Elastic Strain Fields and Dislocation Mobility PDF
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MODERN PROBLEMS IN CONDENSED MATTER SCIENCES Volume 31 Series editors V.M. AGRANOVICH Moscow, USSR A.A. MARADUDIN Irvine, California, USA Advisory editorial board F. Abeles, Paris, France F. Bassani, Pisa, Italy N. Bloembergen, Cambridge, MA, USA E. Burstein, Philadelphia, PA, USA I.L. Fabelinskii, Moscow, USSR P. Fulde, Stuttgart, Germany M.D. Galanin, Moscow, USSR V.L. Ginzburg, Moscow, USSR H. Haken, Stuttgart, Germany R.M. Hochstrasser, Philadelphia, PA, USA I.P. Ipatova, Leningrad, USSR A.A. Kaplyanskii, Leningrad, USSR L.V. Keldysh, Moscow, USSR R. Kubo, Tokyo, Japan R. Loudon, Colchester, UK Yu.A. Ossipyan, Moscow, USSR L.P. Pitaevskii, Moscow, USSR A.M. Prokhorov, Moscow, USSR K.K. Rebane, Tallinn, USSR J.M. Rowell, Red Bank, NJ, USA NORTH-HOLLAND AMSTERDAM LONDON NEW YORK TOKYO ELASTIC STRAIN FIELDS AND DISLOCATION MOBILITY Volume editors V.L. INDENBOM Moscow, USSR J. LOTHE Oslo, Norway H m 1992 NORTH-HOLLAND AMSTERDAM LONDON · NEW YORK · TOKYO © 1992 Elsevier Science Publishers B.V. All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission ofthe publisher, Elsevier Science Publishers B.V., Permissions Department P.O. Box 521, 1000 AN Amsterdam, The Netherlands. Special regulations for readers in the USA: This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred to the publisher. No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. ISBN: 0 444 88773 3 North-Holland Elsevier Science Publishers B. V. P.O. Box 211 1000 AE Amsterdam The Netherlands Library of Congress Cataloging-in-Publication Data Elastic strain fields and dislocation mobility / volume editors, V.L. Indenboni, J. Lothe. p. cm. — (Modern problems in condensed matter sciences ; v. 31) Includes bibliographical references and index. ISBN 0-444-88773-3 1. Dislocations in crysta Is.find s strains. 2. Strains and stresses. I. Indenbom, V. L. II. Lothe, Jens. III. Series. QD921.E49 1992 548'.842—dc20 91-39415 CIP Printed on acid-free paper Printed in The Netherlands MODERN PROBLEMS IN CONDENSED MATTER SCIENCES Vol. 1. SURFACE POLARITONS V.M. Agranovich and D.L. Mills, editors Vol. 2. EXCITONS E.I. Rashba and M.D. Sturge, editors Vol. 3. ELECTRONIC EXCITATION ENERGY TRANSFERS IN CONDENSED MATTER V.M. Agranovich and M.D. Galanin Vol. 4. SPECTROSCOPY AND EXCITATION DYNAMICS OF CONDENSED MOLECULAR SYSTEMS V.M. Agranovich and R.M. Hochstrasser, editors Vol. 5. LIGHT SCATTERING NEAR PHASE TRANSITIONS H.Z. Cummins and A.P. Levanyuk, editors Vol. 6. ELECTRON-HOLE DROPLETS IN SEMICONDUCTORS CD. Jeffries and L.V. Keldysh, editors Vol. 7. THE DYNAMICAL JAHN-TELLER EFFECT IN LOCALIZED SYSTEMS Yu.E. Perlin and M. Wagner, editors Vol. 8. OPTICAL ORIENTATION F. Meier and B.P. Zakharchenya, editors Vol. 9. SURFACE EXCITATIONS V.M. Agranovich and R. Loudon, editors Vol. 10. ELECTRON-ELECTRON INTERACTIONS IN DISORDERED SYSTEMS A.L. Efros and M. Pollak, editors Vol. 11. MEDIUM-ENERGY ION REFLECTION FROM SOLIDS E.S. Mashkova and V.A. Molchanov Vol. 12. NONEQUILIBRIUM SUPERCONDUCTIVITY D.N. Langenberg and A.I. Larkin, editors v MODERN PROBLEMS IN CONDENSED MATTER SCIENCES Vol. 13. PHYSICS OF RADIATION EFFECTS IN CRYSTALS R.A. Johnson and A.N. Orlov, editors Vol. 14. INCOMMENSURATE PHASES IN DIELECTRICS (Two volumes) R. Blinc and A.P. Levanyuk, editors Vol. 15. UNITARY TRANSFORMATIONS IN SOLID STATE PHYSICS M. Wagner Vol. 16. NONEQUILIBRIUM PHONONS IN NONMETALLIC CRYSTALS W. Eisenmenger and A.A. Kaplyanskii, editors Vol 17. SOLITONS S.E. Trullinger, V.L. Pokrovskii and V.E. Zakharov, editors Vol. 18. TRANSPORT IN PHONON SYSTEMS V.L. Gurevich Vol. 19. CARRIER SCATTERING IN METALS AND SEMICONDUCTORS V.F. Gantmakher and LB. Levinson Vol. 20. SEMIMETALS-1. GRAPHITE AND ITS COMPOUNDS N.B. Brandt, S.M. Chudinov and Ya.G. Ponomarev Vol. 21. SPECTROSCOPY OF SOLIDS CONTAINING RARE EARTH IONS A.A. Kaplyanskii and R.M. Macfarlane, editors Vol. 22. SPIN WAVES AND MAGNETIC EXCITATIONS (Two volumes) A.S. Borovik-Romanov and S.K. Sinha, editors Vol. 23. OPTICAL PROPERTIES OF MIXED CRYSTALS RJ. Elliott and I.P. Ipatova, editors VI MODERN PROBLEMS IN CONDENSED MATTER SCIENCES Vol. 24. THE DIELECTRIC FUNCTION OF CONDENSED SYSTEMS L.V. Keldysh, D.A. Kirzhnitz and A.A. Maradudin, editors Vol. 25. CHARGE DENSITY WAVES IN SOLIDS L.P. Gor'kov and G. Grüner, editors Vol. 26. HELIUM THREE W.P. Halperin and L.P. Pitaevskii, editors Vol. 27. LANDAU LEVEL SPECTROSCOPY (Two volumes) G. Landwehr and E.I. Rashba, editors Vol. 28. HOPPING TRANSPORT IN SOLIDS M. Pollak and B. Shklovskii, editors Vol. 29. NONLINEAR SURFACE ELECTROMAGNETIC PHENOMENA H.E. Ponath and G. Stegeman, editors Vol. 30. MESOSCOPIC PHENOMENA IN SOLIDS B.L. Altshuler, P.A. Lee and R.A. Webb, editors Vol. 31. ELASTIC STRAIN FIELDS AND DISLOCATION MOBILITY V.L. Indenbom and J. Lothe, editors Vll Oh, how many of them there are in the fields! But each flowers in its own way- In this is the highest achievement of a flower! Matsuo Basho 1644-1694 PREFACE TO THE SERIES Our understanding of condensed matter is developing rapidly at the present time, and the numerous new insights gained in this field define to a significant degree the face of contemporary science. Furthermore, discoveries made in this area are shaping present and future technology. This being so, it is clear that the most important results and directions for future developments can only be covered by an international group of authors working in cooperation. 'Modern Problems in Condensed Matter Sciences' is a series of contributed volumes and monographs on condensed matter science that is published by Elsevier Science Publishers under the imprint of North-Holland. With the support of a distinguished Advisory Editorial Board, areas of current interest that have reached a maturity to be reviewed are selected for the series. Both Soviet and Western scholars are contributing to the series, and each contributed volume has, accordingly, two editors. Monographs, written by either Western or Soviet authors, are also included. The complete series will provide the most comprehensive coverage available of condensed matter science. Another important outcome of the foundation of this series is the emergence of a rather interesting and fruitful form of collaboration among scholars from different countries. We are deeply convinced that such international collabora tion in the spheres of science and art, as well as other socially useful spheres of human activity, will assist in the establishment of a climate of confidence and peace. The publishing house 'Nauka' publishes the volumes in the Russian language. This way the broadest possible readership is ensured. The General Editors of the Series, V.M. Agranovich A.A. Maradudin IX PREFACE What should go into a book is always a matter of discussion and must also depend on the general purpose of the book. We will not give a full account of our deliberations on this matter, but state that among several motives a thorough treatment of elastic anisotropy and a thorough discussion of dislocation mobil ity have been main objectives. We believe that on these two main topics, the book offers a coverage not found elsewhere. In chapter 1 there is some overlap with material covered in other chapters, and in particular chapters 2-7. Chapter 1 serves a dual purpose. It serves the purpose of a synthesizing and generalizing overview after study of chapters 2-7, as well as the purpose of a theoretical introduction for readers with a sufficiently strong background. Chapter 1 also efficiently underlines, by examples, the relevance of theory for discussion of experiments. In two addenda to chapter 1, methods for direct observation of lattice defects and the phenomena of the production of internal stresses and dislocations in crystal growth are reviewed and discussed. In chapter 2 the reader will find a summary of the solutions of important dislocation problems in the approximation of elastic isotropy. The microscopic (atomic) models for dislocations and cracks are presented in chapter 3. Chapters 4-6 are devoted to dislocations in infinite and semiinfinite anisotropic media. The mathematical apparatus developed in these chapters is applied in chapter 7 to a discussion of uniformly moving dislocations and elastic surface waves. In chapters 8-12 various aspects of dislocation motion and dislocation mobility important for the physical behaviour of materials are reviewed: glide and climb (chapter 10), interaction with point defects (chapter 9), motion in the periodic lattice potential (chapter 8), the dynamical damping connected with interaction with phonons and electrons (chapter 11), and finally, in chapter 12, the particu lar behaviour of dislocations under conditions of irradiation which leads to such phenomena as radiational creep and swelling. We thank all the contributors who have helped us preparing the book. Our special thanks are due to Professor Alshits whose efforts have been essential for the completion of the book. Moscow/Oslo, June 1991 V.L. Indenbom/J. Lothe XI CHAPTER 1 Dislocations and Internal Stresses V.L. INDENBOM A.V. Shubnikov Institute of Crystallography Academy of Sciences of the USSR Leninsky Prospect 59 Moscow, 117333, USSR Elastic Strain Fields and Dislocation Mobility Edited by Elsevier Science Publishers B.V., 1992 V.L. Indenbom and J. Lothe 1 Contents 1. Introduction 5 2. Basic definitions 6 2.1. Classification of the crystal-lattice defects 6 2.2. Dislocations in crystals 7 2.2.1. Microscopic picture 7 2.2.2. Burgers circuit and vector 7 2.2.3. Macroscopic description 9 3. Integral theorems in the theory of internal stresses 11 3.1. Introduction 11 Example 1; internal stresses for twinned crystals 13 Example 2; internal stresses for a dislocation loop 13 3.2. Mean stress theorem and its corollaries 14 Example 3; Eshelby theorem 14 3.3. Colonnetti theorem and its applications 15 Example 4; bending of a plate with an edge dislocation 17 Example 5; twisting of a whisker crystal with a screw dislocation 17 Example 6; the force acting on a dislocation in an external field 19 3.4. Reciprocity theorem; influence function for intrinsic deformations 19 3.5. Reciprocity theorems and influence functions for tensors of dislocation density and deformation incompatibility 20 Example 7; the displacement field of a single dislocation loop in an infinite elastically isotropic medium 22 Example 8; electron microscopy imaging of dislocations under conditions of anomalous transmission (the so-called halo contrast) 23 3.6. Influence functions for the deformation incompatibility tensor (the case of a semi-infinite elastically isotropic medium) 26 Example 9; stresses due to sticking of particles to the crystal surface 28 4. One-dimensional problems 29 4.1. One-dimensional distributions of intrinsic deformations 29 4.2. Internal stresses in thin plates with one-dimensional intrinsic deformations 30 4.3. Three-dimensional distributions of intrinsic deformations; Fourier method 32 4.4. Stress jump at interfaces 34 2
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