Anisotropic elastic and thermal properties of titanium borides by first-principles calculations

The anisotropic elastic and thermal expansions of the titanium borides (TiB₂, Ti₃B₄, TiB Pnma and TiB Fm-3m) are calculated from first-principles using density functional theory. All borides show different anisotropic elastic properties; the bulk, shear and Young's moduli are consistent with those determined experimentally. The temperature dependence of thermal expansions is mainly caused by the restoration of thermal energy due to phonon excitations at low temperature. When the temperature is higher than 500 K, the volumetric coefficient is increased linearly by increasing temperature. Meanwhile, the heat capacities of titanium borides are obtained based on the knowledge of thermal expansion coefficient and the elasticity, the calculations are in good agreement with the experiments.