Numerical simulation of the dense random packing of a binary mixture of hard spheres: Amorphous metals

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Abstract
A new algorithm for the construction of a dense random packing of a binary mixture of hard spheres is presented. The algorithm uses periodic boundary conditions and is capable of handling any binary composition with radius ratio between 1.0 and 2.0. Computed results are relatively insensitive to variations in program parameters. The resulting packings are extremely homogeneous and isotropic. The packing fraction, the radial distribution function, and the Voronoi-cell statistics are all calculated for equal spheres. The packing fraction is also calculated as a function of composition fraction and size ratio for unequal sphere mixtures. For all cases the packing fraction is between 0.64 and 0.68. This contradicts the popular notion that the packing fraction increases rapidly as a function of size ratio for a given composition fraction for dense random packings. Since the mass density scales linearly with packing fraction and amorphous metals have mass densities very close to those of the corresponding crystal, the dense random packing of hard spheres predicts mass densities that are 8–14 % lower than in the crystalline metal. The unlikelihood of this implies that the atoms in an amorphous metal cannot act like hard spheres. Rather they deform in such a way as to pack together more efficiently than a dense random packing of hard spheres.