A structural disorder function linking local symmetry breaking to plastic indicators and strength in amorphous solids

Establishing intrinsic structure-property relationships in amorphous solids remains a central challenge in materials science because the absence of long-range order obscures universal structural descriptors. Here, we introduce a structural disorder function, S_d(r), as a physically interpretable and quantitative metric for atomic-scale disorder in amorphous systems. S_d(r) is formulated as the magnitude of the normalized vector sum from a reference atom to its neighbors within different radial shells, thereby capturing local symmetry breaking analogous in concept to the Burgers vector in crystals. Molecular dynamics simulations across diverse amorphous alloys and glasses, together with colloidal-glass experiments, demonstrate that S_d(r) correlates meaningfully (correlation coefficient > 0.68) with key particle-scale plastic properties, including vibrational mean-square displacement, flexibility volume, atomic stiffness, and vibrational frequency. Liquid-like regions consistently exhibit higher S_d(r) values than solid-like ones, revealing its ability to distinguish mechanical heterogeneity. When averaged over the field, [Formula: see text] monotonically increases with cooling rate and exhibits a universal negative linear relationship with shear strength, τ_p = A - B [Formula: see text], quantitatively linking structural disorder to macroscopic strength. These results establish S_d(r) as a simple, dimensionless, and broadly applicable descriptor that unifies atomic configuration, processing history, and mechanical response in disordered materials, providing a physics-based framework for the rational design of amorphous solids.