## 4 Results and Discussion
### Shape Effect
Figure 4: (**a,b**) Tortuosities and (**c,d**) porosities of the composite electrodes containing different shapes of Al\({}_{2}\)O\({}_{3}\) powders. (**a,b**) Low electrolyte volume fraction (\(\varepsilon_{\text{SE,1}}=0.32\)); (**c,d**) high electrolyte volume fraction (\(\varepsilon_{\text{SE,2}}=0.72\)). On the other hand, it is noteworthy that the fiber type had twice the porosity. This means that when the active fibrous material was used, the solid electrolyte did not smoothly penetrate the pores inside the electrode during the electrode manufacturing process. In the case of the fibrous particles, unlike the other shapes, particle aggregation was observed, and, as a result, countless micropores were formed between the particles (Figure 2c). Thus, it is believed that the electrodes composed of fibrous particles had high porosity and tortuosity values because the solid electrolyte did not sufficiently fill the numerous micropores formed by the aggregation of particles. The above argument was supported by the cross-sectional image of the electrode (Figure 5b). When an active fibrous material is used in an electrode for a lithium-ion battery using a liquid electrolyte, the excellent permeability of the liquid electrolyte generally increases the active material/electrolyte contact area, which is known to be advantageous for realizing a high-power battery [43]. However, given the above results, it is necessary to pay great attention to the low filling rate of the solid electrolyte  
Figure 5: Cross-sectional views of the composite electrodes containing (**a**) plate-shaped and (**b**) fibrous particles at low volume fraction of solid electrolyte (\(\epsilon_{\text{SE,1}}=0.32\)). AM: active material. SE: solid electrolyte. resulting from particle aggregation in all-solid-state battery electrodes, especially when a high proportion of active fibrous material is used. To experimentally verify the above arguments about the low filling results when a solid electrolyte was used with fibrous particles, the same analysis was performed for a high electrolyte ratio (low active material ratio) with a relatively low solid electrolyte permeation problem. As a result, the differences in the tortuosity and porosity values between the fibrous type and the other shapes were significantly reduced at a low active material ratio (Figure 4b,d). It is quite likely that the particle aggregation was suppressed as the electrolyte ratio increased, and the electrolyte filling was also dramatically improved. It should be mentioned that it is not easy to use computer simulation to investigate the microstructure of an electrode for an all-solid-state battery in which active material aggregation and insufficient electrolyte filling occur. In general, when computational simulation is used for tortuosity analysis, it is common to simplify the microstructure of an electrode and then analyze it based on a theoretical formula. The result may have a significant error compared to the actual result. The discrepancy between the theoretical and actual values could also be confirmed using the results for the change in tortuosity in relation to the volume ratio of the solid electrolyte in the electrode (Figure 6). When the Bruggeman relation (Equation (3)) was applied with the low active material ratio (\(\epsilon_{\rm SE}>0.45\)), which was considered to have relatively few problems with dispersion, aggregation, and electrolyte penetration, the Bruggeman coefficient was estimated to be approximately 3.13. It is noteworthy that when the active material ratio was approximately 60% or greater (\(\epsilon_{\rm SE}<0.6\), blue dotted circle in Figure 6), the tortuosity value derived from the actual experiment was larger than the expected value based on the Bruggeman relation, and a larger active material ratio resulted in a more significant difference. These results suggest that erroneous results may be derived when the microporous structure in the electrode for an all-solid-state battery is overly simplified and implemented.