This loop asked for a ternary that could be a good magnet: iron at 60 at.% or more, a uniaxial structure, near the hull. We built 573 such cells on structure types that someone has made, and none of them is both new and near the hull. Following the leads that came out sideways gave one clear result: in the Fe₂P structure the anisotropy needs its phosphorus. With boron on a third of the phosphorus sites the cell still reads 1.46 MJ/m³ at 1.41 T, but it is not stable; with no phosphorus at all it is stable and soft.
Hull distances are from the hull route on its own Orb v3 relaxation. PBE numbers are ABACUS runs at k-spacing 0.2: single points in the TZDP basis for the stability check, and a relaxation followed by the anisotropy route for K₁, in the basis named in the Geometry column. Curie temperatures are Prophet estimates, which rank cells and are not measurements of Tc.
Cell | Geometry | Novelty | Hull, Orb (meV/atom) | PBE balance (meV/atom) | Js (T) | K₁ (MJ/m³) | Curie, Prophet (K) |
|---|---|---|---|---|---|---|---|
Targets: within 25 meV/atom of the hull, new, uniaxial, Js of 1 T or more, and for a permanent magnet K₁ of 1 MJ/m³ or more. No cell meets all of them. Both K₁ values are along c and move little at half the band-sum width (+1.50 and +0.05). ZrFe₅Si₃, Zr₃Fe₁₃B₂ and their prototypes come from Materials Project (CC-BY-4.0); Fe₆P₂B and Fe₆Si₂B are Alexandria cells (CC-BY-4.0) relaxed here.
Boron sits on the 1b site, on the cell edges along c, with phosphorus on the two 2c sites:
The screen itself: 3,960 substitutions into 404 made prototypes (Materials Project's experimental flag, or a COD entry of the same formula); 1,314 dropped because Materials Project, Alexandria or GNoME already holds the formula; 573 distinct cells screened and 572 returned. On the Orb hull: 0. Within 25 meV/atom: 7, of which 6 are Laves phases with two early metals on one sublattice and 1 is ZrFe₁₀Si₂, a made compound (3.9 on Orb, 20.8 against published PBE). Within 50 meV/atom: 33.
H14, made structure types give new near-hull cells ten times as often: refuted. Predicted 5–15 % within 25 meV and 2–12 new candidates; found 1.2 % and none. The databases already hold 133 of the pool's formulas, 17 of them on the published-PBE hull.
H15, at least one near-hull cell is a ferromagnet above 1 T: inconclusive. The only one within 25 meV is the made ZrFe₁₀Si₂.
H16, the hard magnetic phase Zr₁₁.₅Fe₅₃Si₃₅.₅ has a known structure type: inconclusive. The literature reports this phase with Tc of 495–533 K and no assigned structure (doi:10.1016/j.jallcom.2021.162664, arXiv:2212.13595). ZrFe₅Si₃ in the UFe₅Si₃ type is the lowest of eight types we tried at that composition, and the Ti cell of the same type is 190 meV/atom up, as it should be if the Ti sample is a different phase. Against it: PBE puts the cell 15.9 meV/atom above FeSi + Fe₃Si + ZrFeSi, and its moment, 0.51 T or about 61 A m²/kg, is some 2.5 times what is reported for the phase. Its pattern has not been compared with the measured one.
H17, the Fe–Si–B phase listed as Fe₂Si₀.₄B₀.₆ is the Fe₂P type with Si and B swapped: refuted.
This is the candidate structure for the Zr–Fe–Si phase. One Fe site, at the cell centre, carries 2.5 µB in PBE and the other four 0.75:
Substitution into made structure types is finished as a way to find new Fe-rich ternaries here. The stable cells of this pool exist, and the databases found them first.
In the Fe₂P structure the anisotropy follows the metalloids' electron count. Our route reads Fe₂P at 2.0–2.4 MJ/m³ and 1.5–1.8 with Si on a third of the phosphorus sites (earlier work), 1.46 with boron on a third, and 0.09 with no phosphorus. Magnetization and the Curie estimate rise the other way. This agrees with the boron-substituted alloys that have been made, whose room-temperature anisotropy field of 2.5–3 T sits beside our 2.6 T for Fe₆P₂B at 0 K.
A stable, high-moment entry in a database is a soft magnet until its anisotropy is measured. Fe₆Si₂B is on the PBE hull at 1.51 T and has almost none.
This was the first loop on the lab's crystal-database scripts. Screening, classifying and ranking 573 cells took three commands and about 25 minutes, and the PBE check of eight phases about 10.
FeSi came out magnetic from non-magnetic seeds, where published PBE has it non-magnetic. A cross-check against published energies puts it about 28 meV/atom high, which would move the two PBE balances to about +0.4 and +22.
Orb hull distances could not reproduce the measured boron solubility: they are off by 0.2–0.3 eV per boron atom. Prophet overstates the magnetization of weak-moment Zr–Fe–Si cells (0.93 T for a cell PBE puts at 0.21) and understates how fast boron raises the Curie temperature.
The two K₁ values are in different bases (DZP and TZDP). The drop between them should be repeated in one basis before it is quoted as a slope.
Compare ZrFe₅Si₃'s simulated diffraction pattern with the published one for the Zr–Fe–Si phase. It is the only open discovery question from this loop.
K₁ at a boron content that can be made: the 18-atom Fe₂P cell with boron on every second 1b site along c.
List every Fe-rich, uniaxial, computed-only entry on the published-PBE hull in the crystal database, and measure anisotropy only where the structure gives a reason to expect it.
Earlier loops: loop 7
Fe₂P type, B on 1b; DFT-relaxed, DZP |
computed-only (Alexandria agm041963190) |
not run |
1.41 |
+1.46 |
Fe₂P type, Si on 2c, B on 1b; DFT-relaxed, TZDP | computed-only (Alexandria agm002138077) | −2.7 | 1.51 | +0.09 |
UFe₅Si₃ type, P4/mmm; Orb-relaxed | formula in no database; a structure proposal for a made phase | +15.9 | 0.51 | not run | not a ferromagnet on Prophet |
Zr₃Fe₁₃B₂ | CaCu₅-derived, P6/mmm; Orb-relaxed | new composition | not run | 1.50 (Prophet) | not run |
The Fe2P structure with boron on the 1b site and phosphorus on 2c. The same cell is in Alexandria (agm041963190, CC-BY-4.0); this copy was rebuilt and relaxed with PBE (ABACUS, DZP, k-spacing 0.2) on Ouro. K1 +1.46 MJ/m3 with the easy axis along c, 1.41 T. 66 meV/atom above the Orb hull against Fe2B + Fe2P: not a stable compound.
H18, Fe₆Si₂B is an easy-axis magnet with K₁ of 0.5 MJ/m³ or more: refuted. Easy along c at +0.09.
H19, Fe₆P₂B is near the hull and keeps an easy axis: mixed. Not near the hull: 66 meV/atom up and 45 above Fe₂P in the same cell, decomposing to Fe₂B + Fe₂P. It keeps the axis, with κ of 0.96.
H20, dilute boron dissolves in Fe₂P cheaply on our hull numbers: refuted. A boron atom costs 0.39–0.64 eV on the Orb surface at every concentration from 1/24 to 1/6 of the sites, which as an ideal solution at 1100 °C is 1–4 %. The measured limit is 12.5 % (doi:10.3390/ma19081579).
Built by putting Zr on the U site of UFe5Si3 (Materials Project mp-580439, CC-BY-4.0) and relaxed with Orb v3 on Ouro. A candidate structure for the hard magnetic Zr-Fe-Si phase reported by Yamamoto et al. (doi:10.1016/j.jallcom.2021.162664), whose structure is unassigned. 26.0 meV/atom above the Orb hull and +15.9 meV/atom in PBE single points; not yet compared with the measured diffraction pattern.
573 Fe-rich ternary cells on made structure types gave nothing new near the hull. Fe₆P₂B keeps 1.46 MJ/m³ at 1.41 T but is not stable; phosphorus-free Fe₆Si₂B is stable and soft.