A SIMPLE-MODEL FOR THE NONLINEAR MATERIAL BEHAVIOR OF FERROELECTRICS

The nonlinear irreversible hysteretic behavior of ferroelectric cerami cs caused by ferroelectric domain switching is modelled. Single crysta l grains in the tetragonal ferroelectric state are considered. Each gr ain is assumed to be a single domain. In such a structure either 90 de grees or 180 degrees domain switching can result from an electric fiel d, whereas a uniaxial stress field yields only 90 degrees domain switc hing. 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 strai n analytically are derived. For simplicity intergranular interactions are neglected. The model leads to the conclusion that the hysteresis o f the macroscopic strain vs electric field requires both microscopic f erroelectric polarization switching and piezoelectric coupling on the scale of the grains. Despite the simplicity of the model all character istic phenomena of ferroelectricity are represented: the dielectric hy steresis of the polarization vs electric field, the butterfly hysteres is of strain vs electric field as well as the mechanical depolarizatio n under compressive stress. (C) 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.