Stable, unique, novel Fe-rich compounds, loop 6: Fe-Co-X gives orderings, not new compounds

This loop moved the search to Fe-Co and Fe-Co-X. We put Fe and Co onto the two late-metal sites of 3,296 prototype structures, kept 555 new cells and scored them all on the Orb hull. Two landed on the hull and 38 within 25 meV/atom, but none is a new kind of compound. Every one is an fcc or bcc lattice decorated with Fe, Co and X, an Fe/Co ordering of a structure that Fe-X or Co-X already has, or a Heusler with one atom missing. Fe and Co are too alike for a ternary to beat their own mixing, so no SUN compound came out of this chemistry.

What we measured

Cells were relaxed and scored with Orb v3 on the hull route, against MP, Alexandria, GNoME and Ouro references. Novelty came from the novelty route. The five cells that survived the structure checks were also scored on the hull route's published-PBE surface, where the references are published PBE energies but the candidate is still scored by Orb. No DFT was run.

Over the whole batch: 2 of 555 cells sit on the Orb hull (0.36 %), 38 within 25 meV and 87 within 50. Of the 38: 10 are decorations, 24 are Fe/Co orderings of a type already in the databases, 2 are stackings from the same Laves family, 1 is already known (Zr₃Fe₇Co₂, Alexandria agm005622237), and 1 is Fe₃Co₈Ge₄. Zr systems gave 16 of the 38, Ti 9 and Nb 4. Fe-Co-B, -C, -P, -Sn and binary Fe-Co gave nothing within 25 meV; the closest were B at 27, C at 257 and Fe-Co at 101.

For a while Fe₃Co₈Ge₄ looked like the one real new structure, since its all-Fe parent has 15 atoms and it matched no binary type. Its sites give it away. Fe sits on 3c, Co on 8g and Ge on 3d + 1b, with a = 5.65 Å, and the 1a site is empty: it is the FeCo₂Ge Heusler, which is known, with one atom in sixteen removed. Look for the hole at the cube corner:

Fe₉CoB₆ is the only tetragonal cell within 30 meV that is not a decoration. It is (Fe,Co)₅B₃ on the Cr₅B₃ type, built from the made compound Cr₉FeB₆, and it sits about 30 meV above Fe₂B + FeB + CoB on both surfaces:

What the hypotheses did

• H10: what lands on the hull is mostly Fe/Co orderings of a binary type. Supported in kind, refuted on rate. We predicted 1–5 % on the hull, on the grounds that the Fe-Co-X hull has few ternaries to compete with; we got 0.36 %. We predicted at least 70 % orderings; within 25 meV, 34 of 38 cells were decorations, orderings or stackings.

• H11: Fe-Co with a tetrel or early metal holds a true ternary type on the hull. Refuted for this batch. We gave it 40 %. No true-type cell came within 25 meV, and the best near-miss turned out to be a defective Heusler.

• H12: prototypes whose type has a made member give more true-type hits. Inconclusive. Too few hits to compare (1 against 4 within 50 meV).

What changed

• The literature already pointed this way for B, C and Si. A 2026 genetic-algorithm + DFT search of Fe-Co-{B,C,P,Si,S} (JMMM 646, 173978) put every Fe-Co-C cell it found 110–140 meV above the hull and Fe-Co-Si 50–100 meV above, and Fe₃CoB₂, which has been made, about 23 meV above. This loop extends that "no" to Ge, Ga, Al, Sn, Ti, Zr, Nb, V and Mo, for prototypes up to 24 atoms.

• Fe and Co behave as one element near the hull. A new compound type in this chemistry would need a third element that orders against both, the way Ge does in the Heuslers, and the Heuslers are already known.

• The published-PBE surface put every surviving cell 5–19 meV higher than Orb. Loop 5 showed this surface is a fair guide to our own PBE numbers, so no DFT was bought here.

Instruments

Two of our false-positive filters leak. (1) The all-Fe parent check cannot see vacancies, and that is how the defective Heusler got through. (2) An Fe/Co ordering matcher that only looks at MP binaries within 50 meV misses Alexandria's Laves-type stackings, so every Zr-Fe-Co cell first looked new. With the matcher widened to every MP and Alexandria binary and ternary, all of them matched. Both fixes go into the funnel from here on.

Next

1. Co on the sites of this campaign's two compounds. U₆Co₁₂Ge₄C, the made parent of Zr₆Fe₁₂Si₄C, is itself a Co compound. Zr₆(Fe,Co)₁₂Si₄C and Co in the filled G phase test Fe-Co inside a type that is already stable here, where an Fe/Co site preference has something to act on. The Orb screen is free.

2. Add the two filter fixes, then rebuild from made types only, across all symmetries for Fe-rich cells, so later counts can be trusted. Free.

3. A PBE single point on Fe₉CoB₆ (about $0.5), only if you want Orb tested on borides one more time. Orb rated Ti₃Fe₅B₂ too low (loop 3), so this would probably move the wrong way.

Earlier loop: loop 5, two new cubic carbides