Freezing of the hard-sphere liquid

The crystal structure of a hard-sphere system at freezing is determined in the context of the Ramakrishnan-Yussouff theory by allowing for an arbitrary Bravais lattice and no more than two spheres per primitive unit cell. In addition, a class of icosahedral quasiperiodic structures, corresponding to an infinite number of spheres per unit cell, is investigated. It is found that by using the two-point correlations only fcc and hcp structures can be stabilized. By summing an infinite subset of higher-order correlations, which are neglected in the usual applications of the theory, it is shown that hcp structure is eliminated, in agreement with computer simulations.