Dynamical and thermodynamical instabilities in the disorderedRexW1−xsystem

Abstract

The dynamical and thermodynamical stability of the bcc and fcc disordered ${\mathrm{Re}}_{x}{\mathrm{W}}_{1\ensuremath{-}x}$ system is studied within the density-functional theory. The configurational part of the free energy is obtained from ab initio electron structure calculations together with the cluster expansion and the cluster variation formalism. Electronic excitations are accounted for through the temperature-dependent Fermi-Dirac distribution. The lattice dynamics of Re and W is studied using the density-functional linear-response theory. The calculated dispersion curves show that fcc Re is dynamically stable while bcc Re exhibits phonon instabilities in large parts of the Brillouin zone, similar to previous results for fcc W. Interestingly, the phonon dispersion curves for fcc Re show pronounced phonon anomalies characteristic of superconductors such as TaC and NbC. Due to the instabilities in bcc Re and fcc W the vibrational entropy, and therefore the free energy, is undefined. In order to predict the regions where the disordered ${\mathrm{Re}}_{x}{\mathrm{W}}_{1\ensuremath{-}x}$ alloy is unstable we calculate the phonon dispersion curves in the virtual crystal approximation. Then we apply a concentration-dependent nonlinear interpolation to the force constants, which are calculated through a Born--von K\'arm\'an fit to the ab initio obtained dynamical matrices. The vibrational free energy is calculated in the stable regions for the phases as a function of concentration. The complete analysis gives a region where the bcc phase would become thermodynamically unstable towards a phase decomposition into disordered bcc and fcc phases.