Elastic constants of chrome-diopside: application of resonant ultrasound spectroscopy to monoclinic single-crystals

The right-rectangular parallelepiped resonance (RPR) form of resonant ultrasound spectroscopy (RUS) is applied to monoclinic crystal symmetry to determine the 13 adiabatic elastic constants, C-ij, of single-crystal chrome-diopside Di(0.93)Hd(0.03)Ur(0.02)X(0.02) (Di, diopside; Hd, hedenbergite; Ur, ureyite; X, other or unknown). These data represent the first published values of the elastic tensor for a monoclinic single-crystal determined by the RPR method, thus demonstrating the feasibility of this method for studying elasticity of low-symmetry crystals. The lowest 62 modal frequencies of a gem-quality specimen were measured and identified at ambient temperature and pressure. Inverting the modal frequencies results in, respectively C-11, C-22, C-33, C-44, C-55, C-66, C-12, C-13, C-23, C-15, C-25, C-35, C-46 values (GPa) of 228.1(1.0), 181.1(0.6), 245.4(1.3), 78.9(0.3), 68.2(0.2), 78.1(0.2), 78.8(0.5), 70.2(0.7), 61.1(0.7), 7.9(0.5), 5.9(0.5), 39.7(0.4), and 6.4(0.2), where numbers in parentheses indicate experimental uncertainty. The corresponding isotropic bulk, K-S, and shear, G, moduli are 116.5 (0.9) and 72.8(0.4) GPa, respectively. When comparing these results with other pyroxene data, we find systematic correlations between M2 site composition and C-ij values for most, but not all, moduli. Unusual compositional dependence near end-member diopside is seen for a few moduli, and is propagated to the K-S and G moduli, which should prompt a reexamination of some C-ij values of end-member diopside.