Adsorption and diffusion of Ru adatoms on Ru(0001)-supported graphene: Large-scale first-principles calculations.

Large-scale first-principles density functional theory calculations are performed to investigate the adsorption and diffusion of Ru adatoms on monolayer graphene (G) supported on Ru(0001). The G sheet exhibits a periodic moiré-cell superstructure due to lattice mismatch. Within a moiré cell, there are three distinct regions: fcc, hcp, and mound, in which the C6-ring center is above a fcc site, a hcp site, and a surface Ru atom of Ru(0001), respectively. The adsorption energy of a Ru adatom is evaluated at specific sites in these distinct regions. We find the strongest binding at an adsorption site above a C atom in the fcc region, next strongest in the hcp region, then the fcc-hcp boundary (ridge) between these regions, and the weakest binding in the mound region. Behavior is similar to that observed from small-unit-cell calculations of Habenicht et al. [Top. Catal. 57, 69 (2014)], which differ from previous large-scale calculations. We determine the minimum-energy path for local diffusion near the center of the fcc region and obtain a local diffusion barrier of ∼0.48 eV. We also estimate a significantly lower local diffusion barrier in the ridge region. These barriers and information on the adsorption energy variation facilitate development of a realistic model for the global potential energy surface for Ru adatoms. This in turn enables simulation studies elucidating diffusion-mediated directed-assembly of Ru nanoclusters during deposition of Ru on G/Ru(0001).