This study identifies the details for direct synthesis of graphene by carbon ion implantation on Cu, Ni and CuNi alloy. Firstly, diffusion and concentration of carbon atoms in Cu and Ni are estimated separately. The concentrations of carbon atoms near the surfaces of Cu and Ni after carbon ion implantation and subsequent thermal annealing were correlated with the number of atoms and with the coverage or thickness of graphene. Systematic experiments showed that the Cu has higher carbon diffusivity and graphene coverage than Ni but higher temperatures and longer annealing times are required to synthesize graphene, similar to those in chemical vapor deposition method. The CuNi system shows better graphene coverage and quality than that on a single metal catalyst even after a short annealing time, as it has larger carbon diffusivity and lower carbon solubility than Ni and shows lower activation energy than Cu. (C) 2018 Elsevier B.V. All rights reserved.