Analytical expressions to estimate the effective piezoelectric tensor of a textured polycrystal for any crystal symmetry

Abstract

This work introduces a set of analytical expressions that simplifies the procedure of obtaining closed-form formulas to estimate the effective piezoelectric properties of polycrystalline aggregates formed by crystals of all the 21 non-centrosymmetrical classes and with arbitrary textures. The expressions are derived from orientational averages of third-order piezoelectric tensors of the individual crystals that are weighted by orientational distribution functions. The averaging is done by using generalized spherical harmonic series expansions. Improvements with respect to previous works in the literature are twofold: all crystal symmetries are considered and no symmetry restrictions are imposed to texture. The versatility of the introduced expressions is demonstrated on an example of BaTiO3 polycrystals with uniaxial and biaxial textures characterized by single and double Gaussian distributions, respectively. The results for uniaxial texture are in perfect agreement with the results published in the literature. The biaxial texture is discussed in detail and analyzed for a set of limiting cases.