Fractionated crystallization in a polydisperse mixture of hard spheres

We consider the nature of the fluid–solid phase transition in a polydisperse mixture of hard spheres. For a sufficiently polydisperse mixture (σ>0.085) crystallization occurs with simultaneous fractionation. At the fluid–solid boundary, a broad fluid diameter distribution is split into a number of narrower fractions, each of which then crystallize. The number of crystalline phases increases with the overall level of polydispersity. At high densities, freezing is followed by a sequence of demixing transitions in the polydisperse crystal.