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

Abstract

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_0.93Hd_0.03Ur_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.