Topology of Intermetallic Crystals: Classification, Uniformity, and Transitions.

We have analyzed the crystal structures of 7551 binary intermetallic compounds, which are deposited in the inorganic crystal structure database, using a combined geometrical-topological approach as implemented in our program package ToposPro. We represented each crystal structure with two models: (i) the topological model of periodic atomic net and (ii) the geometrical model of the Voronoi partition of crystal space. Within the former model, we have classified all intermetallics into 949 topological types, 20 of which cover 57% of the whole sample.

Hierarchical topological analysis of crystal structures: the skeletal net concept.

Topological analysis of crystal structures faces the problem of the `correct' or the `best' assignment of bonds to atoms, which is often ambiguous. A hierarchical scheme is used where any crystal structure is described as a set of topological representations, each of which corresponds to a particular assignment of bonds encoded by a periodic net. In this set, two limiting nets are distinguished, complete and skeletal, which contain, respectively, all possible bonds and the minimal number of bonds required to keep the structure periodicity.

Local Atomic Configurations in Intermetallic Crystals: Beyond the First Coordination Shell.

We have used a combined geometrical-topological approach to analyze 21,697 intermetallic crystal structures stored in the Inorganic Crystal Structure Database. Following a geometrical scheme of close packing of balls, we have considered the three most typical polyhedral atomic environments of the icosahedral, cuboctahedral, or twinned cuboctahedral shape as well as multi-shell (up to four shells) local atomic configurations (LACs) based on these cores in 10,657 unique crystal structure determinations. In total, half of intermetallic structures have been found to contain one of these configurations, with the icosahedral LACs being the most frequent.

Generating triply periodic surfaces from crystal structures: the tiling approach and its application to zeolites.

Physical properties of objects depend on topological features of the corresponding triply periodic surfaces; thus topological exploration and classification of the surfaces has practical relevance. A general method is developed for generating triply periodic surfaces from triply periodic crystal structures. A triply periodic surface is derived from the natural tiling of a crystal network by an appropriate removal of some tile faces and subsequent smoothing of the resulting facet surface.

Morphotropism in fumarolic mineral-related anhydrous sulfates: novel representatives in AM(SO) and AM(SO) series.

The discovery of numerous endemic anhydrous sulfate minerals in fumaroles of the Tolbachik volcano (Kamchatka, Russia) has revived interest in the whole family of anhydrous sulfates. Herein is reported the crystal structure of CsCu(SO) which adds important data on the `final' contributor with the largest A cation to the A[Cu(SO)] morphotropic series (A = Na, K, Rb, Cs), the `initial' structurally characterized representative of this family being saranchinaite NaCu(SO). With increasing ionic radius of the alkali metal cation(s), embedded in the [Cu(SO)] framework, symmetry-breaking transformations occur.

Topology versus porosity: what can reticular chemistry tell us about free space in metal-organic frameworks?

We present the results of a comprehensive geometrical and topological analysis of 3D coordination networks in 33 790 coordination polymers. We have found relations between topological descriptors and free space of the networks, and have revealed topological types that promote high porosity of metal-organic frameworks.

Nanoporous materials with predicted zeolite topologies.

An increasing number of newly synthesized materials have been found to be previously present in databases of predicted porous materials. This has been observed not only for zeolites, but also for other inorganic materials and for MOFs. We here quantify the number of synthesized zeolites that are present in a large database of predicted zeolite structures as well as the number of other inorganic crystals and MOFs present in this same database.

Packing topology in crystals of proteins and small molecules: a comparison.

We compared the topologies of protein and small molecule crystals, which have many common features - both are molecular crystals with intermolecular interactions much weaker than intramolecular interactions. They also have different features - a considerably large fraction of the volume of protein crystals is occupied by liquid water while no room is available to other molecules in small molecule crystals. We analyzed the overall and local topology and performed multilevel topological analyses (with the software package ToposPro) of carefully selected high quality sets of protein and small molecule crystal structures.

Analysis of migration paths in fast-ion conductors with Voronoi-Dirichlet partition.

In terms of the Voronoi-Dirichlet partition of the crystal space, definitions are given for such concepts as ;void', ;channel' and ;migration path' for inorganic structures with three-dimensional networks of chemical bonds. A number of criteria are proposed for selecting significant voids and migration channels for alkali cations Li+-Cs+ based on the average characteristics of the Voronoi-Dirichlet polyhedra for alkali metals in oxygen-containing compounds. A general algorithm to analyze the voids in crystal structures has been developed and implemented in the computer package TOPOS.