  Specialized Monte Carlo simulation techniques and moment free energy method
calculations, capable of treating fractionation exactly, are deployed to study
the crystalline phase behaviour of an assembly of spherical particles described
by a top-hat "parent" distribution of particle sizes. An increase in either the
overall density or the degree of polydispersity is shown to generate a
succession of phase transitions in which the system demixes into an ever
greater number of face-centred cubic "daughter" phases. Each of these phases is
strongly fractionated: it contains a much narrower distribution of particle
sizes than is present in the system overall. Certain of the demixing
transitions are found to be nearly continuous, accompanied by fluctuations in
local particle size correlated over many lattice spacings. We explore possible
factors controlling the stability of the phases and the character of the
demixing transitions.
