First-principles study of stability of the bcc and ω phases of a low Al concentration Nb_{1 - X}Al_x alloy

The phase stability and site occupancy of bcc (body centered cubic) Nb ₅Al and slightly rearranged atomic structures have been examined by means of first-principles calculations. In order to use first-principles methods, a periodic cell is required and we used ordered Nb₅Al compounds as a tractable example of a low Al concentration Nb _{1 - x}Al_x alloy (in this case, for about 17at.% Al). The instability against an ω-structure atomic displacement was also studied, since this structure is detrimental to ductility. Mulliken population analysis was used to provide an understanding of the hybridization between the atoms and the electronic origin of the site occupancy and instability of the underlying bcc structures. By making calculations for several different configurations of the Nb-Al system we estimated the strengths of the Nb-Nb and Nb-Al bonds. It is shown that the stability of the underlying bcc phases is directly related to Nb-Nb and Nb-Al first-nearest-neighbor interactions. The first-principles calculations were extended to finite temperature by including various contributions to the free energy. In particular, the vibrational free energy was calculated within the quasiharmonic approximation, and it is shown that the contribution of the low energy modes to the lattice entropy helps to stabilize ordered bcc phases against ω-type phase transformations. Semi-quasi-random structures were employed to study the stability of the ordered and disordered bcc phases. Our study showed, in agreement with experiment, that the ω, ordered, and disordered phases can coexist in a nonequilibrium state at finite temperature.