Multiphase-field modeling of domain structure evolution in ferroelectric thin film

The computational determination of domain structures in ferroelectric films is achieved through the implementation of a multiphase-field methodology. In this framework, domain structures are calculated by minimizing the total energy functional with respect to the multiphase-field order parameter 𝝓. This energy functional includes the general interfacial energy, which consists of a multi-obstacle potential and a gradient energy, as well as the phase-dependent bulk energy that incorporates contributions from mechanical forces and electric fields. Using PbTiO3 (PTO) as the chosen model material, we report on the results of investigating domain structures, including an examination of the influence of substrate deformation, variations in misfit strains, different thin film thicknesses, and temperature fluctuations. By implementing the mechanical jump condition approach, the inelastic strain is calculated independently for both the thin film and the substrate, under different conditions. Furthermore, this model demonstrates its ability to investigate domain structures without relying on the Landau potential to characterize the structural stability, providing a valuable reference for studing various ferroelectric thin films that lack higher-order Landau coefficients.