Towards a quantification of disorder in materials: Distinguishing equilibrium and glassy sphere packings

This paper examines the prospects for quantifying disorder in simple molecu lar or colloidal systems. As a central element in this task, scalar measure s for describing both translational and bond-orientational order are introd uced. These measures are subsequently used to characterize the structures t hat result from a series of molecular-dynamics simulations of the hard-sphe re system. The simulation results can be illustrated by a two-parameter ord ering phase diagram, which indicates the relative placement of the equilibr ium phases in order-parameter space. Moreover, the diagram serves as a usef ul tool for understanding the effect of history on disorder in nonequilibri um structures. Our investigation provides fresh insights into the types of ordering that can occur in equilibrium and glassy systems, including quanti tative evidence that, at least in the case of hard spheres, contradicts the notion that glasses are simply solids with the "frozen in" structure of an equilibrium liquid. Furthermore, examination of the order exhibited by the glassy structures suggests, to our knowledge, a new perspective on the old problem of random close packing.