Crystallization of sheared hard spheres at 64.5\% volume fraction

A classic experiment by G.D. Scott $(\it {Nature}$ ${\bf 188}$, 908, 1960) showed that pouring balls into a rigid container filled the volume to an upper limit of 64\% of the container volume, which is well below the 74\% volume fraction filled by spheres in a hexagonal close packed (HCP) or face center cubic (FCC) lattice. Subsequent experiments have confirmed a ``random closed packed" (RCP) fraction of about 64\%. However, the physics of the RCP limit has remained a mystery. Our experiment on a cubical box filled with 49400 weakly sheared glass spheres reveals a first order phase transition from a disordered to an ordered state at a volume fraction of 64.5\%. The ordered state consists of crystallites of mixed FCC and HCP symmetry that coexist with the amorphous bulk. The transition is initiated by {\it homogeneous} nucleation: in the shearing process small crystallites with about ten or fewer spheres dissolve, while larger crystallites grow. A movie illustrates the crystallization process.