Force-frequency effect on the Q-factor of thickness- shear mode quartz and langasite resonator at high temperatures

A theoretical study was conducted for a 20 MHz circular resonator to investigate the force-frequency effect on the Q-factor value for the slow (C-) and fast (B-) thickness-shear mode using the 3-D Lagrangian finite-element model (FEM), and the Sinha-Tiersten perturbation method. The calculations were carried out for doubly rotated quartz cuts and single rotated langasite (LGS) cut. Based on the frequency spectrum analysis, the best aspect ratio for each crystal cut angle was investigated for the force-frequency effect at 25 and 300°C. The Q-factor calculations are based on the intrinsic viscosity of crystalline quartz and LGS. This paper provides the foremost computational result for the force-frequency constants and the Q-factor at 300°C for doubly rotated quartz cuts, and single rotated LGS cut.