Solid Electrolyte Crack-Driven Dendrite Shorting

Cell Conditions

Plating current density 2.0 mA/cm²

Initial flaw size a₀ 5.0 µm

Electrolyte fracture toughness K_IC 0.9 MPa·√m

Applied stack pressure 1.0 MPa

Crack State

Idle

Stress intensity K

0.00 MPa·√m

Crack length a

5.0 µm

Wedging stress σ

0 MPa

Time to short

stable

How it works

Real ceramic and glassy solid electrolytes are never flaw-free — pores and grain-boundary voids left over from sintering sit inside the microstructure. During fast lithium plating, metal deposits into the largest nearby flaw and wedges it open, exactly like ice cracking rock. Whether that crack self-arrests or runs away to a short circuit is a fracture-mechanics competition:

K = σ · √(π·a)         (Griffith stress-intensity factor)
σ ≈ k_p·i − k_P·P_stack (net electrochemical wedging stress)
Grows while:  K > K_IC
Critical flaw: a_c = (K_IC / σ)² / π

K is the stress-intensity factor at the crack tip — it grows both with the wedging stress σ and with the crack's own length a, which is why a flaw that starts growing tends to accelerate.
K_IC is the electrolyte's fracture toughness — a material property (sulfide glasses like Li₃PS₄ sit low, oxide garnets like LLZO sit high). The crack is mechanically arrested whenever K stays below it.
Current density sets how fast lithium metal is forced into the flaw, raising the wedging stress σ.
Stack pressure — the mechanical clamping force real solid-state cells apply across the stack — pushes back against void/crack opening and can suppress growth even at high current, mirroring the pressure-dependent voiding studies (Kasemchainan et al., 2019) that motivate pressurized cell packaging today.
Flaw size a₀ stands in for how well-sintered the ceramic is: a smaller starting flaw needs much more stress to reach the same K, since K scales with √a.

This is a distinct failure mode from bulk mechanical stiffness resisting a dendrite tip (the Monroe–Newman shear-modulus criterion) — here the electrolyte can be arbitrarily stiff in bulk and still fail catastrophically through one pre-existing flaw, which is why manufacturing defect density is treated as seriously as bulk modulus in real solid-state cell design.

Ceramic electrolyte Lithium anode / crack fill Cathode

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