Magic carbon clusters in the chemical vapor deposition growth of graphene

Ground-state structures of supported C clusters, C(N) (N = 16, ..., 26), on four selected transition metal surfaces [Rh(111), Ru(0001), Ni(111), and Cu(111)] are systematically explored by ab initio calculations. It is found that the core-shell structured C(21), which is a fraction of C(60) possessing three isolated pentagons and C(3v) symmetry, is a very stable magic cluster on all these metal surfaces. Comparison with experimental scanning tunneling microscopy images, dI/dV curves, and cluster heights proves that C(21) is the experimentally observed dominating C precursor in graphene chemical vapor deposition (CVD) growth. The exceptional stability of the C(21) cluster is attributed to its high symmetry, core-shell geometry, and strong binding between edge C atoms and the metal surfaces. Besides, the high barrier of two C(21) clusters' dimerization explains its temperature-dependent behavior in graphene CVD growth.