Influence of Stress Distribution on the Ionic Conductivity of a Sulfide All-Solid-State Lithium-Ion Battery
Authors: Ohashi Akinari , Kodama Manabu , Yasuda Tomoki , Hori Satoshi , Suzuki Kota , Kanno Ryoji , Hirai Shuichiro 
Published: May 2020

Introduction, Objective, Methods
It is widely known that the ionic conductivity of a sulfide based solid electrolyte (SE) is enhanced with pressurization[1]. In order to take advantage of this property, sulfide all-solid-state lithium-ion battery (SASSLiB) is expected to be pressurized. The electrodes of SASSLiB are composite material constituted by different substances such as SE and active material (AM). Hence, when pressurized, a non-uniform stress distribution forms within the electrodes due to the unique Young’s moduli of the constituting substances[2]. Considering the pressure dependence of ionic conductivity observed in SE, a non-uniform stress distribution is likely to affect the net ionic conductivity of the electrodes.
Objective of this study is to elucidate the effect of stress distribution on the ion transportation characteristics of an electrode layer in SASSLiB by combining experiment and numerical calculation. The experiment includes internal visualization by x-ray CT and electrochemical measurement of a simplified electrode consisting SE (Li10GeP2S12)[3] and electrochemically stable zirconia. To separate the effect of stress distribution from morphological factors such as volumetric fraction and tortuosity, structural data collected from x-ray CT was used to quantify the volume of non-SE regions and used to quantify tortuosity by numerical calculation employing random-walk algorithm. Additionally, voxel-finite-element-stress calculation and electric field calculation was combined to perform ion transportation simulation. To elaborate, stress distribution was expressed in two different calculation models: isotropic and anisotropic. The isotropic model assumes that the ionic conductivity at a particular voxel is dependent on the minimum principal stress value in all x, y, z directions. The anisotropic model assumes that the ionic conduction occurs anisotropically with different ionic conductivity corresponding to the voxel’s perpendicular stresses in x, y, z direction. Furthermore, the ion transportation simulation was conducted for cases with SE’s Young’s modulus set to 0.3 GPa and 21.7 GPa. The former value is experimentally measured under low pressure condition, and the latter is the value obtained by first principle calculation[4]. We have assumed that the true value of unknown and pressure dependent Young’s modulus of SE lies in between these two values.
Result and Discussion
The ionic conductivity of a composite made by SE and zirconia was significantly lower than that of SE-only sample. Comparing the ionic conductivities obtained experimentally and numerically, the discrepancy was large when only void ratio and tortuosity were considered. When stress distribution was additionally considered, discrepancy drastically decreased. Fig.1 and Fig.2 show the magnitude of discrepancy between experimental and numerical results when composite was under 100 MPa of pressure, and are results obtained by isotropic model and anisotropic model respectively. The points plotted are relative conductivity with respect to a mixture with 0% zirconia, and the points represented are results from the composite with zirconia fraction varying from 19% to 67% from left to right. The dotted line represents a complete alignment of experimental and numerical results, and closer a value is to this line, smaller the discrepancy. It is apparent from the two figures that in both models that there is a significant offset between the line of complete alignment and the case stress distribution was not considered. On the other hand, the line of complete alignment lies in between the results from numerical models obtained with respective Young’s modulus. This validates our assumption that the true Young’s modulus lies in between the values mentioned earlier. Additionally, this implies that by accounting for the non-linearity of stress-strain relationship of SE, the discrepancy between the line of complete alignment and the numerical results can further be decreased.
The discrepancy between the line of complete alignment and the results excluding stress distribution increases as the volumetric fraction of zirconia increases. Additionally, the discrepancy between the numerical results of two different Young’s moduli increases as zirconia fraction increases. These increasing discrepancies with the increased zirconia fraction can be attributed to the decreasing stress in SE, instigating decrease of ionic conductivity, and in turn, widening the discrepancy.
Conclusion
Presence of a material with different Young’s modulus than that of SE alters the ion transportation characteristics of an electrode layer by forming a non-uniform stress distribution. And the impact of such stress distribution is much greater as the volumetric ratio of materials with high Young’s modulus increase. Therefore, stress distribution is an important factor to consider to accurately evaluate the ion transportation characteristics in the electrode layers of SASSLiB, especially as volume of non-SE materials, such as AM, increases.

Figure 1