Methamorphosis of Voronoi polyhedra as a definite measure of the elastic-to-dissipative atomic displacement transition

The present method allows to describe the structure of non-crystalline and crystalline solids by constructing a Voronoi diagram. The method gives a detailed structural information about individual atoms and their surroundings. The deformation and methamorphosis of the Voronoi polyhedron is described for an interstitial atom in an fcc crystal; an associated criterion is given for the elastic-to-anelastic transition. An extension of the idea to include amorphous materials is indicated. Voronoi tessellation has been applied in the fields of materials science, physics and chemistry.