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

TL;DR

This study investigates the kinetics and thermodynamics of carbon atom segregation and graphene growth on Ru(0001), revealing that growth is driven by a supersaturated carbon adatom gas rather than direct bulk exchange, with implications for understanding surface processes.

Contribution

It provides new insights into the mechanisms of graphene growth on Ru(0001), highlighting the role of carbon adatom supersaturation and challenging existing thermodynamic models.

Findings

Graphene growth is driven by a supersaturated C adatom gas.

The bulk-to-surface diffusion controls growth rate at long times.

Discrepancy found between measured and calculated segregation enthalpy.

Abstract

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.