Force-frequency effect of Y-cut langanite and Y-cut langatate

Most recently, langasite and its isomorphs (LGX) have been advanced as potential substitutes for quartz, owing to their extremely high-quality (Q) factors. At least twice higher Q value of LGX than that of quartz has been reported. High Q translates into potentially greater stability. In order to make such materials practical, the environmental sensitivities must be addressed. One of such sensitivities is the force-frequency effect, which relates the sensitiveness of a resonator to shock and vibration via the third-order (non-Hookean) elastic constants. In this paper, we report measured force-frequency coefficients of a Y-cut langanite (LGN) resonator and a Y-cut langatate (LGT) resonator as a function of the azimuthal angle, which is the angle between the crystalline x-axis of a resonator plate and the direction of in-plane diametric force applied to the periphery of the resonator. It was found that the LGN and the LGT behave like AT-cut quartz in the polarity of the frequency changes and the existence of zero-coefficient angle. The maximum magnitudes of the coefficients of the LGN and the LGT are five and seven times smaller than that of stress-compensated cut (SC-cut) quartz, respectively (or, 7 and 10 times smaller comparing to AT-cut quartz). The coefficients of planar-stress, which represent the superposition of a continuous distribution of periphery stresses, also were obtained as 0.52 X 10(-15) m x s/N and 0.38 X 10(-15) m x s/N for the LGN and the LGT, respectively.