All-proportional solid solution versus two-phase coexistence in the Ti–V alloy by first-principles phase field and SQS methods

The microstructures of the Ti–V alloy are studied by purely first-principles calculations without relying on any empirical or experimental parameter. The special quasirandom structure model is employed to treat the all-proportional solid solution β phase, while the first-principles phase field method or its variant is employed to treat the coexistence phases. The linearity of the calculated local free energy against the integer Ti _n V _m composition in the cluster expansion method manifests a clear evidence of the solid solution behavior. From a detailed energy comparison, our results are consistent with the experimental fact that the Ti–V alloy is an all-proportional solid solution of the β phase at high temperatures and exhibits an α +β coexistence at low temperatures. Moreover, it is found that mosaic-type microstructures may appear as a metastable phase, as observed by many experiments. The first-principles criterion for the all-proportional solid solution behavior presented in this paper is very general and can be applied to any other binary or multi-component alloys.