Functional and Smart Materials Structural Evolution and Structure Analysis

Functional and Smart Materials Structural Evolution and Structure Analysis

Z. L. Wang and Z. C. Kang Georgia Institute a/Technology Atlanta, Georgia

PLENUM PRESS • NEW YORK AND LONDON

Library of Congress Cataloging-in-Publication Data

Wang, Zhong Lin. Functional and smart materials structural evolution and

structure analysis / Z.L. Wang and Z.C. Kang. p. cm.

Includes bibliographical references and index.

1. Smart materials. I. Kang, Z. C. (Zhen Chuan) II. Title. TA418.9.S62W36 1998 620.1·98--dc21

ISBN-13: 978-1-4613-7449-7 DOl: 10.1007/978-1-4615-5367-0

© 1998 Plenum Press, New York

e-ISBN-13: 978-1-4615-5367-0

Softcover reprint of the hardcover 1 st edition 1998

A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013

http://www.plenum.com

10987654321

All rights reserved

97-44018 CIP

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

To all of our family members

Foreword

At the end of this century, the technological importance of oxides are growing extremely fast. Most of the information is transported by optical fibers because light can carry more information than conventional electromagnetic waves. This implies new micro lasers and new micro amplifiers where polyoxides, such as lithium niobate crystals, are required. Research on these crystals is experiencing a superfast development and many new discoveries have reached the industrial stage of large scale production. As sparked by the extraordinary discovery of high temperature superconductors in 1986, growth and characterization of oxides are a forefront research field in materials science. Less spectacular, but very important, also are the progresses made during the last thirty years in the field of industrial ceramics, for instance the dramatic improvements obtained with stabilized zirconia. Progresses are made daily in the field of "Research and Development" with oxides presenting some special physical property and functionality. The ·largest domain of interest is presently a possible coupling between at least two different kinds of properties (i.e., the smart structure). These progresses have been possible because of the fundamental understanding of their structure and microstructure. In the book by Z. L. Wang and Z. C. Kang one can find a very interesting concentration of basic physical properties of the most important polyoxides, related to their structures (and microstructures) and evolution behavior. The approach of Z. L. Wang and Z. C. Kang is very interesting and rather new: they have classified oxides through their structures and their physical properties. Rock, salt, rutile, fluorite, perovskite and many other related (or mixed) structure types are comprehensively described in the first four chapters with an emphasis on the connections among different structure systems. The fifth chapter is about the important process known as "Soft Chemistry" or "Chimie Douce". The second part, Chapters 6 through 8, are devoted to the optimal techniques and technologies used for study of these compounds and their physical properties. This book is unique because it focuses specifically on the intrinsic connections among several crystal structure systems and their evolution behavior. It relates the basic principles for molecular and structural design of functional materials to the fundamental structure modules. These materials are describedfrorn the mixed-valence and stoichiometry points of view to understand their structural transformation and the evolution of different materials systems.

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FOREWORD

The mixed valences of transition and rare earth metals have been shown as a fundamental for oxides with specific functionalities. There are numerous books describing the properties, preparations, electronic and crystal structures of transition, rare earth metals and their oxides. This book fills a gap in that field, not only because it focuses on the role played by the evolution of crystal structures in functional materials, but also gives the solution of structure determination through advanced techniques such as spectroscopy and transmission electron microscopy. Because this specific approach has been followed I am confident this book will be a basic reference in the domain of oxides which are to be the basis of functional and smart materials.

C. Boulesteix Pro Univ. Au-Marseille 3, France

Preface

Functional materials, a new emerging materials system, have attracted the interests of many scientists, since they are synthesized to perform specific functionality. Functional materials include but are not limited to smart materials, and they cover a large range of materials with important applications in modem and future technologies. To be unique, this book is not a compiled list of various functional materials, rather it is on the intrinsic connection and evolution behavior among and in different structure systems which are frequently observed in oxide functional materials. Each structural system is described from the basic modules that are the building blocks for constructing all of the related structures. The structural evolution is linked with mixed valences of rare earth and transitional metal elements, and this is shown to be the fundamental principle for producing new materials with unique functionality. The book aims to explore the fundamental structural mosaics that likely lead to some new routes for synthesizing new functional materials. The book is also unique in the way that it integrates structural evolution with structure analysis using transmission electron microscopy and associate techniques.

We have written this book for advanced graduate students and scientists who are interested in studying and developing functional materials. The intended readers are materials scientists, solid state chemists (material chemists), electron microscopists, mineralogists, and solid state physicists (material physicists). The book also fulfills the need as a text book for advanced research and education in oxide functional materials and transmission electron microscopy.

This book was written based on our research experience on the subject. Chapters 2-4 were primarily written by ZCK. The Introduction section, Chapters 6-8 and all of the Appendixes were written by ZLW. Chapters 1 and 5 were co-authored by ZCK and ZLW. ZL W was responsible for organizing and editing the entire manuscript, and he was also cited as liason during the publication process.

We would like to express gratitude to our collaborators related to the research described in this book. Thanks to Professor L. Eyring, a pioneer in the field, for your advice and encouragement. Thanks also go to Professor C. Boulesteix, Dr. D.M. Kroeger, Dr. Jiming Zhang and Professor R.L. Wiletten for collaborative research in the past few years. We are also grateful to those who kindly permit us to use their data for illustrating the text, and each of them is acknowledged in the corresponding figure caption.

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PREFACE

Finally, our heartfelt gratitude goes to our wives, children, and parents, for their constant encouragment, support and understanding. Their support and help are indispensable for finishing this book.

* e-mail: Zhong-Wang@mse.gatech.edu t Currently at: Department of Chemistry, Arizona State University

Zhong Lin Wang* Zhen Chuan Kangt School of Materials

Science and Engineering

Contents

Symbols and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xix Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

PART I STRUCTURE AND STRUCTURAL EVOLUTION

1. Structure, Bonding, and Properties. . . . . . . . . . . . . . . . . . . . . . . . . 9

1.1. Crystal Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2. Structure and Chemical Composition . . . . . . . . . . . . . . . . . . . . . . . . . .. 12

1.2.1. Stoichiometric Phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 1.2.2. Nonstoichiometric Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 13

1.3. Coordination Number and Coordination Polyhedron. . . . . . . . . . . . . . . .. 13 1.4. Isotypism and Polymorphism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16 1.5. Structure and Chemical Bonding. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 18

1.5.1. Bonding and Ion Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " 18 1.5.2. Lattice Energy of an Ionic Compound. . . . . . . . . . . . . . . . . . . . .. 20 1.5.3. Geometric Consideration of a Structure . . . . . . . . . . . . . . . . . . . .. 23 1.5.4. Pauling and Baur's Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 26 1.5.5. Covalent Bonding .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29

1.6. Ligand Field Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31 1.6.1. Octahedral Coordination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32 1.6.2. Tetrahedral Coordination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34 1.6.3. Square Coordination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35

1.7. Ligand Field Stabilization Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36 1.8. Coordination Polyhedra of Transition Metals. . . . . . . . . . . . . . . . . . . . .. 39 1.9. Molecular Orbital Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39

1.9.1. Molecular Orbitals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 39 1.9.2. Hybridization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42

1.10. Band Theory .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 44

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1.10.1. The Peierls Distortion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 46 1.10.2. Two- and Three-Dimensional Bonds. . . . . . . . . . . . . . . . . . . . .. 47

1.11. Mixed Valent Compounds and Functional Materials. . . . . . . . . . . . . . . .. 49 1.11.1. Class I Compounds: (Xv = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50 1.11.2. Class II Compounds: (Xv > 0 but Small. . . . . . . . . . . . . . . . . . . .. 50 1.11.3. Class III Compounds: (Xv = Clmax' • • • • • • • • • • • • • • • • • • • • • • •• 51

1.12. Structure Transformation and Stability. . . . . . . . . . . . . . . . . . . . . . . . .. 52 1.12.1. Phase Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52 1.12.2. Thermodynamic Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55

1.13. Properties of Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 55 1.13.1. Mechanical Property. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 57 1.13.2. Magnetic Property. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58 1.13.3. Piezoelectric Property. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60 1.13.4. Ferroelectric Property. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61 1.13.5. Optical Property. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 62 1.13.6. Electric Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63

1.14. Structure and Property. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 63 1.15. Functional Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 65

1.15.1. Characteristics of Functional Materials. . . . . . . . . . . . . . . . . . . .. 65 1.15.2. Structural Evolution and Functionality. . . . . . . . . . . . . . . . . . . .. 67

1.16. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69

2. Sodium Chloride and Rutile-Related Structure Systems. . . . . . .. 71

2.1. Rock Salt Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 71 2.2. Nonstoichiometric Compounds with Sodium Chloride Structure. . . . . . . . .. 74 2.3. Rutile Structure and Its Family. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 75 2.4. Characteristics of Rutile Structures ... . . . . . . . . . . . . . . . . . . . . . . . . .. 77

2.4.1. Apex Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77 2.4.2. Edge Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . .. 80 2.4.3. Face Sharing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82

2.5. Evolution of Rutile-type Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 82 2.6. Nonstoichiometry and Crystallographic Shear Planes . . . . . . . . . . . . . . . .. 89 2.7. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92

3. Perovskite and Related Structure Systems. . . . . . . . . . . . . . . . . .. 93

3.1. Characteristics of ABOrType Perovskite Structure. . . . . . . . . . . . . . . . .. 93 3.1.1. Vertex Sharing of Oxygen Octahedra. . . . . . . . . . . . . . . . . . . . .. 94 3.1.2. Unit Cell by Taking a Cation as the Origin. . . . . . . . . . . . . . . . .. 96 3.1.3. Oxygen Cubic Close Packing. . . . . . . . . . . . . . . . . . . . . . . . . . .. 97 3.1.4. Anion Close Packing and Formation of

Tetrahedron and Octahedron . . . . . . . . . . . . . . . . . . . . . . . . . . .. 100 3.2. Possible Types of Anion-Deficient Perovskite Structures. . . . . . . . . . . . .. 108

3.2.1. The 14 Fundamental Structure Units. . . . . . . . . . . . . . . . . . . . . .. 108 3.2.2. Constructing the Family of Perovskite-Related Structures. . . . . . . .. 109

3.3. The Tolerance Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 110 3.4. Functional Materials with Perovskite-like Structures. . . . . . . . . . . . . . . .. 110

3.4.1. Ferroelectricity and Ferroelectric Compounds ................ . 3.4.2. Ferromagnetism and Ferromagnetic Compounds .............. . 3.4.3. Insulator-to-Conductor Transition ........................ . 3.4.4. Conductive Perovskites ............................... . 3.4.5. Magnetostrictive, Electrostrictive, and

Piezoelectric Actuator Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.6. Optically Switchable Compounds ........................ .

3.5. Doping and Oxygen Vacancies .............................. . 3.6. Giant Magnetoresistance (GMR) and Colossal Magnetoresistance (CMR) .. . 3.7. Oxygen Migration and Ionic Conductivity of Perovskites ............. . 3.8. Anion-Deficiency Induced Perovskite to

Brownmillerite Structural Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9. Ordered Structural Evolution Introduced by Cation Substitution ........ .

3.10. Sodium Chloride, Rutile, and Perovskite Structures ................. . 3.10.1. Linkage and Comparison ............................. . 3.10.2. Constructing New Materials by Tailoring .................. .

3.11. Summary ............................................. .

4. Fluorite-Type and Related Structure Systems ................ . 4.1. Basic Fluorite Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Fluorite Structure with Anion Deficiency . . . . . . . . . . . . . . . . . . . . . . . . .

4.2.1. Oxygen Migration in Fluorite Structure ..................... . 4.2.2. Modules of Fluorite Structure with Oxygen Deficiency .......... . 4.2.3. Pyrochlores and C-type Rare Earth Sesquioxide Structures ........ .

4.3. Characteristics of Fluorite and Fluorite-Related Structures ............. . 4.3.1. Thermodynamic Property .............................. . 4.3.2. Surface Character of Rare Earth Oxides ..................... . 4.3.3. Disproportionation of Rare Earth High Oxides ................ . 4.3.4. Switchable Chemical Reaction as an Oxygen Pump ............. .

4.4. Structural and Compositional Principles of Rare Earth Homologous Higher Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. Compositional Principle of the Homologous Phases ............. . 4.4.2. The Modular Juxtaposition Rules ......................... . 4.4.3. Building Supercell Structure Using Modules .................. .

4.5. Applications of the Juxtaposition Rules to Known Structures ........... . 4.5.1. R70 12 Phase with n = 7 and m = 1 ....................... . 4.5.2. R90 16 Phase with n = 9 and m = 1 ....................... . 4.5.3. RJI 0 20 Phase with n = 11 and m = 1 ...................... . 4.5.4. R400n Phase with n = 40 and m = 4 ...................... . 4.5.5. R240 44 Phase with n = 24 and m = 2 ...................... .

4.6. Predicting Undetermined Structures Using the Proposed Modules ........ . 4.6.1. ~-polymorph with m = 4 .............................. . 4.6.2. Undetermined Structure with n = 19 ....................... . 4.6.3. Undetermined Structure with n = 16 ....................... . 4.6.4. Undetermined Structure with n = 62 and m = 6 ............... . 4.6.5. Nonstoichiometric (X-phase ............................. .

4.7. Ternary Mixed Rare Earth Oxides ............................. .

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122

128 130 130 132 136

138 142 143 143 147 149

151

151 154 155 156 157 162 162 167 172 176

177 180 182 183 187 188 190 192 194 195 197 198 199 200 201 204 206

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4.7.1. Ternary Mixed Rare Earth Oxides and Oxygen Storage . . . . . . . . .. 207 4.7.2. Cation Coordination Number and Arrangements of Modules. . . . . .. 209

4.8. Thermodynamics of Structural Evolution. . . . . . . . . . . . . . . . . . . . . . . .. 212 4.8.1. Gibbs Free Energy and Structural Stability. . . . . . . . . . . . . . . . . .. 212 4.8.2. Hysteresis in Structural Transformation. . . . . . . . . . . . . . . . . . . .. 214 4.8.3. Phase Transformations and Environmental Conditions ........... 216

4.9. Perovskite, Fluorite Structures, and Spinel Structures .... " . . . . . . . . . .. 217 4.9.1. Structure Comparison ..................... " ........... 217 4.9.2. Superexchange Interaction and Magnetism ................... 220

4.10. Summary ........................................ " ..... 222

5. From Structural Units to Materials Engineering via Soft Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " . .. 223

5.1. Principle of Soft Chemistry .............................. " . .. 224 5.2. Sol-Gel Process ...................................... " . .. 228 5.3. Colloidal Route for Preparation of Monodispersive Spherical Particles .. " ... 231 5.4. Intercalation and Pillaring Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 240 5.5. Self-Assembled Nanocrystal-Engineered Superiattice Thin Films ......... 247

5.5.1. Passivated Metal Nanocrystals. . . . . . . . . . . . . . . . . . . . . . . . . . .. 249 5.5.2. Passivated Semiconductors Nanocrystals . . . . . . . . . . . . . . . . . . . .. 251 5.5.3. Passivated Magnetic Nanocrystals ..................... " . .. 251 5.5.4. Magnetic Co Particles ................................. 252 5.5.5. Magnetic Iron Oxides ...... " . . . . . . . . . . . . . . . . . . . . . . . . . .. 253

5.6. Preparation of Nanoparticles by Aerosol Technique . . . . . . . . . . . . . . . . .. 253 5.7. Summary ............................................... 257

PART II STRUCTURE CHARACTERIZATIONS

6. Electron Crystallography for Structure Analysis .............. 261

6.1. Electron Diffraction in Structure Analysis. . . . . . . . . . . . . . . . . . . . . . . .. 262 6.1.1. Single Scattering Theory ..................... " . . . . . . . . .. 262 6.1.2. Reciprocal Space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 265 6.1.3. Bragg's Law and Ewald Sphere ........................... 268 6.1.4. Indexing Electron Diffraction Patterns. . ... " . . . . . . . . . . . " . . . .. 271 6.1.5. Diffraction from Twinned Crystals ................... " " . . .. 272

6.2. Diffraction Contrast and Defect Analysis ......................... 274 6.2.1. Defects and Dislocations in Materials. . . . . . . . . . . . . . . . . . . . . .. 275 6.2.2. Diffraction Contrast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 277 6.2.3. Two-Beam Condition for Imaging Defects and Dislocations ..... " .. 282 6.2.4. Determination of Burgers Vector ....................... " .. 284 6.2.5. Weak Beam Imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 285

6.3. Atomic Resolution Structure Imaging and Structure Analysis. . . . . . . . . . .. 286 6.3.1. Phase Contrast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 286 6.3.2. Abbe's Imaging Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 288 6.3.3. Aberration and Information Transfer in TEM ................. 291

6.3.4. Contrast Transfer Function and Image Resolution ............. . 6.3.5. Envelope Function and Information Transfer ................. . 6.3.6. Source Coherence in Lattice Imaging ..................... . 6.3.7. Projected Charge Density Approximation ................... . 6.3.8. Multislice Theory for Transmission Electron Imaging ........... . 6.3.9. Image Simulation and Structure Determination ............... .

6.3.10. Image Calculation of Imperfect Crystal and Interface ........... . 6.3.11. Energy-Filtered Electron Lattice Imaging ................... . 6.3.12. Limitation of HRTEM ............................... .

6.4. Electron Holography ...................................... . 6.4.1. Principle of Off-Axis Holography In TEM ................... . 6.4.2. Improvement of Image Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3. Imaging Electrostatic Field and Charge Distribution ............. . 6.4.4. Imaging Spontaneous Polarization at

Domain Boundaries in Ferroelectrics ....................... . 6.4.5. Imaging Magnetic Domains and Flux lines .................. .

6.5. Convergent Beam Electron Microdiffraction ...................... . 6.5.1. Symmetry Analysis .................................. . 6.5.2. Measurement of Lattice Parameters ........................ . 6.5.3. Bloch Wave Theory and Quantitative CBED ................. . 6.5.4. Solid-State Bonding and Charge Redistribution ................ . 6.5.5. Determination of Burgers Vector ......................... . 6.5.6. Measurement of Specimen Thickness ...................... .

6.6. Summary .............................................. .

7. Structure Analysis of Functional Materials. . . . . . . . . . . . . . . . . . . 7.1. Interface and Grain Boundary Analysis .......................... .

7.1.1. Kikuchi Pattern and Grain Boundary Analysis . . . . . . . . . . . . . . . . . 7.1.2. General Description of a Grain Boundary . . . . . . . . . . . . . . . . . . . . 7.1.3. The O-Lattice Theory ................................. . 7.1.4. Coincidence-Site Lattice Theory. . . . . . . . . . . . . . . . . . . . . . . . . . .

7.2. Modulation and Domain Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1. Structural Modulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2. Domains Formed by Anisotropic Crystal Structure ............. . 7.2.3. Boundaries of Structure Domains ......................... .

7.3. Superstructure and Long-Range Ordering ........................ . 7.3.1. Three-Dimensional Superstructure Analysis by a

Double-Pattern Technique .............................. . 7.3.2. Three-Dimensional Superstructure Analysis by a

Single-Pattern Technique ............................... . 7.3.4. Long-Range Ordering of Cation Substitutions ................. .

7.4. Oxygen Vacancies and Short-Range Ordering ..................... . 7.4.1. Kinematical Diffraction Theory of Diffuse Scattering. . . . . . . . . . . . . 7.4.2. Geometrical Description of Diffuse Scattering ................. . 7.4.3. Calculation of Short-Range Ordering Parameter ............... . 7.4.4. HRTEM Study of Short-Range Order ...................... .

7.5. Effects of Substrate on Thin-Film Growth ........................ .

xv

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305 307 309 310 310 312 313 314 316 316

317 318 322 323 325 326 329 332 336 339

341

341 343 346 348 350 352 352 355 360 361

362

367 369 371 373 376 380 382 382

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7.5.1. Lattice Mismatch and Interface Dislocations. . . . . . . . . . . . . . . . . .. 383 7.5.2. Nucleation and Growth of Defects from Substrate Surfaces. . . . . . .. 385 7.5.3. Linkage of Domain Boundaries with Interface Dislocations ........ 387 7.5.4. Linkage of Interface Dislocations with Planar Defects. . . . . . . . . . .. 393

7.6. In Situ Observation of Structure Evolution. . . . . . . . . . . . . . . . . . . . . . .. 395 7.6.1. Temperature-Driven Structure Transformation ................. 395 7.6.2. Electric-Field-Driven Structure Transformation. . . . . . . . . . . . . . . .. 396 7.6.3. Magnetic Moment of the Specimen ........................ 397

7.7. Failure Analysis of Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 398 7.8. Imaging Surfaces of Oxides ..•............................... 400 7.9. Summary ............................................... 404

8. Chemical and Valence Structure Analysis of Functional Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 405

8.1. Inelastic Excitation Processes in Electron Scattering . . . . . . . . . . . . . . . .. 405 8.2. Energy Dispersive X-ray Microanalysis ......................... 408

8.2.1. Composition Analysis ................................. 409 8.2.2. Atom Location by Channeling-Enhanced

Microanalysis (ALCHEMI) ............................. 412 8.3. Valence Excitation EELS ................................... 416

8.3.1. Classical Electron Energy Loss Theory ..................... 418 8.3.2. Surface Plasmon Excitation ............................. 424 8.3.3. Measurement of Dielectric Function ....................... 427

8.4. Atomic Inner-Shell Excitation in EELS .......................... 429 8.4.1. Composition Analysis ................................. 433 8.4.2. Near-Edge Fine Structure and Bonding in Crystals . . . . . . . . . . . .. 435

8.5. Quantitative Determination of Valences in a Mixed Valent Compound .... 437 8.5.1. White Lines of Transition Metals. . . . . . . . . . . . . . . . . . . . . . . .. 437 8.5.2. The Occupation Number of the d-Band Electrons. . . . . . . . . . . . .. 438 8.5.3. White-Line Intensity and Intrinsic Magnetic Moment. . . . . . . . . . .. 442 8.5.4. Double-Derivative Spectrum for

Calculation of White-Line Intensity. . . . . . . . . . . . . . . . . . . . . . .. 444 8.6. Nanoprobe Analysis of Interfaces and Grain Boundaries .............. 445 8.7. Chemical-Sensitive Imaging in STEM .......................... 450 8.8. Energy-Filtered Electron Imaging in TEM ........................ 452

8.8.1. Composition-Sensitive Imaging Using Valence Loss Electrons . . . .. 455 8.8.2. Composition-Sensitive Imaging Using Inner-Shell

Ionization Edge Electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 456 8.8.3. Mapping of Bonding and Valence State ..................... 457

8.9. Phonon Scattering and Chemical-Sensitive Imaging ................. 458 8.9.1. "Z-Contrast" Imaging in STEM. . . . . . . . . . . . . . . . . . . . . . . . .. 458 8.9.2. High-Angle Dark-Field Conical Scan Imaging in TEM .......... 459

8.10. Conjunction of Various Techniques for Structure Refinement of LagSrgC016036-an Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 459 8.10.1. Chemical Composition Analysis ......................... 462 8.10.2. Valence State of Co ................................. 463 8.10.3. HRTEM Lattice Image of LSCO . . . . . . . . . . . . . . . . . . . . . . .. 465

8.10.4. Structure Model of Lao.5SrO.5Co02.25 ...................... 466 xvii 8.10.5. Structure and Magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . 469

8.11. Summary .............................................. 470 CONTENTS

APPENDIXES

A. Physical Constants, Electron Wavelengths, and Wave Numbers .................................... 471

B 1. Crystallographic Structure Systems . . . . . . . . . . . . . . . . . . . . . . . . 473

B2. FORTRAN Program for Calculating Crystallographic Data ..... 477

C. Electron Diffraction Patterns for Several Types of Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483

D. FORTRAN Program for Calculating Single Valence-Loss EELS Spectra in TEM ................. 493

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507

Materials Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 511

Symbols and Definitions

Listed below are the symbols frequently used in this book. All quantities are defined in SI units except that Angstrom (A) is used occasionally for convenience.

rM

rx Pi Si

Zj

d(MX) do dt

\)Ii <Pi S12 cx'v

dG Ml dS

X M H

Mr Hc' Ec Ps

Tc Tg N(E)

IlB

Lattice displacement vector Lattice energy Madelung constant Cation radius Anion radius Coordination number electrostatic bond strength Charge of the jth anion Bond length Energy gap between t and e orbitals in octahedral coordination Energy gap between t and e orbitals in tetrahedral coordination Molecular orbit Atom wave function Overlap integral Valence delocalization coefficient Free enthalpy of reaction Transition enthalpy Transition entropy Magnetic susceptibility Magnetization Magnetic field Remnant magnetization Coercive force/field Spontaneous polarization Ferromagnetic transition temperature (or Curie temperature) Superparamagnetic freezing temperature Density of states Bohr magneton

xix

xx

SYMBOLS AND DEFINITIONS

c ma me e Ua A p Ko,K 8 f:' f; FT FT-1

r b g (or h) U,'t

V(r) VK(r) PK(r) s s Z Vg V(l(g) exp(-W(l) Q r(l

Rn a, b,c a*, b*, c* as' bs ' Cs

a1, b1, c1 9g

dg

® Tobj

Aobj

Cs

Band gap Transfer energy Radius of anions Radius of cation Electronegativity Chemical potential Hardness of atom X Planck's constant =hl2rc Speed of light in vacuum Rest mass of electron Mass of electron with relativistic correction Absolute charge of electron Accelerating voltage of electron microscope Electron wavelength in free space Momentum of incident electron Electron wave-vectors Electron scattering semiangle Electron scattering factor of crth atom X-ray scattering factor of crth atom Fourier transform from real space to reciprocal space Inverse Fourier transform = (x, y, z) real space vector = (x, y) real space vector Reciprocal lattice vector Reciprocal space vector Electrostatic potential distribution in crystal Electrostatic potential of Kth atom Electron density distribution of Kth atom Scattering vector, S = U/2 = (sin 8)/1.. Atomic number Fourier coefficient of crystal potential Fourier transform of Ilth atom in unit cell Debye-Waller factor of Ilth atom Volume of unit cell = r(Il), position of Ilth atom within unit cell Position vector of nth unit cell Base vectors of unit cell Base vectors of reciprocal lattice vector Base vectors of superstructure unit cell Base vectors of reciprocal lattice vectors for the superstructure Bragg angle Interplanar distance Convolution calculation Transfer function of objective lens Shape function of objective aperture Spherical aberration coefficient of objective lens

y U(r) 'P(r) <l>(r)

lXi di) g

Vi

~g d <l>gCr) R(r)

bE UD VpCb) Afs Afc Rs y(b) cr Az PCb, Az) Qn T A B Rn T Vc Z

Defocus of objective lens = eUo[1 + eUoj2mo~], energy of incident electron Fourier coefficient of the modified potential U Velocity of incident electron = (1-(vjcO)2)1/2, relativistic correction factor = (2ymoejh2)V(r), modified crystal potential Electron wave function Electron wave function excluding exp(2rciK . r) factor, <l>(r)='P(r) exp( -2rciK· r) ith branch Bloch wave Wave vector of ith Bloch wave Superposition coefficients of Bloch waves Eigenvector of ith Bloch waves Eigenvalue of ith Bloch waves Two-beam extinction distance Thickness of crystal slab Amplitude of g reflection Static displacement vector of atoms in imperfect crystal Burgers vector of dislocations Direction of dislocation line Projected crystal potential along z direction Scherzer defocus Defocus due to chromatic aberration Scherzer resolution Coherence function = rcey/AE = l/liv. Thickness of crystal slice Propagation function of slice with thickness Az Phase grating function of slice with thickness Az Transformation matrix Vector potential of magnetic field Magnetic field = R(n), position of nth unit cell Temperature Volume of crystal Unit vector along z axis Position of IXth atom in unit cell X-ray absorption coefficient Integrated x-ray line intensity Fluorescence yield Number of A element per unit volume Ionization cross section of the inner shell Fraction of the K, L, or M line intensity measured by the detector Detector efficiency Absorption factor K factor for x-ray microanalysis Concentration of impurity X Fraction of impurity X in B atom sites

xxi

SYMBOLS AND DEFINmONS

xxii

SYMBOLS AND DEFINITIONS

E D BE A £, (m, q) d2Pvldz dm p mp (3j

~ Ll

Electric field Displacement vector Characteristic angle of inelastic scattering Mean-free path length of inelastic electron scattering Dielectric function of solid Differential excitation probability of valence states Free charge density function Resonance frequency of the plasmon Integrated ionization cross section Collection semi angle of the EELS spectrometer Energy width of the integration window

SIGN CONVENTIONS

Free-space plane wave

Fourier transforms

exp [21tiK· r - jmt]

Real space to reciprocal space Reciprocal space to real space

F(u) = f dr exp[-21tiu . r]f(r) == FT[f(r)] f(r) = f du exp[21tiu . r]F(u) == FT-1[F(u)]

where the limits of integration are (-00, (0) unless otherwise specified.

ACRONYMS

ALCHEMI ADF BF bee BZ CBED c.n. CSL CVD DF DOS DTA EDS EELS ELNES fcc FWHM GB HAADF hep HOLZ HOMO

Atom location by channeling-enhanced microanalysis Annular dark field Bright field Body-centered cubic Brillouin zone Convergent beam electron diffraction Coordination number Coincident site lattice Chemical vapor deposition Dark field Density of states Differential thermal analysis Energy dispersive x-ray spectroscopy Electron energy loss spectroscopy Energy loss near-edge structure Face centered cubic Full width at half-maximum Grain boundary High-angle annular dark field Hexagonal close packing High-order Laue zone Highest occupied molecular orbital

HRTEM High-resolution transmission electron microscopy xxiii LACBED Large-angle convergent beam electron diffraction LFSE Ligand field stabilization energy

SYMBOLS AND DEFINITIONS

LMR Longitudinal magnetic recording MOCVD Metal organic chemical vapor deposition MBE Molecular beam epitaxy NCS Nanocrystal superlattices PCM Partial charge model PMR Perpendicular magnetic recording PMN Pb(Mg,Nb )03

PZT Pb(Zr,Ti)03 REM Reflection electron microscopy RHEED Reflection high-energy electron diffraction RT Room temperature SAD Selecting area diffraction SC Soft chemistry STEM Scanning transmission electron microscopy TEM Transmission electron microscopy TDS Thermal diffuse scattering WPOA Weak phase object approximation POA Phase object approximation ZOLZ Zero-order Laue zone I-D One dimensional 2-D Two dimensional 3-D Three dimensional

Functional and Smart Materials Structural Evolution and Structure Analysis