## 3 Results and Discussion
In the case of PAN-based CFs, there was no polarization dependence of the OD contrast in the cross sections in at least five fibers for two different types. In the case of the cross section of pitch-based CFs, the polarization dependence of OD contrast as reported in this paper was observed in at least five fibers for three different types. Areas in a,d in Table 3 shows the visible light microscopy images of the longitudinal sections of the PAN- and pitch-based CFs, respectively. The STXM measurements were performed in the areas enclosed by the red dotted lines in a,d in Table 3. Each X-ray absorption image consists of \(73\times 73\) pixels (1 pixel = 41 nm). We also used polarized X-rays, as indicated by the red and blue arrows in Table 3. For the PAN-based CFs, as shown in b,c in Table 3, homogenous OD contrast images were obtained at both X-ray polarizations. In addition, OD was higher under LV (OD = 2.4, c in Table 3) than under LH (OD = 0.3, b in Table 3), indicating that the orientations of the \(\pi\)-orbitals on the plane radial to the CF axis were nearly perpendicular to the fiber axis. Figure 1 shows the averaged C \(K\)-edge spectra of the CF areas in b,c in Table 3. The spectra were normalized using the OD at 292.0 eV. The difference between the spectra in Figure 1 also indicates that the \(\pi\)-orbitals in the PAN-based CFs were oriented perpendicular to the fiber axis. In addition, the results shown in b-e in Table 2 and b,c in Table 3 suggest that the graphene sheets in the PAN-based CFs have a fiber texture where they are aligned along the fiber direction and randomly oriented within the cross section. Figure 1: Average C \(K\)-edge spectra of the CF areas in b,c in Table 3.  
As far as measured, these results revealed that the size and distribution of the \(\pi\)-orbital-oriented domains were different between the PAN- and pitch-based CFs, as schematically illustrated in Figure 3. The direction of the graphene sheets in the PAN-based CFs is parallel to the axis of the fibers that are randomly oriented within the cross section. The size of the \(\pi\)-orbital-oriented domains, if it exists, is less than approximately 50 nm. By contrast, the pitch-based CFs consist of \(\pi\)-orbital-oriented domains whose sizes are approximately 100 nm-1 \(\upmu\)m. The direction of the graphene sheets in the pitch-based CFs is also parallel to the axis of the fibers. Figure 4 shows the XRD patterns of the PAN- and pitch-based CFs. The bar in Figure 4 denotes the XRD peak position of the (002) plane of the graphite in a previous study [22]. The lattice spacing of the (002) plane of the graphite (\(d(002)\)) and the size of the crystallites were calculated from the position of the peak originating from the diffraction of the (002) planes and the full width at half maximum, respectively (Table 4). The \(d(002)\) value of the pitch-based CFs is closer to those of graphite [22] than that of the PAN-based CFs. This is because the raw material of the pitch-based CFs contains aromatic moieties, while that of the PAN-based CFs is composed of a linear carbon backbone [3]. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **PAN-Based CFs** & **Pitch-Based CFs** & **Graphite** \\ \hline \multicolumn{4}{c}{**The lattice spacing of the (002) plane of the**} \\ \multicolumn{4}{c}{**graphite (\(d(002)\)) (nm)**} \\ \multicolumn{4}{c}{**Crystallite size (nm)**} \\ \end{tabular}
\end{table} 
Table 4: Values of the lattice spacing of the (002) plane of the graphite (\(d(002)\)) and crystallite size of PAN- and pitch-based CFs, and graphite from the literature. Figure 3: Schematic of the distribution of the \(\pi\)-orbital-oriented domains and the stacks of graphene sheets in a single (**a**) PAN- and (**b**) pitch-based CF, respectively. The white and yellow two-way arrows represent the directions of the graphene sheets along the fiber and within the fiber cross section, respectively.