The Coloring of the Voronoi network: Investigation of structural heterogeneity in the packings of spheres

The paper describes how the Voronoi-Delaunay approach can be used for investigation of the structural heterogeneity during the process of liquid crystallization. The basic geometric structure for the analysis is the Voronoi network (the Voronoi diagram in a 3-dimensional space). Every site of the Voronoi network is associated with a Delaunay simplex: four neighboring atoms representing the simplest element of the liquid structure. Having a quantitative measure for the shape of simplexes, we suggest to mark (color) Voronoi sites according to a given physical criterion. As a result, the structural investigation is reduced to a task of cluster analysis on a network. Evolution of aggregates of atoms comprised of tetrahedral configurations is studies on an example of Lennard-Jones liquid crystallization. The experiments show that pseudocrystalline aggregates of pentagonal bipyramids spring up along with the genuine crystalline nuclei. The pseudonuclei can stimulate crystallization at the first stage of the process, but slows it down in the final stage of fusion of crystal regions. The results obtained are important for in-depth understanding of the process of the homogeneous crystallization of simple liquids.