First-principles calculations of mechanical and thermodynamic properties of tetragonal Be₁₂Ti

The elastic and thermodynamic properties of tetragonal Be₁₂Ti under high temperature and pressure are investigated by first-principles calculations based on pseudopotential plane-wave density functional theory (DFT) within the generalized gradient approximation (GGA) and quasi-harmonic approximation (QHA). The calculated lattice parameters and bulk modulus are in good agreement with the available experimental data. The calculated elastic constants of Be₁₂Ti increase monotonously with increasing pressure, and the elastic stability criterion and the phonon dispersion calculation show that the Be₁₂Ti crystal satisfies the mechanical and dynamic stability under applied pressure (0-100 GPa). The related mechanical properties such as bulk modulus (B), shear modulus (G), Young's modulus (E), and Poisson's ratio (ν) are also studied for polycrystalline of Be₁₂Ti; the calculated B/G value shows that Be₁₂Ti behaves in a brittle manner, and higher pressure can significantly improve the brittleness of Be₁₂Ti. The elastic anisotropy is demonstrated by the elastic anisotropy factors. The direction-dependent Young's modulus and bulk modulus of Be₁₂Ti are dealt with in detail under pressure from 0 GPa to 100 GPa. The pressure and temperature dependencies of the relative volume, the bulk modulus, the elastic constants, the heat capacity and the thermal expansion coefficient, as well as the entropy are obtained and discussed using the quasi-harmonic approximation in the ranges of temperature 0-1600 K and pressure 0-100 GPa.