Relative stability of bcc structures in ternary alloys withTi50Al25Mo25composition

In reviewing the literature that concerns the CsCl-type intermetallic compound ${\mathrm{Ti}}_2\mathrm{AlMo}$ (B2), the question arises if this compound is preferably formed with respect to the high-temperature bcc completely disordered structure (A2). Our present work takes an ab initio approach to this subject. The first-principles linear-muffin-tin-orbital method was used to calculate the total energy of a series of bcc structures in the ternary system Ti-Al-Mo. Second, a cluster expansion in the tetrahedron approximation was calculated for each formation energy. Finally, a Connolly-Williams-like inversion scheme was used to obtain the formation energy of both the A2 phase and the partially ordered structure B2. From the calculations, the B2 formation energy came out to be aprox 10 mRy/atom lower than the A2 energy, suggesting a relative greater stability. The relative stability of other possible structures with the same global composition ${\mathrm{Ti}}_{50}{\mathrm{Al}}_{25}{\mathrm{Mo}}_{25}$ is discussed.