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First-principles phase-stability study of fcc alloys in the Ti-Al system.

We present the results of a first-principles study of the composition-temperature phase diagram for fcc-based Ti-Al alloys and the related structural and thermodynamic properties. In the approach taken in this study, local-density-functional theory is combined with the formalism of the cluster-variation method (CVM). In particular, the formation energy, bulk modulus, and atomic volume of metastable fcc Ti, fcc Al, and nine ordered fcc intermetallic Ti-Al compounds have been calculated using the full-potential linear-muffin-tin-orbital method. It is shown how the results of these calculations can be used to obtain a set of volume-dependent effective cluster interactions (ECI's) which parametrize the total energies of fcc-based Ti-Al alloys. We discuss in detail how these parameters can be used to determine formation energies, atomic volume, and bulk moduli for both ordered and disordered alloys, and as an example we calculate these properties for alloys containing random distributions of Ti and Al atoms as a function of composition. Furthermore, these ECI's are used in conjunction with the CVM to calculate the solid-state, fcc, composition-temperature phase diagram.