Electrochemical–Mechanical Coupling Is Essential to Predict Solid-Electrolyte Fracture during Li-Metal Plating
Authors: Jung Taeho , Carmona Eric A , Song Yueming , Albertus Paul 
Published: August 2024

Lithium propagation through the solid electrolyte is a main failure mechanism for the all-solid-state lithium-anode battery. Preceding the lithium penetration is a crack formation, i.e., fracture, in the solid electrolyte, providing a passage for lithium to preferentially grow during plating [1,2], due to the field-enhancement effect at the lithium tip [3]. Therefore, it is vital to understand both the crack initiation and lithium propagation for the prediction of the system behaviors, as well as the optimization of the interfacial design. Mathematical modeling is a key tool for the fundamental understanding of the undergoing physical processes.
There are several solid-electrolyte fracture models in the literature, but they often treat none or a limited amount of the electrochemical–mechanical couplings. This is despite the fact that high stack pressure, as well as the stress build-up at the lithium/electrolyte interface, necessitate the consideration of stress in the thermodynamic, kinetic, and transport constitutive and governing equations. In particular, the Butler–Volmer equation (or alternative interfacial kinetic expression) must be modified to take into account the stress effects on the reaction kinetics. Furthermore, the incorporation of an appropriate lithium mechanical constitutive behavior is equally important for an accurate depiction of the system behaviors.
Consequently, we aim to build a model that brings together (1) rigorous electrochemical–mechanical couplings and (2) appropriate lithium properties at the battery-application length scale to study the crack initiation during battery operation. It features an isolated Gaussian-curved lithium peak in perfect contact with the lithium-lanthanum-zirconium-oxide (LLZO) solid electrolyte. LLZO is treated as an elastic solid, while lithium is modeled as a non-Newtonian fluid. The pseudo-viscosity of lithium is carefully extracted from Haslam et al.’s thin-film compression experiment [4] using the force–displacement relationship in the squeeze-flow experiment. Current flow in the LLZO is treated with Ohm’s law, and the model is solved for a steady-state application of current.
Preliminary results show that electrochemical–mechanical couplings strongly influence the model outputs. The stress distribution is intimately intertwined with the interfacial current distribution, which dictates the fracture initiation. Other key sensitivities include the constitutive model for the lithium metal and the asperity geometry. We also aim to present model parameter values that produce an experimentally observed fracture current density of around 1 mA/cm2.

References

[1] Ning, Z. et al. (2021). Visualizing plating-induced cracking in lithium-anode solid electrolyte cells. Nature Materials, 20(8), 1121–1129.
[2] Ning, Z. et al. (2023). Dendrite initiation and propagation in lithium metal solid-state batteries. Nature, 618(7964), 287–293.
[3] Carmona, E. A., & Albertus, P. (2023). Modeling How Interface Geometry and Mechanical Stress Affect Li Metal/Solid Electrolyte Current Distributions. Journal of The Electrochemical Society, 170(2), 20524.
[4] Haslam, C. G. et al. (2022). The effect of aspect ratio on the mechanical behavior of Li metal in solid-state cells. Journal of Power Sources, 520, 230831.