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

Abstract

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.

The natural tiling approach to cation conductivity in KAlO2 polymorphs

“…sets of migration paths of mobile cations within the framework) from crystallographic data, we used the program package TOPOS modified by Blatov et al (2006) for studying fast-ion conductors. An important difference compared with our previous study of the room-temperature KAlO 2 phase (Voronin et al, 2010) was that we used a novel algorithm based on the natural tiling concept (Anurova & Blatov, 2009) that is most applicable for compounds with rather simple framework topology. As opposed to the Voronoi-Dirichlet approach (Voronin et al, Table 1 Crystallographic data for KAlO 2 phases at different temperatures.…”

“…Blatov et al (2007) showed that natural tiles and their faces (strong rings) correspond to minimal cages and windows of the framework, respectively. The net whose edges connect the centers of the natural tiles and pass through the tile faces is called dual net; it is the net that contains the migration map for fast-ion conductors (Anurova & Blatov, 2009). There is a one-to-one relation between topological elements of the framework and its dual net; in particular, nodes and edges of the dual net correspond to cages and windows of the framework.…”

“…This is true for studies of other types of cation solid electrolytes: despite rich experimental diffraction data, universal structural models of conductivity were not developed. Recently, Blatov et al (2006), Anurova et al (2008), Anurova & Blatov (2009) developed a new method of computer analysis of cation migration paths resting upon standard crystallographic data and the Voronoi-Dirichlet partition of the crystal space; this method was successfully tested with a large number of Li-containing compounds. Using the same approach, Voronin et al (2010) analyzed the migration paths of K + cations in the crystal lattice of the KAlO 2 low-temperature form and showed an essential anisotropy of the K + cation conductivity.…”

A Survey of Quantitative Descriptions of Molecular Structure

“…Recently, a number of descriptors for inorganic materials are very similar to constitutional descriptors - essentially counts of various crystal parameters such as accessible surface areas and volumes [51, 52, 53]. Other descriptors characterize the periodic voids of porous materials via tessellation methods [54, 55]. …”

Periodic‐Graph Approaches in Crystal Structure Prediction

“…Since the nodes and edges of the dual net correspond to cages and rings of the initial net, the dual net can be considered as a system of void centers and channel lines between them. Anurova and Blatov [53] showed that dual nets can be efficiently used to analyze the migration paths in fast-ion conductors, to predict the existence and dimensionality of conductivity. In MOFs, the self-dual nets are of special interest [12] because, being combined with the initial net, they form strongly catenated network arrays.…”