RE García, WC Carter,  SA Langer “The effect of texture and microstructure on the macroscopic properties of polycrystalline piezoelectrics: application to barium titanate and PZN–PT” Journal of the American Ceramic Society, 88(3):750-757, 2005.

Abstract

The effects of crystallographic texture and microstructure are analyzed for polycrystalline tetragonal BaTiO₃, pseudotetragonal PZN–PT, and cubic BaTiO₃. For tetragonal BaTiO₃ and pseudotetragonal PZN–PT, we demonstrate that a high anisotropy of the single-crystal properties induces an apparent enhancement in the macroscopic piezoelectric response. For tetragonal BaTiO₃, the predicted macroscopic piezoelectric constants d₃₁ and d₃₃ are enhanced with respect to its single-crystal value at the expense of the spatial contributions from d₁₅. For samples possessing fiber texture, an optimal response is predicted for samples that are not perfectly textured. Similarly, an apparent enhancement of the macroscopic value of d₁₅ is predicted for PZN–PT. For cubic BaTiO₃, the low anisotropy of the underlying crystal properties induces a uniform decrease of the macroscopic electrostrictive constant, Q₁₁, with decreasing texture. A completely random polycrystal provides 0.85±0.05 times its single-crystal response.