On the Change in Orientation of the Zero-Temperature Contoured SC-Cut Quartz Resonator with the Radius of the Contour

Abstract

Abstract : In order to calculate the dependence of the actual orientation of the zero-temperature electrodes, contoured SC-cut quartz resonators on the radius of the contour, the actual orientation of the zero-temperature unelectroded flat SC-cut quartz plate vibrating in the pure thickness-mode of interest must be known. However, on account of small inaccuracies in the measured temperature derivatives of the elastic constants of quartz, only the nominal phi and theta angles of zero-temperature cuts of the unelectroded flat quartz plates vibrating in pure thickness-modes can be calculated. In recent work on contoured At-cut quartz resonators a 6' correction to the nominal theta angle was obtained. Since the theta angle of the SC-cut is very near the theta angle of the AT-cut, the 6' correction can be taken to hold for the SC-cut also. In this work the corresponding correction to the nominal phi angle is obtained from measurements on zero-temperature electroded, contoured SC-cut quartz resonators at 25 deg C. With this correction to the nominal phi angle, the dependence of the actual orientation of the zero-temperature electroded, contoured SC-cut quartz resonator on the radius of the contour at 25 deg C is calculated for the fundamental and third and fifth harmonics. Originator furnished keywords include: Piezoelectric resonators, Contoured resonators, Zero-temperature cut, SC-cut quartz, Orientation dependence, Frequency perturbations, Thermal deformations, Elastic nonlinearities, Temperature dependence, Biasing states, Piezoelectric plates, Doubly-rotated, Anisotropic.