Equilibrium phase behavior of polydisperse hard spheres

We calculate the phase behavior of hard spheres with size polydispersity, using accurate free energies for the fluid and solid phases. Cloud and shadow curves are found exactly by the moment free energy method, but we also compute the complete phase diagram, taking full account of fractionation. In contrast to earlier, simplified treatments we find no point of equal concentration between fluid and solid or reentrant melting at higher densities. Rather, the fluid cloud curve continues to the largest polydispersity that we study (14%); from the equilibrium phase behavior a terminal polydispersity can thus be defined only for the solid, where we find it to be around 7%. At sufficiently large polydispersity, fractionation into several solid phases can occur, consistent with previous approximate calculations; we find, in addition, that coexistence of several solids with a fluid phase is also possible.