Development and application of an empirical formula for the high temperature behavior of ferroelectric ceramics switched by electric field at room temperature

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.