Cut Angle Dependences of Resonant Characteristics of $\beta$-Phase Quartz

Quartz is one of the excellent materials for piezoelectric and optical applications. Whereas $\alpha$-phase quartz is widely used, $\beta$-phase quartz is not used for any application. We investigated the piezoelectric and elastic properties of $\beta$-phase quartz and observed clear piezoelectric responses from approximately 580 to 1,300 °C. Large positive frequency--temperature characteristics were observed and good reproducibility of the heat cycle was obtained. Because of its large frequency--temperature coefficient, $\beta$-phase quartz is likely applicable for temperature sensors at high temperatures up to 1,200 °C. Since dielectric dissipation affects the resonant characteristics of $\beta$-phase quartz at high temperature, we investigated the cut angle dependence of the dielectric dissipation and obtained an optimum cut angle for $\beta$-phase resonators.