DC bias electric field and stress dependence of piezoelectric parameters in lead zirconate titanate ceramics – Phenomenological approach

The piezoelectric material behavior, including loss mechanism, under external DC electric field and stress biases have been extensively studied in lead zirconate titanate ceramics. However, in order to achieve a better understanding of these effects, development of a comprehensive model is required. The purpose of this paper is to develop a phenomenological model to explain the nonlinear nature of piezoelectric parameters under DC bias electric field and stress. Therefore, the Landau-Devonshire energy function considering external biases was developed and accordingly the material properties were derived, based on first order approximation. In order to explain the compliance and piezoelectric constants change higher order elastic and electrostrictive terms were introduced into the Gibb's free energy function. Accordingly, thermodynamic theory parameters, including higher order parameters, of a soft PZT were measured and characterized based on inverse permittivity behavior near Curie temperature. Finally, the phenomenological model predictions of material property changes under DC bias electric field and compressive stress were compared with experimental data reported by our group. The proposed model succeeded to explain the material properties change under external biases. Furthermore, the effect of DC electric field and compressive stress on loss parameters were explained based on domain wall motion.