Local deformations and incommensurability of high quality epitaxial graphene on a weakly interacting transition metal

We investigate the fine structure of graphene on iridium, which is a model for graphene weakly interacting with a transition metal substrate. Even the highest quality epitaxial graphene displays tiny imperfections, i.e. small biaxial strains, ca. 0.3%, rotations, ca. 0.5^{\circ}, and shears over distances of ca. 100 nm, and is found incommensurate, as revealed by X-ray diffraction and scanning tunneling microscopy. These structural variations are mostly induced by the increase of the lattice parameter mismatch when cooling down the sample from the graphene preparation temperature to the measurement temperature. Although graphene weakly interacts with iridium, its thermal expansion is found positive, contrary to free-standing graphene. The structure of graphene and its variations are very sensitive to the preparation conditions. All these effects are consistent with initial growth and subsequent pining of graphene at steps.