Thermally Activated Non-Affine Rearrangements in Amorphous Glass: Emergence of Intrinsic Length Scales

Abstract

We present a systematic study of temperature-driven nonaffine rearrangements in a model amorphous solid across the full thermodynamic range, from a high-temperature liquid, through supercooled and sub-glass regimes, into deep glassy states. The central result is a quantitative characterisation of the componentwise nonaffine residual displacements, obtained by subtracting local affine maps from particle displacements. For each state point the tails of the probability distributions of these nonaffine components display clear exponential decay; linear fits to the logarithm of the tail region yield characteristic nonaffine length scales {\xi}NA,x and {\xi}NA,y , which quantify the spatial extent of purely nonaffine, local rearrangements. To compare with other length scales, we compute van Hove distributions Gx(ux), Gy (uy ) which capture the full particle displacement field (coherent affine-like motion plus residuals). A robust, key finding is that the van Hove length scale consistently exceeds the filtered nonaffine length scale, i.e. {\xi}VH > {\xi}NA, across all temperatures, state points, and densities we studied. The nonaffine length {\xi}NA quantifies the distance over which complex deformation occurs, specifically nonlinear and anharmonic responses, irreversible (plastic) rearrangements, topological non-recoverable particle rearrangements, and other residual motions that cannot be represented by a local affine map. Moreover, near equality of {\xi}NA,x and {\xi}NA,y in all conditions provides further evidence that nonaffine rearrangements propagate isotropically under thermally driven deformation in contrast to externally driven shear.