Representation of properties of materials by Voronoi polyhedra

Abstract The Voronoi diagram was computed using both a boundary cube and a periodic boundary condition, and two widely different algorithms. Two systems, one a small one of 61 points representing amorphous Si or Ge and another a large one of 500 points representing a high density liquid were studied. Effects of the periodic boundary condition are shown in terms of average numbers of faces, distributions of faces and the radial distribution functions. The results indicate that to decide whether a boundary cube or a periodic boundary condition is preferred for a given application, one has to take into account: boundary condition used to generate the system, inclusion or otherwise of the surface effects, extent of symmetry desired and extent of homogenization required.

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