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

Abstract

SUMMARY 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.

Computational support for a pyrolitic lower mantle containing ferric iron

“…The computational methods, parameters and pseudopotentials are the same as in our previous studies [21][22][23] . Electronic structures are calculated based on density functional theory, and exchange-correlation potential is described by the LSDA+U formula, where the U values (Supplementary Table 2) are determined by the internally consistent method 24 .…”

“…Based on our previous works 22,23 combined with the results of Fe 3+ Al 3+ -bearing MgBr, the magnetic properties and phonon dispersion of MgBr incorporated with Fe and Al are generally Supplementary Fig. 1).…”

“…The thermal EoS and thermodynamic properties of Fe 2+ -bearing MgO (ref. 21) and MgBr with Fe 2+ and Fe 3+ incorporation 22,23 have been calculated comprehensively by using the lattice dynamics approach and the quasi-harmonic approximation. Hubbard U values based on the internally consistent LSDA+U method 24 are used to correct for the large on-site Coulomb interaction in iron-oxide bonding, where LSDA stands for the local spin-density approximation.…”

Seismic Detection of Post-perovskite Inside the Earth

“…Experiments and calculations on binary systems, i.e. ( Mg 1−x Fe x )SiO 3 , have indicated that adding Fe 2+ to MgSiO 3 will decrease the pressure of the phase boundary significantly (Mao et al 2004(Mao et al , 2005Caracas and Cohen 2005a), and measurements by different groups using different pressure standards have consistently shown that for compositions close to (Mg 0.9 Fe 0.1 )SiO 3 , the phase transformation to post-perovskite begins at around 111 GPa at 2500 K (Shieh et al 2006;Catalli et al 2009;Metsue and Tsuchiya 2012). Most studies show that adding aluminium has the opposite effect, increasing the phase boundary by ~5 GPa for ~5 mol% Al 2 O 3 e.g.…”

Detecting a Magnesiowüstite Phase Transition in the Lower Mantle by Inversion of Geomagnetic Data

“…Исследования фазовых переходов минералов при давлениях и температурах, близких к условиям в нижней мантии, представлены в ряде работ [Lin et al, 2007;Овчинников, 2011;Metsue, Tsuchiya, 2012]. В работе [Ohta et al, 2008] выявлено увеличение электропроводности перовскита до значений ≥ 100 См/м при условиях, реализующихся над границей ядро-мантия (CMB) вследствие фазового пе-рехода в постперовскитную фазу.…”