The Measurement Of Elastic Constants Of Anisotropic Crystals By Resonant Ultrasound Spectroscopy

For the design of acoustic wave devices, the reliable elastic constants of piezoelectricmaterials are essential. Traditional methods including the resonant vibration method andultrasonic method have their disadvantages. For ultrasonic measurement method, due tomuch interference, the velocity of crystal axes is very difficult to measure. For resonantmeasurement, there will be high cost in the preparation of specimen.This paper introduces a new method for measuring the elastic constants known asRUSpec (Resonant Ultrasound Spectroscopy) through new software additions to expandthe capability of measurement modules. The RUSpec method is based on both Lagrangianvariational principle and the Levenberg-Marquardt algorithm. Lagrangian variationalprinciple which is based on the fact that specimen in the absence of external loads, thereare no displacement, strain and conversion between kinetic and strain energy. On the basisof derivation of Lagrangian variational equations, we can get free vibration frequencies ofspecimen. Levenberg-Marquardt algorithm matches the free vibration frequency obtainedby Lagrangian variational principle and RUSpec instrument using finite difference methodand gets independent elastic constants and the matching error eventually.We measured the standard aluminum specimen using self-developed program andcompare the results with measurement of RUSpec instrument, and found that the resultsare highly consistent. We developed the trigonal crystal system measurement module andmonoclinic crystal system measurement module afterwards. We found the error can benegligible by comparing with the data has been reported.This self-developed measurement software of the elastic constants can measure elasticconstants of a variety of crystal systems fast and accurately, and significantly reduce thecost of the crystal sample preparation and measurement time.