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. 2.4, pp. 349-350
Section 2.4.2.2. Piezoelectric media^{a}Laboratoire des Verres, Université Montpellier 2, Case 069, Place Eugène Bataillon, 34095 Montpellier CEDEX, France |
In piezoelectric crystals, a stress component is also produced by the internal electric field E, so that the constitutive equation (2.4.2.2) has an additional term (see Section 1.1.5.2 ), where e is the piezoelectric tensor at constant strain.
The electrical displacement vector D, related to E by the dielectric tensor , also contains a contribution from the strain, where is at the frequency of the elastic wave.
In the absence of free charges, , and (2.4.2.9) provides a relation between E and S, For long waves, it can be shown that E and Q are parallel. (2.4.2.10) can then be solved for E, and this value is replaced in (2.4.2.8) to give Comparing (2.4.2.11) and (2.4.2.2), one sees that the effective elastic tensor now depends on the propagation direction . Otherwise, all considerations of the previous section, starting from (2.4.2.6), remain, with c simply replaced by .