Calculation of the effect of pressurizing gases on the resonant modes of single-crystal parallelepiped

Resonant ultrasound spectroscopy provides for an experimental determination of the elastic moduli of a solid sample. The moduli are extracted by matching a theoretically computed resonant spectrum to the experimental vibrational spectrum. To determine the pressure dependence of the moduli, the vibrational spectrum can be taken with the sample in a pressurizing gas. Then the extraction of the intrinsic, pressure dependent moduli requires a theoretical treatment which permits removal of the perturbation of the spectrum due to the surface loading by the pressure and shear waves in the gas. In order to illustrate a treatment which accomplishes this removal, the theoretically computed frequency shifts and the quality factors are reported for two single-crystal parallelepiped pressurized by noble gases.