## 3 Results
### SEM Observation of the Pattern Formed under Cyclic Alternating Voltage  
Figure 13 shows SEM images of the gel sample having multicolored periodic bands formed under the cyclic alternating voltage (other results related to the same sample are shown in Figures 8 and 10, Figures 11 and 12). Figure 13a-c was obtained for the periodic bands of \(n=1\) (the non-main RB band), 2 (the main band), and 12 (the blue band), respectively. For comparison, a region close to the anode is also shown in Figure 13d.  
Figure 13: SEM images (\(\times\)5000 for **(a)** and **(b)**; \(\times\)3000 for **(c)** and **(d)**) of the multicolored pattern formed under the cyclic alternating voltage application, obtained after removing unreacted ions. The positions where these SEM images were acquired are indicated in the uppermost panel. The plate-like crystallites in **(a)** and the irregularly shaped (albeit cube-like) crystallites in **(b)** are indicated by white circles to guide the eye. Scale bars (which were employed for estimating the sizes of the crystallites) are provided in each image.  
As shown in Figure 13d, precipitates close to the anode consisted of crystallites that were definitely cubic, which is characteristic of PBA [23]. In accordance with the relatively high Fe K\(\alpha\) intensity in Figure 11 (i.e., a large amount of Cu-Fe PBA), there were numerous crystallites. The crystallite sizes (1-3 \(\upmu\)m on each side) are somewhat smaller than those of Mn-Fe PBA crystallites formed in agarose gels in the conventional RD setup for Liesegang banding (3-10 \(\upmu\)m on each side) [23]. Despite the different (but comparable) sizes, Figure 13d is very similar to the SEM images acquired previously for precipitation bands of Mn-Fe PBA in agarose gels [23, 31].  
Figure 13b is an SEM image of precipitates formed in the main band of \(n=2\). These precipitates also consisted of cube-like crystallites, even though their sizes were considerably smaller (0.1-0.8 \(\upmu\)m on each side) and the shapes were not perfectly cubic, suggesting the existence of many defects. These small crystallites can be considered to form the reddish-brown background observed in Figure 12b.  
The somewhat irregular shapes of the crystallites in Figure 13b may be a disappointment if one expects well-defined PBA crystallites with few defects for use as electrodes [15, 16, 20] or magnets [19]. However, when used as adsorbents or catalysts, smaller PBA crystallites with many defects would be advantageous because of their inherently large surface area. Indeed, the importance of defects (i.e., porosity) has been reported in several studies on the adsorption/catalytic properties of PBA [17, 18, 20, 21, 22, 32].  
Figure 13a is an SEM image of the precipitates formed in the non-main RB band of \(n=1\). Interestingly, in addition to the cube-like crystallites, there were also plate-like crystallites (indicated by white circles). This finding strongly suggests that the non-main RB bands consisted of two types of crystallites, namely plate-like Cu(OH)\({}_{2}\) and cube-like Cu-Fe PBA.  
Figure 13c is an SEM image of the precipitates formed in the blue band of \(n=12\). Unlike the other images, this image shows only a few cube-like crystallites as expected. Instead, plate-like crystallites were dominant and even formed laminates with the size of \(\sim\)25 \(\upmu\)m. This finding also suggests the large contribution of Cu(OH)\({}_{2}\) to the blue periodic bands.