First-principles lattice dynamics and thermodynamic properties of α-, θ-, κ- and γ-Al₂O₃ and solid state temperature-pressure phase diagram

γ-Al₂O₃ is a commonly observed high temperature alumina phase during Al-based alloy oxidation. Due to the partially ordered, defective nature of the spinel structure arising from the partial occupancy in the Al sites, first-principles prediction of the thermodynamic properties of γ-Al₂O₃ has been challenging. In this work, employing the first-principles quasiharmonic approach, we obtain the finite temperature thermodynamic properties of γ-Al₂O₃, including entropy, chemical potential, heat capacity, thermal expansion coefficient, and elastic constants and the results are compared with those calculated for the other three alumina phases, i.e., α-Al₂O₃, θ-Al₂O₃, and κ-Al₂O₃. The calculated lattice constants and the predicted relative phase stability under 0 K and 0 GPa, α>κ>θ>γ, are consistent with experimental values and existing calculations, respectively. Based on the results, we constructed the temperature-pressure phase diagram covering the four Al₂O₃ phases (α, κ, θ, γ), which could provide for experimentally synthesizing the different alumina phases.