Determination of third-order elastic constants of langasite single crystals through force-frequency effect

Abstract

Langasite resonators are of recent interest for a variety of applications because of their good temperature behavior, good piezoelectric coupling, low acoustic loss, and high Q factor. Third-order elastic constants are responsible for many nonlinear effects associated with langasite resonators including the force-frequency effect. This effect describes the shift in resonant frequency a resonator experiences due to the application of a mechanical load. The determination of the third-order elastic constants through the force-frequency effect relies on an accurate theoretical understanding of this effect. In this article, expressions for the frequency shift of langasite resonators subjected to a pair of diametric forces are obtained using the perturbation integral in conjunction with the finite element method. Experimental measurements of the force-frequency effect for various langasite resonator samples with plano-plano configuration are also discussed. The third-order elastic constants of langasite single crystals are extracted based on the measured data in conjunction with the derived expressions. The results are compared with previous measurements of third-order elastic constants for langasite obtained using transit-time methods. [Work supported by ARO.]