Prediction of ordered structures in the bcc binary systems of Mo, Nb, Ta, and W from first-principles search of approximately 3,000,000 possible configurations

We predict ground states of the refractory alloys $\mathrm{Nb}-\mathrm{Mo}$, $\mathrm{Nb}-\mathrm{W}$, $\mathrm{Ta}-\mathrm{Mo}$, and $\mathrm{Ta}-\mathrm{W}$ by combining first-principles calculated energies of ≳ 50 configurations for each system with a “mixed-basis cluster expansion,” whose interaction types are chosen with a genetic algorithm search. We find ground states that deviate substantially from the simplified predictions in the literature. These ground states are linked to relatively complex underlying interactions, leading to substantially lower order-disorder transition temperatures than would be expected from simple interaction models, consistent with the extent of the experimentally observed bcc solid solution phases.