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International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. D. ch. 1.9, p. 232
Section 1.9.3.1. Calculation procedures
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GZG Abt. Kristallographie, Goldschmidtstrasse 1, 37077 Göttingen, Germany |
Levy (1956![[link]](/graphics/greenarr.gif)
) and Peterse & Palm (1966) have given algorithms for determining the constraints on anisotropic displacement tensor coefficients, which are also applicable to higher-order tensors. The basic idea is that a tensor transformation according to the symmetry operation of the site symmetry under consideration (represented by the point-group generators) should leave the tensor unchanged. For symmetries higher than the identity 1, this only holds true if some of the tensor coefficients are either zero or interrelated. The constraints may be obtained explicitly from solving the homogeneous system of equations of tensor transformations (with one equation for each coefficient).
References
Levy, H. A. (1956). Symmetry relations among coefficients of the anisotropic temperature factor. Acta Cryst. 9, 679.Google Scholar
Peterse, W. J. A. M. & Palm, J. H. (1966). The anisotropic temperature factor of atoms in special positions. Acta Cryst. 20, 147–150.Google Scholar
