  The nucleation of graphene on a transition metal (TM) surface, either on a
terrace or near a step edge, is systematically explored using density
functional theory (DFT) calculations and applying the two-dimensional (2D)
crystal nucleation theory. Careful optimization of the supported carbon
clusters, CN (with size N ranging from 1 to 24), on the Ni(111) surface
indicates a ground state structure transformation from a one-dimensional (1D) C
chain to a two-dimensional (2D) sp2 C network at N ~ 10-12. Furthermore, the
crucial parameters controlling graphene growth on the metal surface, nucleation
barrier, nucleus size, and the nucleation rate on a terrace or near a step
edge, are calculated. In agreement with numerous experimental observations, our
analysis shows that graphene nucleation near a metal step edge is superior to
that on a terrace. Based on our analysis, we propose the use of seeded graphene
to synthesize high-quality graphene in large area.
