A set of new promising solid chalcogenides for Na-ion batteries: yield from the crystal chemical, Monte-Carlo and quantum-chemical calculations.

Free crystal space in more than 600 chalcogenide structures taken out from the ICSD has been theoretically analyzed. As a result, wide voids and channels accessible for Na+-ion migration were found in 236 structures. Among them, 165 compounds have not been described in the literature as Na+-conducting materials. These materials have been subjected to stepwise quantitative calculations. The bond valence site energy method has enabled the identification of 57 entries as the most promising ion conductors in which the Na+-ion migration energy (Em) is less than 0.55 eV for 2D or 3D diffusion. The kinetic Monte-Carlo method has been carried out for these substances; as a result, resulting in nine of the most prospective compounds with Na+-ionic conductivity Ϭ≥10-4 S cm-1 at room temperature were selected, for which the density functional theory calculations have been performed yielding six best candidates. Additionally, a logarithmic relationship was established between the values of Em and the diffusion channel radii as well as a linear relationship between Ϭ and the void radius.

A novel class of multivalent ionic conductors with the La3CuSiS7 structure type: results of stepwise ICSD screening.

The results of high-throughput screening of the inorganic crystal structure database for new promising Ca2+-, Mg2+-, Zn2+- and Al3+-ion conducting ternary and quaternary sulfides, selenides, and tellurides are presented (∼1500 compounds). A geometrical-topological approach based on the Voronoi partition was initially used and yielded 104 compounds, which were unknown as conductors with possible cation migration. All compounds were passed through the bond valence site energy analysis to determine the migration energy Em. Furthermore, we established the logarithmic dependencies of Em on the geometrical parameters of the migration pathways. As a result, 16 out of 104 structures were filtered out as promising conductors. Finally, density functional theory simulations yielded the 11 most prospective compounds with Em < 1.0 eV. Among them, we found a novel class of ionic conductors with the La3CuSiS7 structure, for which ab initio molecular dynamic calculations were performed, revealing diffusion coefficients of ∼10-7 cm2 s-1 and ionic conductivity of ∼10-2 S cm-1 at 300 K.

Novel Topological Motifs and Superconductivity in Li-Cs System.

In this work, we determined the phase diagram and electronic properties of the Li-Cs system by using an evolutionary crystal structure prediction algorithm coupled with first-principles calculations. We found that Li-rich compounds are more easily formed in a wide range of pressures, while the only predicted Cs-rich compound LiCs3 is thermodynamically stable at pressures above 359 GPa. A topological analysis of crystal structures concludes that both Li6Cs and Li14Cs have a unique topology that has not been reported in existing intermetallics. Of particular interest is the fact that four Li-rich compounds (Li14Cs, Li8Cs, Li7Cs, and Li6Cs) are found to be superconductors with a high critical temperature (∼54 K for Li8Cs at 380 GPa), due to their peculiar structural topologies and notable charge transfer from Li to Cs atoms. Our results not only extend an in-depth understanding of the high-pressure behavior of intermetallic compounds but also provide a new route to design new superconductors.

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. We have revealed that even a two-shell configuration strongly predetermines the overall connectivity (topological type) of an intermetallic crystal structure. The chemical and stoichiometric composition of the multi-shell LACs generally obeys the close-packing model: the number of atoms in the subsequent shells (Nk) varies around the value Nk = 10k2 + 2, which is valid for the same size atoms, to reach the densest packing for the kth shell. Deviations from the revealed regularities often indicate inconsistencies in the crystallographic information, unusual features of the structure, or the existence of more stable phases that can be used for the validation of experimental and modeling data.

Predicting crystal growth via a unified kinetic three-dimensional partition model.

Understanding and predicting crystal growth is fundamental to the control of functionality in modern materials. Despite investigations for more than one hundred years, it is only recently that the molecular intricacies of these processes have been revealed by scanning probe microscopy. To organize and understand this large amount of new information, new rules for crystal growth need to be developed and tested. However, because of the complexity and variety of different crystal systems, attempts to understand crystal growth in detail have so far relied on developing models that are usually applicable to only one system. Such models cannot be used to achieve the wide scope of understanding that is required to create a unified model across crystal types and crystal structures. Here we describe a general approach to understanding and, in theory, predicting the growth of a wide range of crystal types, including the incorporation of defect structures, by simultaneous molecular-scale simulation of crystal habit and surface topology using a unified kinetic three-dimensional partition model. This entails dividing the structure into 'natural tiles' or Voronoi polyhedra that are metastable and, consequently, temporally persistent. As such, these units are then suitable for re-construction of the crystal via a Monte Carlo algorithm. We demonstrate our approach by predicting the crystal growth of a diverse set of crystal types, including zeolites, metal-organic frameworks, calcite, urea and l-cystine.

Mining Knowledge from Crystal Structures: Oxidation States of Oxygen-Coordinated Metal Atoms in Ionic and Coordination Compounds.

We propose a universal scheme for predicting the oxidation states of metal atoms in ionic and coordination compounds with a small set of structural descriptors, which include the parameters of atomic Voronoi polyhedra. The scheme has been trained and checked with more than 35,000 crystal structures containing more than 90,000 metal atoms in the oxygen environment. The accuracy of the prediction exceeded 95%; we have detected a number of wrong oxidation states and incorrect chemical compositions in the crystallographic databases using this scheme. The scheme is easily extendable to any kind of atomic environment and can be used to search for correlations between geometrical and physical properties of crystal structures.

Topology of Intermetallic Structures: From Statistics to Rational Design.

More than 38 000 substances made only of metal atoms are collected in modern structural databases; we may call them intermetallic compounds. They have important industrial applications, and yet they are terra incognita for most of our undergraduate students. Their structural complexity and synthesis are not easily adaptable to first years laboratories, keeping them away from the standard curricula. They have been described over the years following alternative and complementary views such as coordination polyhedra, atomic layers, and polyatomic clusters. All of these descriptions, albeit relying on grounded principles, have been applied on a subjective basis and never implemented as a strict computational algorithm. Sometimes, the authors generated multiple views of the same structure reported with beautifully drawn figures and/or photos of hand-crafted models in seminal works of the precomputer age. With the use of our multipurpose crystallochemical program package ToposPro, we explored the structural chemistry of intermetallics with objective and reproducible topological methods that allow us to reconcile different structure descriptions. After computing the connectivity patterns between the metal atoms on the basis of Voronoi partitioning of the crystal space, we were able to group the 38 000 intermetallic compounds into 3700 sets of crystal structures with the same topology of atomic net. We have described the different views used in the literature and shown that 12-vertex polyhedra are the most frequent (33%) and that almost half of them are icosahedron-like (46%), followed by cuboctahedron (25%) and, unexpectedly, by bicapped pentagonal prism (13%). Looking for layers, we have found that the hexagonal lattice, which corresponds to the closest packing of spheres on a plane, exists in more than 11 000 crystal structures, confirming the close-packed nature of intermetallics. We have also applied the nanocluster approach, which goes beyond the first coordination sphere and looks for structural units as multishell clusters that assemble the whole structure. This approach shows that 41% of intermetallics can be assembled with a single nanocluster and that 22.4% of these are packed according to the face-centered cubic motif of the closest packing of spheres in three-dimensional space. We have shown that our approach can easily adopt any other building model and hence could become a platform for a universal predictive scheme. Within this scheme, all of the structural descriptors can be related to experimental data and theoretical modeling results and then can be used to synthesize new intermetallic compounds and to foresee novel materials.

Sulfur- and Selenium-Containing Compounds Potentially Exhibiting Al Ion Conductivity.

We have created a set of crystalline model structures exhibiting straight lines of Al3+ connected to chalcogenides (O2- , S2- , and Se2- ) connected to metal cations of varying valence (Sr2+ , Y3+ , Zr4+ , Nb5+ , and Mo6+ ). They were relaxed with density functional theory computations and analysed by Bader partitioning. As Al3+ ions are supposed to strongly interact with their atomic environment, we studied the electron density topology induced by higher-valent cations in the extended chemical neighbourhood of Al. In fact, we found a general decrease of ionic charges and an increasing displacement of the chalcogenides towards higher-valent ions for the heavier chalcogens. Therefore, we comprehensively screened S- and Se-containing compounds for candidates theoretically exhibiting low migration barriers for Al3+ ions by using Voronoi-Dirichlet partitioning and bond valence site energy calculations. The basis for this search is the Inorganic Crystal Structure Database. Indeed, we could extract six promising candidates with low Al3+ migration barriers. which are even lower than the barriers for any other element inside of these materials. This will encourage efforts towards preparing suitable Al3+ conductors.

A Water-Stable Cl@Ag14 Cluster Based Metal-Organic Open Framework for Dichromate Trapping and Bacterial Inhibition.

Decoding the principles of cluster-based framework assembly at the molecular level remains a persistent challenge. Herein, we isolated and characterized a novel water-stable three-dimensional (3D) metal-organic open framework [Cl@Ag14(cPrC≡C)10Cl2·(p-TOS)·1/3H2O]n (SD/Ag14, cPrC≡CH = cyclopropylacetylene; p-TOS = p-toluenesulfonate), which contains a chloride-templated Ag14 cluster as building block. For SD/Ag14, one chloride acts as the template to shape the Ag14 cluster and the other bridges the clusters to a 3D pcu-h open framework. As revealed by high resolution electrospray mass spectrometry (HRESI-MS), the Ag12-Ag14 species are potential cluster-based intermediates to the 3D pcu-h framework, which authenticates a preconceived idea that the 3D framework is hierarchically assembled from the silver clusters as observed in solid state. Interestingly, SD/Ag14 can be used effectively to remove the environmental pollutant Cr2O72- from wastewater through anion exchange in a single-crystal-to-single-crystal (SC-SC) transformation fashion. Furthermore, SD/Ag14 exhibits excellent antibacterial activity against Staphylococcus aureus, thus making it a potential antibacterial agent.

Topological Motifs in Cyanometallates: From Building Units to Three-Periodic Frameworks.

This review focuses on topological features of three-periodic (framework) p, d, and f metal cyano complexes or cyanometallates, i.e. coordination compounds, where CN(-) ligands play the main structure-forming role. In addition, molecular, one-periodic (chain), and two-periodic (layer) cyanometallates are considered as possible building blocks of the three-periodic cyanometallates. All cyanometallates are treated as systems of nodes (mononuclear, polynuclear, or transitional metal cluster complexes) joined together via CN-containing spacers. The most typical nodes and spacers as well as methods of their connection are described and systematized. Particular attention is paid to the overall structural motifs in the three-periodic cyanometallates, especially to the relations between the local coordination (coordination figure) of structural units and the entire framework topology. The chemical factors are discussed that influence the cyanometallate topological properties due to modification of nodes, spacers, or coordination figures.

On the Way to New Possible Na-Ion Conductors: The Voronoi-Dirichlet Approach, Data Mining and Symmetry Considerations in Ternary Na Oxides.

With the constant growth of the lithium battery market and the introduction of electric vehicles and stationary energy storage solutions, the low abundance and high price of lithium will greatly impact its availability in the future. Thus, a diversification of electrochemical energy storage technologies based on other source materials is of great relevance. Sodium is energetically similar to lithium but cheaper and more abundant, which results in some already established stationary concepts, such as Na-S and ZEBRA cells. The most significant bottleneck for these technologies is to find effective solid ionic conductors. Thus, the goal of this work is to identify new ionic conductors for Na ions in ternary Na oxides. For this purpose, the Voronoi-Dirichlet approach has been applied to the Inorganic Crystal Structure Database and some new procedures are introduced to the algorithm implemented in the programme package ToposPro. The main new features are the use of data mined values, which are then used for the evaluation of void spaces, and a new method of channel size calculation. 52 compounds have been identified to be high-potential candidates for solid ionic conductors. The results were analysed from a crystallographic point of view in combination with phenomenological requirements for ionic conductors and intercalation hosts. Of the most promising candidates, previously reported compounds have also been successfully identified by using the employed algorithm, which shows the reliability of the method.

A Collection of Topological Types of Nanoclusters and Its Application to Icosahedron-Based Intermetallics.

In this study, we carried out a topological and geometrical analysis of more than 27 000 intermetallics. More than 2000 topologically different nanoclusters were determined and stored in an electronic database as the Topological Types of Nanoclusters (TTN) collection. Besides the topology of the nanoclusters, the TTN collection contains the information on their occurrence as well as on motifs of their assembly in intermetallics; it is included to the set of the ToposPro topological collections. With the TTN collection we analyzed the topology of local binding and overall topological motifs in the 1528 intermetallics assembled with icosahedron-based building units. Taking the TTN collection as a starting point, we present the concept of a knowledge database and an expert system that can be used to process a huge set of data to find general regularities in the crystal structures of intermetallics and to predict some of their features.

Vacancy ordering as a driving factor for structural changes in ternary germanides: the new R2Zn(1-x)Ge6 series of polar intermetallics (R = rare-earth metal).

Synthesis and structural characterization of the new compounds R2Zn1-xGe6 (R = La-Nd, Sm, Gd-Ho) is reported. A structural change was revealed along this series by careful analysis of single-crystal X-ray diffraction data. For light rare earths up to Tb the orthorhombic oS72-Ce2(Ga0.1Ge0.9)7 model was established; instead, the Dy compound represents a new structure type (P21/m, mP34, Z = 4, a = 7.9613(3) Å, b = 8.2480(4) Å, c = 10.5309(5) Å, ß = 100.861(1)°) being a superstructure of the mS36-La2AlGe6 prototype. The established structural models support the increase of Zn deficiency along the series, suggested by microprobe analysis, and its key role in governing structural changes. The vacancy ordering criterion was applied as a successful approach to find a general scheme including the structures of the ∼R2MGe6 compounds known up to now (R = rare-earth metal, M = transition metal, Mg, Al, Ga) and highlighting the subtle structural differences within this family. According to this scheme, these structures are obtained from a common aristotype (oS20-SmNiGe3) via symmetry reduction based on group-subgroup relations accompanied by ordering of vacancies. This approach was optimized with the help of the ToposPro software and extended to the R2Zn3Ge6 series, enriched with new members (R = Sm, Gd-Ho) during this work. Electronic structure calculations on La2ZnGe6 confirm the presence of infinite covalent germanium zigzag chains and three-bonded corrugated layers connected via Zn atoms to form a polyanionic network stabilized by La atoms.

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. Special attention is paid to the skeletal net since it describes the connectivity of a crystal structure in the simplest way, thus enabling one to find unobvious relations between crystalline substances of different composition and architecture. The tools for the automated hierarchical topological analysis have been implemented in the program package ToposPro. Examples, which illustrate the advantages of such analysis, are considered for a number of classes of crystalline substances: elements, intermetallics, ionic and coordination compounds, and molecular crystals. General provisions of the application of the skeletal net concept are also discussed.

γ-Brass polyhedral core in intermetallics: the nanocluster model.

Using the TOPOS program package, 26-atom nanoclusters of the γ-brass (Cu5Zn8) type (0@4@22 or 0@8@18) were found in 5918 crystal structures of cubic intermetallics. The nanocluster models were built for all the intermetallics using a recently developed algorithm implemented into TOPOS. The relations of the structures based on the 0@4@22 core are explored as a result of migration of atoms between different shells of the nanoclusters. It is shown that the 0@4@22 nanoclusters frequently occur as building units of intermetallics of different composition and structure type. Regularities in chemical composition of 702 γ-brass-type nanoclusters were found within both the nanoclusters approach (multishell structure) and the nested-polyhedra model. A database containing all topological types of γ-brass nanoclusters is created with which one can search for the corresponding atomic configuration in any intermetallics.

A "strongly" self-catenated metal-organic framework with the highest topological density among 3,4-coordinated nets.

A new type of 3D "strongly" self-catenated metal-organic framework (SDU-9) has been constructed from [Cu2(COO)4] paddlewheel secondary building units and a tripodal carboxylate linker. SDU-9 ([Cu6(H2O)6L4]·24H2O, where [H3L = 4,4',4"-(hydroxysilanetriyl)tris(triphenyl-4-carboxylic acid), represents a rare example of a highly symmetrical coordination network and extremely tight self-catenation. To the best of our knowledge, SDU-9 has the highest topological density among all known 3,4-coordinated nets.

A topological approach to reconstructive solid-state transformations and its application for generation of new carbon allotropes.

A novel approach is proposed for the description of possible reconstructive solid-state transformations, which is based on the analysis of topological properties of atomic periodic nets and relations between their subnets and supernets. The concept of a region of solid-state reaction that is the free space confined by a tile of the net tiling is introduced. These regions (tiles) form the reaction zone around a given atom A thus unambiguously determining the neighboring atoms that can interact with A during the transformation. The reaction zone is independent of the geometry of the crystal structure and is determined only by topological properties of the tiles. The proposed approach enables one to drastically decrease the number of trial structures when modeling phase transitions in solid state or generating new crystal substances. All crystal structures which are topologically similar to a given structure can be found by the analysis of its topological vicinity in the configuration space. Our approach predicts amorphization of the phase after the transition as well as possible single-crystal-to-single-crystal transformations. This approach is applied to generate 72 new carbon allotropes from the initial experimentally determined crystalline carbon structures and to reveal four allotropes, whose hardness is close to diamond. Using the tiling model it is shown that three of them are structurally similar to other superhard carbon allotropes, M-carbon and W-carbon.

The natural tiling approach to cation conductivity in KAlO2 polymorphs.

A detailed analysis of correlations between structural features and cation conductivity is performed for KAlO(2) polymorphs in a wide temperature range of 300-1023 K. To explore the migration maps of K(+) cations we have used neutron diffraction data for low- and high-temperature KAlO(2) polymorphs and applied for the first time a novel algorithm based on the natural tiling concept and implemented it into the program package TOPOS. Five independent elementary channels for the K(+) cation migration have been revealed whose cross-sections were found to be essentially different in the low-temperature form, indicating a high anisotropy of the cation conductivity. During the transition to the cubic high-temperature phase all five channels become equivalent with sharply increased cross-sections that account for the jump-like increase of the cation conductivity and gives rise to its three-dimensional character.

Structure of a new high-pressure-high-temperature modification of antimony(III) oxide, γ-Sb2O3, from high-resolution synchrotron powder diffraction data.

A quenchable new high-pressure-high-temperature modification of antimony(III) oxide, γ-Sb(2)O(3), has been obtained at hydrostatic pressures of 9-11 GPa and temperatures of 573-773 K. Its crystal structure has been determined from high-resolution synchrotron powder diffraction data. γ-Sb(2)O(3) consists of three-dimensionally cross-linked infinite chains of SbO(3)E units (E = lone pair) with the chains forming tetragonal rod-packing. The underlying topology of γ-Sb(2)O(3) (3,3T8) is found very rarely in inorganic structures; it is realised only for the polyanion [Si(4)O(4)N(6)](10-) that occurs in the Ce(4)(Si(4)O(4)N(6))O structure type. The structural relation to the two previously known polymorphs of Sb(2)O(3) at ambient pressure, valentinite and senarmontite is discussed.

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. The labyrinth nets of a generated triply periodic surface are built from the natural tiling, and in turn the topological parameters of the labyrinth nets are used to determine if the surface is isomorphic to a minimal surface. This method has been applied to all known 253 zeolite frameworks and 98 triply periodic surfaces were obtained, which belong to 55 topological types. Twelve surfaces were found to be isomorphic to already known triply periodic minimal surfaces (TPMSs), while four surfaces can be treated as isomorphic to new TPMSs. A procedure has also been developed for transferring the generated surfaces to a 3D-printer-readable format.