First principles calculations of the σ and χ phases in the Mo-Re and W-Re systems.

The total energies of all the ordered configurations of the σ and χ phases have been calculated by using first principles methodology in both Mo-Re and W-Re systems. These two complex structures possess 5 and 4 inequivalent sites generating 32 and 16 different ordered configurations, respectively, for a binary A-B system. The converged total energies of all the fully relaxed structures have been used to compute the occupancy of the inequivalent sites as a function of composition and temperature by using the Bragg-Williams approximation in the complete composition range. It is shown that the configurational entropy stabilizes the σ and χ phases in the Mo-Re and W-Re systems. The results evidence the preference of Re for lower coordination number site occupancy and are in very good agreement with the experimental measurements. Tentative ab initio phase diagrams have also been drawn.