Fundamentals of elasticity of (Mg_1-x, Fe_x) ₂SiO₄ olivine

We study the influence of iron on the elasticity of (Mg_1-x, Fe_x)₂SiO₄ olivine (0≤x≤0.125), a major constituent of the Earth's upper mantle. We calculate static elastic properties by first principles for this solid solution and investigate the effect of atomic arrangement, an artifact of supercell calculations, on all single crystal and poly-crystalline elastic moduli. From calculated wave propagation velocities we find the heterogeneity ratios of shear to compressional wave velocity, and bulk sound to shear wave velocity. Their values are, though limited to composition considerations, marginally consistent with seismic tomography.