APPLICATION OF FIRST-PRINCIPLES METHODS TO BINARY AND TERNARY ALLOY PHASE-DIAGRAM PREDICTIONS

First-principles energy calculations, using the LMTO ASA method, have been performed for seven binary alloys (Ti-Al, Ti-Mo, Ti-Nb,Ti-W, Al-Mo, Al-Nb and Al-W). For the Ti-Mo system, our results lead to stability of the B32 ordered compounds, in contradiction with the experimental phase diagrams, which display a miscibility gap for the BCC lattice. Meanwhile, recent unpublished neutron diffraction measurements have been performed at a high temperature; they indicate the presence of a short-range order by a (1/2 1/2 1/2) q-vector, in perfect agreement with the stability of B32 at low temperatures. Secondly, we proceed to a cluster expansion, using the Connolly-Williams inversion scheme and the formation energies of a finite set of ordered configurations. We obtain, for each alloy, a set of cluster interactions and we test the transferability of this set to the formation energies of other ordered compounds. Finally, in order to calculate a ternary phase diagram (isotherm), the Connolly-Williams inversion scheme has been applied to a ternary formation energy. Then, we have calculated an isotherm of the Ti-Al-Nb system and found perfect agreement with the isotherm already calculated in an earlier publications, using a different approach.