DFT studies of Graphene on Ni(111) and Surface Nickel Carbide Ni$_{2}$C

Graphene with its unique transport properties supported on ferromagnetic materials is a promising candidate for the fabrication of spin-filtering devices. In order to study the growth of graphene on metal surfaces, graphene on Ni(111) is a perfect system from a structural point of view. The CVD growth of graphene on Ni(111) was studied with STM. The experiments showed not only perfect aligned (1x1) structures, but also several moir\'{e} patterns are observed. They are due to grain rotations of graphene on both Ni(111) and also surface nickel carbide Ni$_{2}$C. During CVD growth carbon atoms segregate into the Ni bulk. With an increasing carbon concentration first the surface carbide and then a graphene layer on top is built. We studied the systems using the DFT program package VASP with the DFT-D2 method of Grimme to include van der Waals interactions. In our theoretical analysis we tried to understand the formation of the graphene and Ni$_{2}$C on Ni(111). We calculated the stability of the surface carbide phase and the binding energies of rotated and unrotated graphene on Ni(111) as well as on Ni$_{2}$C in order to understand the experimental findings. Graphene and Ni$_{2}$C have no epitaxial relationship due to their incommensurate lattices, leading to a spread in grain rotations.