Temperature coefficients of sound velocity in piezoelectric ceramics

In piezoelectric devices based on ferroelectric ceramics, where the temperature coefficients of characteristic frequencies cannot be minimized by selection of suitable crystal cuts as in the case of single crystals, low temperature coefficients can be realized if a solid solution system exhibiting more than one ferroelectric phase is chosen. From experimental data on the temperature dependence of the elastic compliance sE11 for a specific composition the temperature coefficients are derived analytically from least square approximations for PbTixZr1-xO3. For the range 0.1 < x < 0.6 the coefficients are found to be strongly dependent on composition becoming zero at four specific compositions in the range 0.4 < x < 0.6 and rather small and independent of composition for x > 0.6. Stabilizing additives depress the temperature coefficients for 0.4 < x < 0.6 and have an enhancing effect for x > 0.6. Additives causing A position vacancies result in the opposite behaviour pointing to the realization of ceramics with low temperature coefficients (-10-5 to -10-4 °C-1) of characteristic frequencies, which are simultaneously insensitive to compositional variations.