The elasticity of the upper mantle orthosilicates olivine and garnet to 3 GPa

Abstract

The elastic moduli of single crystals of pyrope-rich garnet and San Carlos olivine have been measured over a 3 GPa pressure range at room temperature. The combination of improved ultrasonic techniques and this large pressure range provide for more reliable characterization of the pressure dependence of acoustic wave velocities than has previously been possible. First and second pressure derivatives of the velocities have been determined within ∼ 1 percent and ∼ 10 percent respectively. The Hashin-Shtrikman bounds for the pressure dependences of the bulk and shear moduli of the garnet used in this study are; K = 173.6 GPa, K′ = 4.93, K″ = −0.28 GPa⁻¹, G= 94.9 GPa, G′ = 1.56, G″ = −0.08 GPa⁻¹ and the Hashin-Shtrikman least-upper bounds and greatestlower bounds for the pressure dependences of the bulk and shear moduli of the San Carlos olivine are K=129.8 GPa, K′ = 4.66, K″= −0.15 GPa⁻¹, G = 77.8 GPa, G′ = 1.93, G″ = −0.11 GPa⁻¹ and K = 129.2 GPa, K′ = 4.63, K″= −0.15 GPa⁻¹ G = 77.3 GPa, G′=1.96, G″ = −0.11 GPa⁻¹ respectively. The determination of the room-pressure elastic moduli of this pyrope-almandine garnet removes the previously observed anomaly in the predictions of systematic treatments of variations of the elastic moduli of garnets with composition. The determination of the second pressure derivatives of the moduli of garnet and olivine illustrates the importance of these terms in extrapolations to higher pressures — with ϱK/ϱP for these crystals being reduced by ∼ 17 percent and ∼ 9 percent respectively over the 3 GPa pressure range.