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, p. 15
Section 1.1.4.6.2.1. Introduction^{a}Institut de Minéralogie et de la Physique des Milieux Condensés, Bâtiment 7, 140 rue de Lourmel, 75015 Paris, France |
If one takes as the system of axes the eigenvectors of the operator A, the matrix is written in the form where θ is the rotation angle, is taken parallel to the rotation axis and coefficient is equal to +1 or −1 depending on whether the rotation axis is direct or inverse (proper or improper operator).
The equations (1.1.4.1) can then be simplified and reduce to (without any summation).
If the product (without summation) is equal to unity, equation (1.1.4.2) is trivial and there is significance in the component . On the contrary, if it is different from 1, the only solution for (1.1.4.2) is that . One then finds immediately that certain components of the tensor are zero and that others are unchanged.