Temperature-dependent elastic stiffness constants of a- And θ-Al ₂O₃from first-principles calculations

Temperature-dependent elastic stiffness constants (c_ijs), including both the isothermal and isoentropic ones, have been predicted for rhombohedral α-Al₂O₃ and monoclinic Ö-AI2O3 in terms of a quasistatic approach, i.e., a combination of volume-dependent c _ijs determined by a first-principles strain versus stress method and direction-dependent thermal expansions obtained by first-principles phonon calculations. A good agreement is observed between the predictions and the available experiments for α-Al₂O₃, especially for the off-diagonal elastic constants. In addition, the temperature-dependent c_ijs predicted herein, in particular the ones for metastable Ö-Al₂O₃, enable the stress analysis at elevated temperatures in thermally grown oxides containing &- and θ-Al ₂O₃, which are crucial to understand the failure of thermal barrier coatings in gas-turbine engines.