The role of local heteropolyhedral substitutions in the stoichiometry, topological characteristics and ion-migration paths in the eudialyte-related structures: a quantitative analysis

Topological analysis of the heteropolyhedral MT framework (where M and T are octahedral and tetrahedral cations, respectively) in the eudialyte-type structure and its derivatives was performed based on a natural tiling analysis of the 3D cation. To analyze the migration paths of sodium cations in these structures, the Voronoi method was used. The parental eudialyte-type MT framework is formed by isolated ZO₆ octahedra, six-membered [M(1)₆O₂₄] rings of edge-sharing M(1)O₆ octahedra, and two kinds of rings of tetrahedra, [Si₃O₉] and [Si₉O₂₇]. Different occupancies of M(2), M(3) and M(4) sites with variable coordination numbers by the additional Q, T* and M* cations, respectively, result in 12 different types of the MT framework. Based on the results of natural tilings calculations as well as theoretical analysis of migration paths, it is found that Na⁺ ions can migrate through six- and seven-membered rings, while all other rings are too small for the migration. In eight types of MT frameworks, Na⁺-ion migration and diffusion is possible at ambient temperature and pressure, while in four other types cages are connected by narrow windows and, as a result, the Na⁺ diffusion in them is complicated at ambient conditions because of the window diameter, but may be possible either at higher temperatures or under mild geological conditions for long periods of time.