A Thermodynamically Consistent, Phase-Field Electro-Chemo-Mechanical Theory with Account for Damage in Solids—Application to Metal Filament Growth in Solid-State Batteries

Solid-state batteries (SSBs) present a promising technology and have attracted significant research attention owing to their superior properties including increased energy density (3860 mAh), wider electrochemical window (0-5V) and safer electrolyte design. From a safety standpoint, SSBs are particularly appealing in that replacement of flammable conventional organic electrolytes with highly conductive, mechanically stiff inorganic solid-state electrolytes (SSEs) can alleviate failure due to short circuit or ignition. However, operation of SSBs is hampered by numerous chemo-mechanical challenges, the most critical one associated with metal filament growth across the SSE.<br/><br/>Filament protrusions can initiate at perturbations of the interface or microstructural heterogeneities and subsequently grow through the SSE, causing the battery to short-circuit. It is critical to understand from both an experimental and modeling perspective the interplay of various mechanisms including morphology of the SSE microstructure, elastic-viscoplastic behavior of Li-metal, critical current density and stack pressure on the morphology of filamentary protrusions across the SSE. While much has been done to understand the interplay of aforementioned mechanisms from an experimental standpoint, theoretical frameworks on modeling of filaments growth in SSBs are still at their infancy and typically simplify dendrites as pressurized cracks under a linear-elastic fracture mechanics (LEFM) approach.<br/><br/>In this work, we propose a thermodynamically consistent phase-field reaction-diffusion-damage theory to investigate the morphology of filament growth across the SSE under varying chemo-mechanical operational conditions. The theory is fully coupled with electrodeposition at the Li metal-SSE interface impacting mechanical deformation, stress generation and subsequent fracture of the SSE. Conversely, electrodeposition kinetics are affected by mechanical stresses through a thermodynamically consistent, physically motivated driving force that distinguishes the role of various chemical, electrical and mechanical contributions. Concurrently, the theory captures the interplay between crack propagation and electrodeposition phenomena by tracking the damage and reaction field using separate phase-field variables such that metal growth is preceded by and confined to damaged regions within the SSE accessible by Li-metal. This is a critical feature of the theory and confirms experimental observations that the crack front propagates ahead of Li. We specialize the theory and study the role of variations of chemo-mechanical properties (i.e. applied electric potential, SSE fracture energy) on the morphology of metal filament growth and map operational conditions to distinguish between domains of i) stable vs. unstable growth ii) intergranular vs. transgranular growth mode. In doing so, the proposed framework provides a quantitative understanding on mechanisms dictating metal filament growth in SSEs and identifies mitigation strategies to employ in future SSB designs for successful operation.