Force constant and effective mass of 90° domain walls in ferroelectric ceramics

TLDR

Domain wall contributions to the dielectric, piezoelectric, and elastic properties of tetragonal ferroelectric ceramics are calculated. A simple model shows that 90° domain wall motion induces shear deformation and a nearly homogeneous electric field, enabling calculation of the force constant from elastic and electric field energies, and averaging over grain orientations yields the walls’ contributions to material properties for both unpolarized and polarized ceramics. Displacements of 90° domain walls are experimentally validated, are a small fraction of the lattice cell under moderate fields, and the walls possess an effective mass independent of domain width, yielding a resonance frequency lower than the grain’s elastic resonance.

Abstract

Domain wall contributions to the dielectric, piezoelectric, and elastic properties of tetragonal ferroelectric ceramics, as discussed extensively in the past, are calculated. A simple model shows that the motion of 90° domain walls causes a shear deformation and an approximately homogeneous electric field in the grain. The elastic and electric field energies involved allow the calculation of the force constant for the domain wall displacement by external fields. The displacements agree with experimental results. In a moderate electric field the displacement is a small fraction of the lattice cell only. By averaging over the orientational distributions of all grains the contributions of the 90° domain walls to the material properties are calculated for unpolarized and for polarized ceramics and agree with experimental results. The effective mass, which has to be attributed to the domain walls is the mass of the whole grain reduced by the factor S0 (spontaneous deformation), is independent of the domain width. The resonance frequency of the domain walls therefore is lower than the elastic resonance frequency of the grain.