Third overtone frequency turnover temperature-orientation characteristics for quartz plate resonator in the vicinity of AT-cut

This paper describes the third overtone frequency turnover temperature vs. orientation characteristics for quartz crystal plate resonator in the vicinity of AT-cut in the temperature range from -196 to 250°C, and these characteristics are discussed in comparison with the frequency turnover temperature characteristics for the fundamental and fifth overtone modes. From the presented quadric relationships we can demonstrate the useful piezoelectric cuts of quartz for the resonators and sensors at the elevated temperature region. The quadric theory proposed in this paper is a simple and useful one and the coefficients of quadric can be experimentally determined by the least squares method. From these coefficients we can infer the frequency temperature coefficients