From amorphous solid to defective crystal. A study of structural peculiarities in close packings of hard spheres

Abstract

The structure of models of close packings of hard spheres is examined, with density of the packings exceeding the maximum value for uniform disordered packings (K = 0.64). High densities are achieved due to regions of the closest packing (K = 0.74) emerging in the models. Spatial geometry of good tetrahedral atomic configurations and of simplest elements of the crystal structure identified by Delaunay simplices was studied using the Voronoi–Delaunay method. Models with a packing coefficient K varying from 0.639 to 0.706 were considered. At smaller densities, a well-known disordered close “Bernal packing” is realized. At K = 0.706 (the greatest density achieved), a unified crystal structure with numerous defects is formed. At intermediate densities, stochastically oriented crystalline nuclei are observed. Specific atomic aggregates — stacks of five-membered rings in good tetrahedral configurations of spheres — are revealed in models having a substantial fraction of crystalline phase (K = 0.664). Such non-trivial structures can occur only in packings that are intermediate between amorphous and crystalline phases.