Piezoelectric anisotropy–phase transition relations in perovskite single crystals

The orientation dependence of the longitudinal piezoelectric coefficient, d33*, is investigated as a function of temperature in BaTiO3 and PbTiO3 crystals using the Landau–Ginsburg–Devonshire theory. We show that a presence of the ferroelectric–ferroelectric phase transitions in BaTiO3 leads to enhanced d33* along nonpolar directions. The reason for this is that in the vicinity of a phase transition temperature at which a polarization vector changes its direction (tetragonal–orthorhombic/monoclinic, orthorhombic/monoclinic–rhombohedral), the shear piezoelectric coefficients become high. It is shown for all ferroelectric phases of BaTiO3 that the shear stress deforms the crystal cell and changes the polarization direction in a similar way as the corresponding temperature-induced phase transition. The influence of the piezoelectric shear effect on the anisotropy of d33* is particularly pronounced in the orthorhombic/monoclinic phase where the piezoelectric shear coefficients are determined by the presence of both the high-temperature tetragonal and the low-temperature rhombohedral phases. In PbTiO3, which does not exhibit ferroelectric–ferroelectric phase transitions, the shear piezoelectric effect is weak and d33* 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 variations and are valid for all perovskite materials, including complex relaxor–ferroelectric perovskites that have recently attracted attention for their exceptionally large piezoelectric properties.