Exploring the Thermodynamic Landscape of 24 Al ₂ O ₃ Polymorphs: Mapping Pressure–Temperature-Induced Phase Transitions Under Extreme Conditions

The polymorphism of Al2O3 and the resulting variation in structural, energetic, and thermal properties were systematically studied via density functional theory (DFT) employing two generalized-gradient approximation (GGA) exchange–correlation functionals. We optimized 24 distinct polymorphs, encompassing all seven crystal systems and comprising five to 160 atoms per primitive unit cell, to determine total energies and volumes per formula unit. The α-corundum phase, with its relatively small volume, is the most energetically stable polymorph, in agreement with well-established results in the literature. Structures with slightly larger cell volumes exhibit marginally higher energies and intermediate atomic densities, while those with significantly different volumes are substantially less stable. Orthorhombic phases with volumes smaller than α-corundum correspond to recognized high-pressure polymorphs. Analysis of enthalpy as a function of hydrostatic pressure reveals pressure-induced phase transitions, including the well-known transformation from α-corundum to the Rh2O3(II) structure and a newly identified transition to a CaIrO3-type arrangement at pressures that can occur in Earth’s lower mantle where pressures range from about 24 to 136 GPa. Dynamical stability was evaluated through dispersion relations of acoustic phonon branches; only ten polymorphs showed no phonon softening, indicating true local minima on the potential energy surface. For these stable polymorphs, phonon spectra were presented and discussed. Thermal properties, including heat capacity, were computed and compared with Dulong-Petit and Debye models to extract Debye temperatures. Finally, temperature-dependent Gibbs energies were used to predict temperature-induced phase stability, underscoring the exceptional thermal resilience and elevated formation temperature of α-Al2O3 under extreme conditions.