On the physical interpretation of material parameters in phase field models for ferroelectrics

This publication intends to clarify the relations between the free energy expansion and the choice of the order parameter in phase field models for ferroelectrics. The free energy is expanded to include the piezoelectric coupling terms, reflecting the symmetry properties of the material below the Curie temperature. The order parameter can then be interpreted as the material polarization less than the dielectric and piezoelectric contributions. Furthermore, a 1d reduction of the problem is used to identify the physical meaning of the remaining model parameters. The theoretical results are verified by numerical simulations of 180^? and 90^? domain walls. Both the static case, where the emphasis lies on the specific energy and the interface width, and the dynamic case, where interfaces are subjected to an electric driving field, are considered in the simulations.