A continuum electro-chemo-mechanical gradient theory coupled with damage: Application to Li-metal filament growth in all-solid-state batteries

Abstract

We formulate a thermodynamically-consistent electro-chemo-mechanical gradient theory which couples electrochemical reactions with mechanical deformation and damage in solids. The framework models both species transport across the solid host due to diffusion/migration mechanisms and concurrent electrochemical reaction at damaged zones within the solid host, where ionic species are reduced to form a new compound. The theory is fully-coupled in nature with electrodeposition impacting mechanical deformation, stress generation and subsequent damage of the solid host. Conversely, electrodeposition kinetics are affected by mechanical stresses through a thermodynamically-consistent, physically motivated driving force that distinguishes the role of chemical, electrical and mechanical contributions. The framework additionally captures the interplay between growth-induced fracture of the solid host and electrodeposition of a new material inside cracks by tracking the damage and extent of electrodeposition using separate phase-field variables.While the framework is general in nature, we specialize it towards a critical problem of relevance to commercialization of next-generation all-solid-state batteries, namely the phenomenon of Li-metal filament growth across a solid-state electrolyte. We specialize on a Li-metal - Li7La3Zr2O12 (LLZO) system and demonstrate the ability of the framework to capture both intergranular and transgranular crack and Li-filament growth mechanisms, both of which have been experimentally observed. In addition, we elucidate the manner in which mechanical confinement in solid-state batteries plays an important role in the resulting crack/electrodeposition morphology. In modeling this Li/LLZO system, we demonstrate the manner in which our theoretical framework can elucidate the critical coupling between mechanics and electrodeposition kinetics and its role in dictating Li-filament growth. Beyond this application, the theoretical framework should serve useful in a number of engineering problems of relevance in which electrochemical reactions take place within a damage zone, leading to deposition of new material at these locations.