Kinetics and thermodynamics of carbon segregation and graphene growth on Ru(0001)

We measure the concentration of carbon adatoms on the Ru(0001) surface that are in equilibrium with C atoms in the crystal's bulk by monitoring the electron reflectivity of the surface while imaging. During cooling from high temperature, C atoms segregate to the Ru surface, causing graphene islands to nucleate. Using low-energy electron microscopy (LEEM), we measure the growth rate of individual graphene islands and, simultaneously, the local concentration of C adatoms on the surface. We find that graphene growth is fed by the supersaturated, two-dimensional gas of C adatoms rather than by direct exchange between the bulk C and the graphene. At long times, the rate at which C diffuses from the bulk to the surface controls the graphene growth rate. The competition among C in three states - dissolved in Ru, as an adatom, and in graphene - is quantified and discussed. The adatom segregation enthalpy determined by applying the simple Langmuir-McLean model to the temperature-dependent equilibrium concentration seriously disagrees with the value calculated from first-principles. This discrepancy suggests that the assumption in the model of non-interacting C is not valid.