Phase Transitions in Ferroelastic and Co-elastic Crystals

296 Pages·1991·25.359 MB·English

by  E K Salje

PHASE TRANSITIONS IN
FERROELASTIC AND CO-ELASTIC
CRYSTALS
An introduction for mineralogists, material scientists and
physicists
Student edition
Ekhard K.H. Salje
Department of Earth Sciences, Cambridge University
and IRC in Superconductivity
CAMBRIDGE
UNIVERSITY PRESS
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© Cambridge University Press 1990
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permission of Cambridge University Press.
First published 1990
This student edition first published 1993
A catalogue record for this publication is available from the British Library
Library of Congress cataloguing in publication data available
ISBN 978-0-521-38449-0 Hardback
ISBN 978-0-521-42936-8 Paperback
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To Lisa, Henrik, Joelle, Jeanne, Lea-Cecile and Barbara

CONTENTS
Preface
A brief guide for the reader
1 Introduction and some definitions 1
2 Ferroelastic and co-elastic phase transition 9
3 The Landau potential 13
4 The spontaneous strain 20
5 Coupling between the spontaneous strain and the order parameter 28
5.1 Bilinear order parameter-strain coupling 30
5.2 Linear-quadratic coupling between strain and order parameter 39
6 Macroscopic classification of ferroic and co-elastic crystals 44
7 Ferroelastic and co-elastic twin structures 48
7.1 Description of domain walls in terms of dislocation densities 55
7.2 The intersection of two domain walls 59
7.3 The S-domains and triple junctions 64
7.4 The formation of needle shaped domains 71
8 Domain mobilities and elastic instabilities in ferroelastic
and co-elastic materials 76
8.1 Solitary waves and a simple rate law 76
8.2 Early stages of twinning in a cubic-tetragonal
phase transition and some generalisations 90
8.3 Domain walls in tricritical, co-elastic phase transitions 104
8.4 Acoustic instabilities near wall intersections 109
9 Specific heat anomalies and the excess entropy 118
9.1 Landau theory and specific heat anomalies 119
9.2 Influence of fluctuations of the order parameter
on the specific heat anomalies 122
9.3 The influence of lattice imperfections 125
9.4 Order parameter coupling and excess specific heat 136
10 Coupling between order parameters in ferroelastic
and co-elastic crystals 147
10.1 Coupling between two order parameters and the
order parameter vector space 151
10.2 Coupling via common strain components, a
possible coupling mechanism 154
10.3 Analytical solutions for bilinear coupling 157
10.4 Biquadratic coupling between two order parameters 161
11 Gradient coupling and strain modulations 164
11.1 Lock-in phase transitions 174
11.2 Modulations in real space: the soliton lattice 178
11.3 Return to the Landau-Ginzburg energy in reciprocal space
and the Heine-McConnell model 186
12 Some aspects of the kinetic behaviour of ferroelastic
and co-elastic crystals: an outlook 202
12.1 Solution of the kinetic rate law in the Cahn (C) and the
Ginzburg-Landau (GL) limit. 208
12.2 Strain modulations and the effect of local fields 214
References 219
Appendix: An atomistic model for the Landau potential and the origins
of the saturation effect
Table la and 1b
Table 2
References for Table 2
Index

Errata
E. K. H. Salje, Phase transitions in ferroelastic and co-elastic crystals
ISBN 0 521 42936 6
/x\ (x
pl05, equation 8.45, for coth 21 — I read coth21 —
pi33, equation 9.41, first line is missing, equation should read:
pi41, equation 9.51, last term of last line:
for XQQ read X.QQ
od
pi66, equation 11.2, first term in each line
for =£ read f
p207, equation 12.6, for p read n