Thermodynamic properties of (Mg,Fe2+)SiO3 perovskite at the lower-mantle pressures and temperatures: an internally consistent LSDA+Ustudy

Abstract

The thermodynamic properties of (Mg0.9375Fe2+0.0625)SiO3 perovskite have been investigated at the pressure and temperature conditions of the lower mantle by first-principles calculations where iron is incorporated in the high and low-spin states for the first time. The electronic structure of ferrous Fe-bearing perovskite is modelled within the internally consistent local spin density approximation with a Hubbard correction U. The thermodynamic properties are derived from the calculation of the Helmholtz free energy within the quasi-harmonic approximation, which requires the phonon frequencies determined by direct calculations of the dynamic matrices. Incorporation of iron, irrespective of its spin states, decreases the acoustic phonon mode frequencies, but less affects high-energy optic modes, leading to decreasing of the acoustic wave velocities in Fe-bearing MgSiO3 perovskite, consistent with previous studies on the elasticity of this phase. This study suggests that the thermodynamic properties of silicate perovskite, such as the equation of state and isothermal bulk modulus, are not largely modified by the incorporation of 6.25 per cent of ferrous iron. Calculations of the static enthalpy of the iron-bearing perovskite in the 0-150-GPa-pressure range demonstrate that low-spin ferrous iron is unstable at the pressure conditions of the lower mantle. Finally, we clarify the perovskite-to-post-perovskite phase transition boundary in an (Mg0.9375Fe0.0625)SiO3 composition. Ferrous iron is found to decrease the transition pressure between the two phases with a small binary phase loop of 3–4 GPa at the lowermost mantle conditions from 111 to 115 GPa at 2500 K and from 116 to 119 GPa at 3000 K.