A simple model for the nonlinear material behavior of ferroelectrics

The nonlinear irreversible hysteretic behavior of ferroelectric ceramics caused by ferroelectric domain switching is modelled. Single crystal grains in the tetragonal ferroelectric state are considered. Each grain is assumed to be a single domain. In such a structure either 90 degrees or 180 degrees domain switching can result from an electric field, whereas a uniaxial stress field yields only 90 degrees domain switching. From an energy criterion introduced by Hwang et al. (Acta metall. mater., 1995, 43(5), 2073) for domain switching both the orientation distribution and macroscopic average fields of polarization and strain analytically are derived. For simplicity intergranular interactions are neglected. The model leads to the conclusion that the hysteresis of the macroscopic strain vs electric field requires both microscopic ferroelectric polarization switching and piezoelectric coupling on the scale of the grains. Despite the simplicity of the model all characteristic phenomena of ferroelectricity are represented: the dielectric hysteresis of the polarization vs electric field, the butterfly hysteresis of strain vs electric field as well as the mechanical depolarization under compressive stress. (C) 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.