Structure of hard-sphere fluid and precursor structures to crystallization

The structural origin of the commonly observed split second peak of the radial distribution function of a supercooled or glassy liquid is examined in this work using the hard-sphere fluid as an example. A novel approach to the analysis of the microscopic structure of a fluid is described, which permits the decomposition of both the radial distribution function and bond-angle distribution function of a system of particles into contributions from a small number of ring structures. The method uses a modified shortest-path definition of rings appropriate to the analysis of the medium-range structure of dense systems. It is shown that the split peak is an indicator of the emergence of precursor structures to crystal formation. The origin of the split peak provides a structural link between fluid and crystalline phases and our results suggest that it is neither a structural feature peculiar to glassy phases nor a smooth structural continuation of the stable-fluid phase. This structural feature of simple glassy systems is more appropriately described as a signifier of the frustration of emerging crystalline order in a fluid.