Effect of electrical boundary conditions on the polarization distribution around a crack in a ferroelectric single domain

Polarization distributions around an open crack with different electrical boundary conditions in a single crystal ferroelectric are investigated by using a phase field model. The surface effect of polarization is taken into account in the phase field model, which has not been included in previous ferroelectric crack models. The simulation results show that the impermeable crack and the crack filled with air have a significant influence on the polarization distribution, while the permeable and the crack filled with water have little influence. It is also found that the zero boundary condition of polarization increases the influence of the crack on the permeable crack and the crack filled with water.  The results of the present work suggest that a crack filled with air can be approximated as an impermeable crack, and a crack filled with water can be regarded as a permeable crack in ferroelectric materials.