Elasticity and Equations of State of Olivines in the Mg2SiO4-Fe2SiO4 System

Abstract

Summary Presented first in this paper are the elasticity data of seven olivines as a function of pressure, temperature, and Fe/Mg ratio. The elasticity data include (i) P and S wave velocities and their first derivatives with respect to pressure and temperature, (ii) the shear and bulk moduli and their first pressure and temperature derivatives, and (iii) Poisson’s ratio and its pressure and temperature derivatives (all evaluated at zero pressure and at ambient temperature). The critical thermal gradients for density and for P and S wave velocities are presented for olivine with different Fe/Mg ratios. Also presented are the Debye temperature and Gruneisen’s parameters yG and 6, for olivine as a function of Fe/Mg ratio. Next, incorporating these elasticity data with theories, equations-of-state parameters of olivine and olivine-transformed spinel as a function of Fe/Mg are found. The equations of state of olivine are then presented; a pressure-volume-temperature (PVT) relation for olivine is examined as a function of temperature and Fe/Mg ratio. Finally, based on F. Press’s recent Monte Carlo solutions, the present elasticity data are related to the Earth’s upper mantle within the framework of a peridotitic model, Typically, for 100 Fo, 50 Fo, and 100 Fa olivines, values of density po (in g~m-~), the P and S wave velocities (in km s-’), the adiabatic bulk modulus K, (in mb) and its pressure derivative dKJdp, Gruneisen’s parameters yc and 6,, the Debye temperature OD (in OK), and the critical thermal gradients Gi, where i stands for density and P and S wave velocities, are as follows: