Local structure and stability in a model glass

We study the relation between the potential energy of an atom and the shape of the Voronoi polyhedron around the atom in a sodium glass produced by the molecular dynamics method. The energy of an atom decreases with an increasing number of pentagon on the polyhedra, whereas it increases with increasing numbers of tetragon and hexagon. The central atom of the 13-atom icosahedral cluster is found to have the lowest potential energy among the abundant top 13 clusters which appear in the glass. We define the local pair-distribution function (PDF) around atoms with a specified shape of the polyhedron. The splitting of the second peak in the local PDF is the sharpest for the central atoms of the icosahedral cluster. The second peak splitting which appears in the average PDF is due to the existences of the icosahedral cluster and packing order of atoms around the cluster, i.e., the first peak comes from the first shell around the central atom of the icosahedral cluster, the second main peak from the second shell, and the second subpeak from the third shell.