Cluster expansion-accelerated exploration of the surface structure properties of a PdPtAg ternary alloy for the oxygen reduction reaction across the compositional space

A cluster expansion (CE) model was constructed for the ternary alloy Pd/Pt/Ag surface based on density functional theory (DFT) calculations, and Monte Carlo (MC) simulations based on CE were then performed to investigate the surface segregation and atomic ordering on the ternary alloy surfaces at finite temperatures. Results indicated that the local chemical environment of the ternary alloy surface strongly depended on its bulk composition and varied significantly as a function of temperature, producing a significant impact on the catalytic performance. Analysis of depth-resolved composition indicated that even at high temperatures, the dopant metal (Pd or Pt) remained energetically favorable in the bulk, while Ag tended to segregate to the outermost layer to form an enriched layer. DFT calculations indicated that this segregation behavior was driven by the different surface energies between the metals. The Pd concentration exhibited a peak in the second layer and increased with decreasing temperature. Atom ensemble analysis demonstrated that the doped atoms formed a finite number of distinct configurations, with the monomers being the most prevalent surface species. Although surface segregation reduced the number of surface-doped elements, the enrichment of Ag on the surface layer increased the number of unique catalytic active sites on the surface, and the concentration of doped atoms increased by approximately 10% compared with the binary alloy (Pd/Ag or Pt/Ag).