Disorder-Driven Current Filamentation and Electro–Thermal Instability in Halide Solid Electrolytes: A Disordered Network Model with Impedance Signatures

Abstract

Thermal failure in solid-state batteries employing halide electrolytes is usually attributed to interfacial degradation, yet the role of bulk transport heterogeneity has received little scrutiny. This work investigates whether activation-energy disorder in the ionic hopping landscape can, by itself, create conditions favorable for localized electro-thermal instability. Ionic transport is simulated on disordered hopping networks in two and three dimensions (N=15-60, 20 realizations each), and a lumped node-level heat balance is introduced to define the instability boundary. Finite-size scaling across seven 3D system sizes identifies peak filamentation at σ_E=0.170eV with no systematic drift over N=15-60. Large-size extrapolation yields Φ_∞=10.52±0.20, substantially exceeding the 2D peak (Φ≈8.1) within the present normalization. The 3D instability onset occurs at lower disorder than in 2D, and the model-defined instability boundary appears at lower voltages (V_crit∼1.2V at N=25). AC impedance computed from the same disordered networks shows disorder-correlated arc broadening; the Pearson correlation between DC filamentation and DRT width is r=0.61-0.71 across N=15-25, with the non-monotonic broadening trend preserved across all system sizes. These results suggest that conductivity normalized by disorder variance may serve as a more informative stability descriptor than conductivity alone.