Kolpakov Ja.E., Zhilin P.A. Generalized continuum and linear theory of the piezoelectric materials // Proc. of XXIX Summer School - Conference “Advanced Problems in Mechanics”, St.Petersburg, Russia. 2002. P. 364-375.

Piezoelectric materials

The brothers Pierre and Jacques Curie, in 1880, were the first to experimentally demonstrate piezoelectric behavior in a series of crystals, including quartz and Rochelle salt. The first attempt to derive the theory of piezoelectricity was made by Voigt in 1910. Crystals with piezoelectric properties are very useful for different scientific and industrial applications. The direct piezoelectric effect occurs when an applied stress produces an electric polarization. The inverse piezoelectric effect occurs when an applied electric field produces a strain. These coupled effects let the electronic industry to produce many useful devices such as piezoelectric crystals, filters and resonators. First crystals were created by W. Cady in 1923 on the base of the natural α-quartz. To the present time the construction and characteristics of crystals were essentially improved.

There exist a several theories of the piezoelectricity. All of them lead to the very complicated equations. The exact solutions of these equations may be found only for very particular cases. By this reason it is not easy to compare theoretical and experimental results. At the present time it seems to be possible to say that there is no qualitative discrepancies between theory and experiments. From the pure theoretical point of view in the theory of the piezoelectricity there are some serious problems. The first problem. In electrodynamics the choice of the type of the electric field vector E does not matter and there are no reasons to make this choice. In the piezoelectricity it is not so and the type of E is important. In conventional theories the vector E is supposed to be a polar vector. In what follows we consider the theories when the type of E may be changed. The second problem. At least some piezoelectric materials are the dipole crystals. In such a case the rotation degrees of freedom must be taken into account.