TREATISE ON SOLID STATE CHEMISTRY \ Volume 2 Defects in Solids TREATISE ON SOLID STATE CHEMISTRY Volume 1 • The Chemical Structure of Solids Volume 2 • Defects in Solids Volume 3 • Crystalline and Noncrystalline Solids Volume 4 • Reactivity of Solids Volume 5 • Changes of State Volume 6 • Surfaces TREATISE ON SOLID STATE CHEMISTRY Volume 2 Defects in Solids Edited by N. B. ff~nnay Vice President Research and Patents Bell Laboratories Mu"ay Hill, New Jersey PLENUM PRESS • NEW YORK·LONDON Library of Congress Cataloging in Publication Data Hannay, Norman Bruce, 1921- Defects in solids. (His Treatise on solid state chemistry; v. 2) Includes bibliographical references and index. 1. Crystals - Defects. I. Title. QD478.H35 vol. 2 IQD921] 541'.042'ls [548'.842] ISBN-13: 978-1-4684-0831-7 c-ISBN-13: 978-1-4684-0829-4 DOl: 10.1007/978-1-4684-0829-4 74-22197 Six-volume set: ISBN-13: 978-1-4684-0831-7 ©1975 Bell Telephone Laboratories, Incorporated Softcover reprint of the hardcover 1st edition 1975 Published by Plenum Press, New York A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Company, Ltd. 4a Lower John Street, London, WIR 3PD, England All rights reserved 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 Foreword The last quarter-century has been marked by the extremely rapid growth of the solid-state sciences. They include what is now the largest subfield of physics, and the materials engineering sciences have likewise flourished. And, playing an active role throughout this vast area of science and engineer ing have been very large numbers of chemists. Yet, even though the role of chemistry in the solid-state sciences has been a vital one and the solid-state sciences have, in turn, made enormous contributions to chemical thought, solid-state chemistry has not been recognized by the general body of chemists as a major subfield of chemistry. Solid-state chemistry is not even well defined as to content. Some, for example, would have it include only the quantum chemistry of solids and would reject thermodynamics and phase equilibria; this is nonsense. Solid-state chemistry has many facets, and one of the purposes of this Treatise is to help define the field. Perhaps the most general characteristic of solid-state chemistry, and one which helps differentiate it from solid-state physics, is its focus on the chemical composition and atomic configuration of real solids and on the relationship of composition and structure to the chemical and physical properties of the solid. Real solids are usually extremely complex and exhibit almost infinite variety in their compositional and structural features. Chemistry has never hesitated about the role of applied science, and solid-state chemistry is no exception. Hence, we have chosen to include in the field not only basic science but also the more fundamental aspects of the materials engineering sciences. The central theme of the Treatise is the exposition of unifying principles in the chemistry, physical chemistry, and chemical physics of solids. Examples are provided only to illustrate these principles. It has, throughout, a chemical viewpoint; there is, perforce, substantial overlap with some areas of solid- v Foreword state physics and metallurgy but a uniquely chemical perspective underlies the whole. Each chapter seeks to be as definitive as possible in its particular segment of the field. The Treatise is intended for advanced workers in the field. The scope of the work is such that all solid-state chemists. as well as solid-state scientists and engineers in allied disciplines. should find in it much that is new to them in areas outside their own specializations; they should also find that the treatment of their own particular areas of interest offers enlightening perspectives. Certain standard subjects. such as crystal structures. have been omitted because they are so well covered in many readily available standard references and are a part of the background of all solid-state scientists. Certain limited redundancies are intended. partly because they occur in different volumes of the series. but mainly because some subjects need to be examined from different viewpoints and in different contexts. The first three volumes deal with the structure of solids and its relation to properties. Volumes 4 and 5 cover broad areas of chemical dynamics in bulk solids. Volume 6 treats both structure and chemical dynamics of surfaces. N.B.H. vi Preface to Volume 2 Volume I of this Treatise was concerned with the chemical structure of solids. This volume treats disorder in solids in relationship to physical properties. Many of these properties stem from simple defects in crystals, i.e., isolated impurity atoms and the point defects, vacancies, and interstitials. In the case of mechanical properties, dislocations (line defects) are dominant. Control of defects in solids thus provides the key to control of properties in many practical solids. This volume examines this relationship in detail. N. B. H. VII Contents of Volume 2 Chapter 1 Electronic Structure and Spectra of Impurities in the More Ionic Crystals 1 Donald S. McClure I. Introduction............................................ I 2. Incorporation of Impurities and Defects in Crystals. . . . . . . . . . . 5 2.1. Solubility and Heat of Solution of Impurities in Crystals. . 6 2.2. Energies of Defect Formation. . . . . . . . . . . . . . . . . . . . . . . . 22 2.3. Equilibria among Electrons, Impurities, and Defects. . . . . 25 3. Electronic States of Impurity Ions in Crystals. . . . . . . . . . . . . . . . 33 3.1. The Absorption and Emission of Radiation. . . . . . . . . . . . . 34 3.2. Electronic Structure and Spectroscopy of the Transition Group Ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3. Electronic Structure and Spectroscopy of Non-Transition Group Impurities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.4. Electronic Structure and Spectroscopy of Ion Pair Systems 112 4. Conclusions. . . . . . .. .. . . . . . . . . . . . . .. . . .. . . . . . . . . . . . .. . . . . 117 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 IX Contents of Volume 2 Chapter 2 The Imperfect Solid-Color Centers in Ionic Crystals 133 w. Beall Fowler I. Introduction............................................ 133 1.1. General........................................... 133 1.2. Scope............................................. 134 1.3. Units and Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 2. Optical Properties-Perfect Crystals. . . . . . . . . . . . . . . . . . . . . . . . 135 2.1. The Spectrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 2.2. The Infrared Region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 2.3. The Ultraviolet Region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 3. Color Centers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.1. Types of Centers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 3.2. Color Center Creation. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 3.3. Theory of Electronic Structure and Optical Properties. . . . 142 3.4. Optical Properties-Results and Interpretation. . . . . . . . . . 152 3.5. Other Experimental Probes. . . . . . . . . . . . . . . . . . . . . . . . . . . 164 3.6. Color Center Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4. Applications: Infonnation Storage. . . . . . . . . . . . . . . . . . . . . . . . . 170 Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Chapter 3 The Imperfect Solid-Dielectric Properties 183 G. E. Peterson I. Introduction............................................ 183 2. Introduction to Ferroelectrics.... . . . . . . . . . . . . . . . . . . . . . . . . . . 184 2.1. Outline of Ferroelectric Theory. . . . . . . . . . . . . . . . . . . . . . . 185 2.2. Statistical Theory of Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . 191 3. Pyroelectricity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 3.1. Introduction....................................... 197 3.2. Pyroelectric Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . 198 3.3. Effect of Stoichiometry in Strontium Barium Niobate. . . . 200 3.4. Depoling in Triglycine Sulfate. . . . . . . . . . . . . . . . . . . . . . . . 202 3.5. Transition Metal Doping Lithium Tantalate. . . . . . . . . . . . 205 3.6. Pyroelectric Polyvinylidene Fluoride Polymer. . . . . . . . . . . 209 4. Nonlinear Optical Materials.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 4.1. Introduction....................................... 212 4.2. Techniques for Optical Homogeneity Detennination. . . . . 215 4.3. The Method of Parametric Fluorescence. . . . . . . . . . . . . . . 217 4.4. Index Damage Measurements. . . . . . . . . . . . . . . . . . . . . . . . 219 4.5. Optical Homogeneity.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 4.6. Changing Phase-Match Temperature. . . . . . . . . . . . . . . . . . 226 x Contents of Volume 2 4.7. Minimizing Optical Index Damage. . . . . . . . . . . . . . . . . . . . 229 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 Chapter 4 The Imperfect Solid-Transport Properties 237 David Adler I. Introduction............................................ 237 1.1. Types of Disorder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 1.2. Types of Bonding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 2. Electronic Structure of Perfect and Imperfect Solids. . . . . . . . . . . 240 2.1. Energy Band Theory of Solids. . . . . . . . . . . . . . . . . . . . . . . . 240 2.2. Effects of Imperfections in Nearly Perfect Crystals. . . . . . . 245 2.3. Complete Long-Range Disorder. . . . . . . . . . . . . . . . . . . . . . 248 3. Transport Properties of Solids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 3.1. Transport in Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 3.2. Transport in Covalent Semiconductors. . . . . . . . . . . . . . . . . 252 3.3. Transport Properties of Ionic Solids. . . . . . . . . . . . . . . . . . . 255 3.4. Mott Insulators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 3.5. Polarons and Hopping Conduction... . . . . . . . . . . . . . . . . . 262 3.6. Amorphous Semiconductors. . . . . . . . . . . . . . . . . . . . . . . . . 267 4. Insulator-Metal Transitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 4.1. Band Overlap Transitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 4.2. Electronically Induced Phase Transformations. . . . . . . . . . 275 4.3. Mott Transitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 5. Experimental Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 5.1. Metal Oxides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 5.2. Transition Metal Oxides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 5.3. Rare Earth Oxides and Chalcogenides. . . . . . . . . . . . . . . . . 307 5.4. Amorphous Semiconductors. . . . . . . . . . . . . . . . . . . . . . . . . 311 5.5. Metals............................................ 316 Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Chapter 5 The Imperfect Solid-Semiconductors 333 Robert F. Brebrick I. Imperfections in Crystalline Semiconductors. . . . . . . . . . . . . . . . . 333 1.1. Electronic Energy States in the Perfect Crystal. . . . . . . . . . 333 1.2. Atomic Point Defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 1.3. Dislocations, Grain Boundaries, and Surfaces. . . . . . . . . . . 343 1.4. Excitation Defects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Xl