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Using first principle calculations, we study the surface-to-bulk diffusion of C atoms in Ni(111) and Cu(111) substrates, and compare the barrier energies associated with the diffusion of an isolated C atom versus multiple interacting C atoms. We find that the preferential Ni-C bonding over C–C bonding induces a repulsive interaction between C atoms located at diagonal octahedral voids in Ni substrates. This C–C interaction accelerates C atom diffusion in Ni with a reduced barrier energy of ∼1 eV, compared to ∼1.4-1.6 eV for the diffusion of isolated C atoms. The diffusion barrier energy of isolated C atoms in Cu is lower than in Ni. However, bulk diffusion of interacting C atoms in Cu is not possible due to the preferential C–C bonding over C–Cu bonding, which results in C–C dimer pair formation near the surface. The dramatically different C–C interaction effects within the different substrates explain the contrasting growth mechanisms of graphene on Ni(111) and Cu(111) during chemical vapor deposition.


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