The phase stability of large-size nanoparticle alloy catalysts at ab initio quality using a nearsighted force-training approach

Abstract

CoPt nanoparticle catalysts are integral to commercial fuel cells. Such systems are prohibitive to fully characterize with electronic structure calculations. Machine-learned potentials offer a scalable solution; however, such potentials are only reliable if representative training data can be employed, which typically requires large electronic structure calculations. Here, we use the nearsighted-force training approach to make high-fidelity machine-learned predictions on large nanoparticles with $>$5,000 atoms using only systematically generated small structures ranging from 38-168 atoms. The resulting ensemble model shows good accuracy and transferability in describing relative energetics for CoPt nanoparticles with various shapes, sizes and Co compositions. It is found that the fcc(100) surface is more likely to form a L1$_0$ ordered structure than the fcc(111) surface. The energy convex hull of the icosahedron shows the most stable particles have Pt-rich skins and Co-rich underlayers. Although the truncated octahedron is the most stable shape across all sizes of Pt nanoparticles, a crossover to icosahedron exists due to a large downshift of surface energy for CoPt nanoparticle alloys. The downshift can be attributed to strain release on the icosahedron surface due to Co alloying. We introduced a simple empirical model to describe the role of Co alloying in the crossover for CoPt nanoparticles. With 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. Lastly, the order-disorder phase transition for a CoPt nanoparticle exhibits a lower transition temperature and a smoother transition, compared to the bulk CoPt alloy.