Theoretical investigation of superconductivity in Ba(AlSn) under pressure

•The electronic structure calculations showed that the Ba(AlSn) have a metallic character.•The Ba(AlSn) is mechanically and dynamically stable.•The full phonon dispersions at first brillouin zone was obtained as a function of pressure.•The Vicker’s hardness is 8.16 GPa.

The compound of Ba(AlSn) from ternary superconductors exhibits the superconductivity behaviour below the temperature 2.9 K. We report the results of an ab initio study based on electronic, and detailed lattice dynamical properties as a function of pressure of superconducting material. The phonon dispersion curves along the high-symmetry directions and phonon frequencies parameters at the Brillouin zone center are computed by using density functional perturbation theory while the elastic constants are calculated in metric-tensor formulation. The Vickers hardness belonging to the compound is also evaluated clearly. The band structure, partial densities of states and Fermi surface topology are also discussed in detail. At the same time we describe the relationship between the properties determined and superconducting characteristic.