Monte Carlo Modeling of the Graphene Moiré Structure on an Ir(111) Substrate

The article simulates graphene moire patterns on an Ir(111) substrate. The difference in substrate and graphene periods leads to the formation of a moiré superstructure. This superstructure is periodic vertical deformations with hexagonal symmetry. The interaction between carbon atoms in graphene is significantly stronger than with substrate atoms. Therefore, graphene is not stretchable. Van der Waals forces determine the interaction between carbon atoms and substrate atoms. Lennard-Jones' potential models these forces. Surface potential replaces substrate exposure to carbon atoms. Our model calculates the surface potential in one unit cell and translates it using parallel transfer. The surface potential is the sum of the two-particle potentials for the atomic interaction. Comparison with experimental data and unification rules set Lennard-Jones potential parameters. The minimum energy determines the position of the graphene atoms. The simulation describes different orientations of the graphene crystal lattice relative to the substrate lattice. If the main directions of the two lattices coincide, then the period of the moire pattern has a maximum value of (2.54 ± 0.02) nm. This value is in good agreement with the experimental period 2.52 nm. The height of the graphene film above the substrate surface is calculated to be (0.330 ± 0.001) nm. Experimental measurements and ab initio calculations give a value (0.330 ± 0.005) nm. Rotation of the graphene relative to the principal directions of the substrate lattice results in a shorter moire period. A study of the dependence for the moire pattern period on the angle of rotation for the graphene crystal lattice relative to the substrate showed a nonlinear decreasing law.

moire pattern, graphene, metal substrate, iridium, surface potential, Lennard-Jones potential, computer simulation, Monte Carlo method