Table 1.6.6.1

Glazer, A. M.; Cox, K. G.

doi:10.1107/97809553602060000633

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

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International Tables for Crystallography (2006). Vol. D. ch. 1.6, p. 171

Table 1.6.6.1

A. M. Glazer^a ^* and K. G. Cox^b ^‡

^a Department 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 1.6.6.1 | top | pdf |
Symmetry constraints (see Section 1.1.4.10 ) on the linear electro-optic tensor $[r_{ij}]$ (contracted notation)

Triclinic	Monoclinic		Orthorhombic
Point group 1	Point group 2 ( $[2 \parallel x_{2}]$ )	Point group m ( $[m \perp x_{2}]$ )	Point group 222
$[\,\,\pmatrix{ r_{11} & r_{12} & r_{13}\cr r_{21} & r_{22} & r_{23}\cr r_{31} & r_{32} & r_{33}\cr r_{41} & r_{42} & r_{43}\cr r_{51} & r_{52} & r_{53}\cr r_{61} & r_{62} & r_{63} }]$	$[\pmatrix{ 0 & r_{12} & 0\cr 0 & r_{22} & 0\cr 0 & r_{32} & 0\cr r_{41} & 0 & r_{43}\cr 0 & r_{52} & 0\cr r_{61} & 0 & r_{63} } ]$	$[\pmatrix{ r_{11} & 0 & r_{13}\cr r_{21} & 0 & r_{23}\cr r_{31} & 0 & r_{33}\cr 0 & r_{42} & 0\cr r_{51} & 0 & r_{53}\cr 0 & r_{62} & 0 } ]$	$[\pmatrix{ 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr r_{41} & 0 & 0\cr 0 & r_{52} & 0\cr 0 & 0 & r_{63} } ]$
	Point group 2 ( $[2\parallel x_3]$ )	Point group m ( $[m \perp x_3]$ )	Point group mm2
	$[\pmatrix{ 0 & 0 & r_{13}\cr 0 & 0 & r_{23}\cr 0 & 0 & r_{33}\cr r_{41} & r_{42} & 0\cr r_{51} & r_{52} & 0\cr 0 & 0 & r_{63} }]$	$[\pmatrix{ r_{11} & r_{12} & 0\cr r_{21} & r_{22} & 0\cr r_{31} & r_{32} & 0\cr 0 & 0 & r_{43}\cr 0 & 0 & r_{53}\cr r_{61} & r_{62} & 0 } ]$	$[\pmatrix{ 0 & 0 & r_{13}\cr 0 & 0 & r_{23}\cr 0 & 0 & r_{33}\cr 0 & r_{42} & 0\cr r_{51} & 0 & 0\cr 0 & 0 & 0 }]$

Tetragonal		Trigonal
Point group 4	Point group $[\bar 4]$	Point group 3	Point group 32
$[\,\,\pmatrix{ 0 & 0 & r_{13}\cr 0 & 0 & r_{13}\cr 0 & 0 & r_{33}\cr r_{41} & r_{51} & 0\cr r_{51} & -r_{41} & 0\cr 0 & 0 & 0 }]$	$[\pmatrix{ 0 & 0 & r_{13}\cr 0 & 0 & -r_{13}\cr 0 & 0 & 0\cr r_{41} & -r_{51} & 0\cr r_{51} & r_{41} & 0\cr 0 & 0 & r_{63} }]$	$[\pmatrix{ r_{11} & -r_{22} & r_{13}\cr -r_{11} & r_{22} & r_{13}\cr 0 & 0 & r_{33}\cr r_{41} & r_{51} & 0\cr r_{51} & -r_{41} & 0\cr -r_{22} & -r_{11} & 0 } ]$	$[\pmatrix{ r_{11} & 0 & 0\cr -r_{11} & 0 & 0\cr 0 & 0 & 0\cr r_{41} & 0 & 0\cr 0 & -r_{41} & 0\cr 0 & -r_{11} & 0 }]$
Point group $[\bar 42m]$	Point group 422	Point group 3m1 ( $[m \perp x_1]$ )	Point group 31m ( $[m \perp x_2]$ )
$[\,\,\pmatrix{ 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr r_{41} & & 0\cr & r_{41} & 0\cr 0 & 0 & r_{63} }]$	$[\pmatrix{ 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr r_{41} & 0 & 0\cr 0 & -r_{41} & 0\cr 0 & 0 & 0 }]$	$[\pmatrix{ 0 & -r_{22} & r_{13}\cr 0 & r_{22} & r_{13}\cr 0 & 0 & r_{33}\cr 0 & r_{51} & 0\cr r_{51} & 0 & 0\cr -r_{22} & 0 & 0 }]$	$[\pmatrix{ r_{11} & 0 & r_{13}\cr -r_{11} & 0 & r_{13}\cr 0 & 0 & r_{33}\cr 0 & r_{51} & 0\cr r_{51} & 0 & 0\cr 0 & -r_{11} & 0 } ]$
Point group 4mm
$[\pmatrix{ 0 & 0 & r_{13}\cr 0 & 0 & r_{13}\cr 0 & 0 & r_{33}\cr 0 & r_{51} & 0\cr r_{51} & 0 & 0\cr 0 & 0 & 0 }]$

Hexagonal			Cubic
Point group 6	Point group 6mm	Point group 622	Point groups $[\bar 43m]$ , 23
$[\,\,\pmatrix{ 0 & 0 & r_{13}\cr 0 & 0 & r_{13}\cr 0 & 0 & r_{33}\cr r_{41} & r_{51} & 0\cr r_{51} & -r_{41} & 0\cr 0 & 0 & 0 } ]$	$[\pmatrix{ 0 & 0 & r_{13}\cr 0 & 0 & r_{13}\cr 0 & 0 & r_{33}\cr 0 & r_{51} & 0\cr r_{51} & 0 & 0\cr 0 & 0 & 0 }]$	$[\pmatrix{ 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr r_{41} & 0 & 0\cr 0 & -r_{41} & 0\cr 0 & 0 & 0 }]$	$[\pmatrix{ 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr r_{41} & 0 & 0\cr 0 & r_{41} & 0\cr 0 & 0 & r_{41} }]$
Point group $[\bar 6]$	Point group $[\bar 6m2]$ ( $[m \perp x_1]$ )	Point group $[\bar 62m]$ ( $[m \perp x_2]$ )	Point group 432
$[\,\,\pmatrix{ r_{11} & -r_{22} & 0\cr -r_{11} & r_{22} & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr -r_{22} & -r_{11} & 0 }]$	$[\pmatrix{ 0 & -r_{22} & 0\cr 0 & r_{22} & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr -r_{22} & 0 & 0 }]$	$[\pmatrix{ r_{11} & 0 & 0\cr -r_{11} & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & -r_{11} & 0 }]$	$[\pmatrix{ 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0 }]$