Depolarization of ferroelectric materials measured by their piezoelectric and elastic response

Depolarization in ferroelectric materials limits their piezoelectric applications and needs careful calibration for device constructions. With BaTiO₃ and PbSc_0.5Ta_0.5O₃ as prototypic ferroelectrics we demonstrate how to apply Resonant Piezoelectric Spectroscopy, RPS, to measure the direct and the converse piezoelectric effects as a function of temperature to detect depolarization via the collapse of the piezoelectric effect and the anomaly of elastic moduli. Comparison of the RPS data with in-situ d₃₃ measurements on a BaTiO₃ ceramic shows that the temperature evolution of the longitudinal piezoelectric coefficient d₃₃ can be determined with high accuracy. This makes RPS a complementary and convenient method for the investigation of polar phase transitions and the thermal evolution of the piezoelectric effect. Finally, the observation of an elastic anomaly concomitant to depolarization indicates that elastic measurements are an indirect means to measure the depolarization temperature in ferroelectrics.