Loop 6 found that Fe and Co behave like one element wherever a structure gives them a single site. This loop gave them two. We put Co onto the Fe sites of the two compounds found in loop 5, testing every symmetry-distinct arrangement: 1,067 cells, all scored on the Orb hull. In the G phase, Co picks one of the two iron sites, and filling that site gives Zr₆Fe₈Co₈Si₇C. It is cubic, new to every database we check, and on both the Orb hull and the published-PBE surface. In the U₆Co₁₂Ge₄C-type carbide, which has a single site, Fe and Co just separate.
The G phase Zr₆Fe₁₆Si₇ has two sets of 32 iron sites. One set touches four Si atoms and the other touches three. A single Co placed on the site with four Si neighbours is 126.7 meV lower than on the site with three. With carbon in the cage the gap is 55 meV
Cell | Structure | Novelty | Orb hull (meV/atom) | Against the Fe and Co ends (meV/atom, Orb) | Published-PBE surface (meV/atom) |
|---|---|---|---|---|---|
The Fe end is our own Zr₆Fe₁₆Si₇C from loop 5, which our relaxed PBE puts 18.2 meV/atom below its competitors. The sites-swapped rows are the same compositions with Fe and Co exchanged. They sit 22 and 41 meV/atom above the hull, so the order is not a coin flip. The one carbon-free arrangement GNoME already lists is the right one. Carbon still goes into the cage with Co present, though with less gain: −0.83 eV per C against graphite, compared with −1.05 eV in the all-Fe phase.
On the published-PBE surface the Co end reads 19.7 meV/atom above the hull while the ordered mixed cell reads 0. If DFT agrees, the Fe/Co ordering is what makes the Co-containing filled G phase stable.
Zr₆Fe₁₂Si₄C has a single set of twelve Fe sites. All 143 Fe/Co arrangements on it sit 3–17 meV/atom above the line between the Fe end and the Co end. The Co end, Zr₆Co₁₂Si₄C, reads 1.1 meV on Orb and +21 on the published-PBE surface, and it is already in GNoME.
H13: Co enters both carbides with a site preference, and the carbon stays. Supported for the G phase, refuted for the U₆Co₁₂Ge₄C type. We predicted a split of 10–60 meV per Co and got 55 meV with carbon and 127 meV without. We gave the ordered filled cell a 35 % chance of reaching the hull, and it did. We gave the Co end of the U₆Co₁₂Ge₄C type a 50 % chance of reaching the hull, and it missed by 1.1 meV. We expected solid-solution behaviour there and found Fe and Co separating instead.
Fe-Co compounds come from structures with two distinct late-metal sites. Loop 6's 555 cells from single-site structures gave orderings with no driving force. Here one enumeration of a two-site structure gave a 55–127 meV site preference and an ordered phase below both ends.
The new phase is measured on Orb and on published-PBE references only. Nothing has been checked in our own DFT, and no phonons have been run. Novelty is checked against the databases plus two literature searches, which found nothing on carbon-filled Zr-Co G phases.
PBE check: single points on Zr₆Fe₈Co₈Si₇C, its swapped twin, the Co end and the empty ordered phase, against the loop-5 Fe-end numbers. About $2–3. Then phonons on Zr₆Fe₈Co₈Si₇C if it holds. This decides whether it joins the two loop-5 compounds as a SUN result.
The same move on other two-site structures: list each structure type's late-metal site sets and their metalloid neighbours, and put Co onto one set, one cell per type, across the made types. Free. This is the general version of today's result.
Ni in place of Co on the same G-phase site. Zr₆Ni₁₆Si₇ is a known G phase. Free.
Earlier loops: loop 6, Fe-Co-X substitution
Zr6Fe8Co8Si7C, Fm-3m, 30-atom primitive, a = 11.47 A: the Zr6Fe16Si7 G phase with Co on the 32f site that has four Si neighbours, Fe on the 32f site with three, and C in the empty Zr6 octahedron. Relaxed with Orb v3 on Ouro. On the Orb v3 hull, 6.4 meV/atom below the line between Zr6Fe16Si7C and Zr6Co16Si7C; 0 on the published-PBE surface; the reverse Fe/Co order is 22 meV/atom above the hull. Absent from MP, Alexandria, GNoME, COD. Sun-tetragonal loop 7; ML-only, no DFT or phonons yet.
Fm-3m, Co on the Si-rich 32f site |
−6.4 |
Zr₆Fe₈Co₈Si₇C, sites swapped | Fm-3m, Co on the other 32f site | — | +15.9 | not run |
Zr₆Fe₈Co₈Si₇ (no carbon) | Fm-3m | −10.4 |
Zr₆Fe₈Co₈Si₇, sites swapped | Fm-3m | — | +30.2 | not run |
Zr₆Co₁₆Si₇C (Co end) | Fm-3m | known (Alexandria agm009003718) | 0 (end) |
Co on the Fe sites of loop 5's two carbides: in the G phase Co takes the Si-rich site by 55-127 meV, and the ordered filled phase Zr6Fe8Co8Si7C is new and on both hulls (ML, pending DFT).