The direct piezoelectric effect in [001]C-poled relaxor-ferroelectric single crystals: contrasting longitudinal and transverse modes

Direct measurements of longitudinal (d₃₃) and transverse (d₃₁) coefficients have been made on single crystal 0.68Pb(Mg₁3/Nb₂3/)O₃-0.32PbTiO₃ (PMN-32PT) and 0.955Pb(Zn₁3/Nb₂3/)O₃-0.045PbTiO₃ (PZN-4.5PT), poled along the [001]_C direction (C: pseudocubic). The measurements were made in a Berlincourt-type press over a range of dynamic and static bias stresses. The longitudinal response was found to be hysteretic and non-linear, behavior unexpected from corresponding converse (strain-field) measurements. In contrast, for a special sample aspect ratio, the transverse response was found to be essentially anhysteretic with a d₃₁ independent of the dynamic stress amplitude. It is postulated that the different behaviors are related to the concept of polarization rotation, the sense of which is contrary in each case.