Nonlinear Stress Analysis of Compressed Composite Electrode in Sulfide All-Solid-State Lithium-Ion Battery with X-Ray CT
Authors: Horikawa Naoki , Ohashi Akinari , Kodama Manabu , Hirai Shuichiro 
Published: December 2020

Sulfide solid electrolytes display favorable characteristics for applications in all-solid-state batteries.Various solid electrolytes have been developed so far, but in order to realize high ionic conductivity, it is necessary to apply pressure to reduce voids between the solid electrolytes[1][2]. This is important when preparing an electrode layer. Particularly in cathode, which is a mixture of hard cathode active materials and soft sulfide solid electrolyte, inhomogeneous stress distribution could be generated in the solid electrolyte in cathode. It is expected that this results in non-uniform ionic conductivity. Therefore, by analyzing stress distribution in cathode, ion transport phenomenon in the solid electrolyte can be clarified, and we can obtain insights for optimum battery design. There are mainly two methods for analyzing the stress distribution in powder mixture. One is Discrete Element Method (DEM), which treats powder particles as independent discontinuous bodies and analyzes interactions between powder particles. With DEM, while detailed interactions between voids and particles can be analyzed, stress analysis inside the particles is difficult. Moreover, the calculation cost is very high. Another is the Finite Element Method (FEM), which is a method that captures powder and voids as a continuous body that is divided into small elements for analysis. Although detailed interaction between voids and particles cannot be analyzed, the advantage of FEM is that all the stresses in each small area can be solved and the calculation cost is small. In previous study, ion transportation simulation in a pseudo cathode with linear FEM stress analysis was conducted [3][4]. The numerical ionic conductivity is almost same as the experimental results, but the results have large error range since the Young's modulus of the solid electrolyte must be constant in linear stress analysis. But in reality, the Young’s modulus of powder is not constant [5]. This is because the voids decrease as the stress increases. When the stress is low, the Young's modulus is small since many voids remain and there are rooms to fill the voids. However, when the stress is high, the Young's modulus is large since the powder will not strain with small amount of voids. For high accuracy numerical simulation with small error range, the Young’s modulus should not be constant and non-linear stress analysis should be conducted for FEM.
In this study, to focus on the ionic conduction characteristics in the electrode layer, the cathode active material was replaced with an electrochemically stable ZrO2 to suppress the charge / discharge reactions. The prepared composite material was loaded into a cell with excellent airtightness, and three-dimensional structural measurement and strain measurement were performed by X-ray CT. Then, stress analysis by COMSOL was performed using the three-dimensional structural data obtained by X-ray CT.
Figure 1 shows the relationship between Young's modulus and stress of a compressed solid electrolyte. As shown, Young's modulus of solid electrolyte has a strong nonlinearity and increases with stress. Figure 2 shows the stress-strain characteristics obtained from experiment, linear stress analysis, and non-linear stress analysis. Previous studies have shown that the Young's modulus of solid electrolytes is in between 25 MPa and 25 GPa.[5] In this study, we set the lower limit of Young's modulus to 25 MPa and the upper limit to 25 GPa for the error range in linear analysis. In linear analysis, error range is heavily dependent of the Young’s modulus of solid electrolyte. On the other hand, in nonlinear analysis, it is possible to reproduce the strain close to that from the experiment. Figure 3 is a cross-sectional view of the stress distribution in non-linear stress analysis results. In this figure, the stress is normalized by applied pressure. As seen in previous studies, materials with high Young’s modulus acts as pillar in a composite and causes stress concentration. [3].However, the relative stress in the solid electrolyte with applied pressure of 200 MPa is higher than that of 100 MPa. This is a result of reflecting the non-linearity of the solid electrolyte. As shown in Fig.1, the Young's modulus of a solid electrolyte with strong nonlinearity increases with increasing stress. As a result, it is considered that the difference in Young's modulus between ZrO2 and solid electrolyte decreases. And thereby causes the stress concentration on ZrO2 to decrease and causes the relative stress of solid electrolyte to increase. The higher the stress on solid electrolyte, the higher the ionic conductivity. We will also discuss the effect of non-linearity of solid electrolyte on ionic conduction characteristics by conducting electricfield analysis based on stress distribution obtained by non-linear analysis in oral presentation.

Figure 1