Elastic and vibrational properties of Mg2Si1−xSnx alloy from first principles calculations

The structural, elastic and phonon properties of Mg2Si1−xSnx alloy are investigated by performing density functional theory and density functional perturbation theory calculations. The calculated lattice parameter increases with the increase of Sn content obeying Vegard’s Law that is in good agreement with available experimental data. Shear modulus, Young’s modulus and sound velocities are determined from the obtained elastic constants. Phonon dispersion curves show a pronounced softening with increasing of Sn content. The softening mechanism has been discussed based upon the element mass and bond strength. Besides, phonon contribution to the Helmholtz free energy, the entropy and the constant-volume heat capacity are calculated within the harmonic approximation based on the calculated phonon density of states. Results show Mg2Si1−xSnx is thermodynamically more stable with higher Sn content.