Modeling Segregation on AuPd(111) Surfaces with Density Functional Theory and Monte Carlo Simulations
Jacob R. Boes and John R. Kitchin, “Modeling Segregation on AuPd(111) Surfaces with Density Functional Theory and Monte Carlo Simulations”, The Journal of Physical Chemistry C 121(6), 3479–3487 (2017). https://doi.org/10.1021/acs.jpcc.6b12752
This summary was written by a language model from the paper and has not been checked line by line. Rely on the published paper for details.
Question
AuPd alloys are useful catalysts (for example in direct hydrogen peroxide synthesis, where Au suppresses the Pd-catalyzed decomposition step), but the surface composition that controls their behavior differs from the bulk because of segregation. Most guidelines for predicting segregation apply only in the dilute limit, experiments such as low-energy ion scattering (LEIS) usually measure one bulk composition at a time, DFT is too expensive to sample the enormous number of configurations directly, and empirical potentials or cluster expansions trade accuracy for speed or are hard to extend. The paper asks whether a neural network potential trained on DFT can drive Monte Carlo simulations that quantitatively predict adsorbate-free segregation on AuPd(111) across the whole composition range (Boes 2017).
Approach
DFT calculations used VASP with the PBE functional, PAW potentials, a 400 eV cutoff and dense k-point grids. A Behler–Parrinello network was trained with the AMP code, with one small network per element (two hidden layers of three nodes, tanh activation), eight G2 symmetry functions and a 6 Å cutoff, giving 66 weights in total. Training structures came from effective medium theory (EMT) enumeration of all energy-unique configurations of seven-layer (111) slabs with 1 × 1, 2 × 1 and √3 × √3 cells, each at five lattice constants spanning pure Pd (3.934 Å) to pure Au (4.154 Å), 62,706 candidate structures in all. Starting from the 360 smallest-cell structures, the authors repeatedly trained two networks of different architecture, computed with DFT the structures on which they disagreed most (about 1000 per iteration), and retrained. Three iterations gave a final set of 3914 DFT calculations, with 10% held out for validation; validation error was similar to training error. Transferability was tested on about 547,000 configurations of a larger √7 × √7 × 5 slab not in the training set, and against a much larger third network. Canonical Monte Carlo with nearest-neighbor swaps, without relaxation, was then run on 10 × 10 × 15 slabs from 700 to 1000 K and 10 to 90% Au bulk fraction (36 simulations, at least 20,000 accepted steps each). Surface compositions were fit to the Langmuir–McLean form of the Gibbs isotherm to extract a segregation enthalpy (Boes 2017).
Key findings
Every simulation predicted Au enrichment in the top layer, a Pd-enriched second layer and a third layer near the bulk composition, the damped oscillation expected for an alloy with negative mixing enthalpy. At 800 K the predicted top-layer compositions agreed closely with LEIS data from two groups, staying within experimental scatter below 0.6 Au bulk fraction and slightly overpredicting above it. The fitted segregation enthalpy was roughly constant near -10 kJ/mol on the Pd-rich side and fell off rapidly toward the dilute-limit DFT values as the Au fraction increased; a weighted fit gave ΔH = -60.5x³ + 27.5x - 15.5 (kJ/mol, with the quadratic term dropped). Most of the uncertainty came from the isotherm fit, which is very sensitive to scatter at high Au fractions. Dilute-limit calculations with Vegard’s-law lattice constants showed that strain plays only a minor role, and the authors argue the composition dependence could not be recovered from dilute-limit energies alone. Three-atom fcc site distributions favored mixed Pd2Au and PdAu2 sites over pure Au3 and Pd3, and Warren–Cowley parameters were negative at first neighbors, positive at second and near zero by third, consistent with literature values, indicating short-range order that favors Au–Pd bonds at all temperatures studied. DFT relaxations of all 100 unique top-two-layer configurations of a 2 × 2 × 5 slab showed relaxation energies that were small and nearly uniform near the bulk composition, largest only for unfavorable extreme compositions, which supports neglecting relaxation in the MC (Boes 2017).
Significance
The work shows that a very small neural network, trained on a few thousand DFT calculations chosen by an active-learning loop of network disagreement, can replace DFT inside Monte Carlo and give segregation profiles across composition space that match experiment. It provides a composition-dependent segregation enthalpy for AuPd and a quantitative picture of surface short-range order, which matters for counting active sites in alloy catalysts. The DFT data, network parameters and MC code were released in the Supporting Information (Boes 2017).