Prediction of high temperature behavior of ferroelectric ceramics with state dependent thermal moduli

A poled lead titanate zirconate rectangular parallelepiped is subjected to an electric field at a room temperature called reference temperature to reach a specific value of polarization. Then the temperature of specimen is raised at the specific value of polarization under no electric field, measuring polarization and strain changes in the specimen. Pyroelectric and thermal expansion coefficients are estimated from measured responses. A set of modeling equations is proposed to predict the dependence of the thermal moduli on remnant state variables and the relations between remnant state variables at high temperatures.