The averaged dielectric, piezoelectric, and elastic constants of thin polycrystalline barium titanate and lead titanate films are calculated within a modified effective-medium approximation, which takes fully into account piezoelectric interactions between crystallites. Films with c -or a -type crystal texture resulting from mechanical interaction with the substrate are considered when the film becomes ferroelectric under cooling of the heterostructure. The dependences of the effective material constants of textured films on the residual macroscopic polarization of a film are described. An analysis is made of the effect of two-dimensional clamping of a film on a thick substrate on measurements of dielectric and piezoelectric constants.
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Pertsev et al. (1998) studied this question.