Sequentially-built random sphere-packings have been numerically studied in the packing fraction interval 0.329 < γ < 0.586. For that purpose fast running geometrical algorithms have been designed in order to build about 300 aggregates, containing 10 6 spheres each one, which allowed a careful study of the local fluctuations and an improved accuracy in the calculations of the pair distribution P (r) and structure factors S(Q) of the aggregates.Among various parameters (Voronoi tessellation, contact coordination number distribution,...), fluctuations were quantitatively evaluated by the direct evaluation of the fluctuations of the local sphere number density, which appears to follow a power law. The FWHM of the Voronoi cells volume shows a regular variation over the whole packing fraction range.Dirac peaks appear on the pair correlation function as the packing fraction of the aggregates decreases, indicating the growth of larger and larger polytetrahedra, which manifest in two ways on the structure factor, at low and large Q values. These low PF aggregates have a composite structure made of regular polytetrahedra embedded in a more disordered matrix. Incidentally, the irregularity index of the building tetrahedron appears as a better parameter than the packing fraction to describe various features of the aggregates structure.
We study more than 10^{4} random aggregates of 10^{6} monodisperse sticky hard spheres each, generated by various static algorithms. Their packing fraction varies from 0.370 up to 0.593. These aggregates are shown to be based on two types of disordered structures: random regular polytetrahedra and random aggregates, the former giving rise to δ peaks on pair distribution functions. Distortion of structural (Delaunay) tetrahedra is studied by two parameters, which show some similarities and some differences in terms of overall tendencies. Isotropy of aggregates is characterized by the nematic order parameter. The overall structure is then studied by distinguishing spheres in function of their contact coordination number (CCN). Distributions of average CCN around spheres of a given CCN value show trends that depend on packing fraction and building algorithms. The radial dependence of the average CCN turns out to be dependent upon the CCN of the central sphere and shows discontinuities that resemble those of the pair distribution function. Moreover, it is shown that structural details appear when the CCN is used as pseudochemical parameter, such as various angular distribution of bond angles, partial pair distribution functions, Ashcroft-Langreth and Bhatia-Thornton partial structure factors. These allow distinguishing aggregates with the same values of packing fraction or average tetrahedral distortion or even similar global pair distribution function, indicative of the great interest of paying attention to contact coordination numbers to study more precisely the structure of random aggregates.
The structure of monoatomic liquids in the static approximation is described by a soft sphere model and the corresponding equation of state is derived. This geometrical model is then extended to binary liquid or amorphous substitution alloys where both components have the same size. The structure of these alloys is shown to be determined by the first neighbour order parameter which is positive, negative or zero for segregated, ordered or disordered alloys respectively. The variations of the partial structure factors with concentration are presented for these three cases. Size effects are then studied by varying the ratio of atomic diameters. Many experimental results are shown to fit this simple framework.
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