Theory of Alkali Metal Dendrite Growth in Ceramic Solid Electrolytes based on Griffith's Theory

Abstract In solid-state batteries, ceramic solid electrolytes are penetrated by the alkali metal when charging above a critical current density $J_\mathrm{crit}$. A crack will propagate at the longest pre-existing and mechanically constrained interfacial defect of length $c_\mathrm{max}$ if the mechanical power required to crack the ceramic open is less than the Joule heating dissipated by forcing the current to detour around the flaw to the flat electrode surface. Based on this principle of minimal power dissipation, a dependence of $J_\mathrm{crit}\propto c_\mathrm{max}^{-3/2}$ is derived in an analytical fashion. Consequentially, scattering of dendrite growth between samples must follow a Weibull-distribution, similar to the tensile strength of ceramic components but at smaller Weibull-modulus.