Force-frequency effects 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 3 times 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 such sensitivity is the force-frequency effect, which relates the sensitivity 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 LGN resonator and a Y-cut 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 5 and 7 times smaller than that of SC-cut quartz, respectively (or, 7 and 10 times smaller compared to AT-cut quartz). The coefficients of planar-stress, which represent the superposition of a continuous distribution of periphery stresses, were also obtained as 0.52×10^-15 m·s/N and 0.38×10^-15 m·s/N for the LGN and the LGT, respectively.