Rate-Dependent Two-Dimensional Free Energy Model for Ferroelectric Single Crystals.

摘要

The one-dimensional free energy model for ferroelectric materials developed by Smith et al. is generalized to two dimensions. The two- dimensional free energy potential proposed in this paper consists of four energy wells that correspond to four variants of the material. The wells are separated by four saddle points, representing the barriers for 90-degree switching processes, and a local maximum, across which 180-degree switching processes take place. The free energy potential is combined with evolution equations for the variant fractions based on the theory of thermally activated processes. The model is compared to recent measurements on BaTiO3 single crystals by Burcsu et al., and predictions are made concerning the response to the application of in-plane multi-axial electric fields at various frequencies and loading directions. The kinetics of the 90-degree and 180-degree switching processes are discussed in detail.