Phase field simulation of ferroelectric and antiferroelectric single crystals

摘要

Ferroelectric materials exhibit spontaneous polarization, spontaneous strain and domain structures below the Curie temperature. The phase field approach has been used to simulate the formation of ferroelectric domain structures and the ferroelectric-antiferroelectric phase transformation. 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 field leads to change of free energy level and therefore evolution of phase and domain states. In this work the temporal evolution of polarization field was computed by solving the TDGL equation with explicit time integration scheme. The finite difference method was implemented for the spatial description of the polarization. Cubic to tetragonal, cubic to rhombohedral and ferroelectric to antiferroelectric (tetragonal or rhombohedral) phase transformations were modeled and the formation of domain structures were simulated. Field induced polarization switching and the macroscopic material responses were simulated.