Graphene on Ru(0001): A $25\times 25$ Supercell

The structure of a single layer of graphene on Ru(0001) has been studied using surface x-ray diffraction. A surprising superstructure containing 1250 carbon atoms has been determined, whereby $25\times 25$ graphene unit cells lie on $23\times 23$ unit cells of Ru. Each supercell contains $2\times 2$ crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C–C bonds, which helps accommodate the in-plane tensile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.

Figure 1

(a) A LEED image of the graphene/Ru(0001) surface taken at an electron energy of 74 eV. (b) An STM image of graphene on Ru(0001), highlighting the supercell containing four subcells.

Figure 2

Summary of the diffraction data for the graphene/Ru(0001) system. (a) Schematic reciprocal space map showing where data were recorded. The red circular dots indicate points recorded in plane at $l=0.4\mathrm{r}.\mathrm{l}.\mathrm{u}$. The in-plane scan along the $k$ direction in the neighborhood of the (01) CTR of Ru at $l=0.4\mathrm{r}.\mathrm{l}.\mathrm{u}.$ shown in (b) is indicated by the green (gray) line. The positions of superstructure rods shown in (e) are indicated by the orange diamond and blue square. (c),(d) High-resolution scans across the superstructure signal of graphene on Ru, detailing the 25-on-23 reconstruction. The data were fit to a pseudo-Voigt profile (solid black curves), while the positions where 13-on-12 and 12-on-11 reconstruction diffraction signals would lie (dotted lines) are also shown.

Figure 3

Simple parametric model of the graphene-Ru(0001) supercell. (a) The vertical displacement field of the graphene corrugation. The scale is given in angstroms above the Ru substrate. (b) Simulated $21/23$ and $25/23$ superstructure rods of corrugated graphene on Ru(0001), incorporating the qualitative features extracted from the experimental data. The graphene has a peak-to-peak corrugation amplitude of 1.5 Å, while that of the uppermost Ru atomic layer is 0.20 Å. The corrugation amplitude of the Ru drops exponentially by a factor of 0.75 for each successive atomic layer (0.56 per unit cell depth). The minimum graphene-Ru distance is 2.2 Å, and the mean vertical positions between all of the Ru atomic planes assume bulk values.