A Kinetic Criterion for Stokes-Einstein Relation Breakdown Based on Effective Collisional Geometry

Here we propose a kinetic framework for interpreting the Stokes-Einstein (SE) relation breakdown in supercooled liquids by introducing an effective collision diameter, $d_{\mathrm{e}\mathrm{f}\mathrm{f}}$, derived from transport data. Numerical simulation of a model CuZr alloy reveal that $d_{\mathrm{e}\mathrm{f}\mathrm{f}}$ increases upon cooling but saturates near the first peak of the radial distribution function just before SE breakdown. This saturation defines a geometric upper bound for the collisional cross-section beyond which further slowdown is governed by cooperative, heterogeneous motion rather than local collisional transport. Our analysis yields a compact criterion for SE breakdown in a mean-field perspective and provides physically interpretable inputs for future data-driven models of glassy dynamics.