Phase-Dield Simulation of Rhombohedral and Tetragonal Phases in Ferroelectric Single Crystals

Abstract

Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this work the phase field approach has been used to simulate phase transformations and the formation of ferroelectric domain structures. The evolution of phases and domain structures was simulated in ferroelectric single crystals by solving the time dependent Ginzburg-Landau (TDGL) equation with polarization as the order parameter. In the TDGL equation the free energy of a ferroelectric crystal is written as a function of polarization and applied fields. Change of temperature as well as application of stress and electric fields leads to change of the free energy and evolution of phase states and domain structures. In this work the finite difference method was implemented for the spatial description of the polarization and the temporal evolution of polarization field was computed by solving the TDGL equation with an explicit time integration scheme. Cubic to tetragonal, cubic to rhombohedral and rhombohedral to tetragonal phase transformations were modeled, and the formation of domain structures was simulated. Field induced polarization switching and rhombohedral to tetragonal phase transition were simulated.