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

International Tables for Crystallography (2006). Vol. D, ch. 1.1, p. 17

Section Cubic and spherical systems

A. Authiera*

aInstitut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France
Correspondence e-mail: Cubic and spherical systems

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The cubic system is characterized by the presence of threefold axes along the [\langle 111 \rangle] directions. The action of a threefold axis along [111] on the components [x_{1}, x_{2}, x_{3}] of a vector results in a permutation of these components, which become, respectively, [x_{2}, x_{3}, x_{1}] and then [x_{3}, x_{1}, x_{2}]. One deduces that the components of a tensor of rank 2 satisfy the relations [t^{1}_{1} = t^{2}_{2} = t^{3}_{3}.]

The cubic groups all include as a subgroup the group 23 of which the generating elements are a twofold axis along [Ox_{3}] and a threefold axis along [111]. If one combines the corresponding results, one deduces that [t^{2}_{1} = t^{3}_{2} = t^{1}_{3} = t^{3}_{1} = t^{1}_{2} = t^{2}_{3} = 0,]which can be summarized by [Scheme scheme7]

There is a single independent component and the medium behaves like a property represented by a tensor of rank 2, like an isotropic medium.

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