  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.
