Crystal orientation dependence of the piezoelectric d(33) coefficient in tetragonal BaTiO3 as a function of temperature

Using the Landau-Ginzburg-Devonshire approach, the longitudinal piezoelectric coefficient in an arbitrary direction, d(33)()(theta), was calculated as a function of temperature in tetragonal BaTiO3 crystals. The direction along which d(33)()(theta) is maximum is a function of piezoelectric d(ij) coefficients referred to the crystallographic coordinate system. Below a critical ratio of the shear and longitudinal coefficients, d(15)/d(33), the maximum d(33)()(theta) lies along the [001] axis. As the low-temperature orthorhombic phase is approached on cooling, the d(15) increases, reflecting softening of the lattice along the axis of the incipient orthorhombic distortion, and the direction of maximum d(33)()(theta) deviates significantly from the [001] axis. Our results suggest that the enhanced d(33)(*)(theta) coefficient along a direction other than the polar axis recently reported in some ferroelectrics is at least in part controlled by these intrinsic lattice effects. (C) 2002 American Institute of Physics.