About the coupling factor of the gallium orthophosphate (GaPO4) and its influence to the resonance-frequency temperature dependence

The quartz homeotype gallium orthophosphate (GaPO₄) is a representative of piezoelectric single crystals with large electromechanical coupling factor. It is known that its coupling factor k₂₆ 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, and also 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 computed electromechanical coupling factors are compared with the measured ones, and the influences of the coupling coefficient to the resonance-frequency temperature dependencies of the fundamental and third harmonics of selected rotated Y-cut GaPO₄ resonators vibrating in the thickness-shear mode are presented. The precision of computation of the frequency-temperature dependencies of the fundamental and harmonic thickness-shear resonance is discussed. 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 (YXI)0°, (YXI)-11°, and (YXI)-16.4° Y-cut orientations are used for the computations and measurements.