# Characterization of Graphene Carbon Produced by Pulsed Laser Ablation of Sacrificial Carbon Tapes
## 4 Discussion  
The ratio of the D and G band intensities, \(I_{D}\)/\(I_{G}\), is widely used for the quantitative evaluation of defects in graphitic materials [47; 50; 51]. For the given excitation laser wavelength \(\lambda_{l}\), the following expression can be used to evaluate the sp\({}^{2}\) cluster size \(L_{a}\)[51]:  
\[L_{a}(\text{nm})=2.4\cdot 10^{-10}\lambda_{l}^{4}(I_{D}/I_{G})^{-1} \tag{1}\]  
From the \(I_{D}\)/\(I_{G}\) ratio, and the peak's position (Table 2) and shape, we can conclude that the films deposited on sapphire substrates correspond to the first or the second stage of disorder, according to the amorphization trajectory of [PERSON] and [PERSON] [45; 52]. The increase in structural disorder causes broadening of the D and G bands. The combination of the \(I_{D}\)/\(I_{G}\) ratio and full width at half maximum (FWHM) of the G band allows us to distinguish between stages 1 and 2 [48; 53]. The positions of the G line in the spectra are upshifted by 6 cm\({}^{-1}\) and 5 cm\({}^{-1}\) for the GLC/sapphire-1 and GLC/sapphire-2 samples, respectively. We used the FWHM of the G band to evaluate the minimal sp\({}^{2}\) cluster size in the samples, according to [53]. The evaluated minimal size was in the range of 6-10 nm. This allowed us to conclude that the samples correspond to the first stage of amorphization, for which Equation (1) is valid. The characteristic sizes of the graphenic clusters were found to be 15.3 nm and 17.7 nm for the GLC/sapphire-1 and GLC/sapphire-2 samples, respectively. These features in the Raman spectra allow us to conclude that the GLC/sapphire-1 film has a higher degree of structural disorder in comparison with the GLC/sapphire-2 sample. It can also be concluded that the deposited carbon films are similar to nanocrystalline graphite or disordered multilayer graphene in the degree of in-plane structural ordering.  
The 2D Raman band of the graphite-like materials is very sensitive to the stacking order of the graphene layers along the [001] direction [47]. It was shown that the 2D bands in our second-order Raman spectra can be fitted using only one Lorentzian function, centered at 2701 and 2707 cm\({}^{-1}\) for the GLC/sapphire-1 and GLC/sapphire-2 samples, respectively. This indicates that the interaction between the graphenic planes is weak enough that there is no splitting in the \(\pi\)-electron dispersion energies [53; 54], which is typical of the turbostatic structure of disordered multilayer graphene and reduced graphene oxide [26; 27; 31; 33; 34; 55; 34]. We also estimated the sp\({}^{2}\) cluster size based on the FWHM of the 2D bands using the experimental data from the work [55]. The values 22 and 20 nm were obtained for the GLC/sapphire-1 and GLC/sapphire-2 samples, respectively, which is in good agreement with the previous estimations.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{4}{c}{**Pos., cm\({}^{-1}\)**} & \multicolumn{4}{c}{**FWHM, cm\({}^{-1}\)**} \\ \cline{2-9}  & **D** & **G** & **2D** & **D\({}^{\prime}\)** & **D** & **G** & **2D** & \(I_{D}\)/\(I_{G}\)** & \(L_{a}\), nm \\ \hline GLC/sapphire-1 & 1356 & 1587 & 2701 & 1623 & 67 & 50 & 76 & 1.11 & 15.3 \\ \hline GLC/sapphire-2 & 1358 & 1586 & 2707 & 1621 & 45 & 43 & 63 & 0.96 & 17.7 \\ \hline \end{tabular}
\end{table}
Table 2: Positions (Pos.) of the most intense Raman peaks, full width at half maximum (FWHM), integral intensities ratio (\(I_{D}\)/\(I_{G}\)) of the D and G peaks, and sp\({}^{2}\) cluster size estimation (\(L_{a}\)).