The self-organization of carbon atoms close to a nickel surface, which is a process involved in the catalytic growth of carbon nanotubes, is analyzed using grand canonical Monte Carlo simulations based on a specifically designed tight-binding interaction model. This model accounts for the competition between very different local configurations around carbon atoms. In the presence of a Ni(111) surface, four types of configurations corresponding to different reaction steps are identified at 500 and 1000 K, when increasing the C chemical potential: single C atoms adsorbed on the surface or incorporated in interstitial sites, chains creeping on the surface, detached sp(2) C layers, and finally a three-dimensional amorphous C phase. At 1500 K a highly disordered carbide phase is formed.
Amara, H., Bichara, C., & Ducastelle, F. (2006). Formation of carbon nanostructures on nickel surfaces: A tight-binding grand canonical Monte Carlo study. Physical review. B, Condensed matter and materials physics, 73(11). https://doi.org/10.1103/PhysRevB.73.113404 (Original work published 2006)