Phase equilibria of (Mg,Fe)₂SiO₄ at the Earth's upper mantle conditions from first-principles studies

Phase equilibria of α, β, and γ (Mg,Fe)₂SiO₄ are important to understanding the mineralogy of the Earth's upper mantle. Using the first principles approach, we studied thermodynamic properties and phase stability fields of Fe₂SiO₄. We show that the correct phase transition sequence in Fe₂SiO₄ (α→γ) can be obtained with the DFT+self-consistent Hubbard U method, while standard DFT methods (LSDA and σ-GGA) as well as the DFT+constant U method fail the task. The vibrational virtual crystal approximation was used to derive the phonon density of state of the Fe₂SiO₄ polymorphs. High-pressure thermodynamic properties of Fe₂SiO₄ are then derived with the aid of the quasi-harmonic approximation. They are in very good agreement with experiments. The phase diagram of the (Mg,Fe)₂SiO₄ system is calculated under the assumption of ideal mixing within α, β, and γ solid solutions. The model permits the investigation of the temperature and pressure effects on the phase boundaries. The widths of the divariant α-β and β-γ loops are barely sensitive to temperature between 1473 and 1873K. This study shows the promise of applying the DFT+self-consistent Hubbard U method to study phase equilibria of iron-bearing Earth minerals.