Supplementary information files for Stacking-mediated diffusion of ruthenium nanoclusters in bilayer graphene and graphite

Supplementary files for article Stacking-mediated diffusion of ruthenium nanoclusters in bilayer graphene and graphite <br> The diffusion, penetration and intercalation of metallic atomic dopants is an important question for various graphite applications in engineering and nanotechnology. We have performed systematic first-principles calculations of the behaviour of ruthenium nanoclusters on a graphene monolayer and intercalated into a bilayer. Our computational results show that at a sufficiently high density of single Ru atom interstitials, intercalated atoms can shear the surrounding lattice to an AA stacking configuration, an effect which weakens with increasing cluster size. Moreover, the interlayer stacking configuration, in turn, has a significant effect on cluster diffusion. We therefore find different trends in diffusivity as a function of cluster size and interlayer stacking. For monolayer graphene and an AA graphene bilayer, the formation of small clusters generally lowers diffusion barriers, while the opposite behaviour is found for the preferred AB stacking configuration. These results demonstrate that conditions of local impurity concentration and interlayer disregistry are able to regulate the diffusivity of metallic impurities in graphite.