Pseudo-Transient Modeling of Li Stripping in a Li/LLZO ASSB with Interfacial Defects
Authors: Nadeau David , Roué Lionel , Allard Francois 
Published: December 2024

Lithium (Li) secondary batteries are commonly made of two Li insertion electrodes separated and imbibed of a liquid electrolyte. This common design could benefit from two improvements: (i) using a negative electrode of Li metal (3861 mAh g-1) rather than lithiated graphite (372 mAh g-1) and (ii) choosing a dendrite-impeding solid electrolyte rather than a flammable liquid electrolyte. The all-solid-state battery (ASSB) with Li metal aims for improved safety using inorganic solid electrolytes and outstanding energy density.

However, Li’s dendritic behavior and Li-electrolyte contact roughness are some of the issues slowing down the technological development of Li metal-based ASSB. The experimental approach is key to validating technological advancement. Also, it is highly demanding, considering the numerous steps and tests required, the change-of-scale limitations (e.g., from button half-cell to battery pack), and the availability of internal characterization techniques. To these considerations, numerical modeling is positioned as a support to the experimental approach for in-depth and effective technological development. It thoroughly describes multiphysics, multiscale, and multivariate phenomena of cells and batteries.

Modeling studies of ASSB have been published to support experimental works. However, the research now requires transient coupled electrochemical-mechanical modeling to account for the defect's behavior inside the cell, particularly at the Li-electrolyte interface. Li7La3Zr2O12 (LLZO), a single-ion garnet solid electrolyte, is gaining traction for use in ASSB. Three types of interfacial defect at the negative electrode have been identified with this electrolyte: geometrical asperity, void, and contaminant. While other authors have published a stationary coupled electrochemical-mechanical model for interface with geometrical asperity but without void, our study presents a new transient approach. We have developed a finite elements model for the transient prediction and study of various defects at Li-electrolyte interfaces, marking a significant advancement in this field.

Our research involves a detailed study of the anodic interface for an all-solid-state cell with a solid electrolyte and single-ion electrolyte. Unlike previous studies, we do not assume a perfectly flat interface or one with a filled peak or valley. Instead, we consider three cases. The first case is an interface with a lithium peak in contact with a plane electrolyte garnet. The second case is an interface with a plane lithium electrode in contact with a cracked electrolyte garnet. The third case combines the two previous cases: the interface consists of a lithium peak in contact with a cracked electrolyte garnet. To determine the defects’ initial geometry, we use a Gaussian function. The peak is connected to the electrolyte by its tip, creating a void between the electrode and the electrolyte.

A numerical model is developed to simulate the potentials, stress, and strain inside the electrode-electrolyte domain. Two physics are selected: secondary current distribution and solid mechanics. The model involves charge conservation and the equation of motion, as well as transient Li stripping at the interface. These two states are coupled together using a pseudo-transient approach: steady states are computed and compiled, and time steps are calculated to fit the calculated quantity of stripped Li. An internal electrode surface is defined on all the boundaries but is applicable only to contact boundaries between the electrode and the electrolyte domains. The mesh is adapted to the new geometry at each time step to account for the defect's evolution.

For each case, results are extracted for the current density vector, the geometry and mesh deformation, the pressure, and the von Mises stress. Animations and figures are presented to visualize the in-time stripping of Li. We find that the novel pseudo-transient method is consistent for all the studied cases. We also find that plastic deformation is likely to occur when touching boundaries associated with a void. We discuss the influence of interface geometry on the current and pressure distributions, which help to explain what occurs inside an ASSB.

This research work highlights a contribution to the development of a novel pseudo-transient method. This method allows the coupling of the governing equations with the transient Li stripping. This generic approach to time-variable geometry provides a powerful tool for the visualization and optimization of interfaces. With this numerical method, the experimental developers of ASSB will have access to a useful tool to simulate this technology and improve it. Another highlighted novelty is the application of the developed model to the investigation of the electrostripping of Li. Different cases of time-variable interface with geometrical asperity and void are simulated. These simulations enlighten the interfacial distributions of current and pressure around defects.