## 4 Results and Discussion  
### Shape Effect  
Figure 2a-c show electron micrographs of the spherical, plate-shaped, and fibrous Al\({}_{2}\)O\({}_{3}\) particles used for the analyses of the electrode tortuosity according to the shape of the active material, respectively. It was confirmed that each had the designed shape characteristics. The spherical particles were isotropic and were well separated from each other. The plate-shaped particles were anisotropic, which meant that their aspect ratios were distributed in various ways, while the fibrous particles had extremely large aspect ratios and many micropores were formed due to the aggregation of the particles. Figure 1: (**a**) Schematic diagram of an electron-blocking cell used for tortuosity analysis, and (**b**) hypothetical chronoamperometric curve showing steady-state current (\(I_{\text{ss}}\)), together with the equations for tortuosity estimation. To perform a more in-depth analysis of the difference in tortuosity in relation to the particle shape in the all-solid-state battery electrode, the ratio of solid electrolyte in the electrode (\(\epsilon_{\text{SE}}\)) was adjusted: \(\epsilon_{\text{SE,1}}=0.32\), \(\epsilon_{\text{SE,2}}=0.72\). Figure 3 shows the chronoamperometric curves of the test cell fabricated with the three types of active materials, using the high (\(\epsilon_{\text{SE,1}}\), Figure 3a) and low (\(\epsilon_{\text{SE,2}}\), Figure 3b) active material ratios, for a total of six active material conditions. In all six cases, a steady state was reached after an initial rapid decrease in the concentration of the active material. The steady state was reached after an initial rapid decrease in the concentration of the active material. in current. In addition, because the transport of lithium ions was relatively complex with a high active material ratio (\(\varepsilon_{\text{SE,1}}\)), it took longer to reach a steady state compared to the case with the low active material ratio (\(\varepsilon_{\text{SE,2}}\)), and the steady-state current (\(I_{\text{ss}}\)) was also low. The tortuosity was determined based on the steady-state current using the method presented in Section 2, and the results with the high (\(\varepsilon_{\text{SE,1}}\)) and low (\(\varepsilon_{\text{SE,2}}\)) active material ratios are shown in Figure 4a,b, respectively. Figure 3: Chronoamperometric curves at (**a**) low (\(\varepsilon_{\text{SE,1}}=0.32\)) and (**b**) high (\(\varepsilon_{\text{SE,2}}=0.72\)) volume fractions of solid electrolyte. First, under the condition in which the ratio of active material was high (\(\varepsilon_{\text{SE,1}}\)), a significant difference in tortuosity occurred according to the shape (Figure 4a), with tortuosity values two times and three times higher than the spherical shape, for the plate and fiber shapes, respectively. Because the electrodes all had the same electrolyte volume ratio, this difference could be said to reflect a difference in the ease of lithium-ion transport due to the shape of the active material or connectivity difference in the transport path. On the other hand, the spherical and plate-shaped electrodes had almost the same porosity (\(\sim\)20%), while the fibrous electrodes had values that were approximately twice as large (Figure 4c). The fact that the spherical and plate-shaped electrodes had the same porosity suggested that the difference in the tortuosities of the electrodes with these two forms of active material was due only to the complexity of the ion transport path in the solid electrolyte. In the case of plate-shaped particles with a large aspect ratio, considering the previous report that the particles tend to be preferentially arranged in a direction parallel to the substrate during the electrode manufacturing process [21], the tortuosity difference between the spherical and plate-shaped particles with the same porosity was easy to understand. The preferential arrangement of our plate-shaped particles was also observed in the cross-sectional image of the composite electrode (Figure 5a).