Chapter 11 Rotated graphene moiré superstructures on various transition metal surfaces
11.5 Rotated graphene moiré superstructures on other transition metal surfaces
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Figure 11.10 Comparison the total energies of the ultra-flat and corrugated graphene layers on the Ru(0001) substrate with larger rotation angles, and the unit of the total energy here is eV.
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Figure 11.11 (a) Top and side views of the 0º graphene/Rh(111) superstructure. (b) Optimized binding energies and distance of graphene lattice on different sites of the Rh(111) surface. (c) Curvature energies of graphene layers on the Rh(111) surface as a function of the rotation angle and the dashed line denotes the binding energy increase of graphene/Rh(111) with graphene changing from an ultra-flat to a corrugated structure. (d) Height oscillation of graphene layers on the Rh(111) surface regarding to the rotation angle by DFT calculations. (e) Stereo views of graphene/Rh(111) superstructures with different rotation angles.
In contrast with graphene/Ru(0001) and graphene/Rh(111) superstructures, graphene present quite different behaviors in graphene/Ir(111) and graphene/Pt(111) one, as shown in Figures 11.12 and 11.13. The height oscillation degrees of graphene layer on both the Ir(111) and Pt(111) surfaces are very week even with a rotation angle of 0º, because that interactions of graphene and substrate are all similarly weak with values less than 100 meV/C atom on different sites and the optimized distances are all larger than 3.3 Å. From Figures 11.12(b) and 11.13(b), it is worth noting that, the weakest interaction between graphene and the substrate still happens at the ATOP sites whereas the strongest one appears at the HCP site in these weak interacted systems, which are distinguished from the strong interacted graphene/Ru(0001) and graphene/Rh(111) systems. By comparing the differences of graphene on the Ir(111) and Pt(111) surfaces, it is found that the binding energies difference of graphene on different sites of the Ir(111) surface is larger than that of the Pt(111) surface, resulting in a slightly larger height oscillation of graphene layer on the Ir(111) surface than that on the Pt(111) surface. The tendency of graphene height evolution on the Ru(0001) substrate with 𝛾 =-1.25e-3 is stillbe adopted, and curvature energy curves are obtained in Figures 11.12(c) and 11.13(c). The demarcations with graphene layer
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changing from corrugated to ultra-flat for graphene/Ir(111) and graphene/Pt(111) systems are ~15.4º and ~14.3º, respectively, and these results are all consistent with the DFT calculations which are shown in 11.12(d-e) and 11.13(d-e). Besides, experiments have already reported that graphene layers on the Pt(111) surface show height oscillation of 0.05 to 0.08 nm at rotation angles of 2º, 3º and 6º whereas within 0.03 nm at 14º, 19º and 30º,208 which agrees well with our prediction.
Figure 11.12 (a) Top and side views of the 0º graphene/Ir(111) superstructure. (b) Optimized binding energies and distance of graphene lattice on different sites of the Ir(111) surface. (c) Curvature energies of graphene layers on the Ir(111) surface as a function of the rotation angle and the dashed line denotes the binding energy increase of graphene/ Ir(111) with graphene changing from an ultra-flat to a corrugated structure. (d) Height oscillation of graphene layers on the Ir(111) surface regarding to the rotation angle by DFT calculations. (e) Stereo views of graphene/ Ir(111) superstructures with different rotation angles.
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Figure 11.13 (a) Top and side views of the 0º graphene/Pt(111) superstructure. (b) Optimized binding energies and distance of graphene lattice on different sites of the Pt(111) surface. (c) Curvature energies of graphene layers on the Pt(111) surface as a function of the rotation angle and the dashed line denotes the binding energy increase of graphene/Pt(111) with graphene changing from an ultra-flat to a corrugated structure. (d) Height oscillation of graphene layers on the Pt(111) surface regarding to the rotation angle by DFT calculations. (e) Stereo views of graphene/ Pt(111) superstructures with different rotation angles.
All above discussions prove that the morphology of a graphene layer on a TM substrate is determined by the competition of binding energy and curvature energy of the graphene/TM system, and based on this, the demarcation of the corrugated and ultra-flat graphene layers can be obtained based on the 0º graphene/TM superstructure and unit cells of graphene on the four high-symmetric sites of the TM substrate instead of optimizing graphene/TM superstructures with all rotation angles, which saves the computing resources to a large extent.
Finally, the proposal is also used to predict graphene behaviors in two other systems, i.e., graphene/Re(0001) and graphene/Pd(111), as shown in Figure 11.14. Graphene layer on the Re(0001) surface presents a large height oscillation at 0º, however due to the small binding energy increase, the corrugation of graphene layers can only be maintained to ~ 4.6º. Behaviors of graphene layers on the Pd(111) surface are very similar with that on the Ir(111) and Pt(111) surfaces, although the height oscillation is very weak, the very small binding energy different can only maintain the corrugation of graphene layers to ~9.2º.
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Figure 11.14 (a, d) Different views of the 0º graphene/Re(0001) and the 0º graphene/Pd(111) superstructure. (b, e) Optimized binding energies and distance of graphene lattice on different sites of the Re(0001) and the Pd(111) surface. (c) Curvature energies of graphene layers on the Re(0001) and the Pd(111) surface as a function of the rotation angle and the dashed line denotes the binding energy increase of systems with graphene changing from an ultra-flat to a corrugated structure.
Table 11.1 lists the lattice relationships between graphene and various TM surfaces and summarizes the behaviors of graphene layers on these TM surfaces. On one hand, the smaller lattice mismatch between graphene and TM lattices, the larger size of graphene/TM common cell and the smaller curvature energy of graphene layer at a same rotation angle. On the other hand, a large binding energy difference of graphene on different sites of a TM substrate generally implies a large graphene height oscillation and a large binding energy increase, which means the curvature energy can be compensate to a large extend. For example, graphene on the Ru(0001), Ir(111) and Re(0001) surfaces all shows a very large height oscillation at 0º, moreover, graphene/Ru(0001) superstructures have the largest common cells and strongest binding energy increase, and therefore the corrugation of graphene on the Ru(0001) surface can be maintain the largest rotation angle range of 0~19.5º.
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Table 11.1 Summary of lattice parameters of graphene/TM superstructures and graphene behaviors on different TM surfaces.
Graphene/
Ru(0001)
Graphene/
Rh(111)
Graphene/
Ir(111)
Graphene/
Pt(111)
Graphene/
Re(0001)
Graphene/
Pd(111) Lattice constant
of TMs (Å) 2.706 2.690 2.715 2.775 2.760 2.751
Lattice
Mismatch (%) 9.08 9.35 10.35 12.79 12.20 11.84
L0 (Å) 27.08 26.07 23.52 18.92 19.87 20.49
h0 (Å) 1.56 1.53 0.44 0.28 1.53 0.51
Binding energy
change (eV) 136.90 79.50 8.30 3.20 18.50 5.50
Demarcation (º) 19.50 15.00 15.40 14.30 4.60 9.20