First-principles study phonon and thermodynamic properties of binary W-Mo alloys

Abstract

The effects of molybdenum alloying on phonon and thermodynamic properties of binary tungsten-molybdenum alloys have been studied by first principles method based on density functional perturbation theory (DFPT). Firstly, the results of lattice constants display that our calculated values for W 1-x Mo x (x=0, 0.25, 0.5, 0.75, 1) are broadly consistent with other theoretical and experimental data. Next, the lattice dynamics and density of states for binary W-Mo alloys are investigated. The calculated phonon frequencies of W 1-x Mo x (x=0, 0.25, 0.5, 0.75, 1) present a remarkable hardening in the wake of the enhancement of the proportional fraction of Mo, which indicates that doping Mo will improve the lattice stability of W. Finally, several thermodynamic properties of binary tungsten-molybdenum alloys, such as C v , △E, △F, S, are predicted reasonably by utilizing the linear-response techniques. In addition, by investigating the Debye temperature of W 1-x Mo x (x = 0, 0.25, 0.5, 0.75, 1), we observe that the Debye temperature of the system raises with the increase of Mo concentration x, which further confirms that its change is obviously consistent with the results of the phonon dispersion relationship of the sample. • The phonons of W 1-x Mo x present a significant hardening with the increase of x. • The thermodynamic properties of W-Mo alloys including C v , △E, △F and S are predicted. • The Debye temperatures of W 1-x Mo x raise as x is elevated.