Loop 2 ended with two ternaries that were on or within 2 meV/atom of a machine-learned hull and new to the databases. This loop asked the obvious question: do they survive DFT? One does and one does not.
Compound | Reaction tested | ML hull (Orb v3) | PBE reaction energy (meV/atom) | Verdict |
|---|---|---|---|---|
A negative number means the compound is lower in energy than the phases it would decompose into.
For Fe₃Ge₂Al we also tested whether the Al order is real. With Al on the other kind of Ge site (the one inside the kagome plane) the cell is 183 meV per Al higher, and only 9 meV/atom below FeGe + FeAl. So Al has a clear preference for the honeycomb Ge layer between the kagome planes, which argues for an ordered compound and not just Al dissolved in FeGe.
PBE single points with ABACUS (numerical atomic orbitals, the largest basis, k-spacing 0.2 Å⁻¹, ferromagnetic start) on the Orb-relaxed geometry of every phase, on Ouro's ground-state route. The competing phases are the ones the Materials Project entries give as the decomposition on the Orb surface.
Nothing was relaxed with DFT. Residual forces are up to 0.1 eV/Å in the two candidates and 0.29 eV/Å in TiFe₂. Relaxing TiFe₂ would lower it further and make Ti₃Fe₅B₂ look worse, not better.
The magnetic states are whatever a ferromagnetic start gives. FeGe in this structure is an antiferromagnet and TiFe₂ is not a simple ferromagnet either; the true ground states are lower, by amounts we did not measure. For Ti₃Fe₅B₂ that again goes the wrong way. For Fe₃Ge₂Al it would eat into the 39 meV, though an antiferromagnetic gain of that size per atom would be unusual.
Ti₃Fe₅B₂ converged to a nearly non-magnetic state (2.6 μB for ten Fe). A second run started from 3 μB per Fe returned the same state and the same energy, so there is no hidden high-moment solution.
Only two-phase and three-phase decompositions into Materials Project phases were tested. Fe₃Ge₂Al has not been tested on PBE against Fe₃Ge, Fe–Al–Ge phases from Alexandria, or disordered alloys.
The ML hull was wrong about Ti₃Fe₅B₂ by about 30 meV/atom, which is larger than the 25 meV window we had been calling "near-stable". Every candidate from loops 1 and 2 that has not had this check, including Ti₂MnFe₅B₂ from the same structure family, should be read as unconfirmed. Fe₃Ge₂Al moved the other way and is now the campaign's one candidate with DFT support.
The same check on Ti₂MnFe₅B₂ and the rest of the boride family, since their parent just failed.
For Fe₃Ge₂Al: a DFT relaxation, the antiferromagnetic state of FeGe as the reference, and the remaining competitors.
Fe₃Ge₂Al → 2 FeGe (CoSn type) + FeAl (B2) |
0.0 |
−39 (cell, FeGe, FeAl) |
stable against these two |
Ti₃Fe₅B₂ → 2 TiFe₂ (C14) + TiB₂ + Fe | 1.5 | +32 (cell, TiFe₂, TiB₂, Fe) | not stable on PBE |
Fe3Ge2Al, P-6m2, CoSn-type FeGe (kagome Fe net) with Al ordered on one Ge site. Built by substitution into a Materials Project prototype and relaxed with Orb v3 on Ouro. Energy above hull 0.0 meV/atom on the Orb v3 surface; no imaginary phonon modes; absent from MP, Alexandria, GNoME and COD. ML-only: not checked with DFT.
A PBE check of loop 2's two standouts: Fe₃Ge₂Al is 39 meV/atom below FeGe + FeAl with a clear Al site preference; Ti₃Fe₅B₂ is 32 meV/atom above TiFe₂ + TiB₂ + Fe.