  Upon cooling, branched line defects develop in epitaxial graphene grown at
high temperature on Pt(111) and Ir(111). Using atomically resolved scanning
tunneling microscopy we demonstrate that these defects are wrinkles in the
graphene layer, i.e. stripes of partially delaminated graphene. With low energy
electron microscopy (LEEM) we investigate the wrinkling phenomenon in situ.
Upon temperature cycling we observe hysteresis in the appearance and
disappearance of the wrinkles. Simultaneously with wrinkle formation a change
in bright field imaging intensity of adjacent areas and a shift in the moire
spot positions for micro diffraction of such areas takes place. The stress
relieved by wrinkle formation results from the mismatch in thermal expansion
coefficients of graphene and the substrate. A simple one-dimensional model
taking into account the energies related to strain, delamination and bending of
graphene is in qualitative agreement with our observations.
