(Mg,Fe)SiO3 in the lower mantle: phase equilibria and stability, influence of spin on compressibility and elasticity

We studied Fe-bearing magnesium silicate perovskite and post-perovskite over a range of thermodynamic conditions corresponding to the Earth's mantle using computational (density-functional theory) techniques. We analyzed the crystallochemical effects induced by the presence of Fe in the structure and we monitored the compressibility as a function of Fe spin state and Fe content. At 0K in static calculations the high spin states are more stable over low spin states over the whole mantle pressure range for both perovskite and post-perovskite. We find that the compressibility of the structure is slightly anisotropic and depends on the spin state of Fe. The mechanism responsible for this is the tilt of octahedra that act as nearly rigid bodies. We observed that low-spin Fe2+ changes less the crystallochemical properties of MgSiO3 than the intermediate- or high-spin Fe2+ do. We derived the seismic properties of (Mg,Fe)SiO3 perovskite and post-perovskite as a function of Fe2+ spin state and Fe distribution and observed that the effects of Fe2+ spin state are rather small on the compressional seismic wave velocities and larger on the shear seismic wave velocities. However, these variations might not be easily observable in the seismic profiles of the mantle because of other factors, like temperature, spin transitions in magnesiowüstite or the presence of other minor elements in perovskite. During the calculation of elastic moduli from density function perturbation theory, we found several cases where intermediate compositions on the Mg-Fe solid solution are dynamically unstable. We discuss in detail the implications of such instabilities.