Phase-field Simulations of Failure in LLZO: How Flaw Size and Distribution Affect Electrochemical Tolerance

The solid electrolyte, Li₇La₃Zr₂O₁₂(LLZO), is a promising next-generation candidate material for lithium metal batteries. However, LLZO-based cells exhibit crack growth and subsequent Li metal plating, leading to short circuit and failure. In our work, we develop a coupled electrostatics-mechanics phase-field model which characterizes the growth of cracks; this model comprises deterministic and stochastic frameworks to describe the failure of LLZO with a single crack and multiple randomly distributed cracks respectively. Our single-crack model demonstrates that crack propagation under applied electrostatic loads follows an inverse-square law of failure, analogous to classical fracture mechanics. Multiple-crack simulations show that the Weibull model applies to both constant voltage and constant current conditions. Furthermore, an interfacial region of flawless crystal leads to substantial increases in both critical overpotential and critical current. The totality of these results provide some guidance for the rational operation of LLZO-based cells in an industry setting as well as some possible routes for improvement of the material's microstructure for long-term operability.