The paper presents a new approach for revealing regions (nuclei) of crystalline structures in computer models of dense packings of spherical atoms using the Voronoi-Delaunay method. A Delaunay simplex, comprised of four atoms, is the simplest element of the structure. All atomic aggregates in an atomic structure consist of them. The shape of the Delaunay simplex and the shape of its neighbors are used to determine whether the Delaunay simplex belongs to a given crystalline structure. The characteristics of simplexes which define their relationship to FCC and HCP structures are studied. The possibility of using this approach for investigation of other structures is demonstrated. In particular, polytetrahedral aggregates of atoms atypical for crystals are discussed. The occurrence and growth of regions in FCC and HCP structures is studied on an example of homogeneous nucleation of a Lennard-Jones liquid. The volume fraction of these structures in the model during the process of crystallization is calculated.

Keywords: Voronoi diagram; Delaunay simplex; crystallization; homogeneous nucleation