Definitions were given, for concepts such as void, channel and migration-path, in terms of the Voronoi-Dirichlet partition of the crystal space for inorganic structures having 3-dimensional networks of chemical bonds. Criteria were proposed for selecting significant voids and migration channels for alkali cations, Li+-Cs+, based upon the average characteristics of the Voronoi-Dirichlet polyhedra for alkali metals in O-containing compounds. A general algorithm was developed for analyzing the voids in crystal structures and built into a computer program. This was used to predict the positions of Li+ and Na+ cations and to analyze their possible migration paths in the solid superionic materials, Li3M2P3O12 (M = Sc, Fe) and Na1+xZr2SixP3-xO12, whose framework structures consisted of connected M octahedra and T tetrahedra. Using this approach, the most probable places for charge carriers (coordinates of alkali cations) and the dimensionality of their conducting sub-lattice were determined with high accuracy. The theoretically calculated coordinates of the alkali cations in MT frameworks were found to agree, to within 0.33A, with experimental data for the various phases of Na1+xZr2SixP3-xO12 and Li3M2P3O12. This method of computer analysis was suitable for investigating fast-ion conductors having other conducting components.

Analysis of Migration Paths in Fast-Ion Conductors with Voronoi-Dirichlet Partition. V.A.Blatov, G.D.Ilyushin, O.A.Blatova, N.A.Anurova, A.K.Ivanov-Schits, L.N.Demyanets: Acta Crystallographica B, 2006, 62[6], 1010-8