Predictions of mechanical and thermodynamic properties of Mg₁₇Al₁₂ and Mg₂Sn from first-principles calculations

Using first-principles calculations, we predict mechanical and thermodynamic properties of both Mg₁₇Al₁₂ and Mg₂Sn precipitates in Mg-Al-Sn alloys. The elastic properties including the polycrystalline bulk modulus, shear modulus, Youngs modulus, Lames coefficients and Poissons ratio of both Mg₁₇Al₁₂ and Mg₂Sn phases are determined with the Voigt-Reuss-Hill approximation. Our results of equilibrium lattice constants agree closely with previous experimental and other theoretical results. The ductility and brittleness of the two phases are characterized with the estimation from Cauchy pressure and the value of B/G. Mechanical anisotropy is characterized by the anisotropic factors and direction-dependent Youngs modulus. The higher Debye temperature of Mg₁₇Al₁₂ phase means that it has a higher thermal conductivity and strength of chemical bonding relative to Mg₂Sn. The anisotropic sound velocities also indicate the elastic anisotropies of both phase structures. Additionally, density of states and Mulliken population analysis are performed to reveal the bonding nature of both phases. The calculations associated with phonon properties indicate the dynamical stability of both phase structures. The temperature dependences of thermodynamic properties of the two phases are predicted via the quasi-harmonic approximation.