Simulations of domain switching in ferroelectrics by a three-dimensional finite element model

In this paper, a new criterion of domain switching for ferroelectric polycrystals is presented. Based on this criterion, a three-dimensional (3-D) finite element model is developed to simulate domain switching. It is assumed in the model that each crystallite, represented by a cubic element, is a single domain. A domain will undergo 90° or 180° switching when reduction of the Gibbs free energy in a representative element body exceeds the corresponding energy barrier. The model can describe well the measured electric hysteresis loops and butterfly loops, the stress vs. strain curves and the stress vs. electric displacement curves of a soft PZT-51 ceramic. The domain switching process in a 4 × 4 × 5 cubic array is numerically analyzed and displayed in 3-D images. It is interesting to note that domains do not undergo 180° switching directly. In fact, an 180° reorientation undergoes two successive 90° switchings. Another phenomenon is that domains near free boundaries can switch more easily due to weaker constraints. Specific simulations are carried out under an electric field that is applied to the specimens at a range of angles to the poling direction. Although the electric hesteresis curves and the butterfly curves of the specimens vary at the beginning of the loading, they almost converge to a stable hysteresis loop and a stable butterfly loop after a few loading cycles.