Ingress of Li into Solid Electrolytes: Cracking and Sparsely Filled Cracks

The growth of Li dendrites in a solid electrolyte is commonly idealized by a pressure‐filled crack. Recent observations in both garnet and sulfide electrolytes show that sparsely filled cracks exist prior to shorting of the cell, thereby invalidating this assumption. Herein, a variational principle that uses the Onsager formalism to couple Li deposition into the crack, elastic deformation of the electrolyte, and cracking of the electrolyte with the electrochemical driving forces and dissipation within the electrolyte and interfaces is developed. Consistent with observations, it is shown that Li ingress and cracking occur together for garnet electrolytes, but the cracks are sparsely filled. This sparse filling is a direct consequence of the mismatch between the elastic opening of the cracks and the deposition of Li into the cracks across the crack flanks. An increase in the resistance of Li ingress into the tips of Li filaments results in crack propagating ahead of the Li filaments, as observed for sulfide electrolytes. In such cases, the cracks are largely dry. The results provide a framework to model Li ingress into solid electrolytes and explain why the observations are qualitatively so different from dendrites in liquid electrolytes