Dynamical heterogeneities in liquid and glass originate from medium-range order

Slow relaxation and plastic deformation in disordered materials such as metallic glasses and supercooled liquids occur at dynamical heterogeneities, or neighboring particles that rearrange in a correlated, cooperative manner. Dynamical heterogeneities have historically been described by a four-point, time-dependent density correlation function $\chi_4 (r, t)$. In this paper, we posit that $\chi_4 (r, t)$ contains essentially the same information about medium-range order as the Van Hove correlation function $G(r, t)$. In other words, medium-range order is the origin of spatially correlated regions of cooperative particle motion. The Van Hove function is the preferred tool for describing dynamical heterogeneities than the four-point function, for which the physical meaning is less transparent.