First principles calculations of theσ andχ phases in the Mo–Re and W–Re systems

Abstract

The total energies of all the ordered configurations of theσ andχ phases have been calculated by using first principles methodology in both Mo–Re andW–Re systems. These two complex structures possess 5 and 4 inequivalent sitesgenerating 32 and 16 different ordered configurations, respectively, for a binaryA–B system. The converged total energies of all the fully relaxed structures have been used tocompute the occupancy of the inequivalent sites as a function of compositionand temperature by using the Bragg–Williams approximation in the completecomposition range. It is shown that the configurational entropy stabilizes theσ andχ phases in the Mo–Re and W–Re systems. The results evidence the preference of Re forlower coordination number site occupancy and are in very good agreement with theexperimental measurements. Tentative ab initio phase diagrams have also been drawn.