## 4 Discussion  
The determination of the \({}^{13}\)C content by two independent probes, like NRA involving \({}^{12}\)C and \({}^{13}\)C isotopes, and Raman spectroscopy, help to elucidate the mechanism of formation of the TLG observed after carbon implantation at high temperature. The best scenario to explain the results reported here assumes the previous presence of \({}^{12}\)C precursors, which act as nucleation centers. These \({}^{12}\)C atoms diffuse towards preferential nucleation centers as grain boundaries when the sample is heated. It must be noted that we cannot visualize TLG pieces after the RTA step. On the other hand, \({}^{13}\)C atoms, brought by implantation at high temperature, may aggregate to these nucleation centers during the heating and subsequent cooling. The mechanism of graphene formation has been described in the literature on nickel films by using isotopic labeling, starting from a \({}^{13}\)CH\({}_{4}\) gas source [37]. It involves carbon bulk absorption and diffusion into the nickel film, followed by carbon surface segregation and precipitation of the carbon aggregates into graphene pieces (grapheneization). At this stage it is important to distinguish between these two stages: (i) carbon surface segregation, without formation of graphitic-like fragment, and (ii) precipitation into graphene or TLG [38]. This mechanism does not include any nucleation process, but it is likely that \({}^{12}\)C still  
Figure 11: Raman spectroscopy on the \({}^{13}\)C implanted sample. (**a**) Optical micrograph on a large scale displaying the network of grain boundaries; (**b**) Optical micrographon of a TLG with the grain boundaries (continuous lines) and the extrapolated grain boundaries below the TLG (dotted lines); (**c**) Raman mappings of (**c**) the G band; (**d**) the \({}^{13}\)C concentration obtained from the downward wavenumber shift of the G band; (**e**) the \(I_{\rm G}/I_{\rm D}\) and (**f**) \(I_{\rm 2D}/I_{\rm G}\) ratio, respectively. Pixel size is around 0.3 \(\times\) 0.3 \(\upmu\)m\({}^{2}\). existing at the surface may provide in our case the nucleation centers where the carbon surface first segregates. This can explained in that that, generally, a poor \({}^{13}\)C concentration is observed above the grain boundaries below the TLG. Further carbon, including \({}^{12}\)C incorporated into the nickel films as shown by NRA, and \({}^{13}\)C implanted further segregate to the surface and precipitate on these nucleation centers, forming a TLG that now expands towards the grain. Thus, area above the surface of the grain shows generally larger \({}^{13}\)C concentrations. It must be remembered, however, that a clear scrambling of the isotopic label occurs. In addition, it must be noted, however, that the pixel resolution in the Raman mapping is too poor to state if the carbon will aggregate to the nucleation center, either as atoms, giving complete random scrambling of the isotopes around the nucleation center, or as aromatic aggregates, giving distinct \({}^{12}\)C and \({}^{13}\)C 6-fold cycles. Clearly, further investigations are required to resolve this point. In conclusion the results reported here clearly support the mechanism of random carbon incorporation through carbon dissolution, carbon surface segregation, and surface precipitation of carbon aggregates into graphitic-like fragments, a mechanism postulated on nickel films. This is in contrast with the mechanism postulated on copper, where carbon precipitates directly as graphene on the surface. In this latter case, pure \({}^{12}\)C TLG pieces would be observed. As shown by SEM, the nucleation centers are mainly located near microstructured defects like grain boundaries of nickel, preventing a uniform covering of the surface. This preferential nucleation is due to a rapid selective diffusion of carbon towards these defects. Therefore minimizing the grain boundaries, and other microstructural defects will get more uniform at the nucleation sites and consequently will improve the size of the domain.