5.6.15

Worked examples in the GEOMETRY Of CRYSTALS 2nd by H. K. D. H. Bhadeshia



Worked examples in the
Geometry of Crystals 2nd by H. K. D. H. Bhadeshia

THE INSTITUTE OF METALS 1987
ALL RIGHTS RESERVED
British Library Cataloguing in Publication Data
Bhadeshia, H. K. D. H.
Worked examples in the geometry of crystals.
1. Crystallography, Mathematical —–
Problems, exercises, etc.
I. Title
548’.1 QD911
ISBN 0–904357–94–5

SECOND EDITION, published 2001, updated 2006
Published electronically with permission
from the Institute of Materials
1 Carlton House Terrace
London SW1Y 5DB

CONTENT: 

Introduction 1
Definition of a Basis 2
Co-ordinate transformations 3
The reciprocal basis 5
Homogeneous deformations 6
Interfaces 9
ORIENTATION RELATIONS 12
Cementite in Steels 13
Relations between FCC and BCC crystals 16
Orientation relations between grains of identical structure 19
The metric 22
More about the vector cross product 24
SLIP, TWINNING AND OTHER INVARIANT-PLANE STRAINS 25
Deformation twins 31
The concept of a Correspondence matrix 35
Stepped interfaces 34
Eigenvectors and eigenvalues 39
Stretch and rotation 41
Conjugate of an invariant-plane strain 48
MARTENSITIC TRANSFORMATIONS 51
The diffusionless nature of martensitic transformations 51
The interface between the parent and product phases 51
Orientation relationships 54
The shape deformation due to martensitic transformation 55
The phenomenological theory of martensite crystallography 57
INTERFACES IN CRYSTALLINE SOLIDS 70
Symmetrical tilt boundary 73
The interface between alpha and beta brass 75
Coincidence site lattices 76
Multitude of axis-angle pair representations 79
The O-lattice 82
Secondary dislocations 85
The DSC lattice 86
Some difficulties associated with interface theory 89

APPENDIX 1: VECTORS AND MATRICES 91
APPENDIX 2: TRANSFORMATION TEXTURE 96
APPENDIX 3: TOPOLOGY OF GRAIN DEFORMATION 100
REFERENCES 105

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