Stress-Gated Ion Transport Controls Lithium Filament Propagation in Solid Electrolytes: A Second, Exponential Channel of Chemo-Mechanical Coupling

Lithium filaments penetrate solid electrolytes by wedging open pre-existing flaws, and the field has consequently treated the problem as one of fracture mechanics: raise the toughness, close the crack, and penetration is delayed. Here we show that mechanical stress acts on filament growth through a second channel that has been overlooked, and that this channel is exponential rather than linear. Because ion migration in a solid requires a local dilation of the lattice, the ionic conductivity of every solid electrolyte depends on stress through an activation volume ΔV∗, a quantity measured to span 0.6–25 cm³ mol⁻¹ across sulfide and polymer conductors, and never measured at all for the oxide garnets. The stress field of a pressurised filament therefore reshapes the conductivity of the electrolyte that feeds it. Using coupled finite-element simulations of a sharp, Li-filled edge flaw we find that the sign of this feedback is set by the near-tip stress state, and that in an unstressed electrolyte it is adverse: the crack tip sits in tension, transport there is enhanced, and the supply of lithium to the tip rises by 12–22% at the activation volumes measured for sulfide argyrodites (0.58–1.08 cm³ mol⁻¹) and by a factor of 6.6 at the value measured for PEO–LiTFSI (25 cm³ mol⁻¹), even as the supply to the crack flanks falls. We derive a two-constant scaling law, σ ^tip_h = κ (p − λσr) with κ =3.00 and λ = 1.195, which locates a narrow but real operating window, σ_r < p < λσ_r, in which the flaw is open yet its tip remains compressed. Inside that window the feedback reverses sign, giving a predicted 3.6-fold gain in critical current density of which about half is fracture-mechanical in origin. Because the exponent scales with ΔV∗, the effect is a 10–35% correction for stiff inorganic conductors but the dominant term for polymer and polymer-in-ceramic electrolytes, where Γ ≈ 7at crack-tip stresses. The framework predicts that critical current density should correlate negatively with ΔV∗ in unstressed cells, and identifies a concrete architecture—a compressively prestressed gating skin—that converts a known linear benefit into an exponential one.