Structural precursor to freezing in the hard-disk and hard-sphere systems

We show that the simplest model fluids in two and three dimensions, namely, the hard-disk and hard-sphere fluids, exhibit a structural precursor to the freezing transition, which manifests itself as a shoulder in the second peak of the radial distribution function. This feature is not present in the radial distribution function of the low-density fluid. Close examination of the two-dimensional fluid configurations in the vicinity of the freezing transition reveals that the shoulder corresponds to the formation of a distinct structural motif, identifiable as a four-particle hexagonally close-packed arrangement. As the dense fluid approaches the freezing transition, the ordered arrangements form large embryonic domains, commensurate with those seen in the crystal at the melting point. Contrary to the notion that the split second peak is a signature of the amorphous solid, our results support the idea that it is a precursor to the development of long-range order.