Phase Stability of Large-Size Nanoparticle Alloy Catalysts at Ab Initio Quality Using a Nearsighted Force-Training Approach

Co-Pt alloyed catalyst particles are integral to commercial fuel cells, and alloyed nanoparticles are important in many applications. Such systems are prohibitive to fully characterize with electronic structure calculations due to their relatively large sizes of hundreds to thousands of atoms per simulation, the huge configurational space, and the added expense of spin-polarized calculations. Machine-learned potentials offer a scalable solution; however, such potentials are reliable only if representative training data can be employed, which typically also requires large electronic structure calculations. Here, we use the nearsighted-force training approach that allows us to make high-fidelity machine-learned predictions on large nanoparticles with >5000 atoms using only small and systematically generated training structures ranging from 38 to 168 atoms. The resulting ensemble model shows good accuracy and transferability in describing the relative energetics for Co-Pt nanoparticles with various shapes, sizes, and Co compositions. It is found that the fcc(100) surface is more likely to form an L1(0) ordered structure than the fcc(111) surface. The energy convex hull of a 147-atom icosahedron shows that the most stable particles have Pt-rich skins and Co-rich underlayers and is in quantitative agreement with one constructed by brute-force first-principles calculations. Although the truncated octahedron is the most stable shape across all studied sizes of Pt nanoparticles, a crossover to the icosahedron exists for CoPt nanoparticle alloys due to a large downshift of surface energy. The downshift can be attributed to strain release on the icosahedral surface due to Co alloying. We introduced a simple empirical model to describe the role of Co alloying in the crossover for Co-Pt nanoparticles. With Metropolis Monte Carlo simulations, we additionally searched for the most stable atomic arrangement for a truncated octahedron with equal Pt and Co compositions, and also we studied its order-disorder phase transition. We validated the most stable configurations with a new highly scalable density functional theory code called SPARC. From the outermost shell to the center of a large Co-Pt truncated octahedron, the atomic arrangement follows a pattern: Pt -> Co -> L1(2)(Pt3Co) -> L1(2)(PtCo3) -> L1(0)(PtCo) -> center dot center dot center dot -> L1(0)(PtCo). Lastly, the order-disorder phase transition for a Co-Pt nanoparticle exhibits a lower transition temperature and a smoother transition compared to the bulk Co-Pt alloy.