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. 1.1, pp. 30-31
Section 1.1.4.10.7.2. Independent components of symmetric axial tensors according to the following point groups
a
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1.1.4.10.7.2. Independent components of symmetric axial tensors according to the following point groups
Some axial tensors are also symmetric. For instance, the optical rotatory power of a gyrotropic crystal in a given direction of direction cosines is proportional to a quantity G defined by (see Section 1.6.5.4 ) where the gyration tensor is an axial tensor. This expression shows that only the symmetric part of is relevant. This leads to a further reduction of the number of independent components:
In practice, gyrotropic crystals are only found among the enantiomorphic groups: 1, 2, 222, 3, 32, 4, 422, 6, 622, 23, 432. Pasteur (1848a,b) was the first to establish the distinction between `molecular dissymmetry' and `crystalline dissymetry'.
References
Pasteur, L. (1848a). Recherches sur les relations qui peuvent exister entre la forme cristalline, la composition chimique et le sens de la polarisation rotatoire. Ann. Chim. (Paris), 24, 442–459.Google ScholarPasteur, L. (1848b). Mémoire sur la relation entre la forme cristalline et la composition chimique, et sur la cause de la polarisation rotatoire. C. R. Acad Sci. 26, 535–538.Google Scholar