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

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 mech-anisms 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 phe-nomenon 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 con-finement 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 theo-retical 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.

Automated summary

The study presents a thermodynamically-consistent electro-chemo-mechanical gradient theory that couples electrochemical reactions with mechanical deformation and damage in solids. The framework models species transport and electrochemical reactions within the solid host, with electrodeposition impacting mechanical deformation and stress generation, and vice versa. The theory specializes in simulating Li-metal filament growth phenomena in a Li-metal-Li7La3Zr2O12 (LLZO) system, capturing both intergranular and transgranular crack and Li-filament growth mechanisms observed experimentally. The theory has broad engineering applications where electrochemical reactions occur within damage zones, leading to deposition of new material at these locations.