Elasticity of (Mg, Fe)(Si, Al)O3-perovskite at high pressure

The most abundant mineral on Earth has a perovskite crystal structure and a chemistry that is dominated by MgSiO3 with the next most abundant cations probably being aluminum and ferric iron. The dearth of experimental elasticity data for this chemically complex mineral limits our ability to calculate model seismic velocities for the lower mantle. We have calculated the single crystal elastic moduli (cij) for (Mg, Fe3 +)(Si, Al)O3 perovskite using density functional theory in order to investigate the effect of chemical variations and spin state transitions of the Fe3+ ions. Considering the favored coupled substitution of Mg2+-Si4 + by Fe3+-Al3+, we find that the effect of ferric iron on seismic properties is comparable with the same amount of ferrous iron. Ferric iron lowers the elastic moduli relative to the Al charge-coupled substitution. Substitution of Fe3+ for Al3+, giving rise to an Fe/Mg ratio of 6%, causes 1.8% lower longitudinal velocity and 2.5% lower shear velocity at ambient pressure and 1.1% lower longitudinal velocity and 1.8% lower shear velocity at 142 GPa. The spin state of the iron for this composition has a relatively small effect (< 0.5% variation) on both bulk modulus and shear modulus.