This paper examines the prospects for quantifying disorder in simple molecular or colloidal systems. As a central element in this task, scalar measures for describing both translational and bond-orientational order are introduced. These measures are subsequently used to characterize the structures that result from a series of molecular-dynamics simulations of the hard-sphere system. The simulation results can be illustrated by a two-parameter ordering phase diagram, which indicates the relative placement of the equilibrium phases in order-parameter space. Moreover, the diagram serves as a useful tool for understanding the effect of history on disorder in nonequilibrium structures. Our investigation provides fresh insights into the types of ordering that can occur in equilibrium and glassy systems, including quantitative 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.

• Received 1 March 2000

DOI:https://doi.org/10.1103/PhysRevE.62.993