State dependent pyroelectric and thermal expansion coefficients in a PZT wafer

A PZT wafer is subjected to a temperature increase from the reference temperature 20-111 °C under no electric field. During the temperature increase, the variations of remanent polarization in thickness direction and remanent in-plane strain are measured. From the measurements, the values of pyroelectric coefficient in thickness direction and in-plane thermal expansion coefficient are estimated. The temperature experiment is repeated starting at various different values of initial remanent polarization, and the dependency of pyroelectric and thermal expansion coefficients on initial remanent polarization is obtained. In the tested range of temperature, it is found that the pyroelectric coefficient can be given as a linear function of remanent polarization and that the in-plane thermal expansion coefficient is given as a linear function of remanent in-plane strain or as a quadratic function of remanent polarization.