Crystallization of Spheres

Simplified computer models are used to gain insight into more complex real systems. In a reversion of this protocol, a colloidal suspension of submicron spherical particles, approximately hard and uniform, was recently crystallized in space and analyzed for crystal type. The objective was to establish how, and to what structure, hard spheres crystallize without gravity. Computational statistical thermodynamics predicts an equilibrium constant between fcc and hcp of order unity. The microgravity experiments, however, resulted in a random hybrid close-packed structure (rhcp) such that long-range order is two-dimensional. Here we report the mechanism from idealized computer ‘‘experiments’’ for crystallization of spheres from the metastable fluid. Model systems of up to N=64,000 spheres with infinite spatial periodicity have been crystallized in runs of up to 10 billion collisions. When the fluid, initially in a metastable supercooled state at 58% packing, is allowed to nucleate and freeze, a variety of structures emerges. There are three identifiable stages of structural growth: (i) initial nucleation of fcc, rhcp, and also bcc-like (body-ceIntered cubic) local structures; (ii) rapid growth of all incipient nucleites to random stacked twodimensional hexagonal (rhcp) grains, plus some fcc, to fill the volume; and (iii) relatively slow dissolution of unstable rhcp faces at grain boundaries. Eventually, stable nucleites emerge comprising hexagonal layers, arranged so as to contain predominantly either fcc arrangements of spheres or rhcp, in roughly 50% proportions.