Elastic moduli, pressure derivatives, and temperature derivatives of single-crystal olivine and single-crystal forsterite

Abstract

Ultrasonic wave velocities in single-crystal forsterite (F) and single-crystal olivine (O) have been measured as a function of pressure and of temperature near ambient conditions. Shear and longitudinal velocities were measured in eighteen independent modes, so that each of the nine elastic constants could be calculated by at least two independent equations. The adiabatic stiffness constants cij (in Mb), their temperature derivatives dcij/dT (10−4 Mb/deg), and their pressure derivatives dCij/dP, are ij 11 22 33 44 55 66 23 31 12Cij (F) 3.284 1.998 2.353 0.6515 0.8120 0.8088 0.738 0.688 0.639 (O) 3.237 1.976 2.351 0.6462 0.7805 0.7904 0.756 0.716 0.664dcij/dT (F) 3.31 2.81 2.83 1.30 1.32 1.51 0.46 0.82 1.04 (O) 3.40 2.85 2.86 1.28 1.30 1.57 0.51 0.94 1.05dcij/dP (F) 8.47 6.56 6.57 2.12 1.66 2.37 4.11 4.84 4.67 (O) 7.98 6.37 6.38 2.17 1.64 2.31 3.76 4.48 4.74The density ρo and other isotropic properties including the adiabatic bulk modulus Ks, the shear modulus μ, the Poisson ratio σs, and their pressure and temperature derivatives (using the same dimensions as above) computed by the VRH (Voigt-Reuss-Hill) method are ρ Ks μ σs dKs/dT dμ/dT dσs/dT, 10−5 °C−1 dKs/dP dμ/dP dσs/dP(F) 3.224 1.286 0.811 0.240 −1.50 −1.30 0.93 5.37 1.80 0.42(O) 3.311 1.294 0.791 0.246 −1.56 −1.30 0.92 5.13 1.79 0.36