Lattice dynamics and thermodynamic properties of (Mg,Fe²⁺)SiO₃postperovskite

Abstract

[1] Phonon dispersion relations and vibrational density of states of (Mg 0.9375 Fe 0.0625 )SiO 3 postperovskite have been determined by direct first-principles calculations of the dynamical matrix up to 150 GPa. Incorporation of iron in the postperovskite phase, irrespective of the two investigated configurations and the spin state, was found to decrease the acoustic phonon frequencies but to have a minor effect on the optic modes at high frequencies. The phonon dispersion curves exhibit negative phonon frequencies below 10 GPa when iron is incorporated in the high or low spin state and indicate unstable dynamic structures. Then, the calculated phonon frequencies of dynamically stable structures are used to determine vibrational contributions to the Helmholtz free energy within the quasi-harmonic approximation. The high temperature equation of state and several thermodynamic properties are then derived for (Mg 0.9375 Fe 0.0625 )SiO 3 postperovskite and compared with those of pure MgSiO 3 postperovskite. The results show that a low concentration of iron, irrespective of high spin or low spin, in MgSiO 3 postperovskite has a minor effect on the thermodynamic properties at pressure-temperature conditions of the lowermost part of the Earth's mantle.

Single-crystal structure determination of (Mg,Fe)SiO3postperovskite

“…The various model compositions provided a consistent Fe content of ∼10 mol% for the bulk composition in the mantle (1). The consistency of the structural parameters between the Fe-bearing ppv in our experiments and the Fe-free ppv from the theoretically calculated structural model (2) suggests that the Fe content in the mantle has a negligible effect on the crystal structure of the ppv phase, in agreement with the previous theoretical calculations suggesting a minor effect of 6.25 mol% Fe content on the thermodynamic properties of the ppv phase at P-T conditions of the lowermost mantle (20). However, if the ultralow-velocity zones at the very base of the lower mantle are highly enriched in Fe from reacting with the core (6), the ppv phase might alter its space group from Cmcm to Pmcm depending on the degree of Fe enrichment (8).…”

Shear response of Fe-bearing MgSiO₃ post-perovskite at lower mantle pressures

“…19,20) These calculations were performed within the density functional theory 27) implemented in Quantum Espresso. 28) For the calculation of the Fe-bearing system, we adopted the internally consistent LSDA+ U formalism, 29,30) where the on-site Coulomb interaction between the d -states of Fe was determined at 120 GPa in our previous study, 25) equal to 3.639 eV and to 5.408 eV for HS and LS, respectively. We applied the planewave method combined with ab initio psuedopotentials which are the same as those used in our previous studies.…”

“…We applied the planewave method combined with ab initio psuedopotentials which are the same as those used in our previous studies. 8,10,25) The planewave cut-off energy was set to 70 Ry and the Brillouin zone was sampled on a grid built for each supercell geometry.…”

“…The total energy of the Fe-bearing cell with a geophysically relevant iron concentration of 8.3% 24) was calculated within the internally consistent LDA+ U formalism. 25) To examine the influence of the spin state on the shear response, Fe was treated both in the high spin (HS) and low spin (LS) states, even though several studies have suggested that Fe 2+ remains in the HS state in the whole pressure range of the D'' layer. 25,26) …”

“…25) To examine the influence of the spin state on the shear response, Fe was treated both in the high spin (HS) and low spin (LS) states, even though several studies have suggested that Fe 2+ remains in the HS state in the whole pressure range of the D'' layer. 25,26) …”