A simple displacement perturbation method for phase-field modeling of ferroelectric thin film

A displacement perturbation method is proposed for phase-field simulations of the ferroelectric domain structures. A temperature-misfit strain phase diagram is computed to validate this method's accuracy, encompassing rhombohedral, orthorhombic, tetragonal, cubic, and mixed phases by comparing with previous phase-field simulations. The change in free energy density surface with temperature and strain distribution is computed to clarify the mechanism of the mixed phase. The phase diagram, ferroelectric hysteresis, and domain structure all demonstrate that the numerical method of displacement discretization is reliable and practical in solving the time-dependent Ginzburg–Landau equation, consistent with previous simulated and experimental results. This new method offers the advantages of simple programming and easy parallelism, paving the way for advancements in phase-field modeling.