Piezoelectric anisotropy of a KNbO₃ single crystal

Orientation dependence of the longitudinal piezoelectric coefficients (d*₃₃) of a KNbO₃ single crystal has been investigated as a function of temperature by using the Landau-Ginzburg- Devonshire phenomenological theory. It is shown that the maximum of d*₃₃ is not always along the polarization direction of the ferroelectric phase. The enhancement of d*₃₃ along a nonpolar direction is attributed to a ferroelectric phase transition at which a polarization changes its direction. In the tetragonal phase, the maximum of d*₃₃ t at high temperatures is along the tetragonal polar direction and then changes its direction toward the polar direction of the orthorhombic phase when the temperature is close to the tetragonal-orthorhombic phase transition. The maximum of d*₃₃ o of the orthorhombic phase depends on both the high-temperature and low temperature ferroelectric phase transitions. In the rhombohedral phase, the maximum of d*₃₃ r is relatively insensitive to temperature due to the absence of any further phase transitions in the low temperature regime. These results can be generalized to the phase transitions induced by external electric field, pressure, and composition variations.