We put Fe into about 2,400 prototype structures and found one new compound on the hull with a real structure type: Zr₆Fe₁₂Si₄C, a cubic carbide. To test it, we built the phase most likely to beat it: a version of the Zr₆Fe₁₆Si₇ "G phase" from Materials Project with carbon added, which no database lists. In our own DFT, relaxed, both are stable, and neither has an imaginary phonon mode. Zr₆Fe₁₂Si₄C sits on the hull, and the filled G phase sits 18 meV/atom below its competitors, so the check meant to rule out the first compound found a second.
Zr₆Fe₁₂Si₄C takes the structure of U₆Co₁₂Ge₄C, a compound that has been made (Berthebaud et al., J. Solid State Chem. 180 (2007)), with Zr on the U site, Fe on Co and Si on Ge. Each carbon sits at the center of an octahedron of six Zr atoms, and the Fe atoms make up the framework around them. In our DFT, fully relaxed, it is −5.7 meV/atom from the hull: it ties with a mix of the filled G phase, ZrFe₂, Zr₂Fe₃Si and ZrC rather than clearly beating it. Fe carries 1.65–1.8 µB, which gives 0.68 T: a ferromagnet, not a strong one.
The PBE-relaxed cell (23-atom primitive). Look for the C atoms in their Zr₆ cages:
New cubic carbide, 23-atom primitive cell relaxed in PBE (ABACUS, TZDP, k-spacing 0.2, forces < 0.04 eV/Å). 5.7 meV/atom below the hull of our computed competitors (filled G phase Zr₆Fe₁₆Si₇C, ZrFe₂, Zr₂Fe₃Si, ZrC); no imaginary phonon modes. Relaxed from the Orb geometry in this file's family. Sun-tetragonal campaign, loop 5.
Zr₆Fe₁₆Si₇C came out of the check. Zr₆Fe₁₂Si₄C's strongest competitor is the Zr₆Fe₁₆Si₇ G phase (mp-1192960). That phase has an empty octahedron of six Zr atoms, the same kind of cage that holds carbon in Zr₆Fe₁₂Si₄C, and a carbon-filled Nb version (Nb₆Fe₁₆Si₇C) is already among the published-PBE references. If Zr₆Fe₁₆Si₇ took carbon too, it could undercut our compound, and no database has it, so we built it. It is new (not in Materials Project, Alexandria, GNoME or COD; two literature searches found nothing), on the Orb hull, and in our relaxed DFT −18.2 meV/atom below Zr₆Fe₁₆Si₇ + ZrC + Zr₂Fe₂Si₂C + Fe₃Si. With carbon added it is still weakly magnetic (0.21 T; most Fe near 1.35 µB, one site antiparallel).
The filled G phase, PBE-relaxed (30-atom primitive). The carbon is the single atom at the center of a Zr₆ octahedron:
Both are dynamically stable. Harmonic phonons from an ML potential (NequIP-OAM-XL, via the phonon route) show no imaginary modes in either: the lowest frequencies are 0.24 THz in Zr₆Fe₁₂Si₄C and 0.14 THz
DFT: PBE with ABACUS (TZDP basis, k-spacing 0.2 Å⁻¹, ferromagnetic start). The two new compounds and the six competitors that set their margins were relaxed (cell and ions, forces under 0.04 eV/Å); the three siblings are single points on their ML geometries. Each was compared with every competitor named by the Orb or published-PBE hulls. Each cell is scored against the lowest-energy combination of the other computed phases, using compounds only wherever such a balance exists.
Cell | Structure | Novelty | Orb hull (meV/atom) | Our PBE (meV/atom from hull) | Decomposes to | Phonons |
|---|---|---|---|---|---|---|
On or below the hull (≤ 0) counts as stable. Without the filled G phase, Zr₆Fe₁₂Si₄C reads −13.4; the filled G phase brings it to −5.7. Relaxation moved every margin by less than 2 meV/atom (single points at the ML geometry: −4.1 and −19.1), and the plain G phase reached the same energy from default seeds as from tuned ones, so both G phases are compared in the same weakly magnetic state. The balances use compounds only, because this LCAO setup gets formation energies from the elements wrong (loop 4
The screen that found them: 2,389 Fe-rich cells built from Alexandria's near-hull prototypes, 104 variations of last loop's lead Fe₃Ge₂Al, and 334 cells from loops 1–2 that never came back. All were relaxed and scored with Orb v3 by the hull route
H7, Alexandria's prototypes reach the hull at least as often as MP's: mixed. On the hull: 0.42 % (10 of 2,388; predicted 0.3–1.5 %). Within 25 meV: 2.4 % (predicted 5–12 %). True-type and new on the hull: 1 cell, 0.04 % (predicted 0.05–0.3 %). The 1,431 tetragonal cells gave nothing: 4 within 25 meV, all decorations.
H8, the Fe₃Ge₂Al decoration is a family: counts supported, mechanism refuted. 3 of 104 within 25 meV and none on the hull, both as predicted. My reason was wrong, though: I expected the Sn versions to sit lower than their Ge twins, and they sit higher (Ga 20.6 against 8.2).
H9, Zr₆Fe₁₂Si₄C is stable on PBE: supported. Predicted −30 to +20 meV/atom against its published-PBE competitors, 55 % negative; measured −12.8 at the ML geometry and −13.4 relaxed, or −5.7 relaxed with the filled G phase added.
The siblings: refuted. I predicted the Ga, Ge and V cells at roughly −20 to +40 in PBE; all three came out higher (+23 to +49).
Build the competitor. The phase that had the best chance of beating our candidate was missing from every database. Building it turned a marginal result into two new compounds. When a candidate's competitor has an empty site the candidate fills, fill it in the competitor too.
Made structure types are where the hits are. Every on-hull cell with a real structure type in this campaign sits on a type with a made member: Ti₃Co₅B₂ (loop 1), CoSn (Fe₃Ge₂Al) and U₆Co₁₂Ge₄C. Most of Alexandria's prototypes are computed substitutions themselves.
The published-PBE surface is the better filter. On the three cells that failed, Orb read 20–30 meV/atom too low, while the free published-PBE surface (14.5, 22.4
The screen ran at about 70 cells/min once I fixed a slow poll and a state-file race; no runs were lost.
The hull route returns conventional cells. My first DFT run on Zr₆Fe₁₂Si₄C used all 46 atoms of the conventional cell instead of the 23-atom primitive; I cancelled it and the charge was waived. Three runs hit the DFT route's one-hour cap; those are not charged, and retrying resumes from the saved density. The two G-phase relaxations took one and one and a half hours and cost $5.36; I had estimated $3–5 for all eight relaxations, and they came to $7.06.
Other atoms in the G-phase cage: boron or nitrogen instead of carbon, half-filled cages, and the Ti, Hf and Nb versions with Fe and Si. A free Orb screen first.
Settle the elemental-Fe question for Zr₆Fe₁₂Si₄C: relax bcc Fe and check the setup against a published Zr–Fe formation energy. Under $0.10.
A substitution sweep limited to structure types with a made member, across all symmetry classes. Free.
Earlier loops: 1
New carbon-filled G phase, 30-atom primitive cell relaxed in PBE (ABACUS, TZDP, k-spacing 0.2, forces < 0.04 eV/Å). 18.2 meV/atom below Zr₆Fe₁₆Si₇ + ZrC + Zr₂Fe₂Si₂C + Fe₃Si; weakly magnetic; no imaginary phonon modes. Relaxed from the Orb geometry in this file's family. Sun-tetragonal campaign, loop 5.
Im-3m, U₆Co₁₂Ge₄C type |
Fm-3m, filled G phase | Zr₆Fe₁₆Si₇, ZrC, Zr₂Fe₂Si₂C (Alexandria agm002140547), Fe₃Si |
Im-3m, U₆Co₁₂Ge₄C type | ZrFeGe (Alexandria agm002212203), Zr₃GeC₂ (built from Zr₃GaC₂), Zr₂Fe₃Ge, Fe | not run |
Im-3m, same | not run |
I4/m, Hf₈GaRh₁₁ type | not run |
Tetragonal and Fe-rich still pull against each other. V₈Fe₁₁Si was the only tetragonal true-type cell near the hull in two loops, and PBE puts it 49 meV/atom above.
Substitution into ~2,400 prototypes found Zr₆Fe₁₂Si₄C; building its strongest competitor found a second new compound, the carbon-filled G phase Zr₆Fe₁₆Si₇C. Both stay on the PBE hull after relaxation (−5.7 and −18.2 meV/atom) and have no imaginary phonon modes.