Temperature-dependent mechanical properties of alpha-/beta-Nb ₅Si₃ phases from first-principles calculations

The temperature-dependent structural properties and anisotropic thermal expansion coefficients of α-/β-Nb₅Si₃ phases have been determined by minimizing the non-equilibrium Gibbs free energy as functions of crystallographic deformations. The results indicate that the crystal anisotropy of α-Nb₅Si₃ phase is much more temperature dependence than that of β-Nb₅Si₃ phase. The total/partial density of states of α-/β-Nb₅Si ₃ phases are discussed in detail to analyze their electronic hybridizations. It is demonstrated that the bonding of the two phases is mainly contributed from the hybridization between Nb-4d and Si-3p electronic states. The temperature-dependent mechanical properties of α-/β-Nb ₅Si₃ phases are further investigated via the quasi-harmonic approximation method in coupling with continuum elasticity theory. The calculated single-crystalline and polycrystalline elasticity shows that both phases are mechanically stable and exhibit the intrinsic brittleness. The results also suggest that α-Nb₅Si₃ phase possesses a superior ability of compression resistance but an inferior ability of higherature resistance of mechanical properties than those of β-Nb ₅Si₃ phase. The bonding features of α-/β- Nb₅Si₃ phases are discussed by means of charge density difference analysis in order to explain the difference of the temperature-dependent mechanical properties between the two phases.