Resonant ultrasound spectroscopy and homogeneity in polycrystals

Resonant ultrasound spectroscopy (RUS) is capable of determining the bulk elastic properties of a solid from its characteristic vibration frequencies, given the dimensions, density and shape of the sample. The model used for extracting values of the elastic constants assumes perfect homogeneity, which can be approximated by average-isotropic polycrystals. This approximation is excellent in the small grain regime assumed for most averaging procedures, but for real samples with indeterminate grain size distributions, it is not clear where the approximation breaks down. RUS measurements were made on pure copper samples where the grain size distribution was changed by progressive heat treatments in order to find a quantitative limit for the loss of homogeneity. It is found that when a measure of the largest grains is 15% of the sample's smallest dimension, the deviation in RUS fits indicates elastic inhomogeneity.