Hard spheres with a polydispersity above approximately 8% are shown to
crystallise into two phase-separated solid phases. A polydispersity a
bove 8% is too large to be tolerated by a single solid phase but phase
separation produces two fractions with polydispersities sufficiently
narrow to allow them to crystallise. It may not be possible to observe
this in experiment due to the intervention of a glass transition.