Surface and bulk effects in graphene growth and destruction on rhodium

The formation and destruction of graphene islands on rhodium is studies at simultaneous consideration of the processes on the surface and in the bulk of the metal. It is shown that, in the equilibrium state, carbon atoms are distributed between three phases: graphene, solid solution in the metal, and chemisorbed carbon; in this case, an increase in the island area requires a simultaneous increase in the C atom concentration both in the chemisorbed and in the dissolved phases. The absolute concentrations of C atoms have been determined in all three phases at various stages of graphene growth and destruction. It is found that activation energy of detachment of a C atom from the graphene island perimeter on rhodium is $E_{\mathrm{det}}$ = 2.7 eV. The number of graphene island has been estimated to be of 10$^{10}$ per 1 cm$^2$.