Magic Graphene Clusters Formation in the graphene CVD growth process on Ru and Rh

To improve atomically controlled chemical vapor deposition (CVD) growth of graphene, understanding the evolution from various carbon species to a graphene nuclei on various catalyst surfaces is essential. Experimentally, an ultra-stable carbon cluster on Ru(0001), Rh(111) surfaces was observed, while its structure and formation process were still under highly debate. Using ab initio calculations and kinetic analyses, we disclosed a specific type of carbon clusters, composed of a C21 core and a few dangling C atoms around, were exceptional stable in the size range from 21 to 27. The most stable one of them, an isomer of C24 characterized as three dangling C atoms attached to the C21 (denoted as C21-3C), is the most promising candidate for the experimental observation. The ultra-stability of C21-3C originates from both the stable core and the appropriate passivation of dangling carbon atoms by the catalyst surface.