Structural complexity in binary bcc ground states: The case of bcc Mo-Ta

Traditional sorting diagrams for ground states $(T=0\mathrm{}$ stable atomic configurations) of bcc-based binary alloys predict simple crystal structures when simple parametric interactions (e.g., first few pairs) are assumed. However, the range and magnitude of interactions for real systems is not a priori known, and could lead to much greater structural complexity. We combine a density functional theory based, deterministic mixed-basis cluster expansion with an exhaustive enumeration scheme of $3\times {10}^6$ possible structures to determine the ground states of the bcc alloy Mo-Ta. The result is a rich ground-state line, changing one’s outlook on bcc structural stability. We find Mo-rich (100) superlattices (including ${C11\mathrm{}}_{\mathrm{b}}$ and $B2)$ coexisting with complex large-cell structures $({\mathrm{Mo}}_4{\mathrm{Ta}}_9$ and ${\mathrm{Mo}}_4{\mathrm{Ta}}_{12}).\mathrm{}$ We demonstrate that a systematic cluster expansion construction scheme which includes both high-order pairs and many-body figures is a necessity to capture the ground states of Mo-Ta.