Schematic showing the optimized (12 × 12)-graphene moiré/(11 × 11)-Ru(0001) surface in (a) top and (b) side views. The top and lower layers of Ru are colored differently, and the C atoms are colored according to their heights, as an aid to the eye. For clarity, the C atoms are shown as a hexagonal wire network in the top view. In (a), the surface unit cell is outlined by black dashed lines; the symmetry-irreducible zone is indicated by the triangle; the high-symmetry regions are labeled; the high-symmetry C6 rings represented by (3 × 3) surfaces are outlined by hexagons with sites labeled. In (b), d 1 and d 2 indicate the heights of the highest and lowest C atoms in the graphene moiré with respect to the top Ru layer at its bulk-truncated position, with d 1 = 3.693 Å; d 2 = 2.156 Å.
Schematics of the (3 × 3) surfaces: (a) freestanding graphene; (b) fcc, (c) hcp, and (d) ridge versions of Ru(0001)-supported graphene. The symmetry-irreducible zone of each surface is indicated by the shaded region, and the high-symmetry sites are labeled. Graphene is shown as bonds only. Top and second layer Ru atoms are shown as green and grey spheres, respectively.
(a) and (b) Side and top views of the charge density difference (Δρ = ρ total − ρ Ru − ρ graphene) plots for graphene moiré on Ru(0001). The isosurfaces shown are ±0.008 e/Å3 (red/dark = density accumulation; blue/light = density depletion). The graphene moiré is shown as a hexagonal wire network. (c) and (d) Local density of states (LDOS) of the total p states of several C atoms in g/Ru(0001). See Figure 1 for site designation. The Fermi level is indicated by a vertical dashed line. The states near the Fermi level primarily composed of p z states are indicated for t1 and t2.
PES's for Rh1 and Au1 on the (3 × 3) surfaces: (a) freestanding graphene; (b) fcc, (c) hcp, and (d) ridge versions of Ru(0001)-supported graphene. Upper panel is for Rh1, and lower panel is for Au1. Contours are generated based on interpolation as an aid to the eye only. The minimum-energy diffusion path between adjacent local minima is indicated on each surface for each adatom by the dashed line. The corresponding transition state is marked by “X.”
Potential energy surfaces (PES’s) for (a) Rh1 and (b) Au1 sampled at the top and ring center sites in the symmetry-irreducible zone of the full g/Ru(0001) surface. Contours are generated based on interpolation and overlaid onto the graphene network as an aid to the eye only. The minimum-energy diffusion path for each adatom is marked by a dashed line. Key adsorption sites in high-symmetry regions (“A,” “B,” “C” for Rh1; “D,” “E,” and “F” for Au1), and the highest-energy site on each path (“X”), are labeled. See text for detail and the supplementary material for the adsorption energy at each site. 65
Simulation results for the probability mass function of 0.05 ML of adatom deposited on g/Ru(0001). (a) α = 1 (following binomial distribution); (b) α = 0.1; (c) α = 10−4. Results are based on 100 simulations for each value of α.
Adsorption energies (ΔE, in eV) and charge of Rh1 and Au1 on the graphene moiré/Ru(0001) surface and on the (3 × 3) model surfaces of freestanding graphene and Ru-supported graphene. See Figure 2 for site designations on the (3 × 3) model surfaces and Figure 5 for site designations on g/Ru(0001).
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