Figure 2.

Polarization rotation and related shear piezoelectric deformation for (a) tetragonal crystals and (b) rhombohedral crystals under electric field perpendicular to spontaneous polarization direction. The solid red arrows represent the spontaneous polarization for rhombohedral and tetragonal phases, respectively. The dotted red arrows represent the spontaneous polarization under perpendicular electric field. The solid black arrows represent the [011]_C and [001]_C directions in (a) and (b), respectively, in order to indicate the polarization rotation path. (c) Free energy profile for tetragonal crystals, where free energy profile is flattened with temperature approaching T-O phase boundary, corresponding to an easier polarization rotation.