Some second-order effects participating on frequency-temperature behaviour of rotated Y-cut GaPO4 resonators

In this paper, gallium orthophosphate (GaPO₄) resonators in the form of rotated Y-cuts vibrating in thickness-shear mode, are studied. The results of the measured and computed resonance frequency-temperature characteristics of fundamental and third harmonic of Y-cut GaPO₄ resonators vibrating in thickness-shear mode are presented. The calculation is based on the linear elastic stress-strain relations. For the verification of the frequency-temperature behaviour of rotated Y-cut GaPO₄ resonators, a new set of samples of three different orientations YXI (0°), YXI (-11°), and YXI (-16.4°) was measured in our laboratory. The frequency-temperature behaviour of the piezoelectric resonator is mainly given by the temperature dependence of elastic stiffnesses and thermal expansion of the crystals, but they also depend a little on some second-order quantities such as size and arrangement of electrodes, resonator support, etc. This influence is described by the change of temperature coefficients and elastic stiffnesses. The different temperature coefficients of the plated and unplated (by electrode) part of the piezoelectric plate cause the different frequency-temperature characteristics of these parts of the resonator. The resonant-frequency characteristics also therefore depend on the dimension of the electrodes on the plated and unplated parts of the GaPO₄ resonator. The attention was paid especially to the influence of the piezoelectric properties of the GaPO₄ crystal, and the contribution of the elastic properties of the electrodes.