Determination of the electromechanical coupling factor of gallium orthophosphate (GaPO/sub 4/) and its influence on resonance-frequency temperature dependencies

The quartz homeotype gallium orthophosphate (GaPO/sub 4/) is a representative of piezoelectric single crystals of large electromechanical coupling factor. It is known that its coupling factor k/sub 26/ associated with the resonators vibrating in the thickness-shear mode is approximately two times greater than that of quartz. This property increases the spacing between the series and parallel resonance frequencies of resonators, as well as the difference between the resonance frequency temperature dependencies of the fundamental and harmonic resonance frequencies of resonators vibrating in the thickness-shear mode. In this paper, the methods for determination of the coupling factor k/sub 26/ are presented, and the computed values are compared with the measured ones. The influence of the coupling factor to the resonance-frequency temperature dependencies of the fundamental and third harmonics of selected rotated Y-cut GaPO/sub 4/ resonators vibrating in the thickness-shear mode is presented. The purely elastic case for a laterally unbounded plate, which corresponds closely to the limiting case of high harmonic resonance frequency-temperature behavior was assumed for the calculations. The computed temperature coefficients for the Y-cut orientation and calculated turnover point temperatures T/sub TP/ for different (YX1) orientations are presented.