First-principles calculations of thermodynamic properties and phase transitions in Al$_{2}$O$_{3}$ and Ga$_{2}$O$_{3}$ at high temperature and high pressure

Using \textit{ab initio} density functional theory and statistical quasi-harmonic approximation theory, we have calculated thermodynamic potentials of mineral Al$_{2}$O$_{3}$ materials and the related Ga$_{2}$O$_{3}$ materials over a wide range of temperature and pressure (T-P) conditions. The equilibrium T-P phase diagrams are predicted to understand the trend of pressure induced phase transitions in group IIIB oxides. Furthermore, we theoretically explored the possible new high-pressure structures of Ga$_{2}$O$_{3}$. Finally, we derived experimentally measurable thermal properties, such as lattice thermal expansion, heat capacity, and isothermal compressibility. Our calculated thermal properties are in excellent agreement with available experiments.