  We consider the nature of the fluid-solid phase transition in a polydisperse
mixture of hard spheres. For a sufficiently polydisperse mixture
crystallisation 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 crystallises. 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.
