A Switching Rule for Local Domain Wall Motions and for Macroscopic Material Response of Ferroelectrics

Abstract

Polarization switching is driven on the global scale by free energy reduction. The locally equivalent material force on a sharp domain wall can be expressed by Eshelby’s electromechanical energy momentum tensor. In the present paper, we deal with solids, which can be approximated by a linear response in the dissipation-free load range. In this case, the local driving force of dissipative transformations is represented by a particularly simple function of the jump of the linear material properties and of the electric field and mechanical stress on both sides of the domain wall (or before and after switching). Two generic examples for application are considered: (i) a numerical simulation of charge induced domain wall motions at a ferroelectric crystal surface; and (ii) a finite element homogenization procedure for ferroelectric or ferroelastic single domain switching in a volume element, which represents the macroscopic response of a material point.