Surface Segregation Studies in Ternary Noble Metal Alloys: Comparing DFT and Machine Learning with Experimental Data
K. Broderick, R. A. Burnley, A. J. Gellman and J. R. Kitchin, “Surface Segregation Studies in Ternary Noble Metal Alloys: Comparing DFT and Machine Learning with Experimental Data”, ChemPhysChem 25(13), e202400073 (2024). https://doi.org/10.1002/cphc.202400073
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Question
Machine-learned DFT surrogates such as those from the Open Catalyst Project are benchmarked against DFT, not against experiment, largely because large and consistent experimental catalysis data sets do not exist. The authors propose surface segregation in fcc noble metal ternaries as a simpler, catalytically relevant test where composition spread alloy films (CSAFs) provide near-continuous experimental maps of surface versus bulk composition. They ask whether Monte Carlo simulations driven by a fine-tuned graph neural network potential reproduce measured segregation in AgAuCu and AuCuPd, which crystal facet and exchange-correlation functional agree best, and how the remaining errors can be explained (Broderick et al. 2024).
Approach
Random fcc slabs of 7 to 35 atoms (compositions drawn from a Dirichlet distribution, lattice constants randomized between those of the constituent metals) were built for AgAuCu, AuCuPd and CuPdPt and their binaries in the (111), (110) and (100) orientations, and relaxed in VASP (400 eV cutoff, positions only) with either PBEsol plus D3 Becke-Johnson dispersion (2478 slabs) or plain PBE (2118 slabs). Pairs of 60-atom slabs differing by one atom swap served as a test of extrapolation to larger cells. A GemNet-OC model, starting from a public OC20/OC22 checkpoint, was fine-tuned in IS2RE mode (predicting relaxed energy directly from the unrelaxed lattice structure), and learning curves varied how much AuCuPd data and data from the other two ternaries was included. The resulting potential drove canonical lattice Monte Carlo on 10 × 10 × 15 slabs (1500 atoms) with Vegard’s-law lattice constants and Boltzmann acceptance of atom swaps, at 800 K for AgAuCu, 500 K for AuCuPd and 600 K for CuPdPt, with about 200 runs per system, orientation and functional. Surface excess was computed from the 200 surface atoms, and Boltzmann-weighted average segregation energies were compared with empirical segregation free energies derived from the CSAF measurements (Broderick et al. 2024).
Key findings
For atom-swap energy differences in 60-atom AuCuPd slabs, the pretrained checkpoint had a raw energy error above 1 eV, but swap energy differences had an error of only 0.08 eV because errors cancel, and fine-tuning reduced this to 0.05 eV. Converted to transition probabilities at 500 K, the Brier score fell from 0.07 to 0.05; the model separates favorable and strongly unfavorable swaps well but is less accurate in the intermediate region, which is about a fifth of the data. An S2EF model with relaxation was more accurate (0.03 eV) but roughly ten times slower. PBE-trained models saturated after about 200 slabs, whereas PBEsol plus D3 models needed about 1000; data from chemically similar ternaries was essential, and models were accurate even with no AuCuPd data, indicating transfer to a new ternary once its elements have been seen (Broderick et al. 2024).
Against experiment, (110) slabs with the PBEsol plus D3 surrogate gave the closest match for AgAuCu, capturing Ag segregation across the ternary, Au enrichment along the AuCu edge and Au depletion along the AgAu edge, although the strength of Ag segregation was underpredicted (possibly because of Ag surface mobility, not modeled). AuCuPd was reproduced less well: Au segregation was strongly overpredicted and Cu was pushed into the bulk more than observed, though (110) with PBEsol again agreed best. The authors attribute these deviations mainly to surface energy errors of the functionals, which underpredict the Au surface energy (PBEsol less so than PBE), and argue that size mismatch makes the more open (110) facet relieve strain in these alloys. CuPdPt predictions, with no experimental counterpart, show Pt strongly depleted from the surface across the ternary (Broderick et al. 2024).
Significance
The paper turns segregation on CSAFs into a quantitative experimental check on DFT-trained surrogate potentials, showing that fine-tuned general-purpose graph networks are accurate enough for Monte Carlo and that remaining discrepancies trace mostly to the functional rather than the machine learning. It confirms the earlier suggestion that (110) slabs, not (111), best represent polycrystalline films, and argues for better functionals in computational materials discovery. The DFT data are on Zenodo (10.5281/zenodo.10501343) (Broderick et al. 2024).