Modelling local voids using an irregular polyhedron based on natural neighbourhood and application to characterize near-dense random packing (DRP)

Abstract

A model has been developed for finding local voids in randomly packed monodisperse spheres. The voids are polyhedral in shape and are based on the natural neighbourhood concept. The natural neighbourhood is defined in the same spirit of Sibson, who introduced the concept as a refinement of Voronoi tessellation. The model is basically the construction of a Delaunay star, where the centre of the Delaunay star is an arbitrary point in the void and the vertices of the star are the sphere centres. The method is best suited for sampling study. Since the model does not use the radius of the spheres, it can even be used for point distribution in three-dimensional (3-D) space. The model can be improved by using Voronoi vertices as seed points (instead of the arbitrary points) and can be used for crystallochemical studies, where only the electron density distribution is known. It is applicable to non-spherical atoms/particles also. The method is used to analyze near-dense random packing (DRP) and the statistical properties of void structures, e.g. number of vertices per void, cell volume, void volume and void fraction, which do not change from packing to packing in the limit of DRP. The overall local void properties are insensitive to sampling; repeatedly taking 500 void samples in an ensemble did not show considerable change. Most of the voids have 9–12 vertices.

Acknowledgements

KKS acknowledges financial help from the Government of Japan in the form of a MEXT scholarship.