Competing effects of current density and viscoplastic deformation on the critical conditions for dendrite growth into solid-state lithium battery electrolytes

All-solid-state lithium (Li) batteries provide a promising pathway toward high energy and power density. Dendrite penetration through the solid electrolyte causing battery short-circuit, however, persists to be one of the challenges impeding their widespread application. Here, considering a pre-existing surface crack in the electrolyte initially filled with an infinitely thin layer of Li, and assuming Li deposit to behave in accordance with rigid-viscoplasticity, we seek for the steady state Li-filled crack opening profile that could potentially form at a given constant current density. Treating the chemical potential of Li ions in the electrolyte and the electric potential to be uniform along the crack face, the model accounts for the coupling between stress buildup in the dendrite, deposition rate, viscoplastic flow of Li deposit, and crack opening induced by electrolyte deformation using singular integral equations of fracture mechanics. The model establishes limiting conditions for crack growth before a steady state dendrite is reached, triggering a cycle of crack growth and dendrite elongation. Using material properties adopted from literature, the model predicts that the critical condition can be met for a microcrack at typical current densities. The effect of pressure applied to the cell is further discussed.