## 3 Results
### Fe Ka Intensity Distribution of the Pattern Formed under Cyclic Alternating Voltage  
Figure 11 shows the Fe \(K\alpha\) intensity distribution of the gel sample having multicolored periodic bands (shown in Figures 8 and 10) formed under the cyclic alternating voltage. The horizontal axis indicates the distance from the periodic band of \(n\) = 1 (\(X\)), where \(X\) > 0 is on the anode side. The vertical axis is the relative Fe \(K\alpha\) intensity. As already shown in previous studies [27; 28], the Fe \(K\alpha\) distributions of gel samples with formed PBA precipitates provide a good estimate of the Fe elemental distributions. Because the current XRF experiments were conducted after removing the unreacted [Fe(CN)\({}_{6}\)]\({}^{3-}\) ions, the measured Fe \(K\alpha\) distribution should approximate the distribution of Cu-Fe PBA formed in the gel sample.  
The Fe \(K\alpha\) intensity was relatively strong in regions close to the electrodes (\(X\) = \(-\)9.0 and 26.0 mm). This result is consistent with the fact that considerable amounts of deposits (probably Cu-Fe\({}^{\parallel}\) PBA) were present at the electrodes (Figure 6). Interestingly, a strong Fe \(K\alpha\) intensity (\(\sim\)125 in Figure 11) was also observed in the reddish-brown periodic bands on the cathode side (\(n\) = 2-4 in Figure 10a, named \"main bands\" hereafter) with a sharp peak at \(X\) = 0.5 \(\pm\) 0.25 mm (the uncertainty is due to the focus size of incident X-rays), strongly suggesting that Cu-Fe\({}^{\parallel}\) PBA specifically accumulated in the main bands. Such  
Figure 10: (**a**) Periodic bands formed in the sample tube under the cyclic alternating voltage application. The bands are numbered from 1 (the cathode side) to 15 (the anode side). For comparison, 0.5 mm graduations are also shown at the bottom of the image. (**b**) Distances between the adjacent bands in (**a**): \(d_{n}=X_{n+1}-X_{n}\). The average value and dispersion are shown by the red broken line and pink shaded area, respectively.  
highly localized precipitation is expected to cause the depletion of reactant ions (and, thus, also Cu-Fe PBA) nearby. Indeed, the Fe \(K\alpha\) intensity around the main bands was low, resulting in a broad valley-like structure around \(X\) = 3.0 mm where the blue periodic bands (\(n\geq 12\)) are located. This finding supports the hypothesis that the blue bands mainly consist of Cu(OH)\({}_{2}\) instead of Cu-Fe PBA, as indicated by the blue color itself. Except for the main bands, other reddish-brown periodic bands (denoted \"non-main reddish-brown (RB) bands\" hereafter) did not have very strong Fe \(K\alpha\) intensities, although there was a weak peak at \(X\) = 2.0 mm corresponding to the position of non-main RB bands of \(n\) = 7-9. Therefore, it is likely that the non-main RB bands did not contain significant quantities of Cu-Fe\({}^{\rm II}\) PBA.  
Note that the Fe \(K\alpha\) intensities of the wide blue region (8.0 \(<X<\) 23.0 mm) are comparable to those of the non-main RB bands. Thus, to our surprise, Cu-Fe PBA (reddish-brown or ocher in color) also existed in the blue region. Their amount there is estimated to be \(\sim\)2/5 of that in the main bands, based on the Fe \(K\alpha\) intensities (approximately 50 vs. 125). Additional explanation of this interesting feature is given in the next section.