A. Gervois

Voronoi tessellation of packings of spheres: Topological correlation and statistics

Abstract We describe three-dimensional froths obtained by the Voronoi tessellation of monosize packings of spheres at different packing fractions C from C = 0 toC = 0·58. The packings are built numerically. The distribution p(f) of the number f of faces of a cell is well approximated by a Gaussian. The average number m(f) of faces of the neighbours of a f-faceted cell follows the three-dimensional equivalent of the Aboav-Weaire law. The Lewis and the Deschlaws can be generalized to the three-dimensional case to describe the metricproperties of the froths. The distribution of the volumes of the cells is wellfitted by a gamma law at low packing fractions but becomes narrower and more symmetric at higher concentrations.

Arrangement of cells in Voronoi tesselations of monosize packing of discs

Abstract We describe a two-dimensional mosaic obtained by the Voronoi tesselation of a monosize assembly of discs at different packing fractions. The experimental device (hard discs moving on an air table) produces, for every concentration of the discs, a succession of mosaics in statistical equilibrium, which constitutes a statistical ensemble. This ensemble is large enough for fluctuations from the most probable distributions to be negligible. Both topological and metric properties show deviations from those of a totally random mosaic. These deviations can be ascribed to steric exclusions. In particular, distributions of the numbers of sides, of the perimeters and of the areas of the polygons differ from those observed in biological celi assemblies. The Aboav law holds, but with a slope which can be as Iow as 4–66. The Lewis law is obeyed only for smali packing fractions. The variance of the distribution of the number n of polygon sides is a universal function of p 6, the probability of finding a six-si...

Tessellation of binary assemblies of spheres

We describe three-dimensional froths obtained by radical tessellation of random binary assemblies of spheres at different packing fractions C from C=0 to C∼0.60 and for large ranges of composition. The packings are built numerically using different algorithms: collective reorganization, random deposition or molecular dynamics interaction. Both topological and metric properties show deviations from those of a totally random froth. The results are qualitatively similar to those obtained previously on 2D binary mixtures of disks.

Experimental Study of Densification of Disc Assemblies

An air cushion table that we have built and tested has been used to study the structure of 2D assemblies of identical discs of increasing density, going from very dilute systems up to the most compact crystalline array. We analyse the radial and angular distribution functions, calculated from an image analysis treatment, and the progressive structuration of these assemblies. The disorder-order transition is observed for a packing fraction close to the theoretical value of 0.82. It is confirmed by a study of the geometry of the Voronoi polygons.

Voronoi and Radical Tessellations of Packings of Spheres

The Voronoi tessellation is used to study the geometrical arrangement of disordered packings of equal spheres. The statistics of the characteristics of the cells are compared to those of 3d natural foams. In the case of binary mixtures or polydisperse assemblies of spheres, the Voronoi tessellation is replaced by the radical tessellation. Important differences exist.

Arrangement of discs in 2d binary assemblies

We study arrangements of the two species of discs in binary assemblies at an intermediate scale. Small discs rearrange along large ones in clusters whose mass and compactness are analyzed with the tools of percolation. The assemblies are generated analogically on an air table or numerically from RSA or Powell algorithms. At a given packing fraction, an infinite cluster of small discs exists above a critical composition; a phenomenological expression for this threshold is proposed. Like in usual percolation problems, the number of inner links in a cluster is a linear function of its mass, with a slope depending both on the packing fraction, the composition of the mixture and the building procedure. An approximate expression is derived for it.

Crystallization in hard sphere systems: A structural analysis

We present numerical simulation results of crystallization of hard sphere systems. The study of the distribution of a local bond order parameter (Q6) gives precise informations on the structure and allows to detect without ambiguity the presence of fcc or hcp crystalline zones. We have found, as expected, that the fcc symmetry is more stable than the hcp one in hard sphere crystallized systems. The fraction of hcp clusters in the system is found to decrease as the propensity to crystallize increases. The method developed here to detect fcc and hcp order can also be applied to bcc order.