## 3 Results and Discussion  
The Compton scattering X-ray energy spectra obtained from the cathode, separator, and anode of the fresh cell are shown in Figure 2a. The area of these energy spectra was normalized to the same value to clarify the line-shape of each energy spectrum. The x-axis, \(p_{z}\) in Figure 2a, represents the electron momentum along the z-direction, which experimentally corresponds to the scatter vector direction. \(p_{z}\) is given by [24]:  
\[\frac{p_{z}}{mc}=\frac{E_{o}-E_{i}+\left(E_{i}F_{o}/mc^{2}\right)\left(1-\cos \theta\right)}{\sqrt{E_{i}^{2}+E_{o}^{2}-2E_{i}E_{o}\cos\theta}}, \tag{5}\]  
where \(mc\) is \(1/\alpha\) and \(\alpha\) is the fine structure constant (as we used atomic units following the conventions of X-ray spectroscopy). \(E_{0}\) and \(E_{i}\) are the incident and scattering X-ray energy, respectively; \(mc^{2}\) is the rest mass energy of the electron; and \(\theta\) is a scattering angle. The energy spectrum obtained from the separator has a narrow distribution, and the energy spectrum obtained from the anode has a broad distribution, as shown in Figure 2a. Figure 2b shows the internal structure of the fresh VL2020 cell in the discharged state observed using Compton scattering intensity and the S-parameter. These data were obtained from the Compton scattering X-ray energy spectrum, which was measured using the scanning incident X-rays from the lower end of the cathode to the end of the anode. The Compton scattering intensities were obtained by normalizing the number of photons of the Compton scattering X-rays by the number of photons of the incident X-rays, which were measured using an ion-chamber. The measurement time was 30 s at each point. The background colors in Figure 2b indicate the region of each component of the cell. The regions at 0 mm \(\geq\) z \(<\) 0.04 mm, 0.08 mm \(<\) z \(<\) 0.18 mm, 0.21 mm \(<\) z \(<\) 0.42 mm, 0.43 mm \(<\) z \(<\) 0.64 mm, and 0.65 mm \(<\) z \(\leq\) 0.8 mm correspond to the stainless steel outer casing, spacer, anode, separator, and cathode, respectively. The Compton scattering intensity interestingly indicated that the anode had a two-layer structure. Although the Compton scattering intensity and S-parameter had opposite trends in this cell as shown in Figure 2b, we can non-destructively identify the inner structure of the cell using both the Compton scattering intensity and S-parameter. Figure 3a,b depicts the Compton scattering intensity distribution, and Figure 3c,d is the S-parameter distribution of the charged and discharged states in the fresh cell, respectively. The state of charge on the cell changed by a constant current of 2 mA. The separator position shifted about 80 \(\upmu\)m toward the cathode direction by charging the fresh cell in both the Compton scattering intensity and S-parameter distributions. This shift in the separator position is caused by the volume expansion of the anode because the lattice volume of the LiAl alloy expands about 95% compared with that of Al by inserting lithium [31]. Therefore, in the Compton scattering intensity distribution, the intensity of the anode region decreased by charging the cell despite the average electron density increase with the lithium insertion. The S-parameter intensity increased because lithium ions moved to the anode during charge. The averaged S-parameter at the cathode and anode in the charged and discharged states and the corresponding lithium composition are summarized in Table 1. The lithium composition was determined using the calibration curve between the S-parameter and lithium composition, which was measured previously using inductively-coupled plasma (ICP) analysis. Here, the S-parameter obtained from the charged state in the cathode was normalized by the lithium composition in the charged state of the cathode obtained from the ICP analysis, and the S-parameter obtained from the discharged state in the anode was normalized by the lithium composition in the discharged state of the anode obtained from the ICP analysis.