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

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