Equilibrium Properties in Polycrystalline Ferroelectrics

Computational and experimental methodologies have been integrated to define design criteria to maximize the properties of textured and untextured piezoelectric microstructures. Two-dimensional orientation maps measured through electron backscatter diffraction on sequentialparallel layers, are used to reconstruct experimentally-determined three-dimensional samples and thus directly assess the properties and reliability of piezoelectric materials. Three-dimensionally reconstructed microstructures (see right) are used to generate detailed finite element models that realistically capture the shapes and crystallographic orientations of individual

grains, and thus predict the macroscopic piezoelectric response and their associated mechanical and electrical reliability. Based on the knowledge acquired from experimentally analyzed samples, 3D computer-generated facsimiles (below) are assembled to

explore the effects of accessible and inaccessible processing parameters on the macroscopic material properties. Thus, electrical shielding and stress field concentrations (bottom right) underscore locations where ferroelectric domains are pinned, nucleate, and grow, and also point to places where crack growth and arrest will be favored. Developed 3D models incorporate dielectric, elastic, as well as direct and converse piezoelectric effects. In addition, theories are developed to realistically capture the effects of processing, ferroelastic, and ferroelectric texture and thus propose optimal microstructures: grain sizes, poling fields, and textures.