Atomic carbon transport between the rh surface and bulk in graphene formation and destruction

The equilibrium transport of atomic carbon between the Rh surface and bulk, which controls the kinetics of the phase transition resulting in graphene growth or destruction, is investigated. The difference between the activation energy $E_{s1}$ of atomic-carbon dissolution and the energy $E_{1s}$ of its segregation from the bulk to the surface is found to be $\Delta E$ = 0.7 eV. The temperature dependence of the critical coating $N_{eq} = N_{eq}(T)$ in the chemisorbed carbon layer is measured. It is a 2D phase transition that takes place at this coating, and graphene islands start to grow: for example, $N_{eq}$ = 7.7 $\times$ 10$^{14}$ cm$^{-2}$ at $T$ = 1800 K, and $N_{eq}$ = 3.1 $\times$ 10$^{14}$ cm$^{-2}$ at $T$ = 1000 K.