Analysis of ion-migration paths in inorganic frameworks by means of tilings and Voronoi-Dirichlet partition: a comparison.

Two methods using Voronoi-Dirichlet polyhedra (Voronoi-Dirichlet partition) or tiles (tiling) based on partitioning space are compared to investigate cavities and channels in crystal structures. The tiling method was applied for the first time to study ion conductivity in 105 ternary, lithium-oxygen-containing compounds, Li(a)X(b)O(z), that were recently recognized as fast-ion conductors with the Voronoi-Dirichlet partition method. The two methods were found to be similar in predicting the occurrence of ionic conductivity, however, their conclusions on the dimensionality of conductivity were different in two cases. It is shown that such a contradiction can indicate a high anisotropy of conductivity. Both advantages and restrictions of the methods are discussed with respect to fast-ion conductors and zeolites.