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.

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.

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.

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.

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.

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.

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.

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.

B5N3 and B7N5 Monolayers with High Carrier Mobility and Excellent Optical Performance.

An ab initio evolutionary search algorithm was combined with density functional theory (DFT) calculations to predict a series of 2-D BxNy (1 < x/y ≤ 2). Particularly, B5N3 and B7N5 monolayers have sufficiently low formation enthalpy and excellent dynamic stability that make them promising for synthesis in experiments. Electronic structure calculations reveal that B5N3 and B7N5 monolayers possess an indirect band gap of 1.99 eV and a direct band gap of 2.40 eV, respectively. The calculated absorption coefficients for B5N3 and B7N5 monolayers are significantly improved in the low end of the visible region compared with that of 2-D h-BN. Moreover, our calculations reveal that both B5N3 and B7N5 monolayers have high electron carrier mobilities. The narrow band gaps, high carrier mobilities, strong near-ultraviolet absorption, and high synthesis possibility of B5N3 and B7N5 monolayers render them promising new materials for application in novel electronics and environmentally benign solar energy conversion.

Correction: Discovery of intrinsic two-dimensional antiferromagnets from transition-metal borides.

Correction for 'Discovery of intrinsic two-dimensional antiferromagnets from transition-metal borides' by Shiyao Wang et al., Nanoscale, 2021, 13, 8254-8263, DOI: 10.1039/D1NR01103K.

Discovery of intrinsic two-dimensional antiferromagnets from transition-metal borides.

Intrinsic two-dimensional (2D) magnets are promising materials for developing advanced spintronic devices. A few have already been synthesized from the exfoliation of van der Waals magnetic materials. In this work, by using ab initio calculations and Monte Carlo simulation, a series of 2D MBs (M = Cr, Mn or Fe; B = boron) are predicted possessing robust magnetism, sizeable magnetic anisotropy energy, and excellent structural stability. These 2D MBs can be respectively synthesized from non-van der Waals compounds with low separation energies such as Cr2AlB2, Mn2AlB2, and Fe2AlB2. 2D CrB is a ferromagnetic (FM) metal with a weak in-plane magnetic anisotropy energy of 23.6 µeV per atom. Metallic 2D MnB and FeB are Ising antiferromagnets with an out-of-plane magnetic easy axis and robust magnetic anisotropy energies up to 222.7 and 482.2 µeV per atom, respectively. By using Monte Carlo simulation, the critical temperatures of 2D CrB, MnB, and FeB were calculated to be 440 K, 300 K, and 320 K, respectively. Our study found that the super-exchange interaction plays the dominant role in determining the long-range magnetic ordering of 2D MBs. Moreover, most functionalized 2D MBTs (T = O, OH or F) are predicted to have AFM ground states. Alternating transition metals or functional groups can significantly modulate the magnetic ground state and critical temperature of 2D MBTs. This study suggests that the 2D MBs and MBTs are promising metallic 2D magnets for spintronic applications.

Visualization and Quantification of Geometric Diversity in Metal-Organic Frameworks.

With ever-growing numbers of metal-organic framework (MOF) materials being reported, new computational approaches are required for a quantitative understanding of structure-property correlations in MOFs. Here, we show how structural coarse-graining and embedding ("unsupervised learning") schemes can together give new insights into the geometric diversity of MOF structures. Based on a curated data set of 1262 reported experimental structures, we automatically generate coarse-grained and rescaled representations which we couple to a kernel-based similarity metric and to widely used embedding schemes. This approach allows us to visualize the breadth of geometric diversity within individual topologies and to quantify the distributions of local and global similarities across the structural space of MOFs. The methodology is implemented in an openly available Python package and is expected to be useful in future high-throughput studies.

From Simple to Complex: Design of Inorganic Crystal Structures with a Topologically Extended Zintl-Klemm Concept.

We present a novel approach to the generation of new crystalline phases, which is based on a combination of the topological description of crystal structures as a periodic net and the extended Zintl-Klemm concept, which establishes the structural relations between chemically and structurally simpler and more complex inorganic compounds. With this approach, we have explored the structural similarities between all known binary sulfides, selenides, and the corresponding simple sulfates and selenates and have theoretically revealed seven new high-pressure phases in the last two groups of compounds. Using density functional theory methods, we have studied the thermodynamic and mechanical stability of the new phases, have adjusted the transition pathways in the sulfate and selenate systems, and have revealed new structural correlations of the baric polymorphism in these systems. The advantages of the topological approach compared to conventional methods of modeling crystal structures are discussed and illustrated.

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.

CrystalGrower: a generic computer program for Monte Carlo modelling of crystal growth.

A Monte Carlo crystal growth simulation tool, CrystalGrower, is described which is able to simultaneously model both the crystal habit and nanoscopic surface topography of any crystal structure under conditions of variable supersaturation or at equilibrium. This tool has been developed in order to permit the rapid simulation of crystal surface maps generated by scanning probe microscopies in combination with overall crystal habit. As the simulation is based upon a coarse graining at the nanoscopic level features such as crystal rounding at low supersaturation or undersaturation conditions are also faithfully reproduced. CrystalGrower permits the incorporation of screw dislocations with arbitrary Burgers vectors and also the investigation of internal point defects in crystals. The effect of growth modifiers can be addressed by selective poisoning of specific growth sites. The tool is designed for those interested in understanding and controlling the outcome of crystal growth through a deeper comprehension of the key controlling experimental parameters.

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. We find a significant number of real materials are in this predicted database of zeolite-like structures. These results suggest that many other predicted structures in this database may be suitable targets for designer materials synthesis.

A universal algorithm for finding the shortest distance between systems of points.

Three universal algorithms for geometrical comparison of abstract sets of n points in the Euclidean space R3 are proposed. It is proved that at an accuracy ε the efficiency of all the algorithms does not exceed O(n3/ε3/2). The most effective algorithm combines the known Hungarian and Kabsch algorithms, but is free of their deficiencies and fast enough to match hundreds of points. The algorithm is applied to compare both finite (ligands) and periodic (nets) chemical objects.

Construction of (3,8)-connected three-dimensional cobalt(II) and copper(II) coordination polymers with 1,3-bis[(1,2,4-triazol-4-yl)methyl]benzene and benzene-1,3,5-tricarboxylate ligands.

Coordination polymers (CPs) have been widely studied because of their diverse and adjustable topologies and wide-ranging applications in luminescence, chemical sensors, magnetism, photocatalysis, gas adsorption and separation. In the present work, two coordination polymers, namely poly[(µ5-benzene-1,3,5-tricarboxylato-κ6O1:O1':O3:O3:O5,O5'){µ3-1,3-bis[(1,2,4-triazol-4-yl)methyl]benzene-κ3N:N':N''}di-µ3-hydroxido-dicobalt(II)], [Co2(C9H3O6)(OH)(C12H12N6)]n or [Co2(btc)(OH)(mtrb)]n, (1), and poly[[diaquabis(µ3-benzene-1,3,5-tricarboxylato-κ3O1:O3:O5)bis{µ3-1,3-bis[(1,2,4-triazol-4-yl)methyl]benzene-κ3N:N':N''}tetra-µ3-hydroxido-tetracopper(II)] monohydrate], {[Cu4(C9H3O6)2(OH)2(C12H12N6)2(H2O)2]·H2O}n or {[Cu4(btc)2(OH)2(mtrb)2(H2O)2]·H2O}n, (2), were synthesized by the hydrothermal method using 1,3-bis[(1,2,4-triazol-4-yl)methyl]benzene (mtrb) and benzene-1,3,5-tricarboxylate (btc3-). CP (1) exhibits a (3,8)-coordinated three-dimensional (3D) network of the 3,8T38 topological type, with a point symbol of {4,5,6}2{42·56·616·72·82}, based on the tetranuclear hydroxide cobalt(II) cluster [Co4(µ3-OH)2]. CP (2) shows a (3,8)-coordinated tfz-d topology, with a point symbol of {43}2{46·618·84}, based on the tetranuclear hydroxide copper(II) cluster [Cu4(µ3-OH)2]. The different (3,8)-coordinated 3D networks based on tetranuclear hydroxide-metal clusters of (1) and (2) are controlled by the different central metal ions [CoII for (1) and CuII for (2)]. The thermal stabilities and solid-state optical diffuse-reflection spectra were measured. The energy band gaps (Eg) obtained for (1) and (2) were 2.72 and 2.29 eV, respectively. CPs (1) and (2) exhibit good photocatalytic degradation of the organic dyes methylene blue (MB) and rhodamine B (RhB) under visible-light irradiation.