Phase field simulations of hysteresis and butterfly loops in ferroelectrics subjected to electro-mechanical coupled loading

Abstract

Two-dimensional computer simulations of ferroelectric polarization switching have been performed using the phase field simulation model developed by employing the time-dependent Ginsburg-Landau equations. The bulk-free energy, polarization gradient energy, long-range dipole-dipole electrostatic interactions, and elastic energy were taken into account in the above-mentioned simulations. The influences of electric-mechanical coupled loading on the hysteresis and butterfly loops were studied. The results showed that the coupled electro-mechanical loading could change both the coercive field of ferroelectric materials and the symmetry of hysteresis and butterfly loops. © 2005 by The American Ceramic Society.