Dynamical and thermodynamical instabilities in the disorderedRexW1−xsystem

Abstract

The dynamical and thermodynamical stability of the bcc and fcc disordered Re x W 1Ϫx 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 Re x W 1Ϫx 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 Kármán 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.

Metastable cubic and tetragonal phases of transition metals predicted by density-functional theory

“…1 for the ten elastically stable fcc structures revealing that all structures (Sc, Ti, Co, Y, Zr, Tc, Ru, Hf, Re, and Os) are in fact dynamically stable. We note that dynamical stability of fcc Co and fcc Re at 0 K was reported in previous studies of their lattice dynamical properties [20,57].…”

The effect of lattice vibrations on substitutional alloy thermodynamics

“…This model has been commonly used to interpret neutron scattering measurements of phonon dispersion curves in the case of disordered alloys Nagel et al, 1995). It has also been used in a some theoretical investigations (Cleri and Rosato, 1993;Persson et al, 1999). However, the virtual crystal approximation has been repeatedly shown to be insufficiently accurate for the purpose of calculating differences in vibrational entropies between distinct compounds (Althoff et al, 1997;Ravelo et al, 1998;Shaojun et al, 1998).…”

Thermodynamics of ordered and disordered phases in the binary Mo-Ru system

“…7,11,[15][16][17][18][19] Here, Grimvall et al 12 and Persson et al 20 have suggested that dynamical instability of the hcp Mo plays a decisive role.…”