By using molecular dynamics simulations on a large number of hard spheres and the Voronoï tessellation we characterize hard-sphere systems geometrically at any packing fraction eta along the different branches of the phase diagram. Crystallization of disordered packings occurs only for a small range of packing fraction. For the other packing fractions the system behaves as either a fluid (stable or metastable) or a glass. We have studied the evolution of the statistics of the Voronoï tessellation during crystallization and characterized the apparition of order by an order parameter (Q(6)) built from spherical harmonics.

We have studied theoretically and by numerical simulations the topological properties of Voronoi tessellations of slightly perturbed fcc and hcp lattices. The number f of faces of a cell can go from 12 to 18 with a mean value f = 14 very different from the value 12 in the non-perturbed lattices. A face can have 4, 5 or 6 sides; we give the percentages of each type of face both in the cells with given values of f and in the whole tessellation. The study of the topological correlations between neighbouring cells shows that Aboav-Weaire's law is valid.

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