The elastic properties of (Mg_xFe_(1−x))O solid solutions

Abstract

The velocities of compressional (V_p) and shear (V_s) waves in five well-characterized polycrystalline aggregates of (Mg_xFe_(1−x))O (0.85 ≧ x > 0.23) have been measured as functions of hydrostatic pressure (to 6 kbar) using the techniques of ultrasonic pulse transmission and super-position. Both velocities decrease systematically with increasing iron content. The elastic properties of stoichiometric FeO are inferred by inverting the solid solution data using a model in which the single crystal compliances (s_(ij)) vary linearly with the volume fraction of either end member. This model, along with identification of the aggregate moduli with the arithmetic average of the Hashin-Shtrikman bounds, may be used to describe the variation of both bulk (K_s) and shear modulus (μ_s) with composition for polycrystalline aggregates of phases of arbitrary symmetry. For the case of bulk modulus of an isotropic aggregate of crystals of cubic symmetry, the present model yields the formula first proposed by Liu (1968). The isotropic elastic moduli of FeO thus obtained (K_s = 1.82±0.05 Mbar, μ_s = 0.59±0.02 Mbar) are consistent with the wüstite data of Mizutani et al. (1972) but inconsistent with bulk moduli derived from static compression data by Mao et al. (1969) and Rosenhauer et al. (1976). An alternative description of the variation of μ with x based on consideration of the solid solutions as two-phase aggregates is also presented. The observed differences in elastic moduli between MgO (K_s = 1.63 Mbar, μ_s = 1.31 Mbar) and FeO (K_s = 1.82 Mbar, μ_s = 0.59 Mbar) are consistent with the effects of Mg/Fe substitution in other oxide and silicate crystal structures.