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.

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The strain changes during temperature rise of a poled lead titanate zirconate rectangular parallelepiped switched by electric field at room temperature are obtained by integrating thermal expansion coefficients that are measured using an invar-specimen. By estimating and analyzing pyroelectric and thermal expansion coefficients, first-order differential equations are constructed for polarization and strain changes during temperature increase. The solutions to the differential equations are found and used to calculate the high temperature behavior of the materials. It is shown that the predictions are well compared with measured responses. Finally, the developed formulae are applied to calculate strain butterfly loops from a polarization hysteresis loop at a high temperature.

A poled lead titanate zirconate rectangular parallelepiped is subjected to electric field pulses with gradually increasing magnitude at room and high temperatures. From measured electric displacement and strain responses, permittivity and piezoelectric coefficients are estimated and plotted with respect to remnant polarization. Equations for piezoelectric coefficients are proposed as functions of relative remnant polarization and temperature. The so-called reference remnant polarization and strains are calculated from measured remnant polarization and strains. Reference remnant strains are plotted with respect to reference remnant polarization, and their evolutions during polarization reversal are analyzed and compared.

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