What is it about?

The nineteenth century Russian mathematician Georgy Voronoi defined a method of dividing a 3D space consisting of points into polyhedra. This is applied here in order to characterize crystal structures.

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Why is it important?

In addition to algorithmic details, concepts such as polyhedral volume, complementary Voronoi Polyhedra and topological indices are defined. The approach enables a generalised description of all crystal structures.


Following my work on perovskite crystal structures (ABX3), which was ultimately facilitated by the space-filling of AX12 and BX6 polyhedra, the motivation here was to generalise polyhedral space - filling to ALL crystal structures. Follow - on work dealing with applications was never realised due to a change of occupation.

Professor Noel William Thomas
Hochschule Koblenz

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This page is a summary of: An extension of the Voronoi analysis of crystal structures, Acta Crystallographica Section B Structural Science, December 1996, International Union of Crystallography, DOI: 10.1107/s0108768196009202.
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