Phase transitions and domain structures of ferroelectric nanoparticles: Phase field model incorporating strong elastic and dielectric inhomogeneity

An efficient numerical algorithm based on a Fourier spectral iterative perturbation method is proposed to accurately compute the electrostatic fields in three-dimensional (3D) microstructures with arbitrary dielectric inhomogeneity and anisotropy. The method can be conveniently implemented in phase field modeling of microstructure evolution in systems with inhomogeneous dielectric constants as well as inhomogeneous polarization and charge distributions. It is employed to determine the temperature–shape (aspect ratio) phase diagram, domain structures, and domain switching of PbTiO3 nanoparticles using phase field simulations. It is shown that the Curie temperature is enhanced for nanowires and nanorods and reduced for nanodots. The critical sizes below which the ferroelectricity disappears for the nanowire and thin film are estimated to be around 1.4 nm. Vortex domain structures are found in nanorods, nanodots, and nanodisks. Results are in general agreement with existing experimental observations and first principle calculations.