First-principles calculations of finite-temperature elastic properties of Ti2AlX (XÂ =Â C or N)

First-principles calculations were carried out to investigate the finite-temperature elastic properties of Ti2AlX (X = C or N). In particular, the dependence of elasticity on temperature was determined through the stiffness-volume and volume-temperature relationships, i.e., volumetric stiffness and thermal expansion. The volumetric stiffness was achieved from the calculations of elastic constants at different volumes using the stress-strain approach. The thermal expansion was derived from the total free energy of the system taking into account both vibrational and electronic contributions. The vibrational contribution was calculated using the supercell method where the electronic contribution resulted from one-dimensional integration of electronic density of states (DOSs). Calculation results for Ti2AlC are in good agreements with available experiments for temperatures below 1600 K. This lends the predictions of elastic properties for Ti2AlN, of which chemistry are close to Ti2AlC, the eligibility and reliability for the same range of temperature. For temperature above 1600 K, the predictions tend to become less accurate since the DFT approach is not able to capture the fluctuation of external stress fields of which effect on thermal softening becomes stronger at higher temperatures.