First-principles study of phase equilibrium in Ti-V, Ti-Nb, and Ti-Ta alloys

The subsolidus equilibrium phase diagrams of Ti-V, Ti-Nb and Ti-Ta alloys have been computed through cluster expansion, lattice dynamics and Monte Carlo modeling methods combined with Density Functional Theory total-energy calculations. Computed phase boundaries in Ti-V alloy are found to be in good agreement with reported CALPHAD assessed experimental boundaries. For Ti-Ta system, the computed phase boundaries agree well with CALPHAD boundaries for Ta-rich alloys. For Ti-rich alloys, the transformation temperatures are overestimated by up to 200 K. In the case of Ti-Nb system, the calculated boundary of the bcc-solid-solution phase decreases rapidly in temperature with increasing Nb concentration compared to CALPHAD boundary, deviating from the latter by up to 600 K at 80% Nb. Our calculation gives qualitatively correct hcp-solid-solution regions for all the three alloy systems (i.e., solubility of V/Nb/Ta in hcp Ti). A key difficulty in modeling these systems is the presence of mechanical instability in the bcc phase at high Ti concentration. In this work, we circumvent this difficulty by excluding structures exhibiting instability in the cluster expansion construction process. We find that, while such a scheme is often appropriate (as in the Ti-V and Ti-Ta systems), it can become unreliable when the result exhibit a too strong sensitivity to the exclusion rule used (as in the Ti-Nb system). In all systems, we find that the inclusion of lattice vibration effects is crucial to obtain even qualitative agreement with experiment.