International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D, ch. 1.6, p. 178

Table 1.6.7.1 

A. M. Glazera* and K. G. Coxb

aDepartment of Physics, University of Oxford, Parks Roads, Oxford OX1 3PU, England, and bDepartment of Earth Sciences, University of Oxford, Parks Roads, Oxford OX1 3PR, England
Correspondence e-mail:  glazer@physics.ox.ac.uk

Table 1.6.7.1| top | pdf |
Symmetry constraints on the linear elasto-optic (strain-optic) tensor [p_{ij}] (contracted notation) (see Section 1.1.4.10.6[link] )

TriclinicOrthorhombicTetragonalTrigonal
Point group 1 Point groups 222, mm2, mmm Point groups [4, {\bar 4}, 4/m] Point groups [3, {\bar 3}]
[\,\pmatrix{ p_{11}& p_{12}& p_{13}& p_{14}& p_{15}& p_{16}\cr p_{21}& p_{22}& p_{23}& p_{24}& p_{25}& p_{26}\cr p_{31}& p_{32}& p_{33}& p_{34}& p_{35}& p_{36}\cr p_{41}& p_{42}& p_{43}& p_{44}& p_{45}& p_{46}\cr p_{51}& p_{52}& p_{53}& p_{54}& p_{55}& p_{56}\cr p_{61}& p_{62}& p_{63}& p_{64}& p_{65}& p_{66}}] [\,\pmatrix{p_{11}& p_{12}& p_{13}&0&0& 0\cr p_{21}& p_{22}& p_{23}&0&0& 0\cr p_{31}& p_{32}& p_{33}&0&0& 0\cr 0&0&0& p_{44}&0& 0\cr 0&0&0&& p_{55}&0\cr 0&0&0&0&0& p_{66}}] [\,\pmatrix{p_{11}& p_{12}& p_{13}&0&0& p_{16}\cr p_{12}& p_{11}& p_{13}&0&0& -p_{16}\cr p_{31}& p_{31}& p_{33}&0&0& 0\cr 0&0&0& p_{44}& p_{45}& 0\cr 0&0&0&-p_{45}& p_{44}&0\cr p_{61}&-p_{61}&0&&0& p_{66}}] [\,\pmatrix{ p_{11}& p_{12}& p_{13}& p_{14}& p_{15}& p_{16}\cr p_{12}& p_{11}& p_{13}&-p_{14}&-p_{15}& -p_{16}\cr p_{31}& p_{31}& p_{33}&0&0& 0\cr p_{41}&-p_{41}&0& p_{44}& p_{45}& -p_{51}\cr p_{51}&-p_{51}&0&-p_{45}& p_{44}& p_{41}\cr -p_{16}& p_{16}&0&-p_{15}& p_{14}& {1\over 2}(p_{11}-p_{12})}]
Monoclinic Point groups [4mm, {\bar 4}2m, 422, 4/mmm] Point groups [3m, {\bar 3}m, 32]
Point groups [2, m, 2/m \ (2 \parallel x_2)] Point groups [2, m, 2/m\ (2 \parallel x_3)] [\pmatrix{p_{11}& p_{12}& p_{13}&0&0& 0\cr p_{12}& p_{11}& p_{13}&0&0& 0\cr p_{31}& p_{31}& p_{33}&0&0& 0\cr 0&0&0& p_{44}&0& 0\cr 0&0&0&0& p_{44}& 0\cr 0&0&0&0&0& p_{66}}] [\pmatrix{p_{11}& p_{12}& p_{13}& p_{14}&0& 0\cr p_{12}& p_{11}& p_{13}&-p_{14}&0& 0\cr p_{31}& p_{31}& p_{33}&0&0& 0\cr p_{41}&-p_{41}&0& p_{44}&0& 0\cr 0&0&0&0& p_{44}& p_{41}\cr 0&0&0&0& p_{14}& {1\over 2}(p_{11}-p_{12})}]
[\,\pmatrix{p_{11}& p_{12}& p_{13}&0& p_{15}& 0\cr p_{21}& p_{22}& p_{23}&0& p_{25}& 0\cr p_{31}& p_{32}& p_{33}&0& p_{35}& 0\cr 0&0&0& p_{44}&0& p_{46}\cr p_{51}& p_{52}& p_{53}&0& p_{55}&0\cr 0&0&0& p_{64}&0& p_{66}}] [\pmatrix{p_{11}& p_{12}& p_{13}&0&0& p_{16}\cr p_{21}& p_{22}& p_{23}&0&0& p_{26}\cr p_{31}& p_{32}& p_{33}&0&0& p_{36}\cr 0&0&0& p_{44}& p_{45}& 0\cr 0&0&0& p_{54}& p_{55}& 0\cr p_{61}& p_{62}& p_{63}&0&0& p_{66}}]

HexagonalCubicIsotropic
Point groups [6, {\bar 6}, 6/m] Point groups [m{\bar 3}, 23] [\,\pmatrix{p_{11}& p_{12}& p_{12}&0&0&0\cr p_{12}& p_{11}& p_{13}&0&0&0\cr p_{12}& p_{12}& p_{11}&0&0& 0\cr 0&0&0&{1\over 2}(p_{11}-p_{12})&0& 0\cr 0&0&0&0&{1\over 2}(p_{11}-p_{12})&0\cr 0&0&0&0&0& {1\over 2}(p_{11}-p_{12})}]
[\,\pmatrix{p_{11}& p_{12}& p_{13}&0&0& p_{16}\cr p_{12}& p_{11}& p_{13}&0&0& -p_{16}\cr p_{31}& p_{31}& p_{33}&0&0& 0\cr 0&0&0& p_{44}& p_{45}& 0\cr 0&0&0&-p_{45}& p_{44}&0\cr -p_{16}& p_{16}&0&0&0& {1\over 2}(p_{11}-p_{12})}] [\,\pmatrix{p_{11}& p_{12}& p_{21}&0&0&0\cr p_{21}& p_{11}& p_{12}&0&0&0\cr p_{12}& p_{21}& p_{11}&0&0& 0\cr 0&0&0& p_{44}&0& 0\cr 0&0&0&0& p_{44}&0\cr 0&0&0&0&0& p_{44}}]
Point groups [6mm, {\bar 6}m2, 622, 6/mmm] Point groups [{\bar 4}3m, 432, m{\bar 3}m]  
[\pmatrix{p_{11}& p_{12}& p_{13}&0&0& 0\cr p_{12}& p_{11}& p_{13}&0&0& 0\cr p_{31}& p_{31}& p_{33}&0&0& 0\cr 0&0&0& p_{44}&0& 0\cr 0&0&0&0& p_{44}& 0\cr 0&0&0&0&0& {1\over 2}(p_{11}-p_{12})}] [\,\pmatrix{p_{11}& p_{12}& p_{12}&0&0&0\cr p_{12}& p_{11}& p_{12}&0&0&0\cr p_{12}& p_{12}& p_{11}&0&0& 0\cr 0&0&0& p_{44}&0& 0\cr 0&0&0&0& p_{44}&0\cr 0&0&0&0&0& p_{44}}]