International
Tables for Crystallography Volume D Physical properties of crystals Edited by A. Authier © International Union of Crystallography 2013 |
International Tables for Crystallography (2013). Vol. D, ch. 1.1, pp. 4-5
Section 1.1.1.4. Symmetry of the matrix of physical properties^{a}Institut de Minéralogie et de Physique des Milieux Condensés, 4 Place Jussieu, 75005 Paris, France |
If parameter varies by , the specific energy varies by du, which is equal to We have, therefore and, using (1.1.1.5), Since the energy is a state variable with a perfect differential, one can interchange the order of the differentiations: Since p and q are dummy indices, they may be exchanged and the last term of this equation is equal to . It follows thatMatrices and are therefore symmetric. We may draw two important conclusions from this result: