Piezoelectric anisotropy - phase transition relations in perovskite single crystals

The orientation dependence of the longitudinal piezoelectric coefficient is investigated as a function of temperature in BaTiO₃ and PbTiO₃ crystals using Landau-Ginsburg-Devonshire theory. We show that a presence of the ferroelectric - ferroelectric phase transitions in BaTiO₃ leads to an enhanced piezoelectric longitudinal response along nonpolar directions. The reason for this is the abrupt increase of the shear piezoelectric coefficients in the vicinity of a FE - FE phase transition temperature. In PbTiO₃, which does not exhibit such phase transitions, the shear piezoelectric effect is weak and the longitudinal piezoelectric coefficient has its maximum along the polar axis at all temperatures. These results can be generalized to include phase transitions induced by electric-field and composition variation and are valid for all perovskite materials. Further, using Landau-Ginzburg-Devonshire theory and tetragonal BaTiO₃ as an example, we demonstrate that a strong electric bias fields applied anti-parallel to the spontaneous polarization may lead to a large enhancement of piezoelectric properties in monodomain perovskite crystals. The enhancement is due to the field-induced dielectric softening of the crystal.