A phase-field model for ferroelectric materials - Based on the multiphase-field method

A novel phase-field model is developed to investigate the domain structure in ferroelectric materials subjected to an external field. Differing from the time-dependent Ginzburg-Landau (TDGL) theory that describes domain structures based on the spatial and temporal evolution of polarization, our model utilizes the multiphase-field approach to calculate domain structures by minimizing the total energy functional with respect to the multiphase-field order parameter ϕ. The energy functional in the proposed model comprises the general multiphase interfacial energy and the phase-dependent bulk energy, accounting for the contributions from domain walls, and mechanical as well as electric fields. By considering the interplay between the different energy components, the model provides insights into the complex domain structure of ferroelectric materials and their response to external stimuli. This comprehensive approach is validated through simulations of both single-crystal and polycrystalline structures. The approach presented in this study simplifies the computational coefficients required to analyze the domain structure in ferroelectric materials, compared to the TDGL approach, by disregarding the Landau potential. This makes it possible to analyze the domain structure of materials without Landau coefficients. Furthermore, the proposed model serves as a reference for applying the multiphase-field concept to ferroelectric materials.