similar to those from 40 years earlier. The electrons are commonly produced by a heated filament (or an LaB6 source, or even a field emission gun) in an electron gun, which in turn begins the process of directing and shaping the electrons produced into a beam. The energies involved span from a few hundred electron-volts to perhaps 40 keV. The electron beam is then collimated and demagnified to a specific size by condenser magnetic lenses (see Fig. 2.16). These determine the ultimate “spot size” of the beam. A stronger lens, the objective, focuses the beam onto the sample. Some systems add a fourth, often intermediate (IML), magnetic lens to increase the number of possible imaging modes. Also shown in the Figure are the scanning coils, which allows for the beam rastering necessary to create an x–y image. The combination of lenses, combined with modern computer control and automated data acquisition, offers several advantages. First, optical flaws like chromatic and spherical aberrations and astigmatism can be lessened by good lens design and automated computer optimization. Software routines can guarantee a well-centered beam

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Fig. 2.16. Illustration of the column of a scanning electron microscope, highlighting the main components. Figure courtesy of Tescan, Inc.

with minimized aberrations. This, of course, increases the time available for the researcher to carry out data acquisition. The combination of lenses also allows for a variety of imaging modes. Common ones include resolution (highest magnification); depth (useful for layered samples where focus is needed over a wider range of depths); field and wide field (excellent for starting large-scale images of samples, before narrowing down), and even rocking beam (which allows for some crystal analysis). Figure 2.17

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Fig. 2.17. Schematic of various imaging modes, showing the electron beam focusing and sample images. Figure courtesy of Tescan, Inc.

shows an illustration of these various modes, as well as the electron beam paths and sample images. Finally, we note that any experimental scientist who wishes to carry out SEM on inorganic glasses will need the ability to coat the samples with a thin conducting layer, normally gold or perhaps carbon. This can be avoided in more modern SEM instruments with variable pressure capabilities. A sputter coater is often used for this purpose, and adds to the experimental requirements. Larger universities will often have a central user facility with one or more electron microscopes (SEM and transmission electron microscope [TEM], say), as well as other peripheral tools and experienced personnel. A young researcher could benefit greatly from connecting to this type of facility and its technical staff. 2.3.4.3. Energy-Dispersive X-Ray Spectroscopy Often paired with the SEM, energy-dispersive X-ray spectroscopy (EDX) relies on the interactions between the sample and the electron beam used to create the image. These high-energy electrons interact

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with the sample in a variety of ways, from the formation of a continuous X-ray spectrum (bremsstrahlung, caused by the deceleration of the electrons [43]) to the fluorescence arising from the electron jumps in the inner shells of the atoms present in the samples. As the inner electron shells are mostly unaffected by the bonding environment, the outgoing X-rays have energies characteristic of the particular elements present in the glass. This, in turn, can allow for the quantitative determination of the abundance of a particular element. 2.3.4.4. Examples Longer term storage of pharmaceuticals in glass vials can lead to delamination [44], a process by which flakes can peel off the interior glass walls and enter the pharmaceutical liquid. Clearly undesirable, the mechanisms of delamination center around chemical surface changes that create a leach layer where certain elements (e.g., boron) are selectively removed and lead to interactions between the drug buffer and the glass. Figure 2.18(a) shows the corrosion layer imaged by SEM, while (b) illustrates a glass flake that entered the solution. For this particular experiment, ICP analysis of the liquid solution showed elevated levels of boron and sodium, indicating selective dissolution. One may also carry out EDX on the flakes to investigate the chemistry behind the delamination process. 2.3.4.5. Advantages, Disadvantages, and Warnings There are many advantages to having the ability of carrying out SEM measurements on a glass sample. A researcher can look for particulates that contaminate a glass surface; analyze the delamination of polymer films from glass substrates; look for the formation of surface crystals; study the effect of laser beams on a surface; and measure the onset of chemical attack (e.g., durability studies). If EDX is available, the equipment can be utilized to check the chemical composition of samples and to determine the exact stoichiometry of any contaminants. EDX can also be useful in the study of glass phases, nano-crystals (glass-ceramics), and reactions between the glass and any other contact surfaces.

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(a)

(b)

Fig. 2.18. (a) Shows the corrosion of a pharmaceutical vial after chemical attack, while (b) displays a flake produced by the delamination of the interior wall of the vial. Figure from [44], with permission from ContractPharma.

The disadvantages are also worthy of mention. Coated samples are modified, rendering them less useful for other measurements. Spatially, all SEM have a maximum magnification, and some of the more economical models cannot quite get high resolution at the single nanometer regime. The quantification of the chemical composition via EDX carries an error of a few percent (typically), though certain calibration steps can help. Warnings for a young researcher include noting that SEM instruments that operate in a vacuum are not well suited for samples that may be wet — that is, for studies of durability. Variable pressure models are a better choice. Similarly, glasses with low glass transition temperatures may be susceptible to the heat caused by the electron

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beam. And finally, rough glass samples that did not receive a good enough coating will show sporadic white spots, indicating charge buildup. 2.4. Quick Survey of Other Techniques The field of structure and property characterization of glasses (and materials in general) is vast. Below are a few techniques that could not be included in detail, or were not considered to be part of the “most used” set. Dilatometry: A method used to attain the coefficient of thermal expansion of glasses. Though a useful and complementary technique to other thermal measurements, it requires a rather large and wellshaped sample. Laser diffusivity: This technique looks at the diffusion of heat after a laser pulse. It permits the researcher to get the heat diffusion coefficient, though details like optical absorption are important. NMR: The reader is invited to look at Chapter 3 in this book for a description of this powerful structural analysis technique. Neutron diffraction: Often complementary to synchrotron X-ray measurements, this method can help provide insight into difficult glass networks. Elastic and inelastic measurements are complementary and can give information using diffraction data as well as vibrational spectra. Access to a national laboratory — with limited time, subject to proposals — is required. Ionic- and electronic conductivity: The reader is invited to look at Chapter 6 in this book for a description of this powerful structural analysis technique. Mechanical measurements: This encompasses a variety of measurements, from fracture and strength to elastic modulus and plastic deformation. The instrumentation is often affordable within a scientific budget, and the properties are of enormous interest to industry. Specialized knowledge and training is also important.

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Scanning probe microscopy (SPM): This technique is specific to surface characterization. In contrast to SEM or optical imaging, SPM can get quantitative measurements of surface features, allowing for the calculation of parameters like the surface roughness or correlation lengths. Through a suitable selection of probes, SPM can also be used to measure local variations in elastic modulus, conductivity (thermal and electric), friction coefficient, local variations in temperature, resistance and capacitance, and a host of other variables. In many laboratories, though, this reduces to Atomic Force and Scanning Tunneling Microscopies. References 1. Kittel, C. (2005). Introduction to Solid State Physics. (Hoboken, NJ, Wiley), p. 680. 2. Skoog, D., Holler, J., and Crouch, S. (2007). Principles of Instrumental Analysis, 6th Ed. (Belmont, CA, Cengage Learning), p. 1056. 3. Deubener, J., Muller, R., Behrens, H., and Heide, G. (2003). Water and the glass transition temperature of silicate melts, Journal of NonCrystalline Solids, 330, pp. 268–273. 4. Goel, A., et al. (2009). Effects of BaO on the crystallization kinetics of glasses along the Diopside-Ca-Tschermak join, Journal of NonCrystalline Solids, 355(3), pp. 193–202. 5. Zhao, H. Y., et al. (2013). The kinetics of the glass transition and physical aging in germanium selenide glasses, Journal of NonCrystalline Solids, 368, pp. 63–70. 6. Fokin, V. M., et al. (2010). Critical assessment of DTA-DSC methods for the study of nucleation kinetics in glasses, Journal of NonCrystalline Solids, 356, pp. 358–367. 7. Chen, Y., et al. (2017). Resolving glass transition in Te-based phasechange materials by modulated differential scanning calorimetry, Applied Physics Express, 10(10), p. 4. 8. Fowles, G. R. (1989). Introduction to Modern Optics. (Toronto, Canada, Dover Publications). 9. Sundar, V. C., et al. (2003). Fibre-optical features of a glass sponge, Nature, 424(6951), p. 2. 10. Gleason, B., Richardson, K., Sisken, L., and Smith, C. (2016). Refractive index and thermo-optic coefficients of Ge–As–Se chalcogenide glasses, International Journal of Applied Glass Science, 7(3), pp. 374–383.

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11. Ferraro, J. R., Nakamoto, K., and Brown, C. W. (2003). Introductory Raman Spectroscopy, 2nd Ed. (San Diego, CA, Academic Press), p. 434. 12. Turrell, G., and Corset, J. (1996). Raman Microscopy. (San Diego, CA, Academic Press), p. 464. 13. Everall, N. (2004). Depth profiling with confocal Raman microscopy, Part I, Spectroscopy, 19(10), pp. 22–27. 14. Lenting, C., et al. (2018). Towards a unifying mechanistic model for silicate glass corrosion, NPJ Materials Degradation, 2(28), pp. 1–10. 15. Honma, T., et al. (2008). Writing of crystal line patterns in glass by laser irradiation, Journal of Non-Crystalline Solids, 354, pp. 468–471. 16. Leipply, D., et al. (2006). Development of functional borate glass surfaces to inhibit bacterial growth, Glass Technology — European Journal of Glass Science and Technology Part A, 47(5), pp. 127–132. 17. Winterstein-Beckmann, A., et al. (2014). Raman spectroscopic study of structural changes induced by micro-indentation in low alkali borosilicate glasses, Journal of Non-Crystalline Solids, 401, pp. 110– 114. 18. Grimsditch, M., Polian, A., and Wright, A. C. (1996). Irreversible structural changes in vitreous B2 O3 under pressure, Physical Review B, 54(1), pp. 152–155. 19. Fuss, T., et al. (2006). Ex situ XRD, TEM, IR, Raman and NMR spectroscopy of crystallization of lithium disilicate glass at high pressure, Journal of Non-Crystalline Solids, 352, pp. 4101–4111. 20. Carabatos-Nedelec, C. (2001). Raman scattering of glass. In: Handbook of Raman Spectroscopy, edited by Lewis, I. R., and Edwards, H. G. M. (New York, NY, Marcel Dekker). 21. Zajacz, Z., et al. (2005). A composition-independent quantitative determination of the water content in silicate glasses and silicate melt inclusions by confocal Raman spectroscopy, Contributions to Mineralogy and Petrology, 150, pp. 631–642. 22. Smith, B. C. (1996). Fundamentals of Fourier Transform Infrared Spectroscopy, 1st Ed. (Boca Raton, FL, CRC Press), p. 202. 23. Affatigato, M. (2015). Modern Glass Characterization, 1st Ed. (Hoboken, NJ, American Ceramic Society/Wiley), p. 443. 24. Jones, J. R., Ehrenfried, L. M., and Hench, L. L. (2006). Optimising bioactive glass scaffolds for bone tissue engineering, Biomaterials, 27, pp. 964–973. 25. Chryssikos, G. D., Kamitsos, E. I., and Karakassides, M. A. (1989). Far infrared and Raman studies of sodium ion conducting glasses, Physics and Chemistry of Glasses, 30(6), p. 243.

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26. Kamitsos, E. I. (2003). Infrared studies of borate glasses, Physics and Chemistry of Glasses, 44(2), pp. 79–87. 27. Kamitsos, E. I., Chryssikos, G. D., and Karakassides, G. (1988). Glass transition phenomena and cation vibrations in alkali borate glasses, Physics and Chemistry of Glasses, 29(3), p. 121. 28. Kamitsos, E. I., Yiannopoulos, Y. D., Jain, H., and Huang, W. C. (1996). Far-infrared spectra of alkali germanate glasses and correlation with electrical conductivity, Physical Review B, 54(14), p. 9775. 29. Kamitsos, E. I., et al. (1995). Infrared study of AgI containing superionic glasses, Physics and Chemistry of Glasses, 36(3), p. 141. 30. Kumar, A., et al. (2015). Structural and ion transport properties of [(AgI)x(AgBr)0.4-x](LiPO3)0.6 and (AgBr)x(LiPO3 )1-x solid electrolytes, International Journal of Applied Glass Science, 8(1), pp. 97–104. 31. Shankhwar, N., Singh, R. K., and Srinivasan, A. (2017). Evolution of magnetic and bone mineral phases in heat-treated bioactive glass containing zinc and iron oxides, International Journal of Applied Glass Science, 8(1), pp. 105–115. 32. Dalba, G., et al. (1988). EXAFS study of the coordination of phosphorus in AgPO3 glass, Journal of Non-Crystalline Solids, 106(1–3), pp. 181–184. 33. Dalba, G., et al. (2006). XAFS study on the local order of Pb in PbO borate glasses, Physics and Chemistry of Glasses — European Journal of Glass Science and Technology Part B, 47(4), pp. 518–520. 34. Kono, Y., et al. (2016). Ultrahigh-pressure polyamorphism in GeO2 glass with coordination number >6, Proceedings of the National Academy of Sciences, 113(13), pp. 3436–3441. 35. Kotaka, M., et al. (2018). Control of self-powdering phenomenon in ferroelastic beta’-Gd2 (MoO4 )3 crystallization in boro-tellurite glasses, Journal of Non-Crystalline Solids, 501, pp. 85–92. 36. Tsukada, Y., Honma, T., and Komatsu, T. (2009). Self-powdering and nonlinear optical domain structures in ferroelastic beta-Gd2 (MoO4 )3 crystal formed in glass, Journal of Solid State Chemistry, 182, pp. 2269–2273. 37. Hoppe, U., et al. (2003). Environments of lead cations in oxide glasses probed by X-ray diffraction, Journal of Non-Crystalline Solids, 328, pp. 146–156. 38. Akatsuka, C., et al. (2019). Surface crystallization and gas bubble formation during conventional heat treatment in Na2 MnP2 O7 glass, Journal of Non-Crystalline Solids, 510, pp. 36–41. 39. Deng, W., Gong, Y., and Cheng, J. (2014). Liquid-phase separation and crystallization of high-silicon canasite-based glass ceramic, Journal of Non-Crystalline Solids, 385, pp. 47–54.

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40. Rampf, M., et al. (2016). Tailoring the thermal expansion of glass-ceramics by controlled twofold crystallization of Li2 Si2 O5 and CsAlSi5 O12 , International Journal of Applied Glass Science, 7(3), pp. 285–294. 41. Belli, R., et al. (2018). Fracture anisotropy in texturized lithium disilicate glass-ceramics, Journal of Non-Crystalline Solids, 481, pp. 457– 469. 42. Nicoleau, E., et al. (2015). Phase separation and crystallization effects on the structure and durability of molybdenum borosilicate glass, Journal of Non-Crystalline Solids, 427, pp. 120–133. 43. Goldstein, J., et al. (2007). Scanning Electron Microscopy and X-Ray Microanalysis. (New York, NY, Springer), p. 690. 44. Haines, D., Scheumann, V., and Rothhaar, U. (June 5, 2013). Glass flakes, Contract Pharma, 2013, pp. 92–98.

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CHAPTER 3

Nuclear Magnetic Resonance Spectroscopy of Oxide Glasses Randall E. Youngman Corning Incorporated 1 Riverfront Plaza, Corning, NY 14831, USA

3.1. Introduction Nuclear magnetic resonance (NMR) spectroscopy has grown into an indispensable characterization tool for understanding many aspects of glass structure, and thus also rationalization of the important properties of these materials. Since the discovery of NMR in the early part of the 20th century, the number of applications and overall impact of NMR in glass science continues to grow exponentially, advancing our basic understanding and leading to new and exciting applications of glasses, spanning fields from medical to consumer electronics to automotive and architectural uses. This chapter will focus on some of the key aspects of using NMR spectroscopy to study the short-range structure of oxide glasses. A number of different glass families, including silicates, borates, 55

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and phosphates are well-suited for NMR study and thus constitute much of the current NMR work in this field, both in academia and industrial R&D. 3.2. History of Glass NMR NMR was first described by Rabi in 1938 [1] and then extended to liquids and solids by Block and Purcell in 1945–1946 [2, 3]. The first commercial NMR instrument made its appearance in the 1950s. Since this time, the technique has positively impacted all of the natural sciences, becoming a key molecular spectroscopy in chemistry and biology. Materials science, and especially the study of inorganic glasses, has benefitted from the widespread adoption of this technique. In 1958, Bray and Silver published the first study of glass structure using NMR, leveraging this new technique to study boron-containing glasses [4]. The spectra in Fig. 3.1 (Fig. 9 in the original publication) are of two commercial borosilicate glasses.

R Fig. 3.1. 11 B NMR spectra of Corning Code 707 and Pyrex glasses, as measured by the Bray group in the 1950s. Reprinted from [4], with permission of AIP Publishing.

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These researchers clearly demonstrated that NMR of 11 B could be used to differentiate between three- and four-fold coordinated boron, as seen by the broad line identified in part by the 7.1 Mc label and the much narrower feature in the middle of the data, corresponding to three- and four-fold coordinated boron sites, respectively. Through this type of structural analysis, Bray and his co-workers confirmed the three-fold coordinated boron structure in B2 O3 glass and concluded “that the boron has two possible coordination numbers whenever there is a modifier present” [4]. Although this early application of NMR was based on wideline measurements (i.e., low resolution), and the authors admitted great difficulty in measuring some of the 11 B signal, it was clear that the ability to detect different coordination numbers of glass-forming cations would represent an enormous advance in the field. The group of M¨ uller-Warmuth quickly developed their own expertise in solidstate NMR of glasses [5], and over the years, often in parallel with Bray, reported on a variety of glass families which could be better understood from an atomic structure perspective [6–10]. Since these early days of glass NMR, other pioneering researchers, including, for example, Dupree [11], Eckert [12], Stebbins [13], and Massiot [14], demonstrated significant value in the study of glass structure and dynamics using relatively simple NMR methods. One of the key milestones in improving the application of NMR in glass science was the invention of magic-angle sample spinning, or MAS NMR [15, 16]. This technique, commonplace today, enabled researchers to remove much of the anisotropic line broadening in solid-state NMR, resulting in improved spectral resolution and sensitivity. Application of 29 Si MAS NMR on silicate glasses was one of the first to benefit from the development of MAS NMR [17], and as can be seen in Fig. 3.2, the resulting improvement in NMR data on going from static to MAS NMR measurements is striking in that complex lineshapes like that of Q3 silicate groups can be simplified to relatively narrow, Gaussian-shaped peaks under MAS NMR. Details on the specific applications of MAS NMR and interpretation of oxide glass data are provided later in this chapter, but even a simple comparison of the spectra in Fig. 3.2 shows how line narrowing and

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(b)

(a)

Fig. 3.2. 29 Si NMR spectroscopy of a binary potassium silicate glass (9.4 mol% K2 O) using (a) wideline or static NMR and (b) magic-angle spinning NMR. Figure (a) reprinted from [18] with permission of Elsevier.

improved resolution can lead to better and easier interpretation of the data. There is certainly important structural information contained in the low-resolution, static measurements like in Fig. 3.2(a), which can often be used in modern studies of oxide glasses, especially those containing silicon and/or phosphorus, but routine analysis to identify and quantify different silicon environments is admittedly much improved by leveraging the MAS NMR technique. For many years, MAS NMR was the only routine method for line narrowing and therefore achieving high-resolution NMR of solids, including inorganic glasses. This technique, however, does not provide fully isotropic spectra for nuclei with quadrupole moments,

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Fig. 3.3. 11 B NMR spectra of B2 O3 glass using a variety of different approaches, including (a) static NMR, (b) MAS NMR, (c) DOR NMR, (d) DAS NMR, and (e) MQMAS NMR, reproduced from [26]. The two peaks labeled A and B correspond to BO3 units in boroxol ring and non-ring environments, respectively.

as the quadrupolar interaction is only partially averaged under MAS NMR conditions. Yet in spite of this less than ideal resolution for NMR of nuclei such as 11 B and 27Al, wideline (static) and MAS NMR methods are still successfully utilized in the study of these elements in oxide glasses [19, 20]. The advent of truly high-resolution solid-state NMR of quadrupolar nuclei in the late 20th century led to an enormous improvement in the technique.

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Double rotation (DOR) and dynamic angle spinning (DAS) were designed to rotate samples at two different angles such that all of the anisotropic interactions were sufficiently removed. Both techniques required specialized NMR probes and were somewhat difficult to implement, but the resulting high-resolution spectra for 11 B, 27Al, and 17 O (all quadrupolar spins) led to a flurry of research in which DOR and DAS NMR were used to further our understanding of glass structure [21–24]. Within another decade, the technique of multiplequantum magic-angle spinning (MQMAS) NMR was invented by Frydman and co-workers [25], and today this is the method of choice for obtaining high-resolution NMR spectra from quadrupolar nuclei. The technique uses a traditional MAS NMR probe and is widely available with commercial instruments. The examples in Fig. 3.3, for 11 B in glassy B2 O3 , demonstrate the evolution in resolution from the static spectra used so effectively by Bray to MAS NMR and then eventually the ultimate resolution enabled by these latter methods [26]. Note the much broader shift axis necessary to plot the static spectrum in Fig. 3.3(a), which consists of a single resonance exhibiting substantial quadrupolar coupling. 11 B DAS NMR was shown effective in resolving the two BO3 sites in this glass (Fig. 3.3(d)) [27], which were previously unresolved using static and MAS NMR techniques.

3.3. Principles of Magnetic Resonance The ability to perform NMR spectroscopy on a glass of interest depends first on the presence of nuclei having non-zero magnetic moments. This means that only certain isotopes will be affected by an external magnetic field such that their resonances can be probed by radio-frequency radiation. The periodic table is full of nuclear spins which in principle can meet this criterion. Only a few elements do not have isotopes with nuclear spins, and none of these are of practical interest in the study of oxide glass structure. Out of the many non-zero spin isotopes, only approximately 1/3 or fewer are realistically accessible by conventional NMR methods and when applied to inorganic glasses, this number is further diminished [28].

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Fortunately, these include several important elements in glass science, including network-forming cations like Si, P, B, and Al, as well as modifiers like Li and Na. Anions like O and F have some favorable nuclear properties and thus benefit from NMR studies [29, 30]. In addition to having a nuclear spin, those isotopes which are favorable for study in oxide glasses must also have natural abundance of a sufficient level to detect, and for the quadrupolar nuclei (e.g., I > 1/2), their quadrupole moment must not be too large. Isotopic enrichment can overcome the first of these additional limitations, thus 17 O NMR is more widely possible with enriched samples, but the nuclei with very large quadrupoles, including As and Sb, are simply not accessible to most researchers. The nuclei in Table 3.1 represent those elements for which glass researchers using common NMR methods can realistically make routine and interpretable measurements. There are certainly other examples of elements which have been studied in crystalline inorganic solids, and even in glasses, but perhaps are still too new to be widely adopted [28]. Further advances in NMR methodology and application toward more exotic nuclear spins will also lead to more examples in which the “Glass NMR Periodic Table” is expanded. Furthermore, applications in glass NMR will be substantially advanced by the powerful combination of experiment and computational methods, Table 3.1. Common elements in oxide glasses with favorable NMR isotopes and their nuclear spin properties. A magnetic field of 11.75 T is representative of commonly available instrumentation. Other more unusual or difficult nuclei are briefly discussed toward the end of this chapter.

Isotope 29

Si P 27 Al 11 B 17 O 23 Na 7 Li 1 H 31

Spin Quantum Number, I

Natural Abundance (%)

Resonance Frequency at 11.75 T

1/2 1/2 5/2 3/2 5/2 3/2 3/2 1/2

4.7 100 100 80.42 0.037 100 92.58 99.99

99.36 202.46 130.32 160.46 67.80 132.29 194.37 500.13

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where the latter are already being used to calculate NMR observables and to model NMR data [31–33]. 3.3.1. NMR Measurables There are many different parameters which can be measured using NMR spectroscopy, and several of these are critical for determining the local network structure of oxide glasses. First and foremost, the chemical shift, δCS , is necessary for interpreting the peak position of resonances detected with NMR. Assuming proper shift axis referencing, using agreed-upon standards like tetramethylsilane (TMS) for 1 H, 13 C, and 29 Si, the peak position in a given spectrum will correlate with the environment of the nucleus under study. The example of δCS correlation with silicate polymerization will be discussed later, but it’s the ability to accurately measure a chemical shift that makes NMR so attractive for structural studies. Chemical shielding is also used to describe the chemical shift of a particular resonance, with the convention that higher shielding leads to a more negative δCS while deshielding increases δCS . Shielding differences might be qualitatively used to describe multiple peaks in the same spectrum or trends in peak position with changes in glass composition. There are two general complications involved in determining δCS for a given nucleus. First, the static spectra, as in Fig. 3.2(a), contain powder patterns with shapes and frequencies corresponding to the chemical shift anisotropy (CSA), so one cannot obtain these type of wideline spectra and immediately determine δCS . Single, wellresolved powder patterns can be simulated to estimate characteristics related to δCS , but the isotopic value of chemical shift is the average of the three principle axes of the chemical shift tensor. CSA is a description of how the chemical shift deviates from its isotropic value. Under MAS NMR, which is designed to average the chemical shift to its isotropic value (δCS ), this complication is eliminated. This means that MAS NMR of 29 Si and 31 P, for example, provide δCS simply from the frequency shift of each peak. However, this is not the case for quadrupolar nuclei, that is, those with nuclear spins greater than 1/2. For example, the MAS NMR spectrum of 11 B in glassy B2 O3 (Fig. 3.3(b)) contains a second-order quadrupolar lineshape with

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frequency (i.e., position) determined by both δCS and a quadrupolar term. Care must be taken then in reporting the peak position of quadrupolar nuclei, especially since the quadrupolar contribution to MAS NMR peak position exhibits a magnetic field dependence, which means that these types of spectra will have different shapes and positions depending on the static magnetic field used for the measurement. Also with respect to quadrupolar nuclei are two other very useful parameters that can be measured using standard NMR techniques, and which also provide important structural information. The nuclear quadrupole moment interacts with the electric field gradient (EFG) at the nucleus, which results in different contributions to the NMR resonances depending on number and distance of nearby charges (i.e., electrons and nuclei), making this sensitive to coordination number and bonding symmetry of the atom. In the case of borate glasses, as already highlighted with respect to Bray’s seminal contributions to the field, BO3 groups, having planar symmetry with the three bonded oxygen atoms, are distinctly different from BO4 units, which are nearly tetrahedral. The high symmetry of the latter unit results in very little quadrupolar coupling and hence a relatively narrow line. The lower symmetry of BO3 units means stronger quadrupolar coupling and a noticeable change in resonance frequency and lineshape. The key parameters used to describe these effects are the magnitude of the quadrupolar coupling, CQ , and the asymmetry of the quadrupolar coupling, η. CQ is defined as e2 qQ/, where q is the EFG, Q is the nuclear quadrupole moment, and  is the reduced Planck’s constant. This parameter is most often measured in MHz, and can range from less than 1 MHz for highly symmetrical BO4 polyhedra to more than 10 MHz for 27Al in highly distorted sites. CQ can be very large for nuclear spins having large Q, and in some instances, the large CQ makes these resonances difficult or impossible to measure. One common example of this is for 75 As, which has an enormous nuclear quadrupole moment (0.314 barns) and strong coupling to the EFG. The quadrupolar asymmetry, η, is a measure of the distortion. By definition, η ranges from 0 to 1, and in terms of oxide glass NMR,

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is most prevalent in the 11 B NMR study of glasses, as the η for BO3 units is incredibly sensitive to the nature of the surrounding oxygen atoms (i.e., the exact combination of bridging oxygen [BO] and nonbridging oxygen [NBO]). As will be discussed later, the η of 17 O in silicate glasses has also provided critical details on their short-range structure. Both CQ and η can be determined from MAS NMR spectra using accurate lineshape simulations, giving also δCS for the quadrupolar nuclei. The high-resolution MQMAS NMR technique can also provide estimates for δCS and PQ , which is the quadrupolar coupling product and is defined as PQ = CQ (1 + η 2 /3)1/2 . In these experiments, the position of each resonance in the two-dimensional contour plot can be analyzed to determine δCS and PQ , which provides excellent guidance for fitting of MAS NMR data from the same glasses. Although the determination of these different NMR parameters can be difficult, especially for a glass containing many different network structural units, their measurement is necessary to interpret these data and to provide a good understanding of the glass structure. 3.4. Glass Structure Terminology NMR spectroscopy allows one to investigate the atomic coordination and elemental bonding in glasses. This is a bulk technique with sensitivity and bias toward very short-range interactions, thus making this especially useful to examine specific atomic environments in the glass network. The typical NMR measurement provides detailed information on bonding configurations, but is averaged over the entire sample size, which typically spans 10 s to 100 s of mg of powdered glass. The resulting NMR spectrum is therefore an average description of the structure, correlating NMR parameters (e.g., δCS , CQ , and η) with coordination number and network connectivity of the atoms. In the case of silicate and phosphate glasses, the structural description derived from NMR data is based on the coordination number of the cation and the number of BO and NBO atoms. We use the Qn terminology first described in crystalline silicates [34], where Q is

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(a)

Q4

-2

Q3

Q2

Q2

-4

Q1

-1

(b)

Q3

-3

Q0

-2

Q1

65

-3

Q0

Fig. 3.4. Schematic representation of Qn tetrahedra in (a) silicate and (b) phosphate glasses. Open and filled spheres denote the anions (oxygen) and cations (silicon or phosphorus). Dashed lines in (b) represent delocalized charges on the phosphate groups.

the four-fold coordinated cation (e.g., P or Si), and the superscript n refers to the number of BO. Thus pure SiO2 glass contains exclusively Q4 units, and modified silicates and phosphates contain Qn with n ranging from 4 to 0 depending on the amount of network modifier. Figure 3.4 depicts the variation in Qn for silicate and phosphate glasses, and as discussed below in the sections devoted to these two glass families, NMR of the cation is one of the primary approaches for identifying and quantifying these structural building blocks. Other network-forming cations, for example, B and Al, exhibit even more complex structural behavior in oxide glasses, and their coordination environments are incredibly sensitive to glass composition and processing conditions, including thermal history and pressure effects. Boron, as shown many decades ago by Bray, can be found in both three- and four-fold coordination, and even the threefold coordinated B can involve both BO and NBO [35]. Aluminum coordination in oxide glasses is even more diverse, with four-, five-, and six-fold coordination possible [36]. There are other aspects of glass structure which are important, including connectivity between network polyhedra (like and unlike), which constitute intermediaterange structure and can also be investigated using NMR methods. Much of this connectivity is manifested in super-structural units,

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that is, the ring structure in borate glasses [37], or in rings and chains found in a variety of phosphate glasses [38]. Among the anions in a typical oxide glass, oxygen environments are of course the main consideration. 17 O NMR is well-suited to distinguish between BO and NBO, and further, the latter oxygen sites can sometimes be separated into different populations based on the charge-balancing cation (modifier) [39]. Fluorine, although not technically a major constituent in oxide glasses, nonetheless is an important anion in glass science and since oxyfluoride glasses are known, presents another element in which structural understanding can be gained through NMR. Fluorine can replace BO atoms, leading to depolymerized network structures, and bonding of the fluorine can exist with a number of different glass-containing elements [30]. The short-range structure of oxide glasses would not be complete without consideration of the charge-balancing or modifier elements. These can sometimes be studied directly with NMR, as discussed below, but in terms of glass structure, the coordination number and interaction of these cations with different oxygen (both NBO and BO), and other local anionic charges like four-fold coordinated B or Al, are some of the key structural considerations related to modifiers in oxide glasses. Fortunately, there are a number of ways in which NMR spectroscopy can aid in direct interrogation of these environments, or in many cases, the indirect study of their impact on the network-forming elements in the glass. 3.5. NMR of Major Oxide Glass Families 3.5.1. Silicate Glasses Silica (SiO2 ) is one of the simplest glasses in terms of short-range structure, in that it is comprised entirely of corner sharing SiO4 tetrahedra — the Q4 unit in Fig. 3.4(a). The arrangement of these tetrahedra into a three-dimensional glass network is much more complicated, though on-going studies using a variety of computational and experimental approaches are providing new insights into intermediate-range structure, ring statistics, and other structural features of silica that may be influenced by the manner in which

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this single-component glass is made. In terms of NMR studies, silica glass can be examined using both 29 Si and 17 O NMR. The former, with a natural abundance of ∼4.7%, allows for routine static and MAS NMR studies using samples without isotopic substitution, though some researchers have leveraged 29 Si enrichment to increase sensitivity and also enable more complex NMR studies of silica and silicates [40]. 17 O NMR, on the other hand, generally requires isotopic enrichment, which can be done using 17 O-labeled water and sol–gel type chemistries to make SiO2 with elevated amounts of the 17 O isotope. Once appropriate glasses are generated, 17 O NMR can be performed on commonly available instrumentation, though because of the quadrupolar nature of 17 O, higher magnetic fields and advanced NMR experimental methods (e.g., DAS or MQMAS) are generally favored. An example of the 29 Si MAS NMR spectrum for pure silica glass is plotted in Fig. 3.5. This spectrum is comprised of a single NMR resonance, which is consistent with the simple glass composition. The 29 Si NMR peak is centered around −111 ppm and this peak position is quite similar to that of Q4 peaks in crystalline SiO2 polymorphs. The width of the Q4 resonance in MAS NMR data is mostly due to the distribution of bond angles between Si tetrahedra, and there have been some studies in which the 29 Si NMR data were used to derive a bond angle distribution in silica glass. The 17 O MAS NMR spectrum (not shown), also containing but a single peak, shows a broad signal around −10 ppm [41], which does vary with magnetic

Fig. 3.5.

29

Si MAS NMR spectrum of dry, amorphous silica.

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Fig. 3.6. 17 O NMR data and analysis of BO in amorphous SiO2 . Reprinted with permission from [24]. Copyright 2004 by the American Physical Society.

field due to the second-order quadrupolar coupling. This peak is due to BO atoms between Si, and as with the 29 Si NMR data, the simplicity of this glass composition allows one to correlate the 17 O linewidth and various NMR parameter distributions with key details of SiO2 network structure. More elaborate 17 O NMR studies from Grandinetti et al. [24, 41] have yielded important insight into NMR measurables and related distributions in bond distance and angle. For example, the data in Fig. 3.6 demonstrate how careful analysis of the 17 O MAS NMR lineshape, which is described by CQ , η, and δCS , allows for correlation of these NMR-derived parameters with distributions in Si–O–Si bond angles and Si–O distances in silica. Modification of silica by a traditional modifier like Na2 O, leads to substantial changes in network structure and connectivity between silicate tetrahedra. These modifiers are known to depolymerize the structure through introduction of NBOs, which substantially alters their physical properties. 29 Si NMR has been particularly useful in

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Fig. 3.7. 29 Si MAS NMR spectra of binary potassium silicate glasses as a function of K2 O content. Solid and dashed lines correspond to experimental (top curves) and fitted data, respectively. Reprinted from [18] with permission of Elsevier.

following NBO formation with glass composition in binary alkali and other simple silicate glasses. For example, 29 Si MAS NMR of a series of binary K2 O–SiO2 glasses, as plotted in Fig. 3.7, shows conversion of Q4 to Q3 tetrahedra with increasing modifier (K2 O) [18], the behavior of which has been known and understood for some time. Based on similar NMR studies of many different silicates, Maekawa and others have developed structural models which predict Qn speciation in silicate glasses [42]. Often this is the only structural

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information one might need for a set of glasses, for example, to rationalize a glass property like viscosity or Tg , but even more detailed information can sometimes be obtained using standard and widely available NMR techniques. The data in Fig. 3.7 for the binary potassium silicate glasses not only confirms the formation of NBO and gradual depolymerization of the glass network, but there are subtle features in the 29 Si MAS NMR spectra which have been attributed to unique Q4 units having different next-nearest neighbor (NNN) tetrahedra. There is a measurable shift difference for Q4 surrounded entirely by other Q4 , like the −111 ppm resonance in pure silica (cf. Fig. 3.5), and a Q4 tetrahedron surrounded by a mixture of Q4 and Q3 units, which appears as a unique Q4 resonance in these NMR data (labeled as Q4−3 ). This type of differentiation based on NNN structural elements is a complex and subtle feature to these data, but observation and quantification of such fine network structure can be quite useful in refining structural models, for example, the modified random network model of Greaves [43], and can also be validated by computational modeling of oxide glass structure. Due to the many decades of study in this field, there are well-established correlations between 29 Si δCS (i.e., peak position) and Qn speciation. Using data for crystalline silicates, Engelhardt and Michel demonstrated that Q0 to Q4 can cover a range of shielding from −60 to −120 ppm [44], and thus proper measurement of 29 Si NMR spectra can provide very good details on the Qn speciation of binary alkali and alkaline earth silicate glasses. As will be shown in Section 3.5.2, this correlation between Qn and 29 Si NMR chemical shift is much more complex in aluminosilicates. One of the other key features of 29 Si, and also 31 P (see Section 3.5.5) NMR, is that the Qn tetrahedra not only exhibit different chemical shifts, allowing for relatively easy identification in simple glasses, but their symmetry gives rise to different responses in static or wideline NMR. This is due to CSA, and making these types of lowresolution NMR measurements can often aid in qualitative identification of the Qn species present in that glass. As an example, consider the wideline 29 Si NMR spectrum of the binary potassium silicate glass in Fig. 3.2(a), showing a much broader NMR spectrum (cf.

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Q4

Q2

Q3

Q1

29Si

Shift (a.u.)

29Si

71

Shift (a.u.)

29

Fig. 3.8. Si CSA powder pattern NMR lineshapes for the different Qn groups. The small features in some centers of the non-Gaussian powder patterns are simulation artifacts.

Fig. 3.2(b)) with less resolution than might be achieved with MAS NMR. Fortunately, we know from model systems (e.g., crystalline silicates) and also from computed NMR parameters that the high symmetry around a Q4 tetrahedron leads to a Gaussian peak shape under static measurement conditions. Q3 , which has uniaxial symmetry due to the single NBO, has its own characteristic peak shape, as do Q2 and Q1 tetrahedra. Q0 is once again highly symmetric with four NBO, and exhibits a Gaussian peak. These characteristic powder patterns are shown in Fig. 3.8 and comparison of these lineshapes with the experimental data in Fig. 3.2(a) indicates that some of the unique features from the Q3 powder pattern are indeed present, allowing further spectral deconvolution and identification of the types of network polyhedra present in these glasses. Of course the glass composition and 29 Si MAS NMR data are readily determined, and can provide excellent insight into the Qn speciation of this glass, but additional NMR data and fitting using these CSA lineshapes, confirms the MAS NMR peak assignments and thus the short-range structure. Water can also alter the structure of silica, though much less water can be incorporated into SiO2 than the glass modifiers described above. However, if a high surface area silica, for example, silica gel, is made, then the water interaction with these surfaces can resemble the depolymerization of the silicate network caused by

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Q3

Q4

Q2

-40

-60

-80 29Si

-100

-120

-140

Chemical Shift (ppm)

Fig. 3.9. 1 H→29 Si CPMAS NMR spectrum of silica gel. The solid line is the experimental spectrum and dashed lines represent deconvolution into three distinct Qn environments. Signal areas are not quantitative in this type of NMR experiment due to enhancement of sites with adjacent protons.

modifier formation of NBO. 1 H and 29 Si NMR studies of hydrous silica and silica gels can be informative on the different types of water present, as well as the extent of silanol (SiOH) formation. For example, the 29 Si cross-polarization MAS (CPMAS) NMR spectrum in Fig. 3.9 shows the presence of multiple silicon resonances, and those due to silicate Qn tetrahedra with OH groups are enhanced in this type of CPMAS NMR experiment [45]. In this case, there are clearly three different silicon environments, due to Q4 , Q3 , and Q2 , where the latter two polyhedra are formed from one and two SiOH groups, respectively. Furthermore, Eckert et al. used 1 H NMR to examine the different types of water in hydrous silica, which is important in both glass science and geochemistry of magmas [46]. In many applications, amorphous silica is very dry, with only ppm levels of water present in the structure. However, if glasses with appreciable levels of OH are made, for example, using sol–gel chemistries, then the silicon speciation would be impacted by depolymerization of the network by the water, leading to distinct structural differences from pure silica, as well as large changes in their thermophysical properties. The application of 29 Si and 1 H NMR spectroscopies, in the manner described here, are often leveraged in the study of silicate glass surface chemistries and especially in derivatization of silica with different silanes.

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3.5.2. Aluminosilicate Glasses Aluminosilicate glasses typically serve as the foundation of many current commercial products, including in consumer electronics, display technologies, and other fields. Addition of Al2 O3 , an intermediate oxide, has a substantial impact on glass properties, and in most instances, this can be understood by characterizing the network structure of the glass. Aluminum has a single NMR-active isotope which has very favorable nuclear spin properties. At 100% abundance and with a modest gyromagnetic ratio, which determines the resonance frequency, 27Al MAS NMR can be conducted easily with commercial instrumentation. The one minor complication is that 27Al has a modest quadrupole moment, which gives rise to complex and substantially overlapping resonances, even with MAS NMR. However, CQ and η, the sources of these rather complex spectra, contain highly valuable structural information, including especially details on the local symmetry of the Al-containing network unit. Thus 27Al solid-state NMR of glasses is one of the most popular methods in use today, widely deployed throughout academia and industry. Aluminum addition to a binary alkali silicate glass leads to increasing network connectivity through elimination of NBO. This occurs because Al is favored in four-fold coordination, which has a net negative charge and requires some type of charge compensation. Alkalis and most alkaline earth cations can provide this charge compensation, leading to stabilization of AlO4 tetrahedra rather than NBO formation on silicate groups. This structural response can be monitored directly using 17 O NMR spectroscopy, since quantification of BO and NBO sites can be measured [47]. Since this approach typically requires isotopic enrichment, other NMR experiments are often used to detect and quantify changes in short-range structure upon addition of Al. For example, 29 Si NMR can confirm an increase in silicate polymerization through a shift in the Qn population toward higher n. 27Al NMR is also useful in that these data can determine with high efficiency the speciation of Al, with an understanding that each four-fold coordinated Al requires a nearby modifier for charge compensation of this polyhedron.

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So while 29 Si and 27Al NMR data can aid in description of a more polymerized oxide glass network with incorporation of alumina, the data are more complicated than in the simple silicate glasses in Section 3.5.1. The 29 Si MAS NMR spectra of aluminosilicate glasses contain resonances which are deshielded (less negative chemical shift) by NBO, as described before, but each of these Qn peaks can be further deshielded by the interaction of the silicate tetrahedra with neighboring Al polyhedra. This impact of NNN groups on 29 Si chemical shifts, also described in great detail by Engelhardt and Michel [44], is an important NMR response to network connectivity in these types of glasses, as shown by the series of spectra in Fig. 3.10. Here, the addition of Al2 O3 leads to a progressive shift of the 29 Si peaks. Although this shift resembles that of the alkali silicate glasses (Fig. 3.7), the main reason for this change in 29 Si

Fig. 3.10. 29 Si MAS NMR spectra for a series of aluminosilicate glasses with Al2 O3 content in mol% provided to the left of each spectrum. Dashed lines represent a typical deconvolution into different Qn resonances for the Al-free glass data. Reprinted with permission from [48]. Copyright 2012 by the American Physical Society.

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NMR chemical shift is due instead to the presence of Al NNN. As more alumina is added to these glasses, the 29 Si NMR peaks are further deshielded, and this is occurring even as the Qn silicate groups move toward higher n or polymerization. Thus even simple 29 Si MAS NMR data on aluminosilicate glasses can be very difficult to accurately interpret, and quantification of Qn speciation can often be impossible. This is where knowledge of glass composition and empirical chemical shielding correlations can be utilized to further constrain deconvolution of the spectra, such that the results are consistent with the expected number of NBO and the amount of Al in the network. This can be quite laborious and makes this a less than routine analysis of glass structure using NMR spectroscopy. Another approach, especially if determining Qn speciation is the main goal, is to make use of the Qn CSA lineshapes in Fig. 3.8 to examine static 29 Si NMR data from aluminosilicate glasses. Q4 , regardless of the number of Al NNN, generally retains a Gaussian lineshape under static NMR measurements, and the other Qn species also maintain their characteristic CSA lineshapes. Thus an aluminosilicate glass containing Q3 and Q4 silicate groups with mixing of silicate and aluminum polyhedra, may yield interpretable static NMR spectra, although this is perhaps more difficult than it sounds. Take, for example, these same aluminosilicate glasses [48], where 29 Si static NMR data have also been acquired. Here, the low alumina glasses can be fit to Q3 and Q4 powder patterns, and assuming the added Al2 O3 consumes most of the modifier, multiple Q4 lineshapes can be used for the highest Al-containing glass. While reasonable, this type of analysis may yield more than one satisfactory deconvolution and thus more than one plausible glass structure description. Again, using glass composition and other sources of information can aid in constraining fits and thus interpretation (Fig. 3.11). The other aspect of aluminosilicates is the regime in which there is insufficient modifier to charge-compensate Al in four-fold coordination. Most structural models predict that in alkali or alkaline earth aluminosilicate glasses, the peralkaline compositions, where modifier is greater than aluminum, have Al exclusively in four-fold coordination. This continues even for tectosilicates, where Al and modifier are in equal concentration. It is assumed that only when

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Fig. 3.11. An example of static (wideline) 29 Si NMR spectra and possible deconvolutions (dashed lines) into Q3 and Q4 sites for a complex aluminosilicate glass. Adapted with permission from [48]. Copyright the American Physical Society.

aluminosilicate glasses are peraluminous (more Al than modifier) do higher coordinated Al sites become prevalent. A variety of properties and structural measurements have shown this to be generally true, but as with most aspects of glass science, there are exceptions. The CaAlSi ternary glass system, for example, has been extensively studied by a several research groups [49, 50]. Here, the tectosilicate glasses, with CaO=Al2 O3 , clearly have more complicated shortrange structure than predicted, with a non-zero population of Al(V) groups (i.e., insufficient charge balancing of AlO4 ), which then means some Ca2+ is available to form NBO on silicon. The 27Al MAS NMR spectrum of a typical calcium aluminosilicate glass with CaO approximately equal to Al2 O3 is shown in Fig. 3.12. Here, the asymmetric lineshape from AlO4 tetrahedra, at around 60 ppm,

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Fig. 3.12. 27Al MAS NMR spectrum of a charge-balanced (tectosilicate) calcium aluminosilicate glass showing the presence of multiple resonances due to multiple coordination environments for Al.

is accompanied by a noticeable shoulder around 30 ppm, assigned to Al(V) polyhedra. Proper fitting of these data with secondorder quadrupolar lineshapes allows for quantification of the Al coordination number, but sometimes these MAS NMR data are not sufficiently resolved to prove the existence of Al in non-tetrahedral sites. In this case, high-resolution 27Al NMR spectra, obtained using the MQMAS NMR technique, results in clear separation of contours from both four- and five-fold coordinated Al, as shown in Fig. 3.13. The overwhelming benefit of this high-resolution NMR spectroscopy is that resolution of multiple sites from quadrupolar nuclei is possible, and the position in the two-dimensional contour plot provides estimates for NMR parameters of each site — specifically δCS and PQ . Having estimated the value of these parameters for each distinct Al site in this manner, allows for more accurate fitting of the 27Al MAS NMR spectra and therefore more accurate quantitation of the Al coordination number. These types of measurements have proven invaluable for studies of aluminosilicate glasses, and subsequent modeling of their structure and properties. In addition to the complication that these glasses are not perfectly behaved according to peralkalinity or having adequate modifiers for charge compensation, several other systems are of significant technological interest. For example, aluminosilicate glasses containing Mg or Zn have been shown to further deviate from these structural models, with even more high-coordinated Al present in

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Fig. 3.13. 27Al MQMAS NMR spectrum of the charge-balanced calcium aluminosilicate glass from Fig. 3.12. This two-dimensional contour plot, correlating the MAS NMR spectrum with an isotropic spectrum, contains multiple sets of contours due to the presence of more than one Al coordination environment.

sub-aluminous (excess modifier) and tectosilicate compositions. The 27Al MAS NMR data in Fig. 3.14 show how significant the nontetrahedral Al units are in the network structure of ternary ZnAlSi glasses. Here, glasses with sufficient charge-compensating Zn2+ show a large amount of Al(V), and without additional consideration, one might assume the Zn not involved in charge compensation is then creating NBO on silicon tetrahedra. However, we know that high field strength cations like Mg2+ and Zn2+ are also capable of being in four-fold coordination themselves, acting very much like networkforming cations. These are current research topics and much more understanding is possible with NMR and other methods. 3.5.3. Borate Glasses Borate glasses, as discussed above, were some of the first to be studied using solid-state NMR. The 11 B nucleus is particularly

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Fig. 3.14. 27Al MAS NMR spectra of a series of ternary zinc aluminosilicate glasses, with the three different Al coordination environments shown. Dashed lines denote deconvolution of the spectra into distinct 27Al resonances. Analyzed glass compositions to the left are ZnO, Al2 O3 , and SiO2 , respectively.

good for solid-state NMR, being high natural abundance (80%) and having a relatively small quadrupole moment. This is manifested by the striking difference between the NMR lineshape of three- and four-fold coordinated boron. The former gives rise to asymmetric lineshapes with second-order quadrupolar broadening, while the nearly tetrahedral symmetry of the four-fold coordinated boron results in a relatively narrow resonance. These differences enabled Bray and other pioneering researchers to use low-resolution NMR to quantify boron coordination and develop structural models which are still applicable today [9]. 11 B MAS NMR, which is quite straight forward using modern instrumentation, provides nice resolution of different boron coordination environments. The spectrum in Fig. 3.15, measured at a modest field of 11.7 T, shows good resolution of three- and fourfold coordinated boron, and with proper analysis of the trigonal boron lineshape, additional details on short- and intermediate-range structure can be obtained. Multiple sites for three-fold coordinated boron have been detected in pure B2 O3 glass and most simple binary

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Fig. 3.15. 11 B MAS NMR spectrum of a binary sodium borate glass with resonances from trigonal and tetrahedral boron fitted with dashed lines [51]. The shaded peak is a fit to the overlapping satellite transition from four-fold coordinated boron, which is not included in the determination of N4 .

borate glasses. The most deshielded resonance, with an isotropic chemical shift of around 18–19 ppm, corresponds to BO3 polyhedra in rings, or the super-structural units unique to borate glasses. In pure B2 O3 , these are six-membered boroxol rings, and in modified borate glasses, these rings involve both three- and four-fold coordinated boron (e.g., triborate and other structural groupings) [23]. At a minimum, and often most valuable in understanding borate glass properties, 11 B MAS NMR data provide an accurate means by which to quantify boron coordination. The resolution and/or fitting of these peaks, yielding separation of BO3 and BO4 peaks, then provides one of the most effective ways to determine N4 , the fraction of boron atoms in four-fold coordination. Take, for example, the 11 B MAS NMR spectrum in Fig. 3.15. Knowing the different lineshapes and fitting these data, the N4 value can be directly measured by peak areas. Accurate measurement with 11 B NMR involves a couple of extra precautions. First, the excitation of quadrupolar nuclei having very different quadrupolar coupling, as is the case for three- and four-fold coordinated boron, is highly sensitive to the radio-frequency power. Optimized excitation of the two different environments occurs

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at very different powers, so the only way to obtain NMR data that is quantitative is to use very short pulse widths. The customary approach is to use a tip angle shorter than or equal to π/12, such that both boron environments are uniformly excited. The other complication concerns analysis of the resulting MAS NMR data. The quadrupolar nature of the 11 B nucleus means that multiple transitions can be excited and detected in a MAS NMR experiment. The central transition gives rise to the peaks that we normally detect, but satellite transitions sometimes occur, giving rise to additional features in the spectra. This is especially true for the four-fold coordinated boron sites, and consideration of the underlying satellite transition peak intensity is necessary in accurately determining boron coordination using 11 B MAS NMR. The data and fitting shown in Fig. 3.15 identifies these spectral artifacts, and considering the strong overlap between the satellite peak for four-fold coordinated boron, one can see how erroneous peak integration could give incorrect N4 values for any boron-containing glass. Another important aspect to 11 B NMR in borate glasses is the ability to capitalize on the spin-3/2 (quadrupolar) nucleus to make MQMAS NMR measurements, similar to those described above for 27Al or 17 O (both spin-5/2). An example for a binary sodium borate glass is plotted in Fig. 3.16, where the two-dimensional contour plot contains peaks from three- and four-fold coordinated boron. Resolution in the isotropic dimension (left axis) is enhanced over that available from simple MAS NMR, and hence more clear separation of the different boron sites is possible. Most importantly for structural studies of borate glasses, the shift region containing three-fold coordination boron peaks shows the clear presence of multiple resonances, which given their Gaussian lineshapes, provides even more certainty as to the presence of multiple BO3 sites. Projection of the isotropic data results in the 1D, high-resolution spectrum in Fig. 3.17, where the two three-fold coordinated peaks corresponding to ring and non-ring sites, can be fitted. Since these two peaks are characterized by similar quadrupolar couplings, this fit is an accurate quantification of their respective populations. However, N4 cannot be determined using 3QMAS NMR as the three- and

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Fig. 3.16. 11 B MQMAS 15.4Na2 O–84.6B2 O3 [51]. boron sites are marked, isotropic and MAS NMR dimensional plot.

NMR spectrum from a glass having the composition Contours due to the three- and four-fold coordinated as are spinning sidebands (ssb). Projections of the dimensions are shown to the left and top of the two-

Fig. 3.17. Isotropic projection and fitting of the three-fold coordinated boron environments using the 11 B MQMAS NMR data in Fig. 3.16. Dashed curves represent the Gaussian fits to two partially overlapping resonances assigned to ring and non-ring BO3 units.

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four-fold coordinated boron sites are not uniformly excited and thus their relative intensities are not correct. Still, the enhanced resolution provided by 11 B 3QMAS NMR spectra can be leveraged to more accurately fit MAS NMR data. Peak positions in the contour plots (e.g., Fig. 3.16) provide estimates for isotropic chemical shift and quadrupolar coupling parameters, such that these values can be used as starting values in MAS NMR lineshape simulations or to constrain the fitting and generate a useful result. 3.5.4. Borosilicate Glasses The detailed structural information provided by 11 B NMR methods when applied to borate glasses can also aid in understanding structure and properties in borosilicates. This glass family, which is among R R , Borofloat , the most well known in glass science, includes Pyrex and other compositions which have enjoyed tremendous commercial success. Boron was first added to glasses in the mid-19th century in order to make better optical glasses. Shortly thereafter, researchers discovered that borosilicates provided glasses with good thermal shock resistance and excellent chemical durability, leading to the R and similar advantaged glass compositions. development of Pyrex Borosilicates continue to be important in modern technological applications of glasses, and therefore need to be studied in terms of their network structure and relation to their special properties. In terms of NMR studies of structure, these glasses obviously contain two network-forming cations which can be studied with this technique: 11 B and 29 Si. Examples shown above for 29 Si and 11 B NMR applications in silicate and borate glasses apply equally in borosilicates. The latter can determine boron coordination, important for determining the interaction of modifiers with the boron part of the glass structure. Likewise, 29 Si wideline and MAS NMR data informs on the Qn speciation in these multi-component glasses. One of the big differences in NMR studies of these borosilicate glasses over their more simple precursors is that NMR, especially using 11 B, can provide additional information on mixing between the borate and silicate polyhedra. The four-fold coordinated boron

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(a)

(b)

(c)

(d)

11

Fig. 3.18. B MAS NMR spectra of sodium borosilicate glasses with compositions shown. Dashed lines represent deconvolution of the boron resonances. Adapted and reprinted from [52] with permission of Elsevier.

resonance, usually around 0 ppm, often shows additional features in borosilicate glasses due to presence or absence of Si NNN. The 11 B MAS NMR spectra in Fig. 3.18 have been fitted to highlight the different boron resonances, and there are clearly two four-fold coordinated boron peaks, at shifts of 0.4 and −1 ppm. The latter has been assigned to BO4 units with four surrounding Si NNN, and the former is BO4 with 3Si and 1B NNN [52]. Thus the identification and quantification of these peaks provide insight into the extent of mixing between the borate and silicate networks, and could be useful in understanding phase separation, among other features of borosilicate glasses.

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Extensive studies of borosilicate glasses, based on 11 B NMR, were conducted by the Bray group, resulting in structural models still in use. The Yun and Bray model predicts N4 for compositions as a function of both modifier content and SiO2 :B2 O3 ratio. The model has worked well to explain the structure of these glasses, though recent efforts also based on 11 B NMR measurements, have shown deficiencies in this model, as the conversion of boron from three- to four-fold coordination is not necessarily always favored over creation of NBO on Si. The plot in Fig. 3.19 compares NMR determined N4 with the older model of Yun and Bray and a new model proposed in 2011 [53]. This type of research and refinement of structural models in glasses is enabled by new and improved characterization of glasses, including their network structure via NMR spectroscopy. 3.5.5. Phosphate Glasses Phosphate glasses are well known in the field, especially for their novel applications in metal sealing and bioglass applications, both of which are enabled by their low glass transition temperatures. Glasses

Fig. 3.19. Measurement and modeling of the fraction of four-fold coordinated boron (N4 ) in borosilicate glasses as a function of modifier content. Reprinted with permission from [53]. Copyright 2011 American Chemical Society.

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with P2 O5 as the network former can be made over large compositional ranges with a variety of modifiers, including the alkali and alkaline earth ions, but also several transition metals. Fortunately, the 31 P isotope is 100% abundant, is spin-1/2 (i.e., dipolar), and exhibits a high resonance frequency and overall sensitivity. Thus, 31 P NMR studies of phosphate glass structure have been successfully utilized for many years. In binary phosphate glasses, like sodium or calcium phosphates, the network structure exhibits a great deal of similarity to that of the analogous silicate glasses. Phosphorus is found in tetrahedral units, but unlike the silicates, the maximum number of BO is three, and thus Q3 phosphate groups are the most polymerized unit in these simple phosphate glasses. The remaining oxygen in this tetrahedral unit is a doubly bonded oxygen (P=O). There are examples of Q4 phosphate groups in specific and unusual glasses, for example, those with substantial interaction between P and either B or Al. The addition of modifier to P2 O5 converts the Q3 tetrahedra into Q2 , Q1 , and eventually Q0 tetrahedra, similar to the response of silicate groups to increasing modifier. These network building blocks are shown schematically in Fig. 3.4(b). 31 P MAS NMR has been especially useful in delineating between these Qn species, providing accurate quantification of their populations as a function of glass composition. In the simple binary phosphate glasses, for example, something like a ZnO–P2 O5 glass, multiple P resonances can be readily detected with 31 P MAS NMR, as in Fig. 3.20. These peaks are easy to fit, and the resulting peak areas inform on the amount of Qn species in the glass. In this particular example, the glass network is comprised of 46.4% Q3 and 52.9% Q2 units, with a trace amount of Q1 groups [54]. Since these types of studies are relatively simple and can be conducted without unusually fast sample spinning and at modest magnetic fields, there have been many studies of phosphate glasses using NMR spectroscopy, resulting in accurate models of P speciation in a large number of systems. In addition to determining Qn speciation, there are interesting studies showing how the 31 P chemical shifts are sensitive to the field strength of the chargebalancing cation [55], and the idea of disproportionation has been extensively examined with 31 P NMR [56].

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Fig. 3.20. 31 P MAS NMR spectrum and fits for a binary zinc phosphate (60.1ZnO–39.9P2 O5 ) glass. Peak assignments are shown at the top of each resonance. Spinning sidebands, which must be included in determination of Qn site populations, are marked as ssb. Adapted and reprinted from [54] with permission of Elsevier.

A variety of advanced NMR experiments have been used in the study of phosphate glasses, providing even greater details on shortand intermediate-range structure. The latter is a well-known feature of phosphate glasses, as these often contain chain and ring structures. The nuclear spin properties of 31 P have enabled NMR experiments which make use of strong dipolar or J-coupling between 31 P spins, allowing researchers to detect or eliminate from consideration the connectivity between different phosphate Qn units. One example of this, using multiple quantum 31 P MAS NMR, shows clear evidence for Q1 –Q1 connectivity in a glass, as indicated by the auto-correlation peaks in the plot of Fig. 3.21 [57]. Other sophisticated methods, such as J-resolved 31 P MAS NMR, have been leveraged in understanding phosphate glass structure and even phase separation. Another aspect of phosphate glass structure relates to compositions containing P2 O5 and another network-forming oxide, for example, Al2 O3 . Aluminophosphate, borophosphate, and phosphosilicate glasses are known and just like in the borosilicates, there are important structural questions about the nature of the network building blocks (polyhedra) and connectivity between the different network formers. Multi-nuclear MAS NMR, for example, using 29 Si

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Fig. 3.21. An example of a double quantum–single quantum (DQ–SQ) correlation spectrum of 31 P in a calcium phosphate glass, showing connectivity between adjacent Qn polyhedra. Reprinted from [57] with permission from Elsevier.

and 31 P NMR to study phosphosilicates, can be highly useful in ascertaining the phosphate and silicate structures, and even mixing between these. In one study of binary P2 O5 –SiO2 glasses, data for both cations confirms glass homogeneity at the atomic scale, and in higher P2 O5 compositions exhibiting phase separation, the stabilization of silicon in five- and six-fold coordination, both very unusual coordination environments in silicate glasses [58]. Earlier work on NaPSi glasses also showed evidence of octahedral Si in the 29 Si MAS NMR spectra [59]. Other mixed network-former glasses, especially those with both P2 O5 and Al2 O3 , are common. The ability to perform NMR on both cations, and even interrogate their structures through 31 P-27Al correlation methods, allows for an additional level of understanding. The Eckert group has long made use of REDOR NMR to examine connectivity between unlike nuclei in glasses, and in aluminophosphate glasses, these types of measurements provide quantitative estimates on the number of Al NNN or P NNN around P or Al polyhedra, respectively [60]. Figure 3.22 shows the results from this

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1.0 0.8

ΔS/S0

0.6 AlPO4 glass

0.4

5% Al2O3 10% Al2O3

0.2 0.0 0.0000

4spin 3spin 2spin

0.0004

0.0008

0.0012

0.0016

NTr / s

Fig. 3.22. Rotational-echo double-resonance (REDOR) plot of aluminophosphate glasses showing how NMR data can be used to quantify the extent of mixing between Al and P polyhedra. Reprinted with permission of [60]. Copyright 2009 American Chemical Society.

type of investigation, allowing one to confirm P–O–Al connectivity and to estimate the extent of mixing between the various network polyhedra. This information, along with the short-range structure determined by the nature of the Al and P speciation, results in a well-characterized network structure in oxide glasses. Similar types of NMR investigations have been successful for borophosphate and other more complex glasses. 3.5.6. Non-Traditional Oxide Glasses The glasses included in the previous sections are those most familiar to researchers in the field. These are typically the glass families used to develop new materials for a variety of commercial applications. Due to the ability to leverage much of the periodic table of elements in designing glass compositions, there are an unlimited number of glasses to understand, both in terms of glass-formation but also their structure/property relations. Among these are some rather unusual glasses which may interest only those working on fundamental studies of glass, but are nonetheless amenable to NMR characterization.

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One system which has been more recently of interest are glasses based on Ga2 O3 , which is chemically very similar to Al2 O3 . Thus a variety of oxide glasses containing Ga can be made. Gallium has two NMR-active nuclei, both of which have fairly large quadrupole moments and are therefore more difficult to study than 27Al. 71 Ga tends to be the better choice, and with application of fast MAS NMR and use of high magnetic fields, useful NMR spectra can be obtained [61]. Another interesting network former is MoO3 . 95 Mo NMR has been demonstrated by several research groups, and provides information on the coordination number of Mo in glasses [28], as well as confirmation of molybdate salt formation in unstable systems [62]. The latter is especially important to understand in the context of glasses for nuclear waste sequestration. Additional elements can be studied with solid-state NMR methods, even those standard with commercial instrumentation, and the ability to learn more about short- and intermediate-range structure using NMR of their isotopes will continue to grow and increase in importance as more diverse glass compositions are investigated for their beneficial properties.

3.6. NMR Studies of Modifier Cations The previous sections have focused on important network-forming cation and anion studies of oxide glasses, with emphasis on the former. In addition to routine study of Al, B, P, Si, and other network formers, NMR can also provide some information on a few of the modifier or charge-balancing cations. In particular, 23 Na and 7 Li isotopes have very favorable nuclear spin properties (Table 3.1) and are also important in oxide glasses. 23 Na is probably more common in that it is 100% abundant and has a modest quadrupole moment, leading to reasonable NMR lineshapes, even with MAS NMR. 23 Na 3QMAS NMR data are also prevalent throughout the literature, allowing researchers to estimate PQ and δCS for the average sodium environment in modified oxide glasses. Furthermore, because of the relative ease of performing both 23 Na MAS and

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3QMAS NMR experiments, correlations have been made linking these NMR parameters with average coordination number and even to changes in coordination number [63]. This is very useful structural information, especially when considering a series of glass compositions in which the modifier content, or makeup of the network formers is changing. A simple example of how 23 Na MAS NMR can be highly informative is given in Fig. 3.23, where the Na resonance changes shape and position with its structural role. In binary sodium silicate glasses, the Na+ is used to modify the silicate groups, forming NBO. In peraluminous glasses, it is commonly accepted that the main role of Na+ is to charge-compensate AlO4 tetrahedra, and this results in a pronounced shift in the resonance frequency of the 23 Na spins. Unfortunately, even in glasses where it appears that Na+ would have both roles (e.g., many sodium aluminosilicate compositions), resolution of both sites is not achieved (Fig. 3.23). Instead, one sees an average response for Na+ in the different environments. One of the reasons for this is that Na+ and other modifier cations are surrounded by a large number of oxygen atoms, comprised

25Na2O-75SiO2 25Na2O-25Al2O3-50SiO2

25Na2O-13Al2O3-62SiO2

50

0 23 Na

-50

-100

Frequency (ppm)

Fig. 3.23. 23 Na MAS NMR spectra of a series of sodium silicate and aluminosilicate glasses showing how the 23 Na resonance changes with role of the Na+ in these types of glasses. Modified and reproduced from [28].

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in many cases of both BO and NBO types. This also then leads to a distribution in distances between the Na+ and these oxygen atoms, making it very unlikely that discrete structural environments exist and are measurable. The same situation occurs for 7 Li NMR of lithium-bearing glasses, which is made even worse by a smaller chemical shift range for this isotope. Thus 7 Li, and related studies using 6 Li, usually focus on the cation dynamics, for example, the motion of Li+ in glassy electrolytes [64]. Other modifier cations have been investigated using NMR methods, but are less common and usually more difficult for routine types of measurements [28].

3.7. Current/Future Trends The field of glass NMR has evolved and grown rapidly since the first studies by Bray. Improvements in NMR methodologies, including some of the key advances in achieving resolution and sensitivity, have provided routine and widely accessible generation of NMR data and glass structure understanding. Combined with property understanding, compositional design, and new models of glass physics, the ability to gain in-depth structural descriptions of experimental and commercial glass compositions has significantly advanced the field. Continued improvement in NMR techniques, for example, higher magnetic fields or the combination of measurement and modeling, will only accelerate the use and benefit of this important glass characterization method. Already, the ability to calculate NMR observables using simulated glass structures is allowing for even more information to be extracted from relatively simple NMR data. This type of approach, pioneered by Charpentier and others, provides additional value and in some cases, can guide the design of new NMR experiments to confirm the modeling results. All of this information can then be used to refine and generate new structure/property models of oxide and other glasses, leading to continued advancements in glass science. The period table is our playground when it comes to making new and interesting glasses, and the ability to understand many more elements than shown in Table 3.1 will certainly happen, perhaps

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even faster than the advancements made in the past 60+ years of glass NMR.

References 1. Rabi, I. I., Zacharias, J. R., Millman, S., and Kusch, P. (1938). A new method of measuring nuclear magnetic moment, Physical Review, 53, pp. 318–327. 2. Block, F. (1946). Nuclear induction, Physical Review, 70, pp. 460–474. 3. Purcell, E. M., Torrey, H. C., and Pound, R. V. (1945). Resonance absorption by nuclear magnetic moments in a solid, Physical Review, 69, pp. 37–38. 4. Silver, A. H., and Bray, P. J. (1958). Nuclear magnetic resonance absorption in glass. I. Nuclear quadrupole effects in boron oxide, sodaboric oxide, and borosilicate glasses, Journal of Chemical Physics, 29, pp. 984–990. 5. Scheerer, J., M¨ uller-Warmuth, W., and Dutz, H. (1973). Nuclear magnetic resonance investigations of alkali borosilicate glasses, Glastechnische Berichte, 46, pp. 109–112. 6. Mosel, B. D., M¨ uller-Warmuth, W., and Dutz, H. (1974). Structure of alkali silicate glasses as studied by 29 Si NMR absorption and adiabatic fast passage, Physics and Chemistry of Glasses, 15, pp. 154–157. 7. Heitjans, P., et al. (1982). Nuclear spin-lattice relaxation in a lithium-silicate glass, Journal de Physique (Paris), Colloque, 43, pp. 143–147. 8. Jellison Jr., G. E., and Bray, P. J. (1976). A determination of the distributions of quadrupolar coupling constants in borate glasses using B10 NMR, Solid State Communications, 19, pp. 517–520. 9. Yun, Y. H., and Bray, P. J. (1978). Nuclear magnetic resonance studies of the glasses in the system Na2 OB2 O3 SiO2 , Journal of Non-Crystalline Solids, 27, pp. 363–380. 10. Hendrickson, J. R., and Bray, P. J. (1974). Nuclear magnetic resonance studies of 7 Li ionic motion in alkali silicate and borate glasses, Journal of Chemical Physics, 61, pp. 2754–2764. 11. Dupree, R. (1991). MAS NMR as a structural probe of silicate glasses and minerals, Transactions of the American Crystallographic Association, 27, pp. 255–267. 12. Eckert, H. (2018). Spying with spins on messy materials: 60 years of glass structure elucidation by NMR spectroscopy, International Journal of Applied Glass Science, 9, pp. 167–187.

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13. Stebbins, J. F. (2019). Dynamics and structure of silicate and oxide melts: Nuclear magnetic resonance studies, Structure, Dynamics, and Properties of Silicate Melts, 32, pp. 191–246. 14. Massiot, D., et al. (2013). Topological, geometric, and chemical order in materials: Insights from solid-state NMR, Accounts of Chemical Research, 46, pp. 1975–1984. 15. Andrew, E. R., Bradbury, A., and Eades, R. G. (1958). Nuclear magnetic resonance spectra from a crystal rotated at high speed, Nature, 182, p. 1659. 16. Lowe, I. J. (1959). Free induction decays of rotating solids, Physical Review Letters, 2, p. 285. 17. Lippmaa, E., et al. (1982). High resolution 29 Si NMR study of the structure and devitrification of lead-silicate glasses, Journal of Non-Crystalline Solids, 50, pp. 215–218. 18. Sen, S., and Youngman, R. E. (2003). NMR study of Q-speciation and connectivity in K2 O–SiO2 glasses with high silica content, Journal of Non-Crystalline Solids, 331, pp. 100–107. 19. Gresch, R., M¨ uller-Warmuth, W., and Dutz, H. (1976). 11 B and 27 Al NMR studies of glasses in the system Na2 OB2 O3 Al2 O3 (“NABAL”), Journal of Non-Crystalline Solids, 21, pp. 31–40. 20. M¨ uller-Warmuth, W., and Eckert, H. (1982). Nuclear magnetic resonance and Mossbauer spectroscopy of glasses, Physics Reports, 88, pp. 91–149. 21. Chmelka, B. F., et al. (1989). Oxygen-17 NMR in solids by dynamic-angle spinning and double rotation, Nature, 339, pp. 42–43. 22. Youngman, R. E., et al. (1995). Short- and intermediate-range structural ordering in glassy boron oxide, Science, 269, pp. 141–1420. 23. Youngman, R. E., and Zwanziger, J. W. (1996). Network modification in potassium borate glasses: Structural studies with NMR and Raman spectroscopies, Journal of Physical Chemistry, 100, pp. 16720–16728. 24. Clark, T. M., Grandinetti, P. J., Florian, P., and Stebbins, J. F. (2004). Correlated structural distributions in silica glass, Physical Review B, 70, p. 064202. 25. Medek, A., Harwood, J. S., and Frydman, L. (1995). Multiplequantum magic-angle spinning NMR: A new method for the study of quadrupolar nuclei in solids, Journal of the American Chemical Society, 117, pp. 12779–12787. 26. Youngman, R. E., Werner-Zwanziger, U., and Zwanziger, J. W. (1996). A comparison of strategies for obtaining high-resolution NMR spectra of quadrupolar nuclei, Zeitschrift f¨ ur Naturforschung A, 51, pp. 321–329.

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27. Youngman, R. E., and Zwanziger, J. W. (1994). Multiple boron sites in borate glass detected with dynamic angle spinning nuclear magnetic resonance, Journal of Non-Crystalline Solids, 168, pp. 293–297. 28. Youngman, R. E. (2018). NMR spectroscopy in glass science: A review of the elements, Materials, 11, p. 476. 29. Ashbrook, S. E., and Smith, M. E. (2006). Solid state 17 O NMR — An introduction to the background principles and applications to inorganic materials, Chemical Society Reviews, 35, pp. 718–735. 30. Kiczenski, T. J., Du, L. S., and Stebbins, J. F. (1994). F-19 NMR study of the ordering of high field strength cations at fluoride sites in silicate and aluminosilicate glasses, Journal of Non-Crystalline Solids, 337, pp. 142–149. 31. Gambuzzi, E., et al. (2014). Probing silicon and aluminum chemical environments in silicate and aluminosilicate glasses by solid state NMR spectroscopy and accurate first-principles calculations, Geochimica et Cosmochimica Acta, 125, pp. 170–185. 32. Pedone, A., Gambuzzi, E., Malavasi, G., and Menziani, M. C. (2012). First-principles simulations of the 27 Al and 17 O solid-state NMR spectra of the CaAl2 Si3 O10 glass, Theoretical Chemistry Accounts, 131, p. 1147. 33. Angeli, F., et al. (2011). Insight into sodium silicate glass structural organization by multinuclear NMR combined with first-principles calculations, Geochimica et Cosmochimica Acta, 75, pp. 2453–2469. 34. Liebau, F. (1981). In: Structure and Bonding in Crystals II, edited by O’Keefe, M., and Novrotsky, A. (New York, NY, Academic Press), p. 197. 35. Kroeker, S., and Stebbins, J. F. (2001). Three-coordinated boron-11 chemical shifts in borates, Inorganic Chemistry, 40, pp. 6293–6246. 36. Risbud, S. H., Kirkpatrick, R. J., Taglialavore, A. P., and Montez, B. (1987). Solid-state NMR evidence of 4-, 5 and 6-fold aluminum sites in roller-quenched SiO2 -Al2 O3 glasses, Journal of the American Ceramic Society, 70, pp. C-10-C12. 37. Wright, A. C., Vedishcheva, N. M., and Shakhmatkin, B. A. (1995). Vitreous borate networks containing superstructural units: A challenge to the random network theory? Journal of Non-Crystalline Solids, 192–193, pp. 92–97. 38. Tischendorf, B., et al. (2001). A study of the short and intermediate range order in zinc phosphate glasses, Journal of Non-Crystalline Solids, 282, pp. 147–158. 39. Maekawa, H., et al. (1996). Effect of alkali metal oxide on 17 O NMR parameters and Si–O–Si angles of alkali metal disilicate glasses, Journal of Physical Chemistry, 100, pp. 5525–5532.

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40. Zhang, P., Grandinetti, P. J., and Stebbins, J. F. (1997). Anionic species determination in CaSiO3 glass using two-dimensional 29 Si NMR, Journal of Physical Chemistry B, 101, pp. 4004–4008. 41. Trease, N. M., et al. (2017). Bond length-bond angle correlation in densified silica — results from 17 O NMR spectroscopy, Journal of Chemical Physics, 146, p. 184505. 42. Maekawa, H., Maekawa, T., Kawamura, K., and Yokokawa, T. (1991). The structural groups of alkali silicate glasses determined by 29 Si MAS-NMR, Journal of Non-Crystalline Solids, 127, pp. 53–64. 43. Greaves, G. N., et al. (1991). A structural basis for ionic diffusion in oxide glasses, Philosophical Magazine A, 64, pp. 1059–1072. 44. Engelhardt, G., and Michel, D. (1987). High-Resolution Solid-State NMR of Silicates and Zeolites (Chichester, England, John Wiley & Sons). 45. Maciel, G. E., and Sindorf, D. W. (1980). Silicon-29 nuclear magnetic resonance study of the surface of silica gel by cross-polarization and magic-angle spinning, Journal of the American Chemical Society, 102, pp. 7606–7607. 46. Eckert, H., Yesinowski, J. P., Silver, L. A., and Stolper, E. M. (1988). Water in silicate glasses: Quantitation and structural studies by 1 H solid echo and MAS-NMR methods, Journal of Physical Chemistry, 92, pp. 2055–2064. 47. Lee, S. K., and Sung, S. (2008). The effect of network-modifying cations on the structure and disorder in peralkaline Ca–Na aluminosilicate glasses: O–17 3QMAS NMR study, Chemical Geology, 256, pp. 326– 333. 48. Zheng, Q. J., et al. (2012). Structure of boroaluminosilicate glasses: Impact of [Al2 O3 ]/[SiO2 ] ratio on the structural role of sodium, Physical Review B, 86, p. 054203. 49. Neuville, D. R., Cormier, L., and Massiot, D. (2004). Al environment in tectosilicate and peraluminous glasses: A 27 Al MQ-MAS NMR, Raman and XANES investigation, Geochimica et Cosmochimica Acta, 68, pp. 5071–5079. 50. Sundararaman, S., Huang, L., Ispas, S., and Kob, W. (2019). New interaction potentials for alkali and alkaline-earth aluminosilicate glasses, Journal of Chemical Physics, 150, p. 154505. 51. Svenson, M. N., et al. (2016). Volume and structural relaxation in compressed sodium borate glass, Physical Chemistry Chemical Physics, 18, pp. 29879–29891. 52. Wu, X., Youngman, R. E., and Dieckmann, R. (2013). Sodium trace diffusion and 11 B NMR study of glasses of the type

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54.

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58.

59. 60.

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(Na2 O)0.17 (B2 O3 )x (SiO2 )0.83−x , Journal of Non-Crystalline Solids, 378, pp. 168–176. Smedskjaer, M. M., et al. (2011). Topological principles of borosilicate glass chemistry, Journal of Physical Chemistry B, 115, pp. 12930– 12946. Kapoor, S., et al. (2017). Pressure-driven structural depolymerization of zinc phosphate glass, Journal of Non-Crystalline Solids, 469, pp. 31–38. Brow, R. K., Phifer, C. C., Turner, G. L., and Kirkpatrick, R. J. (1991). Cation effects on 31 P MAS NMR chemical shifts of metaphosphate glasses, Journal of the American Ceramic Society, 74, pp. 1287–1290. Montagne, L., Palavit, G., and Delaval, R. (1997). 31 P NMR in (100-x)(NaPO3)-xZnO glasses, Journal of Non-Crystalline Solids, 215, pp. 1–10. Roiland, C., Fayon, F., Simon, P., and Massiot, D. (2011). Characterization of the disordered phosphate network in CaO-P2O5 glasses by 31 P solid-state NMR and Raman spectroscopies, Journal of Non-Crystalline Solids, 357, pp. 1636–1646. Youngman, R. E., Hogue, C. L., and Aitken, B. G. (2007). Crystallization of silicon pyrophosphate from silicophosphate glasses as monitored by multi-nuclear NMR, Materials Research Society Symposium Proceedings, 984, pp. 84–90, MM 12-03. Dupree, R., Holland, D., and Mortuza, M. G. (1987). Six-coordinated silicon in glasses, Nature, 328, pp. 416–417. Aitken, B. G., Youngman, R. E., Deshpande, R. R., and Eckert, H. (2009). Structure-property relations in mixed-network glasses: Multinuclear solid state NMR investigations of the system xAl2 O3 :(30x)P2 O5 :70SiO2 , Journal of Physical Chemistry C, 113, pp. 3322–3331. Ren, J., Doerenkamp, C., and Eckert, H. (2016). High surface area mesoporous GaPO4 -SiO2 sol–gel glasses: Structural investigation by advanced solid-state NMR, Journal of Physical Chemistry C, 120, pp. 1758–1769. Brehault, A., et al. (2018). Compositional dependence of solubility/retention of molybdenum oxides in aluminoborosilicate-based model nuclear waste glasses, Journal of Physical Chemistry B, 122, pp. 1714–1729. Koller, H., Engelhardt, G., Kentgens, A. P. M., and Sauer, J. (1994). 23 Na NMR spectroscopy of solids: Interpretation of quadrupole interaction parameters and chemical shifts, Journal of Physical Chemistry, 98, pp. 1544–1551. Bohmer, R., Jeffrey, K. R., and Vogel, M. (2007). Solid-state Li NMR with applications to the translational dynamics of ion conductors, Progress in Nuclear Magnetic Resonance Spectroscopy, 50, pp. 87–174.

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CHAPTER 4

Contact Damage in Oxide Glass Timothy M. Gross Corning Research and Development Corporation, Corning, NY

4.1. Introduction The usable strength for glass is highly dependent on the population of flaws on the surfaces. As-formed glass with a near pristine surface can have exceptionally high strength. However, this surface strength is quickly degraded as the glass is contacted through typical handling processes. The contacts that result in damage are generally highly localized, so can produce significant stresses even at low applied loads. Depending on the applied load and contact area, we may observe either fully elastic deformation or permanent deformation where the yield condition has been exceeded. In both cases, significant flaw generation is generally observed. By studying the signatures of contact damage observed in glasses in the field, laboratory tools have been developed to closely replicate various damage types. Through this controlled damage replication, glass scientists have been able to determine how to better design glasses to be more resistant to contact damage and flaw formation. This chapter provides an overview of linear elastic fracture mechanics to demonstrate the importance of flaws in the strength of glass. 99

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Once this is established, the various types of flaw-generating contact damage are discussed and potential materials engineering solutions toward contact damage prevention are considered. 4.2. Linear Elastic Fracture Mechanics The theoretical calculations for defect-free oxide glasses predict remarkable strengths for oxide glasses. For example, the theoretical strength of silica glass is approximately 16 gigapascals (GPa) [1] due to the high strengths of the covalent bonds that make up the silica glass network (the strength of Si–O bonds is 444 kJ/mol [2]). To perform the theoretical strength calculation, we first consider the potential energy well showing interatomic potential, U , versus interatomic distance between adjacent atoms, r, as shown in Fig. 4.1(a). The binding energy is labeled as Uo and the equilibrium separation distance between atoms is labeled as ao . The plot is the sum of coulombic attractive energy and repulsive energy due to overlap of electrons and can be represented by the Lennard-Jones potential expression:    a 6  ao 12 o −2 (4.1) U = Uo r r The slope of the potential energy, dU/da, plotted over the same length scale gives the corresponding forces of attraction and repulsion as shown in Fig. 4.1(b). A corresponding stress plot (force/unit area) can then be generated and fit with the following sine function as shown in Fig. 4.2:   2πx (4.2) σ = σm sin λ where x is the increase in atomic spacing. The equilibrium separation is at x = ao and the position of the maximum stress, σm , is at x = ao + λ/4. The energy of two new fracture surfaces should be equal to the work of separation, given by the area under the stress versus distance curve and approximated by area under a sinusoidal curve:    λ 2 λσm 2πx dx = (4.3) σm sin 2˜ af = λ π 0

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8 6

12

Potenal Energy (eV)

=

−2

6

4 2 0 0

0.1

-2

0.2

0.3

0.4

Uo

-4

ao

-6 Interatomic Separaon (nm) (a) 15 10

Force (nN)

5 ao

0 0

0.1

0.2

0.3

0.4

-5 -10 -15 -20 Interatomic Separaon (nm)

(b)

Fig. 4.1. (a) The potential energy versus interatomic separation as represented by the Lennard-Jones potential expression. (b) The positive attractive forces and negative repulsive forces as a function of interatomic separation.

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ao /2

Interatomic Separaon

Fig. 4.2. Stress (force/area) versus interatomic separation with sinusoidal curve fit.

where γf is the fracture surface energy. By rearranging, we get: 2πγf (4.4) λ For an elastic material, Hooke’s law can be used with the strain, , equal to axo : σm =

σ = E = E

x ao

(4.5)

where E is the Young’s modulus. The stress is then proportional to displacement with a slope of aEo . So, the derivative of Eq. (4.2) with respect to x at x = 0 should give this slope value at small displacement:   2πσm dσ E (4.6) = = ao dx x=0 λ If we solve Eq. (4.6) for λ and substitute into Eq. (4.4), we get the Orowan equation [3] for the theoretical strength of glass: γf E (4.7) σm = a0

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Fig. 4.3. A glass surface under applied stress containing a flaw of depth c and radius of curvature ρ.

If we take values for silica, E = 73 GPa, γf = 0.56 J/m2 [1], and ao = 1.62 ˚ A [4], the calculation gives 15.9 GPa as the theoretical strength. However, in practice, the measured strength of glasses is typically several orders of magnitude lower than this theoretical value due to flaws on the glass surface. To demonstrate this, Inglis showed that when the surface contains a flaw of depth c and radius of curvature ρ as shown in Fig. 4.3, the stress is concentrated at the flaw location to a value above the applied stress, σapp [5]:

σconc = σapp

c ρ

(4.8)

Fracture is then expected to occur when σconc = σm . The Inglis formula has a limitation in that the σapp to cause failure is practically zero for infinitesimally small radius of curvature. Griffith suggested that the condition where σconc = σm is not adequate to predict failure, but that the crack length must exceed a critical value [6]. The energetics of crack formation are comprised of competing contributions from the increase in surface energy, Uγ , and loss of elastic strain energy, US . The formation of the crack in Fig. 4.3 should lead to a surface energy increase of 2cγf corresponding to the creation of two new surfaces of length c. The elastic strain energy density, u, is given by: 



σd = Ed =

u= 0

σ2 E2 = 2 2E

(4.9)

and the energy loss region is given by two triangular regions having total area of βc2 as shown in Fig. 4.4. The value of β that satisfies the Inglis solution for plane stress loading is π, so that the overall

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Fig. 4.4. A schematic representation of the unloaded region near the crack tip comprised of two triangles having base c and height βc.

elastic strain energy lost is: σ2 σ 2 πc2 · πc2 = − (4.10) 2E 2E The thickness is taken as unity, so US is the strain energy per unit thickness. The total energy, ETOT is then given as: US = −

σ 2 πc2 (4.11) 2E The energy curves are plotted in Fig. 4.5 and show that above some critical crack size, c*, it becomes energetically favorable for the crack to grow. The critical crack size is then given by: ETOT = Uγ + US = 2cγf −

σ 2 πc dETOT = 2γf − =0 (4.12) dc E Which can be rearranged to give to the Griffith equation for strength of glass for a given flaw size:

2γf E (4.13) σf = πc Due to the importance of Griffith’s work in determining the relationship between glass strength and flaw size, typical flaws existing on glass surfaces are referred to as Griffith’s flaws. The theoretical formula most commonly used to predict failure was subsequently developed by Irwin [7]. The failure criteria are defined as when the stress intensity, KI , reaches a critical value, KIC . Unlike failure strength in brittle materials, this critical value of stress intensity is an intrinsic material property that is also referred to as fracture toughness. The subscript I refers to Mode I crack opening mechanism, as opposed to Mode II in plane shearing or Mode III

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Fig. 4.5. The energy contributions and total energy as a function of crack size.

anti-plane shearing. Since flaw populations are such that Mode I is the dominant failure mechanism in glass, we will only focus on this mode. Irwin’s KI formula shows the importance of considering both flaw size, c, and externally applied stress, σ: √ (4.14) KI = Y σ c The factor Y is the crack shape parameter that depends on the crack geometry. Some commonly used crack shape parameters are √ Y = 1.12 π for through-plate, scratch-like surface cracks [8] and √ Y = 0.73 π for semi-circular half-penny shaped cracks [9]. The values for critical stress intensity for glasses typically range from √ 0.6 to 0.9 MPa m. As shown in Eq. (4.14), the critical stress intensity value can be achieved for low externally applied stresses if the flaw size is large or conversely high externally applied stresses are required to achieve KIC if the flaw size is very small. That being said, the strength of glass surfaces is highly dependent on the handling processes, that is, the flaws introduced by various forms of contact, and the contact damage introduced in the end-use

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application. The upcoming sections will provide a review of the fundamentals of contact mechanics in oxide glasses and describe testing methods that can be used to replicate the contact damage events that are frequently observed. 4.3. Elastic (Hertzian) Contact When a contact load is distributed over a large enough contact area, the local deformation is primarily elastic and recovered upon removal of the load. A ball-type indenter is typically used to replicate this type of blunt contact condition in the lab. Figure 4.6(a) shows a schematic representation of an elastic contact made by pressing a ball of radius R into the surface of a rigid glass plate. To achieve significant local elastic deformation via blunt contact confined to the top surface, the rigidity of the plate needs to high. This produces significant Hertzian

(a)

(b)

Fig. 4.6. (a) Schematic of a cross section of Hertzian contact in a rigid glass plate with elastic deformation confined to the top surface. The contact typically results in the formation of a ring crack at the boundary of contact at the surface that extends into the sub-surface to form a characteristic cone crack. (b) If the plate lacks sufficient rigidity, then the cracking response is dominated by biaxial flexure, that is, crack opening on the bottom surface.

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stresses that create characteristic cracking damage, that is, the ring and cone cracks also shown schematically in Fig. 4.6(a). This type of damage is very often seen in thick, rigid plates of glass exposed to high-pressure elastic contacts such as in the external surface of a car windshield. The rigidity, D, of a glass plate is highly dependent on the glass thickness, t: D=

E · t3 12(1 − ν 2 )

(4.15)

Where E is the elastic modulus and ν is Poisson’s ratio. For lower rigidity, thinner glass plates, the cracking responses are dominated by global bending, that is, biaxial flexure, as shown schematically in Fig. 4.6(b). In this scenario, the biaxial stress on the bottom surface is highly dependent on the resulting bend radius of the glass as it conforms to the radius of the ball: σ=

t 1 E · · 2 1−ν 2 R

(4.16)

While biaxial loading of thin glass is an interesting topic, it is out of scope for the present chapter and can be reviewed elsewhere [10]. Here, we will focus on the contact conditions that result in elastic deformation that gives rise to Hertzian ring and cone cracks. Hertz found that the radius of the circle of contact, a, for a rigid sphere pressed into a flat surface depends on the indenter load, P , the indenter radius, R, and the combined modulus of the sphere and surface materials, E ∗ [11]. a3 =

3 PR 4 E∗

(4.17)

The combined modulus is given as: (1 − v12 ) (1 − v22 ) 1 = + E∗ E1 E2

(4.18)

Where the modulus and poisons ratio of the indenter are given as E1 and ν1 , respectively. These same elastic properties for the flat surface are given as E2 and ν2 . The maximum stress surrounding the circle

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of contact in the flat surface was also determined by Hertz and is given in the following equation [11]: σmax = (1 − 2ν2 )

P 2πa2

(4.19)

If we then combine Eqs. (4.17) and (4.19), we can get a simple expression for the maximum stress in terms of the indenter radius.   ∗ 2/3  1 2 4E 1 − 2ν2 P 3 R− 3 (4.20) σmax = 2π 3 This maximum stress value is responsible for the ring cracks that form perpendicular to the glass surface during ball on glass plate contact. Figure 4.7 shows ring cracks that have formed in the surface of 3 mm thickness soda–lime–silicate following contact with a 1.0 mm diameter tungsten carbide ball at 50 N. Using E1 = 600 GPa, ν1 = 0.2, E2 = 72 GPa, ν2 = 0.2, the contact circle is calculated as 65 μm and the maximum stress outside of the contact circle is calculated to be 1.1 GPa.

Fig. 4.7. Hertzian ring cracks produced in 1/8 thick soda–lime–silicate by pressing a 1.0 mm diameter tungsten carbide ball into the glass at a 50 N load.

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The distribution of stress within the specimen has geometric similarity if all spatial coordinates are normalized by the contact radius a, and all the stresses are normalized by the mean contact pressure, pm = P/πa2 . The stresses in an xz plane perpendicular to the surface can then be given as follows from a solution by Huber [12]:          z 3 3 z 3 1 − 2ν a2 a2 u σxx √ 1− √ + = pm 2 r2 u 2 u u2 + a2 z 2     √ u u a 3 z + (1 + ν) tan−1 √ −2 + √ (1 − ν) 2 2 u a +u a u (4.21)  3   2 σzz z 3 a u √ =− (4.22) 2 pm 2 u u + a2 z 2    2√  rz 2 3 a u σxz (4.23) =− pm 2 u2 + a2 z 2 a2 + u where 1 (4.24) u = {(r 2 + z 2 − a2 ) + [(r 2 + z 2 − a2 )2 + 4a2 z 2 ]1/2 } 2 The principal stresses across the cone crack path are given as: σN (x, z) = σxx sin2 α + σzz cos2 α − 2σxz sin α cos α

(4.25)

where α is the angle between the crack path and the specimen surface and is determined from the following equation: tan 2α =

−2σxz σxx − σzz

(4.26)

The above equations can be used to demonstrate the key features of the Hertzian stress field, namely that the principal stresses directly beneath the contact circle within a droplet-shaped zone are all compressive and the tensile stresses are maximum at the contact circle and decay relatively slowly with radial distance from the contact. Another key feature is that the trajectories of the most compressive principal stresses are initially normal to the surface at the contact circle then fan outward as a function of depth to give the shape of the cone cracks in the sub-surface. The stresses normal

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Fig. 4.8. Trajectories of the minimum (most compressive) principal stress under Hertzian contact loading. Calculated for ν = 0.31. Figure reproduced from Lawn et al. [13] with permission from Springer Nature.

to these trajectories give the greatest tensile principal stresses. Figure 4.8 shows the trajectories of the most compressive principal stresses under Hertzian contact loading as demonstrated by Lawn et al. for a material with ν = 0.31 [13]. As shown in Fig. 4.9(a), an aluminosilicate glass indented with a 1/16 diameter ruby sapphire ball at 300 N is viewed from the surface. Characteristic ring cracks at the surface are observed and can be seen extending into the sub-surface to form the cone. The cone is also viewed through a polished side in Fig. 4.9(b) to show how the cone shape follows a typical cone crack opening stress trajectory. It should also be noted that the Poisson’s ratio will have a large impact on the stress field and predicted cone cracking angles according to the above equations. However, Lawn et al. and Chaudhri and Kurkjian show a discrepancy between the cone angles calculated by the Huber model and experimental results [13, 14]. The formation of the initial ring crack depends on both the stress field generated by the contact as given in Eqs. (4.19) and (4.20) as well as the presence of a surface flaw in this stressed region, so that the KI value given in Eq. (4.14) locally exceeds the critical value, KIC . Since the ring crack formation is dependent on highly variable surface flaw populations and the stressed area is small relative to the overall surface area of a glass plate, the measured distribution of ring

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(a)

(b)

Fig. 4.9. (a) An aluminosilicate glass indented with a 1/16 diameter ruby sapphire ball at 300 N viewed from the surface. Characteristic ring cracks at the surface are observed and can be seen extending into the sub-surface to form the cone. (b) The cone is also viewed through a polished side to show how the cone shape follows a typical cone crack opening stress trajectory.

cracking thresholds is typically large. The data shown in Fig. 4.10 is for 0.5 and 1.0 mm diameter tungsten carbide ball indentation of an alkali aluminosilicate glass. The generation of the ring cracks occurred during application of the load for this experiment and was measured using an acoustic emission sensor attached to the surface of the glass plate. The measured ring cracking loads for the as-received glass are given as open squares in the plot, whereas the ring cracking loads for lightly etched glass specimens are given as filled diamonds. The etching treatment was performed in 5% HF acid solution and the

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400

Ring Crack Threshold (N)

350

Aluminosilicate As-Received Aluminosilicate with Light Etch

300 250 200 150 100 50 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Tungsten Carbide Ball Diameter (mm)

Fig. 4.10. Ring cracking thresholds for 0.5 and 1.0 mm diameter tungsten carbide ball indentation in alkali aluminosilicate glass. As shown, the cracking threshold distribution shifts to higher values for lightly etched glass.

removal depth was approximately 2 microns. For both sets of glass samples, the ring cracking threshold loads show a wide distribution. As expected from the maximum stresses outside of the contact circle for a given load, the 0.5 mm diameter tungsten carbide indenter gives lower threshold values when compared to the 1.0 mm diameter indenter. The wide distributions for these data sets indicate that the flaws being acted upon to form ring cracks are highly variable in size. The shifts in the cracking load distributions for the acid treated parts indicate a reduction in the flaw size distribution as expected. Due to the wide ranges in cracking loads, Weibull statistics are typically employed to generate meaningful data that can be used to compare the cracking response of different glass types. Another point to note is that the formation of ring cracks can occur on either the loading or unloading cycles of a ball indentation experiment. Ring cracking is frequently observed on the unloading cycle because the

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Fig. 4.11. Frictive damage in soda–lime–silicate contacted with a sliding 1/4 tungsten carbide ball at 200 N. Sample was lightly etched in 5% HF solution to reveal chatter marks.

region in contact with the ball gets damaged. Subsequently, during unloading the maximum stress circle decreases in size and intersects this damaged glass. 4.3.1. Sliding Elastic Contact By adding a sliding component to elastic contact, frictive damage can result. An example of frictive damage is shown in Fig. 4.11 for soda–lime–silicate contacted with a sliding 1/4 tungsten carbide ball at 200 N. The damage consists of crescent-shaped cracks sometimes referred to as chatter marks. These crescent-shaped cracks are formed due to the Hertzian ring stress combined with a frictional component that trails the contact as it moves across a surface. These frictive, partial ring cracks can extend into the sub-surface to form partial cone cracks under some loading conditions. The equation that describes the stresses due to sliding elastic contact between a ball and flat surface have been determined by Hamilton and Goodman as follows [15]:   (4 + ν) 3P 1 (1 − 2ν) + μπ (4.27) σt = 2πa2 3 8

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Where the first term in the brackets represents the stress due the normal load alone and when multiplied by the pre-factor is equivalent to Eq. (4.19). The second term in the brackets corresponds to the added stress due to friction, where μ is the coefficient of friction between the flat surface and the sliding ball. The maximum tensile stress on the surface becomes highly dependent on the coefficient of friction, so that the introduction of low μ coatings, for example, fluorine-based amphiphobic coatings, can have a significant impact on the tensile stresses generated. Figure 4.12 shows the calculated maximum tensile stress at the surface for a 0.5 mm diameter aluminosilicate glass contacting a flat plate of the same glass. The maximum tensile stress as a function of normal load is shown to increase in the following order: point loading < sliding

Fig. 4.12. The calculated maximum tensile stress at the surface for a 0.5 mm diameter aluminosilicate glass contacting a flat plate of the same glass. The maximum tensile stress as a function of normal load is shown to increase in the following order: point loading < sliding contact with a μ of 0.1 < point loading with μ of 0.2. The horizontal dashed line is the estimated stress threshold to initiate cracking for a 1 micron flaw population.

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contact with a μ of 0.1 < point loading with μ of 0.2. These contact scenarios simulate a particle of glass originating at the scored and broken edge in contact with a glass surface under pressure with and without sliding motion. Glass particles originating at a scored and broken edge commonly damage the surfaces of glasses packed into crates during shipping, however, this damage can be significantly reduced by application of coatings to a glass surface [16]. If we assume that ring cracks or chatter marks are initially oriented perpendicular to the surface, a simple fracture mechanics calculation can be used to estimate the threshold for crack opening. If the aluminosilicate in Fig. 4.12 has a fracture toughness of 0.7 MPa √ m and we assume a uniform distribution of 1 micron sized semielliptical flaws (this is a reasonable assumption for typical handling practices), then we can calculate the cracking stress by rearranging Eq. (4.14): σ=

√ 0.7 MPa m KIC

√ = = 541 MPa Y a 0.73 π · 10−6 μm

(4.28)

The plot in Fig. 4.12 shows a horizontal dashed line representing the stress threshold for cracking for this hypothetical case. It is then easily shown that point contact requires the highest load to initiate a ring crack and that the addition of the frictional component causes chatter cracking to occur at much lower loads. The benefit of lower μ coatings is also apparent. The damage introduced by Hertzian point and frictive contact is frequently difficult, if not impossible, to observe with an optical microscope even under high magnification. In fact, the glass surface may appear to be in perfect condition, but this appearance can be misleading. Cracks that open under sliding contact frequently close tight once the sliding tensile stress has passed by, so that they cannot be observed by microscope, yet have a big impact on the flexural strength of the glass. Typically, the easiest way to observe frictive damage is to lightly etch the glass surface to reveal these crescentshaped cracks as was done in Fig. 4.11.

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Fig. 4.13. Ball indentation impressions in soda–lime with a 0.5 mm tungsten carbide balls result in dimples in the surface, indicating that the elastic limit was locally exceeded.

As the ball radius gets smaller, the contact deformation ceases to be completely elastic and some permanent deformation is observed. As shown in Fig. 4.13, indenting soda–lime with a 0.5 mm tungsten carbide balls results in dimples in the surface, indicating that the elastic limit of the glass was locally exceeded. This leads into the next sections covering permanent deformation in glasses by highly localized contacts, that is, sharp contacts. 4.4. Glass Hardness For global bending of glass plates or fibers, permanent deformation is typically not observed or its minor plasticity contribution to the overall deformation is practically negligible. However, highly localized, sharp contacts can result in conditions where the elastic limit is exceeded and permanent deformation is observed. The hardness of a material can be thought of as the resistance of a material to permanent deformation. To roughly compare materials with considerably different hardness, a Mohs hardness test can be utilized. The Mohs hardness scale consists of a series of minerals ranked from 1 (softest) to 10 (hardest) as shown in Table 4.1. The series of minerals is used to determine the position of an unknown material on the scale, that is, the position in between a harder mineral that leaves a scratch and a softer mineral that does not leave a scratch. Glass is typically reported to have a Mohs hardness at 5.5–7.0, while polymers have a Mohs hardness of about 1.0. The

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Table 4.1. Moh’s hardness scale. Moh’s Hardness 1 2 3 4 5 6 7 8 9 10

(a)

Minerial

Chemical Formula

Talc Gypsum Calcite Fluorite Apatite Orthoclase feldspar Quartz Topaz Corundum Diamond

Mg3 Si4 O10 (OH)2 CaSO4 · 2H2 O CaCO3 CaF2 Ca5 (PO4 )3 (OH− , Cl− , F− ) KAlSi3 O8 SiO2 Al2 SiO4 (OH− , F− )2 Al2 O3 C

(b)

(c)

(d)

Fig. 4.14. Geometries of commonly used indenter tips: (a) Knoop, (b) Vickers, (c) Berkovich, and (d) cube corner. Tip sharpness is in the following order: Knoop (bluntest) < Vickers = Berkovich < cube corner (sharpest).

test is useful for comparing very different materials such as glasses and polymers, but is too coarse to be useful to compare hardness values within a material set such as in glasses. To compare the hardness of oxide glasses, diamond indentation is the preferred testing method and is adequate to determine small changes in hardness among different glass compositions. The most commonly used diamond indenter for measuring hardness is a Vickers indenter, although other diamond indenter geometries such as Knoop, Berkovich, and cube corner can also be used. Figure 4.14 shows the geometries of these commonly used diamond indenter tips.

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The hardness value for diamond indentation is given by the applied load divided by the surface area of the impression. The Vickers hardness number (VHN) is given by the following equation:   P · 2 sin 2θ P · 1.8544 = (4.29) VHN = 2 l l2 Where P is the applied load, θ is the 136◦ angle between opposite faces of the Vickers indenter, and l is the major diagonal length of the indent impression. The equation is valid for Vickers micro-indentation loads, that is, 50–2000 gf, where the glass that piles up around the periphery of the contact at the edges adds negligible contact area, so that the contact area term given in Eq. (4.29), 2 sin(θ/2)/l2 , is adequate. In the nano-indentation load regime where impression area is significantly smaller, the pileup becomes an important contribution to the overall contact area and correction factors must be applied. The indentation load used to determine hardness should be selected so that the impression is free of cracking. Cracking makes the indentation boundary less well defined and consequently the measurement of the major diagonal length by reticule method is less accurate. The measured indentation hardness has some dependence on the testing environment. In water-containing environments, some water will enter the glass at the impression site and decrease the hardness [17]. This is especially apparent as dwell times are increased as shown for hardness measurements made in water and toluene environments in Fig. 4.15 [18]. If the indentation is made in a dry environment such as performing the indentation through a droplet of dry toluene, the hardness value is initially higher and remains constant as a function of dwell time. Toluene is a non-polar solvent with low water solubility, so is utilized frequently to demonstrate the impact of removing water from the indentation environment. 4.4.1. Indentation Size Effect The indentation hardness is often observed to be load dependent, that is, the indentation hardness decreases with increasing load until

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Fig. 4.15. Hardness of Less Brittle glass as a function of loading time is water and toluene environments. Hardness measurements performed at 100 gf load. Figure reproduced from Gross and Tomozawa [18] with permission from AIP publishing.

a constant hardness is achieved at higher indentation load conditions. This is known as the indentation size effect (ISE). An example of ISE is given in Fig. 4.16 for a series of charge-balanced calcium aluminosilicate glasses [18]. Several researchers have proposed mechanisms for ISE [19–23], but the proposed mechanism from Bernhardt [24] was found to be most applicable to various experimental data. He considered that the energy needed to create additional surface area was the source of the ISE. His formula can be written as follows: P · l = a1 · l2 + a2 · l3

(4.30)

Where P is the indentation load, a1 and a2 are material constants, and l is the major diagonal length. P · l is proportional to the total mechanical energy acquired by the material during indentation, a1 · l2 is proportional to the surface energy acquired by the material, and a2 · l3 is proportional to the volume energy acquired by the material. Bernhardt’s equation assumes that all the mechanical energy is stored in the material, that is, no energy losses

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Fig. 4.16. Hardness as a function of load shows the indentation size effect for a series of charge balanced calcium aluminosilicate glasses. Figure reproduced from Gross and Tomozawa [18] with permission from AIP publishing.

occur. If we divide each side of Eq. (4.30) by l, we get the following: P = a1 · l + a2 · l2

(4.31)

The contact area of a micro-hardness impression is given by l2 /1.8544 according to Eq. (4.29). If divide P by the contact area, A, we get an expression for indentation hardness as a function of indentation size: 1.8544a1 P = + 1.8544a2 (4.32) A l A schematic of hardness versus indentation size is given in Fig. 4.17 to demonstrate the significance of the a1 and a2 coefficients. As shown, a1 is a measure of ISE and a2 is a measure of the load-independent part of micro-hardness. If we divide Eq. (4.31) by l, we obtain: P = a1 + a2 · l l

(4.33)

If P/l is then plotted versus l, we obtain a straight line with an y-intercept equal to a1 and a slope equal to a2 as shown in Fig. 4.18 for a 60%SiO2 20%Al2 O3 20%CaO glass.

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Fig. 4.17. A schematic of hardness vs. indentation size demonstrates the significant of the a1 and a2 coefficients.

Fig. 4.18. By plotting P/l versus l, we obtain a straight line with an y-intercept equal to a1 and a slope equal to a2 as shown for 60%SiO2 20%Al2 O3 20%CaO glass.

If the a1 · l2 term from Eq. (4.30) is considered to originate from the energy required to create additional surface area, γdA, during indentation and only the apparent geometric surface area is considered, the γdA value is smaller than a1 · l2 by several orders of magnitude. Apparently, Bernhardt realized this discrepancy and

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suggested that the additional surface created by indentation should include the formation of sub-surface damage [24]. As will be discussed in the next section, indentation deformation within the sub-surface creates defects such as shear faults and median cracks. It has been demonstrated that the magnitude of the a1 term is closely related to the amount of additional new surface area formed in the sub-surface from these defects. Glass compositions that deformed with little subsurface damage showed minimal a1 [18]. An attempt at quantifying γdA with the inclusion of sub-surface damage gave values much closer to a1 · l2 , but still fell short. However, it is very possible that local heating occurs along shear bands that account for this remaining energy discrepancy [25]. More recently, Smedskjaer provided further data suggesting that ISE is closely related to the energy required to create defects such as shear bands in the sub-surface [26]. The effects of ISE should be considered when comparing the hardness of glasses since different glass types have varying levels of ISE. As shown in Fig. 4.16, a glass with high a1 may appear significantly harder than other glasses at low indentation loads, but once higher loads are achieved this is no longer the case. This can have a big impact from a practical perspective since very localized, low load contacts from hard materials lead to the accumulation of fine groove, micro-ductile scratches in everyday use of glasses. The width of these micro-ductile scratches and thus their visibility will depend on the hardness of the material which is in turn dependent on load. A thorough description of sharp scratch damage will be covered in Section 4.5.7. 4.4.2. Hardness Dependence on Glass Structure The hardness of normal to intermediate glass types typically increases as the Young’s modulus also increases. These three properties are closely linked to the oxygen packing density in these glass types. Figures 4.19 and 4.20 show the hardness and modulus values for normal alkali aluminosilicate (20R2 O–10Al2 O3 – 70SiO2 ) and calcium aluminoborosilicate (15CaO–15Al2 O3 –xB2 O3 – (70-x)SiO2 ) glasses plotted against the oxygen packing density. The calcium aluminoborosilicate glasses are abbreviated in the plots as CABSX with X equal to the mol% B2 O3 . For the CABS5 and

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500

0.39

20Li2O-10Al2O3-70SiO2

0.45

CABS5 TF = 793oC CABS5 TF = 741oC

CABS25 TF = 622oC

0.43

450 400 0.37

CABS15 TF = 707oC

0.41

CABS25 TF = 664oC 10Li2O-10Na2O-10Al2O3-70SiO2

550

20Na2O-10Al2O3-70SiO2

600

10Na2O-10K2O-10Al2O3-70SiO2

650

20K2O-10Al2O3-70SiO2

Vickers Hardness Number (kgf/mm2)

700

0.47

0.49

Oxygen Packing Density

60

CABS5 TF = 741oC

20Li2O-10Al2O3-70SiO2 CABS15 TF =

707oC

0.43

CABS25 TF = 622oC

0.41

CABS25 TF = 664oC

65

10Li2O-10Na2O-10Al2O3-70SiO2

70

20Na2O-10Al2O3-70SiO2

75

20K2O-10Al2O3-70SiO2

Young's Modulus (GPa)

80

10Na2O-10K2O-10Al2O3-70SiO2

85

CABS5 TF = 793oC

Fig. 4.19. Vickers hardness versus packing density for a normal to intermediate alkali aluminosilicate and CABS glasses. Fictive temperature is equal to the anneal pt. temperature unless specified otherwise.

55 50 0.37

0.39

0.45

0.47

0.49

Oxygen Packing Density Fig. 4.20. Young’s modulus versus packing density for a normal to intermediate alkali aluminosilicate and CABS glasses. Fictive temperature is equal to the anneal pt. temperature unless specified otherwise.

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CABS25 glasses, the data in Figs. 4.19 and 4.20 show how the oxygen packing density, Young’s modulus, and hardness decrease with increasing fictive temperature (TF ). The oxygen packing density, Vo , is given by the following equation [27, 28]: Vo = no · v¯o

(4.34)

Where no is the number of oxygen atoms per unit volume and v¯o is the mean volume occupied by one oxide ion. The no value is determined by the following equation:  Xi ni · NA (4.35) no = i Vm Where Xi is the mole fraction of oxide i, ni is the number of oxygen atoms in oxide i, NA is Avogadros number, and Vm is the glass molar volume. The v¯o value is given as:  ki · li · CN i · 43 πro3i (4.36) v¯o = i  i ki · li · CN i Where ki is the mole fraction of each glass forming oxide at a given coordination state, li is the number of cations for a given oxide formula unit, CNi is the coordination number of each network forming species, and roi is the oxide radius corresponding to each network forming species [27, 28]. The oxygen packing density is closely related to the ionic field strength of modifier ions incorporated into a given glass type. Figure 4.21 shows the impact of modifier cation field strength on oxygen packing density for 20R2 O–10Al2 O3 –70SiO2 glasses. The ionic field strength, F , is given by the following equation: F =

Zc (rc + ro )2

(4.37)

Where rc is the cation radius and ro is the oxygen anion radius. The value for ro can be determined from Eq. (4.33) and the values of rc are taken from Shannon [29]. While hardness and Young’s modulus increases with oxygen packing density for normal to intermediate glasses, it has been shown that in the transition from intermediate to anomalous glass, the trend reverses [18, 30]. Where this trend change

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Ionic Field Strength of Alkali Ion

0.3 Li-containing glass

0.25 0.2 Na-containing glass

0.15 0.1

K-containing glass

0.05 0 0.37

0.39

0.41

0.43

0.45

0.47

0.49

Oxygen Packing Density Fig. 4.21. Modifier cation field strength versus oxygen packing density for 20R2 O–10Al2 O3 –70SiO2 glasses.

occurs appears to be dependent on indentation load regime, pileup corrections factors applied to low load indents, and testing environment. The cause for this reversal may be related to the increased amount of elastic recovery of indentation volume as the glass becomes more anomalous. A detailed description of normal, intermediate, and anomalous glasses is provided in Sections 4.5.1 and 4.5.2. 4.5. Indentation Deformation and Cracking Highly localized, sharp contact events are very common and a major source of strength degradation in glasses. When examining field damage in glass plates due to sharp contact, a permanent deformation region is observed along with several characteristic cracking systems. Through lab experimentation, it has been determined that a diamond indenter is a useful tool for replicating field damage and studying the deformation mechanisms and cracking systems generated. The diamond indenter most commonly used to study sharp contact is again the Vickers indenter, although it will be shown that the diamond geometry strongly dictates the response.

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The indentation crack resistance of glasses is quantified using a few different methods. Most typically, the average number of cracks for indents made at several loads is determined. The average number of cracks, zero through four, is then plotted against the load and the data is fit with a sigmoidal curve or other function [31]. Using this plot, the load required to produce two out of a possible four cracks is then defined as the crack initiation load. Another method commonly used is to define the crack initiation load as the load required to produce any number of strength-limiting median/radial cracks in more than 50% of the indents made at a given load [32]. From a strength perspective, any number of cracks produced will result in significant strength degradation, so the number of cracks present does not matter from this standpoint. In this chapter, the second method is used in defining crack initiation threshold. Just like with hardness, the indentation cracking threshold in dependent on the testing environment [17]. Indentation in water-containing environments results in lower cracking thresholds, so care must be taken to perform the tests under the same conditions to generate data that can be compared directly with historical results. Ideally, testing is performed in a controlled environment laboratory with fixed temperature and relative humidity. Another option employed is to perform experimentation in an inert environment, however, this may yield results that are not representative of real-world contact events. The Vickers indentation deformation and cracking mechanisms for glasses are shown schematically in Fig. 4.22. For most glass types, the indenter produces sub-surface shear faulting damage in a roughly hemispherical zone surrounding the impression site. The stress during application of the load acts upon the shear starter flaws to produce a penny-shaped crack below the deformation zone as shown in Fig. 4.22(a). Upon removal of the load, a residual stress field drives the penny-shaped crack toward the surface to form a semi-circular median crack aligned along a major diagonal of the indenter impression. The residual stress field after load removal also acts upon the shear starter flaws to form radial (palmquist) cracks and lateral cracks as shown in Fig. 4.22(b) and 4.22(c). The

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(d)

Fig. 4.22. Schematic of the formation of typical indentation cracking systems. Upper row is representative of loading half cycle. Bottom is representative of unloading half cycle.

median and radial crack types are indistinguishable from each other from the surface view, so are typically referred to as median/radial cracks. Median and radial cracks are both aligned perpendicular to the surface, so are considered strength limiting. Lateral cracks are parallel to the surface so are not considered strength limiting. However, these types of flaws have a high visual impact as light reflects off of this newly formed sub-surface interface. Some glass types such as fused silica will form ring and cone cracks during the application of the load as shown in Fig. 4.22(d). The ring crack initiates from existing surface damage as discussed previously. 4.5.1. Deformation and Cracking in Normal, Anomalous, and Intermediate Glass Compositions When studying the indentation deformation and cracking mechanisms of glass, it is best to consider glasses as falling into three categories: normal, anomalous, and intermediate. At one extreme are normal glasses, for example, soda–lime–silicate, deform to a large extent by volume displacing shear during Vickers indentation [33–36]. These glasses have an abundance of non-bridging oxygens (NBOs),

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that is, monovalent or divalent modifier ions that break up the connectivity of network forming polyhedra by replacing strong covalent bonds with weaker ionic bonds [34]. These weaker ionic bonds associated with NBOs provide pathways where shear faulting readily occurs during a sharp contact event. The alignment of NBOs into pathways has been described by the modified random network (MRN) theory [37]. A MRN structure is shown schematically in Fig. 4.23. The introduction of modifiers also leads to higher packing density [38] which limits possible amount of deformation by volumereducing densification. The cross-sectional view of a 1 kgf indents in normal soda–lime–silicate is given in Fig. 4.24 [28]. Significant sub-surface shear faulting is present and formation of the larger crack systems, that is, median/radial and lateral cracks, initiate from this shearing damage. Not surprisingly, the Vickers cracking threshold for soda–lime glass exhibiting significant sub-surface damage is low, approximately 200 gf. At the other extreme are anomalous glasses, for example, fused silica, that deform primarily by volume-reducing densification during Vickers indentation. These glasses ideally have no NBOs since nearly

Fig. 4.23. Schematic of Modified Random Network (MRN) model for glass. The = linkages represent covalent bonds. The —- linkages represent ionic bonds. The alignment of weaker ionic bonds into channels provides preferential shearing. Figure reproduced from Greaves [37] with permission from Elsevier.

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Fig. 4.24. Cross-section of 1 kgf Vickers indentation in soda-lime silicate glass. Figure reproduced from Gross et al. [28] with permission from Elsevier.

all tetrahedra are connected at all four corners. Anomalous glass has significantly higher free volume when compared to other glass types, thus allowing for significantly greater densification. Since the network is highly connected with strong covalent bonds, that is, the average Si4+ coordination number is four, the glass is also highly resistant to volume displacing shear deformation. The resistance to shear deformation results in high surface tensile stresses around the periphery of the contact and at the bottom of the elastic/plastic boundary. If flaws are present at the surface of the glass, the tensile stresses around the periphery of the contact will form ring cracks that are characteristic of anomalous glasses indented with a Vickers tip. The hemispherical deformation zone consisting now of densified material acts somewhat like a ball indenter being pushed into the glass as the load is applied. Thus, the resulting stress field causes a ring crack to extend into a sub-surface to form a cone crack as explained previously for ball indentation. The stresses at the bottom of the elastic/plastic boundary (deformation zone boundary) can also

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result in the formation of the typical sub-surface cracking systems if any flaws are generated at the boundary due to strain mismatch. Ring cracks generally form at low loads for silica glass, although when indenting a near pristine glass surface prepared by careful polishing and etching, this type of cracking can be avoided and indentation threshold values can be as high as 1 kgf. A cross section of a 1 kgf Vickers indent in silica glass is given in Fig. 4.25 and shows the characteristic ring and cone crack, along with median and lateral cracks [28]. The third category of glass is termed intermediate because the Vickers indentation deformation mechanism consists of significantly more densification than normal glass and significantly more shear deformation than normal glass. A particularly interesting example of an intermediate glass family is NBO-free, calcium boroaluminosilicate glass [28]. The structural units are ideally fully

Fig. 4.25. Cross-section of 1 kgf Vickers indentation in silica glass. Figure reproduced from Gross et al. [28] with permission from Elsevier.

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connected for these glasses, so do not contain the weak ionic bonds associated with NBOs that readily initiate shear faulting in normal glasses. The network connectivity of these glasses is lower than anomalous glasses like fused silica by incorporation of trigonally coordinated boron structural units. The reduced connectivity allows for greater shear deformation when compared to anomalous glasses, thus the intermediate glasses are provided relief from the stresses that form the characteristic ring and cone cracks in anomalous glasses [39]. Intermediate glasses can be further designed such that deformation along shear bands does not easily progress into shear faulting damage. Among the NBO-free, calcium boroaluminosilicate glasses it has been shown that the propensity toward formation of shear faulting in the sub-surface is reduced as the boron content is increased thus resulting in decreased packing density [28]. A 1 kgf Vickers indent cross section in 45% SiO2 15% Al2 O3 25% B2 O3 15% CaO (CABS25 glass) having high boron content and low packing density is shown in Fig. 4.26. This image gives the appearance that the

Fig. 4.26. Cross-section of 1 kgf Vickers indentation in CABS25 glass. Figure reproduced from Gross et al. [28] with permission from Elsevier.

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(a)

(b)

Fig. 4.27. High magnification cross-sectional images of the deformation zones following 1 kgf indentation in a. CABS25 and b. CABS5. Samples lightly etching in 0.1% HF to reveal shear deformation. Figure reproduced from Gross et al. [28] with permission from Elsevier.

deformation zone consists primarily of densified material. However, when the sample was lightly etched and viewed under much higher magnification, the presence of very tightly spaced shear bands can be observed within the deformation zone as shown in Fig. 4.27(a). For 65% SiO2 15% Al2 O3 5% B2 O3 15% CaO glass (CABS5) having lower boron and higher packing density, the overall amount of material displaced by shear during indentation is practically identical, yet the shear deformation mechanism was considerably different. As shown

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in Fig. 4.27(b), the sub-surface consists of significant shear faulting and the spacing between shear bands is much greater. The data can be interpreted as follows: if a constant volume is being displaced, then the displacement across each shear band in a material exhibiting high shear band density needs to only be of a short distance. Conversely, the displacement across each shear band in a material exhibiting low shear band density has to be a greater distance to displace an overall constant amount of material. As the displacement across a shear band gets larger, the propensity for the shear band to progress into a shear fault increases. Consequently, CABS25 glass has a very high Vickers indentation cracking threshold of ∼3 kgf, while CABS5 only has a Vickers cracking threshold of ∼1 kgf. The role of trigonal boron to increase damage resistance in glasses designed for display applications was initially demonstrated by Kato et al. [40]. Since then significant compositional study has been performed [41] to optimize the performance, understand mechanisms, and find the critical shortcomings of these glasses.

4.5.2. Categorizing Glasses as Normal, Intermediate, or Anomalous A simple way to categorize glasses as normal, intermediate, or anomalous is to perform a constant load Vickers of Berkovich diamond scratch test and measure the amount of material displaced into the pileup region surrounding the scratch groove [28]. The Vickers and Berkovich tips can be used interchangeably since they produce the same projected area to depth ratio. Recall that shear deformation is the volume displacing deformation component, so the amount of pileup for a given glass type should be indicative of the tendency toward shear deformation. The cross-sectional pileup area along a nano-scratch is virtually constant, so measurement is simplified when compared to an indent where pileup area varies along the impression edges. As shown in Fig. 4.28, the topography for 30 mN Berkovich scratches was measured with an atomic force microscope to determine the amount of material displaced from the scratch groove into the pileup regions. For normal soda–lime–silicate,

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Fig. 4.28. AFM line scans taken perpendicular to a 30 mN Berkovich scratch in (a) normal, (b) anomalous, and (c) intermediate glass.

50% of the impression volume is displaced into the pileup regions. The anomalous silica glass, only 9% of the impression volume is displaced into the pileup region. The intermediate glass, CABS25, shows intermediate behavior between these two extremes with 30% of the impression volume displaced into the pileup regions. For indents in silica glass, it was shown that significant volume recovery of the impression can be achieved by heat treatments at temperatures considered too low for viscous flow to take place [42, 43]. This recovery was described as the reversal of densification (shear assisted) by applying enough vibrational energy to the system to

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(a)

(b)

Fig. 4.29. A schematic illustration of the densification mechanism proposed by Mackenzie. Figure reproduced from Mackenzie [42] with permission from John Wiley and Sons.

reverse the interlocking of portions of the network via steric hindrance. Figure 4.29 illustrates the interlocking mechanism proposed by Mackenzie that can be reversed by low temperature heat treatments. Subsequently, Yoshida et al. proposed that the application of a specific heat treatment cycle based on Mackenzie’s observations, that is, 0.9 Tg (in K) for 2 hours, can recover the densified material [44]. By measuring the impression and pileup volumes both pre- and postheat treatment, the amount of densification can be quantified by the following equation: VR =

(Vi− − Va− ) + (Va+ − Vi+ ) Vi−

(4.38)

Where VR is the volume recovery assumed to be equivalent to the densified volume. Vi+ and Vi− are the pre-heat treatment pileup volume and impression volume, respectively. Va+ and Va−

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Fig. 4.30. A schematic representation of the procedure used to determine recovered volume. Figure reproduced from Yoshida et al. [44] with permission from Cambridge University Press.

are the post-heat treatment pileup volume and impression volume, respectively. Figure 4.30 shows a schematic illustration of the procedure for determination of VR . Figure 4.31 shows 3D AFM images of soda–lime–silicate and silica glasses both before and after annealing. The VR value for silica glass was determined to be 0.92, whereas the value for soda–lime–silicate was 0.61. By comparing the measured amount of densification, we can then categorize highly densifiable glasses such as silica as anomalous and glass with less densification as normal. Intermediate glasses fall between these extremes. In the pileup region, the volume recovery was practically negligible for both soda–lime and silica, so indicates that pileup region is formed almost completely by a volume displacing shearing mechanism as expected. In applying the VR measurement technique, the testing environment should be controlled to minimize any water present. Hirao and Tomozawa demonstrated that water, if present, enters the

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Fig. 4.31. AFM images of Vickers indentations: (a) soda-lime glass indented at 500 mN before heat treatment, (b) soda-lime glass after heat treatment, (c) silica glass indented at 100 mN before heat treatment, (d) silica glass after heat treatment. Figure reproduced from Yoshida et al. [44] with permission from Cambridge University Press.

sample during indentation [17] and will result in a region that has considerably lower viscosity when compared to the bulk glass. For some more water sensitive glass types, this may result in viscous flow at 0.9 Tg over the specified 2 hours time duration. 4.5.3. Additional Considerations Regarding Glass Composition and Indentation Damage Resistance Increasing the indentation crack resistance of glasses by eliminating NBOs and introducing trigonal boron was discussed in the Section 4.5.1, however, there are additional compositional levers that should

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also be considered. For example, the selection of glass modifiers can have a significant impact on the deformation mechanism. The ionic field strength of modifier ions is given in Eq. (4.37). For most commercial glasses, the modifier ions are monovalent alkali oxides and divalent alkaline earth oxides. The smaller the ion of a given charge, the higher the ionic field strength. To demonstrate the effect of the varying the modifier type in an otherwise fixed glass composition, we will look at 70SiO2 –10Al2 O3 –20R2 O glasses with R2 O = Li2 O, Na2 O, and K2 O. This peralkali system was chosen for ease of preparation. The ionic field strengths and oxygen packing densities for these glasses are given in Fig. 4.21. As expected, the oxygen packing density increases as the field strength of the modifier ion increases. Oxygen packing density calculations were made using Eqs. (4.34–4.36) with aluminum and silicon coordination fixed at four-fold for each of the three glasses (aluminum coordination numbers were confirmed using nuclear magnetic resonance [NMR]). The cross sections of 1 kgf Vickers indents are shown in Fig. 4.32. The Li2 O-containing glass with Vo = 0.47 shows significant shear cracking damage in the sub-surface. The Na2 O-containing glass with Vo = 0.43, requires viewing the deformation zone under higher magnification to find some minor shear damage. The K2 O-containing with the lowest oxygen packing density, Vo = 0.39, does not contain shear cracking in the sub-surface at all. The results here are in good agreement with observations made on the intermediate CABS glasses described above. As the oxygen packing density is decreased within a given glass family, we observe less sub-surface damage within the deformation zone for a given load. These results show that the indentation deformation behavior is highly dependent on packing density in systems where the coordination numbers of glass formers are fixed. Although coordination numbers are fixed, the ring structures will certainly be different for glasses formed around modifiers of various size and ionic field strength. Another interesting observation from the R2 O–Al2 O3 –SiO2 study was that the glasses that produced sub-surface shear faults were prone to delayed median/radial crack formation, while glasses free of sub-surface shear faulting damage did not exhibit delayed crack formation. If

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Fig. 4.32. Cross sections of 1 kgf indents in 20R2 O–10Al2 O3 –70SiO2 glasses. (a) Li-containing glass has the highest oxygen packing density at 0.47 and shows the most shear faulting. (b) Na-containing glass has an oxygen packing density of 0.43 and shows minor shear faulting. Higher magnification was required to reveal the damage. (c) K-containing glass has the lowest oxygen packing density at 0.39 and does not exhibit shear damage.

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we consider the indentation residual stress field and the presence of starter flaws in the form of sub-surface shear faults, it is not surprising that we would be in a stress intensity regime where subcritical crack growth would occur. Up to this point we have only shown damage resistance achieved with structures having reduced oxygen packing densities. The downside to low oxygen packing density glasses is that they have lower hardness and Young’s modulus (refer to Figs. 4.19 and 4.20) and in many cases also have lower fracture toughness. Recently, it has been demonstrated for binary xAl2 O3 –(100-x)SiO2 glasses that the indentation crack resistance, hardness, and Young’s modulus all increase as the Al2 O3 content is increased up to 60 mol% [45]. As Al2 O3 is added to xAl2 O3 –(100-x)SiO2 , the network structure is becoming more highly packed, so the amount of densification should be minimal for these glasses when compared to all other highly crack resistant glasses reported in the literature. For these dense structures, the shear deformation mechanism must dominate the indentation deformation of these glasses. XPS measurements suggest that NBOs are not present in these glasses, so the shear mechanism will be unlike typical normal glasses where shear preferentially takes place along aligned ionic bonds. Rosales-Sosa et al. have proposed that transitions between multiple Al coordination environments could play a role in allowing shear deformation without introducing sub-surface shear faulting damage [45]. Since these glasses are so dense and free of components that promote water interaction, the entry of water into the glass should also be very limited. As mentioned in the previous paragraph, glasses containing some shear damage within the deformation zone tend to produce median and radial cracks in a time delayed manner. If these very dense glasses prevent water entry, then the fatigue mechanism responsible for delayed cracking in shear deforming glasses can potentially be prevented. Figure 4.33 shows characteristic indent impressions the binary xAl2 O3 –(100-x)SiO2 glasses. The highest Al2 O3 glass tested could withstand Vickers indentation loads of 49.03 N (5 kgf) without formation of median/radial cracks. This glass also had the highest Young’s modulus and Vickers hardness of the series with values of

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Fig. 4.33. Vickers indents in xAl2 O3 –(100-x)SiO2 glasses show increasing cracking threshold as Al2O3 content in increased. Figure reproduced from Rosales-Sosa et al. [45] under the Creative Commons Attribution 4.0 International License.

134.2 GPa and 823 kgf/mm2 , respectively. While these glasses are of great technical interest, they can only be produced presently by aerodynamic levitation, so the sample sizes are very limited. 4.5.4. Sharp Indentation Stress Field The indentation cracking responses for normal, intermediate, and anomalous glasses can be explained using the indentation stress field model developed by Yoffe [39]. Yoffe’s model predicts the stress distribution outside of a hemispherical plastic zone with a radius equal to the circle of contact of a pointed indenter under axisymmetric loading. Although this is a simplified contact geometry when compared to pyramidal indenters, it can be used to describe pyramidal indentation cracking observations extremely well. The model combines the Boussinesq solution of the elastic field to a point contact with a plastic blister field solution. The blister field is a combination of the symmetrical center of pressure and the surface forces that account for the specimen free surface. Referring to the

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Fig. 4.34. Spherical polar coordinate system used for Yoffe’s model.

spherical polar coordinate system shown in Fig. 4.34, the stresses are given as follows [39]: P B [1 − 2ν − 2(2 − ν)θ] + 3 4[(5 − ν) cos2 θ − (2 − ν)] 2 2πr r (4.39)   2 B P (1 − ν) cos θ − 3 [2(1 − 2ν) cos2 θ] (4.40) σθθ = 2 2πr (1 + cos θ) r   B P (1 − 2ν) 1 + 3 [2(1 − 2ν)(2 − 3 cos2 θ)] = cos θ − 2 2πr 1 + cos θ r (4.41)

σrr =

σϕϕ

Where P is the indenter load, ν is Poisson’s ratio, and B is a measure of the blister strength. Yoffe reported that the B value is proportional to the displaced volume from within the deformation zone and is reduced by densification. The B value is then dependent on the material behavior, where normal glasses will have the greatest B value and anomalous glass will have the lowest B value for a given indenter tip. For a given glass, the B value shifts to higher values for sharper indenter tips or lower values for blunter indenter tips. Up to this point in this chapter, we have focused on the response of glasses to Vickers indentation, but we need to also consider how the contact geometry effects the deformation and cracking responses to better understand real-world scenarios. To demonstrate how different glasses respond to different contact geometries, normal, intermediate,

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and anomalous glasses were indented at 200 gf with a Vickers tip (136◦ ) and two other four-sided tips configured like the Vickers tip shown in Fig. 4.14(b), but with 120◦ and 150◦ angles between opposite faces. If the load was not sufficient to produce cracks, the load was increased until cracks were observed. 4.5.4.1. Sharp Indentation Stress for Anomalous Glass Recall from Fig. 4.28(b) that very little volume is displaced from a Vickers equivalent contact for silica glass, meaning B should closest to zero when compared to other glass types. In the extreme case of B approaching zero, the highest tensile stress on a glass is σrr at the top surface (θ = π/2) at the periphery of the contact (r = a). This is the stress that acts upon surface flaws to form the ring cracks commonly observed for silica when indented Vickers indenter. Figure 4.35(b) shows a 200 gf Vickers indent in silica glass with characteristic ring cracks. The stress to form median cracks at the bottom of the deformation zone, that is, σθθ = σϕϕ at θ = 0, is also highest as B approaches zero. As shown in Fig. 4.35(b), median cracks are present, but do not extend far from the indent impression due to crack shielding from the cone crack. The cone crack apparently formed first and resulted in a crack interface that terminates median crack extension. When silica is indented with a sharper 120◦ tip,

(a)

(b)

(c)

Fig. 4.35. Indents made in silica at 200 gf with 4-sides pyramidal indenters with angles of (a) 120◦ , (b) 136◦ (Vickers), and (c) 150◦ . Figure reproduced from Gross [32] with permission from Elsevier.

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the B value should increase significantly so that stress to form rings cracks (σrr at θ = π/2) is reduced by ∼7B/r 3 , while the stress to form median cracks (σθθ = σϕϕ at θ = 0) is only reduced by ∼B/r 3 . As shown in Fig. 4.35(a), the ring cracks are suppressed and median cracks are still present. On the other hand, if we indent with the blunter 150◦ tip (B even lower than with the Vickers indenter), the stress for ring cracks is highest, so even an indentation at 200 gf with minimal impression volume will produce the ring crack as shown in Fig. 4.35(c). 4.5.4.2. Sharp Indentation Stress for Normal Glass At the other extreme, normal glasses like soda–lime–silicate produce significant volume displacement from a Vickers equivalent contact as shown in Fig. 4.28(a), meaning the B value is high for Vickers indents when compared to other glass types. With high enough B value, the ring cracking stress (σrr at θ = π/2) will change signs and become compressive. As shown in Fig. 4.36(b), a 200 gf Vickers indent does not show any signs of ring cracking. A tensile median cracking stress (σθθ = σϕϕ at θ = 0), persists up to much higher B values when compared to the tensile ring cracking stress resulting in the median cracks shown in Fig. 4.36(b). There also appears to be some sub-surface lateral cracking which can be explained by the

(a)

(b)

(c)

Fig. 4.36. Indents made in soda-lime at 200 gf with 4-sides pyramidal indenters with angles of (a) 120◦ , (b) 136◦ (Vickers), and (c) 150◦ . Figure reproduced from Gross [32] with permission from Elsevier.

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tensile radial stress (σrr at θ = 0) that is present once the load is removed (P = 0). The stress σrr is ∼12B/r 3 at θ = 0 and causes the lateral crack to open at the plastic boundary and extends parallel to the surface. When soda–lime is indented with a sharper 120◦ tip producing a higher B value, the lateral cracking stress is clearly higher resulting in widespread lateral cracking as shown in Fig. 4.36(a). Also, as B is increased the circumferential stress (σϕϕ at θ = π/2) can become tensile and yield radial crack formation during loading. Some combination of median and radial cracking is often observed for indentation of normal glasses with sharp indenter tips. When soda–lime is indented with a blunter 150◦ tip, the B value gets considerably smaller. Unlike the 200 gf 150◦ indent in silica, the indent in soda–lime–silicate does not consist of any ring cracking damage as shown in Fig. 4.36(c). However, once we increase the load to reach the cracking threshold, it is obvious that ring cracks as well as median cracks are present as shown in Fig. 4.37. 4.5.4.3. Sharp Indentation Stress for Intermediate Glass When indenting an intermediate type of glass composition, the B value is in between that of silica and soda–lime for a given indenter tip. Consider the plot of the stresses in Fig. 4.38 calculated for a 200 gf indentation load with r = 10 microns. What we see is that

Fig. 4.37. Indent made in soda-lime at 5000 gf with the 150◦ indenter tip. Figure reproduced from Gross [32] with permission from Elsevier.

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Fig. 4.38. The stress for formation of different strength-limiting cracks as a function of the Yoffe B parameter.

is that there should be an intermediate value of B where the ring cracking stress is compressive and the median and radial cracking stresses drop to zero. Since crack extension will not take place under compression, only the positive tensile values can produce cracks. So, from a stress perspective alone, there should exist intermediate glasses that are more crack resistant. Obviously, we must keep in mind that sub-surface damage introduced in the deformation zone during indentation plays a critical role as to whether larger crack systems form. An intermediate glass having minimal NBOs and 10 mol% B2 O3 with boron existing in a trigonal coordination state was indented with the series of indenter tips for comparison with normal and anomalous glasses. As shown in Fig. 4.39(b), the Vickers indent does not produce cracking damage of any kind. Once we reach the cracking threshold of 2 kgf for this glass, the cracking systems look typical of a normal glass as shown in Fig. 4.40. As shown in Fig. 4.39(a), indentation with the sharper 120◦ tip produces median cracks. However, lateral cracks are not observed due to the lower B value when compared to soda–lime glass. The 150◦ indentation also did not produce any cracking systems as shown in Fig. 4.39(c). When we reach the cracking threshold as seen in Fig. 4.41, significant

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(c)

Fig. 4.39. Indents made in intermediate glass at 200 gf with 4-sides pyramidal indenters with angles of (a) 120◦ , (b) 136◦ (Vickers), and (c) 150◦ . Figure reproduced from Gross [32] with permission from Elsevier.

Fig. 4.40. Indent made in intermediate glass at 2 kgf with 136◦ Vickers indenter tip. Figure reproduced from Gross [32] with permission from Elsevier.

ring cracking is observed. These observations are all consistent with an intermediate B value when compared to soda–lime and silica. As previously mentioned, axis-symmetry used in the Yoffe model simplifies the contact conditions when compared to the stresses introduced by pyramidal indenters, but even so, the model does fit pyramidal indentation experimental results very well. Yoffe expressed B in terms of indentation parameters and material variables as

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Fig. 4.41. Indent made in intermediate glass at 10 kgf with 150◦ indenter tip. Figure reproduced from Gross [32] with permission from Elsevier.

follows [39]: 5π B (4.42) 6 E Cook and Pharr equated ΔV to the volume of the contact impression multiplied by a factor, f , accounting for non-volume conserving processes [46]. The limits on f are zero for complete densification and 1 for complete volume displacement via shearing mechanisms. The quantification of B may be determined via pileup measurement methods and/or densified volume recovery experiments. The recovery approach has been used to capture how densification is reduced as indenter tip sharpness increases as shown in Fig. 4.42 for a series of three-sided indenters [47]. ΔV =

4.5.5. Tip Sharpness Impact on Sub-Surface Deformation and Cracking Threshold Primarily, indentation cracking resistance studies have been performed using a Vickers indenter. However, as shown in the previous section, even highly crack resistant intermediate type glasses will form strength-limiting cracks at significantly lower loads when even slightly sharper indenter tips are used. The intermediate aluminosilicate glass discussed in the previous section has a Vickers crack initiation load of 1500–2000 gf, but the threshold is reduced

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Fig. 4.42. The amount of volume recovery decreases as the indenter tip becomes sharper for indents in soda-lime glass. (a) 80◦ 3-sided indenter, (b) berkovich indenter (65.03◦ 3-sided indenter), (c) cube corner indenter (35.26◦ 3-sided indenter). Figure reproduced from Yoshida et al. [47] with permission from Cambridge University Press.

to 20–30 gf when indenting with a 120◦ tip [32]. When indenting with an even sharper cube corner indenter, the threshold is less than 10 gf. For very sharp indentation, all glass types exhibit extremely low indentation thresholds and the crack resistance differences between normal, intermediate, and anomalous glasses are negligible. Since the real world provides a wide range of contact conditions, glass surfaces will be contacted by ultra-sharp point contacts and these

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only require very low loads to initiate surface damage. Tremper et al. demonstrated that the surfaces of normal and intermediate display glass types contain significant ultra-sharp contact damage that can be replicated with a 120◦ indenter [48]. By performing 100 gf 120◦ indents in the center of test coupons then doing ring-on-ring (ROR) testing, it was shown that the retained strength is practically equivalent between normal and intermediate glass types as shown in the Wiebull plot in Fig. 4.43 [48]. Due to the strength equivalence following real world-like ultra-sharp contacts, the high Vickers indentation glasses have minimal value for improving the strength of glass plates. If ultra-sharp contact is inevitable, then the only way to ensure that glass is strong is to impart a compressive stress layer by ion-exchange stuffing, tempering, or lamination strengthening with coefficient of thermal expansion (CTE) mismatched glasses.

Fig. 4.43. ROR testing of glass intermediate and normal glasses containing 100 gf 120◦ indents. Results indicate no strength improvement for intermediate glasses following sharp contact [48].

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Fig. 4.44. Cross-sections of 500 gf indents in normal aluminosilicate glass with (a) 120◦ tip, (b) 136◦ (Vickers tip), and (c) 150◦ tip. Figure reproduced from Gross [49] with permission from John Wiley and Sons.

Aside from the unfavorable stress condition imparted in the glass from sharper contacts, the sub-surface damage within the deformation zone also gets significantly worse as the shearing mechanism dominates the deformation behavior. Figure 4.44 shows indent cross sections of a normal aluminosilicate glass indented at 500 gf with 120◦ , 136◦ (Vickers), and 150◦ indenter tips [49]. The sub-surface shear damage and cracking is most severe for the 120◦ tip. On the other hand, the shear deformation seen for the 120◦ and 136◦ tips appears to be completely replaced by densified material when the glass in indented with the 150◦ tip. The indentation cracking thresholds were 15–30 gf for the 120◦ tip, 300–500 gf for the 136◦ tip, and 7000–8000 gf for the 150◦ tip. Figure 4.45 shows 500 gf indents with 120◦ and 136◦ tips for an intermediate glass. Again, it is clearly shown that the damage in the sub-surface increases with tip sharpness. For these intermediate glasses, the indentation cracking thresholds were 30–45 gf for the 120◦ tip and 1100–1200 gf for the

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Fig. 4.45. Cross sections of 500 gf indents in intermediate aluminoborosilicate glass with (a) 120◦ tip and (b) 136◦ (Vickers tip).

136◦ tip. These results also show that the inherent damage resistance is quickly normalized for different glass types as the tip sharpness increases. Ultra-sharp contact is so important to the useable strength of glass that significant effort should be made to make glasses that are resistant to damage and cracking in the cube corner to 120◦ tip sharpness regime. This would certainly be a huge breakthrough for glass technology. 4.5.6. Indentation Cracking During High Speed Contact The intermediate glass discussed in Section 4.5.1 has a quasi-static Vickers indentation cracking threshold of ∼3 kgf. When dynamic Vickers indentation is performed on this glass, the indentation threshold exceeds 5 kgf. A dynamic indentation setup is shown in Fig. 4.46. An air piston propels a test vehicle that contains the indenter and piezoelectric load cell toward the sample holder. The test vehicle moves along the guide rods on frictionless air bearings. The velocity is recorded as the vehicle passes by a pair of photogates. The air bearings allow for a free rebound following high rate indenter contact with the glass sample. At a 5 kgf indentation load, the total time from initial loading to being full unloaded is 1118 μs. For comparison, the full indentation cycle for quasi-static indentation made at 5 kgf takes approximately 20 second. Images comparing the 5 kgf indent impressions are given in Fig. 4.47. The indent size is

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Fig. 4.46. Dynamic indentation system.

slightly larger at 137.1 microns for the quasi-static indentation when compared to the 134.3 microns measured for the dynamic indent. The testing for both quasi-static and dynamic indentation was performed in 50% relative humidity at room temperature. Hirao and Tomozawa have previously shown the hardness or indentation size is dependent on contact time in water-containing environments [17]. They are used Fourier transform infrared spectroscopy (FTIR) to reveal that the water content in the deformation region increases as the indenter is held in contact with the glass in a water-containing environment. A water-rich region has lower viscosity and is more susceptible to flow or indentation creep. They also demonstrated that shorter indentation dwell time improved the indentation crack resistance. This again can be related to water entry into the deformation zone, where indentation crack forming sequences are relying on a fatigue mechanism during application of the load, that is, propagation of flaws via breaking up the network at cracks tips through terminal −OH formation. Lawn and Kurkjian also have done significant work in this area to show the impact of water on indentation deformation and cracking [50, 51]. The studies from Hirao and Tomozawa, Lawn, and Kurkjian suggest that high indentation rate effectively reduces water entry during contact, thus directly impacting the

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Fig. 4.47. (a) 5 kgf indent made in CABS25 glass by dynamic indentation. Average major diagonal length was 134.3 microns and total contact time was 1118 μs. (b) Image of 5 kgf dynamic indent in CABS25 at 75◦ tilt. (c) 5 kgf indent made in CABS25 glass by quasi-static indentation. Average major diagonal length was 137.1 mm and total contact time was 20 second. (d) Image of 5 kgf quasi-static indent in CABS25 at 75◦ tilt.

water-assisted crack growth that result in lower cracking thresholds for quasi-static indents [17, 50, 51]. 4.5.7. Sharp Contact Scratch Behavior Sliding sharp contact results in surface damage that can degrade the strength and appearance of glass surfaces. A sharp object that is harder than glass will produce a scratch groove as it slides across a glass surface. At low scratch loads for a given sharp contact geometry, the scratch grooves are not accompanied by any cracking damage. This scratch behavior is defined as being in the microductile regime. These fine, micro-ductile scratch grooves are difficult to observe with the naked eye until they begin to accumulate on

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the glass surface. The glass hardness (Section 4.4) determines the width of the scratch groove for a given contact hardness, load, and geometry. As expected, the accumulation of micro-ductile scratches is more easily observed in softer glasses having wide scratch groove widths. Again, we can replicate the scratch damage observed in real-life contacts using diamond indenters. For example, a microductile groove produced by a Berkovich indenter at a constant load of 30 mN in the surface of the CABS15 intermediate glass composition described in Section 4.5.1 is shown in Fig. 4.48. Scratch grooves will contain pileup material as previously discussed in Section 4.5.2. The amount of pileup is highly dependent on composition as well as contact geometry. If we increase the scratch load to 160 mN, we begin to observe the presence of scratch curls as shown in Fig. 4.49. As shown in Fig. 4.50, AFM line scans performed perpendicular to the scratch direction indicate that the curls consist of detached segments of glass from the pileup region [28]. Once we move beyond the micro-ductile regime, larger cracks systems, that is, median and lateral cracks, begin to accompany the scratch groove. Just as in indentation cracking, the larger crack systems initiate from sub-surface damage generated during sharp scratching. That being said, the same composition rules that

Fig. 4.48. A micro-ductile groove produced by a Berkovich indenter with a constant 30 mN load in the surface of the CABS25 intermediate glass.

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Fig. 4.49. A micro-ductile groove produced by a Berkovich indenter with a constant 160 mN load in the surface of the CABS25 intermediate glass. Figure reproduced from Gross et al. [28] with permission from Elsevier.

Fig. 4.50. AFM line scans performed perpendicular to the scratch direction indicate that the curls consist of detached segments of glass from the pile-up region. The light grey line on the right-hand side indicates a line scan taken over a non-peeled region. The dark grey line on the right-hand side indicates a line scan taken over a peeled region. Figure reproduced from Gross et al. [28] with permission from Elsevier.

enable higher Vickers indentation cracking thresholds will result in higher resistance to crack formation during scratching with contact geometries such as Vickers and Knoop. At the sharper end of the contact spectrum, these differences are again negated as with indentation. Figure 4.51 shows the typical sequence of large crack system formation as contact load is increased [49]. Initially, a median

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Fig. 4.51. The typical sequence of large crack system formation as contact load is increased. The larger crack systems initiate from damage produced within the plastically deformed zone. Figure reproduced from Gross [49] with permission from John Wiley and Sons.

crack forms from the bottom of the deformation zone. From the surface, the median crack is not always evident since it is oriented perpendicular to the surface, thus has very little visual impact. However, this type of crack is highly detrimental to strength. As the scratch load is further increased, a lateral crack is generated from the bottom of the deformation zone and is oriented parallel to the surface. While this type of crack system does not have a significant strengthreducing effect, it is highly visible due to light reflection from this newly formed surface. As higher loads yet, the lateral crack curls upward and intersects the surface causing a chip out of the material. To demonstrate the differences in scratch behavior between normal and intermediate glasses, Knoop indenter scratches were made at 0.5, 1.0, and 1.5 kgf. The normal glass is free of B2 O3 and has an oxygen packing density of 0.47, while the intermediate glass 16.5 mol% B2 O3 (boron primarily in a trigonal coordination state) and has an oxygen packing density of 0.43. The normal glass shown in Fig. 4.52 has surpassed the threshold to produce lateral cracks at 1.0 kgf. On the other hand, the intermediate glass does not form lateral cracks at any of the three loads used for analysis as shown in Fig. 4.53. On the sides of the scratch grooves, some frictive damage is present as expected for tips like the Knoop that have high contact area for a given load. As mentioned in the previously paragraph, the presence of the median crack is difficult to determine from the top view, even when attempting to view from an angle.

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Fig. 4.52. Knoop scratch images for a normal alkaline earth aluminoborosilicate glass at (a) 0.5 kgf, (b) 1.0 kgf, and (c) 1.5 kgf.

The best method of determining the median cracking threshold is by strength testing the parts at increasing scratch loads until an obviously strength reduction occurs. The Knoop indenter tip reveals large changes in scratch resistance for different glass types, but, just like with indentation, this difference quickly diminished as the tip angle becomes sharper. When it comes to degradation in surface appearance, the intermediate glass types are more resistant to highly visual lateral crack formation for a significant portion of the contact spectrum, resulting in an overall decrease in the number of visible scratches on a surface following in-use conditions.

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Fig. 4.53. Knoop scratch images for an intermediate alkaline earth aluminoborosilicate glass at (a) 0.5 kgf, (b) 1.0 kgf, and (c) 1.5 kgf.

4.6. Conclusion The strength of glass is highly dependent on the flaw size distribution as described by basic linear elastic fracture mechanics. Contact to a glass surface readily degrades the strength from the pristine surface case by introducing damage. The types of damage that are introduced into a glass surface depends on many factors, for example, the applied load, the contact shape, contact hardness, and interaction with the specific glass composition. It has been shown that glass composition can be tailored to be more resistant to certain types of contacts. For example, so-called intermediate glasses can have exceptional resistance to crack formation by Vickers indentation. Before we conclude that these glasses possess higher usable strength, it needs to be considered that strength-limiting flaws form at much lower loads for contacts just slightly sharper than a Vickers indenter. Furthermore, the difference in cracking threshold for sharper contacts is negligible for different glass types. In the real world, all types of contacts occur, even those considerably sharper than Vickers. Since failure occurs from the largest flaw on a surface under tension, we easily find the sharp contact damage and do not see any

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strength differences between glasses with extremely different Vickers indentation threshold after being subjected to typical handling damage. To manage the strength of glass subjected to sharp contact damage, the only methods that have been successful is to impart stress profiles that envelop the damage via tempering, ion-exchange, or CTE mismatch lamination strengthening. If glass researchers are ever successful in finding glass compositions that are resistant to crack formation from ultra-sharp contact, this would be a critical breakthrough that could eliminate the need for compressive stress profile strengthening. However, when it comes to the accumulation of visible scratch damage, the damage-resistant intermediate glasses have considerable advantages. Again, all contact types occur and the sharpest of these will produce visible lateral cracking damage in any type of glass, but the wide-angle contacts similar to Vickers or Knoop indenters do not easily produce visible damage for intermediate glasses. The number of visible scratches is always significantly less for a glass plate of intermediate glass when compared to a normal glass. The fundamental understanding of contact damage is a highly active area of research due to the recent growth of glass in mechanically demanding applications, for example, cell phone cover glass. The rate of recent progress has been astounding and, out of this work, we will see glass usage in more and more mechanical applications in the near future.

Acknowledgment I’d like to thank all the people that I’ve collaborated with over the years on these topics. I’ve been extremely fortunate to work with the best fracture mechanics experts including Minoru Tomozawa, Scott Glaesemann, and Jim Price. The scanning electron microscopy (SEM) imaging from Dave Baker and AFM analysis Ruchi Yongsunthon has been invaluable in gaining new insights into deformation and cracking behavior of glasses. Finally, I’d like to thank Charlene Smith, Jingshi Wu, and Alex Mitchell for critical review of this manuscript.

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References 1. Kelly, A., and MacMillan, N. H. (1986). Strong Solids, 3rd Ed. (Oxford, Oxford University Press). 2. Sun, K.-H. (1947). Fundamental condition of glass formation, Journal of the American Ceramic Society, 30, pp. 277–281. 3. Orowan, E. (1949). Fracture and strength of solids, Reports on Progress in Physics, 12, pp. 185–232. 4. Brown, G. E., Farges, F., and Calas, G. (1995). X-ray scattering and x-ray spectroscopy studies of silicate melts, Reviews in Mineralogy and Geochemistry, 23, pp. 317–410. 5. Inglis, C. E. (1913). Stresses in a plate due to the presence of cracks and sharp corner, Transaction of the Institution of Naval Architect, 55, pp. 219–230. 6. Griffith, A. A. (1920). The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London, A221, pp. 163–198. 7. Irwin, G. R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics, 24, pp. 361– 364. 8. Wachtman, J. B., Cannon, W. R., and Matthewson, M. J. (2009). Mechanical Properties of Ceramics, 2nd Ed. (Hoboken, NJ, John Wiley and Sons). 9. Glaesemann, G. S., Jakus, K., and Ritter, J. E. (1987). Strength variation of indented soda-lime glass, Journal of the American Ceramic Society, 70, pp. 441–444. 10. Garner, S. M. (2017). Flexible Glass: Enabling Thin, Lightweight, and Flexible Electronics (Hoboken, NJ, John Wiley and Sons). 11. Hertz, H. (1881). On the contact of elastic solids, Journal f¨ ur die Reine und Angewandte Mathematik, 92, pp. 156–171. 12. Huber, M. T. (1904). Zur Theorie der Ber¨ uhrung fester elastischer K¨ orper, Annalen der Physik, 14, pp. 153–163. 13. Lawn, B. R, Wilshaw, T. R., and Hartley, N. E. W. (1974). A computer simulation study of Hertzian cone crack growth, International Journal of Fracture, 10, pp. 1–16. 14. Chaudhri, M. M., and Kurkjian, C. R. (1986). Impact of small steel spheres of the surfaces of “normal” and “anomalous” glass, Journal of the American Ceramic Society, 69, pp. 404–410. 15. Hamilton, G. M., and Goodman, L. E. (1966). The stress field created by a circular sliding contact, Journal of Applied Mechanics, 33, pp. 371–376.

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16. Chen, J., Gross, T. M., Tammaro, D. A., and Wang, L. (2014). Slip agent for protecting glass. U.S. Patent 8,821,970. 17. Hirao, K., and Tomozawa, M. (1987). Microhardness of SiO2 glass in various environments, Journal of the American Ceramic Society, 70, pp. 497–502. 18. Gross, T. M., and Tomozawa, M. (2008). Fictive temperatureindependent density and minimum indentation size effect in calcium aluminosilicate glass, Journal of Applied Physics, 104, 063529-1-10. 19. Li, H., Ghosh, A., Han, Y. H., and Bradt, R. C. (1993). The frictional component of the indentation size effect in low load microhardness testing, Journal of Materials Research, 8, pp. 1028–1032. 20. Swain, M. V., and Wittling, M. (1996). Fracture Mechanics of Ceramics (New York, NY, Plenum). 21. Yoshioka, N., and Yoshioka, M. (1996). Dynamic observation of indentation process: A possibility of local temperature rise, Philosophical Magazine A, 74, pp. 1273–1286. 22. Quinn, G. D., Patel, P. J., and Lloyd, I. (2002). Effect of loading rate of conventional ceramic microindentation hardness, Journal of Research of the National Institute of Standards and Technology, 107, pp. 299– 306. 23. Nix, W. D., and Gao, H. (1998). Indentation size effects in crystalline materials: A law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 46, pp. 411–425. 24. Bernhardt, E. O. (1941). On the microhardness of solids at the limit of Kick’s similarity law. Zeitschrift f¨ ur Metallkunde, 33, pp. 135–144. 25. Spaepen, F. (2006). Must shear bands be hot? Nature Materials, 5, pp. 7–8. 26. Smedskjaer, M. M. (2014). Indentation size effect and plastic compressibility of glass, Applied Physics Letters, 104, pp. 251906-1-3. 27. Zeidler, A., Salmon, P. S., and Skinner, L. B. (2014). Packing and the structural transformations in liquid and amorphous oxides from ambient to extreme conditions, Proceedings of the National Academy of Sciences, 111, pp. 10045–10048. 28. Gross, T. M., et al. (2018). Crack-resistant glass with high shear band density, Journal of Non-Crystalline Solids, 494, pp. 13–20. 29. Shannon, R. D. (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides, Acta Crystallographica Section A, 32, pp. 751–767. 30. Lamberson, L. (2016). Influence of atomic structure on plastic deformation in tectosilicate calcium-aluminosilicate, magnesiumaluminosilicate, and calcium galliosilicate, Cornell Thesis.

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31. Sehgal, S., and Ito, S. (1988). A new low-brittleness glass in the soda-lime-silica family, Journal of the American Ceramic Society, 81, pp. 2485–2488. 32. Gross, T. M. (2012). Deformation and cracking behavior of glasses indented with diamond tips of various sharpness, 358, pp. 3445–3452. 33. Peter, K. W. (1970). Densification and flow phenomena of glass in indentation experiments, Journal of Non-Crystalline Solids, 5, pp. 103– 115. 34. Ernsberger, F. M. (1977). Mechanical properties of glass, Journal of Non-Crystalline Solids, 25, pp. 292–321. 35. Arora, A., Marshall, D. B., Lawn, B. R., and Swain, M. V. (1979). Indentation deformation/fracture of normal and anomalous glasses, Journal of Non-Crystalline Solids, 31, pp. 415–428. 36. Hagan, J. T. (1980). Shear deformation under pyramidal indentations in soda-lime glass, Journal of Materials Science, 15, pp. 1417–1424. 37. Greaves, G. N. (1985). EXAFS and the structure of glass, Journal of Non-Crystalline Solids, 71, pp. 203–217. 38. Livshits, V. Y., Tennison, D. G., Gukasyan, S. B., and Kostanyan, A. K. (1982). Acoustic and elastic properties of glass in the Na2 OAl2 O3 -SiO2 system, Soviet Journal of Glass Physics and Chemistry, 8, pp. 463–468. 39. Yoffe, E. H. (1982). Elastic stress fields caused by indenting brittle materials, Philosophical Magazine A, 46, pp. 617–628. 40. Kato, Y., et al. (2010). Effect of B2 O3 content on crack initiation under Vickers indentation test, Journal of the Ceramic Society of Japan, 118, pp. 792–798. 41. Ellison, A. J., and Gross, T. M. (2014). Alkaline earth aluminoborosilicate crack resistant glass. U.S. Patent 8,796,165. 42. Mackenzie, J. D. (1963). High-pressure effects on oxides glasses: I, densification in rigid state, Journal of the American Ceramic Society, 46, pp. 461–476. 43. Neely, J. E., and Mackenzie, J. D. (1968). Hardness and lowtemperature deformation of silica glass, Journal of Materials Science, 3, pp. 603–609. 44. Yoshida, S., Sangleboeuf, J. C., and Rouxel, T. (2005). Quantitative evaluation of indentation-induced densification in glass, Journal of Materials Research, 20, pp. 3404–3412. 45. Rosales-Sosa, G. A., Masuno, A., Higo, Y., and Inoue, H. (2016). Crackresistant Al2 O3 -SiO2 glasses, Scientific Reports, 6:23620, pp. 1–7. 46. Cook, R. F., and Pharr, G. M. (1990). Direct observation and analysis of indentation cracking in glasses and ceramics, Journal of the American Ceramic Society, 73, pp. 787–817.

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47. Yoshida, S., et al. (2010). Effects of indenter geometry on indentationinduced densification of soda-lime glass, Journal of Materials Research, 25, pp. 2203–2211. 48. Tremper, A., Van Duyne, E., and Gleasemann, G. S. (2017). The surface strength of thin display glass, 12th Pacific Rim Conference on Ceramic and Glass Technology. 49. Gross, T. M. (2012). 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, edited by Varner, J. R., and Wightman, M. (Hoboken, NJ, John Wiley and Sons), Vol. 230, pp. 113–122. 50. Lawn, B. R., Dabbs, T. P., and Fairbanks, C. J. (1983). Kinetics of shear-activated indentation crack initiation in soda-lime glass, Journal of Materials Science, 18, pp. 2785–2797. 51. Kurkjian, C. R., Kammlott, G. W., and Chaudhri, M. M. (1995). Indentation behavior of soda-lime silica glass, fused silica, and single quartz at liquid nitrogen temperature, Journal of the American Ceramic Society, 78, pp. 737–744.

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CHAPTER 5

Aqueous Corrosion of Glass Dien Ngo and Seong H. Kim Penn State University University Park, PA 16802, USA

The degradation of glass surface due to reactions with water is called aqueous corrosion. Such corrosion can occur when glass is exposed to water-containing environments such as humid air, liquid water, or aqueous solutions containing ions or electrolytes. Comprehensive understanding of aqueous corrosion behaviors is very important to design glass composition and manufacturing process for specific functions or performances. When glass is used as a host matrix for nuclear waste, it should have a chemical durability of glass for hundreds of thousands of years. Even for a container glass used for storage of liquid or gas, aqueous corrosion can affect its mechanical durability. In the first part of this chapter, recent findings about various stages of aqueous corrosion of glass are presented with deeper insights on the chemical and structural properties of the alteration layer. Kinetics models are then briefly presented that show attempts to understand and predict glass corrosion behaviors in specific conditions. Near-field materials and electrolytes have also been shown to significantly affect glass corrosion and their effects on the corrosion process are shown in the third part. Atmospheric corrosion, vapor phase hydration, and corrosion of pharmaceutical glass are then briefly discussed. The chapter concludes with suggestions for future research of glass corrosion.

5.1. Introduction Corrosion of glass surfaces is a serious problem that affects optical, window, and container glasses [1–8]. It is also of great concern

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for nuclear waste glasses since corrosion can cause the release of radioactive elements in the glass into the biosphere [9–11]. Glass corrosion has therefore attracted much study in recent years, especially related to nuclear waste glass materials to better understand glass corrosion mechanisms and design more corrosion-resistant glasses. Glass corrosion occurs in various environmental conditions, including corrosion in aqueous solution [12–15], atmospheric corrosion [16, 17], and corrosion by vapor hydration [18, 19]. In these conditions, various reaction parameters such as temperature, glass composition, solution pH, electrolyte, and glass surface condition play critical roles in corrosion behaviors of glass, and a better understanding of the effects of these parameters on corrosion mechanisms is essential for designing glass with higher corrosion resistance. The interactions between glass and surrounding medium lead to the formation of a thin surface layer called the “alteration layer,” which has the composition and structure different from that of the bulk [20–23]. Corrosion of glass (powder, monolith, or coupon) has been studied using a number of modern analytical techniques, which provides information such as corrosion kinetics, surface chemical composition, elemental depth profile, and porous structure of the alteration layer formed at the interface of the glass and aqueous reaction medium. This chapter mainly reviews recent understanding of aqueous glass corrosion based on experimental and theoretical studies; many examples come from model systems related to glass forms used for immobilization and containment of nuclear waste materials. It is not intended to review the entire field in a chronological order — readers are also referred to recent reviews of glass corrosion [11, 24–26]. Atmospheric corrosion and vapor hydration of glass are also reviewed in a separate section since they have both similarities and differences in comparison to aqueous corrosion. Corrosion of pharmaceutical glass is discussed briefly due to the recent increased interest in its chemical durability. Chemical compositions of the glasses discussed in this chapter are listed in Table 5.1. Although knowledge of glass corrosion has improved significantly, more studies are still needed to gain a better understanding of glass corrosion processes.

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Table 5.1. Chemical compositions of glasses listed in the book chapter. P0798 [28]b

Zn13 [12]a

U212 [29]b

U213 [29]b

PNL 76-68 [30]b

CJ8 [31]b

52.69 14.02 3.39 5.01 11.39 0.00 1.54 0.00 0.00 1.31 1.45 4.60 0.00 0.38 0.85 0.00 0.01 0.00 2.15 1.22

60.10 15.97 3.84 5.73 12.65 0.00 1.72 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

42.96 9.37 5.76 6.40 20.01 0.28 1.59 0.39 1.10 0.41 0.31 4.37 2.43 0.00 0.00 0.57 0.87 0.00 2.41 0.78

46.60 14.20 5.00 3.00 10.00 0.00 1.46 0.00 0.00 2.04 0.00 3.00 0.00 0.37 1.45 0.00 0.02 0.00 3.00 9.86

58.9 15.7 0.00 0.00 12.4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 13.0 0.00

39.60 11.56 4.24 0.00 12.69 4.12 0.00 0.00 0.00 12.05 0.00 3.54 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.72

39.60 11.29 5.07 0.00 12.38 4.03 0.00 0.00 0.00 12.05 0.00 3.45 0.00 0.00 0.00 0.00 0.00 0.00 0.00 5.65

39.80 9.47 0.00 2.00 12.80 0.00 0.00 0.00 0.00 10.34 0.00 0.00 0.00 0.00 2.42 0.00 0.00 2.97 4.97 15.23

62.00 19.10 0.00 5.50 13.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

mol %; b weight %.

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SiO2 B2 O3 Al2 O3 CaO Na2 O K2 O ZrO2 Cl F Fe2 O3 LN2 O3 Li2 O MgO MnO2 MoO3 SO3 SnO2 TiO2 ZnO Others

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5.2. Glass Corrosion Although the mechanism of glass corrosion is not yet fully understood, the generally accepted view is that the corrosion process involves three different stages with characteristic alteration rates (Fig. 5.1) [11, 24, 26, 32, 33]. Glass corrosion initially occurs fast, then gradually slows to a very low corrosion rate. This period is called “stage I” and the initial corrosion rate is called the “forward rate.” The decrease in corrosion rate during stage I is mainly due to the increase of corrosion products in aqueous solution and the formation of a transport-limiting layer between the solution phase outside the glass and the reaction front inside the glass [11]. This layer is called the “alteration layer.” The next stage, “stage II,” is characterized by a much slower corrosion rate called the “residual rate” and can last for a long time (ideally, thousands or millions of years). A study by Gin et al. showed that there is no obvious relation between the forward and residual rates [12]. After a certain time in the latency period (stage II), the corrosion process may resume under certain

Fig. 5.1. Schematic of glass corrosion process showing different stages (Reprinted from Ref. [32], with permission).

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conditions (typically, pH > 10 and/or temperature >100◦ C); this resumption period is called “stage III” [12]. 5.2.1. Initial Rate and Rate Drop (Stage I) During stage I of aqueous corrosion of silicate glass, ion exchange occurs between the solution species (H3 O+ , OH− , H2 O, alkali ions, etc.) and the glass matrix elements (leachable network modifiers and some dissolvable network formers). The remaining network in the sub-surface region of the glass becomes silica-rich and hydrated. Depending on the solution conditions, the network can be hydrolyzed, which leads to the release of silicon-containing species from the glass (mostly ionized forms of silicic acid which depend on pH of solution). For silicate glasses containing boron, it is known that boron is readily released into neutral or basic solution media; the dissolution kinetics of boron and its concentration profile are similar to the leaching kinetics of alkali ions [26]. The glass network is modified following the release of boron and network modifiers. The initial dissolution rate in stage I is determined by the hydrolysis of the glass network, as it is the rate at which the corrosion solution remains dilute enough that any solution feedback is avoided. Solution feedback is the effect of solution chemistry of corrosion products on the rate of glass corrosion [34]. Glass corrosion products, for example, can slow down the corrosion process by reducing the chemical affinity for silica network dissolution. The magnitude of the initial rate depends on various factors such as glass composition, temperature, solution pH, and in some cases, concentrations of aluminum and iron in the leaching solution [26]. The accumulation of corrosion products near the surface region slows down the overall corrosion process and initiates the transition phase of stage I [11]. This effect is observed as the concentration of dissolved silica species increases [26]. The reason for the slowdown of corrosion rate has been debated for a long time; two main factors considered in the literature are the change in chemical affinity and the growth of a passive gel layer [26]. This transition regime was shown to be strongly influenced by dissolved silica and surface area to solution volume (S/V) ratio [12].

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Fig. 5.2. Normalized forward dissolution rate of EWG-C glass at different solution temperatures and solution pH values [27].

The effects of temperature, pH, and glass composition on the initial rate of stage I (forward dissolution rate, rf ) have been extensively studied [12, 27, 31, 35–39]. Figure 5.2 shows the forward dissolution rate of EWG-C glass (Table 5.1) as a function of pH and at different solution temperatures [27]. The results obtained with EWG-C and other model nuclear waste glasses show that temperature and solution pH account for 90% of the variance in rf [27]. The glass composition might have larger effects on dissolution rate under conditions in which solution feedback is significant; however, more studies are needed to verify this assertion. The relation between the forward dissolution rate (rf ), intrinsic rate constant (ko ), pH power law coefficient (η), apparent activation energy (Ea ), ideal gas constant (R), and absolute temperature (T ) is given in Eq. (5.1) [27]:   Ea ±η·pH (5.1) exp − rf = k0 10 RT The positive and negative signs in front of η are for acidic and basic pH conditions, respectively. In a model study with International

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Fig. 5.3. Forward dissolution rate (denoted as ro in this case) of ISG and P0798 glasses as a function of pH and temperature (Reprinted from Ref. [41], with permission).

Simple Glass (ISG, Table 5.1), a model nuclear waste glass that was made and shared among glass corrosion groups for round-robin study among multiple research groups [32], Elia and co-workers reported that the forward dissolution rate increases as the solution pH increases above 5 [27, 35, 36]. The forward rate of ISG as a function of pH shows a V-shape, while P0798 (Table 5.1), a Japanese reference waste glass, exhibits a U-shape (Fig. 5.3) [36, 40, 41]. The reason for the difference in corrosion behavior of these glasses is not fully understood; however, it was suggested that the difference in alkali contents can be one of contributing factors. The V-shape pH dependence was also obtained for the forward dissolution rate of a simple analogue nuclear waste glass by Knauss et al. [42]. The forward rate of simulated aluminoborosilicate waste glasses at different pH values studied by Pierce et al. also showed similar pH dependence as ISG and P0798 glasses at pH higher than 7 [37]. 5.2.2. Residual Rate (State II) The glass corrosion process enters stage II when the aqueous solution is saturated with soluble silica polymorphs [31]. Stage II is characterized by a very slow alteration rate called the “residual rate.”

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The alteration rate in this stage is determined by the formation of a passivating layer, as well as the transformation of this layer into a more stable but non-protective structure and the formation of secondary silicate phases [12, 43, 44]. While the formation of a passivating layer slows down the glass alteration rate, the formation of a non-protective layer and secondary phases can increase it [12]. The residual rate, as a result, depends on the competition between these effects. The formation of the alteration layer could occur via the precipitation of solution species onto the glass surface or the self-reorganization of the silicate network in the alteration (or passivating) layer, which depends on the corrosion conditions [20, 23, 45–50]. Although the glass surface in stage II is in contact with the solution saturated with soluble silica species, the corrosion process can still continue at extremely slow but finite rates of mobile element leaching from the alteration layer/glass interface and subsequent rearrangement of remaining networks in the alteration layer [20]. Using time-of-flight secondary ion mass spectrometry (ToF-SIMS) and energy-filtered transmission electron microscope (EF-TEM), Gin et al. showed that for ISG glass samples corroded for 7, 209, and 363 days in silica-saturated solution, there is a gradient of mobile elements (B, Na, Ca) in the region of the alteration layer close to the pristine glass, and dissolution and precipitations occurred on the glass surface even in silica-saturated solution [20]. Nuclear magnetic resonance (NMR) analysis results from this study also indicated an in situ reorganization of the silicate network during the corrosion process [20]. The passivating (protective) effect of the altered layer (gel) on the glass surface in stage II could be attributed to various factors including self-reorganization of the porous structure, which would be consequences of hydrolysis–condensation reactions within the layer [20, 23]. The nano-porous gel layer can affect the transport of hydrous species from solution toward the pristine glass and the leaching of mobile elements in the glass matrix into aqueous solution. To study the mobility and reactivity of water in a gel layer formed on ISG glass, Gin et al. performed isotopic-tagging experiments by immersing altered ISG samples in mixtures of H2 18 O and H2 16 O [23].

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(a)

(b)

Fig. 5.4. ToF-SIMS depth profiles of the 18 O/16 O ratio and B in the one-year corroded ISG sample. Water mobility in the gel layer as indicated by the 18 O/16 O ratio (a) after different immersion times of gel layer in isotopic water. The boron profile in (b) shows that 18 O already reached the reactive interface after only 3 minutes [23].

This isotopic study revealed a significant increase in the 18 O/16 O ratio in the region near the reactive interface (reaction front, Fig. 5.4) that might be due to a larger amount of exchangeable oxygen atoms in this reactive region [23]. The 18 O/16 O exchange study showed that for ISG samples corroded for one year, 18 O reached the reaction front after only 3 minutes of immersion in the isotopeenriched water. However, only about 6% of the mobile oxygen in the gel was exchanged with 18 O even after three months in contact with the isotopically enriched solution. This may be due in part to water molecules and silanol groups in closed pores that do not exchange easily with solution water. The porous structure of the gel layer formed in glass surfaces has been characterized using different techniques [20, 43, 51, 52]. Using a post-tracing test experiment, it was shown that the central part of the altered layer formed on an ISG sample corroded for

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209 days in silica-saturated solution has pores smaller than 1 nm [20]. To determine the pore size distribution in the alteration layer, adsorption–desorption experiment has been used [53]. Using spectroscopic ellipsometry, Ngo et al. measured adsorption–desorption isotherms of water on ISG samples corroded for different times in aqueous solution [51]. Analyzing the isotherms with the Kelvin equation for condensation, they have shown that samples corroded for less than 30 days have pores with a diameter less than 2 nm, while the sample corroded for 1625 days has a significant fraction of pores larger than 2 nm. Combining results from infrared spectroscopy and ellipsometry, this study revealed that the pore size distribution in the alteration layer evolves during the corrosion process [51]. This study provides important information on how pore structure changes over time in stage II; thus, it provides glass corrosion scientists more realistic and slowly evolving glass network structures in the alteration layer. Transport simulations of mobile species in the alteration layer can now be simulated with pore size distributions that are more realistic (Fig. 5.5).

(a)

(b)

(c)

Fig. 5.5. ISG coupon altered in SiO2 -saturated solution with 40 mM KCl for 1625 days: (a) Optical model of the sample at 0% RH (L1−4 are surface layers); (b) Isotherm of water in layer 2 (deeper region close to the bulk); (c) Isotherm of water in layer 3 (thick middle region). The dashed lines in (b, c) are the void volume fraction determined by fitting the SE data at RH = 0% [51].

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Effects of dissolved silica and glass composition on the residual rate of borosilicate glass corrosion were studied by Gin and coworkers [12, 13]. The silicon-containing species in solution were found to influence the transition regime of stage I more than the residual rate regime of stage II [12, 54]. Most nuclear waste glasses have Zn and Fe as their major components. The equivalent thickness of a glass containing Zn (Zn13, Table 5.1) was found to increase linearly with time; this constant dissolution is due to the precipitation of Zn-silicates on the glass surface [12]. Iron has two competing effects on glass corrosion in stage II: detrimental and beneficial [12]. The detrimental effect is due to Fe-silicate precipitation that consumes silica and then enhances glass dissolution. The mechanism of the beneficial effect of Fe on protective properties of the gel layer is not well understood. Minor components like Zr can also have significant impacts on chemical durability, glass transition temperature, density, and viscosity [12, 55]. The effect of Zr on glass dissolution kinetics depends on its relative concentration. When its total concentration is low, the addition of Zr was reported to slow the dissolution kinetics due to the high insolubility of zirconia; however, continued addition of Zr to higher concentrations leads to a higher degree of corrosion in latter stages [56]. Self-reorganization of the gel layer in the presence of Zr can be a major determinant of the glass alteration rate [23, 57]. The effect of S/V on glass corrosion in stage II was studied, and the results showed that the residual rate does not depend significantly on the S/V ratio as long as the solution pH is well controlled [12, 13]. Although samples of different S/V ratios will reach the residual rate regime at different times (i.e., the duration of stage I), differences in their residual rates at stage II are relatively small. The fluctuation of their residual rates could be attributed to the diffusion of solution species via the passivating reactive interface (PRI) and the precipitation of secondary silicate compounds from aqueous solution [12]. 5.2.3. Resumption of Alteration (Stage III) Glass may be in stage II for thousands or even millions of years; however, the protective properties of the surface layer may fail due

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to unclear causes and resumption of glass alteration can occur as indicated by a sudden increase of alteration rate. Alteration resumption (stage III) has been observed in laboratory experiments under specific experimental conditions such as high pH, high temperature, and high S/V ratio [58–63]. The resumption in this stage appears to be associated with zeolite precipitation on the glass surface or in aqueous solution. Although the original cause of alteration resumption is still unclear, addition of zeolite seeds to corrosion solutions was reported to initiate resumption [61]. The reduction or disturbance of the latency period (stage II) of glass corrosion by zeolite addition allows study of stage III at pH values close to that found in a geological repository. A study by Fournier et al. showed that when zeolite is added to the leaching solutions of ISG glass at high pH and temperature, there is a significant increase in altered glass fraction (AGf, the ratio of boron in the solution to the total boron in the glass before corrosion) and a decrease in aluminum concentration in aqueous solution (Fig. 5.6) [61]. The effect of zeolite precipitation on alteration rate is reduced with decreasing pH and temperature. Glass composition has complex effects on the resumption of alteration. A change in glass composition can lead to large differences in occurrence time of resumption [58]. It has been reported that, for two glasses of very similar compositions, U212 and U213 (Table 5.1), U212 glass quickly shows acceleration of alteration in controlled pH experiments while U213 shows no evidence of alteration resumption [29]. Although resumption of alteration has been reported to be associated with precipitation of zeolites consisting of aluminum, there is a special case in which resumption of alteration occurred for a glass (CJ8, Table 5.1) without aluminum [31]. The effects of S/V ratio, temperature, and pH on the resumption of glass alteration have been investigated in many studies [28, 29, 64–67]. A high S/V ratio was reported to induce resumption of alteration more readily due to higher reaction progress and quicker change of solution pH [29, 64]. The resumption also occurs earlier with higher temperatures, which reduces the incubation period and accelerates nucleation of zeolite crystals [58]. It has been reported

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Fig. 5.6. Seeded test experiment of ISG glass at high pH and 90◦ C. AGf and aluminum solution concentration (CAl ) are plotted as a function of time [61].

that the resumption of alteration occurs around pH 11, and solution pH decreases with the resumption [58]. 5.3. Corrosion Models Glass corrosion is very slow at ambient conditions and it can persist in stage II for years even at elevated temperatures [43]. It is therefore important to develop corrosion models to understand and predict the behavior of glasses in different corrosion stages as well as their

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service life in a specific condition. Various glass corrosion models have been developed using different approaches [26, 68, 69]. Transition state theory (TST) was used by Aagaard and Helgeson to model the surface dissolution of aluminosilicate minerals [11, 68]. The general equation of glass dissolution is [11, 68]:   −A  −ni ai (t) (5.2) r(t) = k exp 1 − σRT where r, k, A, σ are dissolution rate, rate constant, overall reaction chemical reactivity, and decomposition rate of the activated complex relative to that of the overall reaction, respectively. The other parameters, R and T , are the gas constant and temperature, respectively. The stoichiometric reaction coefficient for reactant i is denoted as ni and Πai is the product of the activities of solution components involved in the reaction. The parameter σ is the average stoichiometric number for the overall reaction process and is defined in Eq. (5.3), in which σj and Aj are the stoichiometric number and chemical affinity, respectively, of the jth reaction [68].  A j σj Aj = (5.3) σ=  j Aj j Aj The theory was applied to the corrosion of nuclear waste glass by Grambow and colleagues [70, 71]. The dissolution rate was rewritten (Eq. (5.4)) with the introduction of silicic acid (H4 SiO4 ) concentration, which was found to be the primary factor affecting the rate [11, 70, 71]:   [H4 SiO4 ](t) (5.4) r(t) = ro 1− [H4 SiO4 ]sat Here, ro is the forward dissolution rate as a function of temperature, ionic strength solution, and glass composition, and [H4 SiO4 ]sat is the saturation concentration of the silicic acid species [72]. Equation (5.4) indicates that the dissolution rate is zero when the solution is saturated with H4 SiO4 . However, experimental results show that the rate does not become completely null when H4 SiO4 is saturated in solution [12, 31, 73]. Grambow and M¨ uller extended previous works

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and proposed a new glass corrosion model known as “GM2001” model [11, 69]. In this model, the diffusion of water through glass and that of H4 SiO4 -related species through the altered layer are considered. The rate-limiting step is determined by the concentration of silicon-containing species in solution, and the fates of silicon and boron species are represented by empirical equations [11]. Studies of protective properties of thin layers formed on glass surfaces during corrosion have led to another noticeable model for long-term glass corrosion called the “GRAAL (glass reactivity with allowance for the alteration layer)” model [11, 26]. In the GRAAL model, the rate-limiting step is water diffusion through the PRI. The PRI thickness and total dissolved PRI thickness at time t are denoted as e(t) and E(t), respectively. The dissolution (dE/dt) and formation (de/dt) rates of the PRI are related to the initial dissolution rate of the PRI (rdisso ), the concentration of silicon-containing species in the solution at time t and saturation (CSi (t), CSi,sat ), the hydrolysis rate of the pristine glass creating the PRI (rhydr ), and the water diffusion coefficient in the PRI (DPRI ) by the following equations [11, 26]:   CSi (t) dE = rdisso 1 − (5.5) dt CSi,sat rhydr de = e·rhydr dt 1 + DP RI −

dE dt

(5.6)

Here, the PRI layer is conceptual and its location as well as structure are still the subject of various experimental and theoretical studies [11]. More details of the GRAAL model can be found in the works of Frugier and colleagues [26, 74–78]. The model has been successfully applied to understanding the alteration of borosilicate glass in different stages of glass corrosion [76–81]. The aforementioned glass corrosion models have been applied to the corrosion of different glass systems, and they provide some basic understanding of glass corrosion mechanisms [78, 79, 82]. However, more fundamental research is necessary to validate and refine the current models and make them less empirical [82, 83]. The GRAAL model, for example, is dependent on empirical parameters calculated

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for each specific glass composition, and it is not yet verified for a range of temperatures and glass compositions [83]. 5.4. Effects of Electrolytes and Near-Field Materials on Glass Corrosion In addition to the indigenous species dissolved from the glass, exogenous species present in corrosion solutions are also shown to affect glass corrosion process significantly. Such species are naturally present electrolytes in aqueous solution or electrolytes produced by corrosion of metals or other ceramic compounds nearby. It was reported that during stage I, the dissolution rate increases significantly in the presence of alkali and alkali earth metal ions in the corrosion solution [84–87]. Jollivet et al. studied the forward dissolution rate (rf ) of SON68 glass in clay-equilibrated ground water (GW; Fig. 5.7) [84]. The results showed that alkali (Li+ , Na+ , K+ , Rb+ , Cs+ ) and alkali earth metal ions (Mg2+ , Ca2+ , Sr2+ , Ba2+ ) increase rf of the glass in comparison to that in deionized water (DW), while the effect of anions such as carbonate, chloride, and sulfate is insignificant. This study also showed that the forward rate

Fig. 5.7. Forward dissolution rate versus temperature of SON68 glass in DW and GW (Reprinted from Ref. [84], with permission).

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in solutions containing alkali earth cations is generally higher than that in alkali solutions, with an exception in the case of magnesium. The rate was reported to increase with the ionic strength of the corrosion solution. To explain the effects of these cations on the forward rate of SON68 glass, it was hypothesized that the Si–O bonds are more hydrolysable in the presence of the studied alkali and alkali earth cations [84]. The pH dependent effects of Ca2+ on the initial dissolution rate of a borosilicate glass at different pH values and concentrations were studied by Mercado-Depierre et al. [88]. Under the presence of Ca2+ , the initial glass dissolution rate was shown to increase up to pH 10.5; however, the rate drops sharply when pH exceeds 11. The antagonistic effects of Ca2+ concentration and pH may play critical roles in the overall dissolution rate of glass. Dove and co-workers studied corrosion kinetics of silica in various single- and mixed-alkali and alkali earth chloride solutions [85–87, 89]. A small concentration of electrolyte was reported to increase the dissolution rate significantly in comparison to that in DW. The dissolution study at 200◦ C indicated the order of electrolytes in increasing silica dissolution rate as NaCl ≈ KCl > LiCl > MgCl2 > H2 O [87]. It was proposed that the cations form coordinated complexes with the silica surface, and that these complexes disturb the surface structures. Using sum frequency generation (SFG) spectroscopy, Yang et al. showed that interactions of cations such as alkalis with the silica surface via electrostatic interaction lead to a significant perturbation of the hydrogen-bond network at the silica/water interface [90]. These studies demonstrated that a disturbed interface (surface) enables more direct access of water to the Si–O–Si bonds, which results in a higher dissolution rate of silica. The effects of electrolytes on glass corrosion in stage II have also been studied. Colin et al. performed leaching experiments of ISG glass in silica-saturated solutions containing single alkali chlorides at different concentrations [14]. The corrosion kinetics of ISG is presented in terms of equivalent thickness of the alteration layer calculated from boron concentration in leaching solutions (ET(B)). The results obtained showed different effects of LiCl, NaCl, KCl,

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(a)

(b)

Fig. 5.8. Alteration kinetics of ISG in silica-saturated solution containing single alkali chloride. ET(B) is the equivalent thickness of the alteration layer calculated from boron concentration in leaching solutions and AG is altered glass (%) [14].

and CsCl on the corrosion of ISG in stage II. While the alteration kinetics of ISG in solutions containing LiCl or NaCl is quite similar to that in DW, the alteration rate is decreased in KCl and CsCl solutions (Fig. 5.8). The linear dependence of ET(B) versus time1/2 up to 130 days indicates that, in LiCl, NaCl, and no alkali solutions, the rate-limiting process in this period is the diffusion of reactive species through the alteration layer. The study further showed that the alteration rate decreases with increasing KCl and CsCl concentration. The retention of Ca in the gel was found to vary in the following order: KCl > CsCl > NaCl  LiCl. Although the results obtained showed significant effects of these electrolytes on glass alteration kinetics in stage II, it is still not obvious why the electrolytes show different effects on glass corrosion rate in stage II and more studies are needed. A deeper understanding of these effects could help design nuclear glasses with better corrosion resistance. During the corrosion process, glass may be in contact with nearfield materials and/or their corrosion products, and as a result, its corrosion behavior can be affected. A synergistic effect between iron and PNL 76-68 glass (Table 5.1) was reported wherein corrosion of both materials was enhanced [30]. The effects of magnetite on glass corrosion were studied extensively and an acceleration of glass corrosion was often reported [81, 91–94]. In these studies, Fesilicates were detected on glass surfaces and the incorporation of

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iron into the alteration layer was also reported. The enhancement of glass corrosion by magnetite and its corrosion products is mainly due to the consumption of silicon-containing species in solution by several processes: sorption of silica on near-field materials containing iron, precipitation of iron silicate minerals, and silica precipitation on the near-field materials [92]. The incorporation of iron into the alteration layer may also be a possible contributor; however, its effects on the properties of the alteration layer are not well understood [93]. Results from a study by Neil et al. showed that the effect of magnetite on glass corrosion is more severe when cracks are present on the glass surface (Fig. 5.9) [91]. The initial surface condition is thus an important parameter in determining glass corrosion behavior [95]. Using two different ISG samples that were

Fig. 5.9. SEM images of an ISG sample corroded for 358 days. In the upper left, the total monolith is shown with the polished side on the right and the unpolished side on the bottom left. All unpolished surfaces show enhanced alteration. Bottom left image shows a magnification of one of the altered areas that surrounds a crack in the surface. The EDS mapping of Na, Fe, and Si of the same region are shown on the right [91].

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polished-only and polished-then-annealed, Liu et al. showed that the corrosion behaviors of these two samples are significantly different under mild corrosion conditions (30◦ C) and relatively similar in more severe conditions (90◦ C) [95]. This suggests that initial surface condition should be considered as a parameter in glass corrosion studies, especially at temperatures close to ambient conditions (far below 90◦ C).

5.5. Atmospheric and Vapor Phase Corrosion Glass is subject to atmospheric corrosion while being used, and its corrosion behavior depends on humidity, temperature, air pollutants (CO2 , SO2 , N2 Ox ), composition, micro-organisms, and so on [16, 17, 96, 97]. Centuries-old glass artifacts such as medieval windows were studied extensively to understand the durability of glass kept indoors and outdoors for long periods of time. Various corrosion products were observed on weathered glass surfaces such as gypsum (CaSO4 · 2H2 O), CaCO3 , and double salt syngenite (K2 SO4 · CaSO4 · H2 O) [16, 17, 98, 99]. The presence of calcium oxalate was also reported due to the action of lichens or bacteria [17]. The type of corrosion products observed was found to depend on the time of exposure [100]. Chemical attack could lead to the formation of pits on glass surfaces with a reduced content of K2 O and CaO inside the pits [99]. The proposed corrosion mechanism is that ion exchange first occurs between alkaline ions (Na+ and/or K+ ) in the glass and H+ from a water film on the glass surface. The increased pH then induces the depolymerization of the silicate network and leaching of calcium that then forms Ca(OH)2 . The calcium hydroxide then reacts with air pollutants to form different corrosion products on the glass [99]. The degradation of glass by humid air is a serious problem [7, 8]. The effects of various relative humidity (RH) and cycling conditions (between 77% and 98% RH) on 26 glass compositions were investigated by Walters et al. [96]. The study showed that the static condition at 98% RH is more severe than the cycling condition. Rapid appearance of corrosion products was observed by scanning electron microscopy (SEM) on a poorly corrosion-resistant soda–lime glass

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Fig. 5.10. Electron micro-graphs of soda–lime glass before and after weathering at 98% RH, 50◦ C (53 000 X): Before weathering (upper left), weathered 6 hours (upper right), weathered three (bottom) days (Reprinted from Ref. [96], with permission).

after 6 hours of weathering, and permanent damage was recorded after three days of exposure (Fig. 5.10). In disposal repositories of nuclear waste glass, vapor phase corrosion might occur due to humidity and high temperature before liquid phase corrosion [18]. Therefore, it is important to understand the corrosion behavior of glass in water vapor as well as that of glass in contact with liquid water after being corroded in water vapor. Glass corrosion experiments were performed in the vapor phase [18, 19, 58, 101]; this condition is relevant to the corrosion behavior at extremely high glass surface area to solution volume ratio (S/V) because only a thin film of water is present on the sample surface and corrosion products are kept in the water film. Neeway et al. studied vapor hydration of SON68 glass from 90◦ C to 200◦ C and at various RHs [18]. The results obtained showed that the composition

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Fig. 5.11. SEM micro-graph cross section of a sample that was corroded in the vapor phase at 150◦ C, 92% RH for 99 days (right), and then leached at 50◦ C in DW water for 57 days (left). The thickness of the layer on the left is ∼4.5 µm, while the layer on the right is 3.4 µm measured from Fourier transform infrared spectroscopy (FTIR; Reprinted from Ref. [18], with permission).

of the alteration layer depends on the experimental conditions, and hydration rate at 90◦ C and 91 ± 1% RH is 10 times faster than the corrosion rate of the same glass in liquid water at 90◦ C. Various corrosion products were formed on the SON68 glass such as tobermorite (Ca5 Si6 O16 (OH)2 · nH2 O), analcime (NaAlSi2 O6 · H2 O), powellite (CaMoO4 ), and calcite (CaCO3 ). The presence of analcime is likely due to a high pH environment in the thin liquid film on the glass surface. The analcime was formed on SON68 glass corroded in aqueous solutions with pH over 10.5 [102, 103]. The SEM images in Fig. 5.11 show a large difference in gel layer structure between a sample corroded in vapor only and a sample that was corroded in vapor and then leached in DW. The surface composition of these samples were also reported to be different [18]. The alteration rate in vapor phase has been shown to be relatively higher than that in the liquid phase [18, 19]; however, more studies are needed to determine the corrosion mechanism as well as controlling factors [18]. 5.6. Corrosion of Pharmaceutical Glass Corrosion of pharmaceutical glass is also of great concern. Glass used in the pharmaceutical industry is susceptible to delamination

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or flaking due to surface defects and/or corrosion caused by incompatible solutions [104]. The occurrence of delamination or flakes is accompanied by chemical changes of the glass surface and release of elements into solutions contained in glass vials and containers. As a result, the quality of pharmaceutical solutions is affected, which is unacceptable. It is therefore important to understand the interaction of glass containers with drug-containing solutions so that delamination as well as release of chemical elements can be minimized. Iacocca et al. studied the corrosion of glass vials in contact with a pharmaceutical compound, and particulates were observed in vials stored at 30◦ C and 40◦ C [104]. Analysis results showed that the glass flakes were from the interior of the vials (Fig. 5.12). In the vial manufacturing process, glass cane is first produced, then cut, welded, and annealed to form the bottom and neck of the vial [104]. It was reported that the chemical resistance of the vial can be significantly affected by the manufacturing process [104, 105]. Excessive heat during glass cane production and vial formation can lead to an enrichment of sodium on the vial surface, which reduces the

Fig. 5.12. Representative scanning electron micro-graph showing glass delamination on the interior of a Type I glass vial (from [104], with permission). Type I glass is the pharmaceutical nomenclature for borosilicate glass. The main oxides in a Type I glass are SiO2 , B2 O3 , Al2 O3 , and Na2 O.

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chemical durability of the vial when in contact with pharmaceutical compounds [104]. A migration of sodium can also be caused by the heat used during sterilization and depyrogenation. Recent studies showed that, for borosilicate glasses, the root cause for delamination is boron volatization during the conversion of glass tube into the glass vial [106]. During the converting process, boron species volatize from the vial base and are then incorporated into the heel leading to the decreased chemical durability of this region. It was also showed that aluminosilicate glasses significantly reduce delamination [106, 107]. Chemical properties of the stored drug and storage conditions may make glasses susceptible to delamination [105].

5.7. Future Directions Glass corrosion has been studied using various techniques and under diverse experimental conditions. Information obtained from numerous studies by different groups has improved understanding of glass corrosion. However, in order to have more comprehensive corrosion models or mechanisms, many more studies are needed. The current corrosion models are based on dissolution kinetics data determined from the solution analysis and depth profiling of the alteration layer without considering information about the structure of the alteration layer. More corrosion studies with molecular spectroscopy such as vibrational spectroscopy and X-ray absorption spectroscopy are required to provide structural information of the surface layer. The use of advanced imaging techniques such as cryo-based atom probe tomography (cryo-APT) is also very helpful in providing porous structure, depth profiling, and chemical composition of the alteration layer in the hydrated state. Since the alteration layer has the chemical composition and density that are quite different from that of the bulk glass, the presence of residual stress in the layer is also possible. The residual stress in this case might contribute to the instability of the layer in stage II (crack formation leading to direct contact between the corrosive fluid and the pristine glass), and then the occurrence of stage III. It would therefore be interesting to understand the effects of residual stress, if possible, on glass

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corrosion. The thermodynamic properties of the passivating layer formed on glass surfaces are not well understood. Dynamics or transport properties of hydrous species in the surface layer are also important for a better corrosion model. Effects of electrolytes and near-field materials on glass corrosion have been considered; however, knowledge of these effects is currently limited. Although resumption of glass alteration has been reported to be associated with zeolite precipitation, the exact cause of resumption is not well understood, and more studies are necessary. Corrosion studies have been performed following some standard protocols that may not reflect real conditions in nuclear waste glass disposal repositories, so the design of new experiments is necessary [108]. Although glass compositions and corrosion conditions are drastically different, there might be some commonalities among corrosion behaviors of different types of glasses used for different purposes; comparison of corrosion kinetics among these seemingly irrelevant glass materials might provide some critical insights into surface reactions of glass in contact with water in general. Acknowledgment This work was supported as part of the Center for Performance and Design of Nuclear Waste Forms and Containers, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0016584. References 1. Walters, H., and Adams, P. (1968). The chemical durability of optical glass, Applied Optics, 7, pp. 845–848. 2. Theis, C. D., Fleming, D. A., and Osenbach, J. W. (2000). Proceedings. 50th Electronic Components and Technology Conference (Cat. No.00CH37070), pp. 989–996. 3. Niu, Y.-F., et al. (2009). Aqueous corrosion of the GeSe4 chalcogenide glass: Surface properties and corrosion mechanism, Journal of the American Ceramic Society, 92, pp. 1779–1787, doi:10.1111/j.15512916.2009.03132.x.

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30. McVay, G. L., and Buckwalter, C. Q. (1983). Effect of iron on waste-glass leaching, Journal of the American Ceramic Society, 66, pp. 170–174, doi:10.1111/j.1151-2916.1983.tb10010.x. 31. Gin, S., et al. (2012). Effect of composition on the short-term and long-term dissolution rates of ten borosilicate glasses of increasing complexity from 3 to 30 oxides, Journal of Non-Crystalline Solids, 358, pp. 2559–2570, doi:10.1016/j.jnoncrysol.2012.05.024. 32. Gin, S., et al. (2013). An international initiative on long-term behavior of high-level nuclear waste glass, Materials Today, 16, pp. 243–248, doi:10.1016/j.mattod.2013.06.008. 33. Poinssot, C., and Gin, S. (2012). Long-term behavior science: The cornerstone approach for reliably assessing the long-term performance of nuclear waste, Journal of Nuclear Materials, 420, pp. 182–192, doi:10.1016/j.jnucmat.2011.09.012. 34. Wang, Y., Jove-Colon, C. F., and Kuhlman, K. L. (2016). Nonlinear dynamics and instability of aqueous dissolution of silicate glasses and minerals, Scientific Reports, 6, p. 30256, doi:10.1038/srep30256, https: //www.nature.com/articles/srep30256#supplementary-information. 35. Elia, A., Ferrand, K., and Lemmens, K. (2017). Determination of the forward dissolution rate for International Simple Glass in alkaline solutions, MRS Advances, 2, pp. 661–667, doi:10.1557/adv. 2016.672. 36. Inagaki, Y., Kikunaga, T., Idemitsu, K., and Arima, T. (2013). Initial dissolution rate of the International Simple Glass as a function of pH and temperature measured using microchannel flow-through test method, International Journal of Applied Glass Science, 4, pp. 317– 327, doi:10.1111/ijag.12043. 37. Pierce, E. M., et al. (2008). An experimental study of the dissolution rates of simulated aluminoborosilicate waste glasses as a function of pH and temperature under dilute conditions, Applied Geochemistry, 23, pp. 2559–2573, doi:10.1016/j.apgeochem.2008.05.006. 38. Strachan, D. (2017). Glass dissolution as a function of pH and its implications for understanding mechanisms and future experiments, Geochimica et Cosmochimica Acta, 219, pp. 111–123, doi:10.1016/j.gca.2017.09.008. 39. Hamilton, J. P., et al. (2001). Dissolution of nepheline, jadeite and albite glasses: Toward better models for aluminosilicate dissolution, Geochimica et Cosmochimica Acta, 65, pp. 3683–3702, doi:10.1016/ S0016-7037(01)00724-4. 40. Inagaki, Y., et al. (2012). Initial dissolution rate of a Japanese simulated high-level waste glass P0798 as a function of pH and

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78. Frugier, P., et al. (2018). Modeling glass corrosion with GRAAL, npj Materials Degradation, 2, p. 35, doi:10.1038/s41529-018-0056-z. 79. Fournier, M., Frugier, P., and Gin, S. (2018). Application of GRAAL model to the resumption of International Simple Glass alteration, npj Materials Degradation, 2, p. 21, doi:10.1038/s41529-018-0043-4. 80. Frugier, P., Chave, T., Gin, S., and Lartigue, J. E. (2009). Application of the GRAAL model to leaching experiments with SON68 nuclear glass in initially pure water, Journal of Nuclear Materials, 392, pp. 552–567, doi:10.1016/j.jnucmat.2009.04.024. 81. Godon, N., Gin, S., Rebiscoul, D., and Frugier, P. (2013). SON68 glass alteration enhanced by magnetite, Procedia Earth and Planetary Science, 7, pp. 300–303, doi:10.1016/j.proeps.2013.03.039. 82. Gin, S. (2014). Open scientific questions about nuclear glass corrosion, Procedia Materials Science, 7, pp. 163–171, doi:10.1016/j.mspro.2014. 10.022. 83. Hunter, F. M. I., Hoch, A. R., Heath, T. G., and Baston, G. M. N. (2015). Review of glass dissolution models and application to UK glasses. 84. Jollivet, P., Gin, S., and Schumacher, S. (2012). Forward dissolution rate of silicate glasses of nuclear interest in clayequilibrated groundwater, Chemical Geology, 330–331, pp. 207–217, doi:10.1016/j.chemgeo.2012.09.012. 85. Dove, P. M. (1999). The dissolution kinetics of quartz in aqueous mixed cation solutions, Geochimica et Cosmochimica Acta, 63, pp. 3715–3727, doi:10.1016/S0016-7037(99)00218-5. 86. Dove, P. M., and Nix, C. J. (1997). The influence of the alkaline earth cations, magnesium, calcium, and barium on the dissolution kinetics of quartz, Geochimica et Cosmochimica Acta, 61, pp. 3329–3340, doi:10.1016/S0016-7037(97)00217-2. 87. Dove, P. M., and Crerar, D. A. (1990). Kinetics of quartz dissolution in electrolyte solutions using a hydrothermal mixed flow reactor, Geochimica et Cosmochimica Acta, 54, pp. 955–969, doi:10.1016/ 0016-7037(90)90431-J. 88. Mercado-Depierre, S., Angeli, F., Frizon, F., and Gin, S. (2013). Antagonist effects of calcium on borosilicate glass alteration, Journal of Nuclear Materials, 441, pp. 402–410, doi:10.1016/j.jnucmat.2013. 06.023. 89. Dove, P. M., Han, N., Wallace, A. F., and De Yoreo, J. J. (2008). Kinetics of amorphous silica dissolution and the paradox of the silica polymorphs, Proceedings of the National Academy of Sciences, 105, pp. 9903–9908, doi:10.1073/pnas.0803798105.

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90. Yang, Z., Li, Q., and Chou, K. C. (2009). Structures of water molecules at the interfaces of aqueous salt solutions and silica: Cation effects, The Journal of Physical Chemistry C, 113, pp. 8201–8205, doi:10.1021/jp811517p. 91. Neill, L., et al. (2017). Various effects of magnetite on international simple glass (ISG) dissolution: Implications for the long-term durability of nuclear glasses, npj Materials Degradation, 1, p. 1, doi:10.1038/s41529-017-0001-6. 92. R´ebiscoul, D., et al. (2015). Reactive transport processes occurring during nuclear glass alteration in presence of magnetite, Applied Geochemistry, 58, pp. 26–37, doi:10.1016/j.apgeochem.2015. 02.018. 93. Michelin, A., et al. (2013). Silicate glass alteration enhanced by iron: Origin and long-term implications, Environmental Science & Technology, 47, pp. 750–756, doi:10.1021/es304057y. 94. Dillmann, P., et al. (2016). Effect of natural and synthetic iron corrosion products on silicate glass alteration processes, Geochimica et Cosmochimica Acta, 172, pp. 287–305, doi:10.1016/j.gca.2015. 09.033. 95. Liu, H., et al. Effects of surface initial condition on aqueous corrosion of glass — A study with a model nuclear waste glass, Journal of the American Ceramic Society, doi:10.1111/jace.16016. 96. Walters, H. V., and Adams, P. B. (1975). Effects of humidity on the weathering of glass, Journal of Non-Crystalline Solids, 19, pp. 183– 199, doi:10.1016/0022-3093(75)90084-8. 97. Munier, I., Lef`evre, R.-A., and Losno, R. (2002). Atmospheric factors influencing the formation of neocrystallisations on low durability glass exposed to urban atmosphere, 43. 98. Melcher, M., and Schreiner, M. (2005). Evaluation procedure for leaching studies on naturally weathered potash-lime-silica glasses with medieval composition by scanning electron microscopy, Journal of Non-Crystalline Solids, 351, pp. 1210–1225, doi:10.1016/ j.jnoncrysol.2005.02.020. 99. Carmona, N., Villegas, M. A., and Navarro, J. M. F. (2006). Characterisation of an intermediate decay phenomenon of historical glasses, Journal of Materials Science, 41, pp. 2339–2346, doi:10.1007/s10853005-3948-6. 100. Melcher, M., and Schreiner, M. (2006). Leaching studies on naturally weathered potash-lime-silica glasses, Journal of Non-Crystalline Solids, 352, pp. 368–379, doi:10.1016/j.jnoncrysol.2006.01.017.

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101. Abrajano, T. A., Bates, J. K., and Mazer, J. J. (1989). Aqueous corrosion of natural and nuclear waste glasses II. Mechanisms of vapor hydration of nuclear waste glasses, Journal of Non-Crystalline Solids, 108, pp. 269–288, doi:10.1016/0022-3093(89)90297-4. 102. Gin, S., and Mestre, J. P. (2001). SON68 nuclear glass alteration kinetics between pH 7 and pH 11.5, Journal of Nuclear Materials, 295, pp. 83–96, doi:10.1016/S0022-3115(01)00434-2. 103. Ribet, S., and Gin, S. (2004). Role of neoformed phases on the mechanisms controlling the resumption of SON68 glass alteration in alkaline media, Journal of Nuclear Materials, 324, pp. 152–164, doi:10.1016/j.jnucmat.2003.09.010. 104. Iacocca, R. G., and Allgeier, M. (2007). Corrosive attack of glass by a pharmaceutical compound, Journal of Materials Science, 42, pp. 801–811, doi:10.1007/s10853-006-0156-y. 105. Ditter, D., et al. (2018). Evaluation of glass delamination risk in pharmaceutical 10 mL/10R vials, Journal of Pharmaceutical Sciences, 107, pp. 624–637, doi:10.1016/j.xphs.2017.09.016. 106. Schaut, R. Attacking delamination by addressing root cause. (2014). https://www.corning.com/media/worldwide/global/documents/Att acking delamination by addressing root cause 2014 Corning Incorpo rated.pdf 107. Weeks, W. P., Schaut, R. A., DeMartino, S. E., and Peanasky, J. S. (Google Patents, 2016). https://patents.google.com/patent/ US9474688B2/en 108. Chinnam, R. K., Fossati, P. C. M., and Lee, W. E. (2018). Degradation of partially immersed glass: A new perspective, Journal of Nuclear Materials, 503, pp. 56–65, doi:10.1016/j.jnucmat.2018.02.040.

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CHAPTER 6

Electrical Properties of Glass Caio Barca Bragatto Coe College

6.1. Introduction At our time and age, we all depend heavily on electronic devices. From smartphones in our pockets to artificial satellites in orbit over our heads, materials with interesting electrical properties are everywhere and the demand for better suited, cheaper, and especially more ecologically friendly materials is only increasing. The electrical resistance of a material is defined by the response to withstand electrical current, which is the diffusion of charged carriers through it. This fundamental property is expressed as R = ρ · I/A, where ρ is the electrical resistivity (ρ) and it is generally given in Ω·cm, but the most common way to represent ρ is through electrical conductivity (σ), simply the inverse of ρ, given in S·cm−1 . Much like ceramics, glasses are generally known as electrical insulators. As an example, values of σdc (electrical conductivity with a direct current) for window glass vary from 10−14 to 10−9 S·cm−1 , at room temperature [1]. For reference, potable water normally has an electrical conductivity from 10−3 to 10−2 S·cm−1 at room temperature [2]. Nonetheless, specific oxide glasses can achieve electrical conductivities of up to 10−2 S·cm−1 at room temperature, mainly due to their chemical composition [3, 4]. 199

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Electrically conductive glasses may be classified accordingly to the charge carrier’s nature, that is, ionic conductors and electronic conductors. It is possible to make glasses with both charge carriers — those are called mixed conductive glasses. Much of our knowledge on the topic is borrowed from other areas, such as ionic crystals, semi-conductors, molten salts, and thermodynamics, but there is still much to be understood. In the following paragraphs, a current view of the study of electrical properties in oxide glasses is presented. 6.2. Ionic Conductivity In 1884, Emil Warburg was the first to study ionic conductivity in glasses by attesting Faraday’s law due to the transport of sodium ions through a thin window glass between two sodium and mercury amalgams [5]. Since this first observation, many other compositions were developed and studied, fit for different applications, such as energy storage devices, ionic membranes, electrochemical sensors, and solid-state super-ionic stamping. Highly ionic conductive oxide glasses normally comprised of monovalent cations, such as Na+ , Li+ , K+ , or Ag+ introduced in the glass as salts or oxides, and any of the traditional glass formers (examples include SiO2 , P2 O5 , or TeO2 ). The conductivity strongly depends on the nature of the cation as well as their concentration and the type of glass former. Most ionic conductive glasses have cations as their sole charge carriers, but it is known that some glasses anions such as Fl− , Cl− , Br− , or I− can also move in the glass matrix and contribute to the conductivity [6]. One of the biggest advantages ionic conductive glasses have over crystalline materials as applicable materials is that they present an ionic transport number close to 1, that is, they conduct electricity almost exclusively by the movement of ions, reducing drastically the chance of an eventual short-circuit in batteries, for example. 6.2.1. Ionic Conductivity and Diffusion Diffusion is defined as the movement of molecules or atoms from one region to another, due to random movement of these molecules or

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atoms caused by a driving force. Therefore, the movement of ions in a glass matrix due to an electrical field may be interpreted as a specific case of diffusion. Fick [7] first developed the mathematical concept of diffusion flux. Fick’s first law states that the diffusive flux ϕ (mol· m−2 · s−1 ) is proportional to the number of ions moving through an area during a given time: ϕ = −D

dn dx

(6.1)

where D (m2 · s−1 ) is the diffusion coefficient, proportional to the average jump distance and the average frequency of successful jumps, n is the concentration of the diffusing species (mol· m−3 ) and x is the position (m). Taking into account how the concentration changes with time leads to Fick’s second law. Assuming that D is constant, it can be written as: d2 c dc =D 2 dt dx

(6.2)

From the concepts of diffusion flux and of the random movement of particles in a given medium known as the Brownian motion, Albert Einstein developed a relation known as the Einstein relation [8]: D=

vd · kB · T = u · kB · T F

(6.3)

where vd is the terminal drift velocity of the particle diffusing due to an applied force F and kB is the Boltzmann constant (1.38 10−23 m2 kg s−2 K−1 ). The relation vd /F is also known as the mobility of the diffusing species u (m· s−1 ). For the specific case of electric conductivity, the force applied per unit of charge carrier is E · Z · e, where E is the electrical field, Z is the valence of the charge carrier, and e is the charge of an electron (1.60·10−19 C). Therefore, the mobility of the charge carrier in the case of electric conductivity (μ in cm2 · s−1 · V−1 ) can be related to the mobility u: u=

μ Z·e

(6.4)

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Therefore, using Einstein’s relation and the relation of mobility with electrical mobility, we have that: μ=

D·Z ·e kB · T

(6.5)

and from the limiting molar conductivity, the electrical conductivity σdc can be written as: σdc = Z · e · n · μ

(6.6)

Substituting the mobility in the molar ionic conductivity with Einstein’s relation, the diffusion of ionic species relates to ionic conductivity by:  2 2  Z ·e ·n ·D (6.7) σdc = kB · T known as the Nernst–Einstein equation [9]. Since diffusion is an activated process, the diffusion coefficient may be written as:   −EDif (6.8) D = D0 · exp kB · T where D0 is the maximum diffusion coefficient (m2 · s−1 ) and EDif is the activation energy for the process (J· mol−1 ). Thus, the ionic conductivity may be written as a function of the energy barrier associated with the formation movement and diffusion of the charge carrier ions (Eσ ) and temperature as:   −Eσ A (6.9) σ = · exp T kB · T where A is a pre-exponential constant (K · S · cm−1 ). 6.2.2. The Haven Ratio Experimental results show that the diffusion coefficient for Fick’s law (Eq. 6.2) — determined by radiotracers — and the diffusion coefficient for the Nernst–Einstein relation (Eq. 6.7) — determined by electrical conductivity — may be different. This is true not only for glasses but for crystals as well.

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For an ionic crystal in which the mobile ion follows a random walk by a direct interstitial mechanism, the values for diffusion coefficient are the same. If the mobile ion follows a different random walk, in which some of the jumps are not allowed, the diffusion coefficient will be different for the ionic conductivity and self-diffusion of radiotracers. This difference is expressed by the Haven ratio (HR ) [10]: HR =

Dσ D

(6.10)

For crystals, the determination of the Haven ratio helps determining the diffusion mechanism, but not for glasses due to their irregular structure. For oxide glasses, the value of HR is normally between 0.3 and 0.6 for glasses with a high concentration of mobile ions, and closer to 1 for glasses with a lower concentration. Therefore, it is assumed that the Haven ratio for glasses is related to the interaction of the diffusing ions. 6.2.3. Modeling the Ionic Conductivity Below Tg Trying to unveil a model for describing and predicting the ionic conductivity is no easy task. The main difficulty for doing so arises from the difficulty to define and experimentally separate the number of effective charge carriers and its mobility from Eq. (6.6). Many different models can be found on the literature, and there is still no consensus on which model better fits experimental data, or even if there is a single model that could explain all glasses in all temperature ranges [11]. Some of the most discussed models in the literature are presented in the following paragraphs. 6.2.3.1. Anderson and Stuart Model A first approach for the transport mechanism below the Tg was based on classic ideas of ionic crystal theory and elastic theory, developed by Anderson and Stuart in 1954 [12]. In their work, they suggest that the movement of the charge carriers depends on two activation energies: the binding energy that holds an ion on its place (EB , given in kJ· mol−1 ), which it has to break free from to move, and the energy

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to distort the network during its movement to the next site (ED , given in kJ· mol−1 ), very similar to a Frenkel defect in crystalline ceramics. The binding energy is given by: EB =

β · Z · ZO γ · (r + rO )

(6.11)

where β is the so-called finite displacement factor and is related to the size of the ion, Z and ZO are the charges of the cation and the oxygen, respectively, γ is related to the relative dielectric permittivity of the material, and r and rO are the radii of the ion and oxygen, respectively (˚ A). The distortion energy is given by: ED = 4 · π · G · rO · (r − rD )2

(6.12)

where G is the shear modulus of the glass (GPa) and rD is the radius of the network constriction, that is, the distance the cation has to move (˚ A). A representation of the energy landscape for the movement of an ion according to this model can be seen in Fig. 6.1. Using this model to compare different ions for conduction, with an increasing ion radius, the binding energy will decline due to a decrease of the electronegativity of the ions, but the energy necessary to distort the network will increase. Considering the total energy for the ionic diffusion to be a sum of these two competing terms, the total energy of systems with similar structure is expected to present a direct relation with ion size, as found for alkali silicates [14]. One of the most important assumptions this model takes into account is the fact that all sites are available for the ions to move to. That means that all ions can move to nearby sites as long as they have enough energy to distort the network to do so, therefore the limiting energy barrier is not the number of charge carriers or available sites for conduction (n) but their mobility or how easily the ions can move through the network (μ). 6.2.3.2. Charles Model Another way to approach this challenge is by an interstitial pair model, developed by R. J. Charles in 1961 [15], in which the charge

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Fig. 6.1. Energy landscape illustration describing the charge carrier movement from a non-bridging oxygen (NBO) for an ionic glass, while distorting the position of some bridging oxygen (BO), following the Anderson and Stuart model. Adapted from Ref. [13].

carrier is considered to consist of two cations sharing an equilibrium site. For an oxide glass, this means that the charge carrier is a “defect site” formed when two cations share a NBO. The formation of a charge carrier, and its following movement, for the interstitial pair model is illustrated in Fig. 6.2: By the interstitial pair process, we can model a temperature dependency of the ionic conductivity. Assuming an activated process for the formation of the charge carriers in the glass, one can write n from Eq. (6.6) as:   Ef (6.13) n = n0 exp − 2 · kB · T where n0 is the total number of possible charge carriers in the glass and Ef is the energy of formation of an interstitial pair and a cationic

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Fig. 6.2. Formation and movement of the charge carrier in an oxide glass, according to the interstitial pair model. Adapted from Ref. [16].

vacancy, hence the factor 2. The mobility μ can be estimated using Eq. (6.5), when rewritten as a function of the characteristic jump attempt frequency and the probability of a successful jump: μ=

e · λ2 · ν e·D = · Ω1 kB · T 6 · kB · T

(6.14)

where ν is the characteristic jump attempt frequency (s−1 ), λ is the jump distance (˚ A). The term Ω1 is the probability of a successful jump, and if it can be written as an activated process as:   Em Ω1 = exp − kB · T

(6.15)

where Em is the energy required for the migration of a charge carrier. With this, Eq. (6.6) can be rewritten as:   Ef /2 + Em e2 · λ2 · ν exp − σ = Z · n0 · 6 · kB · T kB · T

(6.16)

As it can be seen from Eq. (6.16), for this model, the ionic conductivity depends entirely on the energy for the formation and migration of the charge carriers, and the pre-exponential terms can be reasonably estimated. Considering a monovalent cation Z equals as 1022 ions· cm−3 , the jump distance λ 1, n0 can be estimated  3 1/n0 and the jump frequency ν is estimated relates with n0 as

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to be 1013 Hz. The value for the pre-exponential term based on these estimations is close to 105 K· S· cm−1 , a value comparable to what is found experimentally for many glasses [17]. Differently from the Anderson and Stuart model, the Charles model considers as charge carriers the ionic pairs and not the total number of ions in the glass. Hence, the energy of formation of the charge carrier contributes to the total energy barrier of the ionic conductivity, as well as the energy for these ions to move. 6.2.3.3. Ravaine and Souquet Model This approach, first presented by Ravaine and Souquet in 1977 [18, 19], takes the idea of weak electrolytes used in chemistry to describe partially dissociated solute in a solvent, for example, acetic acid in water, proposing a way to calculate the energy necessary to create a charge carrier from the interstitial pair model. Therefore, the activation energy of the formation of the charge carriers is related to the dissociation energy of the solute. For a binary glass (M X–SiO2 , for example), the dissociation equilibrium is given by: M X ←→ M + + X − K

(6.17)

where M is the cation and X is the anion of the dopant salt equilibrium may be rewritten using the Kr¨ oger–Vink notation of defects in a crystalline structure: 

∗ ∗ ∗ + OnbO ←→ (M 2 )·M + VM + OnbO 2MM K

(6.18)

Assuming that the glass is an ionic solution, the dissociation constant (K) is given by:   Ef0 (6.19) K = exp − kB · T where Ef0 is the energy of dissociation for a given solvent. For very low values of Ef0 , all ions are dissociated and the solution is considered to be a strong electrolyte. On the other hand, if the dissociation energy

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is high, the solution is considered a weak electrolyte. For the above equilibrium, the dissociation constant can also be written as: K=

γ + · γX − · [M + ] · [X − ] aM + · aX − = M aM X [M X]

(6.20)

in which a is the thermodynamic activity of a given species, γ is the activity coefficient of a given species and the term in angle brackets represents the concentration of the given species. Knowing that M + is the charge carrier and assuming [M X] ≈ 1 due to the low dissociation, n from Eq. (6.6) can be rewritten as: n=

(γM +

1 1/2 · K 1/2 · aM X 1/2 · γX − )

(6.21)

This model was developed mainly to explain the enhancement of orders of magnitude for the ionic conductivity of binary glasses by increasing the concentration of the solute. For this, the authors of the model assume that the variation of μ from Eq. 6.6) with temperature and composition is negligible. By doing so, n and μ can be calculated from experimental results. As predicted, n has a very low value when compared with the total concentration of possible mobile ions in the glass (n0 ), and μ has a value close to 10−4 cm2 · V−1 · s−1 [16]. This mobility was also found by Hall measurements [20] and is close to the mobility of ions in liquids, such as water [21]. 6.2.4. Modeling the Ionic Conductivity Above Tg The ionic conductivity of glasses follows a different pattern above Tg , which can be attributed to an additional process that take place, associated with a free volume mechanism, first proposed by Cohen and Turnbull [22]. Above Tg , the density fluctuations on the glassformer chains can permit a jump of the ion from one site to the next without an entropic cost, which means that the energy generated by the deformation caused by the movement of the ion is zero. In this case, the probability of a successful jump (Ω2 ) is given by:   Vf∗ (6.22) Ω2 = exp − ¯ Vf

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where Vf∗ is the free volume required for a jump and V¯f is the mean free volume available. The mean free volume available can be estimated as: V¯f = V0 · (αl − αg ) · (T − T0 )

(6.23)

with α being the linear thermal expansion coefficient of the liquid and the corresponding glass, and V0 the volume necessary for the moving species at the ideal glass transition temperature, T0 . 6.2.5. Ionic Conductivity as a Function of Temperature There are still open questions about how to physically describe the activation energy, but it is widely accepted that these glasses follow the Arrhenius equation below Tg :   Ea (6.24) σ · T = A exp − kB · T where A is the pre-exponential term (K · S · cm−1 ), Ea is the activation energy for the diffusional process (J) and kB is the Boltzmann constant. Typical values for A ranges from 104 to 105 K · S · cm−1 and values for Ea vary from 50 to 150 kJ · mol−1 [23]. Therefore, the expression that shows the dependency of the conductivity with temperature is given by:   Ea (6.25) σ = σ0 exp − kB · T where σ0 equals A · T −1 . This is due to the fact that, on a limited range of temperature (from a few hundred to a few degrees below Tg ), the variation of A with T may be neglected, and expressing the value of conductivity directly, without the influence of T , makes it easier to compare materials for practical applications. There is an additional mechanism observed with experimental results above Tg , which can be fitted as follows:     B Ea exp − (6.26) σ · T = A exp − kB · NA · T (T − T0 )

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Fig. 6.3. Ionic conductivity dependency with temperature for some alkali silicate glasses. It is possible to identify the two migration mechanisms, above and below Tg . Adapted from Ref. [16].

where B is a constant related to the probability of a successful jump of an ion. The ionic conductivity dependency with temperature above and below Tg for a few example glasses can be seen in Fig. 6.3. 6.2.6. Future Challenges for Ionic Conductive Glasses A great deal of the future challenges for the field of ionic conductive glasses is the modeling of the conductivity and some of its most fundamental components. One example of this is the mixed alkali effect [24], which is the variation of some properties, including the ionic conductivity, which can vary by orders of magnitude by mixing

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two different alkali elements, with a peak normally found on a 1:1 ratio. A unified theory on the ionic conductivity on glasses, capable of explaining all the properties observed experimentally, is still beyond our grasp. The theories presented here were developed in the last 70 years, and even though new theories were developed, there is no consensus on the literature about a unified model that would be able to predict the ionic conductivity of glasses. From a more practical point of view, there are challenges involving making the highly ionic conductive glass chemically stable and cheaper. Despite the many uses that glassy electrolytes have in the industry, the crystalline materials still make up the majority of products found on the market [25].

6.3. Electronic Conductivity The electronic conductivity in glasses has been studied for over 100 years and the interest on it has greatly increased recently, due to many applications in areas like the photocopying process, solar cells, smart windows, and computer memory. The electronic conductivity of oxide glasses can be described by the energy gap between the valence and conduction bands (Eg ), very similar to the one used for crystalline semi-conductors. It is known that the Si orbitals in crystalline silicon are arranged as four hybrid σsp3 orbitals. The valence band is formed by these ∗ σsp3 orbitals, while the conduction band is the σsp 3 anti-bonding orbitals. The semi-conducting behavior of the material comes from the electrons jumping from the σsp3 orbitals, known as the valence ∗ band, to the conduction band formed from the σsp 3 orbitals, where they can move. The bands are similar in glassy materials, but due to the irregular nature of the material, the energy gaps are not well defined. Also, the addition of transition metals introduces intermediary donor and acceptor energy bands, known as dangling bonds. Depending on the valence state of the transition metal, they can behave as n-type or

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p-type semi-conductors. Normally the semi-conducting oxide glasses contain V, W, Mo, Fe, Ti, Cu, Mn, Co, or Ni ions associated with the common glass formers, such as SiO2 , P2 O5 , or TeO2 . The band gaps and density of states was first described by Cohen, Fritzche, and Ovshinsky [26] and Davis and Mott [27]. Cohen et al. assumed in their model conduction and valence bands with “tails,” and that these tails might overlap and that the density of states at the Fermi level are somewhere in this overlap, with a limited density of states. Davis and Mott improved the model by assuming that the lack of long-range order for glassy materials result in a variation of energies for the valence and conduction band (instead of EV and EC , ΔEV and ΔEC ) and “pinning” the Fermi level by assuming that there is an additional density level in between the conduction and valence band. The two models can be better compared in Fig. 6.4:

Fig. 6.4. Energy band models for oxide glasses, proposed by Cohen, Fritzche, and Ovshinsky and Davis and Mott. Adapted from [27].

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6.3.1. Modeling the Electronic Conductivity The electronic conductivity on glasses was first modeled by Mott in 1968 [28]. Above the melting temperature, the transition metal is in equilibrium with oxygen from the surroundings, as given by: 1 2M n + O−2  2M n−1 + O2 2

(6.27)

Below the melting temperature, there is hardly any oxygen diffusion and the equilibrium previous established does not change. Since this equilibrium defines the number of ions with higher and lower valence, the melting process has a large influence on the number of sites for the charge carriers and therefore, the electronic conductivity of the glasses [29]. The total number of each species in the glass stays the same, but there is a local change in the structure when an electron goes from one ion to the next. In oxide glasses, this change results in small changes on the first neighbors’ atoms as well, generating a distortion. The activation energy densities for this process can be divided in two sub-energies, the hopping energy (EH ) due to the energy necessary to transfer the electron from one ion to the next, and the disorder energy (ED ), both given in J· mol−1 , due to the local structural changes that arise from the change of the ion’s valence. Very similar to the ionic conductivity, the electronic conductivity can be written as an Arrhenius dependency: 

EH + 12 ED σ · T = A exp − kB · NA · T 

 (6.28)

where A is the pre-exponential constant for the electronic conductivity, related to different factors than for the pre-exponential constant from ionic conductivity, such as phonon frequency, the ratio of the ion concentration, and the average hopping distance. Since the transport of electrons is associated to a small change in the glass structure around the ions which change their valence, this mechanism is known as “small polaron hopping.” At temperatures below Tg and above Θ/2, where Θ is the Debye temperature, A can

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be written as: 

A =

υph · e2 · d2hop · C · (1 − C) kB · T

exp(−2 · α · R)

(6.29)

where υPH is the phonon frequency, C is the ratio of the low-valence ion to the total amount of ions, dhop is the average hopping distance for the electron and α is related to the overlap of the wave functions. Therefore, the electronic conductivity, according to Mott’s model, depends on three factors: (i) A donor and an acceptor site adjacent to each other, represented by C · (1 − C); (ii) The energy overlap of these two sites, allowing the electron hop from one  site to the other, represented by υPH · E +1E

2 D ; exp · − kH B ·NA ·T (iii) The probability of the electron to actually hop, represented by exp (−2 · α · R).

This mechanism is only valid at higher temperatures, where the local fluctuations allow step (ii) to occur. At temperatures lower than Θ/2, the small polarons move by tunneling up to several interatomic distances, on a process called “variable range hopping” [28]. The hopping distance for this case (dhop ) can be estimated as a function of temperature and the density of states near the Fermi level N (E F ) by: d hop ≈ [α · kB · NA · T · N (E F )]−1/4

(6.30)

6.3.2. Electronic Conductivity as a Function of the Temperature The electronic conductivity also follows an Arrhenius behavior below Tg , as seen in Eq. (6.28). Typical values of EH + 1/2 ED are between 30 and 50 kJ mol−1 and for A between 101 and 102 K · S · cm−1 [30]. This change at low temperatures, where the behavior comes closer to:   1 (6.31) σ · T ∝ exp − 1/4 T

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Temperature (oC)

Conductivity (log (σ·T), σ·T in S·cm-1·K)

700

100 0

-100

-150

-175

-2

-2

-4

-4

-6

-6

-8

-8

-10

-10

-12

-12

-14

-14

-16

0.4 V2O5 0.5 TeO2 0.1 Bi2O3 0.3 V2O5 0.5 TeO2 0.2 Bi2O3 0.2 V2O5 0.5 TeO2 0.3 Bi2O3

-16 2.0x10-3

6.0x10-3

1.0x10-2

1.4x10-2

2.0x10-1

-1

Temperature (K )

2.5x10-1

3.0x10-1

Temperature (K

3.5x10-1

-1/4

)

Fig. 6.5. Electronic conductivity dependency with temperature for a few glasses. It is possible to see the two different mechanisms for the three temperature zones (above, below, and way below Tg ) [31].

due to the changes of mechanisms described before. Examples of different electronic glasses and their conductivity as a function of temperature can be found in Fig. 6.5. 6.3.3. Mixed Conductive Glasses Mixed conductive glasses are those in which both ionic and electronic diffusion can be achieved simultaneously, by having mobile ions and transition metals with different valence numbers present in the glass. These materials are interesting mainly for applications to batteries and micro-batteries as mixed conductive cathode material. Mixed conductive glasses are prepared by adding any mobile ion to an electronic conductive glass from the two previous electric conductive glasses discussed, for example, adding Li2 O to a V2 O5

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electronic conductive glass. When considering the mechanisms by which the conductivity is given, each type of charge carrier may follow the previously discussed mechanisms. 6.3.4. Future Challenges for Electronic Conductive Glasses Electronic conductive glasses have been studied and modeled on the past 50 years and much of their mechanisms are well predicted by the models presented in the last paragraphs. The idea of a semiconductor relates well with the dependency of the glass electronic conductivity with the ratio of the difference valences of the transition metals in the glass matrix. There is large interest by industry on better understanding electronic conductive glasses, mainly for applications to batteries and photoconductive materials. By itself, the electronic conductivity on glasses is not that applicable in industry, but the mixed conductive glasses, with both electronic and ionic charge carriers, present great possibilities on the industry. Even more, the mixed conductive glasses, are of great interest for the industry and can help solve some of their more urgent demands. 6.4. Measurement by Electrical Impedance Spectroscopy Normally, resistance measurements can be made with a simple multi-meter. This kind of equipment follows Ohm’s law, in which the resistance of the material (R) is related to the voltage (V ) and current (I) that flows through the material. Unfortunately, this relation can only be applied to ideal resistors, that is, the resistance is the same independently of the voltage applied. A more accurate way of measuring the electrical properties of a solid material is by electrical impedance spectroscopy (EIS). The impedance is measured by applying a sinusoidal voltage and measuring the out-of-phase response, at different frequencies. These signals are converted to a complex number with a real and an imaginary part, and the final response gives the real (Z  ) and imaginary (Z  ) parts of the complex impedance (Z ∗ ) as a function

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of the frequency (f ). This dependency can be expressed as: Z ∗ (f ) = Z  (f ) ± i · Z  (f )

(6.32)

An ideal result for a homogeneous glass sample can be seen in Fig. 6.6: The projections are known as the Nyquist plot (imaginary part as a function of the real part of an impedance function) and the Cole–Cole plot (real or imaginary part of an impedance function as a function of the frequency). The signals can be expressed in other forms as well, those being the admittance (Y ), the electric modulus (M ), and the electric permittivity (ε). These four properties are related by the expression: −1

Z ∗ · i · 2πf · C0 = Y ∗

−1

· i · 2πf · C0 = M ∗ = ε∗

(6.33)

where C0 is the Permitivity of the empty measurement cell (F· m−1 ).

Fig. 6.6. Real (Z  ) and imaginary (Z  ) part of the impedance as a function of the frequency (f ). The 3D curve represents the complex impedance measured by the EIS.

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Fig. 6.7. Equivalent RC circuit representing and ideal sample which gives the response seen in Fig. 6.6.

The main method to analyze EIS data is by equivalent circuits. The concept is to find an electric circuit which would give the same result as the sample being tested. For example, the equivalent circuit for the result in Fig. 6.6 is a simple parallel RC circuit, expressed in Fig. 6.7: The sample property resistance (R) given in Ω, relates to the fundamental property resistivity (ρ) for a given material by the relation: a (6.34) ρ=R d where a is the area of the electrode (cm−2 ) and d is the thickness of the sample (cm). It is usual for this kind of measurement to have the electrode deposited on the surface of the sample, for example, by sputtering a conductive material or painting it with a conductive paint (such as silver or platinum paint). For a real sample, more components may be added to the equivalent circuit to make it reasonable, such as inductance and another resistance due to the equipment wires, a double layer effect for ionic samples, a resistance for the charge transfer on the sample/electrode interface, two-phases, and many more. Keep in mind that these paragraphs are just a small introduction. For a deeper description of the technique, please refer to [32–37]. 6.5. Concluding Remarks Despite much research being done in the field, there is still much to be unveiled on the topic of electrical properties in glasses. Their

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applications are vast and of the uttermost interest for our modern society, therefore the development and understanding of such materials is essential to our progress. We can find both electronic and ionic conductive oxide glasses, depending on their chemical composition, and much of our knowledge on both conductivity mechanisms is borrowed from the theories developed for ceramic crystals. Highly ionic conductive glasses are prepared mainly with mobile monovalent cations, and even though this property has been known known for several years, there is still no consensus on a model to describe this property. The two most accepted models are the “strong electrolyte” and the “weak electrolyte,” also known as “structural model” and “thermodynamic model.” Electronic conductive glasses get their property from the movement of the electron from neighboring transition metal with different valences. Hence, the property heavily depends on the concentration of both valence species in the glass. The by which this electronic conductivity happens is known as “small polaron,” since the change of valence due to the movement of electrons also alter the surroundings of the donating and receiving atoms. Mixed conductive glasses have both charge carriers diffusing due to an electric field being applied to the material. The glasses are mainly interesting for applications to solid-state batteries as a mixed cathode, presenting a solution for some of the difficulties found with current portable batteries containing liquid cathodes. The mechanisms found on these glasses are the same as the ones seen in this chapter, happening simultaneously. In general, the electrical properties of glasses are measured by EIS, a methodology that allows accurate electrical measurements on non-ideal resistors. Presented in this chapter was a very brief introduction to what is the technique and why it is applied, but the reader is encouraged to go deeper on the topic with the help of other sources found in the references. References 1. Ezz Eldin, F. M., and El Alaily, N. A. (1998). Electrical conductivity of some alkali silicate glasses, Materials Chemistry and Physics, 52(2), pp. 175–179.

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2. EPA. (2018). 5.9 Conductivity. In Water: Monitoring and Assessment. Retrieved from https://archive.epa.gov/water/archive/web/ html/vms59.html. 3. Malugani, J.-P., et al. (1978). Conductivite ionique dans les verres AgPO3 -AgX (X = I, Br, Cl), Materials Research Bulletin, 13(5), pp. 427–433. 4. Malugani, J.-P., et al. (1983). De nouveaux verres conducteurs par l’ion lithium et leurs applications dans des generateurs electrochimiques, Solid State Ionics, 9–10, pp. 659–665. 5. Warburg. E. (1884). Uber die electrolyse des festen glases, Annalen der Physik, 257(4), pp. 622–646. 6. Coon, J., and Shelby, J. E. (1990). Properties and structure of lead halosilicate glasses, Journal of the American Ceramic Society, 73(2), pp. 379–382. 7. Fick, A. (1995). On liquid diffusion (Reprint), Journal of Membrane Science, 100(1), pp. 33–38. 8. Einstein, A. (1905). On the motion of small particles suspended in a stationary liquid, as required by the molecular kinetic theory of heat (translation), Annalen Der Physik, 322, pp. 549–560. 9. Murch, G. E. (1983). The exact Nernst-Einstein equations and the interpretation of cross phenomenological coefficients in unary, binary, and ambipolar systems, Radiation Effects, 73, pp. 299–305. 10. Haven, Y., and Verkerk, B. (1965). Diffusion and electrical conductivity of sodium ions in sodium silicate glasses, Physics and Chemistry of Glasses, 6(2), p. 38. 11. Dyre, J. C., Maas, P., Roling, B., and Sidebottom, D. L. (2009). Fundamental questions relating to ion conduction in disordered solids, Reports on Progress in Physics, 72(46501), p. 15. 12. Anderson, O. L., and Stuart, D. A. (1954). Calculation of activation energy of ionic conductivity in silica glasses by classical methods, Journal of the American Ceramic Society, 37, pp. 573–580. 13. Martin, S. W., and Angell, C. A. (1986). DC and AC conductivity in wide composition range Li2 O P2 O5 glasses, Journal of Non-Crystalline Solids, 83(1–2), pp. 185–207. 14. Yao, W., and Martin, S. W. (2008). Ionic conductivity of glasses in the MI+M2 S+(0.1Ga2 S3 + 0.9GeS2 ) system (M = Li, Na, K and Cs), Solid State Ionics, 178(33–34), p. 1777. 15. Charles, R. J. (1961). Polarization and diffusion in a silicate glass, Journal of Applied Physics, 32, pp. 1115–1126. 16. Souquet, J.-L., Nascimento, M. L. F., and Rodrigues, A. C. M. (2010). Charge carrier concentration and mobility in alkali silicates, Journal of Chemical Physics, 132, p. 034704.

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17. Moynihan, C., Gavin, D., and Syed, R. (1982). Pre-exponential term in the Arrhenius equation for electrical conductivity of glass, Journal de Physique Colloques, 43(C9), pp. C9-395–C9-398. 18. Ravaine, D., and Souquet, J.-L. (1977). A thermodynamic approach to ionic conductivity in oxide glasses — Part 1 — Correlation of the ionic conductivity with the chemical potential of alkali oxide in oxide glasses, Physics and Chemistry of Glasses, 18(2), pp. 27–31. 19. Ravaine, D., and Souquet, J.-L. (1977). A thermodynamic approach to ionic conductivity in oxide glasses — Part 2 — A statistical model for the variations of the chemical potential of the constituents in binary alkali oxide glasses, Physics and Chemistry of Glasses, 19(5), pp. 115– 120. 20. Cl´ement, V., Ravaine, D., D´eportes, C., and Billat, R. (1988). Measurement of Hall mobilites in AgPO AgI glasses, Solid State Ionics, 28–30(2), pp. 1572–1578. 21. Laidler, K. J. (2003). Physical Chemistry (Boston, MA, Houghton Mifflin Harcourt). 22. Cohen, M. H., and Turnbull, D. (1959). Molecular transport in liquids and glasses, The Journal of Chemical Physics, 31(5), pp. 1164– 1169. 23. Ngai, K. L. (2011). Relaxation and Diffusion in Complex Systems. (London, UK, Springer-Verlag). 24. Day, D. E. (1976). Mixed alkali glasses — their properties and uses, Journal of Non-Crystalline Solids, 21, pp. 343–372. 25. Minami, T., et al. (2005). Solid State Ionics for Batteries (Tokyo, Japan, Springer-Verlag). 26. Cohen, M. H., Fritzsche, H., and Ovshinsky, S. R. (1969). Simple band model for amorphous semiconducting alloys, Physical Review Letters, 22(20). 27. Davis, E. A., and Mott, N. F. (1970). Conduction in non-crystalline systems V. Conductivity, optical absorption and photoconductivity in amorphous semiconductors, Philosophical Magazine, 22(179), pp. 903– 922. 28. Mott, N. F. (1968). Conduction in glasses containing transition metal ions, Journal of Non-Crystalline Solids, 1, pp. 1–17. 29. Mustarelli, P., Tomasi, C., Magistris, A., and Scotti, S. (1993). Water content and thermal properties of glassy silver metaphosphate: Role of the preparation, Journal of Non-Crystalline Solids, 163, pp. 97–103. 30. Braunger, M. L., et al. (2012). Electrical conductivity of silicate glasses with tetravalent cations substituting Si, Journal of Non-Crystalline Solids, 358(21), pp. 2855–2861.

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31. Ghosh, A. (1993). Adiabatic hopping conduction in vanadium bismuth tellurite glasses, Journal of Physics: Condensed Matter, 5(46), pp. 8749–8754. 32. Barsoukov, E., and MacDonald, J. R. (2005). Impedance Spectroscopy: Theory, Experiment, and Applications (Wiley Inter-Science). 33. Orazem, M. E., and Tribollet, B. (2008). Electrochemical Impedance Spectroscopy. 34. Scully, J. R., Silverman, D. C., and Kendig, M. W. (1993). Electrochemical Impedance — Analysis and Interpretation (ASTM). 35. Linford, R. G., and Hackwood, S. (1981). Physical techniques for the study of solid electrolytes, Chemical Reviews, 81, pp. 327–364. 36. Irvine, J. T. S., Sinclair, D. C., and West, A. R. (1990). Electroceramics: Characterization by impedance spectroscopy, Advanced Materials, 2(3), pp. 132–138. 37. Bonanos, N., Pissis, P., and MacDonald, J. R. (2012). Impedance spectroscopy of dielectrics and electronic conductors. In: Characterization of Materials, edited by Kaufmann, E. N.

Recommended Literature [a] Souquet, J. L. (1995). In: Solid State Electrochemistry, edited by Bruce, P. G. (Cambridge, Cambridge University Press), p. 74. [b] Ingram, M. D. (1997). Superionic glasses: Theories and applications, Current Opinion in Solid State and Materials Science, 2(4), pp. 399– 404. [c] Varshneya, A. K. (1994). Permeation, diffusion and ionic conduction in glass. In: Fudamentals of Inorganic Glasses. (Academic Press).

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CHAPTER 7

Glass Fiber Processing and Applications Elam A. Leed Johns Manville, Inc. P. O. Box 5108 Denver, CO 80217-5108

7.1. Introduction Every hour billions of kilometers of glass fiber are produced by stretching glass in the molten state. A modest size home in the United States can contain 40–60 million kilometers of fiber, found in wall insulation, attic insulation, gypsum wallboard, asphalt shingles, carpet backer, ceiling tile, air filtration, water filtration, printed circuit boards, duct insulation, pipe insulation, appliance insulation, and many glass fiber reinforced plastic products. Every day thousands of square kilometers of new glass fiber surface area are produced to interface with solids, liquids, and gases in their particular environments and applications. Average fiber diameters range from 0.2 to 25 μm for most common glass fiber applications, resulting in specific surface area values from 0.08 to 10 m2 /g. The high surface area differentiates glass fiber from most other glass applications, but there is another common theme that is perhaps more important than surface area in driving the use of glass fiber. If surface area creation were the only driving force for glass fiber production, it could be substituted for high surface area glass or 223

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Fig. 7.1. Tortuous paths in a fiber network (left) and a scanning electron microscope image of glass fiber wool (right).

crystalline mineral powders at a lower cost. But powders are not a good starting point for most applications in which glass fibers are used. A powder does not lend itself to the creation of low density thermal insulation, self-supporting filtration media, two-dimensional structural fabric, or polymer reinforcement. Nearly all glass fiber applications rely on the fiber aspect ratio and the ability to form a two- or three-dimensional network to meet the basic performance needs. In many cases, the fundamental ability of a glass fiber network to create tortuous paths is the key to its utility (Fig. 7.1). Thermal insulation creates tortuous paths for air movement (convection) and infrared radiation; filtration media creates tortuous paths for particulates in a fluid stream; and glass fiber reinforcement imparts impact strength by creating tortuous paths for crack propagation [1–3]. With the need for some combination of high surface area, two- or three-dimensional network, and/or tortuous paths established, the question becomes how to economically manufacture glass fibers to meet these needs and maintain a sufficient degree of service life or durability.

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7.2. Compositions Most glass fiber is produced from silicate glass compositions with 40%–80% SiO2 by weight; the focus of this chapter is silicate glass fibers. Glass fiber made only from silica would meet the needs of many applications but is rarely used due to the high requisite melting and fiber forming temperatures. Most silicate glass additives serve to reduce the melting and fiber forming temperatures, while maintaining processing properties such as devitrification and product properties such as chemical durability. Although it is not discussed in this chapter, optical waveguide glass fiber is one example of an application of silica glass fiber. Sodium can be a highly effective flux and is common in many glass fiber compositions, but chemical durability can become a problem at higher levels of sodium in some applications. Calcium is another very common flux in glass fiber, but higher levels can lead to devitrification problems in some manufacturing processes. Other alkali and alkaline earth modifiers are used in lesser amounts and are generally limited by cost, in addition to the drawbacks listed above. Aluminum and boron are common additions in glass fiber that can provide a good balance or compromise between lower processing temperatures and chemical durability. A significant downside of these components, particularly with boron, is the added cost. In some glass fiber compositions, the boron oxide can be 5% by weight of the total glass formula, but comprise 25% of the raw material cost. Glass fibers can be divided into two categories based on their method of manufacture. Continuous filament (CF) glass fiber is stretched from the molten state and pulled for hundreds of kilometers without a break. Wool fiber, sometimes called discontinuous filament, involves manufacturing processes that inherently break the fibers into pieces as they are drawn. See Table 7.1 for an overview of some of the similarities and differences between CF and wool fiber. Note that in many cases, CF fibers are chopped in downstream processing and no longer retain their continuous nature. Typical composition ranges for some of the common glass fiber families are shown in Table 7.2. E-glass was developed many decades

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The World Scientific Reference of Amorphous Materials — Vol. 2 Table 7.1. Overview of CF versus wool glass fiber. CF

Processing

Pulled in a CF parallel with other strands (often chopped downstream)

Typical fiber diameters Glass types

4–30 µm E-glass, C-glass, R-glass, S-glass, AR-glass, A-glass, D-glass, basalt, others

Uses

Reinforcement (chopped fiber, rovings, wovens, non-wovens) filtration, battery separators, facers, fireblocking

Wool (Discontinuous) Process inherently creates discontinuous sections of fiber that have random orientation 0.2–10 µm Soft alkali borosilicates, mineral wool, modified slag and basalt, vitreous refractory ceramic fiber (RCF), others Thermal insulation (blanket, board, pipe, paper), acoustic insulation, filtration, battery separators, fireblocking

ago specifically for CF fiber production and the vast majority of CF fiber produced today is made with E-glass. The composition of E-glass is roughly based around a eutectic that can be found in the SiO2 , CaO, Al2 O3 phase diagram. The eutectic, along with the addition of boron, provides a glass that meets the viscosity and devitrification requirements for processing, while maintaining a relatively high degree of durability in many applications. E-glass evolved over time from B2 O3 content greater than 10% by weight to levels today that range from 0% to 6% [4]. Boron reduction results in lower cost raw materials but can lead to higher fiberization temperatures and/or higher liquidus temperatures. Mineral wool was one of the earliest compositions in the category of wool fibers, based on basalt with some alkaline earth added as a flux. Soft borosilicate glasses were developed with lower viscosity and much lower liquidus temperatures to avoid devitrification in flame attenuated processes. As internal centrifuge fiberization was developed, even lower viscosity borosilicate glasses were created,

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Table 7.2. Select glass fiber composition ranges (weight %). CF Wool SiO2 Al2 O3 B2 O3 Fe2 O3 * R2 O E-glass [4] ECR-glass [4] C-glass A-glass [4] AR-glass [4] D-glass [4] R-glass [4] S-glass [4] Basalt Soft borosilicate Mineral wool Vitreous RFC ∗

X X X X X X X X X

X X X X

52–62 58.2 60–70 72 71 72–76 60 65.5 45–55 55–70 40–50 40–70

12–16 11.6 3–10 1 1 0–1 25 25 12–16 1–6 15–25 0–25

0–10 0–10