Crystallization of Hard-Sphere Glasses

We study by molecular dynamics the interplay between arrest and crystallization in hard spheres. For state points in the plane of volume fraction (0.54 <or= varphi <or= 0.63) and polydispersity (0 <or= s <or= 0.085), we delineate states that spontaneously crystallize from those that do not. For noncrystallizing (or precrystallization) samples we find isodiffusivity lines consistent with an ideal glass transition at varphig approximately 0.585, independent of s. Despite this, for s < 0.05, crystallization occurs at varphi > varphig. This happens on time scales for which the system is aging, and a diffusive regime in the mean square displacement is not reached; by those criteria, the system is a glass. Hence, contrary to a widespread assumption in the colloid literature, the occurrence of spontaneous crystallization within a bulk amorphous state does not prove that this state was an ergodic fluid rather than a glass.