Crack in the Battery: Why Dendrites Grow express
A metal filament as thin as a hair grows through the ceramic like a root through asphalt. In solid-state batteries, such filaments are called dendrites, and they appear when the charging current exceeds a critical threshold. The ceramic electrolyte is solid but brittle, like glass. A dendrite grows from an existing defect at the metal-ceramic interface: if opening a crack is cheaper than forcing the current to go around, metal deposits right at the tip of the filament.
The authors linked the critical current to the length of the longest thin defect. The longer the defect, the lower the threshold at which growth begins. The relationship is a power law: the critical current is proportional to the defect length to the power of three halves. It's like a crack in a windshield: the longer it is, the less force is needed to make it spread.
The scientists extended the theory to the case where the ceramic conducts a little electricity. Then, at the dendrite tip, stress corrosion occurs under voltage, and growth continues even below the critical current. The scatter between samples follows a Weibull distribution — the same law that describes the strength of ceramic parts: a few weak spots determine the fate of the whole battery.
Original abstract
as written by the authors arXiv:2603.20113
In solid-state batteries, ceramic solid electrolytes are penetrated by dendrites when plating above a critical current density $$J_\mathrm{crit}$$. A dendrite will propagate by metal deposition at a pre-existing dendrite tip if the mechanical energy required to crack the ceramic open is less than the electrical energy (Joule heating) wasted by forcing the current to detour around the dendrite 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. $$c_\mathrm{max}$$ is the length of the longest preexisting, sufficiently thin interfacial defect. Furthermore, the theory is expanded to include electrochemical stress-corrosion-cracking at dendrite tips due to residual electron conduction of the solid electrolyte. The resulting subcritical dendrite growth follows the same defect dependence. 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.
The Weibull distribution, used to describe the scatter in ceramic strength, was originally proposed to describe the scatter in the strength of cotton fibers.
In Andy Weir's novel "The Martian," the protagonist uses a radioisotope thermoelectric generator, but the problem of dendrites in solid-state batteries is a real challenge for future Mars missions.