Study of the structure of simple liquids and amorphous solids by statistical geometry methods

The authors summarize the work of various authors on the study of computer models for disordered systems using the language of Voronoi polyhedra and Delaunay simplexes. We consider the dependence of the properties of Voronoi polyhedra and Delaunay simplexes on the phase state of the material. We have established the predominance of atomic configurations in the form of a tetrahedron and a quadrant of an octahedron in all close-packed disordered systems. We have demonstrated the absence of crystalline and icosahedral configurations of atoms in such systems. We emphasize the need for eliminating thermal excitations (transition to the essential structure) in formulating the structural principles of a liquid