  Motivated by old experiments on colloidal suspensions, we report molecular
dynamics simulations of assemblies of hard spheres, addressing crystallization
and glass formation. The simulations cover wide ranges of polydispersity s
(standard deviation of the particle size distribution divided by its mean) and
particle concentration. No crystallization is observed for s > 0.07. For 0.02 <
s < 0.07, we find that increasing the polydispersity at a given concentration
slows down crystal nucleation. The main effect here is that polydispersity
reduces the supersaturation since it tends to stabilise the fluid but to
destabilise the crystal. At a given polydispersity (< 0.07) we find three
regimes of nucleation: standard nucleation and growth at concentrations in and
slightly above the coexistence region; "spinodal nucleation", where the free
energy barrier to nucleation appears to be negligible, at intermediate
concentrations; and, at the highest concentrations, a new mechanism, still to
be fully understood, which only requires small re-arrangement of the particle
positions. The cross-over between the second and third regimes occurs at a
concentration, around 58% by volume, where the colloid experiments show a
marked change in the nature of the crystals formed and the particle dynamics
indicate an "ideal" glass transition.
