Freezing of polydisperse hard spheres

Freezing of polydisperse hard spheres is studied by Monte Carlo simulation and the results are interpreted with a cell model of the solid. The results supplement an earlier study of freezing of nearly monodisperse hard spheres and, within the assumption of a substitutionally disordered solid, a complete description of the freezing behavior is obtained. The density and polydispersity of the precipitate are characterized by a single curve, regardless of the composition of the fluid from which it is formed. Fractionation enables a fluid of arbitrary polydispersity to precipitate a solid of small polydispersity, dispeling the long-held notion of a fluid-phase ``critical'' polydispersity, beyond which it cannot form a solid. Nevertheless, a primary conclusion from the previous study is confirmed: a solid crystalline phase of polydispersity exceeding 5.7% of the average sphere diameter cannot be precipitated from a fluid phase.