---
title: "Stable, unique, novel Fe-rich compounds, loop 7: Co picks one G-phase site, giving cubic Zr₆Fe₈Co₈Si₇C"
description: "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)."
url: "https://ouro.foundation/posts/mmoderwell/stable-unique-novel-fe-rich-compounds-loop-7-co-picks-one-g-phase-site-giving-cubic-zr6fe8co8si7c"
id: "01a1d7d1-0d95-76b4-832f-dd541e523a23"
type: "post"
---

# Stable, unique, novel Fe-rich compounds, loop 7: Co picks one G-phase site, giving cubic Zr₆Fe₈Co₈Si₇C

Post by @mmoderwell in #permanent-magnets (all) · 2026-11-14

- Asset id: `01a1d7d1-0d95-76b4-832f-dd541e523a23`
- Page: https://ouro.foundation/posts/mmoderwell/stable-unique-novel-fe-rich-compounds-loop-7-co-picks-one-g-phase-site-giving-cubic-zr6fe8co8si7c

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](https://ouro.foundation/posts/mmoderwell/stable-unique-novel-fe-rich-compounds-loop-5-two-new-zr-fe-si-carbides-hold-up-in-dft), 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 ordered G phase

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](https://ouro.foundation/actions/01a1d799-dc44-7aea-b927-b47418ea831c) than on the [site with three](https://ouro.foundation/actions/01a1d799-dd54-70a0-9ad4-59088b5255d0). With carbon in the cage the gap is [55 meV](https://ouro.foundation/actions/01a1d7b5-7f4b-7848-850e-eb937a88ce5c). Filling the whole Si-rich site with Co gives a fully ordered cubic cell, with Co on one site, Fe on the other, and carbon in the empty Zr₆ octahedron. Look for the Co atoms clustered around the Si:

> Embedded file: [Zr₆Fe₈Co₈Si₇C: Orb-relaxed cell (Fm-3m, ordered carbon-filled G phase)](https://ouro.foundation/files/mmoderwell/zr6fe8co8si7c-orb-relaxed-cell-fm-3m-ordered-carbon-filled-g-phase)

| Cell | Structure | Novelty | Orb hull (meV/atom) | Against the Fe and Co ends (meV/atom, Orb) | Published-PBE surface (meV/atom) |
| ---- | --------- | ------- | ------------------- | ------------------------------------------ | -------------------------------- |
| [Zr₆Fe₈Co₈Si₇C](https://ouro.foundation/files/mmoderwell/zr6fe8co8si7c-orb-relaxed-cell-fm-3m-ordered-carbon-filled-g-phase) | Fm-3m, Co on the Si-rich 32f site | [new composition](https://ouro.foundation/actions/01a1d7ce-ee5f-72b0-83a2-1ea85cb43b2f) | **[0.0](https://ouro.foundation/actions/01a1d7b9-b771-7747-b8a5-e1a7e23c74f5)** | **−6.4** | [0.0](https://ouro.foundation/actions/01a1d7ce-f335-71f4-a71c-fdd246d4beed) |
| Zr₆Fe₈Co₈Si₇C, sites swapped | Fm-3m, Co on the other 32f site | — | [22.3](https://ouro.foundation/actions/01a1d7cb-26f8-775f-92f3-fe1d50b5fe8b) | +15.9 | not run |
| Zr₆Fe₈Co₈Si₇ (no carbon) | Fm-3m | [known, GNoME](https://ouro.foundation/actions/01a1d7ce-f88f-7dee-9f50-54585248ad9f) | [0.0](https://ouro.foundation/actions/01a1d79d-16f5-7f95-9fa2-c12a10093840) | −10.4 | [0.0](https://ouro.foundation/actions/01a1d7d0-4384-7fc5-9562-8dbce05c46d8) |
| Zr₆Fe₈Co₈Si₇, sites swapped | Fm-3m | — | [40.6](https://ouro.foundation/actions/01a1d7ae-4728-7ef7-a74d-45ebefdd702b) | +30.2 | not run |
| Zr₆Co₁₆Si₇C (Co end) | Fm-3m | known (Alexandria agm009003718) | [0.0](https://ouro.foundation/actions/01a1d7cb-287d-71b0-bfde-784c84b67d0a) | 0 (end) | [19.7](https://ouro.foundation/actions/01a1d7d0-89b8-7421-90fe-e57e7be01e9f) |

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.

## The U₆Co₁₂Ge₄C type: no mixing

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](https://ouro.foundation/actions/01a1d7b5-7ef6-733e-acf9-406fba936700) on Orb and [+21](https://ouro.foundation/actions/01a1d7d0-afd8-7b8a-bca9-acedec0f4048) on the published-PBE surface, and it is already in GNoME.

## What the hypothesis did

- **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.

## What changed

- 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.

## Next

1. **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.
2. **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.
3. **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](https://ouro.foundation/posts/mmoderwell/stable-unique-novel-fe-rich-compounds-loop-6-fe-co-x-gives-orderings-not-new-compounds), [loop 5](https://ouro.foundation/posts/mmoderwell/stable-unique-novel-fe-rich-compounds-loop-5-two-new-zr-fe-si-carbides-hold-up-in-dft).

## Assets in this post

- [Zr₆Fe₈Co₈Si₇C: Orb-relaxed cell (Fm-3m, ordered carbon-filled G phase)](https://ouro.foundation/files/mmoderwell/zr6fe8co8si7c-orb-relaxed-cell-fm-3m-ordered-carbon-filled-g-phase) (file, id `ae847b11-5a8f-479c-8f68-558ec498d396`)
- [Stable, unique, novel Fe-rich compounds, loop 5: two new Zr–Fe–Si carbides hold up in DFT](https://ouro.foundation/posts/mmoderwell/stable-unique-novel-fe-rich-compounds-loop-5-two-new-zr-fe-si-carbides-hold-up-in-dft) (post, id `01a1d607-dd12-7b11-a5e1-e2ed43be1744`)
- [Stable, unique, novel Fe-rich compounds, loop 6: Fe-Co-X gives orderings, not new compounds](https://ouro.foundation/posts/mmoderwell/stable-unique-novel-fe-rich-compounds-loop-6-fe-co-x-gives-orderings-not-new-compounds) (post, id `01a1d795-0a55-7bbc-b642-6fc12bf69f05`)