Atomistic modeling of epitaxial graphene on Ru(0001) and deposited ruthenium nanoparticles

A bond-order potential is presented for the Ru-C system, aiming to model epitaxial graphene on Ru(0001) and ruthenium nanoparticles on such substrates or on graphite. The model has been parametrized on electronic structure calculations and improved to account for long-range London dispersion forces following an approach similar to the Grimme D2 correction scheme, as well as possible nonadditive screening effects that are relevant for epitaxial graphene on metal. The model correctly reproduces a variety of structural properties for different commensurate moir\'e structures as observed in experiments or predicted by density-functional theory calculations, although limitations are noted for very small adsorbates likely due to the lack of explicit charge transfer. The energetic and thermal stabilities of Ru nanoparticles on graphite and epitaxial graphene have been addressed using local optimizations and molecular dynamics simulations. While the nanoparticles exhibit relatively fast diffusion on the graphite substrate, the corrugation of epitaxial graphene strongly stabilizes them against internal rearrangement and global diffusion. The simulated vibrational spectra of epitaxial graphene show variations with the moir\'e structure and temperature that provide insight into anharmonicities and emphasize the role of strain.