Homogenization of textured as well as randomly oriented ferroelectric polycrystals

Microstructural features such as spatial correlation of crystallographic orientations and morphological texture in piezoelectric polycrystals is modeled computationally. The mathematical homogenization of piezoelectric material is implemented using the finite element method (FEM) by solving the coupled equilibrium electrical and mechanical fields. A three-dimensional (3D) FEM model is adapted to polycrystalline medium. The dependence of macroscopic electromechanical properties on domain orientation and texture of single-crystalline as well as polycrystalline ferroelectric BaTiO3 and PbTiO3 are demonstrated based on this model. The homogenized piezoelectric moduli of the polycrystals and single-crystals of these materials exhibit remarkable but contrasting behaviors. The aggregate texture for polycrystalline ferroelectrics is assumed to have a Gaussian (normal) distribution. The longitudinal piezoelectric strain coefficient d33 assumes a higher value than the corresponding single-crystalline value of BaTiO3 at a distribution characterized by σ between 0.5 and 0.7 However, for PbTiO3 the maximum is shown at the perfect {0 0 1} texture. Therefore, polycrystalline materials are expected to be improved in their global piezoelectric performance by engineering the texture of the microstructure.