Topological Analysis with Voronoi Tessellation

The analysis of the VT has shown that the bottleneck radius for Na(l)-Na(3) transport along the principal axis is 2.08 A, and that for the oblique (211) path is 2.22 A Our analysis of a great number of sodium-containing oxide compounds [84] has shovm that these values are characteristic of poor and good Na+ ion conductors, respectively. Thus, Na(l)-Na(3) sites cannot provide ahigh mobility, and only Na(4)-Na (6) sites are responsible for ionic conduction. The most interesting result, however, is that there are no bottlenecks at all between the two Na(5) sites of the different (211) 

The algorithms of Voronoi polyhedra construction may easily be used for the high-throughput analysis of new materials to identify the presence ofan infinite network of channels with suitable size for ionic conductivity or molecular diffusion. At the same time, the approach has a limited applicability for those systems where the topological and geometric factors do not play a significant role, such as proton conductors, or where the framework is not truly immobile and participates in the conduction process, for example, via a paddle-wheel mechanism. 

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