Temperature dependence of the complete material coefficients matrix of soft and hard doped piezoelectric lead zirconate titanate ceramics

We have used resonance methods to determine the variation of all the independent piezoelectric, elastic, and dielectric material coefficients, as well as the corresponding electromechanical coupling factors, of soft and hard doped piezoelectric lead zirconate titanate (PZT) ceramics with compositions near the morphotropic phase boundary, as a function of temperature ranging between -165 and 195 °C. The material coefficients were obtained by analyzing the fundamental resonance of the impedance or admittance spectra as a function of frequency for several sample resonance geometries. The piezoelectric coefficients d₃₃, -d₃₁, and d₁₅, as well as the dielectric permittivity coefficients ε₁₁^T and ε₃₃^T, generally increased with temperature for both soft and hard PZT samples. However, the elastic compliance coefficients S ₁₁^E, -S₁₂^E, S₃₃ ^E and S₅₅^E exhibited abnormal variations seen as broad peaks over parts of the tested temperature range. Additionally, thermal hystereses were observed in all the studied material coefficients over the temperature cycle. Finally, it was noted that, overall, the material coefficients of soft PZT varied significantly more than those of hard PZT under changing temperature conditions.