Mechanisms Responsible for the Large Piezoelectricity at the Tetragonal-Orthorhombic Phase Boundary of (1-x)BaZr0.2Ti0.8O3-xBa0.7Ca0.3TiO3 System

Recently it was found that in the lead-free (1-x)BaZr0.2Ti0.8O3-xBa0.7Ca0.3TiO3 (BZT-xBCT) system, the highest piezoelectric d33 coefficient appears at the tetragonal (T) - orthorhombic (O) phase boundary rather than the O - rhombohedral (R) phase boundary, but the physical origin of it is still unclear. In this work we construct the phase diagram of the BZT-xBCT system using a generic sixth-order Landau free energy polynomial and calculate the energy barrier (EB) for direct domain switching between two variants of the stable low-symmetry ferroelectric phase. We find that the EB at the T-O phase boundary is lower than that at the O-R phase boundary and EB may serve as a rigorous quantitative measure of the degree of polarization anisotropy through Landau potential. The calculations may shed some light on the physical origin of the highest piezoelectric coefficients as well as the softest elastic compliance at the T-O phase boundary observed in experiments.