Effect of preparation on the commensurabilities and thermal expansion of graphene on Ir(111) between 10 and 1300 K

Abstract

The effects of the temperature on the structure of a single layer of graphene on Ir(111) have been investigated in situ in the growth chamber by grazing incidence x-ray diffraction between 10 and 1300 K. In addition, the effect of two growth temperatures has been studied. The graphene lattice parameter of the main, nonrotated phase displays a characteristic hysteresis whose lower and upper branches correspond to phases in which integer numbers ($m$,$n$)${}_{\mathrm{Ir}}$ of the Ir lattice parameters match integer numbers ($p$,$q$)${}_{\mathrm{Gr}}$ of the graphene lattice parameters, i.e., commensurate phases, (19,0)${}_{\mathrm{Ir}}$\ifmmode\times\else\texttimes\fi{}(21,0)${}_{\mathrm{Gr}}$ and (9,0)${}_{\mathrm{Ir}}$\ifmmode\times\else\texttimes\fi{}(10,0)${}_{\mathrm{Gr}}$, respectively. With a higher growth temperature, graphene presents, in addition to a main nonrotated, incommensurate phase, domains with a small rotation (2.37\ifmmode^\circ\else\textdegree\fi{}) relative to the substrate, corresponding to a (7,2)${}_{\mathrm{Ir}}$\ifmmode\times\else\texttimes\fi{}(8,2)${}_{\mathrm{Gr}}$ commensurate phase. Despite the weak interaction between graphene and iridium, the thermal expansion coefficient of graphene is positive at all temperatures, even at liquid helium temperature contrary to free-standing graphene. It is also close to the iridium thermal expansion because of the tendency to form commensurate phases, which creates a strong link between the graphene and substrate lattices and decreases the elastic energy.