An effective Fourier spectral phase-field approach for ferroelectric materials

In this article, we propose an efficient iterative numerical algorithm applying a Fourier spectral method to accurately compute the coupled elasto–electrostatic equilibrium equations in ferroelectric microstructures. The method is implemented for a phase-field model for domain pattern formation and domain kinetics evolution in tetragonal perovskite ferroelectrics, that uses spontaneous polarization as order parameter and includes the piezoelectric effect in the constitutive equation. The scheme is based on a two-scale homogenization approach, introducing local perturbations for stress and dielectric displacement. Green's functions are derived in Fourier space for the coupled constitutive equations. Furthermore, using model parameters for BaTiO3 we investigate domain formation in 2D and 3D, and the polarization switching process starting from a critical nucleus subjected to an applied electric field and compressive stress. The simulation results based on the proposed method reveal that for polarization switching under external fields, intermediately appearing domains with 90° rotated polarization are formed, that reduce electrostatic or elastic strain energy.