Crystal orientation dependence of the piezoelectric d33 coefficient in tetragonal BaTiO3 as a function of temperature

This is the authors' abstract. We don't add key points for this paper.

Using the Landau–Ginzburg–Devonshire approach, the longitudinal piezoelectric coefficient in an arbitrary direction, d33*(θ), was calculated as a function of temperature in tetragonal BaTiO3 crystals. The direction along which d33*(θ) is maximum is a function of piezoelectric dij coefficients referred to the crystallographic coordinate system. Below a critical ratio of the shear and longitudinal coefficients, d15/d33, the maximum d33*(θ) lies along the [001] axis. As the low-temperature orthorhombic phase is approached on cooling, the d15 increases, reflecting softening of the lattice along the axis of the incipient orthorhombic distortion, and the direction of maximum d33*(θ) deviates significantly from the [001] axis. Our results suggest that the enhanced d33*(θ) 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.