Honeycomb on Square Lattices: Geometric Studies and Strain Analysis of Moiré Structures at a Symmetry-Mismatched Interface

Moiré superstructures are common for epitaxial graphene on transition metal surfaces and can strongly influence the mechanical and electronic properties of the overgrown film. To date, most of the reported investigations have focused on the moiré patterns on sixfold close-packed substrates, where the superstructures also exhibit hexagonal modulations. Herein, graphene moiré patterns on a fourfold Ni(100) surface have been investigated on the basis of a simple geometric model assuming the existence of coincidence lattices. The moiré motif changes from stripes to rhombic networks as the misorientation angle between graphene and the substrate increases. The unit cells of the observed moiré superstructures are described within a matrix formalism, allowing the lattice parameters to be accurately determined. In all cases, the graphene lattice was found to be anisotropically strained in order to obtain commensurability in the moiré supercells. Our work for the first time determines the atomic configurations for a variety of graphene moiré superstructures on a fourfold substrate, on the basis of a coincidence lattice model. The resulting atomic-scale details will serve as a reference for future experimental and theoretical studies of this specific system and will shed light on the geometric and strain analysis of two-dimensional films supported by a symmetry-mismatched surface.