Temperature dependence of self-consistent full matrix material constants of lead zirconate titanate ceramics

Abstract

Up to date, there are no self-consistent data in the literature on the temperature dependence of full matrix material properties for piezoelectric materials because they are extremely difficult to determine. Using only one sample, we have measured the temperature dependence of full matrix constants of lead zirconate titanate (PZT-4) from room temperature to 120 C by resonant ultrasound spectroscopy. Self-consistency is guaranteed here because all data at different temperatures come from one sample. Such temperature dependence data would make it a reality to accurately predict device performance at high temperatures using computer simulations. V C 2015 AIP Publishing LLC.

Functional Piezocrystal Characterisation under Varying Conditions

“…Therefore, the alternative methods outlined previously are under development, with the aim to reduce the number of samples required [13,14]. However, such methods leave two issues unresolved.…”

Characterization of Full Set Material Constants and Their Temperature Dependence for Piezoelectric Materials Using Resonant Ultrasound Spectroscopy

“…Figures 5 and 6 show the measured elastic constant tensor components and piezoelectric coefficient tensor components, respectively, as a function of temperature for the demonstration sample PZT-4 ceramics 10 . One can see from Figure 5 that the elastic constants ${\mathrm{normalc}}_{11}^{\mathrm{normalE}}$, ${\mathrm{normalc}}_{33}^{\mathrm{normalE}}$, and ${\mathrm{normalc}}_{44}^{\mathrm{normalE}}$ increase with temperature while the elastic constants ${\mathrm{normalc}}_{12}^{\mathrm{normalE}}$ and ${\mathrm{normalc}}_{13}^{\mathrm{normalE}}$ are nearly independent of temperature in the temperature range from 20 to 120 °C.…”

“…Calculate the free dielectric constants ${\epsilon }_{11}^{\mathrm{normalT}}$ and ${\epsilon }_{33}^{\mathrm{normalT}}$ from the inversion results and compare them with directly measured ones (Figure 7) 10 .Check the obtained data set to see whether they obey the condition of thermodynamic stability, for example, $({\mathrm{normalc}}_{11}^{\mathrm{normalE}}+{\mathrm{normalc}}_{12}^{\mathrm{normalE}}){\mathrm{normalc}}_{33}^{\mathrm{normalE}}>2{\left({\mathrm{c}}_{13}^{\mathrm{E}}\right)}^2$ for the PZT case.Compare the values of d 15 calculated using ${\mathrm{normald}}_{15}=\sqrt{1-{\mathrm{normalc}}_{44}^{\mathrm{normalE}}∕{\mathrm{normalc}}_{44}^{\mathrm{normalD}}}\sqrt{{\epsilon }_{11}^{\mathrm{normalT}}{\mathrm{normals}}_{44}^{\mathrm{normalE}}}$, and ${\mathrm{normald}}_{15}={\mathrm{normale}}_{15}{\mathrm{normals}}_{44}^{\mathrm{normalE}}$, and the values of d 33 calculated using ${\mathrm{normald}}_{33}=2{\mathrm{normale}}_{31}{\mathrm{normals}}_{13}^{\mathrm{normalE}}+{\mathrm{normale}}_{33}{\mathrm{normals}}_{33}^{\mathrm{normalE}}$ and ${\mathrm{normald}}_{33}=\sqrt{true({\mathrm{normals}}_{33}^{\mathrm{normalE}}-{\mathrm{normals}}_{33}^{\mathrm{normalD}}true){\epsilon }_{33}^{\mathrm{normalT}}}$.Note: These relationships will differ for different symmetries, but the principle is the same. Generally, if the relative error is less than 5% between predicted and measured quantities, the results will be considered self-consistent 11 .…”

“…Calculate the free dielectric constants ${\epsilon }_{11}^{\mathrm{normalT}}$ and ${\epsilon }_{33}^{\mathrm{normalT}}$ from the inversion results and compare them with directly measured ones (Figure 7) 10 .…”

Determination of temperature dependence of full matrix material constants of PZT-8 piezoceramics using only one sample

“…Unfortunately, it is not easy to perform such property characterization at high temperatures, particularly when the material sare strongly anisotropic and sensitive to temperature changes, like piezoelectric materials. Therefore, self-consistent data on the temperature dependence of full matrix material properties for piezoelectric materials were seldom measured[6]. There are some reports on the elastic and piezoelectric constants of PZT-8 as well as lead-free piezoceramics using the resonance and anti-resonance method.…”