Observations on Modes of Vibration and Temperature Coefficients of Quartz Crystal Plates

The characteristics of piezo-electric quartz crystal plates of the perpendicular or Curie cut are compared with parallel or 30-deg. cut plates with reference to the type of vibration of the most active modes, the frequency of these modes as a function of the dimensions, and the magnitude and sign of the temperature coefficients of these frequencies. It is pointed out that the two principle modes of the perpendicular cut plate appear to be of the longitudinal type, the high-frequency mode being a function of the thickness while the low-frequency is a function of the width (along the electric axis). Both modes have a negative temperature coefficient of frequency. Of the two corresponding modes of the parallel cut plates, a shear vibration is responsible for the high frequency. This frequency has a positive temperature coefficient. The low-frequency mode is of the longitudinal type and has a negative temperature coefficient. Considering only the high-frequency vibration of these plates it is observed that there are characteristic variations of the frequency and temperature coefficient with the ratio of dimensions of the plate and the temperature, which are peculiar to the parallel cut plate. These variations can be attributed to a coupling of the shear and longitudinal modes. It is then shown that if the parallel cut plate be treated as a group of coupled oscillatory systems with appropriate temperature coefficients the usual coupled system analysis will explain the curves of frequency vs. dimensional ratio, frequency vs. temperature, and temperature coefficient vs.