Table Of ContentRANDOM, NON-RANDOM AND PERIODIC
FAULTING IN CRYSTALS
Taylor & Francis
Taylor & Francis Group
http://taylora ndfra ncis.com
RANDOM, NON-RANDOM
AND PERIODIC FAULTING
IN CRYSTALS
M.T. SEBASTIAN
CSIR Regional Research Laboratory, Trivandrum
Kerala, India
AND
P. KRISHNA
Rajghat Education Centre, Rajghat Fort
Varanasi, India
R Routledge
O
U
T
DEL Taylor & Francis Group
G
E
LONDON AND NEW YORK
First published 1994 by
Gordon and Breach Science Publishers
This edition published 2014 by Routledge
2 Park Square, Milton Park, Abingdon, Oxon 0X14 4RN
711 Third Avenue, New York, NY 10017
,
Routledge is an imprint of the Taylor & Francis Group an informa business
Published under license by Gordon and Breach Science Publishers S.A.
Library of Congress Cataloging-in-Publication Data
Sebastian, M. T., 1952-
Random, non-random, and periodic faulting in crystals / M. T.
Sebastian and P. Krishna,
p. cm.
Includes bibliographical references and index.
ISBN 2-88124-925-6
1. Crystals— Defects. 2. Polymorphism (Crystallography)
I. Krishna, P. (Padmanabhan) II. Title.
QD931.S43 1993
548'.81-dc20 93-27315
CIP
No part of this book may be reproduced or utilized in any form or by any
means, electronic or mechanical, including photocopying and recording,
or by any information storage or retrieval system, without permission in
writing from the publisher.
To our teacher, Professor Ajit Ram Verma D.Sc. (London), FNA,
who was the first to initiate research in this field in India
Taylor & Francis
Taylor & Francis Group
http://taylora ndfra ncis.com
CONTENTS
Foreword xiii
Acknowledgements xv
1 Introduction 1
2 Stacking faults in dose-packed structures 9
2.1 The description of close-packed structures 10
2.2 The voids in a close-packing 12
2.3 The hexagonal close-packing (ABAB . . .) 13
2.4 The cubic close-packing (ABCABC . . .) 13
2.5 Other close-packings 16
2.6 The basic structure of some important polytypic materials 17
2.6.1 Zinc sulphide 17
2.6.2 Silicon carbide 19
2.6.3 Cadmium iodide 22
2.6.4 Gallium selenide 23
2.7 Notations used for describing close-packed structures 24
2.7.1 Ramsdell notation 24
2.7.2 The ABC notation 25
2.7.3 The Hagg notation 25
2.7.4 Zhdanov notation 26
2.7.5 The h-k notation 26
2.7.6 Notations for more complex layered materials 26
2.8 Stacking faults in close-packed structures 28
2.8.1 Growth fault configuration 29
2.8.2 Deformation fault configuration 29
2.8.3 Layer displacement fault configuration 30
2.8.4 Extrinsic fault configuration 32
2.8.5 Stacking faults bounded by partial dislocations 33
2.8.6 Slip planes and slip directions 35
vii
viii Contents
2.9 Stacking fault energy (SFE) 37
2.10 The reciprocal lattice for close-packed structures 41
2.11 Conditions for hexagonal and rhombohedral
polytypes 42
2.12 Symmetry and space groups of polytypes 44
2.13 Possible lattice types in poly types 45
2.14 Relationship between diffraction patterns of hep and
fee structures 48
2.15 Experimental techniques for investigating disordered
and polytype structures 50
2.15.1 X-ray methods 50
2.15.2 Synchrotron X-ray topography 55
2.15.3 Transmission electron microscopy and electron
diffraction 57
2.15.4 Reflection high energy electron diffraction
(RHEED) 61
2.15.5 Raman spectroscopy 61
References 62
3 Diffuse X-ray scattering from randomly faulted
close-packed structures 67
3.1 Introduction 68
3.2 Intensity of scattered X-rays from a small crystal 68
3.3 Diffraction effects from close-packed structures
containing random stacking faults 74
3.4 The general theory of X-ray diffraction from
randomly faulted close-packed structures 77
3.5 X-ray diffraction effects from hep crystals containing
a random distribution of growth and deformation
stacking faults 90
3.5.1 Calculation of the scattered diffuse intensity 91
3.5.2 Half-widths of the diffuse reflections in reciprocal
space 94
3.5.3 Prediction of diffraction effects for 2H crystals
containing only deformation faults (a = 0) 96
3.5.4 Prediction of diffraction effects for 2H crystals
containing a random distribution of growth faults
only (j8 = 0) 98
3.6 Diffraction effects from fee crystals containing a
random distribution of growth (twin) and
deformation faults 99
Contents ix
3.6.1 Calculation of the scattered diffuse intensity 99
3.6.2 Prediction of diffraction effects for fee crystals
containing random deformation faults only
(a = 0) 102
3.6.3 Prediction of diffraction effects for fee crystals
containing only twin faults (/3 = 0) 103
3.7 Diffraction effects from crystals containing a
random distribution of extrinsic faults 105
3.7.1 Diffraction effects from hep crystals containing a
random distribution of extrinsic faults 105
3.7.1.1 Prediction of diffraction effects 111
3.7.2 Diffraction effects from fee crystals containing a
random distribution of extrinsic faults 111
3.7.2.1 Prediction of diffraction effects 117
3.8 X-ray diffraction effects from crystals containing a
random distribution of layer displacement faults 117
3.8.1 hep crystals 117
3.8.2 fee crystals 122
3.9 Comparison of the diffraction effects in hep and fee
structures containing different types of stacking faults 124
3.10 Random faulting in the 4H structure 125
3.11 Random faulting in the 6H structure 127
3.12 Random distribution of stacking faults in 9R and
12R structures 130
3.13 Application of the theory of random faulting to ZnS:
Experimental results 131
3.13.1 Random faulting in 2H ZnS crystals 132
3.13.2 Random faulting in 3C ZnS crystals 133
3.14 Deviation from random faulting in ZnS 136
3.15 Application to the study of random faulting in SiC 139
3.16 Application to the study of random faulting in other
materials 140
3.17 Measurement of directionally diffuse intensity using
a single-crystal diffractometer 146
3.18 The validity of the different assumptions of the
theory of X-ray diffraction 152
3.18.1 Effect of solute segregation at stacking faults
(Suzuki effect) 152
3.18.2 Domain size broadening 157
3.18.3 Effect of change in the layer spacings at stacking
faults 158
