Transmitted Light Microscopy of Rock-Forming Minerals: An Introduction to Optical Mineralogy 3031196112, 9783031196119

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Transmitted Light Microscopy of Rock-Forming Minerals: An Introduction to Optical Mineralogy
 3031196112, 9783031196119

Table of contents :
Acknowledgements
Contents
1 Introduction
A Selection of Books on Optical Mineralogy, Books with a Chapter on Optical Mineralogy, and Publications Relevant to the Subject
Further Reading
2 Basic Concepts
2.1 Light as the Tool of Examination in Optical Mineralogy
2.3 Retardation of Rays in Anisotropic Minerals and Birefringence
2.4 Passage of Light Through Crystalline Matter: Optic Orientation and the Optical Indicatrix
2.5 Location of the Optical Indicatrix with Reference to the Crystal Systems and Crystallographic Directions
2.5.1 Location of the Optical Indicatrix in Isotropic Minerals
2.5.2 Location of the Optical Indicatrix in Uniaxial Minerals
2.5.3 Location of the Optical Indicatrix in Biaxial Minerals
2.6 Understanding How a Mineral is Cut in a Thin Section
References and Suggested Further References
Further Reading
3 The Petrographic Microscope: A Polarized Light Microscope
3.1 Substage Assembly
3.2 Upperstage Assembly
3.3 Circular Rotating Microscopic Stage and Objective Lens Revolver
3.4 Objective Lenses
3.5 Accessory Plates (Retardation Plates, Compensator Plates)
3.6 Adjustment of the Microscope
3.6.1 Checking the Orientation of the Polarizer and the Correct Alignment of the Analyzer
3.6.2 Adjustment of the Oculars
3.6.3 Centering the Objective Lenses
3.6.4 Calibrating the Ocular Micrometer
3.6.5 Adjustment of the Aperture Diaphragm
3.6.6 Focusing and Centering the Condenser
3.6.7 Adjustment of the Field Diaphragm
3.7 The Object of Study: The Thin Section
3.8 Illumination and Comfort While Working at the Microscope
References and Suggested Further Reading
4 Optical Properties of Minerals in Plane Polarized Light (PPL)
4.1 Color and Pleochroism
4.1.1 Appearance of Color in Thin Section
4.1.2 Intensity of Color
4.1.3 Pleochroism
4.1.4 Causes of Color
4.2 Crystal Habit and Textural Relationships
4.2.1 Appearance of Crystal Habit
4.2.2 Causes of Different Habit
4.3 Relief
4.3.1 Appearance of relief
4.3.2 Mathematical Formulation of Relief Formation Between Air and Mineral
4.3.3 Formation of Relief Between Minerals and the Becke Line Method
4.4 Cleavage
4.4.1 Appearance of Cleavage
4.4.2 Causes of cleavage
References
Further Reading
5 Optical Properties of Minerals in Cross Polarized Light (XPL)
5.1 Birefringence
5.1.1 Appearance of Birefringence
5.1.2 The Michel-Lévy and the Raith-Sørensen Interference Color Charts
5.1.3 How to Determine the Maximum Interference Color of a Mineral
5.1.4 Transmission of Light by the Analyzer and Extinction Behavior
5.1.5 Extinction Angle and Types of Extinction
5.2 Elongation
5.3 Twinning
5.3.1 Appearance of Twinning
5.3.2 Types of Twinning
5.3.3 Causes of Twinning
5.4 Crystal Zoning
5.4.1 Oscillatory Zoning
5.4.2 Concentric Zoning
5.4.3 Sector or Sectoral Zoning
References
Further Reading
6 Conoscopic Observations and Interference Figures
6.1 Interference Figures of Uniaxial Minerals
6.1.1 Uniaxial Centered Optic Axis Figure (OA Figure)
6.1.2 Uniaxial Off-Centered Interference Figure
6.1.3 Flash Figure of Uniaxial Minerals
6.1.4 Genge’s Birefringence Ball of Uniaxial Minerals
6.2 Interference Figures of Biaxial Minerals
6.2.1 Bxa Figure
6.2.2 Biaxial-Centered Optic Axis Figure (OA Figure)
6.2.3 Flash Figure of Biaxial Minerals
6.2.4 Genge’s Birefringence Ball of Biaxial Minerals
6.2.5 Determination of the 2V Angle in Biaxial Minerals
6.3 How to Obtain an Interference Figure
References and Books with Chapters on Conoscopic Observations
Further Reading
7 Igneous Rocks: Some Basic Concepts
7.1 Classification of Igneous Rocks
7.1.1 Classification Based on Modal Composition
7.1.2 Classification Based on Texture
7.2 Chemical Classification of Igneous Rocks
References and Suggested Further Reading
Further Reading
8 Metamorphic Rocks: Some Basic Concepts
8.1 Classification of Metamorphic Rocks
8.1.1 Textures of Metamorphic Rocks
8.1.2 Modal Composition and Mineral Assemblage
8.1.3 Protolith
8.2 Common Textures in Metamorphic Rocks
Selection of Books on Metamorphic Petrology and Cited Reference
Further Reading
9 The Mineral Plates and How to Use Them
9.1 Introduction to the Mineral Plates
9.2 Mineral Plates
Some References for the Determination of Minerals in Thin Section
Further Reading
Appendix_1
Appendix_2
Appendix_3
Index

Citation preview

Susanne Theodora Schmidt

Transmitted Light Microscopy of Rock-Forming Minerals An Introduction to Optical Mineralogy

Springer Textbooks in Earth Sciences, Geography and Environment

The Springer Textbooks series publishes a broad portfolio of textbooks on Earth Sciences, Geography and Environmental Science. Springer textbooks provide comprehensive introductions as well as in-depth knowledge for advanced studies. A clear, reader-friendly layout and features such as end-of-chapter summaries, work examples, exercises, and glossaries help the reader to access the subject. Springer textbooks are essential for students, researchers and applied scientists.

Susanne Theodora Schmidt

Transmitted Light Microscopy of Rock-Forming Minerals An Introduction to Optical Mineralogy

123

Susanne Theodora Schmidt Department of Earth Sciences University of Geneva Geneva, Switzerland

ISSN 2510-1307 ISSN 2510-1315 (electronic) Springer Textbooks in Earth Sciences, Geography and Environment ISBN 978-3-031-19611-9 ISBN 978-3-031-19612-6 (eBook) https://doi.org/10.1007/978-3-031-19612-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Cover illustration: Blueschist showing a muscovite-epidote-glaucophane assemblage, Ile de Groix, France. Compositional zoning is well visible in epidote in PPL and XPL. Photo by Susanne Theodora Schmidt (see also El Kohr et al., 2009)

To all students learning optical mineralogy and their teachers explaining this wonderful tool

Acknowledgements

I am indebted to many colleagues and former students for valuable suggestions and discussions and for having provided thin sections or images. I thank PD Dr. Afifé El Kohr (University of Fribourg) for reading all chapters and suggesting important improvements in the text and the figures. I thank Dr. Florence Bégué (University of Geneva) for reading and improving remarks on various chapters. Special thanks for commenting on various drafts are due to Prof. Richard Bevins (Natural Museum of Wales), Sam Carmalt (University of Geneva), Dr. William Cannon (US Geological Survey), and Dr. Kenneth M. Towe (Smithonian Institute, Washington). I am particularly thankful to Prof. John C. Green (University of Minnesota, Duluth) for carefully editing Chap. 2. I thank Tino Furrer, Nikon, for discussion and the permission to use some figures from the Nikon microscopic handbook. I thank Mark Holtkamp for discussion on crystal symmetry and the permission to use figures created by the Smorf applet. I thank Dr. Matthew J. Genge (Imperial College, London) for providing the images of Genge’s birefringence balls in Chap. 6. I received valuable advice from Prof. Martin Jakob Gander (Section de Mathématiques, University of Geneva) concerning mathematical calculations in Chap. 5 and from Dr. Ulrich Finkenzeller concerning the basic principles of light in Chap. 2. I also thank Prof. Bastien Chopard for financial support (Commission informatique, University of Geneva). I thank Dr. Annette Süssenberger (University of Geneva) and Dr. Maria Ovtrachova (University of Geneva) for reading the chapter on metamorphic rocks and Dr. Massimo Chiaradia (University of Geneva) for reading the chapter on magmatic rocks. I thank Prof. Lluís Fontboté (University of Geneva) for many fruitful discussions on optical mineralogy and for critical reading some chapters. I also thank Prof. Michael Raith (University of Bonn) for discussion on the Michel-Lévy color chart. I thank Moritz Fontboté Schmidt for the calculation of the extinction behavior using a transfer-matrix formalism in Chap. 5, for writing programs to plot the ellipsoids in Chaps. 2 and 6, for stimulating discussions on the optical properties of minerals and their relationship to concepts in physics, as well as his help in the computer applications and at the microscope. Special thanks are due to my former teaching assistants at the Department of Earth Sciences at the University of Geneva, especially PD Dr. Afifé El Kohr, Dr. Isabelle Chambefort, Dr. Johannes Mederer, Dr. Jean Vallance, Dr. Raphaël Normand, Dr. Erich Herwaagen, Dr. Annette Süssenberger, Dr. Maria Ovtrachova, Dr. Christian Bergemann, Dr. Maria Teresa ix

x

Acknowledgements

Bellver-Baca, Line Probst, Dr. Allen Fries, and Dr. Oliver Higgins. I also thank Jacqueline Berthoud (University of Geneva) and Fabio Capponi (University of Geneva) for their continuous support and help. I owe special thanks to Jean-Marie Boccard (University of Geneva) for the preparation of hundreds of excellent thin sections used in this book, as well as to François Gieschig. Many thanks go also to Fred Arlaud (University of Geneva) for his continuous engagement and maintenance of the microscopic room and his constant willingness to help maintain the best conditions for learning at the microscope. Many colleagues have provided thin sections or images. I am thankful to PD Dr. Afifé El Korh (University of Fribourg) for having provided thin sections of lawsonite, to Dr. Kalin Kouzmanov (University of Geneva) for the quartz crystal with fluid inclusions, to Dr. Lore Kiefert (Gübelin Gem Lab, Lucerne) for the images of some gemstones, to Emilie Elmaleh for the images of sapphire, to Prof. Lluís Fontboté (University of Geneva) for thin sections of anhydrite, atacamite, and andalusite from various mineral deposits, to Dr. Antoine de Haller (University of Geneva) for the scapolite sample, to Dr. Gregor Weber (University of Geneva) for a SEM image of plagioclase, to Dr. Aaron Hantsche (University of Geneva) for the johannsenite sample, to Prof. Leander Franz (University of Basel) for the winchite sample, to Dr. Joshua Vaughan-Hammon (University of Lausanne) for thin sections of staurolite, to Dr. Elias Samankassous (University of Geneva) for the image of zonation in a sediment, to Prof. Luca Caricchi (University of Geneva) for the sample of nosean, to Prof. Bertrand Rottier (University Laval, Canada) for the image of quartz as seen in cathodoluminescence and the images of the melt inclusions, to Dr. Florence Bégué and Dr. Massimo Chiaradia for images of magmatic textures and rocks, and to Prof. Sébastien Potel (University LaSalle, France) for images of pumpellyite and stilpnomelane. Furthermore, I thank Sindhu Sundararajan, Karthik Raj Selvaraj and Annett Büttner from Springer Nature for support while writing the book, as well as for careful editing and lay-out. I thank Dr. Jorge Alvar for his artistic view on microscopic images and inspiring discussions on many aspects of life. I would also like to thank Caterine for bringing delicious lunch with fresh fish caught by Luc and Olivier in Lake Geneva to help to stay focused on the task and Montserrat for support and stimulating conversations during her visits, as well as my late parents Rutherna and Martin and my family members Sabine and Helmut, Bettina and Wolfgang, Peter, Sibylle and Peter, Cornelia and Micha, Martina, Burkard, Tim and Rick, Montserrat, Xavi and Anna, Pol and Clara, as well as Jordi, Angels and Berta. Last, but not least I thank “meine Männer”, Lluís and Moritz, for fruitful, sometimes controversial discussions on aspects of teaching, often at the dinner and breakfast table, and for inspiring ideas during the preparation of this book, for cooking together, and for sharing their life with me. Without their help I would not have finished this book. Geneva, Switzerland Summer 2022

Susanne Theodora Schmidt

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Selection of Books on Optical Mineralogy, Books with a Chapter on Optical Mineralogy, and Publications Relevant to the Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Light as the Tool of Examination in Optical Mineralogy . . . 2.2 Refractive Index, Dispersion, Polarization, and Double Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Retardation of Rays in Anisotropic Minerals and Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Passage of Light Through Crystalline Matter: Optic Orientation and the Optical Indicatrix . . . . . . . . . . . . . 2.5 Location of the Optical Indicatrix with Reference to the Crystal Systems and Crystallographic Directions . . . . 2.5.1 Location of the Optical Indicatrix in Isotropic Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Location of the Optical Indicatrix in Uniaxial Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Location of the Optical Indicatrix in Biaxial Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Understanding How a Mineral is Cut in a Thin Section . . . . References and Suggested Further References . . . . . . . . . . . . . . . .

7 7

3 The Petrographic Microscope: A Polarized Light Microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Substage Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Upperstage Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Circular Rotating Microscopic Stage and Objective Lens Revolver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Objective Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Accessory Plates (Retardation Plates, Compensator Plates) . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Adjustment of the Microscope . . . . . . . . . . . . . . . . . . . 3.6.1 Checking the Orientation of the Polarizer and the Correct Alignment of the Analyzer . . . . 3.6.2 Adjustment of the Oculars . . . . . . . . . . . . . . . . .

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Contents

3.6.3 Centering the Objective Lenses . . . . . . . . 3.6.4 Calibrating the Ocular Micrometer . . . . . 3.6.5 Adjustment of the Aperture Diaphragm . . 3.6.6 Focusing and Centering the Condenser . . 3.6.7 Adjustment of the Field Diaphragm . . . . 3.7 The Object of Study: The Thin Section . . . . . . . 3.8 Illumination and Comfort While Working at the Microscope . . . . . . . . . . . . . . . . . . . . . . . . References and Suggested Further Reading . . . . . . . . .

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4 Optical Properties of Minerals in Plane Polarized Light (PPL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Color and Pleochroism . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Appearance of Color in Thin Section . . . . . . . . 4.1.2 Intensity of Color . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Pleochroism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Causes of Color . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Crystal Habit and Textural Relationships . . . . . . . . . . . 4.2.1 Appearance of Crystal Habit . . . . . . . . . . . . . . . 4.2.2 Causes of Different Habit . . . . . . . . . . . . . . . . . 4.3 Relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Appearance of relief . . . . . . . . . . . . . . . . . . . . . 4.3.2 Mathematical Formulation of Relief Formation Between Air and Mineral . . . . . . . . . . . . . . . . . 4.3.3 Formation of Relief Between Minerals and the Becke Line Method . . . . . . . . . . . . . . . 4.4 Cleavage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Appearance of Cleavage . . . . . . . . . . . . . . . . . . 4.4.2 Causes of cleavage . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Optical Properties of Minerals in Cross Polarized Light (XPL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Appearance of Birefringence . . . . . . . . . . . . . . . 5.1.2 The Michel-Lévy and the Raith-Sørensen Interference Color Charts . . . . . . . . . . . . . . . . . 5.1.3 How to Determine the Maximum Interference Color of a Mineral . . . . . . . . . . . . . . . . . . . . . . 5.1.4 Transmission of Light by the Analyzer and Extinction Behavior . . . . . . . . . . . . . . . . . . 5.1.5 Extinction Angle and Types of Extinction . . . . . 5.2 Elongation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Twinning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Appearance of Twinning . . . . . . . . . . . . . . . . . . 5.3.2 Types of Twinning . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Causes of Twinning . . . . . . . . . . . . . . . . . . . . . 5.4 Crystal Zoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Oscillatory Zoning . . . . . . . . . . . . . . . . . . . . . . .

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Contents

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5.4.2 Concentric Zoning . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.4.3 Sector or Sectoral Zoning . . . . . . . . . . . . . . . . . . . . . 122 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6 Conoscopic Observations and Interference Figures. . . . . . . . . . 6.1 Interference Figures of Uniaxial Minerals . . . . . . . . . . . . . . . 6.1.1 Uniaxial Centered Optic Axis Figure (OA Figure) . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Uniaxial Off-Centered Interference Figure . . . . . . . . . 6.1.3 Flash Figure of Uniaxial Minerals . . . . . . . . . . . . . . . 6.1.4 Genge’s Birefringence Ball of Uniaxial Minerals . . . 6.2 Interference Figures of Biaxial Minerals . . . . . . . . . . . . . . . . 6.2.1 Bxa Figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Biaxial-Centered Optic Axis Figure (OA Figure) . . . 6.2.3 Flash Figure of Biaxial Minerals . . . . . . . . . . . . . . . . 6.2.4 Genge’s Birefringence Ball of Biaxial Minerals . . . . 6.2.5 Determination of the 2V Angle in Biaxial Minerals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 How to Obtain an Interference Figure. . . . . . . . . . . . . . . . . . References and Books with Chapters on Conoscopic Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125 126

7 Igneous Rocks: Some Basic Concepts . . . . . . . . . . . . . . . . 7.1 Classification of Igneous Rocks . . . . . . . . . . . . . . . . . . 7.1.1 Classification Based on Modal Composition . . . 7.1.2 Classification Based on Texture . . . . . . . . . . . . 7.2 Chemical Classification of Igneous Rocks . . . . . . . . . . References and Suggested Further Reading . . . . . . . . . . . . . .

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8 Metamorphic Rocks: Some Basic Concepts . . . . . . . . . . . . 8.1 Classification of Metamorphic Rocks . . . . . . . . . . . . . . 8.1.1 Textures of Metamorphic Rocks . . . . . . . . . . . . 8.1.2 Modal Composition and Mineral Assemblage . . 8.1.3 Protolith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Common Textures in Metamorphic Rocks . . . . . . . . . . Selection of Books on Metamorphic Petrology and Cited Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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9 The Mineral Plates and How to Use Them . . . . . . . 9.1 Introduction to the Mineral Plates . . . . . . . . . . . . 9.2 Mineral Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . Some References for the Determination of Minerals in Thin Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

128 131 131 131 134 137 137 141 141 141 143 143

Appendix A: Abbreviation of Minerals . . . . . . . . . . . . . . . . . . . . . . 263 Appendix B: Transfer-Matrix Formalism for the Extinction Behavior in Anisotropic Minerals . . . . . . . . . . . . . . . 265 Appendix C: Examples of Examination Questions . . . . . . . . . . . . . 267 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

1

Introduction

This book is a compact guide for the identification of rock-forming minerals in a thin section using a polarized light microscope and transmitted plane polarized light. It is based on my teaching experience at the Universities of Heidelberg (Germany), Basel (Switzerland), and Geneva (Switzerland). It is intended to be mainly useful to Bachelor’s students in optical mineralogy and petrography and to microscopists who need to brush up their knowledge in optical mineralogy and the determination of magmatic and metamorphic rocks. The use of a polarized light microscope to examine a rock is a critical and relatively inexpensive tool in geologic investigations. Following a general tendency in the Earth Sciences curriculum the hours of teaching optical mineralogy as well as igneous and metamorphic petrology have been reduced over the years to make time for new topics in Earth Sciences. This was also the case at the University of Geneva. What I used to teach in three semesters had to be condensed into a one-semester class. Yet, identifying minerals and solid phases in a thin section continues to be an essential skill, not only in academic research projects, but also in applied mineral sciences. Many students will work in exploration for ore deposits, hydrocarbons, and geothermal reservoirs. These skills are also needed for asbestos determination, phase identification in the cement industry, in the forensic sciences, and in monitoring the incineration of household garbage. In addition, gemology, the

study of precious minerals, requires knowledge of mineralogy. Therefore, my teaching has had to be adapted to these changing requirements. Although the principles of optical mineralogy have been treated in many books over more than a century (see list of books at the end of this chapter) and many websites exist for optical mineralogy, I soon realized that I also had to provide the appropriate teaching materials in a compact form to motivate the students and to ensure that a student had some basic theoretical and practical skills after a one-semester course, as well as providing a reference which they could continue to consult. I was forced to make compromises on the subjects taught. To this end, I wrote two manuals: “Le P’tit guide de minéralogie optique” (Schmidt 2002-[50]) and “An atlas of rock forming minerals under the microscope” (Schmidt [51]). In addition, a software assistant, OpticMin©, was developed and is available at https://athena.unige.ch/athena/mineral/opticminsearch-intro.html [40, 52]. The software allows observed parameters to be entered resulting in mineral suggestions and corresponding mineral plates with the optical and crystallographic parameters and microscopic images to help with identification. Computer-assisted microscopy and image analysis of microscopic images are powerful for detailed examination and provide additional information about a sample, but the characterization of a specimen in plane polarized light under the microscope remains essential and straightforward.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. T. Schmidt, Transmitted Light Microscopy of Rock-Forming Minerals, Springer Textbooks in Earth Sciences, Geography and Environment, https://doi.org/10.1007/978-3-031-19612-6_1

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This book covers selected aspects of optical mineralogy. It aims to help learning optical mineralogy in the most effective way possible. It summarizes essential principles, uses numerous figures, and displays the optical characteristics of the most common rock-forming minerals on 73 mineral plates with more than 1000 microscopic images. Optical mineralogy relies on research carried out by many scientists mainly in the late nineteenth and twentieth centuries. It is rewarding to read some of these old textbooks in different languages: Rosenbusch [46] in German, considered to be the pioneer in the microscopy of minerals and rocks, Fouqué and Michel-Lévy [12] in French with astonishing 55 hand-colored microscopic images and the so-called MichelLévy color chart, or Winchell and Winchell [64] in English. These books illustrate well the high level of knowledge of optical mineralogy already available at that time. Johannsen [21] published tables with the maximum birefringence, the maximum refractive indices, and an alphabetical list of minerals with the main optical properties of common rock-forming minerals. Compilations of optical and crystallographic data of the nonopaque minerals in the form of tables were published as a report of the US Geological Survey (USGS) by Larson and Berman [24] which was updated by Fleischer et al. [11]. In 1952 Tröger published, in German, his famous description of common rocks and compilation of optical and crystallographic data which was updated in 1971 (Tröger [56, 57]) and subsequently translated into English [58]. He introduced figures with crystal morphology in relation to optical and crystallographic parameters which have been used widely since by many authors. Following this introductory Chap. 1, Chaps. 2 –6 treat the basic principles of optical mineralogy and how to determine the optical parameters used for the identification of minerals. Chapter 2 explains the necessary basic principles to understand the behavior and interaction of light in a mineral. Chapter 3 presents the polarized light microscope with its special devices for the determination of the optical parameters of minerals in a thin section. In Chap. 4 the optical properties color, pleochroism, habit, relief, and

1

Introduction

cleavage visible in the orthoscopic illumination mode and in plane polarized light are explained. Chapter 5 presents the optical parameters birefringence, extinction, extinction angle, elongation, twins, and zoning visible in the orthoscopic illumination mode and in cross polarized light. Chapter 6 introduces the conoscopic illumination mode and the interference figures for uniaxial and biaxial minerals. Chapters 7 and 8 are a compact guide to magmatic and metamorphic rocks, as well as to common magmatic and metamorphic textures and to the classification of these rocks based on microscopic observations. I tried also to include some physical background to quantify the optical parameters such as for the extinction behavior and the formation of the interference colors in Chap. 5 using transfermatrix formalism and in the cleavage Sect. 4.4 where cleavage is explained because of the different forms and interactions of electron clouds as postulated by quantum mechanics. Chapter 9 includes 73 mineral plates of 65 common rock-forming minerals. Most books on optical mineralogy list minerals and their optical characteristics according to structural criteria or based on the optical classification in isotropic, anisotropic uniaxial, and anisotropic biaxial minerals. But a beginner often finds this organization difficult to work with. The organization of this chapter is slightly different. Like a book for determining wildflowers, the minerals are grouped in five categories according to color in plane polarized light in a thin section of 30 lm. Within each color category, minerals are listed according to decreasing order of interference color. I have used this approach because color is the first optical property to be observed, even though minerals may change color according to composition. Each mineral plate depicts the general formula, the international abbreviation in lower case, the main crystallographic and optical parameters, the crystal habit, the common occurrence in different geological environments, and characteristic microscopic images. This will allow the student and any other reader to visualize the appearance and the characteristic parameters as a concise summary mostly on one page which can be viewed on a tablet next to the

1

Introduction

microscope, where the space is normally limited. The same mineral might look slightly different in various geological environments but will share certain optical characteristics. If a student has seen one to three characteristic microscopic images of a mineral and learned to use the optical and crystallographic relationships, he/she will remember it for the future. Microscopic images of rock-forming minerals have inspired many artists. The Fig. 1.1 is the artistic interpretation by Dr. Jorge Alvar of aegirine in alkali granite, Khan Bogd pluton, Gobi Desert, Mongolia. I hope that this book will facilitate a fast and effective learning of optical mineralogy and that the reader may enjoy this subject as much as I do.

Fig. 1.1 Artistic interpretation by Dr. Jorge Alvar of aegirine in alkali granite, Khan Bogd pluton, Gobi Desert, Mongolia

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A Selection of Books on Optical Mineralogy, Books with a Chapter on Optical Mineralogy, and Publications Relevant to the Subject 1. Barker AJ (2015) A key for identification of rockforming minerals in thin section. Taylor & Francis Group, p 182 2. Bloss FD (1999) Optical crystallography. Mineralogical Society of America, p 239 3. Borradailie GJ, Bayly MB, Powell CMcA (1982) (eds) Atlas of deformational and metamorphic rock fabrics. Springer-Verlag Berlin Heidelberg New York, p 551 4. Browning P (1996) UKESCC: Optical mineralogy. Terra Nova 8:386-389 5. Deer WA, Howie RA, Zussmann J (2013) An introduction to the rock-forming minerals, 3rd edn.

4

1

6. 7. 8.

9.

10.

11.

12.

13.

14.

15. 16. 17. 18.

19.

20.

21.

22. 23. 24.

25.

26.

Berforts Information Press, Stevenage, Herfordshire, p 498 Delly JD (2019) Essentials of polarized light microscopy. The McCrone Group Demange M (2012) Mineralogy for petrologists. CRC Press Taylor & Francis Group, p 182 Dyar MD, Gunter ME, Tasa D (2008) Mineralogy and optical mineralogy. Mineralogical Society of America, Chantilly, VA, p 708 Duparc L, Pearce F (1907) Traité de technique minéralogique et pétrographique. Première partie: Les méthodes optiques. Veit, Leipzig, p 483 Ehlers EG (1987) Optical mineralogy, theories and techniques/mineral descriptions, two volumes. Blackwell Scientific publications Fleischer M, Wilcox RE, Matzko JJ (1984) Microscopic determination of the nonopaque minerals. 3rd ed. U.S. Geol. Surv. Bull. 1627 (revision of Bull 848), p 453 Fouqué F, Michel Lévy A (1879) Introduction à l'étude des roches éruptives françaises, Minéralogie micrographique. vol 1, A. Quantin, p 509 Gaines RV, Skinner HC, Ford, EE, Mason B, Rosenzweig A (1997) Dana's New Mineralogy with sections by Vandall T. King, Illustrations by Eric Dowty John Wiley & Sons, Inc. Genge M (2011) Optical mineralogy: new colour in a dying art. The Geologists’ Association & The Geological Society of London, Geology Today, 27/3 Girault J (1989) Caractères optiques des minéraux transparents: tables de détermination. Masson, 176 p Gribble CD, Hall AJ (1985) A practical introduction to optical mineralogy. George Allen & Unwin, 249p Gribble CD, Hall AJ (1992) Optical mineralogy: principles and practice. UCL Press, London, p 320p Groth P (1896–1921) Elemente der physikalischen und chemischen Krystallographie. R. Oldenbourg, Berlin und München, p 371 Gunter ME (2004) The polarized light microscope: Should we teach the use of a 19th century instrument in the 21st century? J Geosci Educ 52:34–44 Heilbronner R, Barret S (2014) Image analysis in the earth sciences—microstructure and textures of earth materials. Springer Verlag Heidelberg, p 520 Johannsen A (1908) A key for determination of rockforming minerals in thin section. John Wiley & Sons, p 576 Kerr PF (1959) Optical mineralogy. McGrawHill Book Company, p 442 Kerr PF (1977) Optical mineralogy. 4st edition, McGrawHill Book Company, p 492 Larsen ES, Berman, H (1934) The microscopic determination of the nonopaque minerals. US Geological Survey, 2nd edition, USGS Bulletin 848, p 266 MacKenzie WS, Adams AE, Brodie AH (2017) Rocks and minerals in thin section. CRC Press Taylor & Francis Group, p 227 MacKenzie WS, Adams AE (1994) A coulour atlas of rocks and minerals in thin section. Manson, p 192

Introduction

27. MacKenzie WS, Adams (1999) Initiation à la pétrographie—avec 180 photos en couleur de roches et minéraux en lame minces. Dunod, p 192 28. McCrone WC, Delly JG (1984) Polarized light microscopy. McCrone Research Institute Inc., Chicago 29. McCrone WC, Draftz RG, Delly JG (1967) The particle atlas. Ann Arbor Science Publishers Inc., Ann Arbor, Michigan 30. Melgarejo JC (1997) Atles d’associacions minerals en làmina prima. Edicions de la Universitat de Barcelona, p 1074 31. Melgarejo JC, Martin RF (2011) Atlas of non-silicate minerals in thin section. Special Publication 7 of The Canadian Mineralogist, Mineralogical Association of Canada, Quebec, Canada, p 522 32. Michel-Lévy MA (1883) Mesure du pouvoir biréfringent des minéraux en plaques minces. Bull Minér 6:143–161 33. Michel-Lévy A, Lacroix A (1888) Les minéraux des roches. Volume 1 Michel-Lévy A, Application des méthodes minéralogiques et chimiques à leur étude microscopique. Volume 2 Michel-Lévy A, Lacroix A. Données physiques et optiques. Librairie polytechnique Baudry et Cie, Paris, 334p (et une planche en couleurs) 34. Müller G, Raith M (1976) Methoden der Dünnschliffmikroskopie. Clausthaler Tektonische Hefte 14:151p 35. Nesse WD (2013) Introduction to optical mineralogy. Fourth edition, Oxford University Press, p 361 36. Neumayr M (1886) Allgemeine Geologie. Verlag des Bibliographischen Instituts, Leipzig, Erster Band 37. Okrusch M, Frimmel HE (2020) Mineralogy. Springer-Verlag Germany, p 719 38. Raith MM, Raase P, Reinhard J (2012) Guide to thin section microscopy. 2nd edn, p 127. ISBN 978–3– 00–037671–9 (PDF) 39. Perkins D, Henke KR (2000) Minerals in thin section. Prentice Hall, Upper Saddle River, N.Y., Pearson Printing Hall, p 125 40. Perroud P, Schmidt ST, Süssenberger A (2016) OPTiCMin©: a new electronic teaching tool for optical mineral identification. Abstract Volume, 14th Swiss Geoscience Meeting, Genève 41. Phillips WR (1981) Optical mineralogy: the nonopaque minerals. WH Freeman San Francisco 42. Philpotts A. R. (2003) Petrography of igneous and metamorphic rocks. Prentice Hall, p 178 43. Pichler H, Schmitt-Riegraff C (1987) Gesteinsbildende Minerale im Dünnschliff. Enke, Stuttgart, p 288 44. Pichler H, Schmitt-Riegraff C (1997) Rock forming minerals in thin section. Chapman & Hall, p 220 45. Reinhard J (2004) Optical mineralogy in a modern earth sciences curriculum. J Geosci Educ 52:60–67 46. Rosenbusch H (1873) Mikroskopische Physiographie der petrographisch wichtigen Mineralien: ein Hülfsbuch bei mikroskopischen Gesteinsstudien. E. Schweizerbart’sche Verlagshandlung, Stuttgart, p 398

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Introduction

47. Roubault M, Fabriès J, Touret J, Weibrod A (1963) Détermination des minéraux des roches au microscope polarisant. Editions Lamarre-Poinat, p 348 48. Russ JC (2012) Computer-assisted microscopy: the measurement and analysis of images. Springer science & business media, p 470 49. Saywer EW (2008) Atlas of Migmatites. The Canadian Mineralogist, Mineralogical Association of Canada, National Research Council Canada, Monograph Publishing Program, Special Publication 9, p 372 50. Schmidt ST (2019a) Le P’tit Guide de Minéralogie optique. Université de Genève. 12th edition, p 136 51. Schmidt ST (2019b) Atlas of rock-forming minerals. University of Geneva, p 108 52. Schmidt ST, Perroud P, Süssenberger A (2017) OPTiCMin©: an online teaching tool for mineral identification in thin section, GSA Meeting, Seattle 2017, Paper 105–7 53. Shelley D (1992) Igneous and metamorphic rocks under the microscope. Classification, Textures, Microstructures and Mineral Preferred Orientations, London Chapman and Hall, London, p 445 54. Sørensen RE (2013) A revised Michel-Lévy interference colour chart based on first-principles calculations. Eur J Miner 25:5–10 55. Stoiber RE, Morse SA (1994) Crystal identification with the polarizing microscope, Springer-Science +Business Media Dordrecht. Originally published by Chapman & Hall, p 358 56. Tröger WE (1971a) Optische Bestimmung der gesteinsbildenden Minerale. Teil 1 Bestimmungstabellen, 4. Auflage, E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, p 188

5 57. Tröger WE (1971b) Optische Bestimmung der gesteinsbildenden Minerale. Teil 2 Textband. E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, p 822 58. Tröger WE (1979) Optical determination of rockforming minerals. E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, p 188 59. Verma PK (2010) Optical mineralogy. Taylor & Francis, Ane Books Pvt, Ltd, p 367 60. Vernon RH (2018) A practical guide to rock microstructure. 2nd edn, Cambridge University Press 61. Wenk H-R, Bulakh A (2016) Minerals, Cambridge University Press, p 640 62. Wahlstrom EE (1951) Optical crystallography. John Wiley and Sons, London, p 247 63. Wahlstrom EE (1979) Optical crystallography, 5th edn. John Wiley & Sons, New York, p 488 64. Winchell NH, Winchell AN (1922) Elements of optical mineralogy. An introduction to microscopic petrography, Part 1: principles and methods. John Wiley & Sons, p 216

Further Reading 1. Holtkamp M (2004-2019) Smorf Crystal Models. www.smorf.nl

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Basic Concepts

2.1

Light as the Tool of Examination in Optical Mineralogy

The interaction of light with the atomic structure of minerals is the basic principle for the identification of minerals in a rock using the petrographic microscope. Light is electromagnetic radiation (Fig. 2.1), is a small portion of the electromagnetic spectrum with wavelengths of 390 nm (violet) to 770 nm (red) and is visible to the human eye. The electromagnetic spectrum includes on one side waves with very long wavelengths (from 100 Mm to 0.77 lm) which are low in energy and have low frequencies, such as radio waves, microwaves, or infrared waves. Very short wavelengths (from 0.39 lm to 1 pm), high in energy and with high frequency, such as ultraviolet rays, X-rays or Gamma rays, are located on the other side of the electromagnetic spectrum (Fig. 2.1). Light is currently best described through quantum electrodynamics (QED), a theory unifying Maxwell's electrodynamics with Schrödinger's quantum mechanics. It is one of the most accurate physical theories ever developed and stood the test of time after nearly a century of scrutiny and tests. QED describes light as being composed of photons, i.e., massless, uncharged particles or quanta of electromagnetic radiation traveling at the speed of light, whose behavior resembles both waves and particles. Its quantum mechanical nature being hard to interpret,

physicists commonly use the term the waveparticle duality. In the wave theory light travels as a wave, while in the particle theory light is considered a particle with a given energy. Both theories, the particle and the wave theory, are considered correct and are complementary to each other, and both have their application in optical mineralogy. The interpretation of light as a particle beam or as a wave depends on the context. In the particle theory light is a collection of energy or photons (light particles) of zero mass. When an atom is excited by absorption of energy produced by light, heat, or radiation, the outer electrons of an orbit go to a higher energy level. After a certain time, the electrons fall back to their initial energy state and spontaneously emit a photon of a precise energy, corresponding to the difference between the two energy levels. The particle theory allows understanding of the behavior of electrons in the orbitals and their interaction with their neighbors and of the optical properties such as color and cleavage. The wave theory explains the interaction of light with the atomic lattice as well as the phenomena of refraction, reflection, polarization, and interference. Light is described as having two components, an electric and a magnetic vector vibrating at a right angle to each other and traveling at a right angle to these two vectors along the direction of propagation (Fig. 2.2). Light propagates like a wave from one point to another, just like the waves when a rock is thrown into water. In

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. T. Schmidt, Transmitted Light Microscopy of Rock-Forming Minerals, Springer Textbooks in Earth Sciences, Geography and Environment, https://doi.org/10.1007/978-3-031-19612-6_2

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Fig. 2.1 Visible light as part of the electromagnetic spectrum and corresponding range of wavelength, frequency, and energy. As wavelength increases, energy

optical mineralogy we can simplify this concept and consider only the electric vector interacting with the lattice of the crystal, the atoms, and the bonding character of the minerals, and which will be changed during its travel through the mineral. The change of the propagation direction of light and change of refractive index are diagnostic for a mineral, and this chapter outlines the basic principles. Many books have covered these basic principles in great detail [12, 13, 9, 1–5]. This chapter summarizes some necessary basic principles based on my personal experience in teaching optical mineralogy. A light wave is described by its velocity V, its wavelength k, and the frequency f. The wavelength k is the distance from one crest to the next, and the frequency is the number of crests per second. The amplitude A is a measure of the intensity or the brightness of the light wave.

2 Basic Concepts

and frequency decrease. Key units are: 1 mm = 1000 lm = 1,000,000 nm = 10,000,000 Å

f ¼

V k

ð2:1Þ

The velocity of light is constant in a given medium. If the frequency changes, the wavelength also must change. If two rays vibrate in the same plane and have the same propagation direction, they will interfere. The distance that one wave lags behind another wave is called retardation (C). Retardation is described either in terms of the distance in nanometers or in the number of wavelengths. When the retardation is an integer of the wavelength, the two waves are in phase and the peaks and troughs overlap. A new wave is produced which is the arithmetic sum of the two. This is known as constructive interference (Fig. 2.3a). When the retardation equals half a wavelength or (i þ 12), the peaks of one phase coincide with the troughs

2.2 Refractive Index, Dispersion, Polarization, and Double Refraction

9

Fig. 2.2 Relationship between the direction of propagation, direction of vibration, wavelength k, amplitude, electric and magnetic vector as used in the wave theory for light. Oscillation or vibration direction of light is perpendicular to the direction of propagation (modified from Nesse [3])

of the other phase and cancel each other. The waves are out of phase. This is known as destructive interference (Fig. 2.3b). When the retardation equals a quarter wavelength or (i þ 14), there is constructive and destructive interference as shown in Fig. 2.3c. Constructive and destructive interference of waves in minerals are more complex and explained in Chap. 5.

2.2

Refractive Index, Dispersion, Polarization, and Double Refraction

The Snell-Descartes law The velocity c of light in vacuum or Vvacuum is 299 792 km/s which means that you could travel around the world 7.5 times in a second. The velocity of light is reduced in denser media. Velocity in a medium is expressed as the refractive index nmedium which is defined as the ratio of the velocity of light in a vacuum to that in a medium and varies with temperature and wavelength.

nmedium ¼

V vacuum V medium

ð2:2Þ

The refractive index can also be considered as the factor the light is faster in the vacuum as compared to the concerned medium. For example, the refractive index of pure water is on average 1.333 and would indicate that the light in the vacuum travels 1.333 times faster than in water. The velocity of light in water is calculated at 224 900 km/s and is therefore slower than for light in the vacuum. As a light ray passes across the boundary separating two media, in our case air and a mineral, the path of the light ray is bent. The path of the light follows the law of Snell-Descartes. ni sinhr ¼ nr sinhi

ð2:3Þ

ni sinhi ¼1 nr sinhr

ð2:4Þ

where n1 and nr are the refractive indices of the two media, and hi and hr are the angles of incidence and refraction between the normal to the surface between the two media (Fig. 2.4). Note that the light ray in Fig. 2.4 is going from bottom to top, which is the direction of light in a petrographic microscope. When a light ray passes from a less dense and therefore less refractive medium to a more dense and therefore more refractive medium, it will be refracted toward the normal and the angle of refraction is smaller than

10 Fig. 2.3 Constructive (a), destructive (b), and combined interferences (c) of waves as observed in one plane. The new wave resulting from positive or negative interference is shown in black

2 Basic Concepts

(a)

(b)

(c)

the angle of incidence (Fig. 2.4a). When a light ray passes from a more refractive medium to a less refractive medium, it will be refracted away from the normal resulting in a larger angle of refraction than the angle of incidence (Fig. 2.4b). As a rule, light is always bent toward the normal in the denser medium. At a certain angle called the critical angle a ray of light traveling from a denser medium to a less dense medium is not refracted anymore. It is trapped and reflected in the denser medium at the interface between the two media (Fig. 2.4c). Total reflection occurs when the angle of incidence is greater than the critical angle (Fig. 2.4d). This is important for understanding the origin of the optical phenomenon called “relief” (see Sect. 4.3).

Dispersion of light Ray velocity, and thus the refractive index, changes with wavelength (except for in a vacuum). This phenomenon is known as dispersion of light and is well demonstrated using an equilateral prism. An equilateral prism splits light into its components of color due to the different refraction of the various wavelengths of visible light, and the rainbow colors are seen (Fig. 2.5). White light enters the prism with a certain angle of incidence and is refracted according to the Snell-Descartes law. The light rays of the different wavelengths travel with different velocities through the prism and exit the prism where they are again refracted (Fig. 2.5). The material of the prism changes the propagation

2.2 Refractive Index, Dispersion, Polarization, and Double Refraction (a)

(b)

(c)

Fig. 2.4 Refraction and conditions for the critical angle and for total internal reflection. a a light ray traveling from a less dense (in blue) to a more dense medium (in gray) is refracted toward the normal to the surface, and the angle of refraction is smaller than the angle of incidence; b a light ray traveling from a denser to a less dense

11 (d)

medium is refracted away from the normal and the angle of refraction is larger than the angle of incidence; c critical angle of refraction where a light ray does not cross the boundary; d total internal reflection where a light ray is reflected back into the denser medium

Fig. 2.5 Dispersion of white light in an equilateral prism which splits white light during its passage into the components of color. Blue light on one side of the spectrum is more refracted than red light on the opposite side of the spectrum

direction, and the light rays are split into different wavelengths corresponding to different colors with different refraction indices and refraction angles (Fig. 2.5). A ray of shorter wavelength such as violet is slowed down by the prism the most, is refracted the most or at a larger angle and has a higher index of refraction than a ray of longer wavelength such as red which travels faster in the prism, is refracted less and has a lower index of refraction (Fig. 2.5). The exit angle depends on the refractive index of the material of the prism, the angle of incidence and the prism angle. The angle of dispersion and refractive index are proportional to each other: increasing the refractive index of the prism will increase the angle of dispersion. Dispersion is

therefore higher for minerals with a high refractive index than for minerals with a lower refractive index. Polarization of light Plane polarized light is the basis for optical mineralogy and used as the light source of the polarized light microscope. Plane polarized light interacts with the crystal lattice which deviates the light entering the crystal. Ordinary light such as sunlight or artificial light vibrates in all possible directions at right angles to the direction of propagation. The vibration direction of plane polarized light is restricted to one specific plane, the plane of polarization, which is perpendicular to the direction of propagation. It is important to

12

2 Basic Concepts

understand how the crystal changes the velocity and the direction of the propagation of light. As shown in Fig. 2.6a, a ray of plane polarized light is considered as a simple electromagnetic sine wave with an oscillating electric field for a wavelength k and an amplitude A. Plane polarization of light can be generated in different ways (Fig. 2.6b–e). Polarization by selective

(b)

(a)

(c)

absorption is the technique used to polarize light in most modern polarization filters (Fig. 2.6b). A typical polarizing filter selectively absorbs light (Fig. 2.6b) and is made from polyvinyl alcohol plastic (PVA), a water-soluble synthetic polymer with the idealized formula [CH2CH (OH)]n. Mechanically stretched sheets of PVA contain polymer chains or chain molecules which

(d)

Fig. 2.6 Polarization of light. a plane polarization by selective absorption of the electric sine wave, the wavelength k and the amplitude A; b plane polarization by selective absorption in a PVA polarization filter; light vibrating parallel to the green arrow is absorbed by the electrons in the iodine atoms, while light oscillating perpendicular is transmitted as indicated by the red arrow;

c plane polarization by selective absorption; d plane polarization by reflection for Brewster angle conditions. Part of the light is reflected and 100% polarized, while most of it is refracted and only partly polarized; e plane polarization by total refraction in the Nicol prism as formerly used in a petrographic microscope to generate plane polarized light

2.2 Refractive Index, Dispersion, Polarization, and Double Refraction

are stretched and aligned in parallel during the manufacturing process. Valence electrons from an iodine dopant are able to oscillate linearly along the polymer chains, but not transverse to them. Light rays vibrating parallel to the long polymer chains will therefore interact with the valence electrons and be absorbed by them, whereas light rays vibrating perpendicular to the polymer chains will pass through the filter and be transmitted as plane polarized light vibrating perpendicular to the polymer chains or N-S in Fig. 2.6b. In the crystal in Fig. 2.6c light is split into two rays and one ray is absorbed while the other ray is transmitted and exits the mineral, and a color results. This is discussed in more detail under pleochroism in Sect. 4.1.3. Polarization also occurs when unpolarized light strikes the polished surface of a transparent optical medium at an oblique angle (Fig. 2.6d). The same phenomenon can be observed on a water surface (e.g., a lake). Most of the light is refracted while a smaller part of the light is reflected. An angle of 90° between the reflected and refracted light ray will result in a refracted light ray which is 100% polarized but reduced in intensity. The angle of incidence h to produce this 90° angle is called the Brewster angle and can be calculated using the Snell-Descartes law. In older microscopes the Nicol prism is used to produce plane polarized light by double refraction and total reflection of one light ray (Fig. 2.6e). The Nicol prism consists of a crystal of calcite which has been cut along the crystallographic c-axis with the pieces remounted using Canada balsam, the natural oleoresin of the balsam fir tree (Abies balsamea). In the example light enters from the left and is split into the x and e rays vibrating at an angle of 90°. The ordinary x ray (nx = 1.658) has a higher refractive index than Canada balsam (nCB = 1.53) and the angle of incidence is greater than the critical angle, and the ray is therefore totally reflected at an inner face of the cut crystal. The extraordinary e ray (ne = 1.486) with the smaller refractive index is transmitted through the interface, and plane polarized light will leave the crystal. When two polarizers are placed in the light ray such that their polarization directions

13

are perpendicular, they will block all the light; while Nicol prisms are no longer common, the term “crossed Nicols” is retained to describe analysis resulting from two polarizers at right angles being inserted in the ray of light. Terms commonly used are observation under crossed polarizers or XPL and if working with one polarizer the observations are carried out in plane polarized light or PPL. Double refraction in anisotropic minerals: example calcite In anisotropic minerals light does not propagate at the same velocity in all directions. Light entering a crystal is split into two rays that take different paths during their journey through the crystal and emerge from the crystal as separate light rays. These rays vibrate at right angles, have different velocities giving different refraction indices for the mineral and may have different absorption behavior. This phenomenon is called double refraction. In Fig. 2.7a, a light ray forms a wave front which is just the envelope, i.e., the tangent surface of many little spherical waves. This wavefront is perpendicular to the direction of propagation and the ray travels through the crystal and emerges at the other side. This ray is called the ordinary ray. In Fig. 2.7b, the wave front of the refracted light rays spreads out as ellipsoids and the so-called optic axis is the major axis of the ellipsoid. The propagation direction is not parallel to the wave front. This ray is called the extraordinary ray. Both rays exit the crystal parallel to the incident beam but are displaced and responsible for the double refraction. Macroscopically, double refraction is best seen in a calcite cleavage rhomb (CaCO3 Fig. 2.8). A calcite rhomb placed on a line of dots produces two lines of dots as shown in the images of the left column in Fig. 2.8a. For normal incidence or at an angle of 0° of incidence of light with respect to the plain rhomb surface, the incoming light is split into two waves resulting in two images (Fig. 2.8a, b). One ray travels straight through the crystal while the other is displaced as it traverses the crystal. During rotation of the calcite rhomb one line of dots

14

Fig. 2.7 Light path in an anisotropic medium; a light path of the ordinary ray. The wave front with spherical waves is perpendicular to the direction of propagation; b light path of the extraordinary ray. The wave front is formed by ellipsoids which are not perpendicular to the direction of propagation. Both rays exit the crystal parallel to the incident beam but are separated and displaced. The optic axis lies in the plane of the paper

stays stationary, while the other pivots around the stationary one (Fig. 2.8a). The stationary image is produced by the so-called ordinary ray which obeys the Snell-Descartes law (if angle of incidence is 0°, there will be no refraction), and the rotating one by the so-called extraordinary ray which does not obey the Snell-Descartes law. The two rays vibrate at right angles and travel with different velocities. In the right column the same image is shown as in the left column, but a polarizer (gray-brown rectangle) is overlying the crystal and vibrates N-S. It cuts out the ordinary ray or the extraordinary ray according to their vibration directions with respect to the polarizer. If the vibration direction of the polarizer is perpendicular to the vibration direction of either the

2 Basic Concepts

extraordinary or the ordinary rays in the calcite crystal, the respective ray will be extinct (Fig. 2.8a, right column). The extraordinary wave vibrates in the plane that includes the caxis, and the ordinary wave vibrates perpendicular to it (Fig. 2.8c). Along the c-axis light is not refracted or polarized and the direction is called the optic axis of the crystal. In calcite, it represents the crystallographic c-axis of threefold rotation (Fig. 2.8c). The crystal structure of calcite drawn with CrystalMaker is shown in Fig. 2.8d–f. In Fig. 2.8d the calcite structure is shown looking nearly along the crystallographic a-axis. The triangular CO3 clusters are visible as pink triangles with a magenta carbon and three associated yellow oxygen atoms (Fig. 2.8d). The structure of the crystal appears dense producing an interaction of the light ray with the electron clouds of the encountering atoms and creates two rays. By looking down the crystallographic c-axis or Zaxis as in Fig. 2.8f the c-axis and the parallel optic axis are almost perpendicular to the plane of paper and to the triangular CO3 clusters. The structure appears to be more regular than in Fig. 2.8d viewed nearly down the X-axis or crystallographic a-axis, and the light is not refracted. We can easily calculate the velocity of light propagation in the uniaxial calcite. Ray ne (ne = 1.486 for a wavelength of 590 nm) or the fast ray travels at 201,884 km/sec and the slow ray nx (nx = 1.658 for a wavelength of 590 nm) travels at 180,941 km/s. This is impossible to see! But we can calculate how big the retardation is between the two rays in the calcite rhomb of a thickness of 4 cm. The retardation between the two rays is 6.88 mm and allows us to discriminate the two images.

2.3

Retardation of Rays in Anisotropic Minerals and Birefringence

The double refraction in calcite illustrates that rays travel with different velocities and therefore the crystal has different refractive indices for light vibrating in different directions. This implies that in a crystal the slow ray lags behind

2.3 Retardation of Rays in Anisotropic Minerals and Birefringence (a)

15

(b)

(c)

Fig. 2.8 Double refraction of calcite as seen by the duplication of the word “calcite”, a line of red dots and a black straight line as produced by the extraordinary ray e and the ordinary ray o, a the left column with five images of a calcite crystal (cleavage block) shows from top to bottom how the e ray pivots around the stationary o ray when rotating counterclockwise from 0° to 180°. In the right column the same image is shown as in the left column but a polarizer (grey-brown rectangle) is overlying the crystal and vibrates N-S (orange arrow) cutting out either the extraordinary and ordinary rays according to their vibration directions with respect to the polarizer. Use

brown oval handle to turn counterclockwise. The handle also points to the location of the crystallographic c-axis which is parallel to the optic axis; b and c appearance of double refraction in calcite; Crystal is drawn using the Smorf applet; (Holtkamp 2004–2019) d–f crystal structure of calcite drawn with CrystalMaker; d, e looking along the X- or crystallographic a-axis; f looking almost along the Z-axis, the crystallographic c-axis and the direction of the optic axis with the triangular CO3 clusters (magenta carbon and three associated yellow oxygen atoms) parallel to the plane of paper. The structure appears to be more regular than shown in d, e

16

the fast ray and their difference on emergence is called the retardation C which is 12 k in Fig. 2.9. This situation is used in the examination of minerals in cross-polarized light and is explained in the following paragraph (see also Sect. 5.1 Birefringence). In a polarized light microscope (see Chap. 3), the light emitted beyond the lower polarizer vibrates in a single plane which can be N-S or E-W depending on the microscope design and therefore is plane polarized. When this plane polarized light passes through an anisotropic medium, in this case a uniaxial mineral, the light is doubly refracted or split into two waves, the slow and the fast ray

2 Basic Concepts

(Fig. 2.9) or the ordinary and extraordinary rays, vibrating at 90° and traveling with two different velocities. The light entering the mineral is influenced and its path and velocity are affected by the atomic structure, the electron cloud, the bonding of atoms and molecules, the composition, and the density of the electron distribution of the crystal. This means that the crystal lattice and the chemical composition of a mineral govern the double refraction and the difference in velocity and refractive indices and are highly characteristic for a mineral. When the two rays exit the mineral above the thin section plane, the fast ray will be ahead of the slow ray and the slow ray will lag behind the fast ray by a certain distance called retardation C (Fig. 2.9). The magnitude of this retardation depends on the thickness d of the mineral and the values of the refractive indices for the two vibration directions can be calculated. The slow ray needs more time to travel through the crystal. The time trslow (time of the slow ray) can be calculated as trslow ¼

d V rslow

ð2:5Þ

Vrslow is the velocity of the slow ray, and d is the distance (thickness) traveled. During the time trslow, the fast ray not only traveled through the crystal, but already covered an additional distance outside the crystal called the retardation C. Vrfast is the velocity of the fast ray and V the velocity of light in air (for practical purposes, the same as in a vacuum). T rslow ¼

d V rfast

þ

C V

ð2:6Þ

By combining and rearranging the equations, we get d d C ¼ð þ Þ V rslow V rfast V Fig. 2.9 Retardation of rays, perspective view. Plane polarized light enters an anisotropic crystal from below and is split into two rays, a slow (white) and a fast ray (green). The slow ray lags behind the fast ray by a certain distance or shown as 12 k which is called the retardation C

C ¼ dð

V V  ÞÞ V rslow V rfast

ð2:7Þ

ð2:8Þ

2.4 Passage of Light Through Crystalline Matter: Optic …

C ¼ dðnrslow  nrfast Þ

anisotropic minerals. A three-dimensional model uses the vibration directions and the refractive indices to describe optical characteristics of crystals and is called the optical indicatrix. The vector of the indices of refraction are plotted from a point of origin in the center of the crystal on axes, called the indicatrix axes X, Y, and Z, in both directions. They are parallel to the vibration direction and perpendicular to the propagation direction. The model for materials that have only one index of refraction results is a sphere, think of a grapefruit or an orange (Fig. 2.10). If a mineral has two indices of refraction an ellipsoid is obtained which can be prolate, think of a lemon (Fig. 2.11a) or oblate, think of a mandarin (Fig. 2.11b) depending on which vibration direction with its corresponding refractive index is used for the rotational axis, the larger index or the smaller index. If three indices of refraction are required, the 3D model is a triaxial ellipsoid similar to a kiwi (Fig. 2.12a). In isotropic minerals light is transmitted with the same velocity, and all directions have the same index of refraction n and are equal (Figs. 2.10a, b). These minerals are monorefringent. By rotating the vector of the refractive index from a central point a sphere (grapefruit or orange image) is produced (Fig. 2.10b). The group comprises the isometric minerals, rock glass, amorphous minerals such as some clays or

ð2:9Þ

The retardation C is the distance the slow ray has lagged behind the fast ray on emergence and depends on the thickness of the mineral the light travels through. It is given in nm or wavelength k depending on the context. Since thin sections are normally at a thickness of 30 lm, we can omit the thickness d and just use the difference between the indices of refraction of the slow and the fast ray. Nslow  nfast ¼ d ¼ Dn

ð2:10Þ

which is called the birefringence. The birefringence is an important optical characteristic and is a main determination key used in this book. Birefringence is discussed in detail in Sect. 5.1.

2.4

Passage of Light Through Crystalline Matter: Optic Orientation and the Optical Indicatrix

Optic parameters are fundamentally related to crystal structure. Based on the behavior of light traveling through the crystalline structure two groups can be distinguished: isotropic and Sphere

(a)

(b)

View

View Z Z

X

17

Z Y

X

Fig. 2.10 Construction of the isotropic indicatrix for isotropic substances including the isometric minerals. a the rotation of the index of refraction n from a central

point gives a sphere; b optical isotropic indicatrix for isometric minerals with the refractive index n (any radius), similar to an ideally round grapefruit

18

2 Basic Concepts

(a)

(b)

(c)

(d)

Fig. 2.11 Construction of the uniaxial indicatrix for uniaxial minerals of tetragonal, hexagonal, and rhombohedral symmetry by rotating the vectors of two indices of refraction, ne and nx, from a central point along the indicatrix axes X and Z, a the axis of rotation contains the

larger vector; b the axis of rotation contains the smaller vector; c uniaxial positive indicatrix U+ where ne > nx; d uniaxial negative indicatrix U− where ne < nx. Circular section is shown in blue

opal, air, and liquids. In isometric minerals, the symmetry is high, and the chemical bonding is the same in all directions. The light experiences the same electronic environment and is not

affected by a varied atomic structure in different directions. The optical indicatrix of anisotropic minerals of tetragonal, hexagonal, and trigonal crystal

2.4 Passage of Light Through Crystalline Matter: Optic …

19

(a)

(b)

(c)

(d)

Fig. 2.12 Construction of the biaxial indicatrix for orthorhombic minerals. a the plot of three vectors of the refractive indices na, nb, and nc parallel to the indicatrix axes X, Y, and Z around a central point results in a triaxial ellipsoid; b biaxial indicatrix for a biaxial positive orthorhombic mineral: There are two circular sections shown in blue with a radius equal to nb. Two optic axes are perpendicular to the circular sections and form the acute angle 2V bisected by Z with nc which is called Bxa. The obtuse angle between the optic axes is bisected by the

obtuse bisectrix, called Bxo, with the vibration direction X with na; c biaxial negative: The optic angle is bisected by the vibration direction X with na, and the obtuse bisectrix is bisected by the vibration direction Z with nc; d biaxial indicatrix with the location of the XZ or ac plane with na and nc which is the optic plane. The XY or ab plane contains na and nb, and the YZ or cb plane contain nc and nb. Shown is only the trace of one circular section with nb as its radius

systems is an ellipsoid and is traditionally defined by the vectors of two refractive indices ne and no along the vibration directions E and O. In this book the vibration directions are termed

Z and X or the indicatrix axes Z with refractive indices ne and X with refractive index nx. This is in analogy to the terminology of the biaxial minerals. Indicatrix axis Z contains always ray e

20

with its corresponding refractive index and indicatrix axis X contains always ray x with its corresponding refractive index. The length of the vectors of the refractive indices varies (Fig. 2.11a, b). Depending on which vibration direction with its corresponding vector serves as the axis of rotation, one with the larger or the smaller refractive index, the optical indicatrix will have a prolate or oblate form, or the form of a lemon (Fig. 2.11c) or a mandarin (Fig. 2.11d). If ne is greater than nx, the mineral is optically positive (lemon, Fig. 2.11c). If nx is greater than ne, the mineral is optically negative (mandarin, Fig. 2.11d). Refractive indices between ne and nx are named ne0 . The refractive index perpendicular to the axis of rotation is equal in all directions and forms a circular section with the vibration direction X containing nx (Fig. 2.11c, d). The axis perpendicular to the circular section contains ne and is called the optic axis. Light traveling along the optic axis behaves as light in isotropic minerals, is not polarized, and has a single velocity. Since there is a single optic axis present, minerals of this group are called uniaxial minerals . The optic axis is parallel to the crystallographic c-axis of the tetragonal and hexagonal symmetry groups and may not necessarily be parallel to the elongation of a crystal. Anisotropic minerals of orthorhombic, monoclinic, or triclinic crystal systems are modeled with three indices of refraction na, nb and nc along the indicatrix axes X with na, Y with nb and Z with nc. The lengths of the vectors of the refractive indices are plotted from a central point along lines in opposite directions, and this results in a triaxial ellipsoid. By convention it is na < nb < nc. Refractive indices between a and b are referred to as a0 and between a and b are referred to as c0 . Similarly, the indicatrix axes may be labeled as X0 ; Y0 or Z0 if their values are intermediate between their corresponding refractive indices. The optical indicatrix has two circular sections (Figs. 2.12b, c and d) with the radius of the refractive index nb. The YZ plane is an elliptic section with nb and nc, the XY plane is an

2 Basic Concepts

elliptic section with na and nb, and the XZ plane is also an elliptic section with na and nc (Fig. 2.12d). The two optic axes, responsible for the name biaxial indicatrix or biaxial minerals, are normal to the circular sections, form an obtuse and an acute angle together totaling 180° (Figs. 2.12b–c). They lie in the plane na-nc or the ac plane, or the XZ plane called the optic plane. The acute angle formed by the two optic axes is referred to as the optic angle 2V. The optical character of a biaxial mineral, either positive or negative, may be determined in different ways and depends on whether the refractive index nb of the circular section is closer to na or nc, or depends on how steeply inclined the circular sections are with respect to the axis of rotation of the ellipsoid. A mineral is biaxial positive if nb is closer to na than to nc. If this is the case, the acute angle, 2V, between the optic axes is bisected by Z with nc and it is said that Z with nc lies in the acute bisectrix or Bxa (Fig. 2.12b). The 2V angle contains Z and therefore is named 2VZ. A mineral is biaxial negative if nb is closer to nc than to na. If this is the case, the acute angle, 2V, between the optic axes is bisected by X with na and it is said that X with na is the acute bisectrix or Bxa (Fig. 2.12c). The 2V angle contains X and therefore is named 2VX. If nb were to have the same value as na, there would only be one circular section, and the mineral would be uniaxial positive with ne > nx. If nb is equal to nc only one circular section results and the mineral is uniaxial negative with nx > ne.

2.5

Location of the Optical Indicatrix with Reference to the Crystal Systems and Crystallographic Directions

The location of the indicatrix axes and their corresponding refractive indices with respect to crystal systems or the crystallographic axes a, b and c follows certain rules. It is important to

2.5 Location of the Optical Indicatrix with Reference …

understand the relationship between crystallographic directions and the optical indicatrix axes with their vibration directions and refractive indices. This paragraph gives examples, and it is worth the time to study them carefully. The optical indicatrix and its relationship to the mineral habit, together with the crystallographic parameters are shown on the upper right side of the mineral plates in Sect. 9.2.

2.5.1 Location of the Optical Indicatrix in Isotropic Minerals In isotropic and isometric minerals, the optical indicatrix is a sphere with one index of refraction (Fig. 2.13a). No matter how you cut this optical indicatrix, a circle is obtained with the radius of the refractive index n. A crystal of isometric fluorite is cut perpendicular to (100) and (010) (Fig. 2.13b). In both sections only the index of refraction n is visible. If this section is viewed under cross-polarized light, n will be canceled by the analyzer and the mineral will be extinct. The isometric crystal habit of fluorite (Fig. 2.13c) illustrates the crystallographic relationship, and the octahedral cleavage is shown.

Fig. 2.13 a Location of the isotropic indicatrix which is a sphere in fluorite. Crystal is drawn using the Smorf applet; (Holtkamp 2004–2019) b any section cut through

21

2.5.2 Location of the Optical Indicatrix in Uniaxial Minerals In uniaxial minerals of tetragonal, hexagonal, and trigonal symmetry the indicatrix has two axes, Z and X with the refractive indices ne and nx. The location of the optical indicatrix in quartz is shown in Fig. 2.14a. The crystal and its optical and crystallographic parameters are shown in Fig. 2.14b. The crystallographic c-axis coincides with the vibration direction of the ray with the refractive index ne along the indicatrix axis Z. The vibration direction X associated with the refractive index nx is located at 90° in the circular section. Light traveling perpendicular to the circular section goes along the optic axis, where light is not refracted, as in the isometric minerals. In quartz ne is greater than nx and the optical indicatrix has a lemon shape, and the mineral is said to be uniaxial positive or U+. Sections of this type of optical indicatrix give rise to different elliptical shapes, and Fig. 2.14c illustrates the three so-called principal sections. Circular section or section perpendicular to the optic axis and the c-axis The mineral is cut perpendicular to the optic axis or the c-axis and only the vibration direction with

the mineral will give a circular section with the index of refraction n; c isometric crystal habit of fluorite with octahedral cleavage

22

2 Basic Concepts

(a)

(c)

Fig. 2.14 Optical indicatrix and its relationship to the crystal system for the uniaxial positive mineral quartz. a location of the uniaxial indicatrix within the quartz crystal. Crystal is drawn using the Smorf applet; (Holtkamp 2004–2019) b crystal of quartz with

crystallographic directions; c location of the three principal sections, the optic axis, the vibration directions with their corresponding refractive indices, birefringence, and their relationship to crystal morphology

the x ray is visible as we view a circular section with a radius equal to nx. Since there is no retardation between rays, Dn equals zero. If this section is viewed under cross-polarized light, nx will be canceled by the analyzer and the mineral will be extinct during a 360° rotation of the microscopic stage (see Sect. 5.1 Birefringence).

Parallel section or parallel to the optic axis and the c-axis The mineral is cut parallel to the c-axis or Zdirection and parallel to the optic axis. Both rays are now visible and the retardation between the rays is at maximum or Dn = d = ne−nx. During a

2.5 Location of the Optical Indicatrix with Reference …

360° rotation of the microscopic stage in crosspolarized light the mineral shows maximum birefringence d or Dn four times at 90°, as well as extinction at four positions in between (see Sect. 5.1 Birfringence). Oblique section The mineral is cut somewhere between the parallel and the circular section, and we see the vibration directions with the rays with nx and ne0 or Dn ¼ ne0  nx . Depending on the sectioning ne0 will be close to nb or closer to ne. It will

23

show birefringence d or D ¼ ne0  nx which is close to the maximum if the mineral is cut close to ne and if cut close to the circular section the birefringence d or Dn may be very low. Figure 2.15 illustrates the optical and crystallographic relations of the three principal sections for the uniaxial negative crystal calcite. The location of the optical indicatrix within a calcite crystal is shown in Fig. 2.15a, and the crystal and its crystallographic relationships are given in Fig. 2.15b. The mineral has a very good rhombohedral cleavage. In calcite ne is smaller than

(c)

Fig. 2.15 Optical indicatrix and its relationship to the crystal axes for the uniaxial negative mineral calcite. a Location of the ellipsoid and the circular section within a calcite crystal. Crystal is drawn using the Smorf applet; (Holtkamp 2004–2019) b rhombic crystal of calcite with

optical and crystallographic directions; c location of the three principal sections and the optic axis, the vibration directions with their corresponding refractive indices, birefringence, and their relationship to crystal morphology and rhombohedral cleavage

24

2 Basic Concepts

Fig. 2.16 Location of the indicatrix axes X, Y, and Z of biaxial minerals in orthorhombic, monoclinic, and triclinic minerals with respect to the crystallographic axes. In orthorhombic minerals the three indicatrix axes coincide with the crystallographic axes but in no necessary order. In monoclinic minerals only one crystallographic axis, normally the b-axis, coincides with one indicatrix

axis and the others form an angle with the indicatrix axes, the extinction angle s, which is normally referenced as Z^c, X^a, or Y^b. In triclinic minerals no axis of the indicatrix coincides with any of the crystallographic axes (although there are exceptions). Crystals are drawn using the Smorf applet; (Holtkamp 2004–2019)

nx, the optical indicatrix is an oblate ellipsoid, like a mandarin, and the mineral is optically negative (Fig. 2.15c). The section perpendicular to the c-axis displays only the nx and the retardation is 0. The section parallel to the c-axis exhibits the vibration directions with their indices of refraction ne and nx and therefore shows maximum birefringence. The oblique section shows the x and e0 rays with nx and ne0 and where Dn may vary between close to the maximum or the minimum birefringence depending on the section.

crystallographic axes has implications for the optical behavior such as the extinction angle (see Sect. 5.1.5). In the orthorhombic system the vibration directions or the indicatrix axes X with na, Y with nb, and Z with nc are parallel to the crystallographic axes a, b or c, but not necessarily in that order, and six combinations exist to assign the indicatrix axes to crystallographic directions. These orthorhombic minerals will show straight or parallel extinction (see Sect. 5.2). In the monoclinic crystal system only one axis of the indicatrix coincides with a crystallographic axis, and in most cases the Y axis with nb is aligned with b, as in the amphibole group. The two other indicatrix axes are not oriented parallel to crystallographic axes and form oblique angles, called the extinction angle s which is also referred to as Z^c, X^a, or Y^b (see Sect. 5.2). In triclinic minerals, no axis or rarely one of the indicatrix axes coincides with a crystallographic axis; the indicatrix is inclined in two directions and many orientations are

2.5.3 Location of the Optical Indicatrix in Biaxial Minerals Biaxial minerals follow certain rules relating the optical indicatrix to the crystallographic axes (Fig. 2.16). The alignment of the indicatrix axes or vibration directions with respect to the

2.5 Location of the Optical Indicatrix with Reference …

possible. The orientation of the indicatrix axes within the crystal is shown in the crystal figure of the mineral plates in Chap. 9 and serves to explain the relationships with the crystallographic parameters. Examples of biaxial minerals of the orthorhombic, monoclinic, and triclinic crystal systems and their optical orientation with respect to the crystallographic directions are given in Figs. 2.17, 2.18, 2.19 and 2.20. In Fig. 2.17a the location of the biaxial positive indicatrix of the orthorhombic Mg-pyroxene enstatite is shown and in Fig. 2.17b the crystal morphology with optical and crystallographic orientations is illustrated as used in this book’s mineral plates. In enstatite the indicatrix axes X, Y, and Z with their corresponding refractive indices na, nb, and nc are parallel to the crystallographic axes b, a, and c, respectively. The acute bisectrix is Z with nc and the mineral is biaxial positive. The mineral has two distinct cleavages along the {210} prism forming an angle of 86° and two optic axes that lie in the plane (100) or XZ plane (Figs. 2.17a, b). In Fig. 2.17c the main sections are shown as observed under the microscope. In red the (001) section shows two prismatic cleavage directions and is cut perpendicular to the acute bisectrix Bxa; in yellow the (100) section is cut parallel to Z with nc and the c-axis, and with X with na visible. The cleavage parallel to (010) can be recognized. In green ((010) section) the mineral is cut parallel to Z with nc and the caxis and with Y with nb. The prismatic cleavage parallel to the (100) section and the c-axis is present. In Fig. 2.17d the location of these sections in the indicatrix is presented and the sections are labeled with their corresponding refractive indices and resulting birefringence. The sections perpendicular to the optic axis exhibit a birefringence of zero and remain extinct in cross-polarized light. In the (001) section or the section perpendicular to the Bxa the Y and X axes with the refractive indices nb and na are present and the birefringence is low. This section shows an interference figure (see Chap. 6) if 2V

25

is small (ca. < 28°). In the (100) section parallel to Z with nc and X with na birefringence is maximum or the diagnostic maximum birefringence. The section cut parallel to Z with nc and the c-axis and with Y with nb visible shows moderate birefringence. The location of the biaxial negative indicatrix of the orthorhombic olivine member fayalite is shown in Fig. 2.18a, and in Fig. 2.18b the crystal morphology with optical and crystallographic orientations as used in the mineral plates is illustrated. The indicatrix axes with their corresponding refractive indices are parallel to the crystallographic axes. The acute bisectrix Bxa is X with na, and the mineral is biaxial negative. The mineral has poor cleavage normally not well seen but does have cracks and fissures following no particular crystallographic directions. The identification of sections with respect to crystallographic and optical parameters (Fig. 2.18c) is only straightforward in euhedral crystals in volcanogenic rocks. In Fig. 2.18d the location of these sections in the indicatrix is shown and the sections are labeled with their corresponding refractive indices, resulting birefringence, and the location of the optic axes. In Fig. 2.19 the location of the biaxial negative indicatrix of the monoclinic clinoamphibole glaucophane is shown. Figure 2.19a illustrates the location of the two circular sections within the crystal, and in Fig. 2.19b the crystal morphology and its relationship with optical and crystallographic parameters is shown. Glaucophane has the typical perfect amphibole cleavage on {110} intersecting at about 124° and 56° in the section perpendicular to the [001] direction which is called the basal section (Fig. 2.19c). The two cleavage directions allow to locate the crystallographic axes. The indicatrix axis Y with nb is parallel to the crystallographic axis b. The two other indicatrix axes form an acute or obtuse angle with the crystallographic axes. The determination of this angle, the extinction angle, is used in amphibole and clinopyroxene identification and this is observed in cross-polarized light

26

2 Basic Concepts

(a)

(d)

(b)

2.6 Understanding How a Mineral is Cut in a Thin Section b Fig. 2.17 Optical indicatrix of the biaxial positive

mineral enstatite and its location with respect to crystallographic parameters. a location of the optical indicatrix in the crystal. Crystal is drawn using the Smorf applet (Holtkamp 2004-2019); b crystal morphology and relationship with optical and crystallographic parameters as

(see also Sect. 5.1). There are two sections with one good cleavage visible, which are the (100) and (010) sections. In Fig. 2.19c the main sections are shown as observed under the microscope. In red the section (100) shows the cleavage direction parallel to (010) and is cut perpendicular to the acute bisectrix Bxa. In yellow (the basal section (001)) the mineral is cut parallel to X' with na0 and the a-axis and to Y with nb and the b-axis visible, and in green (section (010)) the mineral is cut parallel to Z' with nc0 parallel to the c-axis and with X' and na0 parallel to the a-axis. This section is used for the determination of the extinction angle Z^c in clinoamphiboles. In Fig. 2.19d the location of these sections in the indicatrix is given and the sections are labeled with their corresponding refractive indices, resulting birefringence, and the location of the optic axes. In Fig. 2.20 the location of the biaxial negative indicatrix within the triclinic mineral kyanite is shown. Figure 2.20a illustrates the location of the two circular sections within the crystal, and in Fig. 2.20b the crystal morphology and the relationship to optical and crystallographic parameters as used in the mineral plates is given. The mineral has a perfect cleavage on (100) and a good cleavage on (010). In thin section, it is sometimes possible to identify the different cleavage directions and to observe that the (100) cleavage is better developed than that in the (010) direction. These two cleavage directions help to identify the location of the crystallographic and indicatrix axes. Indicatrix axis X is almost parallel to the crystallographic a-axis and the other indicatrix axes form angles of different sizes with the crystallographic axes. The indicatrix axis Z forms an angle between 27° and 32° with the crystallographic axis c, and the indicatrix axis Y displays an angle of about 30° with the crystallographic axis b. In Fig. 2.20c the main

27

used in the mineral plates; c the main crystal sections are shown as observed under the microscope with their corresponding refractive indices and their relationship to crystal morphology; d location of principal sections in the biaxial indicatrix and their corresponding refractive indices and birefringence

sections are shown as observed under the microscope. In red the mineral is cut perpendicular to the acute bisectrix Bxa, and this (100) section shows the cleavage parallel to (010). In yellow (section (001)) the mineral is cut parallel the crystallographic a- and b-axis. The indicatrix axis X with na is parallel to the a-axis but Y with nb is not related to a crystallographic direction. In green (section (010)) the mineral is cut parallel to the c-axis with nc0 as well as with X with na almost parallel to the crystallographic a-axis. In Fig. 2.20d the location of these sections in the indicatrix is shown and the sections are labeled with their corresponding refractive indices, resulting birefringence, and the location of the optic axes. A summary of the main optical parameters for isotropic, uniaxial, and biaxial minerals is given in Tables 2.1 and 2.2. It also includes the terminology used by French and German mineralogists. Since most of the literature uses the terminology ne and nx for uniaxial minerals and na, nb, and nc for biaxial minerals as adopted by American and English mineralogists they are used in this book. However, the terminology of Tröger [10, 11] also adapted by Raith et al. [6] is straightforward since the refractive index nz is along the indicatrix axis Z, nY along the indicatrix axis Y, and nX along the indicatrix axis X. It is not obvious to get the terminology right and I would like to quote Genge [7]: “Terminology so often throws a banana skin under the feet of understanding”.

2.6

Understanding How a Mineral is Cut in a Thin Section

In a thin section, the minerals are cut in different optical or crystallographic orientations, and you see different sections with many different

28

2 Basic Concepts

(a)

(b)

(d)

Fig. 2.18 Optical indicatrix of the biaxial negative orthorhombic mineral fayalite and its location with respect to crystallographic parameters. a location of the optical indicatrix in the crystal. Crystal is drawn using the Smorf applet (Holtkamp 2004–2019); b crystal morphology and relationship with optical and crystallographic parameters

as used in the mineral plates; c the main crystal sections are shown as observed under the microscope. Note that olivine has no cleavage but characteristic curved cracks; d location of principal sections in the biaxial indicatrix and the sections with their corresponding refractive indices and birefringence

2.6 Understanding How a Mineral is Cut in a Thin Section

29

Fig. 2.19 Optical indicatrix of the biaxial negative monoclinic clinoamphibole glaucophane and its location with respect to crystallographic directions. a location of the optical indicatrix in the crystal and location of the two circular sections with nb in blue. The optical axes emerge from the paper plane. Crystal is drawn using the Smorf applet (Holtkamp 2004–2019); b crystal morphology and relationship with optical and crystallographic parameters as used in the mineral plates; c principal crystal sections to determine optical parameters and their relation to crystallographic directions; d location of main sections in the biaxial indicatrix and the sections with their corresponding refractive indices and birefringence

(b)

(a)

(c)

(d)

interference colors. It is important to filter this voluminous amount of information. One must scan to locate the most suitable sections for the determination of the optical properties. This is illustrated by a series of fruit sections (Fig. 2.21). The orange (1) and the grapefruit

(2) are very round and resemble a sphere and are analogues of isotropic optical properties. The mandarin (3) has an oblate form and is flattened in one direction and the lemon (4) has a prolate form and is flattened perpendicular to the axis of rotation. They are like uniaxial minerals. The

30

2 Basic Concepts

(a)

(b)

(c)

(d)

2.6 Understanding How a Mineral is Cut in a Thin Section b Fig. 2.20 Optical indicatrix of the biaxial negative

triclinic kyanite and its location with respect to crystallographic directions. a location of the optical indicatrix in the crystal and the two circular sections with nb in blue. The optical axes emerge from the paper plane. Crystal is drawn using the Smorf applet (Holtkamp 2004–2019); b crystal morphology and relationship with optical and

31

crystallographic parameters as used in the mineral plates; c main crystal sections showing optical directions and their relation to crystallographic and cleavage directions; d location of main sections in the biaxial indicatrix and the sections with their corresponding refractive indices and birefringence

Table 2.1 Summary table with optical parameters for isotropic, uniaxial, and biaxial minerals including different terms used for the description of the optical indicatrix. The symbol g stands for French “grand” (big), m for “moyen” (middle), and p for “petit” (small) Characteristics of the optical indicatrix

Isotropic

Uniaxial

Biaxial

Optical indicatrix

Sphere

Ellipsoid ne is rotation axis: ne > nx, positive U+ “lemon” nx is rotation axis: ne < nx, negative U− “mandarin”

Triaxial ellipsoid na and nc are the two rotation axes; nb lies in two circular sections; Positive B+ “kiwi” Bxa is Z with nc, Bxo is X with na Negative B− “kiwi” Bxa is X with na, Bxo is Z with nc

Indices of refraction

n

ne, nx; ne′ between ne and nx nX, nZ (Tröger terminology) ne, no; np, ng (French terminology)

na, nb, nc; na < na0 < nb < nc0 < nc; nX, nY, nZ; nX < nY < nZ (Tröger terminology) np, nm, ng; np < nm < ng (French terminology)

Number of vibration directions or indicatrix axes with refractive indices



2:Z, X; E, O

3:X, Y, Z

Number of circular sections

All sections

1

2

Number of optic axes



1

2

Optic angle 2V, 2VZ, 2VX





The angle between the optic axes or the angles between the normal to the circular sections 2VZ is the optic angle measured over Z and between 0° and 90°, and 2VX is the optic angle measured over X and between 0° and 90° (continued)

32

2 Basic Concepts

Table 2.1 (continued) Characteristics of the optical indicatrix

Isotropic

Uniaxial

Biaxial

Optic axis



Light propagates perpendicular to the circular section, is not polarized and travels with one velocity

Light propagates perpendicular to the circular sections, is not polarized and travels with one velocity

Orientation of indicatrix axes with respect to crystallographic directions

Parallel to crystallographic axes

Z parallel to the crystallographic c-axis; X perpendicular to Z

Orthorhombic system: The indicatrix axes are parallel to the crystallographic axes in any order Monoclinic system: Y with nb lies parallel to one crystallographic axis, others do not Triclinic system: No crystallographic axis is parallel to any indicatrix axis (rare exceptions)

Crystal system

Isometric

Tetragonal, hexagonal, trigonal

Orthorhombic, monoclinic, triclinic

Table 2.2 Terminology used in optical mineralogy which varies according to the author. For example, five expressions are used to describe the same optical devise, the k-plate. (“Terminology so often throws a banana skin under the feet of understanding” [7]) Term

Short definition

a, b, c a1, a2, a3, c

Crystallographic axes according to terminology used in the different crystallographic systems

Accessory plate, retardation plate, compensator plate

An accessory plate introduces a fixed amount of retardation; common accessory plates are the k-plate or the ¼ k-plate

Analyzer (of the microscope)

Upper polarizer vibrating at 90° to the polarizer. It forces the rays emerging from the crystal to vibrate into one plane and recombines all wavelengths which results in the interference color

B+

Optic sign; biaxial positive B+ ; Bxa is Z with nc, Bxo is X with na

B−

Optic sign; biaxial negative B−, Bxa is X with na, Bxo with Z with nc

Birefringence d=Dn = nslow−nfast, nc−na

Birefringence d or Dn or difference between the refractive indices of the slow and the fast rays

Bxa

The acute bisectrix is a line that bisects the acute angle between the optic axes in biaxial minerals and is a vibration direction in the optic plane. It is the reference for the optical character

Bxo

The obtuse bisectrix is a line that bisects the obtuse angle between the optic axes. Acute and obtuse bisectrix form an angle of 90° (continued)

2.6 Understanding How a Mineral is Cut in a Thin Section

33

Table 2.2 (continued) Term

Short definition

d

Thickness of a crystal expressed in mm or lm

Elongation l− or l+

Determination which ray vibrates along the c-axis in elongated minerals: if the slow ray is along the c-axis, the mineral has a positive elongation and is l+; if the fast ray is along the c-axis the mineral has a negative elongation and is l−

Indicatrix axis X, Y, Z

Indicatrix axes are vibration directions along which the vector of the corresponding refractive index is aligned

Interference figure

An interference figure is the projection of the Dn of two rays on a 2D surface plane in the Amici-Bertrand lens as a function of the rays arriving with different retardations as imposed by the lower condenser. An interference figure allows to determine the optical character of a mineral. Best-suited interference figures are obtained in sections perpendicular to the optic axis in uniaxial minerals and perpendicular to one of the optic axes in biaxial minerals, as well as perpendicular to the Bxa

k (nm)

Wavelength of a ray, often 536 nm is used as an average value for light. Visible spectrum is between 390 nm (violet) and 770 nm (red)

k-plate = gypsum plate = wave plate = 1st red compensator = sensitive tint plate

The k-plate is an accessory plate, has a retardation between 530 and 570 nm, and is introduced at an angle of 45° to the N-S direction of the microscope. The values slightly change according to the microscope manufacturer. Nikon gives a value of 530 nm

¼ k-plate = mica plate

The ¼ k-plate or mica plate is an accessory plate, introduces a retardation between 137 and 150 nm, and is introduced at an angle of 45° to the N-S direction of the microscope. Nikon gives a value of 147 nm

Melatope

Emergence of an optic axis in an interference figure

n

Refractive index of isometric minerals

ne, nx, ne0

Refractive indices of uniaxial minerals

na, nb, nc, na0 , nc0

Refractive indices of biaxial minerals

Optic angle 2V

The angle between the two optic axes in a biaxial mineral. 2VX (negative) or 2VZ (positive), 2Vx + 2VZ = 180°

Optic axis (OA)

An optic axis is the direction perpendicular to a circular section of the indicatrix which has a radius of either nx for uniaxial minerals or nb for biaxial minerals. Light along the optic axis is not polarized and there is no change of vibration direction

Optic plane (OP) = optic axial plane = (OAP)

Plane containing the two optic axes which are perpendicular to the two circular sections or the XZ plane or the ac plane

Optic normal (ON)

The optic normal in biaxial minerals is the vibration direction (indicatrix axis) perpendicular to the optic plane XZ, which is Y

Optic sign

Biaxial positive (B+) if Bxa is Z with nc; biaxial negative (B−) if Bxa is X with na

Polarizer (of the microscope)

Lower polarizer vibrating at 90° to the analyzer and transforms the light from the source into plane polarized light

Optical indicatrix

The 3D projection of the vector of the refractive indices along the vibration direction starting from a central point, having one axis for a sphere (isotropic), having two 2 axes in an ellipsoid (uniaxial mineral) or three axes in a triaxial ellipsoid (biaxial mineral)

Retardation C

The difference between a slow and a fast ray as a function of thickness and expressed in nanometer (nm)

U+

Uniaxial positive, ne>nx

U−

Uniaxial negative, ne nx). Try to find the circular section for the kiwi! It is less obvious to find the circular sections.

5b

Fig. 2.21 Thin section of fruits documenting the different types of sections and their optical characters. Fruits similar to isotropic minerals: orange (1) and grapefruit (2); fruits similar to anisotropic minerals: uniaxial negative: mandarin (3); uniaxial positive: lemon (4); biaxial: kiwi (5)

kiwi is a “biaxial fruit” with three axes in order to describe the triaxial ellipsoid. We can cut these fruits in different ways: We cut the orange or the grapefruit by the center of the fruit (1a or 2a) and we always obtain a circular section with a single radius in all directions. These fruits resemble isotropic minerals with only one index of refraction. Polarized light—vibrating N−S or E−W—passing through the crystal does not change speed or direction and will be stopped by the analyzer which vibrates at 90° to the first polarizer, and the mineral will stay extinct. For the mandarin (3), lemon (4), and kiwi (5) we have more choices. We can cut the mandarin or the lemon perpendicular to the long or short axis of rotation and we will have a circular section (3a, 4a). We can cut the lemon or the mandarin parallel to the axis of rotation in the way that we obtain a section with a maximum surface with

References and Suggested Further References 1. Bloss FD (1999) Optical crystallography. Mineralogical Society of America, p 239 2. Kerr PF (1977) Optical mineralogy, 4th edn, McGrawHill Book Company, p 492 3. Nesse WD (2013) Introduction to optical mineralogy, 4th edn, Oxford University Press, p 361 4. Stoiber RE, Morse SA (1994) Crystal identification with the polarizing microscope. Springer-Science + Business Media Dordrecht. Originally published by Chapman & Hall, p 358 5. Verma PK (2010) Optical Mineralogy. Taylor & Francis, Ane Books Pvt. Ltd, p 367 6. Raith MM, Raase P, Reinhard J (2012) Guide to thin section microscopy, 2nd edn, 127 p. ISBN 978-3-00037671-9 (PDF) 7. Genge M (2011) Optical mineralogy: new colour in a dying art. The Geologists’ Association & The Geological Society of London, Geology Today, 27/3 8. Holtkamp M (2004–2019) Smorf Crystal Models. www.smorf.nl 9. Phillips WR (1981) Optical mineralogy: the nonopaque minerals. WH Freeman San Francisco 10. Tröger WE (1971) Optische Bestimmung der gesteinsbildenden Minerale. Teil 2 Textband. E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, p 822 11. Tröger WE (1979) Optical determination of rockforming minerals. E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, p 188 12. Wahlstrom EE (1951) Optical Crystallography. John Wiley & Sons, London, p 247 13. Wahlstrom EE (1979) Optical Crystallography. 5th edition, John Wiley & Sons, New York, p 488.

Further Reading

Further Reading 1. Demange M (2012) Mineralogy for petrologists. CRC Press Taylor & Francis Group, p 182 2. Dyar MD, Gunter ME, Tasa D (2008) Mineralogy and optical mineralogy. Mineralogical Society of America, Chantilly, VA, p 708 3. Ehlers EG (1987) Optical mineralogy. theories and techniques/mineral descriptions, 2 Vols. Blackwell Scientific publications

35 4. Pichler H, Schmitt-Riegraff C (1987) Gesteinsbildende Minerale im Dünnschliff. Enke, Stuttgart, p 288 5. Pichler H, Schmitt-Riegraff C (1997) Rock forming minerals in thin section. Chapman & Hall, p 220 6. Wenk H-R, Bulakh A (2016) Minerals. Cambridge University Press, p 640

3

The Petrographic Microscope: A Polarized Light Microscope

The petrographic microscope is a specialized microscope which uses plane polarized light. It has the usual components of a microscope and is additionally equipped with a smoothly rotating circular stage with a graduation of 360° or a stage goniometer and additional devices to understand the behavior of light in minerals in a thin section (Figs. 3.1 and 3.2). Light is plane polarized by a first polarizer, called the polarizer, and enters the mineral from below. Because of the atomic structure of anisotropic minerals, it is split into two rays, the ordinary and extraordinary rays, vibrating at an angle of 90° to each other (Fig. 3.1). The second polarizer, called the analyzer and located below the oculars, recombines the two waves emitted from the mineral, allowing an understanding of the optical orientation and parameters with respect to the mineral's crystallographic parameters. A mineral's optical parameters are diagnostic and allow the identification of the mineral. The petrographic microscope consists of a microscope body, a substage assembly, and an upperstage assembly. The illuminator of the microscope is located in the base of the microscope body (Figs. 3.1 and 3.2). Knobs for coarse and fine focus on both sides of the body enable focusing the specimen. The substage assembly includes the field diaphragm, the polarizer transforming the light from the light source into plane polarized light, the aperture diaphragm, and the condenser. The polarizer may rotate either N-S or E-W, depending on the microscope

model. An aperture diaphragm and a condenser lens, which in some microscopes can swing in and out, are located beneath the circular stage. The circular rotating stage or rotating goniometer stage with a graduation of 360° allows the measurement of angles. A mechanical stage on top of the rotating stage enables a user to displace a thin section in small lateral steps in both the horizontal x and y directions while looking simultaneously through the microscope. Above the stage the rotating revolver with the objective lenses is located. Most modern microscopes are equipped with up to five different objective lenses for working in air, with the most common magnifications being 4x, 10x, 20x, 50x, 63x, or 100x. For special applications, such as reflected polarized light microscopy, oil immersion objective lenses are also used. Above the objective revolver the upperstage assembly hosts the second polarizer, called the analyzer, the Bertrand lens or Amici-Bertrand lens, a slot mounted at 45° with respect to the analyzer in order to slide in accessory plates and the oculars allowing further magnification, normally 10x (Figs. 3.1 and 3.2). A camera connected to a computer with the appropriate software can be attached to the tube. At the Department of Earth Sciences in Geneva (Switzerland), the microscopic room is equipped with twenty-one workstations that consist each of a Nikon binocular SMZ-745 T and a Nikon eclipse Ci Pol microscope with a linked camera and computer (Fig. 3.3).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. T. Schmidt, Transmitted Light Microscopy of Rock-Forming Minerals, Springer Textbooks in Earth Sciences, Geography and Environment, https://doi.org/10.1007/978-3-031-19612-6_3

37

38

3 The Petrographic Microscope: A Polarized Light Microscope

Fig. 3.1 Nikon eclipse Ci Pol microscope with illumination device for transmitted and reflected light (black lamp house) and the path of light. See text for explanation. With permission of Nikon

Fig. 3.2 Main units of a petrographic microscope (Nikon eclipse Ci Pol) using plane polarized light are the substage assembly, the rotating circular stage, the revolver with the objective lenses, and the upperstage assembly. Modified and with permission of Nikon

Appropriate software and a high-resolution projector allow projection from any workstation onto a central screen which enables an effective, student–teacher interaction. This makes teaching optical mineralogy, rock petrology, ore microscopy, and paleontology highly effective and which is enjoyed by students and teachers.

3.1

Substage Assembly

The main components of the substage assembly are the light source, the polarizer transforming the light into plane polarized light, the aperture diaphragm, and the condenser lens which may

3.2 Upperstage Assembly

39

Fig. 3.3 Microscope laboratory at the Department of Earth Sciences at the University of Geneva with 21 interconnected workstations, each equipped with a Nikon eclipse Ci Pol microscope for transmitted and reflected

light, a Nikon binocular SMZ-745 T, a camera, and a computer. This allows projection from each workstation onto a central screen or on all workstations

swing in or out in some microscopes. Some models have holders for filters to swing in, such as a blue daylight filter to correct the artificial light into sunlight or a green filter for black and white photography. The polarizer (see also Chap. 2 and Fig. 2.6) is made of a polarizing film and mounted into a ring which can often be rotated up to 360° and allows light rays to vibrate either N-S (Leitz) or E-W (Nikon and Olympus) directions. Today a polarizing filter (Fig. 3.4a) is made from polyvinyl alcohol plastic (PVA), a water-soluble synthetic polymer. It has the idealized formula [CH2CH(OH)]n. Sheets of PVA contain polymer chains or chain molecules which are stretched and aligned in parallel during the manufacturing process. Valence electrons from an iodine dopant are able to move linearly along the polymer chains, but not transverse to them. Light rays vibrating parallel to the long polymer chains will interact and be absorbed, whereas light rays vibrating perpendicular to the polymer chains will pass the filter and be transmitted as plane polarized light vibrating N-S. Older microscopes use the birefringent property of minerals to produce plane polarized light. The best known is the Nicol Prism (Fig. 3.4b) which consists of a crystal of calcite which has been cut along the crystallographic c-axis with the pieces remounted using Canada balsam. Light enters from the left and is split into the x and e rays vibrating at an angle of 90°. The

ordinary x ray (nx = 1.658) has a higher refractive index than Canada balsam (nCB = 1.53) and is therefore totally reflected at the interface of the cut crystal. The extraordinary e ray (ne = 1.486) with the smaller refractive index is transmitted through the interface without deflection, and plane polarized light will leave the crystal. The aperture diaphragm changes the size of the incoming cone of light. Closing the aperture diaphragm will decrease the light and enhance the contrast of the image. The use of the aperture diaphragm improves observation of the relief of a mineral and the visibility of the fine dark lines of the traces of cleavage planes in a mineral grain (see Sect. 4.4). The condenser lens (Fig. 3.5) is mounted directly below the rotating stage and may be either fixed or swing in and out in the optical path. It produces a cone of light rays (see also Fig. 6.1) and is a special device to produce interference figures with high magnifications. Some microscopes have a twofold Abbey condenser which allows the use of objective lenses, both, low and high magnification.

3.2

Upperstage Assembly

The main components of the upperstage assembly include the ocular, the Bertrand or AmiciBertrand lens, the analyzer and the auxiliary slot

40

3 The Petrographic Microscope: A Polarized Light Microscope

Fig. 3.4 Producing plane polarized light (see also Chap. 2). a Modern polarization filters are composed of polymers. The light passed through the polarizer will be plane polarized light and vibrates N-S; b Nicol Prism using the

effect of the critical angle to produce plane polarized light by total reflection of the x ray of a cut and glued calcite crystal. The emerging e ray is plane polarized. See explanation in text

in crosspolarized light or under crossed Nicols or abbreviated as XPL. If working only with the lower polarizer and the analyzer is removed out of the optical path, our observations are performed under parallel Nicols or in plane polarized light or abbreviated as PPL. In routine microscopic observation the analyzer is always aligned at 90° to the polarizer.

3.3 Fig. 3.5 Location of swing in and out condenser. With permission of Nikon

positioned at 45° to the analyzer (Figs. 3.1 and 3.2). The Bertrand lens or Amici-Bertrand lens (Fig. 3.2) is located below the ocular and can be mounted in the optical path to make interference figures visible (Chap. 6). An iris diaphragm is built into some microscopes in order to allow the restriction of the field of view. The auxiliary slot positioned at 45° to the analyzer allows the insertion of accessory plates or compensator plates (Fig. 3.2). Oculars allow the magnification of the image from the objective lens (Fig. 3.2). Often one ocular contains a hair cross and/or a micrometer scale to allow measurement of the size of grains (see calibration under Sect. 3.6.4). The analyzer (upper polarizer) is located below the oculars and can be slid in or out. In routine analysis, the analyzer vibrates at an angle of 90° in relation to the lower polarizer, and the vibration directions must be perfectly aligned at 90° to each other. If the analyzer is in the optical light path, observations are said to be carried out

Circular Rotating Microscopic Stage and Objective Lens Revolver

The smoothly rotating circular stage with graduations of 360° or the stage goniometer is an important device for the determination of the optical properties of minerals (Fig. 3.6). It allows rotation of a mineral which enables the observer to understand its optical parameters with respect to its crystallographic orientation and the polarizers. An attachable mechanical stage on top of the rotating stage allows moving the position of the mineral under observation in x and y directions (Fig. 3.6b). Alternatively, two cranks allow holding the thin section in place (Fig. 3.6a). Angles between cleavage planes can be measured and extinction angles determined using the 360° graduation of the circular stage. The rotating objective lens revolver hosts the objective lenses (Fig. 3.6a). Objective lenses are normally aligned by turning clockwise from one to the next objective lens position thereby increasing the magnification. The magnification, numerical aperture, correction length of the microscope tube (normally 170 mm in older

3.4 Objective Lenses

41

microscopes) or infinity in modern ones, and thickness of the cover slip of the thin section used (0.17 mm, standard in the preparation of thin section) are also written on the objective lens itself. Additionally, objective lenses are often marked with a color ring corresponding to a magnification (Fig. 3.6a).

3.4

Objective Lenses

A microscopic image from an objective lens does not project a point as a bright spot with defined contours, but as the accumulation of the so-called Airy pattern composed of a slightly blurred spot in the center which contains approximately 84% of the luminous energy and is surrounded by the Airy disk (Fig. 3.7). This phenomenon is caused by diffraction or scattering of the light as it travels through the crystalline materiel. An important parameter observing textures under the microscope is the resolution (d) which is defined as the smallest distance between two points that can still be distinguished (Fig. 3.7). The resolution of a lens is calculated by k ð3:1Þ 2NA where k is the wavelength of light and NA the numerical aperture. The numerical aperture defines the resolving power of an objective lens. It is defined as d¼

Fig. 3.6 a Circular rotating stage and objective revolver with corresponding color rings and optical parameters of the Nikon eclipse Ci Pol microscope; b mechanical stage

Fig. 3.7 Airy pattern a and Airy disk b. Two Airy pattern profiles are superimposed and create a valley between their maxima. In the valley the intensity of light is reduced by approximately 16% and allows observation of two separate points as expressed in the resolution d

NA ¼ n sin

AA 2

ð3:2Þ

where n is the index of refraction which is 1 for air between the objective lens and the thin section and AA is the angular aperture which is the angle of the cone of light collected by the objective and determined by the focal length of the objective. It is obvious from the equation that increasing the refractive index by using oil (refractive index = 1.515) increases the numerical aperture. In Fig. 3.8 the angular aperture and numerical aperture for three objective lenses are given. The resolution is a value that can be derived theoretically and depends on the wavelength as given in Table 3.1. Lateral resolution is generally

which can be mounted on the goniometer stage allowing x–y displacement. With permission of Nikon

42

3 The Petrographic Microscope: A Polarized Light Microscope

Fig. 3.8 Angular aperture and numerical aperture for three objectives. The numerical aperture increases with increasing angular aperture and therefore the resolution increases

better than vertical resolution. Observing the limit of resolution is subjective in certain ways, since an image may appear unsharp, but may still be resolved by the viewer. Other factors influencing the resolution are the numerical aperture of the substage condenser, the illumination, and partial closure of the diaphragm aperture. The larger the angular aperture, the higher the numerical aperture and therefore a better resolution is achieved.

3.5

Accessory Plates (Retardation Plates, Compensator Plates)

The upperstage assembly of a polarized light microscope houses a slot mounted at 45° with respect to the analyzer in order to slide in an accessory plate. An accessory plate or retardation plate or compensator plate is an optically transparent materiel which resolves a light ray

Table 3.1 Resolution (lateral) of achromatic objective lenses (Nikon) for a wavelength of 550 nm and 380 nm calculated with the NA (numerical aperture) as engraved on the objective lens Objective lens

NA

Resolution in (lm) for 550 nm

Resolution in (lm) for 380 nm

4

0.1

2.75

1.9

 10

0.25

1.10

0.76

 20

0.4

0.69

0.48

 40

0.65

0.42

0.29

 50

0.8

0.34

0.24

 60

0.75

0.37

0.25

 100

0.9

0.31

0.21

 50 oil

0.9

0.31

0.21

 100 oil

1.25

0.22

0.15

3.6 Adjustment of the Microscope

43

(a)

(b)

(c)

(d)

Fig. 3.9 Accessory plates: a A Nikon accessory plate combining k-plate and 1\4 k-plate routinely used in microscopic examination. The middle position is empty and used during standard examination; b schematic sketch of vibration directions of the Leitz accessory k-plate with respect to the vibration directions of the polarizers as positioned in the 45° slot in the upperstage assembly; note

that the slow ray is indexed as c which is used in this book; c quartz wedge with a continuous increase of retardation up to the 6k or ca. 3000 nm; d color induced by accessory plates. The left image is isotropic in XPL; the middle magenta image is produced by the addition of 550 nm or the k-plate; the right image, a gray of first order, results from the insertion of the 1\4 k-plate or 137 nm

into two components vibrating at 90° to each other and recombines them into a new ray with new characteristics (Fig. 3.9). Since their optical orientation is known and by superposing them in the optical light path, they allow determination of the vibration direction of the light rays passing through the mineral under investigation. The vibration directions of the fast (x’ or a or smaller refractive index) and the slow rays (z’ or c or higher refractive index) and the retardation in nm or wavelength k are indicated on the accessory plate (Fig. 3.9). If the accessory plate is inserted, the slow ray c or z’ vibrates NE-SW or at 45° and the fast ray a or x’ NW–SE. It is the slow ray c or z’ which serves as reference for the mineral investigation. The most common auxiliary plate is the kplate, also called the gypsum plate, first-order red plate or sensitive tint plate (Figs. 3.9a, b and Table 2.2), where an anisotropic quartz crystal is mounted with a slow ray and a fast ray cut parallel to the optic axis. It has a thickness of 62 lm and produces a retardation of k or ca. 530 nm (values between 530 nm and 570 nm are used) equivalent to the red of the first order (the first-order red) (Fig. 3.9d). The ¼ k-plate, also called mica plate (Fig. 3.9a) since it was originally produced from mica, introduces a retardation of ca. 147 nm (values between 137 and 150 nm are given in the literature) which results in the gray of the first

order (Fig. 3.9d). Not used in routine analysis is the quartz wedge which is a piece of quartz cut into wedge showing a continuous increase of retardation up to the 6k or ca. 3000 nm (Fig. 3.9c).

3.6

Adjustment of the Microscope

A microscope is a high-quality instrument and if properly aligned and carefully handled does not need much maintenance. Nevertheless, the routines below help to check the correct alignment of the microscope. The most important adjustments are explained with details and how to manipulate the microscope. Most important is to gain experience by actually using a microscope.

3.6.1 Checking the Orientation of the Polarizer and the Correct Alignment of the Analyzer The direction of the vibration of the polarizer can be easily determined using a pleochroic mineral in PPL (Fig. 3.10). The polarizer vibrates either N-S (Leitz) or E-W (Nikon and Olympus), and its orientation can be checked by using

44

3 The Petrographic Microscope: A Polarized Light Microscope

pleochroic biotite (Fig. 3.10). Biotite shows maximum absorption or a strong brown color when a section with the prominent (010) cleavage plane is aligned parallel to the vibration direction of the polarizer. Biotite will be lightest in color when aligned at 90° to this direction. During routine microscopic observations in XPL, the analyzer is aligned at 90° to the polarizer. Most microscopes allow changing the vibration direction of the analyzer on a rotating dial (Fig. 3.11). In microscopic examination, it often happens that the knob securing the analyzer is unscrewed accidentally and the polarizers are no longer perfectly aligned, leading to surprising and erroneous results. It is therefore important to regularly check for the correct alignment of the polarizers and verify that the clamp screw is tight. It is best to check the correct alignment by observing a mineral with a parallel extinction and a prismatic habit such as apatite (Fig. 3.10c), zircon, or tourmaline. You can check that the polarizers are crossed by using the glass slide at the border of the section or garnet which are both isotropic and remain extinct when the circular stage is rotated. This check can also be made with quartz by turning the analyzer and simultaneously finding the lightest and darkest extinction position.

(a)

3.6.2 Adjustment of the Oculars With binocular oculars, you should see one image. If it is not the case (Fig. 3.12a), adjust first the interpupillary distance or distance between your two eyes or the two oculars until the fields of view for the right and left eyes coincide (Fig. 3.12b). Focus your eyes as if you were looking at a distant object. Observe with the left eye and adjust the left ocular by focusing the crosshair with the left ocular knob (Fig. 3.11a). Now focus the specimen with the coarse/fine focus knobs. Now observe with the right eye only and focus with the right ocular knob. You should see one image simultaneously, and the crosshair and the image should both be in focus. (Fig. 3.12b). Use two hands to carefully move oculars (Fig. 3.12c).

3.6.3 Centering the Objective Lenses During a 360° rotation of the circular stage, an object positioned in the center of the crosshair should stay stationary and not depart from its position. If it leaves the center of the crosshair during rotation, the objective lens is not centered. Apply the following steps to center the objective

(c)

(b) A P

Fig. 3.10 a and b: Determination of the vibration direction of the polarizer in PPL using pleochroic biotite for different vibration directions of the polarizer. a The vibration direction of the polarizer is E-W; b the vibration direction is N-S. At 90° to the vibration direction, the

biotite is brightest. c Correct alignment of both polarizers in XPL. A hexagonal uniaxial prismatic crystal of apatite is in parallel extinction position if the c-axis is aligned N-S or E-W. Direction of vibration of polarizers (A and P) is shown by the orange arrows

3.6 Adjustment of the Microscope

(a) Fig. 3.11 a The rotating analyzer should be set at 0° in order to be aligned at 90° to the polarizer located in the substage assembly. The screw can get loose and needs checking from time to time; with permission of Nikon;

45

(b)

(c)

b anisotropic quartz (XPL) showing different orientations and extinction positions; c isotropic garnet (XPL) indicating that the two polarizers are well aligned at 90°

c

(a)

(b)

(c)

Fig. 3.12 Adjust the interpupillary distance by moving the oculars so that they fit your eyes. a The image is seen in every ocular; b one image is seen after adjustment;

c use two hands to carefully move the oculars. With permission of Nikon

Fig. 3.13 Centering the objective lens. A Put a marker in the center of the crosshair. If it moves away from the center of the crosshair while rotating the stage clockwise as shown in b, use the two screws of the objective lens to displace the marker halfway of the distance A-B indicated by the blue arrow; c position the marker again in the

center d using the x–y displacement as shown by the green arrow and repeat the process until the grain stays in the center during the rotation of the circular stage. e Position of the holes for the screws for centering the objective lens. With permission of Nikon

lens. This centering procedure must be carried 1) Align a distinct marker, such an opaque or colored mineral, as a reference grain in the out for each objective lens (Fig. 3.13) and may center of the crosshair (Fig. 3.13a). have to be repeated several times.

46

3 The Petrographic Microscope: A Polarized Light Microscope

2) Rotate the grain to find the most distant location with respect to the crosshair. Draw in your head a line between the displaced marker and center of crosshair and cut the distance in half (Fig. 3.13b). 3) Insert the two fine centering screws in the objective lens. The centering screws allow the x–y displacement of the grain, and very little movement of the screws is necessary. Move the grain halfway back to the center of the crosshair as shown with the blue arrow (Fig. 3.13c). 4) Bring your reference grain back to the center of the crosshair with the x–y mechanical stage or manually as shown with the green arrow (Fig. 3.13d) and repeat the centering process as many times as necessary, until the grain stays in the center during a 360° rotation.

mounted in a thin section which normally has a length of 1 mm or 1000 lm and a graduation of 10 lm. Apply the following routine. Place an objective micrometer with a known length, normally 1000 lm on the rotating stage as if it was a specimen and compare the scalars of the two micrometers (Fig. 3.14a). Depending on the size of the magnification, you see the full object micrometer (low magnification) or only a portion of it (high magnification). Find a suitable distance with overlapping bars of the two micrometers and determine the distance. In the case shown four major units would be 32 lm and one division of the ocular micrometer would be 6 lm. The dimensions of crystals can now be measured (Fig. 3.14b).

3.6.5 Adjustment of the Aperture Diaphragm 3.6.4 Calibrating the Ocular Micrometer One ocular is normally equipped with a crosshair, while the other one might have an ocular micrometer; this will have equidistant divisions, but the spacing of them is not known and depends on the magnification of the objective lens. The micrometer scale in the ocular is calibrated using an object micrometer or a scale

Fig. 3.14 Calibrating the distance of an ocular micrometer by using an object micrometer of known distance and a high magnification. a The distance indicated by the red arrow is the known distance from the object micrometer.

The aperture diaphragm adjusts the illumination and hence controls the brightness, the contrast, and the focal depth of the image. It is located above the condenser and manipulated with a ring, allowing opening or closing of the diaphragm (Fig. 3.15). For ordinary use it should be set to 70% to 80% of the objective used. Closing the aperture diaphragm reduces resolution and brightness but increases the contrast and the depth of focus. Working with a slightly closed or

The dimensions determined for the ocular micrometer are given in blue; b example of measuring the width of a crystal

3.6 Adjustment of the Microscope

47

Fig. 3.15 a Location of the aperture diaphragm (with permission of Nikon), b setting the aperture diaphragm at ca. 80%

closed aperture diaphragm is often done when (3) Use a 40  magnification. If the aperture diaphragm is out of focus, adjust it with the determining the relief or looking for cleavage condenser focus knobs (z direction). planes or fine textures. (4) Adjust field diaphragm size so that it has almost the same size as the field of view 3.6.6 Focusing and Centering (Fig. 3.16c).

the Condenser The condenser and the field diaphragm should be aligned. (1) Swing in the condenser or move the substage assembly as close as possible to the rotating stage. (2) Start with a 10  magnification and close the field diaphragm and check its position (Fig. 3.16a). If it is not centered, move the condenser with the condenser centering screws (x–y direction) until it is at the center of the field of view (Fig. 3.16b).

Fig. 3.16 Adjustment of the condenser lens and position of the condenser centering screws. a-b At magnification of 10x, close the aperture diaphragm. If it is off-centered, move the condenser with the condenser centering screws (x–y direction) until it is at the center of the field of view;

3.6.7 Adjustment of the Field Diaphragm The field diaphragm is used to restrict the illumination of the observed area and should be set up to illuminate almost the total area of the observation field of view (Fig. 3.17). By closing the field diaphragm, the image contrast and depth of field are increased. Working with a slightly closed or closed field diaphragm is often done

c at a magnification of 40  focus the aperture diaphragm with the condenser focus knobs (z direction) and adjust the field diaphragm to the size of the field of view; d position of condenser centering screws. With permission of Nikon

48

3 The Petrographic Microscope: A Polarized Light Microscope

Fig. 3.17 Adjustment of the field diaphragm which should circumscribe the field of view

(Abies fraser), the Colorado fir (Abies concolo), the douglas fir (Pseudotsuga menziesii), and the Canadian or Eastern hemlock (Tsuga canadensis).

Fig. 3.18 Thin section and a schematic cross section through a thin section

when determining fine textures. Opening the field diaphragm increases the aperture of illumination and leads to a loss of image contrast.

3.7

The Object of Study: The Thin Section

In order to study a rock under the microscope, a rock slab of 2 to 3 cm thickness is glued on a glass slide (1 mm or 1500 lm thick) and polished down to 30 lm (Fig. 3.18). In routine microscopic analysis this rock is covered by a thin glass slide with a thickness of 0.17 mm and glued with Canada balsam, the natural oleoresin of Abies balsamea, the balsam fir growing in the boreal forest of North America. It has a refractive index nCB between 1.538–1.542. Other firs delivering the Canada balsam are the Fraser fir

3.8

Illumination and Comfort While Working at the Microscope

Time flies when working at the microscope, and you should make yourself comfortable while working. Adjust also the high of your seat and the illumination in the microscopy room and be organized at your working place. Do not eat or drink while you are at the microscope, rather take a break to exchange with your colleague and share with them a cup of coffee or tea.

References and Suggested Further Reading 1. Bloss FD (1999) Optical crystallography. Mineralogical Society of America, p 239 2. Ehlers EG (1987) Optical mineralogy. Theories and techniques/Mineral descriptions, two volumes. Blackwell Scientific publications 3. Kerr PF (1977) Optical mineralogy. 4st edition, McGrawHill Book Company, p 492 4. Nikon Polarizing light microscope Eclipse CiPol: Instructions, p 66

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

This chapter is concerned with the optical parameters color (Sect. 4.1), habit/form (Sect. 4.2), relief (Sect. 4.3), and cleavage (Sect. 4.4). They are determined in plane polarized light in the socalled orthoscopic illumination mode. The polarizer in the substage assembly forces the light rays from the light source to vibrate in one plane perpendicular to the microscopic stage and plane polarized light is produced. The light rays enter the crystal in the thin section and vibrate parallel to each other (see also Fig. 6.1).

4.1

Color and Pleochroism

Color perception in the human eye is the result of a complex set of physiologic and neurologic responses to the wavelengths of light received. With that in mind, human color perception can be understood by using the color wheel, as illustrated in Fig. 4.1a. Color results from light of different wavelegths combining; when all visible wavelengths (390 nm to 770 nm) combine we perceive that as white. Colors formed by a combination of different wavelengths are additive colors and are shown in Fig. 4.1b. Conversely, when a specific wavelength is removed from white light we also perceive a color; such colors are termed substractive colors as illustrated in Fig. 4.1c.

Color is immediately recognized and determined in thin section. Colorless minerals transmit the electromagnetic radiation of all wavelengths of white light with wavelengths between 390 nm (violet) to 770 nm (red), and the intensity of light might be changed. Opaque minerals absorb almost all wavelengths of the visible spectrum and therefore appear black in transmitted light. No material in nature is known to absorb all incoming electromagnetic radiation. Color is the result of selective absorption of certain wavelength(s) and intensities by the crystal structure of the mineral. The nonabsorbed or transmitted color or the combination of the remaining wavelengths are perceived as color. If we observe a color, we can use the color wheel (Fig. 4.1a) to predict the absorption of a wavelength, although for minerals a combination of absorption of wavelengths is the reason for color. If the mineral is yellow-green, violet is absorbed, or if the mineral is orange, blue is absorbed. For example, in the red variety of corundum or ruby, the violet, green and yellow part of the electromagnetic spectrum are absorbed and red and blue combine to the typical dark red of ruby. The color of a mineral is said to be idiochromatic, if it is produced by selective absorption within the crystal structure, and allochromatic by mineral inclusions or impurities dispersed within the mineral.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. T. Schmidt, Transmitted Light Microscopy of Rock-Forming Minerals, Springer Textbooks in Earth Sciences, Geography and Environment, https://doi.org/10.1007/978-3-031-19612-6_4

49

50

(a)

4

(b)

620 nm

770 nm 390 nm

Optical Properties of Minerals in Plane Polarized Light (PPL)

(c)

592 nm

446 nm

579 nm

501 nm

Fig. 4.1 Color wheel: a opposing colors cancel out; b addition of colors; c subtraction of colors

4.1.1 Appearance of Color in Thin Section A thin section with a thickness of 30 lm of a common rock shows a large range of “colored” minerals as seen in Fig. 4.2. Color changes according to the sectioning or crystallographic orientation of the mineral which is known under the term pleochroism. In plane polarized light, rock-forming minerals are either transparent (they transmit an image), translucent (they transmit light), or colorless (Fig. 4.3). They may also be of a color or “colored” (Figs. 4.4–4.7). Many oxides and sulfides are opaque or “black” in a conventional 30 lm thick thin section (Fig. 4.2). Color in a mineral depends on the vibration direction of the light rays of the indicatrix axes X, Y and Z and their corresponding refractive indices a; b; c in biaxial minerals or e and x in uniaxial minerals with respect to the direction of the first polarizer. Each indicatrix axis with its refractive index displays its own color. Therefore, it is important to know the vibration direction of the first polarizer, whether it is NS or EW (see Chap. 3 for instruction on how to determine and align the direction of the first polarizer). Recognizing the various color shades in a thin section is important for mineral determination. Most minerals are transparent and colorless. Mineral plates for transparent to gray, green, brown, blue, and red minerals emphasize the wide range of possible color shades in a thin section (Figs. 4.3–4.7). Colored anisotropic

minerals are pleochroic and the image taken captures just an example of the possible color and intensity as displayed four times during a 360° rotation. It is necessary to familiarize yourself with these different colors and shades. Even transparent minerals appear in different grades of colorless being more white, beige, or gray (Fig. 4.3). The color green comes in varying intensities and shades of yellow, blue or brown and characteristic shades may be determinative, such as the pistachio green color of epidote or the green-turquoise color of celadonite (Fig. 4.4). The color brown shows light to dark, as well as more yellowish or more reddish shades (Fig. 4.5). The color blue may appear as quite pale blue, dark blue, green–blue or violet-blue (Fig. 4.6). The color red ranges from orange in a basaltic hornblende to a red-violet in thulite (Fig. 4.7). The color of a mineral changes with composition. This is especially true for the amphibole and chlorite groups, where Mg-rich members are colorless to light green and Fe-rich ones are green to dark green. Fe-poor members are always less green than Fe-rich members. Isotropic minerals possess only one index of refraction and display only one color, no matter how the crystal is cut. For example, isometric red garnet will not change color nor intensity when turning the microscopic stage (Fig. 4.8a). Spinel behaves like garnet (Fig. 4.8b). In Fig. 4.8c an opaque mineral (Fe-Ti oxide) is shown which will not change its black appearance during rotation of the microscopic stage.

4.1 Color and Pleochroism

51

(a)

Fig. 4.2 Variety of color shades of minerals in a thin section of 30 lm thickness (PPL). a Green clinopyroxene, colorless plagioclase and dark-brown groundmass in a basalt; b brown amphibole colorless plagioclase,

(b)

orthopyroxene, opaque minerals and fine-grained groundmass in basalt. For mineral abbreviations see Table A.1 in Appendix A.

Fig. 4.3 Colorless to gray minerals. For mineral abbreviations see Table A.1 in Appendix A

52

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.4 Green to blue-green pleochroic minerals. The microscopic images give an idea of the color since these minerals are pleochroic and change color according to

their crystallographic orientation with respect to the polarizer. For mineral abbreviations see Table A.1 in Appendix A

4.1 Color and Pleochroism

Fig. 4.5 Brown to reddish-brown and yellowish pleochroic minerals. The microscopic images give an idea of the color since these minerals are pleochroic and change color according to their crystallographic orientation with respect to the polarizer. Isotropic minerals such as garnet

53

and spinel are an exception with the color remaining constant during rotation since they only have one index of refraction. Some clays may also not change color during rotation. For abbreviations see Table A.1 in Appendix A

54

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.6 Blue pleochroic minerals. Haüyne and sodalite are isotropic and do not change color on rotation. For abbreviations see Table A.1 in Appendix A

Fig. 4.7 Red and pinkish-red minerals. Thulite is strongly pleochroic and garnet is isotropic. For abbreviations see Table A.1 in Appendix A

4.1.2 Intensity of Color If light passes through a mineral, the intensity of light may be decreased, because some light energy is transformed into heat. This is known as light absorption and is formulated as Lambert’s law. Fig. 4.8 Examples of colored isometric minerals possessing only one index of refraction and showing no pleochroism. a Garnet; b spinel

I ¼ ekt I0

ð4:1Þ

4.1 Color and Pleochroism

55

where I is the intensity of the light before the passage and I0 the intensity of the light after the passage, t is the thickness, e is the base of the natural logarithm and k is the absorption coefficient of the mineral in which the light is traveling. ln

I ¼ kt I0

ð4:2Þ

or I ¼ I0 ekt

ð4:3Þ

Some intensity of I is lost when the light enters the mineral due to reflection at the surface, and intensity I0 is also decreased when light emerges from the mineral. The absorption coefficient is dimensionless. Values of the absorption coefficient depend on the concentration of the chromophore elements and may be different for different wavelengths within the same mineral. Often the absorption coefficient decreases for longer wavelengths. The absorption coefficient is independent of thickness but is not a parameter used in mineral identification in a thin section, but in the determination of color in gemstones (see Dubinsky et al. [12]).

4.1.3 Pleochroism In colored anisotropic minerals light is absorbed differently depending on the crystallographic and optical orientation of the indicatrix axes. Rotating a colored mineral under plane polarized light, will result in different colors and/or intensities. This color change due to different orientation of the vibration directions with respect to the polarizer is known as pleochroism. The color of the rays of pleochroic euhedral minerals can be determined easily, if the vibration directions of the rays can be correlated with crystallographic directions, for example, the direction of a c-axis in an elongate hexagonal mineral. Examples are given in Figs. 4.9–4.11. Since tetragonal, hexagonal, and trigonal minerals are uniaxial minerals with two indices of refraction, they may show two colors, one for ray e and another for

ray x, also known as dichroism. Biaxial minerals of the orthorhombic, monoclinic, and triclinic crystal systems have three indices of refraction and may therefore show three different colors, one for ray a, as well as for rays b and c. This is known known as trichroism. In hornblende, for example, the ray vibrating parallel to the Z indicatrix axis shows the most absorption, Y is less, and X is the least absorbed. Pleochroism is expressed by the absorption formula or absorption relationship between the indicatrix axes X, Y, and Z and their corresponding rays. For biaxial common hornblende the absorption formula is Z > Y > X or for the uniaxial blue tourmalines it is e\x In the mineral plates, the colors of the refractive indices along the X and Z axes for uniaxial minerals and along the X, Y, and Z axes for biaxial minerals are indicated. In Fig. 4.9 the pleochroism of tourmaline is explained in detail. The c-axis of the crystal is aligned N-S. Ray e vibrates along the c-axis, and if it is aligned with the lower polarizer which vibrates N-S the color of e is displayed. If rotated at 90°, the color of x is seen. A section perpendicular to the c-axis will only display x in the circular section, and the color will not change during rotation of the stage. In the diagram absorption coefficient k versus wavelength (Fig. 4. 9) k is close to zero for all wavelengths for the ray e which is transferred and appears colorless while for the ray x only k for the blue wavelength is close to zero and therefore appears blue. Other examples of pleochroic minerals are biotite, orthopyroxene, and hornblende (Fig. 4.10). Figure 4.11 illustrates the color determination of rays a and b in glaucophane and hornblende. As most minerals are not pleochroic, this optical property pleochroism is crucial and easy to observe. Table 4.1 summarizes the most frequent colored minerals. Strong pleochroic behavior is present in members of the dark mica group, such as biotite and phlogopite, members of the amphibole group, such as hornblende or glaucophane and members of the chlorite group, as well as chloritoid and pumpellyite. Biotite and arfvedsonite may appear black due to the absorption of almost all wavelengths. Other

56

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.9 Pleochroism in tourmaline during rotation of the microscopic stage (PPL). The term k is the absorption coefficient and is shown for the e and x rays. See text for explanation

4.1 Color and Pleochroism

57

Fig. 4.10 Pleochroism and absorption during clockwise rotation of biotite, orthopyroxene, and hornblende (PPL). Clockwise rotation of the stage is in steps of 15°, or from 0° to 15° to 30°, and to 45°

58

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.11 Pleochroism in glaucophane and hornblende and the rays a, b and c using principal sections (PPL). Clockwise rotation of the microscopic stage is in steps of 30° or from 0° to 30°, 60°, and 90°. Glaucophane a-d: Section ⊥c: since polarizer is N-S and parallel nb ; nb is displayed and is lavender blue in a, whereas in b na ' is transferred and is light yellow-green. c nc0 vibrates

parallel to N-S polarizer and is ultramarine blue. d na ’ is parallel to polarizer and displays light yellow-green. Hornblende e–g: Section ⊥c: since polarizer is N-S and parallel to nb ; nb is displayed and is brown in e, whereas in f na '’is transferred and light brown. g nc0 vibrates parallel to N-S polarizer and is dark brown. h na ’ is parallel to the polarizer and is light brown

4.1 Color and Pleochroism

59

Table 4.1 Common pleochroic minerals. Intensity and/or color of pleochroism may change with the chemical composition and minerals are therefore displayed sometimes in two groups, such as members of the chlorite or pumpellyite group Green, strong pleochroism

amp chl cld aeg-aug pmp ep arf tur

Green, weak pleochroism

cpx ep chl act

Green, very weak pleochroism

fay opx omp pmp jad Mg-chl srp

Brown, strong pleochroism

bt phl stp tur

Brown, weak pleochroism

bt stp

Blue, strong pleochroism

gln arf crn rbk tur spr

Blue, weak pleochroism

gln brl

Red, strong pleochroism

thu

Mineral abbreviations are listed in Table A.1 in the Appendix A

mineral groups may show only weak pleochroism, such as members of the clinopyroxene family. Extremely strong pleochroism is shown for piemontite, yoderite, and thulite (see mineral plate in Chap. 9) which changes color from yellow to pink.

4.1.4 Causes of Color Color is the result of the interaction between the electric vector of the light and the interaction of the electronic clouds or certain electrons in the crystal structure of the mineral. Different mechanisms explain, for example, the color blue (Table 4.2) and three main theories of color formation will be shortly explained in the following paragraphs. The transition elements titanium, vanadium, chromium, manganese, iron, cobalt, nickel, and copper are particularly involved, and are called chromophore elements. For example, natural corundum occurs in a range of colors and different chromophore elements or combinations of chromophore elements (Table 4.2), as well as other electron interactions are responsible for color in natural corundum (Dubinsky et al. [12]). The concentrations of chromophore elements vary according to the intensity of the color. Concentrations of chromophore elements are generally in the ppm range but may also attain up to several weight % oxide of the chromophore. For example, in almandine or olivine, chromophore concentrations of Fe

may attain up to decimal weight %. Causes of color are especially well studied for gemstones (Dubinsky et al. [12]). F-center (FC) A F-center from the German word for “Farbe” (color) is the result of structural defects or point defects in the lattice of a crystal (Fig. 4.12). A common example is halite or NaCl. A F-center consists of a trapped electron in an anion vacancy. Ionizing radiation causes a halide mineral to lose an electron which moves through the crystal structure until it is trapped in a preexisting anion vacancy. Simultaneously a halogen atom is formed. The halogen atom interacts with a halide ion to form the molecular ion Cl2− which is commonly referred to as a “H-center “ point defect. F-centers may cluster to two, three or four designated as M-, R-, and N-centers, respectively. The trapped electron interacts with a photon absorbing visible wavelengths, and color will result. Another example is fluorite (CaF2) which occurs in hydrothermal veins in granitic rocks together with radiogenic minerals. Natural radiation or a and b particles knock out the F anion and an electron is trapped at the F− site. The trapped electron will interact with a photon from the light spectrum, visible wavelength(s) will be absorbed and a color will result. The crystal field theory (CFT) The crystal field theory Burns [6] explains color as the result of the electrostatic interactions

60

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Table 4.2 Causes of colors for some minerals according to 1Taran and Langer [35], 2Chopin and Langer [9], 3 Greenidge [17], 4Schwarzinger et al. [31], 5Shermann [33], 6Schmetzer et al. [30]. 7Dubinsky et al. [12], 8Merkel and Breeding [24], 9Bank et al. [4], 10Bačík et al. [2], 11Vennari and Williams [38] Mineral name

Gemstone variety

Color

Origin of color

Fluorite

purple

FC

Halite

blue, yellow

FC

3

yellow, blue

FC, Al in tetrahedral site, trapped hole

amethyst

violet

FC, Fe3+-O

ruby

red, pink

CFT, Cr3+, V3+

sapphire

deep blue

CFT V3+, IVCT Fe2+–Ti4+ face + edge-sharing octahedra

Corundum1

light blue

IVCT Fe2+–Fe3+

Corundum7

orange

Trappd hole-Cr3+

7

Corundum

yellow

Fe3+, trappd hole-Fe3+

Corundum7

green, purple

CFT V3+

Spessartine

yellow-orange

FC, Mn2+

violet

IVCT Fe2+–Fe3 +edge-sharing octahedra/tetrahedra

Topaz

Quartz Corundum1,

7

1, 7

Corundum

Fe-cordierite1

iolite

IVCT Fe2+–Ti4+

Ilmenite11 (high pressure) blue

IVCT Fe2+–Ti4+, Fe2+–Fe3+

blue

IVCT Fe2+–Ti4+ face-sharing octahedra

Riebeckite1

green

IVCT Fe2+–Fe3+ edge-sharing octahedra

Phlogopite1

green

IVCT Fe2+–Fe3+ edge-sharing octahedra

green

IVCT Fe2+–Fe3+ edge-sharing octahedra

blue

IVCT Fe2+–Fe3+

brown

IVCT Fe2+–Fe3 in M1 and M2 site

Magnetite5

opaque

IVCT Fe2+–Fe3

Ellenbergerite2

violet

IVCT Fe2+–Ti4+ face-sharing octahedra

Tourmaline

blue, greenish-blue, blue

Fe2+ + Cu2+

Kyanite Dumortierite

1

Clinopyroxene1,

5

Glaucophane5 Biotite

5

Tourmaline8,

9

pink, purple, violet

CFT Mn3+, Cu2+

Tourmaline4,

6

green

CFT V3+, V3+ + Cr3+

brown

IVCT Fe2+–Ti4+ IVCT Fe2+–Fe3+

brownish yellow

IVCT Fe2+–Ti4+ edge-sharing octahedra

Tourmaline1 Tourmaline

10

dravite elbaite

yellow

CFT Mn

3+

FC: F-center, CFT: Crystal field theory, IVCT: Inter valence charge transfer.

+

4.1 Color and Pleochroism

+

Cl-

Cl- + H-center

+

Cl-

+

61

Cl-

Cl- + Cl- + Cl + Cl-

Cl- + Cl- +

Cl- +

+ Cl-

+ Cl-

Cl- + Cl- +

Cl- +

+ F-center

e-

+

Cl-

Fig. 4.12 F- and H-centers in a halide. A Cl− ion is expelled from its site and the e− is trapped in a preexisting anion vacancy, called F-center. The Cl− ion becomes a Cl atom which combines to Cl 2 called a Hcenter

between the orbital energy levels of a transition metal ion and its surrounding which are negatively charged anions such as O2−, OH− or SO42− (Figs. 4.13 and 4.14). These anions are termed ligands, are considered point negative charges, and are located around the transition metal ion. The transition elements titanium, vanadium, chromium, manganese, iron, cobalt, nickel, and copper have unpaired electrons in their five partially filled 3d-orbitals, while the lanthanides and actinides display partially filled 4f-orbitals. In a metal ion, the five d-orbitals have the same energy (Fig. 4.14a). This is different in an octahedral coordination, common in many minerals, where six ligands of anions approach the metal cation in an xyz space and have different geometric arrangement (Figs. 4.13 and 4.14). Electrons of the 3d-orbitals which lie within the dx2-y2 and dz2 space experience greater expulsion from the metal ion and will increase their energy level, called eg, in order to stay at their position. Electrons within the dxz, dyz, or dxy space will decrease their energy levels, called t2g (Fig. 4.14b). This splitting of the energy into two energy sets of d-orbitals is known as crystal field splitting. The oxidation state and the strength of the ligands determine the splitting of the energy levels. The higher the oxidation state or the stronger the ligand, the larger the energy

splitting. Ligands are classified as strong or weak and are I− < Br− < Cl− < F− < OH− < H2O < NH3 < NO2− < CN−. The energy it takes to move from the energy level eg to t2g is the energy that the complex will absorb from the visible light spectrum. It is this interaction between the two energetically sets of the 3dorbitals eg and t2g that determines the color. In the case of ruby, the red Cr-variety of corundum, the energy of 2.2 eV from the light spectrum causes excitation and the yellow-green part will be absorbed. An energy of 3.0 eV from the light spectrum will cause absorption in the violet part of the spectrum. The ruby will therefore have a red color. Intervalence charge transfer (IVCT) Intervalence charge transfer (IVCT) is the origin of the dark colors of stoichiometric Fe2+-Ti4+ minerals such as hematite, ilmenite, green clinopyroxene, green phlogopite, violet Fecordierite, green riebeckite, brownish-yellow dravite, blue dumortierite and light and dark blue sapphire (Sherman [33], Mattson and Ranger [23]; Taran and Langer [35]; see also Table 4.2). IVCT is defined as a process in which an electron between two metal ions in close proximity to each other is transferred between them, temporarily changing the oxidation state of both cations (Fig. 4.15). The metal cation pairs are Fe2+–Fe3+ (Smith [34]) and Fe2+–Ti4+ and a third one, Ti3+–Ti4+, found in meteorites. This is schematically shown in Fig. 4.15 for a sapphire (Al2O3) containing Fe3+ and Ti4+ in the ppm range. Ti and Fe will replace Al in the same lattice site. The deep blue color results from the IVCT of Fe2+–Ti4+ to Fe3+–Ti3+. There is overlap between the d-orbitals of Fe2+ and Ti4+ in neighboring face- and edge-sharing octahedra which allows the electrons to be transferred from one anion to the other. The transfer is initiated by visible light absorption, and the associated optical excitation energy is 1.85 eV for face-sharing octahedra and 1.76 eV for edge-sharing octahedra Bristow et al. [5]. Fe2+–Ti4+ and Fe3+–Ti3+ IVCT is also reported in tetrahedral coordination in Ti-bearing garnet (see Smith, [14]). It is common practice to heat sapphires in order to

62

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.13 Five 3d-orbitals and their geometric arrangement in an xyz space and their corresponding energy levels in octahedral coordination

Fig. 4.14 a Five 3d-orbitals have the same energy in a single metal ion. b In an octahedral coordination, the electrons split into a lower and higher energy level, called t2g and eg, respectively. The energy it takes to uplift the

electron to a higher energy level is extracted from the light spectrum and the not absorbed energy of the wavelengths will combine to the observed color

Fig. 4.15 Intervalence charge transfer in sapphire for the neighboring face (in brown) and the edge-sharing octahedra (in blue) and corresponding energy of light absorption. Crystal models modified after Bristow et al. [5]

4.2 Crystal Habit and Textural Relationships

deepen their color, and which is due to changing the oxidation state of Fe. Many minerals are colorless in a 30 lm thick thin section. A transparent mineral transmits the entire visible spectrum and may change intensity. An opaque mineral absorbs (almost) the entire visible spectrum. A white mineral reflects the entire visible spectrum. A colored mineral selectively absorbs wavelengths known as pleochroism and the color of a mineral is the color that has not been absorbed. All possible colors are combinations of 2 or more wavelengths: purple: combination of red and purple: brown: combination of red, blue and yellow. Colored minerals are pleochroic and anisotropic (exception are colored isometric minerals). The color of a mineral changes due to its composition, sectioning or the crystallographic and optical orientation. Color is explained by F-centers, the crystal field theory and intervalence charge transfer (IVCT). Transition elements (Ti, V, Cr, Mn, Fe, Co, Ni, Cu) with partially filled 3d-orbitals are particularly effective. Intervalence charge transfer (IVCT) is at the origin for the dark colors of hematite and ilmenite as well as the dark colors of amphibole, pyroxene, tourmaline, or in the sapphire families. Sensibility for seeing colors and the color memory must be trained to recognize fine variations of color tones and color intensities.

4.2

Crystal Habit and Textural Relationships

4.2.1 Appearance of Crystal Habit The three-dimensional form of minerals is seen in a thin section only as a two-dimensional form. The three-dimensional appearance of a mineral is

63

called the crystal habit. Crystal habit is a combination of crystal forms and their development in the different crystallographic directions. The great variety of crystal habits was already well documented in the descriptive nine volumes of “Atlas der Krystalformen” by Goldschmidt [16] at the beginning of the last century. Habit is especially well studied for snow where crystal habit depends on temperature and supersaturation. Crystal habit is a clue to the conditions of crystal formation and reflects the types of crystal growth due to crystallization, partial dissolution, melting, undercooling of the system, and grain boundary migration. In a thin section the outlines of a mineral significantly help in their identification. It is therefore important to understand, how a mineral is sectioned and how its outline will vary. This will be influenced by the crystallographic system the mineral belongs to. According to their crystallographic symmetry minerals as crystalline phases are assigned to six crystal systems: the isometric, tetragonal, hexagonal, trigonal/ rhombohedric, orthorhombic/rhombic, monoclinic, and triclinic systems. Most minerals crystallize in the monoclinic system (31.5%) followed by the orthorhombic system (22.0%), while trigonal, triclinic and hexagonal minerals are represented by around 8–9%, isometric ones by 10%, and amorphous phases are represented by 0.75% (Kostov and Kostov, [21], based on a total of 3685 minerals). The 2D-outline of a mineral in a thin section commonly suggests to which crystallographic system a mineral might belong. Crystal systems, some characteristic habits, and minerals according to their respective crystal system are given in Fig. 4.16. Crystals are drawn using the Smorf applet (Holtkamp, [20]). The main crystallographic faces are labeled with their Miller indices (hkl) in Fig. 4.16. Miller indices describe the orientation of a crystal plane with respect to the crystallographic axes a, b, c. Miller indices are given as a three-digit numbers which are the reciprocal values of the intercepts of the axes, normalized to the lowest common denominator (e.g., see summary in Wenk and Bhulak [40]; Okrusch and Frimmel [26]). Miller indices are often referred to when cleavage traces

64

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.16 Crystal systems and some characteristic crystal habits. Most common minerals of the respective crystal systems are given in the right column. Crystals are drawn

using the Smorf applet (Holtkamp [20]). Terminology of crystal faces according to Nespolo [25]. For abbreviations see Table A.1 in Appendix A

4.2 Crystal Habit and Textural Relationships

65

Isometric

grt

grt

hyn

py

lct

rt

zrn

ves

tur ⊥c

tur ∥c

Tetragonal

Hexagonal

nph ⊥c

ap ∥c

opx

and

amp

amp

Orthorhombic

ol lws Monoclinic

Ʃn

czo

Fig. 4.17 Cross sections of minerals of different crystal systems. For abbreviations see Table A.1 in Appendix A

and cleavage directions are determined and are used throughout this text. A thin section may display many different cross sections of a mineral, and as a result it is possible to determine which crystal system a mineral might belong to. Figure 4.17 illustrates cross sections of euhedral minerals of some crystallographic systems allowing a determination of their possible crystal system.

Amphibole is a good example for understanding its various sections, the outlines allowing interpretation of the crystallographic orientation. (Fig. 4.18a-b). An amphibole crystallizing in a volcanic rock may display different outlines when cut parallel to the {110} prism, parallel to the c-axis or in any other direction. The sections parallel to the {110} prism and parallel to the c-axis are easily recognized by

66

4 (a)

(b)

(c)

(e)

Optical Properties of Minerals in Plane Polarized Light (PPL) (c)

Fig. 4.18 Mineral habit according to section orientation. (a-b) Amphibole cut perpendicular to the c-axis or parallel to it in volcanogenic rock (PPL); c columnar sillimanite in garnet-sillimanite gneiss is sectioned along the c-axis and other individuals are cut perpendicular to

the c-axis (XPL); d quartz crystals in quartzite with many different optical orientations as seen by the variety of interference colors (XPL); e muscovite oriented in the schistosity plane (XPL)

their forms. Sillimanite in a metamorphic gneiss displays sections both parallel to the c-axis and perpendicular to it (Fig. 4.18c). Rocks with an isotropic texture such as a metamorphic quartzite will show crystals with similar form, no matter in which direction the rock is cut (Fig. 4.18d). A deformed rock with muscovite in the schistosity plane will have a preferred orientation of minerals (Fig. 4.18e), and cross sections are therefore restricted to certain directions which will limit the determination of their optical parameters. Therefore, a number of thin sections with differing orientations are often prepared especially when studying deformed rocks. Minerals may develop perfect crystallographic faces if they do not interfere with each other during their growth. In a magmatic melt, minerals may crystallize simultaneously or in a defined sequence, known as the “Bowen sequence”. They precipitate according to a temperature/pressure gradient or other changing parameters such as fluid pressure or a changing magma composition. In metamorphic rocks the term “crystalloblastic series” describes the sequence of minerals starting from the more euhedral to the more anhedral minerals. Titanite, rutile, spinel, garnet, sillimanite, staurolite, tourmaline, epidote, magnetite, ilmenite, andalusite, pyroxene, amphibole, micas, kyanite, cordierite, vesuvianite, and feldspars are

more likely to grow in their proper crystallographic form than quartz, chlorite, olivine, calcite, and dolomite. Three terms are traditionally used according to the development of crystallographic faces in a mineral (Fig. 4.19). Euhedral, automorphic, or idiomorphic minerals (Fig. 4.19) show welldefined crystal faces and angles. Euhedral crystals are most frequently found in igneous rocks where the first crystals that begin to form are more likely to have well-developed crystal faces because they have crystallized first in a magmatic melt where unimpeded growth is possible. In metamorphic rocks, minerals may develop euhedral forms, especially garnet, staurolite, epidote, or amphibole. In addition, excellent examples of euhedral minerals are observed in veins of quartz, calcite, zeolite, or prehnite. Subhedral crystals (Fig. 4.19) have developed some crystal faces. This is often the case for mica, feldspar, or amphibole. Anhedral, allotriomorphic, or xenomorphic minerals (Fig. 4.19) do not have crystal faces, in particular quartz, calcite, or dolomite. Most minerals may occur in any of these forms, such as garnet in a metamorphic rock. Amorphous glass and opal are not crystalline and therefore do not develop crystal faces as they lack any crystal structure.

4.2 Crystal Habit and Textural Relationships

67

Fig. 4.19 Crystals are named according to the presence of crystal faces: euhedral, automorphic or idiomorphic, subhedral, and anhedral, allotriomorphic or xenomorphic

Textural relationships of large crystals in relation to the groundmass are linked to the terms phenocryst, porphyroblast, poeciloblast, and porphyroclast and are a useful criteria for a rapid initial classification of a rock (Fig. 4.20 and Table 4.3). A phenocryst (Fig. 4.20a) is a large crystal embedded in a finer-grained groundmass of an igneous porphyritic rock which can be of volcanic or intrusive origin. A porphyroblast (Fig. 4.20b) is also a phenocryst, but one which has grown during the metamorphism, sometimes incorporating the former bedding plane or an earlier schistosity such as is seen in a snowball garnet. Certain minerals such as garnet, staurolite, biotite, chloritoid, or kyanite are the most common to crystallize as phorphyroblast. A poeciloblast is a porphyroblast or a phenocryst containing numerous inclusions, which is often the case of garnet or staurolite. A porphyroclast (Fig. 4.20c) is a former phenocryst such as feldspar, mainly of a magmatic rock or a coarsegrained sedimentary rock, but also of an earlier metamorphic event, that is overprinted by later

metamorphic or deformational events. Other specific terms characteristic of mineral habits are given in Tab. 4.4 and in Fig. 4.21. Hibbard [18] proposes a complex descriptive bimodal classification of crystal morphology comprising nine types and integrating the traditional terms euhedral, subhedral, and anhedral (Fig. 4.22). One criterium is the correspondence of the morphology to the crystal structure, also named “structural expression” and which lies on the y-axis. The other criterium is the completeness or “integrity” of the crystals which is along the x-axis (Fig. 4.22). The degree of correspondence of crystal form to crystal structure is expressed as “eustructural” (high correspondence), “substructural” (medium correspondence), and “astructural” (low correspondence). The observation to define the type includes crystal faces, cleavage twins, mineral inclusions, and zoning. The completeness or “integrity” of the crystals has also three main types: A low integrity describes crystals that are spongy, skeletal, dendritic, sieved, or cellular on one side

Fig. 4.20 a Phenocryst of plagioclase in a fine-grained groundmass of a volcanic rock; b porphyroblast of garnet in a mica schist; c porphyroclast in an orthogneiss partly

altered along its crystal edges and embedded in mica oriented in a schistosity plane

68

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Table 4.3 Most common phenocrysts in magmatic rocks and porphyroblasts in metamorphic rocks. Phenocryst (magmatic rock)

Porphyroblast (metamorphic rock)

Amp fsp bt cpx hyn lct nph nsn ol opx sa sdl

Amp and bt cld crd fsp grt ky lws sil st

For abbreviations see Table A.1 in Appendix A

Table 4.4 Other terms often used for the description of habit Term

Description

Example

Acicular

Thin, long, needle shape

aeg-aug dum ntr sil stb tlc zeo

Botryoidal

Several layers of cauliflowers

prh

Columnar

Long prismatic crystals are arranged as columns

ep scp sil

Dendritic

Thin and long branches

cpx ol ox

Fibrous

Thin long crystals attached to each other or as single crystals

tlc chl pmp act sil atg ctl

Granular/ equant

Crystals have similar size and form

qz ol cal dol anh alu ep anl

Helicitic

A crystal encloses other crystals, traces an original bedding or schistosity plane

st grt bt

(continued)

4.2 Crystal Habit and Textural Relationships

69

Table 4.4 (continued) Term

Description

Example

Prismatic

Shape of prism with two parallel crystal faces in a long crystal

pl sil kfs

Radiating

Radiating, often starting from one point

pmp prh aeg ep chl lmt ntr zeo

Tabular

rectangular

and px

For abbreviations see Table A.1 in Appendix A

of the spectrum and includes crystals that have enclosed former crystals such as poikiloblasts. High integrity on the opposite of the spectrum refers to crystals having developed crystal faces or euhedral crystals, while the medium integrity category is located between the two types. The combination of the criteria results in nine types which are the basis for genetic interpretations. Feldspar is used as an example in Fig. 4.22. It is astructural/low integrity (AL) in the case where a feldspar was partially melted. Astructural/high integrity (AH) is observed in a metamorphic rock which has statically recrystallized. Eustructural/ high integrity (EH) would represent the classic example of a euhedral crystal characterized by completeness and correspondence with crystal structure and which is common as phenocrysts in magmatic systems.

4.2.2 Causes of Different Habit Attempts to relate habit, crystal size, and textural relationships to the physical conditions of growth have been addressed for magmatic and metamorphic rocks (e.g., Kostov and Kostov [21]; Shelley [32]; Higgins [19]). Habit or the development of the outer form of a crystal depends on

the kinetic conditions of crystal growth, such as temperature, pressure, presence of a fluid phase and available elements. Crystal growth occurs if the total energy of the crystallizing environment will reduce the total energy of the system. Dissolution of crystals may also reduce the total energy of a system. Three processes are involved in the crystallization of a new mineral: nucleation, diffusion, and growth (Shelley [32]). The concept of crystal size distribution (CSD) developed by Randolph and Larson [29] and Marsh [22] has been used to differentiate different growth populations and to correlate them to physical conditions and geological events (see summary in Higgins [19] Cashman, [8]). By way of example, Armienti et al. [1] examined crystal size distribution in lavas from the 1991–1993 eruptions of Mount Etna and suggested that the largest crystals grew at depth in the magma chamber and a second-generation nucleated and crystallized within the conduit during magma ascent. The technique of CSD has also been applied in metamorphic rocks where quantitative information about crystal nucleation and growth rates, growth times, and the degree of temperature overstepping of metamorphic reactions can be evaluated (see, e.g., Cashman and Ferry [7]) and when combined with isotopic and chemical

70

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.21 Subhedral to anhedral minerals and other crystal habits. For abbreviations see Table A.1 in Appendix A

data, it allows for a profound understanding of geological events within geological systems. According to Kostov and Kostov [21] growthrate anisotropy in different crystallographic directions is responsible for crystal habit variety. Some crystallographic faces might be favored during growth conditions, and it is the slowest growing crystal face that determines the habit. Kostov and Kostov [21] provide many examples

of habit related to growth conditions. A mineral may develop different habits according to the physical conditions of growth, and zones with different habits may develop in a geological system. For example, a zonal distribution of fluorite habits is observed in the Mikhalkovo deposit in Bulgaria (Kostov and Kostov [21]). Development of different habits of fluorite are recognized within individual crystals and on a

4.2 Crystal Habit and Textural Relationships

71

Fig. 4.22 Bimodal morphological classification using the correspondence of the morphology to the crystal or “structural expression” as plotted on the y-axis and the completeness or “integrity” of the crystals along the x-

axis. The types are represented by a feldspar crystal. Gray area is seen in thin section, and dashed lines are inferred from the morphology of the crystal. Modified from Hibbard [18]

regional scale. A “normal zonality” is characterized by a specific habit formed during higher temperature and lower supersaturation while a zonal distribution where the conditions changed to lower temperature and higher supersaturation (Fig. 4.23a) is called “reversed zonality” and displays a different habit. Recurrences of habits within individual crystals suggest pulsatory crystallization and changing conditions. Regional zonations of habits are observed around magmatic bodies, along faults fissures and dikes supplying mineral solutions. These zonations of the distribution of habit have also been applied in the exploration for ore deposits. Mineral habits and their relationship to the textural and chemical development of a

geological environment are used to understand the crystallization of complex igneous systems in space and time (for a summary see Higgins [19]). The habits of tetragonal zircon have been studied in detail due to its use as a geochronometer (Corfu et al. [10]). They vary from bipyramidal to prismatic, while pseudocubic and acicular habits also occur. Zircon may grow preferentially as a dipyramid with a prism with elongation ratios (length to width) from 0.1 to 5. Acicular zircon crystals are reported from rapidly crystallized volcanic or sub-volcanic intrusions. Therefore, the length to width ratio is considered to reflect the crystallization velocity. Pupin [28] relate zircon morphology to the origin of granites where zircon morphology derived from granites

72

4 T °C

165

145

pH Ca2+x103 mol

5.52

5.34

1.2

1.6

TLiquidus Polyhedral olivine

Zircon

interface-controlled Conditions near equilibrium Temperature Δ T from TLiquidus

Fluorite

Optical Properties of Minerals in Plane Polarized Light (PPL)

Dry magma

Magma rich in alkalies

- 20°

Skeletal olivine Surface nucleation growth Conditions far from equilibrium

- 60°

Dendritic olivine Continuos growth Diffusion-controlled Conditions far from equilibrium

(a)

115

4.95

4.6

(b)

Fig. 4.23 a Different habits of fluorite related to temperature, pH and saturation of Ca2+; b temperature and saturation control on the habit of zircon (modified

of crustal or mainly crustal origin or autochthonous and aluminous granites is different from granites of crustal-mantle origin or hybrid granites (calc-alkaline and sub-alkaline series granites) and granites of mantle or mainly mantle origin (alkaline and tholeiitic). Kostov and Kostov [21] suggest a general relationship between the crystal habit of zircon, the temperature of formation and the alkalinity of the magma (Fig. 4.23b). In a detailed study of olivine in basalts from La Réunion Welsch et al. [39] show that the degree of undercooling (temperature drop below the liquidus) controls the habit of olivine following the sequence polyhedral > skeletal > dendritic habit and that growth is often dendritic followed by ripening (Fig. 4.23c). Polyhedral olivine crystallizes at a low cooling rate ( 60 °C) and high cooling rates (47–1890° Ch−1) and the growth process is diffusioncontrolled. Habit or the outer appearance of a crystal as well as its textural relationship with respect

T Hydrous magma

(c)

from Kostov and Kostov, [21]); c different habits of olivine as the result of undercooling (modified from Welsch et al. [39])

to the groundmass or the matrix depends on the orientation of the sectioning of the crystal. Habit is helpful in identifying a mineral’s crystal system and is a useful parameter in mineral identification. Traditional common terms used are euhedral, anhedral or subhedral for the crystal form, whereas phenocryst (general term), porphyrblast, poiciloblast, and porphyroclast imply that the rock type and its history are known. A binary classification uses the correspondence of the morphology to the crystal or “structural expression” as plotted on the y-axis and the completeness or “integrity” of the crystals along the x-axis. The classification describes habit in nine types integrating also the traditional terms. Habit depends on kinetic conditions of crystal growth, such as temperature, pressure, saturation, undercooling, presence of a fluid phase, and available elements and can be related to the geological environment of formation. Crystal size distribution (CSD) and textural relationships provide information about nucleation and growth rates in igneous and metamorphic rocks. The regional and local analysis of changing habit or the observation of zonal distribution in habit allows to constrain changing conditions in a geologic system.

4.3 Relief

73

Fig. 4.24 Relief and corresponding relief category for some common minerals. For abbreviations see Table A.1 in Appendix A

4.3

Relief

4.3.1 Appearance of relief Relief expresses the relative difference in refractive indices of neighboring phases, i.e., the minerals and/or the mounting medium. It manifests itself by the appearance of more or less pronounced black contours on the outline of a mineral in a thin section (Fig. 4.24). Relief results from the internal total reflection of light rays at the interface between minerals and/or the mounting medium. The intensity of the contour is directly proportional to the difference in refractive indices of the interfacing media, thus a

“thick black line” around a mineral means a bigger difference in refractive indices between neighboring phases, whereas no relief means that mineral and mounting medium have a similar refractive index. Relief of a mineral varies depending on the orientation of refractive indices with respect to the crystallographic directions and the substage polarizer and is most pronounced for minerals with high or very high refractive indices, for example for the carbonate family. When rotating the microscopic stage, the relief of calcite changes according to the orientation of the ray with respect to the vibration direction of the polarizer. This is known as “twinkling”. Relief is constant for a mineral of the isometric crystal system since it has only one

74

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

index of refraction. Relief may change with composition for a mineral group. For example, refractive indices may vary in mineral groups which show Fe–Mg solid solution (e.g., chlorite, amphibole, pumpellyite, or olivine) where Mgrich compositions have a lower relief than the Ferich varieties. Relief is examined at the contact of minerals or where minerals are in contact with the mounting medium. The mounting medium used for the preparation of thin section is an epoxy resin, normally Canada balsam, the natural oleoresin of Abies balsamea, fir tree, which has a refractive index of nCB = 1.538–1.542 (see also Sect. 3.7). In routine microscopic studies, rock slabs are generally glued with an epoxy resin on the glass slide, while the coverslip is glued with Canada balsam, once the thickness is reduced to 30 lm. The refractive index of Canada balsam is the reference to compare observed relief and refractive indices of minerals. The principsal refractive indices were determined on individual fragments using the immersion method and are compiled by many authors (Tröger [37]; Fleischer et al. [13]; Phillips [27]; Deer et al. [11]). Individual crushed crystals with fresh surfaces are immersed in successive liquids of known refractive indices until a match is found and the refractive indices determined. Seven categories of relief are defined (Table 4.5): VH for very high, H for high, M for medium, and L for low refractive index. There is a plus sign after the letter for the relief category if the relief is above the refractive index of Canada balsam and a minus sign, if the relief category is below the refractive index of Canada balsam. Most minerals have a relief between L- (n = 1.50–1.54) and H+(n = 1.66–2.0) and few minerals have a relief of VH or H-. A mineral may appear in two relief categories because of different compositions. For example, a Mg-rich chlorite will rather have a relief of L+, while an Fe-rich variety will have a higher relief of M+ (Table 4.6) Relief allows for an estimation of refractive indices in thin sections, and difference of ± 0.02 can well be distinguished. It is important to make first the fact-based observation since relief is a relative measure depending on which mineral

phases are involved and how large is the difference of the respective refractive indices. In Fig. 4.25a biotite (nbt ≅ 1.6, M+) is in contact with apatite (nap ≅ 1.6, M+), and because of their similar refractive indices the contour of apatite in contact with biotite is a fine black line. If biotite is in contact with kyanite (nky ≅ 1.7, H+), the dark line at the contact biotite/kyanite is well pronounced indicating a bigger difference of refractive indices between the bordering minerals (Fig. 4.25b). Another example showing different grades of relief is given in Fig. 4.25c where titanite (nttn ≅ 1.9, VH+) is in contact with glaucophane (ngln ≅ 1.6, H+) and the relief is well visible. Garnet (ngrt ≅ 1.7, H+) shares borders with feldspar (nfsp ≅ 1.5, L−) and the relief can well be recognized. Chlorite (nchl ≅ 1.58, L+) produces a weaker relief with feldspar (nfsp ≅ 1.5, L−), as well as with muscovite (nms ≅ 1.6, L+). A moderate relief is seen between chlorite (nchl ≅ 1.58, L+) and clinozoisite (nczo ≅ 1.7, H+) or muscovite (nms ≅ 1.6, L+).

4.3.2 Mathematical Formulation of Relief Formation Between Air and Mineral The formation and the degree of relief can be explained by using Snell-Descartes’s law. The formation of the relief is governed by the critical angle of refraction (see also Chap. 2), the refractive index of the concerned mineral and the mounting medium or the neighboring minerals. One can determine the critical angle in the following manner. First, invoke SnellDescartes’s law: sinðhr Þ  nr ¼ sinðhi Þ  ni

ð4:4Þ

where i and r are two media in contact: ni is the refractive index of the medium of the incident ray, in this case of our mineral, nr is the refractive index of the neighboring medium, in this case of air, and hi ; hr the angles of incidence and refraction, respectively. Then, observe that at reflection, one has hr ¼ 90 . Using this fact and that sinð90 Þ ¼ 1 yields:

4.3 Relief

75

Table 4.5 Category of relief with range of refractive indices Symbol

Range of refractive indices

H-

Example

< 1.42

zeolites

M-

1.42–1.50

fl wrk stb mor zeolites

L-

1.50–1.54

or pl tlc qz gp crd cpt scp mes php clay

ca. 1.538–1.542

Canada balsam

1.54–1.58

qz chl bt

M+

1.58–1.66

bt ol opx hbl chl and jd

H+

1.66–2.0

sil ep cld ttn zr aeg omp std ky spr ol

L+

VH

> 2.0

rt

VH very high, H high, M medium, and L low. The refractive index of Canada balsam marks the limit between positive and negative relief For abbreviations see Table A.1 in Appendix A

Table 4.6 Comparison of critical angles for common minerals of varying refractive indices and their corresponding relief category fl

qz

cal

grt

zrn

ttn

ni

1.43

1.53

1.658

1.77

1.9

2.1

nr

1

1

1

1

1

1

Critical angle (°)

44.4

40.8

37.1

34.4

31.8

28.4

Relief category

M−

L−

M+

H+

H+

VH+

The smaller the critical angle, the higher will be the relief category; ni refractive index of mineral, nr refractive index of air For abbreviations see Table A.1 in Appendix A

(a)

(b)

Fig. 4.25 Relief as a result of difference of refractive indices: a The fine black line between biotite (bt, nbt ≅ 1.6, M+) and apatite (ap, nap ≅ 1.63, M+) indicates that their refractive indices are similar; b thick dark line between biotite (bt, nbt ≅ 1.63, M+) and kyanite (ky, nky ≅ 1.7, H+) and larger difference in refractive indices; c strong relief of titanite (ttn, nttn ≅ 1.9, VH+) bordering

(c)

blue glaucophane (gln, ngln ≅ 1.6, H+), strong relief of garnet (grt, ngrt ≅ 1.7, H+) in contact with feldspar (fsp, nfsp ≅ 1.5, L−) and between chlorite (chl, nchl ≅ 1.58, L +) and clinozoisite (czo, nczo ≅ 1.7, H), moderate relief between feldspar (fsp, nfsp ≅ 1.5, L−) and chlorite (chl, nchl ≅ 1.58, L+) and weak relief between chlorite (chl, nchl ≅ 1.58, L+) and muscovite (ms, nms ≅ 1.6, L+).

76

4

Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.26 Critical angles for titanite and quartz and area of total internal reflection (schematic). The area of total reflection for titanite is larger than for quartz resulting in a

(a)

(b)

larger area of refraction of the light rays or a thicker “black” line or a higher relief category than for quartz

(c)

Fig. 4.27 Determination of the higher and lower refractive indices by using the Becke line method in an artificial rock of garnet (ngrt ≅ 1.7, H+), fluorite (nfl ≅ 1.43, M−) and quartz (nqz ≅ 1.54, L+) and mounted in Canada balsam (nCB ≅ 1.538). a Minerals are in focus; b the focus is above the focal plane. The Becke line is seen

outside fluorite, but inside garnet. No Becke line is visible in quartz. c The focus is below the focal plane. The Becke line is now seen inside fluorite, but outside garnet. No Becke line is visible in quartz. The observations allow to conclude that nqz ≅ nCB, nfl nCB

  nr 1  nr ¼ sin hi;crit  ni , ¼ sin hi;crit ni   1 nr ) hi;crit ¼ sin ni

critical angle, light will be refracted and traverses the mineral. Light arriving at angles greater than the critical angle results in the total reflection of the light. This will produce a dark area or the relief of the mineral. In Fig. 4.26 and Table 4.3 the critical angles of quartz and titanite are compared schematically. It shows that the area of total reflection in titanite starts at an angle of incidence at 28.4°. At this angle and higher values, the light is totally reflected. The calculated critical angle for quartz is 42.3°and clearly

ð4:5Þ where hi;crit is the critical angle of reflection. Any light ray incident at a larger angle will be completely reflected. This angle is the critical angle where light is not refracted anymore and is internally reflected. At angles lower than the

4.3 Relief

Fig. 4.28 Formation of the Becke line. The bundle of light rays is shifted to the right producing the Becke line in the mineral with the higher refractive index n1. Modified after Tertsch (1949)

bigger than for titanite. It implies that the area of total reflection of quartz is smaller, whereas the area of refracted light is bigger. This results in a thinner “black” line or lower relief category. The critical angles for fluorite, quartz, calcite, garnet, zircon, and titanite are given for comparison in Table 4.6. It is evident that the critical angle of incidence decreases with increasing refractive index resulting in larger areas of total reflection. Minerals with a higher refractive index therefore yield higher relief or higher category of relief.

4.3.3 Formation of Relief Between Minerals and the Becke Line Method In most cases, relief between minerals does not allow to state which of the two minerals has the higher refractive index. The Becke line method allows us to determine which of the media has the higher refractive index. In Fig. 4.27 an artificial rock constitutes the artifcial mineral assemblage fluorite (nfl ≅ 1.43, M−), garnet (ngrt ≅ 1.7, H+), and quartz (n ≅ 1.54, L+) in the mounting medium Canada balsam (ncb ≅ 1.538).

77

The image is in focus in Fig. 4.27a. By slightly defocusing the grains or increasing the distance between the objective and the thin section, a fine light line called Becke line will appear at the grain contacts with the mounting medium (Fig. 4.27b). If the focus point is above the focal plane, the Becke line is inside garnet, but outside fluorite (Fig. 4.27b). No light line is visible in quartz. If the focus point is below the focal plane, the contrary takes place (Fig. 4.27c). The Becke line is now within fluorite, but outside garnet. Again, no light line is visible in quartz (Fig. 4.27c). These observations infer that when increasing the distance between the objectives and the thin section, the Becke line will move inwards the mineral with the higher index of refraction. By decreasing the distance between the objective and the mineral, the light line will be displaced inside the mineral with the lower index of refraction. Quartz has the same refractive index as the mounting medium and therefore shows no relief and no Becke line will appear. In my lectures it is named ILH rule. When increasing the distance between the objective and the mineral, the light line will move inwards the mineral with the higher index of refraction or using the 3H rule in German for “Beim Heben des Tubusses wandert die helle Linie ins höher brechende Mineral”. The Becke line method needs a high magnification objective lens (suggested 20  or higher), and the aperture diaphragm should be almost closed. The formation of the Becke line also follows the Snell-Descartes’ law and the critical angle of refraction. An explanation is given by Tertsch [36]. A bundle of light rays will be modified according to their position and angle. In Fig. 4.28 a bundle of rays arrives at a vertical interface of two minerals, where n1 is greater than n2. All rays between rays a and b enter the mineral with higher refractive index n1, are refracted, deviated, and traverse the mineral with the lower refractive index n2. They appear as rays a’ and b’. Rays c, d, and e will enter from the mineral with the lower refractive index n2 and will be refracted at the interface between the two minerals away from the normal since they enter a mineral with a higher refractive index. These

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Optical Properties of Minerals in Plane Polarized Light (PPL)

Fig. 4.29 Cleavage, cleavage sets, lack of cleavage and mineral diagnostic cracks for some common minerals. For abbreviation see Table A.1 in Appendix A

4.4 Cleavage

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rays are shifted to the right and appear refracted as rays c’, d’, and e’. This results in the appearance of the Becke line in the mineral with the higher refractive index n1 and which is visible slightly above the focal plane of the mineral. Relief and the Becke line are governed by the Snell-Descartes law and the critical angle of refraction. Relief category of a mineral depends on its critical angle of refraction which is controlled by the refractive index. Most minerals have a positive relief, and few minerals have a low negative or very high positive relief. Relief has categories VH for very high, H for high, M for medium, and L for low refractive index which is either positive or negative with respect to the reference refractive index of Canada balsam (nCB = 1.538–1.542). If minerals are in contact with each other or the mounting medium at the border of the rock slab, the Becke line method is used to identify the mineral with the higher refractive index. The ILH rule (Increase distance between specimen and objective lens. If the light line moves into the mineral, it has the higher refractive index. Relief and the Becke line are observed with the aperture diaphragm almost closed and an objective with a magnification >20x. Go to the rims of the thin section where the minerals are in contact with the mounting medium or search for good mineral–mineral contacts.

4.4

Cleavage

4.4.1 Appearance of Cleavage Cleavage is the preferred orientation of splitting along crystallographic directions or crystal faces reflecting weak bonding and is related to the crystal structure. Cleavage or lack of cleavage is diagnostic of a mineral and an important criterion for its identification. In thin section cleavage is seen as fine black to gray lines which are the traces of the splitting planes cutting through the mineral in oriented directions. Cleavage traces are oriented parallel to crystallographic directions and are smooth and straight, as opposed to fractures. Different cleavage directions in one section make a cleavage set. Cleavage directions and the absence of cleavage provide information about the crystallographic orientation of the mineral in a two-dimensional thin section. It may happen that the most characteristic sections to determine cleavage are not seen in a section because of unfavorable preparation of the thin section. Characteristic cleavage sets and cleavage directions as well as lack of cleavage are illustrated in Fig. 4.29. Cleavage can be perfect, very good, good, or poor (Table 4.7) which may vary according to the crystallographic orientation and is known as cleavage anisotropy. A well-known example is kyanite. If the cleavage traces traverse almost the whole crystal, it is termed perfect, as in mica or kyanite. If the cleavage trace stops abruptly, it is called good, and if it is irregularly distributed, it is known as poor cleavage. Certain minerals do not show any cleavage, such as quartz or are fractured such as olivine. Cleavage is observed in

Table 4.7 Categories of cleavage for some common rock-forming minerals. Cleavage visibility depends on the section of the mineral. Minerals may display different cleavages in different crystallographic orientation, and the highest category of cleavage is given Category

Example

Perfect

mica cpx opx amp gln aeg ky anh sil ntr lmt hul

Very good

fl scp wrk stb

Good

or pl and gp crd cpt scp mes php

Poor

pl or clay crd

No cleavage

qz ol mica ⊥ (001)

For abbreviations see Table A.1 in Appendix A

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(a)

Optical Properties of Minerals in Plane Polarized Light (PPL)

(b)

Fig. 4.30 Cleavage visibility and correlation with the crystallographic orientation of biotite. a In the thin section the grain to the right shows no cleavage and the darkbrown (001) plane is visible, whereas to the left the

(010) plane with the cleavage is clearly seen; b dependance of visibility of cleavage according to the section of biotite and appearance as two-dimensional form in the thin section

plane polarized light with the aperture diaphragm almost closed. Cleavage visibility depends on the crystallographic orientation of the crystal in the twodimensional thin section. The thin section should be examined to find the section with the best corresponding crystallographic orientation. Magmatic rocks with a high variability of mineral orientations often allow the recognition of the cleavage directions since they show no preferred orientation during crystallization. Metamorphic rocks with a schistosity may reveal well the cleavage of mica, if the thin section

orientation is prepared with respect to the cleavage orientations. This is also the case for the amphibole group. Figure 4.30 shows the dependance of visibility on the appearance of cleavage using biotite. If a crystal of biotite is sectioned parallel to (001), no cleavage is visible. But if the mineral is cut parallel to (010), the cleavage is clearly visible. This (001) cleavage is characteristic for the mica group (Figs. 4.29e–g). Cleavage and angle of cleavage sets in a crystal depend on both the crystal structure and the orientation of the crystal cut with respect to the structure. Figure 4.31 illustrates this with two

Fig. 4.31 Aegirine-augite in two different sections. a Two prismatic cleavages of {110} intersecting at about 87° perpendicular to (001); b only one prismatic cleavage is visible along the c-axis

4.4 Cleavage

Fig. 4.32 Different sections of actinolite in an actinolite schist. (1) Sections with cleavage sets and the characteristic amphibole angle of 124°; (2) sections with inclined cleavage sets due to different cutting angles; (3) sections with the prismatic cleavage directions

cuts across a crystal of aegirine-augite. In Fig. 4.31a the cut is perpendicular to the c-axis, and the two cleavages intersect at 87° forming a cleavage set characteristic of pyroxene, whereas in Fig. 4.31b the cut is parallel to the c-axis and only one prismatic cleavage is seen. An actinolite schist (Fig. 4.32) showing random orientation of individual crystals displays a great variety of sections with different crystallographic orientations and therefore also a variety of corresponding cleavages or cleavage sets. Different sections with different cleavages or cleavage sets can be recognized. The {110} cleavage planes or cleavage set form an angle of 124° and 56°, but more inclined cleavage sets are also present due to different cutting angles. Clearly visible is also one prismatic cleavage trace in some crystals. Actinolite has grown isostatically and was not exposed to a stress regime. Characteristic cleavage sets and lack of cleavage for some common minerals are summarized schematically in Fig. 4.33 and the corresponding crystal structure drawn with CrystalMaker is shown and the plane responsible for the cleavage is indicated. In the plate illustrating cleavage (Fig. 4.29), minerals may display one cleavage direction along a crystallographic axis or crystallographic faces such as the prismatic cleavage trace in scapolite visible as fine lines (Fig. 4.29a) or in sillimanite (Fig. 4.29b). Fluorite displays an

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octahedral cleavage (Fig. 4.29c). The intersection of (110) is seen in andalusite (Fig. 4.29d). Typical mica cleavage cut parallel to (010) is depicted in (Fig. 4.29e–g), and if a mica is cut perpendicular to (001) no cleavage is visible (Fig. 4.29h). Certain minerals display up to three cleavage directions which combine to form cleavage sets, but only two are normally visible in a section (Fig. 4.29i–o). The angle of 124° between cleavage traces in a cleavage set is especially characteristic for the amphibole group (Fig. 4.29i–j) and is 87° in the pyroxene group (Fig. 4.29m–o). Kyanite shows a cleavage set of the intersection of the {100} and {010} cleavage traces (Fig. 4.29p). Lack of cleavage is also an important criterion. Some minerals show no cleavage at all such as quartz (Fig. 4.29q), olivine (Fig. 4.29r) or garnet (Fig. 4.29s) or have small cracks as sillimanite (Fig. 4.29t). Cracks and fissures provide access to fluids. This is especially characteristic for the members of the olivine group where hydrothermal fluids may replace olivine and low temperature minerals such as serpentine, chlorite, or iddingsite become stable. Replacement is sometimes observed along the fluid pathways, and sometimes only the original crystal outline is preserved and a pseudomorph is present. Such textures can also be often observed in pyroxene, amphibole or garnet, with a variety of possible alteration products (e.g., chlorite, amphiboles, talc, calcite, epidote, quartz, magnetite or iron hydroxides) depending on chemistry and physico-chemical conditions (pressure, temperature, fluid properties).

4.4.2 Causes of cleavage Cleavage is a mechanical property related to the crystal structure and the electric forces that bind atoms together in a crystal. Traditionally, bonding types are defined based on the electronic structure of an atom or the electron shells and its nearest neighbor. Four types of bonding are distinguished in minerals: metallic, ionic, covalent, and Van der Waals bonding (see summary in Wenk and Bulhak, [40]; Okrusch and Frimmel, [26]). In the metallic bonding some

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Optical Properties of Minerals in Plane Polarized Light (PPL)

(a)

(b)

qz with fluid inclusions

ol (fo) with cracks

grt with cracks

bt cut ⊥(001) with ap and pleochroic halos

Mg Mg

Fig. 4.33 Examples of cleavage. a Minerals with cleavage and corresponding view of the crystal structure with the cleavage plane indicated; b lack of cleavage and corresponding crystal structure. The axes X, Y, and Z correspond to crystallographic axes a, b, c. Structures are drawn with CrystalMaker

electrons of the outer electron shells can move freely producing an electron cloud which binds the atoms together. In ionic bonding atoms have either positive or negative charge. An atom can donate an electron of its outer shell becoming positively charged and called cation while an atom receiving the electron becomes negatively charged and is known as anion. Their electron shells do not overlap. The involved elements

achieve therefore an inert gas configuration where electron shells are filled. For example, in NaCl the atom Na attains neon and the atom Cl argon configurations. In covalent bonding, single electrons are shared between two atoms in a common orbital. Van der Waals bonding results from interaction between neutral atoms since the electron distribution is not uniform. Van der Waals bonding is the weakest of the bonding

4.4 Cleavage Fig. 4.34 Crystal structure of biotite and the location of the cleavage plane (in red) in the K interlayer (crystal structure drawn with CrystalMaker)

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Biote K(Mg,Fe)3AlSi3O10(OH)2 T-O-T mineral Tetraheder (T) Octaheder (O) Tetraheder (T) Interlayer with K cleavage plane

types and plays an important role in the preferred cleavage direction of most sheet silicates. An example is shown for biotite where the cleavage plane is parallel to the K interlayers containing the van de Waals bonds (Fig. 4.34). Combinations of bonding are common in minerals. For example, the important Si–O bond involves covalent and ionic forces, the bond in the Si tetrahedron is traditionally considered as of mainly covalent character, while the atoms in octahedral sites (Fe, Mg) are bond by ionic bonds. The type and strength of bonding or cleavage behavior and chemical properties of a crystal have also been investigated by mapping the distribution of electron density with X-ray diffraction and neutron diffraction (Bader [3]; Gibbs et al. [14, 15]). A 3-dimensional map with the topography of the electron-density distribution consists of isolines of the same electron strength comparable to the isolines for the altitude in topographic maps. An electron

localization function (ELF) is generated which is the spatial arrangement or localization of the electron-density distribution and produces a three-dimensional electron domain around the respective atoms. It illustrates the bonding in different directions of the crystal lattice and consists of characteristic geometric spatial arrangements created by either a bonding pair of electrons between atoms or a lone pair of electrons. The last configuration is also called a nonbonding pair and describes an electron domain which is only bound to one atom. Electron domains are negatively charged and repel each other. The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them. The electron localization function (ELF) is shown in Fig. 4.35 for talc. Talc (Mg3(Si2O5)2(OH)2) is a 2:1 sheet silicate (T-O-T) that consists of a layer of edge-sharing MgO4(OH)2 octahedra sandwiched between two layers of SiO4 tetrahedra linked together in six member rings and of which the apex of the

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Optical Properties of Minerals in Plane Polarized Light (PPL)

(a)

(b)

Fig. 4.35 Cleavage in talc a Electron localization function (ELF) and various forms of electron domains viewed down [100] (from Gibbs et al., [14]). The cleavage of talc is the result of the absence of electron domains

tetrahedra of each layer points to the octahedral sheet. The electron localization function of talc (Gibbs et al. [14]) depicts various electron domains (Fig. 4.35). Along the Si-O bond vector between tetrahedral and octahedral layer a hemispherical domain of electrons is ascribed to a localized bond pair. The kidney-shaped domain of the Si-O-Si angle between tetrahedral and octahedral layer caps a bridging O. Nonbridging O atoms are capped by a mushroom-shaped domain in the octahedral layer and banana domains are characteristic for bridging O in the tetrahedral layers. The H atoms are enclosed in almost spherical domains. The ELF clearly demonstrates that no electron domains are detected in between the 2:1 layers. This is the reason for the pronounced cleavage and softness of talc. Why does the structure hold together? Gibbs et al. [14] argue that half of the base of the Si tetrahedra lie above a banana-shaped domain in the adjacent layer and that weak bonded interactions between the Si atoms and the lone pair domains of the bridging O are responsible for binding the neutral layers together.

bridging the composed tetrahedra-octahedra-tetrahedra layers; b crystal structure of talc (drawn with CrystalMaker). For explanations see text

Cleavage and cleavage sets are seen as fine black to gray lines and are the traces of the splitting planes traversing the mineral in oriented directions and depend on the sectioning of the mineral with respect to its crystallographic orientation and crystal structure. Cleavage and cleavage sets are characteristic for mineral groups (mica group {001}, amphibole group {110} with an angle of 124° or the pyroxene group {110} with an angle of 87°). The lack of cleavage is also a criterion for quartz, garnet, staurolite, and olivine. In addition, some crystallographic directions such as the section cut⊥ (001) in the mica group do not show cleavage. Cracks are characteristic for sillimanite, garnet, and olivine. Olivine group members are often altered to varying degrees starting along the fractures, eventually being totally replaced by the alteration mineral (pseudomorph). Cleavage is related to the electron localization function (ELF) which ascribes electrons to a spatial

References

arrangement called electron domain which vary in shape. Cleavage develops best where electron domains are not or poorly connected.

References 1. Armienti P, Pareschi MT, Innocenti F, Pompilio M (1994) Effects of magma storage and ascent on the kinetics of crystal growth. The case of the 1991–93 Mt. Etna eruption. Contrib Miner Petrol 115:402– 414 2. Bačík P, Fridrichová J, Štubňa J, Antal P (2015) Application of spectroscopic methods in mineralogical and gemmological research of gem tourmalines. Acta geologica slovaca 7(1):1–9 3. Bader RFW (1998) A bond path: a universal indicator of bonded interactions. J Phys Chem A 102:7314–7323 4. Bank H, Henn U, Bank FH, v. Platen H, Hofmeister W (1990) Leuchtendblaue Cu-fuhrende Turmaline aus Paraíba, Brasilien. Zeitschrift der Deutschen Gemmologischen Gesellschaft, 39(1):3–11 5. Bristow JK, Tiana D, Parker SC, Walsh A (2014) Defect chemistry of Ti and Fe impurities and aggregates in Al2O3. J Mater Chem A 2:6198–6208 6. Burns RG (1993) Mineralogical applications of crystal field theory. 2nd edn, Cambridge University Press, p 551 7. Cashman KV, Ferry JM (1988) Crystal size distribution (CSD) in rocks and the kinetics and dynamics of crystallization. Contrib Miner Petrol 99:401–415 8. Cashman KV (2020) Crystal size distribution (CSD) analysis of volcanic samples: advances and challenges. Front. Earth Sci.10 9. Chopin C, Langer K (1988) Fe2+-Ti4+ charge transfer between face-sharing octahedra: polarized absorption spectra and crystal chemistry of ellenbergerite. Bull Minér 111(1):17–27 10. Corfu F, Hanchar J, Hoskin P, Kinny P (2003) Atlas of zircon textures. Rev Mineral Geochem 53(1):469– 500 11. Deer WA, Howie RA, Zussmann J (2013) An introduction to the rock-forming minerals. 3rd ed, Berforts Information Press, Stevenage, Herfordshire, p 498 12. Dubinsky EV, Stone-Sundberg J, Emmett JL (2020) A quantitative description of the causes of color in Corundum. Gems Gemol 56(1) 13. Fleischer M, Wilcox RE, Matzko JJ (1984) Microscopic Determination of the Nonopaque Minerals. 3rd ed. U.S. Geol. Surv. Bull. 1627 (revision of Bull 848): p 453

85 14. Gibbs GV, Cox DF, Ross NL, Crawford TD, Burt JB, Rosso KM (2005) A mapping of the electron localization function for earth materials. Phys Chem Miner 32:208–221 15. Gibbs GV, Downs RT, Cox DF, Ross NL, Prewitt CT, Rosso KM, Lippmann T, Kirfel A (2008) Bonded interactions and the crystal chemistry of minerals: a review. Z Kristallogr 223:1–40 16. Goldschmidt V (1913–1923) Atlas der Krystalformen”. Carl Winters Universitätsbuchhandlung, Heidelberg, 7 Bände. 17. Greenidge D (2018) Investigations of color center phenomena in Topaz and Quartz through electron spin resonance with reference to optical absorption and nuclear magnetic resonance: Implications for extended mineral applications. Malaysian Journal of Fundamental and Applied Sciences. Special Issue on Chromatography and Other Analytical Techniques: 142–149 18. Hibbard JM (1994) Petrographic classification of crystal morphology. J Geol 102:571–581 19. Higgins MD (2006) Quantitative textural measurements in igneous and metamorphic petrology. Cambridge University Press, p 265 20. Holtkamp M (2004–2019) Smorf crystal models. www.smorf.nl 21. Kostov I, Kostov RI (1999) Crystal habit of minerals. Bulgarian Academic Monographs 1. Sofia: PensoftPublishers and Prof. Marin Drinov Academic Publishing House 22. Marsh BD (1988) Crystal size distribution (CSD) and the kinetics and dynamics of crystallization. I Theory Contrib Miner Petrol 99:277–291 23. Mattson SM, Rossman GR (1988) Fe 2 +–Ti 4 + charge transfer in stoichiometric Fe2+, Ti4+. Miner Phys Chem Miner 16:78–82 24. Merkel PB, Breeding CM (2009) Spectral differentiation between copper and iron colorants in gem tourmalines. Gems Gemology 45(2):112–119 25. Nespolo M (2015) The ash heap of crystallography: restoring forgotten basic knowledge. J Appl Crystallogr 48:1290–1298 26. Okrusch M, Frimmel HE (2020) Mineralogy. Springer-Verlag Germany, p 719 27. Phillips, WR (1981) Optical mineralogy: the nonopaque minerals. WH Freeman San Francisco 28. Pupin JP (1980) Zircon and granite petrology. Contrib Miner Petrol 73:207–220 29. Randolph AD, Larson MA (1971) Theory of particulate processes. Academic Press, New York, p 251 30. Schmetzer K, Bernhardt H-J, Dunaigre C, Krzemnicki MS (2007) Vanadium-bearing gem-quality tourmalines from Madagascar. J Gemmol 30:413– 433 31. Schwarzinger C, Wildner M, Ulatowski S, Sawyer M (2019) Vanadium-bearing tourmaline from the commander mine, Nadonjukin, Tanzania. J Gemmol 36:534–543 32. Shelley D (1992) Igneous and metamorphic rocks under the microscope. Classification, textures,

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33.

34.

35.

36.

37.

38.

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Optical Properties of Minerals in Plane Polarized Light (PPL)

microstructures and mineral preferred orientations. London Chapman and Hall, London 445p Sherman DM (1987) Molecular orbital (SCF-XaSW) theory of metal-metal charge transfer processes in minerals I. application to Fe2 +! Fe3+ charge transfer and “electron delocalization” in mixedvalence iron oxides and silicates. Phys Chem Miner 14:355–363 Smith G (1978) Evidence for absorption by exchange-coupled Fe2+-Fe3+ pairs in the near infrared spectra of minerals. Phys Chem Miner 3:375–383 Taran M, Langer K (1998) Temperature and pressure dependencies of intervalence charge transfer bands in spectra of Fe- and Fe, Ti-bearing oxygen-based minerals. Neues Jb Mineral Abh 172:325–346 Tertsch H (1949) Die Beckesche Lichtlinie. Mikroskopie-Zentralblatt für mikroskopische Forschung 4:296–307 Tröger WE (1979) Optical determination of rockforming minerals. E. Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, p 188 Vennari CE, Williams Q (2021) A high-pressure Raman study of FeTiO3 ilmenite: fermi resonance as a manifestation of Fe-Ti charge transfer. Phys Chem Miner 48:34

39. Welsch B, Faure F, Famin V, Baronnet A, Bachèlery P (2012) Dendritic crystallization: a single process for all the textures of olivine in basalts? J Petrol 54:539–574 40. Wenk H-R, Bulakh A (2016) Minerals. Cambridge University Press, p 640

Further Reading 1. Bloss FD (1999) Optical crystallography. Mineralogical Society of America, p 239 2. Dyar MD, Gunter ME, Tasa D (2008) Mineralogy and optical mineralogy. Mineralogical Society of America, Chantilly, VA, p 708 3. Kerr PF (1977) Optical mineralogy. 4st edition, McGrawHill Book Company, p 492 4. Nesse WD (2013) Introduction to optical mineralogy. 4th edn, Oxford University Press, p 361

5

Optical Properties of Minerals in Cross Polarized Light (XPL)

5.1

Birefringence

In an anisotropic medium light is split into two rays, a slow ray and a fast ray. The difference in velocity results in a lag between the two rays which is called the retardation. The retardation is the distance that the slow ray lags behind the fast ray (see also Sect. 2.3). It is called birefringence when expressed as the difference between the indices of refraction between the slow and the fast rays or d ¼ Dn ¼ ne  nx (uniaxial minerals) or d ¼ Dn ¼ nc  na (biaxial minerals). It is a key diagnostic parameter and depends on the orientation of the indicatrix axes (vibration directions) and their corresponding refractive indices with respect to the polarizers and their relationship to the crystallographic directions. Birefringence (d or Dn) is observed when simultaneously using the lower polarizer and the analyzer (= upper polarizer) vibrating at 90° to each other. These working conditions are said to be in cross polarized light or XPL or under crossed Nicols. The analyzer is now the key tool as already suggested by its name. It will be inserted and removed frequently during the examination of the minerals. Occasionally the kplate will be inserted to identify the vibration directions of the slow or fast rays (see Sect. 3.5 Accessory plates and Sect. 5.2 Elongation).

5.1.1 Appearance of Birefringence In Chap. 2 constructive and destructive interferences were discussed where waves were vibrating in a single plane. The situation is different in a plane polarized light microscope where the 3D orientation of the waves must be considered. Light is polarized by the first polarizer and enters the anisotropic crystal where the light ray is split into two rays, a slow and a fast ray. Two rays emerge from the anisotropic crystal (Fig. 5.1). They do not lie within a plane and vibrate at right angles. If the retardation is 1=2k, the rays are forced by the analyzer to recombine in the plane of the analyzer, interfere constructively, and add to a new wave. The mineral appears bright with a characteristic color called the interference color (Fig. 5.1). Destructive and constructive interferences are explained in detail in Figs. 5.2 and 5.3. Contrary to the 2D situation, where a retardation of D ¼ nk between two waves produces a constructive interference, and a retardation D ¼ nk þ 1=2 nk results in a destructive interference in a single plane, the inverse phenomenon is observed in 3D. Plane polarized light vibrating N–S is split into two waves by an anisotropic crystal. The two waves a and b leaving the crystal have the retardation nk and lie in planes 1 and 2 vibrating at right angles to each other (Fig. 5.2). The

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. T. Schmidt, Transmitted Light Microscopy of Rock-Forming Minerals, Springer Textbooks in Earth Sciences, Geography and Environment, https://doi.org/10.1007/978-3-031-19612-6_5

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Fig. 5.1 Schematic path of a light ray from the light source, being plane polarized by the polarizer, traversing an anisotropic mineral, is split into two rays by the crystal

Optical Properties of Minerals …

vibrating at 90° to each other and is recombined to a new wave by the analyzer

Δ=nλ

Plane 2 wave b Plane 1 wave a

Fig. 5.2 Destructive interference for two waves emerging from an anisotropic crystal and having the retardation nk. Polarizers are shown as orange arrows

Fig. 5.3 Constructive interference for two waves emerging from an anisotropic crystal and having the retardation D ¼ nk þ 1=2 nk. Polarizers are shown as orange arrows

5.1 Birefringence

resultant wave arrives at the analyzer at an angle of 90°, cancels out, and the mineral appears extinct. In Fig. 5.3 the retardation between waves is D ¼ nk þ 1=2 nk. Plane polarized light vibrating N–S is split into two waves by an anisotropic crystal. The two waves c and d leaving the crystal have the retardation D ¼ nk þ 1=2 nk and lie in planes 3 and 4 vibrating at right angles to each other (Fig. 5.3). The resultant wave arrives at the analyzer at an angle of 0°, is transferred, the mineral appears bright, and the interference color will appear. The examples given above describe the two extremes of light transfer by an anisotropic crystal which are either the maximum transfer of light or no transfer of light at all arriving at the analyzer. The role of the analyzer is to force the incoming waves to vibrate in one plane and merge these waves through constructive or destructive interference giving rise to a combination of new waves that result in the birefringence color. In fact, since white light is composed of many waves there will be an indefinite number of waves arriving, and they all will contribute to the interference color. This is illustrated in Fig. 5.4 where six wavelengths of white light are plotted along the x-axis as a function of their retardation expressed in nm. Their intensity is plotted along the y-axis with the intensity for D ¼ nk being zero, and the intensity for D ¼ nk þ 1=2 nk maximum. The resulting interference color can now be observed at a specific value of retardation along a vertical line as the sum of the various proportions of the respective wavelengths and is plotted as bar graphs. The color is then projected as a point onto the Michel-Lévy color chart (which is discussed later in more detail). For example, at a retardation of 200 nm, the combination of all wavelengths results in white called “first-order white” shown as a white circle in Fig. 5.4. Retardation is related as Dn or the difference between the refractive indices of the slow and the fast rays which are projected on the horizontal axis of the Michel-Lévy color chart. The value suggests a difference of refractive indices

89

between the slow and the fast ray of 0.008 for a thickness of 30lm (see Sect. 2.3 for the relationship between retardation, refractive indices, and thickness). At a retardation of 600 nm, there is main intensity for blue and violet, the interference color is called “second-order blue” as represented by a blue circle, and the difference of refractive indices between the slow and the fast rays is 0.023. At a retardation of 900 nm, the main proportions in the bar graph are for the wavelengths yellow and orange with minor amounts of red, violet, and green while blue wavelengths are absent. The resulting refore yellow, also called “second-order yellow” depicted as a yellow circle, and the difference of refractive indices between the slow and the fast is 0.029.

5.1.2 The Michel-Lévy and the RaithSørensen Interference Color Charts All possible retardations expressed in nm, representing the wavelengths of colors of white light and how they relate to the difference of refractive indices and the thickness, are summarized in the Michel-Lévy color chart. This chart was already published by Auguste Michel-Lévy as a first version in 1883 and then together with Alfred Lacroix in 1888. Over the centuries many versions of this interference color chart have been published. Figure 5.5 shows the classic chart as published by Nikon, and in Fig. 5.6 the chart of ZEISS is given. The thickness (d in lm) of the anisotropic crystal is plotted along the y-axis, and along the x-axis the difference of refractive indices between the two rays, the slow and the fast, is noted. The color spectrum in the MichelLévy color chart starts with black for a retardation of zero. This means that there is no difference in refractive indices or only one refractive index is visible as in a section perpendicular to an optic axis of anisotropic minerals or as for a isometric mineral with only one index of refraction. At a retardation of 250 nm all colors

90 Fig. 5.4 Intensity of six wavelengths of white light plotted along the y-axis for the intensity D ¼ nk which equals zero intensity and for the maximum of intensity where D ¼ nk þ 1=2nk. The resulting interference colors are plotted as bar graphs and projected as a point onto the Michel-Lévy color chart. See text for detailed explanation (modified after Stoiber and Morse [10])

5

Optical Properties of Minerals …

5.1 Birefringence

91

Fig. 5.5 Classical Michel-Lévy color chart as published by Nikon (with permission of Nikon). The orders of birefringence can be compared with the octaves of a piano

are present as explained also in Fig. 5.4, and “first-order white” will result. Between 350 nm and 500 nm yellow, orange, and red colors of longer wavelengths dominate while shorter wavelengths are not present. At a wavelength of 551 nm a characteristic red occurs called “firstorder red”. The colors green, yellow, and orange with intermediate wavelengths are suppressed, and red is the dominant component with some amount of blue and violet. This color marks the limit of the so-called first-order birefringence which corresponds to Dn between 0 and 0.018. The color sequence restarts again but the colors change shades and become brighter. We can compare this with the octave in music where the octaves correlate with the orders of birefringence. The next interval of 551 nm–1102 nm, the second or “second-order birefringence” (Dn ¼ 0:018  0:036), is brighter and starts with blue going through green, yellow, and orange until a more pinkish-red, named “second-order red”, appears at 1102 nm. The following third or

“third-order birefringence” shows very bright luminous colors (Dn ¼ 0:036  0:054) with a retardation interval between 1102 nm and 1653 nm. In the fourth or the “fourth-order birefringence” (Dn ¼ 0:054  0:072, 1653– 2204 nm) the colors become paler and are dominated by greenish and reddish shades. Further increasing birefringence and higher orders will result in colors reminiscent of colors in iridescent white pearls or in out washed clothes. We cannot differentiate these higher orders anymore. Values of birefringence, the retardation in nm, and characteristic color sequences in each order are summarized in Table 5.1. Sørensen [9] has revised the Michel-Lévy color chart and recalculated the relationship between light transmission and wavelengths using MATLAB. Two of his newly calculated interference color charts were modified by Raith et al. [8] and include on top of the chart the range of refractive indices and the resulting maximum birefringence of common rock-

92

5

Optical Properties of Minerals …

Fig. 5.6 Classical Michel-Lévy interference color chart as published by ZEISS [14]. With permission of ZEISS Table 5.1 Orders of interference colors, corresponding range of d ¼ Dn, retardation, and description of corresponding colors in the Michel-Lévy interference color chart Order of birefringence

Dn ¼ d ne  nx nc  na

Retardation (nm)

Interference colors within the order Note: the observed sequence might slightly be modified, especially in the second and third order

First order

0–0.018

0–551

Black ! iron gray ! lavender gray ! gray blue ! clear gray ! pure white ! yellowish white ! yellow ! orange ! red ! deep red

Second order

0.018–0.036

551–1102

Colors are luminous and bright Purple ! violet ! indigo ! turquoise ! green ! yellowishgreen ! yellow ! orange ! bright orange red ! purplish redviolet (magenta)

Third order

0.036–0.054

1102–1653

Colors are less luminous and pastel colored Colors are less luminous Violet-red ! blue ! greenish blue ! green ! greenish-yellow ! yellow ! pale purple (pale magenta)

Fourth order

0.054–0.072

1653–2204

Colors resemble colors seen in pearls or washed-out clothes of yellow and green shades

forming minerals. Figure 5.7 is the classic layout with the thickness of the crystal along the y-axis and birefringence along the x-axis. Figure 5.8 displays a new layout including the range of refractive indices and the maximum

birefringence for common rock-forming minerals. This version might be easier to use. When developing the new color chart Sørensen [9] found some differences to the earlier color charts as shown in Fig. 5.9a. For example, in the

5.1 Birefringence

93

Fig. 5.7 Classical layout of the interference color chart with the newly calculated range of interference colors by

Sørensen [9] for common rock-forming minerals (Raith et al. [8]). With permission of Raith and Sørensen

second order a large band of bright green is present in the earlier color charts of Nesse [6], ZEISS [26], and Bloss [2]. According to his new calculations this bright green range is missing,

being replaced by a band of turquoise and a whitish green. The calculated color chart color resembles the color chart of Dyar et al. [4]. In Fig. 5.9 the earlier and the Raith-Sørensen color

94

5

Optical Properties of Minerals …

Fig. 5.8 Raith-Sørensen interference color chart with the new layout for common rock-forming minerals (Raith et al. [8]). With permission of Raith and Sørensen

charts are compared with the first four orders of birefringence of a transparent naturally occurring zircon crystal of amphibolite facies conditions (Fig. 5.9b). The zircon also reveals the presence of the turquoise range of the secondorder birefringence. However, there are several diverging interference color bands between the interference color chart of the zircon and the one by Raith-Sørensen. (1) A small range of orange is present before the appearance of the secondorder red. (2) A small green range is still observed after the turquoise band in the secondorder of the zircon crystal. (3) The third-order turquoise is not seen in the zircon crystal and is only represented by a small blue band. (4) The green range of the third order is much larger in the zircon crystal than in the calculated interference color chart by Sørensen [9], and the yellow appears as a small band only. 5) The fourth order starts with a light yellow whereas in

all color charts it is a light green which occurs after the third-order red. Sørensen [9] states that the coincidence of his new interference color chart shows the best correlations with an olivine crystal. The divergence of interference colors or the variations in the color bands of the various interference color charts, their absence, and replacement by other shades are a common phenomenon and, although minor, must be evaluated by studying in detail the sequence of the observed color bands in the various interference color charts. These differences are probably related to structural and chemical differences of the crystal lattice. Colorless minerals show the interference color as seen in the color chart of Michel-Lévy or Raith-Sørensen, and examples are given for the various orders of birefringence in Fig. 5.10. However, the interference color of colored minerals is masked by the addition of their own color

5.1 Birefringence

95

Fig. 5.9 Comparison of commonly used interference color charts with four orders of birefringence in a naturally occurring transparent zircon from an amphibolite facies rock. a Comparison of interference color charts as published in Sørensen [9]; b naturally occurring crystal of zircon of amphibolite facies conditions viewed in XPL with its characteristic sequence of interference colors of four orders of birefringence. See explanation in text

and deviates from the interference colors as seen in the Michel-Lévy color chart. This results in the so-called anomalous interference colors not displayed by the Michel-Lévy color chart (Fig. 5.11). Their birefringence as determined from the difference between the slow and the fast rays often suggests a first-order gray to white or pale yellow, but colors other than the ones predicted from the Michel-Lévy color chart are seen. The best example is chlorite which may show yellow-ochre, yellowish-brown, blue, or violet interference colors (Fig. 5.11). Variation of Mg, Al, Fe3+, and Fe2+ in the octahedral sheet and substitution of Si4+ by Al3+ in the tetrahedral sheet of chlorite are probably responsible and change the refractive indices and the optical character of chlorite. Another example is reddish amphibole which has a distinct green of the second order and Ti-augite with anomalous yellow-ochre interference colors (Fig. 5.11). These anomalous interference colors are diagnostic for certain minerals and an additional criterion for their identification.

5.1.3 How to Determine the Maximum Interference Color of a Mineral Looking for the first time at the range of interference colors can be confusing, and an inexperienced petrologist might expect a range of minerals to be present. The range of interference colors is related to the different crystallographic orientations and its relationship to the polarizers. One must scan the section visually and try to filter the information. It is necessary to observe the range of interference colors, compare with the optical properties seen in PPL, and compile an inventory of the range of interference colors observed. It is also worth checking at the margins of crystals where the grains become thinner, the orders of birefringence decrease toward the thinner edge of the crystal, and the order of birefringence can be determined (Fig. 5.12). The maximum order is normally found in the center of the mineral. Chemical zoning may result in a

96

5

Optical Properties of Minerals …

Fig. 5.10 Representative examples of different orders of birefringence of some common rock-forming minerals. For mineral abbreviations see Table A.1 in appendix A

5.1 Birefringence

Fig. 5.11 Anomalous interference colors. a Chlorite with blue-violet (rim) to yellow-ochre (center) interference colors filling an amygdule in a basalt; b retrograde chlorite with ochre-yellow interference colors occurring in a garnet amphibolite; amphibole shows birefringence of

(a)

Fig. 5.12 Determination of interference colors at crystal edges using an objective lens with a large magnification. a Crystal of clinopyroxene showing first and second-order birefringence up to red second order and a maximum

97

first order and lower second order; c intensive green of second order in Fe-rich hornblende from an andesite; d Ti-augite with yellow–brown interference colors and an hourglass texture

(b)

birefringence of d ¼ 0:036; b anhydrite grain showing three orders of birefringence with maximum red of third order or d ¼ 0:055. The red of the first, second, or third order is indicated by the red arrow

98

change of birefringence from the rim to the center, which is often the case, for example, in epidote. Crystals should therefore also be examined in PPL to detect any chemical zoning. In Fig. 5.13 a monomineralic quartzite consisting mainly of quartz shows a large range of interference colors. The three principal sections for uniaxial quartz, their appearance in the thin section with their resulting birefringence, and the relationship between optical and crystallographic parameters are indicated. The refractive indices

5

Optical Properties of Minerals …

of quartz are ne ¼ 1:554 and nx ¼ 1:545 resulting in the bright white of the first order (Dn ¼ d ¼ ne  nx ¼ 1:554  1:545 ¼ 0:009, based on a thickness of 30lm). This is the bright white crystal which is in the 45° position representing a section parallel to the optic axis. Crystals with various gray tones are sections inclined to the optic axis. The dark, black crystals are either sections in the extinction position or sections cut perpendicular to the optic axis which remain extinct during the rotation of the stage.

Fig. 5.13 Relationship between observed interference color of uniaxial quartz in a monomineralic metamorphic quartzite with optical and crystallographic parameters

5.1 Birefringence

99

Fig. 5.14 Relationship between observed interference color of uniaxial calcite in a marble with optical and crystallographic parameters

Figure 5.14 shows a marble with mainly calcite and a large range of interference colors. The three principal sections for uniaxial calcite, their appearance in the thin section with their resulting birefringence, and the relationship between optical and crystallographic parameters are indicated. Since the difference of velocity of the two rays in calcite is high (Dn ¼ d ¼ nx  ne ¼ 1:658  1:486 ¼ 0:172), first, second, third, and higher orders of birefringence are visible. Figure 5.15 shows a peridotite with olivine and a large range of interference colors. Four sections of olivine, their appearance in the thin section with their resulting birefringence, and the relationship between optical and crystallographic

parameters are indicated. The maximum interference color determined is red of the third order or d ffi 0:042. Other sections with different colors of the second order as well as the lower first order with gray and yellow colors are also present.

5.1.4 Transmission of Light by the Analyzer and Extinction Behavior While observing the interference colors and turning the microscope stage a full circle of 360°, the mineral will go into extinction or appears

100

5

Optical Properties of Minerals …

Fig. 5.15 Relationship between observed interference color of biaxial olivine in a peridotite with optical and crystallographic parameters

“black” every 90°, and in between it will have a position with maximum birefringence. This happens four times, and there are four extinction positions and four positions with maximum transmission of light (Fig. 5.16). The color of the mineral will not change but the intensity T or the amplitude of light does as shown in Fig. 5.17. The mineral is in the extinct position when an axis of the indicatrix with the corresponding light ray coincides with the lower polarizer and the light arriving in the analyzer vibrating at 90° with respect to the polarizer will be canceled. In the

brightest position in between the extinction positions, the vibration directions of the crystal are not parallel to the polarizers. The light splits into two waves which combine in the analyzer leading to the corresponding birefringence color. This position, called the 45° position, and occurring also at 135°, 225°, and 315° yields the maximum birefringence in minerals with parallel extinction (Fig. 5.16). This maximum value for d or Dn is given in the interference color charts. When describing the extinction behavior of a crystal, the crystallographic axes a, b, c or the

5.1 Birefringence

101

0°/360°

45°

90°

135°

180°

225°

270°

315°

Fig. 5.16 Anisotropic mineral (muscovite) shows four times extinction and four times the brightest position while rotating the microscopic stage from 0° to 360°

crystallographic faces, the cleavage traces, or a twinning plane are used as a reference direction. The extinction behavior is best observed in euhedral and elongate crystals where the crystallographic reference directions can be easily identified. In Fig. 5.17 the extinction behavior of an elongate uniaxial hexagonal tourmaline crystal is explained. A euhedral tourmaline crystal is oriented N-S with its long crystallographic caxis. In this position the light ray vibrating along the indicatrix axis Z with ne is parallel to the polarizer and the crystallographic c-axis and will be canceled by the analyzer vibrating at 90°. The mineral is in the extinction position. The mineral is then rotated at an angle of 22.5° and to the 45° position which shows the highest transmission of light or maximum brightness and the maximum birefringence. There is no change of color but a change of intensity when rotating from the 90° position to the 45° position (Fig. 5.17a). The location of the indicatrix axes with corresponding refractive indices and the crystallographic c-axis is shown in Fig. 5.17b. Figures 5.17c–e explain the observed extinction behavior. The light ray vibrates along the c-axis and parallel to the polarizer and the indicatrix axis Z with ne and is canceled by the analyzer (Fig. 5.17c). In Fig. 5.17d the light ray vibrating parallel to the polarizer is split into two rays vibrating at 90° to each other or ne0 and nx , and a certain amount of

light is transmitted. In Fig. 5.17e the crystal is in the 45° position with both rays at a maximum distance from the polarizers, and maximum light is transmitted, and the mineral shows maximum birefringence. The closer the indicatrix axes or vibration directions are to the polarizers, the less light is transmitted until the mineral arrives at the 45° position, and maximum transmission is obtained. Figure 5.17 shows that between the position of brightest light and the extinct position, the luminosity of the mineral will decrease but the colors stay the same. A mineral is in the extinction position when the transmission of light T by the analyzer is zero or when the angle s which is the extinction angle (for more details see Sect. 5.3.1) has values of 90°, 180°, 270°, or 360°. The maximum light is transferred if s ¼     45 ; 135 ; 225 or 315 (Fig. 5.16) or the 45° positions (see also Fig. 5.16). The transmission of light by the analyzer can be calculated by transfer-matrix formalism (see Appendix B for details of calculation by Moritz Fontboté Schmidt) and is given by the equation   pdDn 2 T ¼ sin sinð2sÞ2  100 ½% k

ð5:1Þ

where T is the transmitted light intensity as the percent of the incoming light, d the thickness of

102

5

Optical Properties of Minerals …

(a)

(b)

(c)

(d)

Fig. 5.17 Extinction behavior in hexagonal, euhedral, and uniaxial tourmaline with parallel extinction and oriented N-S with its crystallographic c-axis. a Ray with ne vibrates parallel to the crystallographic c-axis and the polarizer and is canceled by the analyzer. On rotation the crystal shows highest transmission at the 45° position. Turn the brown handle clockwise for orientation; b schema of the images in a with location of the indicatrix axes X and Z and corresponding refractive indices ne and nx ; c–e explanation of observed extinction behavior: c a polarized light ray (dashed blue line) arrives from the polarizer, vibrates along the c-axis and parallel to the polarizer and the indicatrix axis Z with ne and is

(e)

canceled by the analyzer; d light ray (dashed blue vector) coming from the polarizer is split into two rays, ne0 and nx , which are retarded by nk þ 12 k and the vectorial components of the rays with ne and nx (red and green vectors) are transmitted as shown as the pink arrows. They will be resolved in the analyzer as a new wave; e crystal is in the 45° position. The light ray (dashed blue vector) coming from the polarizer is split into two rays, ne0 and nx (red and green vectors), which are retarded by nk þ 12 k. The vectorial components of the rays ne0 and nx shown as pink arrows are transmitted and resolved as a new wave in the analyzer

5.1 Birefringence

103

Fig. 5.18 Extinction behavior in a mineral calculated for Dn ¼ 0:009 and a wavelength of k ¼ 536 nm. The mineral goes into the extinction position at T = 0% four times and shows maximum brightness at T = 100% four times. The maximum brightness conditions occur at 45°, 135°, 225°, and 315° and the extinction positions at 90°, 180°, 270°, and 360°

the sample (in nm), Dn ¼ n1  n2 or the difference in refractive index of the two light rays (fast and slow rays), k the wavelength of the light (in nm), and s the angle of extinction (in radians). This equation is mathematically identical to the one given in Johannsen [5] and normally cited as such as in Okrusch and Frimmel [7] which is    180 C  T ¼  sin2 sin 2s sin 2 s  90 100 k ð5:2Þ In applying the Eq. (5.1) and plotting the values T versus 360°, which is a full rotation of the mineral under the microscope, it is evident that T = 0 occurs four times which is the extinction position of the mineral and four times T = 100 corresponding to a maximum brightness (Fig. 5.18). We can predict the interference color observed in the microscope by calculating the relationship between Dn and the % of transmitted light T using the transfer-matrix formalism. This is shown in Fig. 5.19 for quartz, clinopyroxene, and olivine. Quartz has a maximum birefringence of Dn ¼ 0:009 or first-order white. As calculated,

the wavelengths for red, blue, and green are transmitted almost at maximum intensity, and the mineral appears as first-order white (Fig. 5.19a). Maximum birefringence of clinopyroxene is Dn ¼ 0:024 or second-order blue. The calculation shows that mainly the blue and some green wavelengths are transmitted, but red is not present, and the resulting color is a blue (Fig. 5.19 b). Birefringence of olivine has Dn ¼ 0:03 or second-order orange yellow. The calculated color profile shows that mainly the yellow and red wavelengths are transmitted, but blue is not transferred, and the resulting color is a secondorder orange yellow (Fig. 5.19c). These three cases with different Dn can also be plotted as a function of wavelengths and transmitted light intensity T (Fig. 5.19d). The black line (Dn ¼ 0:009) is the transmission for quartz, and almost all wavelengths are transferred at almost maximum intensity which results in the firstorder white. The blue line (Dn ¼ 0:024) represents clinopyroxene, and the wavelengths mainly transmitted are between 420 nm and 560 nm or for wavelengths of blue and green colors the resulting birefringence color is a blue. The red line (Dn ¼ 0:032) is the transmission of light for olivine, and the wavelengths mainly transmitted

104

Optical Properties of Minerals …

5

Δn = 0.024

Δn = 0.009 100

100

(b)

(a)

80

60

Transmission T [%]

Transmission T [%]

80

λ = 470 nm λ = 536 nm λ = 700 nm

40

60

40

20

20

0

0 0

50

100

150

τ [◦ ]

200

250

300

0

350

Δn = 0.03

50

100

150

τ [◦ ]

200

250

300

350

(d) 100

(c) 70 60

80

50 λ = 470 nm λ = 536 nm λ = 700 nm

40 30 20

Max Tranmission T [%]

Transmission T [%]

λ = 470 nm λ = 536 nm λ = 700 nm

60

40

20 10

Δn = 0.009 Δn = 0.024 Δn = 0.03

0

0 0

50

100

150

τ [◦ ]

200

250

300

350

Fig. 5.19 Relationship between Dn, % of transmitted light T, and observed interference color for quartz, clinopyroxene, and olivine. Microscopic images of minerals are shown rotated from 0° to 45°, to 90 and to 135° yielding maximum and minimum transmission. a Quartz Dn ¼ 0:009 or first-order white or maximum birefringence. The wavelengths for red, blue, and green are transmitted at almost 100%, and the mineral appears white; b clinopyroxene Dn ¼ 0:024 or second-order blue

400

450

500

550

600 λ [nm]

650

700

750

or maximum birefringence. Mainly blue and green wavelengths are transmitted, but red is not present, and the resulting color is a blue interference color; c olivine Dn ¼ 0:03 or second-order orange yellow. Mainly the yellow and red wavelengths are transmitted, but blue is not transferred, and the resulting color is an orange yellow; d transmitted intensity T as a function of the wavelengths for Dn of quartz (black line), of clinopyroxene (blue line), and of olivine (red line)

5.1 Birefringence

105

c-axis

Z

Z

c (100)

(100)

Fig. 5.20 Extinction angle s and Z ^ c on (100). The extinction angle is determined by rotating the mineral from the extinction position to the brightest position in both directions, and the smallest angle < 45° determined is used. Polarizers indicated as orange arrows

are between 530 nm and 700 nm or wavelengths for yellow and red colors resulting in an orangeyellow birefringence color.

5.1.5 Extinction Angle and Types of Extinction The extinction angle s is the angle between a crystallographic axis, a cleavage direction, a cleavage set, and an indicatrix axis with its corresponding refractive index (Figs. 5.20 and 5.21). In pinacoidal and prismatic sections of hexagonal, tetragonal, and orthorhombic minerals the extinction angle is zero because the crystallographic axes are aligned parallel to the indicatrix axes or symmetric to crystallographic references. In monoclinic and triclinic minerals, the crystallographic axes are not aligned parallel to the indicatrix axes but form the extinction angle s which varies according to the location of

(a)

(b)

Fig. 5.21 Different types of extinction behavior; a minerals are in extinction positions; b minerals are in brightest position; the polarizers are indicated in orange and the vibration directions of the indicatrix axes in red

106

the optical indicatrix with respect to the crystallographic axes. Since there are three indicatrix axes and three crystallographic axes, there are also three extinction angles and the term s is replaced by a different terminology. The relationship between crystallographic and indicatrix axes or the angle of extinction is expressed as Z^c, X^a, or Y^b, and the angles are given in degrees. The symbol ^ is read as “makes angle with”. A less common terminology used in the literature is c : c or Z:c. For cleavage traces, the plane might be indicated in which the extinction occurs by using the Miller indices. The most common relationship is Z^c or Z^(hkl) as shown in Fig. 5.20. The position of maximum brightness is determined, and the microscope stage is rotated to the left and the right to find the extinction position and the angles are determined. These two angles add up to 90° since extinction always happens at 90°. By convention always the smaller angle is quoted. The angle is considered to be diagnostic of the members of the clinopyroxene group, the clinoamphibole group, and the triclinic feldspar members and their chemical composition. Barker [1] uses the extinction angle and the color in PPL as the two main keys to identify a mineral in a thin section. Extinction behavior of minerals is classified into five types of extinction (Figs. 5.21, 5.22, 5.23, and 5.24). It is related to the crystallographic system, the crystallographic axes, or other morphological elements such as cleavage planes, crystallographic faces, or a twinning plane. The five types of extinction (Fig. 5.21) are: (1) parallel or straight extinction, (2) inclined or oblique extinction, (3) symmetric extinction, (4) extinction without reference, and (5) undulatory or undulate extinction. (1) In parallel or straight extinction, the indicatrix axes —X and Z for uniaxial minerals and X, Y, and Z for biaxial orthorhombic minerals—and their corresponding refractive indices coincide with the crystallographic reference directions and the polarizers. If the mineral is aligned with its reference crystallographic direction parallel to the polarizers, either N-S or E-W, the mineral will be in the extinction position. There is no angle between the extinction position and a

5

Optical Properties of Minerals …

crystallographic direction, and the extinction angle s is zero. This is the case for minerals of the tetragonal, orthorhombic, hexagonal, and trigonal symmetry classes. Examples are given in Figs. 5.21 and 5.22. (2) If a mineral shows inclined or oblique extinction, extinction does not occur parallel to the crystallographic reference directions, but with a certain angle s to them. Minerals of lower symmetry of the monoclinic and triclinic classes are characterized by an inclined extinction (examples in Figs. 5.21 and 5.23a). (3) In symmetric extinction, the extinction position of an indicatrix axis bisects two equivalent reference directions such as crystal faces or cleavage sets and forms the same angle on both sides of the indicatrix axis (examples in Figs. 5.21 and 5.23b). (4) Anhedral minerals without cleavage traces and no crystallographic faces have no reference directions and do not allow measurements of an extinction angle. They have an extinction without reference (Figs. 5.21 and 5.24). (5) In deformed rocks minerals may show undulatory or undulate extinction (Figs. 5.21 and 5.24). The strain induced in the mineral offsets the crystallographic lattice and results in slightly different optical orientations within the crystal. During stage rotation, the crystal therefore slowly moves from one extinction position to the next which gives an aspect of a wave traversing the mineral. Undulatory extinction is well documented and discussed in the textbook of microstructures by Vernon [12]. An example of the extinction behavior of the monoclinic tremolite-actinolite-ferroactinolite series is given in Fig. 5.25. In crystals of the monoclinic systems the crystallographic axes a and c are perpendicular to b but not to each other. The indicatrix axes X, Y, and Z or the vibration directions are mutually perpendicular. The crystallographic axis b always coincides with one of the indicatrix axes X, Z, or Y, the latter being the most frequent one aligned to the crystallographic b-axis. The other two indicatrix axes lie in the planes of the crystallographic aand c-axes. The extinction angle reported is the Z ^ c and lies in the (010) plane. One vibration direction lies nearer to the crystallographic axis than the other one, and the convention is to report

5.1 Birefringence

Fig. 5.22 Parallel extinction in tetragonal zircon, orthorhombic orthopyroxene, and hexagonal apatite, as well as in monoclinic biotite in the section (010). Mineral

107

is shown in PPL and in two extinction positions and two 45° positions with maximum brightness in XPL. Rotation is clockwise

108

5

Optical Properties of Minerals …

(a)

(b)

Fig. 5.23 Extinction behavior of monoclinic and triclinic minerals. a Inclined extinction in clinopyroxene. It is the angle < 45° which is the characteristic extinction angle;

b symmetric extinction in monoclinic hornblende using the characteristic {110} cleavage set

the extinction angle which is less than 45°. The monoclinic tremolite-actinolite-ferroactinolite series has an extinction behavior of Y = b; Z ^ c ¼ 11  28 ; X ^ a ¼ 4  13 (Fig. 5.25). This means that in the (001) section Y vibrates parallel to nb , and the crystal shows symmetric extinction with reference to the characteristic amphibole cleavage set. The extinction behavior Z ^ c is determined in the section (010) where two vibration directions or indicatrix axes are present and which shows the maximum birefringence. The extinction angles of the clinoamphibole and clinopyroxene members are summarized in Fig. 5.26. Most amphiboles have an extinction angle < 20° while most clinopyroxenes show extinction angle > 20°. In addition, color is an important parameter for identifying members of these groups. These values are approximate values, and different authors give slightly different ranges for the extinction angles, but they allow for some qualitative estimation of the mineral composition. Nevertheless, quantitative chemical composition analysis is now routinely carried out by electron microprobe analysis to classify and name these minerals. In the triclinic system all sections show inclined extinction. There are, however, rare

cases where an indicatrix axis overlaps with a crystallographic axis. For example, the extinction behavior of the triclinic mineral kyanite is indi   cated as Z ^ c ¼ 27  32 ; Y ^ b ¼ 5 ;  X ^ a ¼ 30 . It is important to verify that the N-S direction is indeed the Z direction with nc . For example, in an amphibole the (010) plane is the one used for the determination of Z ^ c and shows the prismatic cleavage. This can be done by means of the k-plate. The assumed Z direction is rotated into the 45° position. The interference colors are observed, and the k-plate is inserted (see Sect. 3.5 Accessory plates and Sect. 5.2 Elongation for explanation). If we obtain addition, as seen by the increase of interference colors, we are looking at the Z direction with nc . If subtraction is observed, we have measured X^a. Extinction angles can also be used to determine the chemical compositions of plagioclase in terms of the albite and anorthite content (see for example, Barker [1]; Wenk and Bulakh [13], Burri et al. [3]), and precise measurements are possible with a universal stage. Measurements of extinction angles allow a first estimate. However, today the chemical composition of plagioclase is routinely analyzed by electron microprobe analysis. In general extinction angles increase with the anorthite content. Two methods allow to

5.1 Birefringence

109

Fig. 5.24 a–b Extinction without reference: a quartz in mica schist; b olivine in basalt; c–i undulatory extension: c–d quartz in metagranite; e quartz in gneiss shows bulging indicated by red arrows. Along the grain boundaries the undulatory crystal recrystallizes into smaller

grains (see Vernon [12] for detailed documentation of textures of deformation as observed in XPL); f plagioclase in metagranite; g muscovite in metagranite; h biotite in mylonitic granite; i olivine in peridotite

determine the approximate composition of plagioclase. (1) The so-called Michel-Lévy method and (2) the double twin method using Carlsbad albite twins which is not discussed in this book (see for both methods in Burri et al. [3]). The Michel-Lévy method determines the extinction angle perpendicular to the [100] direction and within the plane (010) which is correlated with the anorthite content in plagioclase using determinative diagrams by Tröger [11] or Burri et al. [3]. Different determinative curves have been defined for extrusive and intrusive rocks. The example shown (Fig. 5.27) is a plutonic rock, and a crystal of plagioclase is selected for which the twin lamellae are ideally uniformly

illuminated when oriented N-S. In the (001) section, a cleavage and the albite law (010) are visible. In such a section the (010) twin plane is parallel to the N-S direction and perpendicular to the [100] direction. This can be verified by changing the focus. The outline, as seen as fine black contour lines, should not shift or move sideways when changing the focus. The thin section is then rotated counterclockwise until one set of twins becomes extinct and the angle with the N-S direction is measured; in the example in Fig. 5.27 it is 10°. Returning to the start position at 0° the crystal is rotated clockwise until the other set of twins becomes extinct, and the angle measured is 14°. Averaging the two angles

110

Fig. 5.25 Extinction behavior in the monoclinic tremolite-actinolite-ferroactinolite group. The extinction behavior Z ^ c is determined in the section (010)

(a)

5

Optical Properties of Minerals …

(maximum birefringence). Rotation in the extinction position is clockwise. Polarizers are indicated as orange arrows

(b)

Fig. 5.26 Extinction angles Z ^ c in the (010) section of the monoclinic clinoamphibole a and clinopyroxene groups b the orthopyroxene enstatite and the

orthoamphibole anthophyllite are included. The extinction angles were determined using a universal stage

comes to 12°. It must now be verified if we look indeed at na0 and the trace of the (010) plane for the albite twins. This can be done by rotating the crystal into the 45° position and adding the k-

plate. If there is subtraction, we are looking at na0 . The determinative diagrams by Tröger [11] are different for volcanic and intrusive rocks, and the angle of extinction varies by more than 40°

5.1 Birefringence (a)

111

τ1

(001)

τ2 0°

10°



(b)

14°

(c) (e)

(d)

Fig. 5.27 Determination of the extinction angle and composition in terms of albite and anorthite contents of plagioclase; a plagioclase as it appears under the microscope; b determinative curves for plagioclase composition

as of Tröger [11]; c determination of the refractive index in relation to nCB; d relationship between anorthite content and Dn for plagioclase composition; e determination curves after Burri et al. [3]. See text for explanations

and is around 10° in albitic compositions, and in anorthitic ones the value reaches up to 45°. Since it is an intrusive rock, we use the solid line for intrusive rocks. The determined averaged value of 12° intersects the plutonic line at two values of An10 mol% and An28 mol%, and we have to add another optical parameter of plagioclase to distinguish which composition is the correct one. This is the index of refraction for plagioclase. A relief with n > nCB gives values > An24 mol%, whereas a relief with n < nCB gives values < An24 mol%. In our case n > 1.538 is measured using the Becke line method, and the composition can be determined to be An28 mol%. If the thickness of the section is known, the birefringence can be used additionally to estimate roughly the anorthite content. The birefringence

is higher for Ca-rich compositions than for Narich ones. The same is done using the determinative curves by Burri et al. [3], and the values are almost identical with a determined value of An27 mol% anorthite (Fig. 5.27e). Birefringence, d or Dn; is observed in XPL and is the difference between the slow and the fast rays nslow–nfast or d ¼ Dn ¼ ne  nx (uniaxial minerals) or d ¼ Dn ¼ nc  na (biaxial minerals). It is expressed as the interference color in the interference color chart of Michel-Lévy or the revised Raith-Sørensen interference color chart. The maximum interference color is the most important diagnostic optical

112

5

5.2 parameter and may change in a mineral group according to the chemical composition. Based on repetitive intervals of d ¼ 0:018 or 551 nm, birefringence is classified into orders as first order and up to d ¼ Dn ¼ 0:018 or the color sequence grayyellow-white-red, second order and up to d ¼ Dn ¼ 0:036 with colors that are brighter starting with a color sequence of blue-light-green-yellow-orange-pinkishred, third order and up to d ¼ Dn ¼ 0:054 with bright luminous colors of blue-greenyellow-orange-intensive pinkish-red, and fourth order and up to d ¼ Dn ¼ 0:072 where greenish, yellowish, and pinkish colors dominate. Further orders have colors reminiscent of iridescent white pearls or in washed-out clothes. Some minerals show anomalous interference colors of a yellowochre, yellowish-brown, blue, or violet interference color such as members of the chlorite family and which are diagnostic. Minerals show (1) parallel or straight extinction, (2) inclined or oblique extinction, (3) symmetric extinction, (4) extinction without reference, and (5) undulatory or undulate extinction which is related to deformation. The extinction angle s is expressed as Z ^ c or Z ^ ð100Þ and is used as an important criterion as, for example, to distinguish the members of the clinopyroxene and clinoamphibole groups. Scan the section to find the grain with the highest interference color. Look at borders of the grains or at the imaginary beaches along the grain boundaries to see the upward moving interference colors and use the highest color in the center of the grain as maximum birefringence (verify in PPL that the mineral is not compositionally zoned). Always opt for the highest one, and be aware that you might not have encountered the highest interference colors.

Optical Properties of Minerals …

Elongation

Elongated minerals are used to examine the elongation, which can be positive (l+) or negative (l−). Elongation determines which ray vibrates along the c-axis of elongated tetragonal and hexagonal minerals: is it the slow ray which vibrates along the c-axis, then the elongation is l (+) or is it the fast ray which vibrates along the caxis, then the elongation is l(−). The information allows to determine the optical character. In uniaxial minerals the sign of elongation and the optical character are often the same. The method is also used to determine in specific crystal sections the vibration direction of the fast or slow rays. An elongated uniaxial mineral displays two vibration directions with refractive indices e and x. Ray e vibrates along the c-axis and ray x at an angle of 90°. If elongated hexagonal apatite is positioned with the c-axis parallel to the N-S direction in XPL, it is in the extinct position, since the vibration directions of the rays e and x are oriented parallel to the polarizers of the microscope, that is N-S and E-W (Fig. 5.28a, b). The question is asked: Which ray—the fast or the slow ray—vibrates along the c-axis? The determination of the elongation uses the 45° position and the k-plate. The k-plate imposes a retardation by a whole order (551 nm). Overlapping the vibration directions of the slow c ray of the k-plate with a vibration direction in a mineral may result in positive or negative interference and is best seen in minerals with a birefringence of the first or the second order. The mica plate is used for minerals with higher birefringence. The determination of the elongation is shown for uniaxial apatite in Fig. 5.28. Apatite is aligned N-S with its long crystallographic c-axis. The interference color of apatite is first-order gray with a retardation of 158 nm (Fig. 5.28a, b). The mineral is rotated from the parallel extinction position to the 45° position (Fig. 5.28c), and therefore the NE-SW oriented vibration direction of ray e of the mineral and the vibration direction of the slow ray c of the k-plate are overlapping. The addition of the k-plate with 551 nm of retardation to the observed retardation of 158 nm

5.2 Elongation

Fig. 5.28 Negative elongation l(−) in uniaxial apatite (XPL). a, b elongate crystal of apatite oriented N-S as seen in PPL and XPL; c, d in the 45° position the interference color changes from gray to yellow when the k-plate is added; e, f apatite is rotated at an angle of 90°,

113

and the interference color changes from gray to blue when the k-plate is added; g Raith-Sørensen interference color chart with the observed shift of colors. See text for explanation

114

5

displays a yellow color (Fig. 5.28c, d). The observed match is to the left in the RaithSørensen interference color chart (Fig. 5.28g). This indicates that there is destructive interference and means that the slow ray c of the k-plate vibrates parallel to the fast ray of the mineral. This is called subtraction. The crystal is then rotated at an angle of 90°. In this position the NW–SE oriented vibration direction of ray x of the mineral and the vibration direction of the slow ray c of the k-plate are overlapping. The color blue of the second order is observed (Fig. 5.28e, f), and the birefringence has increased in the Raith-Sørensen interference color chart (Fig. 5.28g). The resulting retardation is now 158 nm + 551 nm = 681 nm (Fig. 5.28g). This indicates that there is constructive interference and that the slow ray c of the k-plate vibrates parallel to the slow ray x of the mineral. This is called addition. The conclusion can be drawn that e along the c-axis of the mineral is the fast ray, ray x is the slow ray and that the elongation is l(−).

Optical Properties of Minerals …

and optical orientations. The physical interface between the twinned individuals, the twinning plane, also called the composition plane, is the plane of intergrowth and mirrors a particular crystallographic plane. It is easily recognized under the microscope in XPL and normally seen as a straight, fine dark line providing a clear separation between the twinned individuals. The individuals have different optical orientations and therefore display different birefringence. In deformed or metamorphosed rocks, the twin plane may be displaced, offset, or altered as well, but can still be recognized. Twins are common in phenocrysts of magmatic and metamorphic rocks. The following types of twinning can be distinguished: simple twinning, polysynthetic or lamellae twinning, complex twinning including penetrative twinning, and cyclic twinning. Twins of common minerals are shown in Figs. 5.29 and 5.30 and twin laws are summarized in Table 5.2.

5.3.2 Types of Twinning Rule to remember elongation in uniaxial elongated minerals. l (−) Length fast ! negative elongation or slow ray c of k-plate overlaps with fast ray of mineral. l (+) Length slow ! positive elongation or slow ray c of k-plate overlaps with slow ray of mineral.

5.3

Twinning

5.3.1 Appearance of Twinning Twinning is so characteristic in certain minerals that it may serve as a key parameter to identify a mineral in addition to the birefringence. Examples are plagioclase or microcline. Twinning is the symmetric intergrowth of individuals slightly offset and having different orientations of the lattice and therefore different crystallographic

There are several ways to characterize twinning. When dealing with contact twins, the (hkl) twinning or composition plane is often used. The “curly” brackets {hkl} are used to refer to a set of planes or a zone. The direction of the twin axis is normally given in square brackets [hkl]. Twins can also be considered as reflection twins or as rotation twins. Simple twinning or contact twinning consists of two individuals that have different crystallographic orientations and therefore show different extinction positions, when the microscopic stage is rotated. Examples of the most common minerals with simple twins are shown in Fig. 5.29 and are summarized in Table 5.2. Simple twinning is diagnostic in magmatic phenocrysts of orthoclase. Figure 5.29 illustrates two twinned individuals on the composition plane (010) with a twofold rotation about the c-axis named the Carlsbad law which is a penetration twin although not necessarily seen in thin section. Simple twins occur also in the clinopyroxene as well as in the

5.3 Twinning

115

Fig. 5.29 Simple twinning. For mineral abbreviations see Table A.1 in Appendix A

amphibole members of volcanogenic rocks and in chloritoid (Fig. 5.29) but are also common in other minerals such as kyanite. Polysynthetic twinning includes numerous individuals with parallel twin planes and different optical orientation. Examples are given in Fig. 5.30. The most common example is plagioclase twinned under the albite law where the (010) plane is the twinning plane and twinning occurs perpendicular to the crystallographic baxis. It is ubiquitous in magmatic rocks. Complex twinning is present in crosshatched or tartan-twinning in microcline and is clearly diagnostic. Tartan-twinning is a combination of albite and pericline twin laws with (010) and (100) twin planes. It is visible when the crystal is cut parallel to (001). It is common in intrusive rocks. It may also be preserved in metamorphic

rocks, such as gneiss or immature sandstone. In Fig. 5.30 three images show microcline as a fresh grain, a slightly deformed one, and a grain recrystallizing under metamorphic conditions. In penetrative twins crystals interpenetrate each other. Staurolite penetration twins produce at right angle a cross on {031} and a cross at 60° on {231} known as the cross of St. André (Fig. 5.30). Quartz may be twinned but since twinning is often parallel to the c-axis, the two members go into extinction simultaneously, and it is not necessarily evident in microscopic observation. Cyclic twinning is diagnostic for cordierite and involves twinning parallel to {110} and {130}. Twin axes are not parallel. It is best seen when adding the k-plate as is shown for cordierite in Fig. 5.30. It is also characteristic for aragonite.

116

5

Optical Properties of Minerals …

Fig. 5.30 Polysynthetic, complex, penetrative, and cyclic twinning. For mineral abbreviations see Table A.1 in Appendix A

5.3 Twinning

117

Table 5.2 Common diagnostic twin laws for selected minerals Mineral

Twin law

Type of twin

Composition/twinning plane (hkl) Twin axis [hkl] Zone {hkl}

Plagioclase

Albite law

Contact, polysynthetic

(010)

Orthoclase

Carlsbad law

Contact, simple

[001]

Orthoclase

Baveno law

Contact, simple

(021)

Orthoclase

Manebach law

Contact, simple

Pericline law

Pericline law

Microcline

Crosshatched pattern, Tartan pattern, pericline and albite law

(001) Twin axis [010] perpendicular to (010)

Complex, polysynthetic

(010) and [010]

Chloritoid

Simple, polysynthetic

{001} {001}

Leucite

Polysynthetic

parallel to {110}

Titanite

Simple polysynthetic (deformation)

{100} {221}

Staurolite

Penetration

{031} right-angled cross {231} cross at about 60o

Calcite

Simple, contact twin

{0001}, {01 1 2}

Gypsum swallow tail

simple

(100)

Aragonite

Cyclic, contact

{110}

Quartz

Brazil law

Penetration

{11 2 0}

Quartz

Dauphiné law

Penetration

[0001] {11 22}

Quartz

Japanese law

Contact

Spinel group

Spinel law

Contact

{11 1}

Cordierite

Cyclic, contact

{110} and {130}

Rutile

Cyclic contact twins

{011}

Analcite

Polysynthetic

{001} and {110}

Aragonite

Cyclic, penetration

(110)

5.3.3 Causes of Twinning Twinning often occurs as the result of a phase transition. The crosshatched pattern or tartantwinning in microcline is related to the transformation from monoclinic sanidine or orthoclase to triclinic microcline during temperature decrease. Twinning in leucite is related to a temperature decrease and a sequential change from isometric to tetragonal symmetry [15]. Deformation twins are the result of gliding and offsets of the crystal

lattice. They are often observed in calcite, pyroxene, or plagioclase. The environment of crystallization in igneous as opposed to metamorphic rocks may explain the differences in twinning laws. Rapid crystal growth during primary polysynthetic twinning in plagioclase is favored by supersaturation. Overstepping of reaction boundaries during metamorphism is suggested for cordierite twinning. In the last two decades research has focused on the twin walls or twin boundaries and their

118

5

simple

polysynthec

penetraon

Optical Properties of Minerals …

complex

cyclic

Fig. 5.31 Types of twinning as seen in a thin section. Common examples are given in Table 5.2

properties. They often display different properties such as an ability for chemical storage, polarity, and piezoelectricity inside the walls, while these effects are not observed in the adjacent twin domains [16]. Simple, polysynthetic, complex, penetrative, and cyclic twinning are diagnostic for many minerals. Twinning often occurs as a phase transition such as in perthite or microcline during temperature decrease or is related to a deformational event. Rapid crystal growth and overstepping reaction boundaries are also suggested. Twin walls or twin boundaries show different properties than the adjacent twin domains such as an ability for chemical storage, polarity, and piezoelectricity.

be visible with the plane polarized light microscope. Other sensitive imaging techniques must be applied such as electron backscattered electron imaging, cathodoluminescence, the analysis of the chemical composition by microprobe analysis (EPMA), by Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LAICPMS), or by quantitative evaluation of minerals by scanning electron microscopy (QEMSCAN). The last one produces maps of the mineral assemblages based on their chemical composition. The modern imaging techniques enhance the visibility of zoning in crystals. The following types of zoning (Figs. 5.32 and 5.33) can be distinguished: oscillatory zoning, concentric zoning, and sectoral or sector zoning, and combinations are also possible.

5.4.1 Oscillatory Zoning

5.4

Crystal Zoning

Crystal zoning is a primary growth texture related to growth and dissolution processes (see Jamtveit and Meakin [19]). The development of visibly different layered or sector zones in a crystal is the result of discontinuous growth. It can be seen in PPL as a change of color as well as in XPL as zones with different interference colors. It reflects the chemical variation of major or trace elements or, both, in the various zones in the crystal. In isotropic and colorless minerals such as garnet or fluorite, crystal zoning may not

Oscillatory zoning (Figs. 5.32, 5.33 and 5.34) is characterized by an onion-like texture as the result of the variation in the chemical composition of major and trace elements of growth shells from tens of nanometers to tens of micrometers in thickness (see summary in Shore and Fowler [23]). Oscillatory zoning allows to study the development and history of complex magmatic systems and magma chamber processes as well as hydrothermal systems in veins and diagenetic processes in sedimentary rocks. The growth layers are parallel to crystallographic planes of low Miller indices and are concentric with the external margins of the crystal. This suggests that

5.4 Crystal Zoning

119

Fig. 5.32 Different types of zoning in minerals. For mineral abbreviations see Table A.1 in Appendix A

these crystals have maintained their euhedral shape throughout much of their growth. Oscillatory zoning may be present from the center to

the margins of a crystal, but an unzoned core and a zoned outer margin are quite common (Figs. 5.32 and 5.34a, b). Oscillatory zoning is

120

5

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 5.33 Types of zoning: a oscillatory zoning in plagioclase (XPL); b concentric zoning as a result of changing composition during crystal growth (PPL); c concentric zoning as a result of changing pressure and/or temperature marked by inclusions (PPL); d–f

(a)

(b)

Optical Properties of Minerals …

zoning is not visible in PPL nor in XPL: d concentric zoning in garnet as the result of changing conditions; e sectoral zoning in fluorite due to different fractionational uptake of REEs in different crystal faces; f combination of oscillatory and sectoral zoning in quartz

(c)

Fig. 5.34 Oscillatory zoning. a in nepheline marked by inclusions and color change (PPL); b oscillatory zoning in zircon evident by different interference colors (XPL);

c concentric prograde metamorphic zoning of epidote in a mafic rock of greenschist facies seen by different interference colors (XPL)

best known for phenocrysts of magmatic minerals such as plagioclase and in minerals of alkaline rocks such as nepheline (Fig. 5.34a) but may occur also in metamorphic rocks in skarn, in hydrothermal settings, as well as in calcite

cements in sandstone. Although not always visible with the polarized light microscope, oscillatory zoning was shown to be present in 75 different minerals from the group of the silicates, sulfides, oxides, halides, carbonates, phosphates,

5.4 Crystal Zoning

and sulfates [24]. Oscillatory zoning is well documented in alkaline rocks varying from nepheline syenite to trachyte and their characteristic assemblage of plagioclase, nepheline, diopside, melilite, and kaersutite. Not only major rock components are zoned, but also apatite, titanite (sphene), melilite, and sodalite. Oscillatory zoning may be stable up to amphibolite facies conditions but does not normally develop under regional metamorphic conditions. Oscillatory zoning has been shown to be mainly binary. Two compositional endmembers vary over short distances. The most common example is plagioclase where the oscillatory zoning involves the coupled substitution NaSi () CaAl as well as the trace element Ba and Sr. Fe () Mg and Al exchange is the reason for oscillatory zoning in mafic minerals. Oscillatory zoning as the result of variation in trace element composition has been shown in augite (aluminum diopside) of an alkaline basalt [23]), where antithetic variation between compatible (Cr, Sc) and moderately incompatible (V, Sr, Zr) elements lead to mm thick zones. Oscillatory zoning may also be used as an exploration tool as shown in the tungsten skarn mineral deposit of the Sangdong and Weondong deposits in South Korea (Park et al. [22]). Fe-rich garnets forming oscillatory layers in the skarn system are LREE enriched, and tungsten is strongly fractionated. These layers of Fe-rich garnets are attributed to rapid growth by infiltration metasomatism during disequilibrium and an input of hydrothermal fluids. The trace elements are considered to reflect the composition of the oreforming fluid. Oscillatory zoning is also known in Zn-Pb deposits of the Mississippi Valley type where it is related to episodic fluid flow and rapid mineralization interrupted by long quiet periods. Two main theories have been put forward to explain the formation of oscillatory zoning. Oscillatory zoning is either controlled by extrinsic or intrinsic parameters. Oscillatory zoning is a primary growth texture and reflects “non-equilibrium chemistry” [24]. Cyclic variation in extrinsic parameters such as physical and chemical changes, crystal settling, large-scale convection, fluid mixing, or change in reservoir

121

composition results in a new growth layer. These variations may arise spontaneously and have been termed “chemical oscillators” by Gray and Scott [18]. Fine oscillatory zoning has been reported in carbonate cement and is related to fluctuations in Fe and Mn due to changing redox conditions during diagenesis [20]. Oscillatory zoning may be the result of intrinsic factors linked to local phenomena at the site of oscillatory formation. Feedback between crystal growth and solute diffusion or surface effects may be the reason for the oscillating layers. The growing crystal is surrounded by a small boundary layer that is depleted in growth constituents with respect to surrounding bulk liquid, and crystal growth is constrained by chemical and thermal diffusion. Other reasons for oscillatory crystallization are buildup and relaxation of elastic strain due to cell parameter mismatch in zoned growth layers. Small variations (nω nε 1.554 nω 1.543 Δn=0.009 (50 μm thickness)

(a)

(b) Interference image seen in ocular lens

V

Bertrand lens with interference image Melatope

Isogyres

(c) c=Z=opƟc axis

ObjecƟve with high aperture d

d+x

n

Uniaxial mineral opƟc axis

n a1

Auxiliary condenser with high aperture

n’

Circular secƟon

XPL

a2

n a3

Xn

a

Fig. 6.4 Formation of the interference figure of uniaxial quartz cut perpendicular to the optic axis or the c-axis and viewing the circular section with nx . a An auxiliary condenser produces light rays traveling with distance d or

d + x and different retardations; b schema of the interference figure and terminology used; c the crystal of quartz seen in XPL, the habit of the crystal, and the location of the circular section shown in blue with nx

Fig. 6.5 Centered optic axis figure (OA) or interference figure perpendicular to the optic axis of uniaxial positive quartz; a schema of the conoscopic image; b schema of the conoscopic image with the k-plate inserted; c image in

XPL, conoscopic image as seen in the microscope without and with the k-plate; d change of the order of birefringence as observed in the Raith-Sørensen color chart

130

6 Conoscopic Observations and Interference Figures

Tourmaline δ=0.017 U- nε90

148

7

Igneous Rocks: Some Basic Concepts

Fig. 7.2 QAPF or Streckeisen diagrams and IUGS classification and nomenclature of plutonic and volcanic rocks based on the modal proportions of quartz (Q), alkali feldspar (A), plagioclase (P), and feldspathoid (F)

Fig. 7.3 a–b IUGS classification and nomenclature of the gabbro group based on the proportions of a plagioclase (pl), pyroxene (cpx, opx), and olivine (ol); b plagioclase, pyroxene, and hornblende (hbl); c–d Streckeisen diagrams and IUGS classification and nomenclature of ultramafic rocks peridotites, pyroxenites, and hornblendites based on the proportion of c olivine (ol), orthopyroxene (opx), and clinopyroxene (cpx); d based on the proportion of olivine, pyroxene, and hornblende

7.1 Classification of Igneous Rocks

149

techniques. Estimation of modal proportion is difficult in fine-grained volcanogenic rocks or very coarse-grained plutonic rocks, and these rocks are classified based on their bulk rock composition as determined by chemical analysis (see Sect. 7.2). Most igneous rocks contain less than 90 vol% of mafic minerals (mica, amphibole, olivine, pyroxene, or opaque minerals, such as magnetite and ilmenite as well as zircon) and are classified in two ternary plots joint along one line and named the QAPF diagram, also known as Streckeisen diagrams [16]. Q stands for quartz or other SiO2 minerals, A for alkali feldspars (orthoclase, microcline, perthite, anorthoclase, sanidine, and albite up to an anorthite content of 5 mol%), P for plagioclase (An 5–100), and F for feldspathoids (leucite, nepheline, sodalite, nosean, haüyne). The rock must contain a total of at least 10 vol% of Q, A, P or F. Two double ternary plots [7, 8] are used: one for plutonic and one for volcanogenic rocks (Fig. 7.2). The modal proportion of felsic and mafic minerals must be known to use this classification and can be estimated roughly in a thin section. For example, a rock with Q = 10%, A = 30%, P = 20%, and M = 40% gives the

recalculated values of Q = 16.7%, A = 50%, P = 33.3%. The rock can be plotted directly in the diagram and is a quartz monzonite. Most common rocks of plutonic and volcanic origin with M < 90% are correlated in Table 7.3. A magma that contains enough SiO2 to form silica-rich minerals (quartz, feldspars, pyroxenes) is silicasaturated or silica-oversaturated. If a magma is silica-undersaturated silica-poor minerals crystallize (feldspathoids, olivine). In the QAPF diagram, silica-saturated and silica-oversaturated rocks plot in the upper triangle, while silicaundersaturated rocks plot in the lower triangle. Mafic rocks are grouped into gabbros (sensu lato), peridotites, pyroxenites, and hornblendites (Fig. 7.3a–d) according to their relative proportion of plagioclase, olivine, orthopyroxene, clinopyroxene, and hornblende. The gabbros (sensu lato) contain a Ca-rich plagioclase and are further subdivided according to their relative proportion of plagioclase, olivine, orthopyroxene, and clinopyroxene (Fig. 7.3a, b). Some common members and their essential minerals are listed in Table 7.4. The ultramafic rocks peridotites, pyroxenites, and hornblendites with M > 90% (Fig. 7.3c, d) lack Ca-rich plagioclase

Table 7.3 Correlation of common plutonic and effusive rock names (see also Figs. 7.2 and 7.3) Plutonic rock

Volcanic rock

SiO2-saturated and -oversaturated rocks Gabbro

Basalt

Monzonite

Latite

Syenite

Trachyte

Monzodiorite

Andesite

Diorite

Andesite

Granodiorite

Dacite

Granite

Rhyolite

SiO2-undersaturated rocks Alkali feldspar syenite

Alkali feldspar trachyte

Foid-bearing syenite

Foid-bearing alkali feldspar trachyte

Foid-bearing syenite

Foid-bearing trachyte

Foid-bearing monzonite

Foid-bearing latite

Foid-bearing monzosyenite

Phonolite

Foid-bearing monzodiorite

Phonolite

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7

Igneous Rocks: Some Basic Concepts

Table 7.4 Common rock names of gabbros (sensu lato) and their essential minerals (see also Fig. 7.3a, b) Name of rock

Essential minerals

Gabbro

pl-cpx

Norite

pl-opx

Troctolite

pl-ol

Gabbronorite

pl with almost equal amounts of cpx and opx

Orthopyroxene gabbro

pl-cpx and minor amounts of opx

Clinopyroxene norite

pl-opx and minor amounts of cpx

Hornblende gabbro

pl-hbl with < 5% px

For abbreviations see Table A.1 in Appendix A Table 7.5 Common rock names of the ultramafic rocks peridotites and pyroxenites and their essential minerals and range of modal composition (see also Fig. 7.3c, d) Name of rock

Range of modal composition of essential minerals

Dunite (peridotite)

ol > 90 vol% px and cpx < 10 vol%

Harzburgite (peridotite)

40 vol% < ol < 90 vol% px < 40 vol% cpx < 10 vol%

Lherzolite (peridotite)

40 vol% < ol < 90 vol% opx-cpx

Websterite (pyroxenite)

opx-cpx-ol < 10 vol%

Wehrlite (peridotite)

40 vol% < ol < 90 vol% 40 vol% < cpx < 90 vol% opx < 10 vol%

For abbreviations see Table A.1 in Appendix A

or show less than 10 vol% of plagioclase and are classified according to their content of the mafic minerals olivine, orthopyroxene, clinopyroxene, and hornblende. Common rock names of peridotites and pyroxenites and their essential minerals are listed in Table 7.5.

7.1.2 Classification Based on Texture In the geological nomenclature, the terms texture, structure, and fabric are used traditionally to describe the arrangement of the components of a magmatic rock and are partly related to the scale of observation. Smith [15] provides a summary on the historic development of the use of these terms. The term texture is used to describe the crystallinity, granularity, and shapes and arrangements of the components (crystals, glass, and voids) of a rock from the most minute size up to hand specimen scale [15]. The texture is controlled by the cooling rate, the diffusion rate, and the growth rate of the crystals. The structure of a rock is usually observed from hand specimen to outcrop scale. It is a feature “composed of the

disposition, attitude, arrangement, or relative positions of the components of a rock” [15]. An example would be banding along the contacts of a dike. The term fabric describes features from the thin section to hand specimen and outcrop scale and must be defined by some concrete textural or/and structural feature or “the manner in which textural and structural features are oriented in space” [15]. An example is a rock in which crystal alignment and amygdale alignment define a planar fabric element dipping 15° to the east [15]. The usage of the terms is not strictly applied, and texture is used throughout the text as observed in the microscope. Quantitative textural studies have been carried out recently to understand the formation and development of crystalline rock texture (for a summary see Higgins [4]) and to aid chemical and isotopic methods. Higgins [4] uses texture in a general way which involves the same components as used by Smith [15] such as size and shape of grains, crystals and bubbles, orientation of grain, crystal shapes, crystal lattices, position and connectedness of crystals, and the relationships between different phases. Texture,

7.1 Classification of Igneous Rocks

structure, and fabric determination provide a comprehensive understanding of the formation of magmatic rocks and aid the interpretation of the chemical and isotopic results. For a review on the various methods and the potential of a textural study and analysis see Shelley [14] or Higgins [4]. Imaging methods based on microscopic images captured with the polarized light microscope have been developed to evaluate textures in magmatic, metamorphic, and sedimentary rocks related to physical processes, such as ordered or heterogenous distribution of nucleation processes, grain boundary sliding, solution-

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precipitation, crack-seal mechanisms or subgrain rotation recrystallization [3]. In any case, the textural analysis starts with the inspection of the rock at outcrop and hand specimen scale, and more details are gained from a thin section study. Terms to describe the habit of minerals are given also in Sect. 4.2. The most common technical terms such as degree of crystallinity, granularity, shape and relative size of the crystals, relations between crystals, the orientation of the crystals or the intersection of crystals are shortly explained in the following paragraph, and some textures are defined and shown in Table 7.6.

Table 7.6 Common terms to describe the texture in igneous rocks Shape and relative shape Equigranular/inequigranular

The size of all the crystals is the same/variable. Example is a granodiorite

Porphyritic

A rock has a distinct difference in crystal size. Large crystals are set in a mediumgrained matrix (plutonic rocks) or aphanitic matrix (volcanic rocks). Example is a volcanic rock

Microlithic

Small crystals ( 0.1 mm). It is characteristic for plutonic rocks. In an aphanitic texture minerals are very small and only visible with a magnifying glass or under a microscope (ca. < 0.3 mm). Volcanic rocks often have an aphanitic texture, which indicates rapid cooling of the magma. In a porphyritic texture euhedral crystals macroscopically visible occur in a finer-grained or glassy groundmass. The texture is typical for volcanic rocks but also observed in intrusive rocks. The term eutaxitic texture is used for welded ignimbrite. The texture develops while the rock is still hot and plastic. Pumice clasts called “fiamme” (Italian for flames) in a fine-grained groundmass of ash are flattened. An eutaxitic texture is formed when

hot, pumice-rich material is erupted explosively and is then quickly covered and compressed by overlying volcanic rocks. The textural terms panidiomorphic, hypidiomorphic, and allotriomorphic are used to define the shapes of the crystals present in the rock. In a panidiomorphic texture, most minerals are euhedral, in a hypidiomorphic texture some minerals are euhedral and some are anhedral or subhedral, while all minerals are anhedral in an allotriomorphic texture. Crystal size is easily observed and can be measured. The following terms are used: macrophenocrystals have a size > 5 mm, phenocrystals are between 0.3 mm and 5 mm, microphenocrystals are between 0.03 mm and 0.3 mm in size and microlites are < 0.3 mm in length. The concept of crystal size distribution (CSD) or the distribution of crystal size in three dimensions per unit volume has been used to give information on fundamental petrological parameters, such as crystal growth rate and nucleation or other aspects of the thermal history of the magma (see Rannou and Caroff [11]).

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Fig. 7.4 Degree of crystallinity. a holocrystalline texture in tonalite (fully crystallized rock); b hypocrystalline texture in dacite (crystal > glass); c hypohyaline texture

in submarine basalt (crystal < glass); glass is isotropic and extinct in XPL

The terms holocrystalline and holohyaline, hypocrystalline and hypohyaline describe the degree of crystallinity or the amount of crystalline components in relation to the glassy matrix (Fig. 7.4a–c). Holocrystalline describes a fully crystallized rock, characteristic of plutonic rocks (Fig. 7.4a). It results from slow cooling of the magma. The minerals that crystallize first are euhedral (automorphic, idiomorphic), while the later minerals fill the free spaces left by the early minerals and are anhedral. Holohyaline, vitreous, or hyaline characterize a glassy effusive rock, where rapid cooling prevented the crystallization of minerals and glass formed. Examples are obsidian or pumice. Hypocrystalline (Fig. 7.4b) is used for a rock composed by crystals and glass, but the volume of crystals is greater than the volume of glass. In a rock with a hypohyaline texture the volume of glass is greater than the volume of crystals (Fig. 7.4c). Common rock types are shown in the Figs. 7.5 and 7.6.

analysis (inductively coupled plasma mass spectrometry) and is treated in many books [1, 2, 12, 13]. It is based on the quantitative analysis of the main metal oxides occurring in a rock which are SiO2, Al2O3, FeO, CaO, Na2O, K2O, MgO, TiO2, P2O5, and MnO. Chemical analysis of rock suites is important to understand the development of magmatic systems. A first chemical classification is based on the SiO2 content and classifies the rock into ultrabasic, basic, intermediate and acid rocks (Fig. 7.7). This classification generally correlates with the color index M, and leucocratic rocks being richer in SiO2 than melanocratic rocks. An important classification is the division in alkaline magmatic rocks which have (Na2O + K2O) > Al2O3 and subalkaline rocks with (Na2O + K2O) < Al2O3. Subalkaline rocks are more abundant than alkaline rocks. These two groups are further divided into an (1) alkaline magma series and include members which are either (a) Na-dominant (sodic), (b) K-dominant (potassic), and (c) Krich (high-K) and (2) the subalkaline magma series which includes (a) the calc-alkaline magma series which may be K-poor (low Ktype) or K-rich (high K-type) and (b) the tholeiitic rock suite (tholeiitic magma series). The TAS diagram (total alkali versus silica) of volcanic rocks after Le Bas et al. [5, 6] is a diagram routinely used to classify fine-grained volcanic rocks (Fig. 7.8).

7.2

Chemical Classification of Igneous Rocks

Today chemical bulk rock analysis is used to further classify a magmatic rock. Chemical classification of igneous rocks is not further elaborated in detail since it requires an XRF analysis (X-ray fluorescence analysis) or ICPMS

7.2 Chemical Classification of Igneous Rocks

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Fig. 7.5 Microscopic images of ultramafic to mafic rocks (magnification  2.5). For mineral abbreviations see Table A.1 in Appendix A

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Igneous Rocks: Some Basic Concepts

Fig. 7.6 Microscopic images of felsic and undersaturated rocks (magnification  2.5). For mineral abbreviations see Table A.1 in Appendix A

References and Suggested Further Reading

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Fig. 7.7 Chemical classification of igneous rocks based on SiO2 content of the whole rock composition as determined by chemical analysis

Fig. 7.8 TAS diagram (total alkali versus silica) according to Le Bas et al. [5, 6] (q = normative quartz, ol = normative olivine)

References and Suggested Further Reading 1. Frost BR, Frost CD (2014) Essentials of igneous and metamorphic petrology. Cambridge University Press 2. Gill R (2010) Igneous rocks and processes. a practical guide. Wiley-Blackwell 3. Heilbronner R, Barret S (2014) Image analysis in the earth sciences—microstructure and textures of earth materials. Springer Verlag Heidelberg 4. Higgins MD (2006) Quantitative textural measurements in igneous and metamorphic petrology. Cambridge University Press 5. Le Bas MJ, Le Maitre RW, Streckeisen A, Zanettin B (1986) A chemical classification of volcanic rocks based on the total alkali–silica diagram. J Petrol 27:745–750 6. Le Bas MJ, Le Maitre RW, Woolley AR (1992) The construction of the total alkali–silica chemical classification of volcanic rocks. Mineral Petrol 46:1–22

7. Le Maitre RW (ed) (1989) Igneous rocks: a classification and glossary of terms, recommendations of the International Union of Geological Sciences Subcommission on the systematics of igneous rocks. Blackwell Scientific Publications 8. Le Maitre RW (ed) (2002) Igneous rocks: a classification and glossary of terms, recommendations of the International Union of Geological Sciences Subcommission on the systematics of igneous rocks, 2nd edn. Cambridge University Press, New York 9. Philpotts AR, Auge JJ (2022) Principles of igneous and metamorphic rocks. Cambridge University Press 10. Rannou E, Caroff M (2010) Crystal size distribution in magmatic rocks: proposition of a synthetic theoretical model. J Petrol 51(5):1087–1098 11. Rollinson H (1993) Using geochemical data: evaluation, presentation, interpretation. Longman, Harlow, Essex 12. Rollinson H, Pease V (2021) Using geochemical data. In: Using geochemical data: to understand geological processes (p. I). Cambridge University Press

160 13. Shelley D (1992) Igneous and metamorphic rocks under the microscope. classification, textures, microstructures and mineral preferred orientations. London Chapman and Hall, London 445 p 14. Smith JV (2002) Structural analysis of flow-related textures in lavas. Earth Sci Rev 57(3–4):279–297 15. Streckeisen AL (1974) Classification and nomenclature of plutonic rocks recommendations of the IUGS subcommission on the systematics of Igneous Rocks. Geol Rundsch 63(2):773–786

Further Reading 1. Best MG (2002) Igneous and metamorphic petrology. Blackwell Science, Boston 2. Carmichael ISE, Turner FJ, Verhoogen J (1974) Igneous petrology. McGraw-Hill, New York

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Igneous Rocks: Some Basic Concepts

3. Cox et al (1979) The interpretation of igneous rocks. George Allen and Unwin, London 4. McBirney AR (2007) Igneous petrology. Jones and Bartlett, Boston 5. MacKenzie WS, Donaldson CH, Guilford C (1982) Atlas of igneous rocks and their textures. Wiley, New York 6. Middlemost EA (1986) Magmas and magmatic rocks: an introduction to igneous petrology 7. Pirajno F, Santosh M (2015) Mantle plumes, supercontinents, intracontinental rifting and mineral systems. Precambr Res 259:243–261 8. Vernon RH, Clarke GL (2008) Principles of metamorphic petrology. Cambridge University Press 9. Wimmenauer W (1985) Petrographie der magmatischen und metamorphen Gesteine. Enke, Stuttgart 10. Wilson M (1989) Igneous petrogenesis: a global tectonic approach. Unwin Hyman, London 11. Winter JD (2010) Principles of igneous and metamorphic petrology. Prentice Hall, New York

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Metamorphic Rocks: Some Basic Concepts

A metamorphic rock is a rock derived from a preexisting sedimentary or igneous rock, in which the minerals have changed due to changing P–T conditions. Recrystallization and neoformation of minerals are the prevailing processes which occur mainly as solid-state transformations. Mineral, structural and chemical changes occur according to the geodynamic setting. The limit between diagenetic and metamorphic processes is arbitrary and often indicated as occurring at temperatures of between 100 and 150 °C. Metamorphism can be classified based on the driving mechanism or process: dynamic metamorphism, if the metamorphism is dominated by pressure, thermal metamorphism, if temperature is the main controlling factor, and dynamo-thermal metamorphism, if temperature and pressure interplay. Dynamo-thermal metamorphism mainly occurs in orogenetic settings, also referred to as regional metamorphism, in subduction zones, or in burial metamorphic settings in basins of sedimentary and volcanogenic sequences (burial metamorphism). Thermal metamorphism is recognized on the ocean floor under the effect of seawater, also known as ocean floor metamorphism, in hydrothermal fields on the continents by interaction of hot meteoric, saline, or metamorphic fluids in crustal or sedimentary rocks (hydrothermal metamorphism), at the contact of intrusive magmatic rocks with a country rock (contact metamorphism), in rocks in contact with a source of very high temperature on the surface, such as a lava flow, in rocks within naturally burned coal

bed (pyrometamorphism) and even during lightning. Dynamic metamorphism typically occurs along fault, shear, and thrust zones (cataclastic or fault zone dynamic metamorphism) but can also result from a meteorite impact (impact metamorphism) (Fig. 8.1). In general metamorphism is isochemical with change of water, and other volatiles such as CO2, CH4, Cl, F, and SOx only, but infiltration of hydrothermal fluids serving as the medium of transport along shear zones, thrust zones, and fault systems which leads to hydrothermal alteration, are common. Such hydrothermal fluids are often externally derived as meteoric or seawater fluids or mixed with fluids released during dehydration reactions of metamorphic mineral assemblages. Metasomatism is named the process where fluid–rock interactions significantly change the rock composition by removal or addition of chemical species. All types of hydrothermal metamorphism (including ocean floor metamorphism, hydrothermal alteration around intrusive complexes, or fluid–rock interactions related to burial metamorphism) generally involve metasomatism. It is the aim of studying metamorphic rocks to understand the pressure–temperature-time path of a rock (P–T-t path) in the Earth's crust. For example, a pelitic rock may be buried and consequently metamorphosed (Fig. 8.2). It will follow a prograde path where temperature and pressure increase. As the rock is heated, the minerals will transform according to their

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. T. Schmidt, Transmitted Light Microscopy of Rock-Forming Minerals, Springer Textbooks in Earth Sciences, Geography and Environment, https://doi.org/10.1007/978-3-031-19612-6_8

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Fig. 8.1 Schema of some geological settings of metamorphism in the Earth's crust. Contact metamorphism (1) with hydrothermal alteration (2); back arc basin with burial metamorphism (3); subducted oceanic crust from

Fig. 8.2 Hypothetical simple trajectory and P–T field of a pelitic rock during regional metamorphism. The rock experiences metamorphism taking either a clockwise or counterclockwise path. Approximate lines for dehydration reactions resulting in the liberation of a fluid are given for chlorite, muscovite, and biotite. Anhydrous minerals such as feldspar or pyroxene become stable on the right side of the reaction isograde

stability fields. At a certain time, the rock will experience maximum pressure conditions and temperature will rise until the temperature maximum condition is reached. At some later date the rock may be exhumated following decompression, which can be along an isothermal trajectory or not, and will arrive at the surface. The path

8 Metamorphic Rocks: Some Basic Concepts

(4) low-temperature–high pressure (blueschist facies) to (5) high-temperature–high pressure conditions (eclogite facies); ocean floor metamorphism (6); metamorphism by lightening (7) (modified from Spears [18])

from the maximum P–T conditions to surface conditions is called the retrograde path where temperature and pressure progressively decrease. It is often the case that the maximum peak of pressure does not coincide with the maximum peak of temperature. A clockwise path is called the trajectory of a rock in the P–T field where the pressure maximum is reached first and proceeded by the temperature maximum. In a counterclockwise path the opposite is the case. Trajectories may show different shapes depending on the geological history and geological settings, with complex paths being observed where a sequence of rocks experienced polyphase metamorphism. By dating minerals formed during the prograde path, during peak pressure and temperature conditions and during the retrograde path time constraints are added to the pressure– temperature path. Regional polyphase metamorphism proceeds over tens of millions of years, while intrusive-related hydrothermal alteration is short lived with estimated durations on the order of < 1 million years. A metamorphic rock can often be identified as such at the hand specimen scale if metamorphic minerals and a metamorphic texture are recognized macroscopically. This is especially the case for medium to high-grade metamorphic rocks. The detailed examination of a rock in thin section

8.1 Classification of Metamorphic Rocks

allows for a better evaluation of possible various stages in metamorphism as revealed by the mineral assemblage and the texture. If a metamorphic rock is finer grained, as is often the case for lowgrade metamorphic rocks, a classification on the hand specimen scale is difficult. The study of thin sections and other methods such as X-ray diffraction and determination of the illite or chlorite crystallinities are necessary (e.g., Frey and Robinson [10]). Parameters to classify metamorphic and cataclastic rocks of dynamic metamorphism are summarized and briefly explained in the following chapters as a first introduction to the complex, often polymetamorphic history of metamorphic rocks. Metamorphic rocks are treated in many books at various levels of knowledge and in books on specific rock types (see references at the end of this chapter). In metamorphic petrology, a rock is generally named by applying strictly descriptive terms according to the characteristic parameters, such as texture, modal composition, and protolith. Different names can be simultaneously used to describe the same metamorphic rock, e.g., a glaucophane-bearing eclogite or a garnetomphacite-bearing blueschist, which corresponds to a metabasite stable at the transition between blueschist and eclogite facies. A geologist can name the rock according to the interest of her/his project and may highlight the characteristics that seem desirable. The main classification criteria are (1) texture, (2) the modal composition, and (3) the protolith. Terms based on texture are termed root terms and the modal composition as qualifier. This classification of metamorphic rocks is suggested by the Subcommission of Systematics of Metamorphic rocks of the International Union of Geological Sciences (IUGS), Fettes and Desmond [6]; North American Geologic-Map Data Model Science Language Technical Team [11], Roberson [15]. The modal composition is controlled by the protolith or the bulk rock or whole rock composition and is used as a qualifier [15] which in combination with a root term of the texture classification further characterizes the rock. Examples are biotite schist or garnetbiotite-quartz granofels or sillimanite gneiss,

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each of which indicates an approximative P–T stability field for the mineral assemblage.

8.1

Classification of Metamorphic Rocks

8.1.1 Textures of Metamorphic Rocks The main criterion of texture (for definition of term texture, fabric, structure, see Chap. 7) is the absence or presence of a planar structure, such as foliation, slaty cleavage, or schistosity. Foliation is a planar arrangement of layers formed by the preferred orientation of elongated minerals (mica, phyllosilicates, or amphiboles). Foliation can also be created by metamorphic differentiation (e.g., in a gneiss). Schistosity describes a planar structure along which the rock preferentially breaks. Planes are generally large enough to be visible to the naked eye. The slaty cleavage is typical of slates and results from the preferred orientation of finegrained mica (often sericite) and/or phyllosilicates. The root terms based on texture are defined and summarized in Table 8.1 and Fig. 8.3. Metamorphic rocks are grouped as foliated metamorphic rocks and granoblastic rocks. Cataclastic rocks as a product of dynamic metamorphism or cataclastic metamorphism are usually included. The reader is referred to books on structural geology for more detail (e.g., Fossen [13]). Foliated metamorphic rocks comprise the non-mylonite series with schistose rock, slate, phyllite, schist, gneiss, non-layered gneiss, layered gneiss, and augengneiss. The mylonite series includes protomylonite, mylonite, phyllonite, ultramylonite, blastomylonite (if recrystallization is significant), and pseudo-tachylite (glass has formed) which are discussed in textbooks of structural geology (e.g., Fossen [8]), and a short definition is given in Table 8.1. As intensity of metamorphism increases, the crystal size and the thickness of foliation may increase as well. Granoblastic rocks are granofels and hornfels but can also be marble, quartzite, and eclogite. They lack a foliation and are hard to split. The reason is the absence of mica, phyllosilicates, or amphiboles and the interlocking of newly crystallized

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Table 8.1 Most common terms used for classifying metamorphic rocks based mainly on the definition by Fettes and Desmons [6], North American Geologic-Map Data Model Science Language Technical Team [11] and Robertson [15]. The definition is based on hand specimen, but characteristic textures leading to the classification of a rock are often well recognized in thin section Term

Definition

Breccia

Generic classification for an incohesive tectonic rock in which penetrative fractures separate visible fragments (>0.1 mm in diameter) that form > 30% of rock, and fragments are rotated relative to each other. Result of brittle deformation

Broken rock

Incohesive cataclastic rock which is fractured by brittle deformation but with little evidence of granulation or rotation of fragments. Matrix < 10% of the rock

Cataclastic rock (of dynamic metamorphism)

Rock produced in zones of differential stress and movement and containing angular fragments that have been produced by the crushing and fracturing of preexisting rock. Subdivisions are cohesive and incohesive cataclastic rocks

Foliated metamorphic rock

A rock with distinctive repetitive layers such as layers of mica alternating with more quartz-rich layers

Foliation

Distinctive closely spaced layers are repeated as a result of deformation

Gneiss Orthogneiss Paragneiss

A gneiss is a medium to coarse-grained rock with a well-developed preferred orientation of minerals, mainly mica. Foliation or layering is more widely spaced, irregular, or discontinuous than in a schist but transitions to schists are common. Paragneiss has a sedimentary protolith, orthogneiss a magmatic protolith

Gouge

Incohesive cataclastic rock which is lacking evidence for primary cohesion during deformation, in which visible fragments (> 0.1 mm in diameter) constitute < 30% of the rock mass. Protolith of fragments assumed to be recognizable

Granoblastic rock

A very general term for a phaneritic rock hard to split with a granoblastic texture and a lack of foliation

Granofels

A general term for a phaneritic rock hard to split with a granoblastic texture and a lack of foliation. Often used in relation to contact metamorphism

Hornfels

An aphanitic rock hard to split, with little or no foliation and well crystallized during high-temperature contact metamorphism in the inner part of a contact metamorphic aureole. But this genesis is not a requirement of this descriptive definition

Layered gneiss

Phaneritic rock that lacks well-developed, continuous schistosity but shows compositional layering > 5 mm thick

Migmatite

A heterogeneous composite rock consisting of two or more petrographically distinct parts, often layered, resulting from partial melting. The original mostly high-grade country rock is called paleosome. The newly formed part is named neosome. The leucosome is the partial melt which crystallized as leucocratic granitoid material comprising the leucocratic, quartzofeldspathic, or feldspathic fraction of the rock. The melanosome is complementary to the leucosome and is the melanocratic, mafic-rich part. The neosome comprises both the leucosome and the melanosome. Non-melted remnants of the non-melted rock within the neosome are named mesosome and have a color between the leucosome and the melanosome. Often used as qualifier such as migmatitic granite

Mylonite

A fault rock or cohesive cataclastite which is part of the mylonite series and consists of 50–90% matrix showing evidence of tectonic grain size reduction. Mylonite has a well-developed foliation

Mylonite series

Foliated cataclastic rock series which comprises protomylonite, mylonite, blastomylonite, phyllonite, and ultramylonite. Pseudo-tachylite is sometimes included (continued)

8.1 Classification of Metamorphic Rocks

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Table 8.1 (continued) Term

Definition

Ortho-

Used as prefix for a metamorphic rock of magmatic origin, such as orthogneiss

Para-

Used as prefix for a metamorphic rock of sedimentary origin, such as paragneiss

Phyllite

Rock that has a well-developed, continuous schistosity with a silky or lustrous sheen on the foliation surface imparted by white mica (including muscovite, paragonite, and phengite), chlorite, and may be biotite. They are oriented parallel to the foliation. Individual micas can be seen with the aid of a hand lens. Average grain size is between 0.01 mm and 0.25 mm. In the literature of alpine geology, they are called “schistes lustrés”

Phyllonite

A cohesive fault rock or cataclastite or mylonite of phyllitic appearance dominated by platy minerals. Along shear planes mica and chlorite have crystallized

Protomylonite

A cohesive fault rock or cataclastite which is part of the mylonite series and formed at low temperature due to overthrusting at the contact surfaces between a magmatic intrusion and the country rock. Matrix makes 10–50% matrix

Pseudo-tachylite

A glassy fault rock in a tectonic shear zone appearing as basaltic glass (tachylite) or a cohesive cataclastite in which rock components occur in a glassy groundmass produced by frictional melting

Slate

General name of an aphanitic compact rock with a strong fissility and an average grain size < 0.1 mm (excluding porphyroblasts). Slates part into thin plates and are typical for low-grade metamorphic mudstones. Because of their good fissility they have been used as roof tiles in Europe, and if rich in organic material, they were used at schools as chalk boards

Schist

Phaneritic metamorphic rock having a well-developed schistosity where > 50% of the rock consists of mineral grains having a tabular, lamellar, or prismatic habit such as mica and amphibole

Schistose rock

A rock with a certain schistosity

Ultramylonite

A fault rock or cohesive cataclastite which is part of the mylonite series and formed at higher temperature than the protomylonite. More than 90% of the matrix has undergone grain size reduction, and recrystallization has occurred. The rock has become homogenous and dense with little foliation observed. If partial melt is formed, the rock is called pseudo-tachylite

minerals during high-temperature metamorphism, especially during contact metamorphism. Both terms are also generally used as descriptive terms without any genetic context. Unfoliated cataclastic rocks are the cataclastic rocks, and if they lack cohesion, the terms broken rock, breccia, and gouge are applied.

8.1.2 Modal Composition and Mineral Assemblage The modal composition or the metamorphic mineral assemblage reflects the metamorphic pressure–temperature conditions. The modal

composition is controlled by the protolith or the bulk chemical composition of the rock and is used as qualifier [15] which in combination with a root term of the fabric classification further characterizes the rock, such as biotite schist or garnet-biotite-quartz granofels indicating an approximative P–T field. How a rock reacts to changes in temperature and pressure depends on its chemical and modal compositions. In sedimentary rocks, dehydration and decarbonatization are important processes at the onset of metamorphism. During diagenesis of pelitic rocks, clay is transformed from smectite to illite which contains less total H2O and silica, and these are liberated. With the increase of

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8 Metamorphic Rocks: Some Basic Concepts

Fig. 8.3 Classification of metamorphic rocks and cataclastic rocks of dynamic metamorphism using root terms based on the absence or presence of foliation (modified from North American Geologic-Map Data Model Science Language Technical Team [11])

temperature, illite is transformed into muscovite, which leads to a further fluid release. The beginning of the transformation is different in mafic rocks, and the transformation will proceed through the hydration of the rock. The primary anhydrous mineral assemblage will change to a mineral assemblage including hydrated minerals or containing OH-groups. Under low-grade P–T conditions, anhydrous magmatic plagioclase in a basalt may be transformed into prehnite, which is composed of the same elements but includes additionally OH-groups in the lattice. With increasing P–T conditions, the mineral assemblage of the hydrated rocks changes again, anhydrous minerals become stable again, and a fluid is often liberated at the same time. Dehydration reaction for chlorite, muscovite, and biotite is shown in Fig. 8.2. Metamorphic reactions involving a fluid release including CO2 are named dehydration or devolatilization reactions. Some bulk rock compositions will not reflect changing metamorphic conditions easily such as rocks rich in SiO2, while rock compositions containing major values of FeO, MgO, Al2O3, or K2O reveal characteristic facies assemblages. The following groups can be distinguished:

– Ultramafic rocks with high values of MgO and FeO and very low in SiO2 – Mafic rocks with high values of CaO, MgO, and FeO and low in SiO2 – Pelites with high values of Al2O3, K2O, and SiO2 – Carbonaceous rocks with high values of CaO, MgO, and CO2 – Quartzo-feldspathic rocks with high values of SiO2, K2O, Na2O, and Al2O3 and very low in MgO and FeO. Ultramafic, mafic, and pelitic compositions are best suited to record the T conditions since they develop characteristic mineral assemblages related to a specific P–T field. Other methods have been developed for quartz-feldspar dominated rocks. For example, Bambauer et al. [1] define a quartz recrystallization isograde in the Variscian granite of the northern Aar massif in Switzerland. This quartz recrystallization isograde is defined by the first occurrence of newly formed quartz at the expense of the former undulatory magmatic quartz. With increasing metamorphic grade toward the South of the Alps, the volume of newly formed quartz increases at

8.1 Classification of Metamorphic Rocks

the expense of the undulatory magmatic quartz up to complete recrystallization. In addition, there is an increase in the size of the recrystallized grains with increasing metamorphic grade. A first rough estimation of the temperature of the appearance of the formation of the quartz recrystallization isograde suggests temperatures around 290 °C [1] and is comparable to greenschist facies conditions. The characteristic metamorphic facies assemblage develops according to the whole rock composition and has a characteristic stability field (Fig. 8.4). The limits of the facies are defined by isogrades or the appearance of a new mineral(s) or mineral assemblage. Terminology for metamorphic facies is based on mineral assemblages crystallized in mafic rocks. Table 8.2 gives the metamorphic facies and a general correlation of the metamorphic assemblages in mafic, pelitic, carbonaceous, and ultramafic whole rock compositions. The limits of the P–T fields and the facies names used may vary slightly. For example, the amphiboliteepidote facies is shown to occupy an individual

Fig. 8.4 P–T diagram showing the fields for the metamorphic facies based on the reaction isogrades or the first appearance of a mineral or mineral assemblage

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field at lower temperature than the amphibolite facies but is often included in the field of the amphibolite facies. Facies names and limits for contact metamorphic settings are not included and overlap in part with the assemblages of regional metamorphism. The reader is referred for detail to the reference list at the end of the chapter. The limits of the various fields are not absolute and are indicated as dashed lines since the stability field of a metamorphic assemblage may change in a geologic setting depending on factors such as bulk rock composition or the presence of a fluid phase. For example, the first appearance of staurolite is controlled by the Al2O3 content and occurs in a rock rich in Al2O3 (ca. 30 weight% Al2O3) at a lower temperature than in a rock poor in Al2O3. Polymetamorphic rocks often reveal a complex P–T path when examined in detail. Thermodynamic programs such as PERPLEX [5], THERIAK-DOMINO [4], or THERMOCALC [13] allow modeling the stability field or the P–T conditions of a mineral assemblage in a rock with known chemical composition (Table 8.3). Metapelitic rocks and metacalc-silicates contain phyllosilicates which are used to constrain a temperature field from diagenetic to greenschist facies conditions. The clay mineral illite progressively crystallizes to white mica, and this progress can be measured by using the Kübler index (KI) or illite crystallinity (IC) (for details see Frey [9]; Frey and Robinson [10]; Warr and Ferreiro Mählmann [22]; Warr and Cox [21]; Warr [20] and references therein). Illite has a strong (001) reflection from the basal plane in Xray diffraction, and the shape of the peak changes with the metamorphic grade. In diagenetic to low-grade metamorphic rocks, the illite peak is relatively large becoming sharper in greenschist facies rocks (Fig. 8.5). The peak width of the illite peak is measured at half maximum peak height (FWHM) above the background as analyzed by X-ray diffraction and is expressed as D° 2H, the unit used in X-ray diffraction. This value is used to define IC or KI. Three zones are defined (Frey and Robinson [10]; Warr and Ferreiro Mählmann [22]; Warr and Cox [21]; Warr [20]):

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Table 8.2 Metamorphic facies and corresponding key mineral assemblage for mafic, pelitic, calc-silicate rock, and ultramafic compositions mainly based on Barker [2] Okrusch and Frimmel [12], and Yardley and Warren [23] Metamorphic facies

Metabasic rock High values of MgO, FeO, CaO

Metapelitic rock High values of K2O, Al2O3 SiO2

Metacalc-silicate High values of MgO, CaO, CO2

Metaultrabasic rock High values of MgO, FeO, low SiO2

Zeolite

zeo lmt hul wa anl

Mixed-layered clays kln ± ilt ± chl

cal-dol-ilt/sm

srp-cal-tlc srp-cal-chl

Prehnitepumpellyite

prh ± pmp

Chlorite zone kln-ilt/chl-chl/sm ab ± chl-phengitic ms ± stp ± pg

tlc-cal-ab-ms ± chl Kübler Index

srp-tlc ± chl srp-brc

Greenschist

ep/zo-ab-act

Biotite zone chl-ms-ab-pl ms-chl-ctd-ab bt-ab-ms-chlphengitic ms pyl-chl-crd

cal-dol ank-cal-chl-abchl ± bt

srptlc ± chl ± tr ± br

Epidote– amphibolite

tr/act-ep-ab

Garnet zone Grt (alm)-bt-chl-ms-pl

Zoisite zone cal-zo-tr-bt

srp-fo

Amphibolite

amp-grt-ab/olg

Staurolite-garnet zone st-grt-bt-ms-cld-pl ms-chl-ctd-st ± grt Kyanite zone grt-bt-ms-pl-ky Upper amph zonesillimanite zone 1 grt-sil-bt-pl ± ky-rt

tr-cal-qtz-py cal-di-tr-qz-py cal-di-grs-qz dol-cal-tr hbl-an di-plg-mc-qz

fo-ath-tlc-chl ath-tr-tlc-chl fo-di-tr en-ath-tr

Granulite

grt-cpx-opx-an cpx-opx-pl

Sillimanite zone 2-no ms! sil-crd-grt-kfs-pl High P–T zone spr-qz osm-grt opx-sil-qz

fo-cal-qz di-an-cal-dol wo-di-cal wo-srp-cal

fo-en fo-en-cpx-spl

Blueschist

gln-ep-ab-ttn gln-lws-ab-ep/zo High p jd-gln-phe-ttn

gln-phe-chl-ep-ttn phe-lws-gln-ttn gln-grt-phe-ep/zo

ara/cal-qz-chl

srp-mag-mgs-dol

Eclogite

gr-omp-rt

Kyanite-garnet zone grt-ky-qtz ky-ph-qz grt-tlc-ky (high pressure) tlc-phe-ky-cld

di-qz-cal dol-phl

fo-opx-cpx-grt

For abbreviations see Table A.1 in Appendix A

Diagenetic zone ( 0.52 D°2H (conditions from diagenesis to zeolite facies). Anchizone (200°–300 °C) KI 0.52–0.32 D° 2H (± prehnite-pumpellyite, lower greenschist facies).

Epizone (>300 °C) KI < 0.32 D°2H (± greenschist facies). A high value for the peak width at half maximum peak height (FWHM) means a low illite crystallinity or small crystallite size, and a small

8.1 Classification of Metamorphic Rocks

169

Table 8.3 Definition of specific terms for defining a metamorphic rock

a

Term

Definition

Amphibolitea

Rock composed largely of hornblende and plagioclase and the origin may be magmatic or sedimentary

Augengneiss

A gneiss with macroscopically visible anhedral crystal of K-feldspar or quartz called Augen (German for eyes) which are porphyroclasts having formed either in a magmatic rock such as a coarse-grained granite or a sedimentary environment, such as a coarsegrained quartz conglomerate and are enveloped by a foliation

Blueschista

Mafic metamorphic rock containing glaucophane and indicative of high pressure subduction-related metamorphism. Although gray in hand specimen, glaucophane is blue in thin section giving rise to the name

Calc-silicate rock

Rock dominated by calc-silicate minerals such as grossular, wollastonite, or diopside. Calc-silicate skarn or hornfels occur within impure limestone or dolomite strata adjacent to an intruding igneous rock

Eclogitea

A dense mafic rock with > 70% of garnet and omphacite (jadeitic clinopyroxene) and which may contain glaucophane, kyanite, mica and occurring at high pressure– temperature conditions in subduction zones or orogenic belts

Fenite

Desilicated crustal rocks or quartzo-feldspathic rock consisting of alkalic feldspar, with some aegirine, subordinate alkali-hornblende, and which formed by alkali metasomatism and hydrothermal fluids rich in Na and K

Granulite or granulite facies rocka

Granulite facies rocks, commonly referred to simply as “granulite” formed at high pressures and temperature where PH2O < < PTotal, and hydrous minerals become unstable. A granofelsic texture with anhydrous mafic minerals will develop. Chemical changes or significant depletion of incompatible elements may occur either by the removal of mobile elements within the fluids released during dehydration or by the loss of a partial melt

Greenschista

A greenschist, normally a metabasite comprising mainly epidote/clinozoisite, chlorite, albite, and titanite

Greisen

The roof zone of a granitic rock altered by hydrothermal fluids derived from the magma and often rich in Li, F, and B

Marble

A rock composed of carbonate minerals, mainly calcite, dolomite, and calc-silicate

Prasinite

Term used in the literature of alpine geology and refers to a greenschist

Rodingsite

A rock associated with serpentinites and comprising Ca-rich minerals such as grossular or Ca-pyroxene which represent the Ca-rich fraction expelled during serpentinization

Quartzite

A hard rock consisting mainly of quartz and lacking facies indicative minerals. Estimations of metamorphic facies can be made using the quartz recrystallization isograde

Serpentinite

Rock composed mainly of serpentine and the result of the hydration of ultramafic rocks such as peridotite

Skarn

Term commonly used but not recommended. General term for a zone of metasomatic calc-silicate rock in a metamorphic thermal aureole

Rocks used for the definition of metamorphic facies

value at half maximum peak height means a high illite crystallinity or a large crystallite size. Two extreme examples of illite crystallinity (IC) or Kübler index (KI) are shown in Fig. 8.5: a diagenetic pelitic rock with a Kübler index (KI) of 1.17 D°2H and a rock of greenschist facies conditions with a Kübler index (KI) of 0.19D°2H.

The Árkai index (ÁI) is based on the same principle but uses the (001) chlorite peak of the basal plane as determined by X-ray diffraction. Because of lack of chlorite in diagenetic and low anchizonal rocks, the ÁI is mainly used in upper anchizonal and epizonal rocks. Determination of KI and the ÁI index are important tools in

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8 Metamorphic Rocks: Some Basic Concepts

which is straightforward, such as metagranite, metabasalt, or metagraywacke.

8.2

Fig. 8.5 Kübler index (KI) or illite crystallinity (IC) in a pelitic rock. a KI of low-grade diagenetic conditions; b KI of greenschist facies conditions. The peak width or the horizontal red line at the maximum half height is the value used for the KI and is expressed as D°2H (modified from Ferreiro Mählmann et al. [7])

metamorphic sedimentary sequences to understand thrust formation, their stacking in orogenic belts, in the reconstruction of mountain belts or in the determination of the paleoclimate conditions.

8.1.3 Protolith In weakly metamorphosed rocks, the structural and mineralogical features of the protolith or the precursor rock might still be recognized, and a rock can be named according to the protolith

Common Textures in Metamorphic Rocks

Most common terms to describe textures in metamorphic rocks are listed and defined in Table 8.4, and frequent metamorphic textures are shown in Figs. 8.6, 8.7, 8.8, and 8.9. Barker [2] provides a systematic detailed description of metamorphic textures. Undulatory extinction is shown in Fig. 5.21c–i in Chap. 5 and is a general indication of deformation and metamorphism. The observed crystallization sequence of minerals and the mineral assemblage allow differentiation of metamorphic events, such as prograde metamorphism during rising temperature and/or pressure, the peak of metamorphism, or retrograde metamorphism during falling temperature and/or pressure. The schistosity may be used as a reference and defines pretectonic, syntectonic, and post-tectonic growth. In Fig. 8.6a, the beginning of metamorphism at low temperature will lead to the appearance of a first foliation in an anchizonal pelitic rock or at beginning zeolite facies conditions. Water and other volatiles leave the rock through fractures. Crossmicas or alternating stacks of chlorite/muscovite may form in open space recording the development of a first foliation (Fig. 8.6b, c). Chlorite crystallizes in the interstitial space of a terrigenous sediment (Fig. 8.6d). Vesicles in a basalt fill up with lowtemperature clays (Fig. 8.6e). Porphyroclasts are witnesses of the protolith, such as a lithoclast of a quarzite or a metagranitic rock (Fig. 8.6f), or feldspar phenocrysts of a magmatic rock (Fig. 8.6g, h) which are enveloped by a foliation defined by muscovite. Detrital mica in a marble is overgrown by a syntectonic rim of muscovite (Fig. 8.6i). A porphyroblast of biotite englobes a former foliation containing epidote and opaque minerals (Fig. 8.6j), and a porphyroblast of staurolite englobes opaque minerals and quartz (Fig. 8.6k). Untwinned albitic plagioclase may grow in equilibrium with other phases such as epidote and chlorite during greenschist facies

8.2 Common Textures in Metamorphic Rocks

171

Table 8.4 Some common terms to describe metamorphic textures. See also Figs. 8.6, 8.7, and 8.9 and Fig. 5.21c–i for undulatory extinction Term

Definition

Atoll texture

Often observed in garnet where a crystal of garnet has a core of a different mineral assemblage, mainly phengitic muscovite, quartz, or chlorite. The earlier formed core results from fluid-controlled reactions often during exhumation and the rim equilibrated to changing P–T conditions. The breakdown of garnet occurred from the inside and recrystallization occurred from the outside toward the inside

Crenulation cleavage

An earlier formed schistosity is folded which may be symmetric or asymmetric depending on the orientation of the stress field of the second deformation with respect to the first schistosity. Depending on the rock composition, commonly a pelitic protolith, P (phyllosilicate) domains and Q (quartz-feldspar) domains may develop. Common in intermediate to high T rocks

Helicitic

Mineral inclusions related to an earlier foliation and contained in a porphyroblast

Pinnitization

The retrograde alteration often postdating ductile deformation, mainly of cordierite, to a fine matrix of muscovite and chlorite. Alteration starts along fissures within the crystal and may advance to the total replacement or pseudo-morphosis of the crystal

Porphyroblast

A large crystal grown during metamorphism, often englobing former foliation during growth and being often chemically zoned due to changing P–T conditions

Porphyroclast

A large relict rigid crystal is often enveloped by a schistosity which has not yet recrystallized at the prevailing metamorphic conditions. This is often the case for Kfeldspar or quartz which have a large P–T stability field

Post-tectonic/postkinematic

A post-tectonic mineral has grown after the main deformation event or after a defined deformation event

Pretectonic/prekinematic

A pretectonic mineral has grown before the main deformation event or before a defined deformation event

Pressure shadow Strain shadow

A region on opposing sides of a rigid bigger crystal, often a porphyroclast and which was protected from deformation. The rock matrix seems to be detached along the contacts

Pseudo-morph

A pseudo-morph is a mineral being totally replaced by a former mineral and which has inherited the original habit of the former mineral

Pseudo-morphosis

The complete transformation of a mineral into a pseudo-morph

Sericitization

Alteration of a mineral into a fine-grained mica, called sericite occurring at lowtemperature conditions

Serpentinization

Retrograde, low-temperature alteration of mafic minerals consisting of serpentine and with input of a fluid

Snowball garnet

Spiraled or S-shaped inclusions occur in a syntectonic porphyroblast. They are either explained by the rotational model where the inclusions are formed during the rotation of the crystal or by the non-rotational model where the foliations result from changes in the stress fields as evidenced by distinct domains of different crystallographic orientation of the host garnet

Symplectite

Complex intergrowth of two or three simultaneously crystallizing minerals as the result of the decomposition of a former high pressure or/and high-temperature mineral assemblage during retrogression in a granulite facies rock. One phase is often vermicular

Syntectonic/synkinematic

A syntectonic mineral has grown simultaneously during deformation and the formation of the schistosity

Undulatory extinction Undulous extinction (See also Sect. 5.1.4)

Distinct poorly confined zones of extinction slowly move across the crystal which gives an aspect of a wave traversing the mineral. Strain induced in the mineral offsets the crystallographic lattice and results in slightly different optical orientations within (continued)

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8 Metamorphic Rocks: Some Basic Concepts

Table 8.4 (continued) Term

Definition the grain. Common in quartz, feldspar, mica, and olivine. Recrystallization often takes place along grain boundaries in the form of smaller grains with different optical orientations

Uralitization

Partial alteration or pseudo-morphic replacement of primary igneous pyroxene by metamorphic/hydrothermal actinolite, tremolite, or hornblende

conditions (Fig. 8.6l). The crenulation cleavage witnesses two deformation events (Fig. 8.6m, n). Post-tectonic mica overgrowths of a syntectonic mica generation and their different interference colors and different crystallographic orientations show the two generations of metamorphism (Fig. 8.6o). Garnet is particularly able to record the metamorphic history of a rock and often occurs as porphyroblast (Fig. 8.7a–i). It can include an earlier foliation (Fig. 8.7a), and sometimes inclusions are well aligned called a helicitic texture (Fig. 8.7b). Post-tectonic static crystallization of garnet overgrows the former foliation, and a euhedral porphyroblast develops (Fig. 8.7 c). In a snowball garnet (Fig. 8.7d) spiraled or Sshaped inclusions occur. They are either explained by the rotational model where the inclusions formed during the rotation of the crystal or by the non-rotational model where the foliations result from changes in the stress fields as evidenced by distinct domains of different crystallographic orientation of the garnet. Pretectonic garnet or a garnet porphyroclast shows pressure shadows or strain shadows on opposing sides (Fig. 8.7e, f). Garnet is often altered during retrograde metamorphism. (Fig. 8.7g–i) and displays partial alteration to chlorite at low temperature (Fig. 8.7g) or is pseudo-morphosed to chlorite and amphibole (Fig. 8.7h). An atoll garnet (Fig. 8.7i) has a rim-like often euhedral zone with a core of a different mineral assemblage, mainly phengitic muscovite, chlorite, and quartz. The assemblage of the core results from fluid-controlled reactions often related to exhumation and the garnet rim equilibrated to changing P–T conditions. The breakdown of garnet occurred from the inside because of fluid infiltration along fractures and recrystallization

occurred from the outside toward the inside. Symplectites (Fig. 8.7j–l) are complex intergrowths of two or three simultaneously crystallizing minerals (one is often vermicular) as the result of the decomposition of a former high P or/and high T mineral assemblage during retrogression in a granulite facies rock. The example shows diopside and quartz as well as diopside and plagioclase at the contact of a garnet crystal. Symplectites often allow one to decipher the retrograde exhumation path. The angular contact between crystals forming an angle of 120° is considered as an equilibrium texture as shown in a marble and a feldspathic rock (Fig. 8.7m, n) but also occurs in other monomineralic rocks such as quartzite. Metamorphism is also documented by vein formation such as a prehnite vein in a metagranite (Fig. 8.7o) during prehnitepumpellyite facies conditions. Metamorphism is evident by the alteration of minerals such as the chloritization of biotite (Fig. 8.8a), the sericitization of feldspar (Fig. 8.8 b), the prehnization of feldspar (Fig. 8.8c), the alteration of mafic minerals to tremolite, actinolite, or amphibole called uralitization (Fig. 8.8d), the alteration of olivine or pyroxene to serpentine called serpentinization (Fig. 8.8e), or the alteration of cordierite to fine-grained mica known as pinnitization (Fig. 8.8f). Sagenitic biotite witnesses the alteration of a Ti-rich biotite which is crystallized under higher T conditions and recrystallized to a Ti-poor biotite under lower temperature conditions. The Ti content of the high-temperature biotite is crystallized as oriented lamellae of rutile in the low-temperature biotite (Fig. 8.8g). Another evidence of retrogression is the replacement of pyroxene stable under granulite facies conditions to an amphibole stable at amphibole facies conditions (Fig. 8.8h).

8.2 Common Textures in Metamorphic Rocks

173

Fig. 8.6 Metamorphic textures and rocks. For explanation see text. For mineral abbreviations see Table A.1 in Appendix A

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8 Metamorphic Rocks: Some Basic Concepts

Fig. 8.7 Metamorphic textures and rocks. For explanation see text. For mineral abbreviations see Table A.1 in Appendix A

8.2 Common Textures in Metamorphic Rocks

175

Fig. 8.8 Metamorphic textures and rocks. For explanation see text. For mineral abbreviations see Table A.1 in Appendix A

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8 Metamorphic Rocks: Some Basic Concepts

Fig. 8.9 Metamorphic textures and rocks. For explanation see text. For mineral abbreviations see Table A.1 in Appendix A

Selection of Books on Metamorphic Petrology and Cited Reference

The accessory minerals rutile, titanite, and anatase have a great potential to illustrate a P–T path of a rock. In Fig. 8.8i, rutile is altered to titanite and witnesses the retrograde alteration of the rock where rutile was first stable at high temperature. The rock left the stability field of rutile and entered the stability field of titanite, which replaces rutile at lower pressure/lower temperature. This replacement texture is common in retrogressed eclogitic rocks. Figures 8.8j–o are examples of partial melting and recrystallization. The crystal boundaries become soft and rounded and zones of melting and recrystallization can well be differentiated by their different extinction behavior. Melt production can be better visualized by inserting the k-plate (see Fig. 8.8o). In Fig. 8.9a–o, some tectonic-related textures are illustrated (see textbooks on microtectonics, e.g., Passchier and Trouw [14]; Vernon [19]). Brittle deformation is common in feldspar crystals (Fig. 8.9a–c) and is also seen in pyroxene (johannsenite) in a contact metamorphic aureole (Fig. 8.9d) or in a clinozoisite/epidote greenschist (Fig. 8.9e). Ductile deformation is witnessed in muscovite overgrown by a metamorphic muscovite with blue interference colors (Fig. 8.9f), in plagioclase (Fig. 8.9g–j), in quartz (Fig. 8.9k), in muscovite (Fig. 8.9l), and in biotite (Fig. 8.9m, n). The so-called mica fish is a kinematic indicator in schists and mylonites. They are porphyroclasts or former porphyroblasts which were sheared by a combination of plastic and ductile deformation. The (001) cleavage plane can be used to determine the sense of shear (Fig. 8.9o).

Selection of Books on Metamorphic Petrology and Cited Reference 1. Bambauer H, Herwegh M, Kroll H (2009) Quartz as indicator mineral in the Central Swiss Alps: The quartz recrystallization isograd in the rock series of the northern Aar massif. Swiss J Geosci 102:345–351 2. Barker AJ (2013) Introduction to metamorphic textures and microstructures. Routledge 3. Bucher K (2023) Petrogenesis of metamorphic rocks. Springer-Verlag

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4. De Capitani C, Petrakakis K (2010) The computation of equilibrium assemblage diagrams with Theriak/ Domino software” American Mineralogist 95/7:1006– 1016 5. Connolly JAD (1990) Multivariable phase-diagramsan algorithm based on generalized thermodynamics. Am J Sci 290:666–718 6. Fettes D, Desmons J (Eds) (2007) Metamorphic rocks: a classification and glossary of terms, recommendations of the International Union of Geological Sciences. Subcommission on the systematics of metamorphic rocks. Cambridge University Press 7. Ferreiro Mählmann R, Bozkaya Ö, Potel S, Le Bayon R, Šegvić B, Nieto F (2012) The pioneer work of Bernhard Kübler and Martin Frey in very lowgrade metamorphic terranes: paleogeothermal potential of variation in Kübler-Index/organic matter reflectance correlations. A review. Swiss J Geosci 105:121–152 8. Fossen H (2016) Structural geology, 2nd edn. Cambridge University Press 9. Frey M (1987) Low temperature metamorphism. Blakie, Glasgow and London, 351 p 10. Frey M, Robinson D (eds) (1999) Low-grade metamorphism. Blackwell Science, Oxford, p 313 p 11. North American Geologic-Map Data Model Science Language Technical Team (2004) Report on progress to develop a North American science-language standard for digital geologic-map databases; Appendix B–Classification of metamorphic and other composite-genesis rocks, including hydrothermally altered, impact-metamorphic, mylonitic, and cataclastic rocks, Version 1.0 (12/18/2004), In: Soller DR (ed) Digital mapping techniques ’04—workshop proceedings: U.S. Geological Survey Open-File Report 2004–1451, 56 p 12. Okrusch M, Frimmel HE (2020) Mineralogy. Springer Verlag 13. Powell R, Holland T, Worley B (1998) Calculating phase diagrams involving solid solutions via non-linear equations, with examples using THERMOCALC. Journal of Metamorphic Petrology 16:577–588 14. Passchier CW, Trouw RAJ (1996) Microtectonics. Springer Verlag, New York 15. Philpotts AR, Auge JJ (2022) Principles of igneous and metamorphic rocks. Cambridge University Press 16. Robertson S (1999) BGS rock classification scheme, Volume 2, classification of metamorphic rocks. British Geological Survey, Research Report RR 99–02:24p 17. Snoke AW, Tullis J (1998) An overview of fault rocks. Snoke, AW, Tullis, J, Todd VR Fault-related Rocks. Princeton University Press, NJ, A Photographic Atlas. Princeton, pp 3–18 18. Spear FS (1993) Metamorphic phase equilibria and pressure-temperature-time paths. Mineralogical Society of America, Monograph, p 1 19. Vernon RH (2018) A practical guide to rock microstructure. Cambridge University Press, 2nd edn

178 20. Warr LN (2018) A new collection of clay mineral ‘Crystallinity’ Index Standards and revised guidelines for the calibration of Kübler and Árkai indices. Clay Miner 53(3):339–350 21. Warr LN, Cox SC (2016) Correlating illite (Kübler) and chlorite (Árkai) “crystallinity” indices with metamorphic mineral zones of the South Island, New Zealand. Appl Clay Sci 134:164–174 22. Warr LN, Ferreiro Mählmann R (2015) Recommendations for Kübler index standardization. Clay Miner 50(3):283–286 23. Yardley BWD, Warren C (2021) An introduction to metamorphic petrology. Cambridge University Press, 2nd edn

Further Reading 1. Best MG (2002) Igneous and metamorphic petrology. Blackwell Science, Boston 2. Blatt H, Tracy RJ (1996) Petrology: igneous, sedimentary, and metamorphic, 2nd edn. Freeman, New York, W.H 3. Borradailie GJ, Bayly MB, Powell CmcA (eds) (1982) Atlas of deformational and metamorphic rock fabrics. Springer-Verlag Berlin Heidelberg New York, 551 p 4. Bucher K, Frey M (1994) Petrogenesis of metamorphic rocks, 6th edn. Springer-Verlag, Complete Revision of Winkler’s Textbook 5. Bucher-Numinen K, Frey M, Bucher K (1998) Petrogenesis of metamorphic rocks. Springer Verlag

8 Metamorphic Rocks: Some Basic Concepts 6. Evans BW (ed) (2007) Metamorphic petrology. Landmark Papers No. 3. Mineralogical Society of Great Britain and Northern Ireland 7. Hollocher K (2012) A Pictorial guide to Metamorphic Rocks in the Field. Taylor & Francis Group, London 8. Hyndman DW (1985) Petrology of igneous and metamorphic rocks. McGraw-Hill, New York 9. Kornprobst J (1994) Métamorphisme et roches métamorphiques. Dunod, Paris 10. Mehnert KR (1968) Migmatites and the origin of granite rocks. Elsevier, Amsterdam 11. Miyashiro A (1994) Metamorphic petrology. Oxford University Press, New York 12. Sanders I (2018) Introducing metamorphism. Dunedin Press 13. Saywer EW (2008) Atlas of Migmatites. The Canadian Mineralogist, Mineralogical Association of Canada, National Research Council Canada, Monograph Publishing Program, Special Publication 9:372 p 14. Sibson RH (1977) Fault rocks and fault mechanisms. J Geol Soc London 133:191–213 15. Vernon RH. Clarke GL (2008) Principles of metamorphic petrology. Cambridge University Press, 478p 16. Wimmenauer W (1985) Petrographie der magmatischen und metamorphen Gesteine. Enke, Stuttgart 17. Yardley BWD (1989) An introduction to metamorphic petrology. Wiley, Longman Earth Science Series, New York 18. Yardley BWD, MacKenzie WS, Guilford C (1990) Atlas of metamorphic rocks and their textures. Longman, Harlow

9

The Mineral Plates and How to Use Them

9.1

Introduction to the Mineral Plates

This chapter includes seventy-three mineral plates of sixty-five common rock-forming minerals. A mineral plate summarizes the optical and crystallographic parameters and their relationships and shows it in characteristic microscopic images in PPL and XPL (Figs. 9.1 and 9.2). Color in PPL in a thin section of 30 l m thickness is used as the first parameter for the organization of the mineral plates since it is a parameter easily recognized (Tables 9.1, 9.2, 9.3, 9.4, and 9.5). Five color categories are distinguished: (1) colorless, (2) green to blue-green and yellow, (3) brown, (4) blue, and (5) rose to red and pinkish. The color category is indicated as a color bar on the upper right side of each mineral plate. Depending on the chemical composition, a mineral may occur in more than one color category and therefore will appear in more than one color category. For example, garnet may be colorless, brownish, or reddish. It is therefore listed in the color categories colorless, brown, and red. Within each color category, minerals are arranged according to the decrease of birefringence. A mineral with a high birefringence appears therefore at the beginning of the color category and an isotropic mineral is listed at the end. This grouping of minerals allows to reduce the potential mineral candidates. The focus can then be on additional parameters such as form/habit, relief, cleavage, twins, zonation, and

elongation that together with interference figures can be used to finalize the identification of the mineral. The rectangle in the upper part of the mineral plate (Fig. 9.1) displays to the left the mineral name and its international abbreviation in lower case [5]. Below the mineral name, the general chemical formula and crystallographic and optical parameters are indicated. A section in the middle part highlights the main optical characteristics for identification. Typical geological occurrences are also added. In certain cases, small microscopic images highlight the main optical characteristics. In the right part of the rectangle, the color bar(s) and the classification after Strunz and Nickel [2] are given. The habit (according to Tröger [3]) is used to show the relationships between the crystallographic and optical parameters (Fig. 9.2). Below the rectangle, microscopic images illustrate the optical characteristics in PPL and XPL. Samples are from my teaching collection and from master and PhD theses carried out over many years. Images were acquired with three different types of microscopes and different cameras and software: Leitz Orthoplan, Nikon eclipse Ci Pol, and Leitz DMLP. There are key minerals and mineral groups which are frequent and easy to identify such as feldspar, quartz, mica, pyroxene, olivine, amphibole, garnet, kyanite, sillimanite, andalusite, and chlorite. They have characteristic optical properties and can be the framework and help to identify other minerals within the rock specimen.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. T. Schmidt, Transmitted Light Microscopy of Rock-Forming Minerals, Springer Textbooks in Earth Sciences, Geography and Environment, https://doi.org/10.1007/978-3-031-19612-6_9

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The Mineral Plates and How to Use Them

Fig. 9.1 Example of the upper rectangle of a mineral plate. See text for explanation

Fig. 9.2 Examples of the relationship between the crystallographic and optical parameters (see also Chap. 2). The crystallographic axes and the vibration directions with their corresponding refractive indices can coincide in a tetragonal a and an orthorhombic mineral b in all directions,

can coincide in one direction as in monoclinic crystals c and differ in all directions in a triclinic mineral (d). The optic axes, the location of the optic plane, and the vibration directions and their corresponding indices of refraction are indicated according to Tröger [3, 4]

Certain minerals commonly occur with other (4) Determine possible twinning, type of extinction (parallel, inclined, symmetric, minerals due to the geological setting and the without reference), mineral zoning, incluchemical composition of the rock. Also, the sions, or alteration textures. occurrence of a mineral may exclude other minerals. For example, nepheline and quartz do (5) Determine elongation in adequate sections. not generally occur in the same rock, nor does Examine in the conoscopic illumination mode Mg-rich olivine and quartz. (high magnification, XPL, condenser, k-plate, This is the recommended approach to deterAmici-Bertrand lens). mine a mineral in a thin section: Examine in the orthoscopic illumination mode in (6) Determine the optical character by performing an interference figure (uniaxial or biaxial plane polarized light (PPL). mineral) and determine the optical character (1) Determine color and possible pleochroism. and the 2V angle for biaxial minerals. (2) Determine habit/form, relief, and cleavage. Consider the geological context of your sample Examine in the orthoscopic illumination mode in and verify your results. crosspolarized light (XPL). (7) Summarize the results and name the speci(3) Determine maximal birefringence or if it is men. Compare with the hand specimen an isotropic mineral or a section perpendic(Fig. 9.3). ular to an optic axis.

9.1 Introduction to the Mineral Plates

181

Table 9.1 Colorless minerals as observed in PPL and arranged according to decreasing birefringence Mineral

Birefringence Relief

Optical

δ Δn

character

category

Abbreviation Additional color

Calcite

0.172

M- H+

U-

cal

Zircon

0.042-0.065

H+ VH

U+

zrn

Anhydrite

0.040-0.044

M+

B+

anh

Olivine

0.035-0.052

M+ H+

B+ B-

ol

Muscovite

0.035-0.049

L+ M+

B-

ms

Prehnite

0.022-0.051

M+

B+

prh

Talc

0.010-0.05

L+ M+

B-

tlc

Pectolite

0.037

M+

B+

pct

Johannsenite

0.022-0.029

H+

B+

jhn

Dumortierite

0.011-0.037

H+

B-

dum

Scapolite

0.004-0-034

L+ M+

U-

scp

Sillimanite

0.018-0.022

H+

B+

sil

Alunite

0.010-0.023

M+

U+

alu

Kyanite

0.012-0.016

H+

B-

ky

Laumontite

0.010-0.012

L-

B-

lmt

Lawsonite

0.010-0.012

M+ H+

B+

lws

Andalusite

0.009-0.013

M+

B-

and

Cordierite

0.008-0.018

L- L+

B+

crd

Quartz

0.009

L+

U+

qz

Albite

0.009-0.010

L- L+

B+

ab

Corundum

0.008-0.009

H+

U-

crn

Plagioclase

0.007-0.018

L- L+

B+ B-

pl

Myrmekite

0.005-0.008

L- L+

Orthoclase-perthite

0.005-0.008

L-

or

Microcline

0.005-0.008

L- L+

mc

Sanidine

0.005

L-

B-

Clinozoisite

0.004-0.015

H+

B+ B-

czo

Nepheline

0.003-0.006

L- L+

U-

nph

Apatite

0.001-0.007

M+

U-

ap

Analcime/analcite

0.004

M-

B-

anl

Vesuvianite

0.003-0.006

M+

B+ B-U+ U-

ves

Nosean

isometric

M-

isotropic

nsn

Haüyne

isometric

M-

isotropic

hyn

Leucite

0.00-0.001

L- L+

U+

lct

Fluorite

isometric

M-

isotropic

fl

Garnet

isometric

Glass/Obsidian

mym

sa

H+

isotropic

grt

M+ H+

isotropic

glass

182

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The Mineral Plates and How to Use Them

Table 9.2 Green minerals as observed in PPL and arranged according to decreasing birefringence Mineral

Birefringence

Relief

δ Δn

category character

Optical

Abbreviation Additional color

Aegirine-augite

0.030-0.060

H+

B-

aeg-aug

Atacamite

0.049 anomalous

H+

B-

ata

Olivine

0.035-0.052

M+ H+

B+B-

ol

Stilpnomelane

0.030-0.110

H+

U-

stp

Biotite

0.028-0.07

L+ M+

U- B-

bt

Prehnite

0.022-0.051

M+

B+

prh

Epidote

0.015-0.051

H+

B- B+

ep

Clinopyroxene

0.018-0.034

H+

B+

aug

Tourmaline

0.017-0.035

M+ H+

U-

tur

Glauconite

0.022-0.032

M+

B-

glt

Johannsenite

0.022-0.029

H+

B+

jhn

Dumortierite

0.011-0.037

H+

B-

dum

M+ H+

B+B-

amp

Amphibol (general) 0.019-0.027 Celadonite

0.018-0.022 anomalous

M+

B-

cel

Pumpellyite

0.018-0.022

H+

B-

pmp

Winchite

0.018-0.022

M+

B-

wnc

Barroisite

0.018

H+

B-

brs

Actinolite

0.017-0.022

M+ H+

B-

act

Omphacite

0.012-0.028

H+

B+

omp

Orthopyroxene

0.007-0.020

M+ H+

B-

opx

Chlorite

0.00-0.02 anomalous

L+ M+

B- B+

chl

Chloritoid

0.005-0.022 anomalous

H+

B+

cld

Arfvedsonite

0.005-0.012 anomalous

M+ H+

B-

arf

Phlogopite

0.003-0.008 anomalous

L+ M+

B-

phl

Serpentine

0.00-0.017

M+ H+

B-

srp

9.1 Introduction to the Mineral Plates

183

Table 9.3 Brown minerals as observed in PPL and arranged according to decreasing birefringence Mineral

Birefringence

Relief

Optical

δ Δn

category

character

Abbreviation Additional color

Rutile

0.286-0.296

VH+

Zircon

0.042-0.065

H+ VH

U+

zrn

Titanite

0.010-0.192

H+

B+

ttn

Stilpnomelane

0.030-0.110

H+

U-

stp

Biotite

0.028-0.07

L+ M+

U- B-

bt

Tourmaline

0.017-0.035

M+ H+

U-

tur

Amphibol (general)

0.019-0.027

M+ H+

B+B-

amp

Anthophyllite

0.005-0.022

M+ H+

B-

ath

Phlogopite

0.003-0.008 anomalous

L+ M+

B-

phl

Staurolite

0.011-0.014

H+

B+

st

Vesuvianite

0.003-0.006

M+

B+ B-U+ U-

ves

Nosean

isometric

M-

isotropic

nsn

Garnet

isometric

H+

isotropic

grt

Spinel

isometric

H+

isotropic

spl

U+

rt

Table 9.4 Blue minerals as observed in PPL and arranged according to decreasing birefringence Mineral

Birefringence

Relief

Optical

δ Δn

category

character

Abbreviation

Johannsenite

0.022-0.029

H+

B+

jhn

Dumortierite

0.011-0.037

H+

B-

dum

Tourmaline

0.017-0.035

M+ H+

U-

tur

Glaucophane

0.012-0.028

M+ H+

B-

gln

Lawsonite

0.010-0.012

M+ H+

B+

lws

Kyanite

0.012-0.016

H+

B-

ky

Chloritoid

0.005-0.022 anomalous

H+

B+

cld

Sapphirine

0.005-0.012

H+

B- B+

spr

Corundum

0.008-0.009

H+

U-

crn

Nosean

isometric

M-

isotropic

nsn

Haüyne

isometric

M-

isotropic

hyn

Fluorite

isometric

M-

isotropic

fl

Additional color

Table 9.5 Red, rose and pinkish minerals as observed in PPL and arranged according to decreasing birefringence Mineral

Birefringence δ Δn

Relief category

Optical character

Abbreviation Additional color

Rutile Thulite Tourmaline Garnet

0.286-0.296 0.006-0.018 anomalous 0.017-0.035 isometric

VH+

U+

rt

H+

B+

thu

M+ H+

U-

tur

H+

isotropic

grt

184

It is best to learn to identify the most frequent minerals. Start with scanning the thin section to get familiar with it. Try to be as systematic and as precise as possible and to work on more than one individual mineral grain. Although it is easy to take microscopic images, take colored pencils and sketch some minerals as shown below in the example of a

9

The Mineral Plates and How to Use Them

metamorphic rock [1]. This helps to pin down the characteristic parameters and to remember the mineral for the future. Normally it is not necessary to use the complete toolbox of optical mineralogy, and three or four optical parameters are often sufficient to identify a mineral. And it is always good to remember the geological environment of a rock specimen.

Fig. 9.3 Example of the description of a rock by Afifé El Korh and the identification of its minerals [6]

9.1 Introduction to the Mineral Plates

Fig. 9.3 (continued)

185

186

9

The Mineral Plates and How to Use Them

Determination of the rock The rock is composed of the minerals quartz, muscovite, plagioclase, epidote, garnet and titanite. Accessory zircon is also observed (