Polyhedr Voronoi

The most natural geometrical framework for full-potential methodology is that of space-filling polyhedral atomic cells, mathematically a Voronoi lattice construction in three dimensions. Space is subdivided by perpendicular bisector planes of... 

The Voronoi tessellation divides space into polyhedral regions that are closer to the center of a given particle than to any other. Joining pairs of particle centers whose Voronoi polyhedra share a face yields a dual tessellation of space into Delaunay simplices. 

Corresponding system plastic-strain increments are also obtained at the atomic level from the displacement gradients between the four relevant neighboring corner atoms of Delaunay tetrahedra for each external distortion increment and are allocated subsequently as an atomic site average to each Voronoi polyhedral atom environment by a special procedure of double space tessellation developed by Mott et al. (1992) for this purpose, leading eventually to volume averages of strain-increment tensors of all Voronoi atom environments to attain the system-wide strain-inerement tensor. 

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