Sergey V. Krivovichev

Are the compressive effects of encapsulation an artifact of the bond valence parameters

Abstract The large bond valence sums found for O2– en-capsulated by Pb2+ ions are shown to result from the use of inappropriate bond valence parameters. New values of ro = 1.963 Å and b = 0.49 Å are recommended for Pb2+-O bonds.

Anion-centered tetrahedra in inorganic compounds.

Sergey V. Krivovichev,*,†,‡ Olivier Mentre,́ Oleg I. Siidra,† Marie Colmont, and Stanislav K. Filatov† †St. Petersburg State University, Department of Crystallography, University Emb. 7/9, 199034 St. Petersburg, Russia ‡Institute of Silicate Chemistry, Russian Academy of Sciences, Makarova Emb. 6, 199034 St. Petersburg, Russia UCCS, Equipe de Chimie du Solide, UMR CNRS 8181, ENSC LilleUST Lille, BP 90108, 59652 Villeneuve d’Ascq Cedex, France

Combinatorial topology of salts of inorganic oxoacids: zero-, one- and two-dimensional units with corner-sharing between coordination polyhedra

A method of graphical representation of heteropolyhedral units is applied to a wide range of salts of inorganic oxoacids (phosphates, arsenates, sulfates, chromates, molybdates, selenates, selenites, tellurites, etc.). Only those heteropolyhedral units that fulfill the following criteria are considered: (i) units with corner-sharing between coordination polyhedra only; (ii) units with no linkage between chemically and geometrically identical polyhedra; (iii) only zero- (finite clusters), one- (chains) and two- (sheets) dimensional units. More than 80 different topologies are considered. For 2D units (sheets), the concepts of basic graph and topological isomerism are formulated. Three different types of geometrical isomerism are recognized for chains, sheets and finite clusters: orientational isomerism, cis–trans-isomerism, and isomerism induced by the presence of cations with stereoactive lone pairs of electrons. Different geometrical isomers can be described by means of orientation matrices and connectivity diagrams. Relationships between different topologies are investigated.

Structural complexity of minerals: information storage and processing in the mineral world

Abstract Structural complexity of minerals is characterized using information contents of their crystal structures calculated according to the modified Shannon formula. The crystal structure is considered as a message consisting of atoms classified into equivalence classes according to their distribution over crystallographic orbits (Wyckoff sites). The proposed complexity measures combine both size- and symmetry-sensitive aspects of crystal structures. Information-based complexity parameters have been calculated for 3949 structure reports on minerals extracted from the Inorganic Crystal Structure Database. According to the total structural information content, IG, total , mineral structures can be classified into very simple (0-20 bits), simple (20-100 bits), intermediate (100-500 bits), complex (500-1000 bits), and very complex (> 1000 bits). The average information content for mineral structures is calculated as 228(6) bits per structure and 3.23(2) bits per atom. Twenty most complex mineral structures are (IG, total in bits): paulingite (6766.998), fantappieite (5948.330), sacrofanite (5317.353), mendeleevite-(Ce) (3398.878), bouazzerite (3035.201), megacyclite (2950.928), vandendriesscheite (2835.307), giuseppetite (2723.097), stilpnomelane (2483.819), stavelotite-(La) (2411.498), rogermitchellite (2320.653), parsettensite (2309.820), apjohnite (2305.361), antigorite (m = 17 polysome) (2250.397), tounkite (2187.799), tschoertnerite (2132.228), farneseite (2094.012), kircherite (2052.539), bannisterite (2031.017), and mutinaite (2025.067). The following complexity-generating mechanisms have been recognized: modularity, misfit relationships between structure elements, and presence of nanoscale units (clusters or tubules). Structural complexity should be distiguished from topological complexity. Structural complexity increases with decreasing temperature and increasing pressure, though at ultra-high pressures, the situation may be different. Quantitative complexity measures can be used to investigate evolution of information in the course of global and local geological processes involving formation and transformation of crystalline phases. The information-based complexity measures can also be used to estimate the ‘ease of crystallization’ from the viewpoint of simplexity principle proposed by J.R. Goldsmith (1953) for understanding of formation of simple and complex mineral phases under both natural and laboratory conditions. According to the proposed quantitative approach, the crystal structure can be viewed as a reservoir of information encoded in its complexity. Complex structures store more information than simple ones. As erasure of information is always associated with dissipation of energy, information stored in crystal structures of minerals must have an important influence upon natural processes. As every process can be viewed as a communication channel, the mineralogical history of our planet on any scale is a story of accumulation, storage, transmission and processing of structural information.

Topological complexity of crystal structures: quantitative approach.

The topological complexity of a crystal structure can be quantitatively evaluated using complexity measures of its quotient graph, which is defined as a projection of a periodic network of atoms and bonds onto a finite graph. The Shannon information-based measures of complexity such as topological information content, I(G), and information content of the vertex-degree distribution of a quotient graph, I(vd), are shown to be efficient for comparison of the topological complexity of polymorphs and chemically related structures. The I(G) measure is sensitive to the symmetry of the structure, whereas the I(vd) measure better describes the complexity of the bonding network.

Which Inorganic Structures are the Most Complex

The discovery of the diffraction of X-rays on crystals opened up a new era in our understanding of nature, leading to a multitude of striking discoveries about the structures and functions of matter on the atomic and molecular scales. Over the last hundred years, about 150,000 of inorganic crystal structures have been elucidated and visualized. The advent of new technologies, such as area detectors and synchrotron radiation, led to the solution of structures of unprecedented complexity. However, the very notion of structural complexity of crystals still lacks an unambiguous quantitative definition. In this Minireview we use information theory to characterize complexity of inorganic structures in terms of their information content.

Minerals and synthetic Pb(II) compounds with oxocentered tetrahedra: review and classification

The crystal structures of minerals and inorganic compounds with OPb4 oxocentered tetrahedra are reviewed. It is shown that the OPb4 tetrahedral units may link by sharing common Pb atoms to form structural units of various shape and dimensionality. These units determine basic topology of the structures and influence their stability and properties. The high strength of the OPb4 te trahedral units involves interplay between high basicity of additional O2– anions and stereochemical activity of the 6s2 lone electron pairs on Pb2+ cations. The structural chemistry of polycations based upon OPb4 tetrahedra, in general, follows major trends previously observed for cation-centered tetrahedral units (silicates, phosphates, metal sulphides with MS4 tetrahedra, etc.). One may conclude that the basic structural correlations depend upon size and charge parameters of the ions only, irrespective of their positive or negative sign.

Structural topology of potassium uranyl chromates: crystal structures of K8[(UO2)(CrO4)4](NO3)2, K5[(UO2)(CrO4)3](NO3)(H2O)3, K4[(UO2)3(CrO4)5](H2O)8 and K2[(UO2)2(CrO4)3(H2O)2](H2O)4

Abstract Crystals of four potassium uranyl chromates, K8[(UO2)(CrO4)4](NO3)2 (1), K5[(UO2)(CrO4)3](NO3)·(H2O)3 (2), K4[(UO2)3(CrO4)5](H2O)8 (3) and K2[(UO2)2·(CrO4)3(H2O)2](H2O)4 (4), have been synthesized by evaporation of aqueous solutions of (UO2)(NO3)2(H2O)6 and K2CrO4. The structure of (1) (triclinic, P1̅, a = 7.0397(6), b = 9.7341(9), c = 9.7568(9) Å, α = 105.846(2), β = 97.992(2), γ = 93.271(2)°, V = 633.8(1) Å3, Z = 1) was solved by direct methods and refined to R1 = 0.044 (wR2 = 0.098). It is based upon clusters of composition [(UO2)(CrO4)4] that consist of UrO4 square bipyramids (Ur: UO22+ uranyl ion) that share corners with four different CrO4 tetrahedra. The clusters are arranged in layers parallel to the (100) plane. K+ cations and NO3- groups are located between the clusters. The crystal structure of (2) (orthorhombic, P212121, a = 6.1112(11), b = 12.136(2), c = 27.464(4) Å, V = 2036.9(6) Å3, Z = 4) was solved by direct methods and refined to R1 = 0.047 (wR2 = 0.071). it contains chains of composition [(UO2)(CrO4)3] that are parallel to the b axis. The chains consist of UrO5 pentagonal bipyramids that share all equatorial corners with different CrO4 tetrahedra. Planes containing the equatorial ligands of the UrO5 pentagonal bipyramids are approximately parallel to the (100) plane. K+ cations, NO3 groups and H2O groups are between the chains. The crystal structure of (3) (monoclinic, P21/c, a = 8.2336(7), b = 18.8042(17), c = 21.2413(18) Å, β = 89.979(2)°, V = 3288.7(5) Å3, Z = 4) has been solved by direct methods from a crystal twinned on the (001) plane and refined to R1 = 0.060 (wR2 = 0.125). The structure is based upon topologically complex sheets of composition [(UO2)3(CrO4)5] with UrO5 pentagonal bipyramids that share their corners with CrO4 tetrahedra. The sheets are parallel to the (010) plane. K+ cations and H2O groups are located in the interlayer between the sheets. The crystal structure of (4) (monoclinic, P21/c, a = 10.7417(5), b = 14.5290(7), c = 14.1387(6) Å, β = 108.135(1)°, V = 2097.0(2) Å3, Z = 4) was solved by direct methods and refined to R1 = 0.036 (wR2 = 0.067). It is based upon sheets of composition [(UO2)2(CrO4)3(H2O)2] that are parallel to the (010) plane. K+ cations and additional H2O groups are in the interlayer. Nodal representations of uranyl chromate structural units are developed, and a comparison with related structures are presented.

Allabogdanite, (Fe, Ni)2P, a new mineral from the Onello meteorite: The occurrence and crystal structure

Abstract Allabogdanite, (Fe,Ni)2P, is a new mineral from the Onello iron meteorite (Ni-rich ataxite). It occurs as thin lamellar crystals disseminated in plessite. Associated minerals are nickelphosphide, schreibersite, awaruite, and graphite. Crystals of the mineral, up to 0.4 × 0.1 × 0.01 mm, are flattened on (001) with dominant {001} faces, and other faces that are probably {110} and {100}. Mirror twinning resembling that of gypsum is common, with possible twin composition plane {110}. Crystals are light straw-yellow with bright metallic luster. Polished (001) sections look silverywhite against an epoxy background. In reflected light in air, the mineral has a creamy color, with distinct anisotropy from light to dark creamy tint. No bireflectance was observed. R1/R2 (λ, nm) in air: 48.4/37.2(440), 46.7/36.8(460), 47.0/37.6(480), 47.5/38.1(500), 47.6/38.8(520), 48.2/39.2(540), 49.0/39.9(560), 49.6/40.7(580), 50.1/41.6(600), 50.5/41.9(620), 51.9/43.0(640), 52.3/44.3(660), 53.3/ 45.0(680), 54.4/46.2(700). No cleavage or parting was observed. Moh’s hardness is 5-6; the mineral is very brittle, and its calculated density 7.10 g/cm3. Its chemical composition (determined by microprobe methods, average of nine analyses) is: Fe 57.7, Ni 20.7, Co 1.4, P 20.4, Total 100.2 wt%, corresponding to (Fe1.51Ni0.50Co0.03)2.04P0.96 (three atoms per formula unit). Crystal structure: R1 = 0.040 for 138 unique observed (|Fo|≥ 4σF) reflections. Orthorhombic, Pnma, unit-cell parameters refined from powder data: a = 5.748(2), b = 3.548(1), c = 6.661(2) Å, V = 135.8(1), Å3, Z = 4; unitcell parameters refined from single-crystal data: a = 5.792(7), b = 3.564(4), c = 6.691(8) Å, and V = 138.1(3) Å3. Strongest reflections in the X-ray powder diffraction pattern are [d in Å, (I) (hkl)]: 2.238(100)(112), 2.120(80)(211), 2.073(70)(103), 1.884(50)(013), 1.843(40)(301), 1.788(40)(113), 1.774(40)(020). The mineral is named for Alla Bogdanova, Geological Institute, Kola Science Centre of Russian Academy of Sciences

Geometrical isomerism in uranyl chromates. I. Crystal structures of (UO2)(CrO4)(H2O)2, [(UO2)(CrO4)(H2O)2](H2O) and [(UO2)(CrO4)(H2O)2]4(H2O)9

Abstract Three uranyl chromate hydrates, (UO2)(CrO4)(H2O)2, [(UO2)(CrO4)(H2O)2](H2O) and [(UO2)(CrO4)(H2O)2]4(H2O)9, have been prepared by evaporation from aqueous solutions. The crystal structure of (UO2)(CrO4)(H2O)2 (monoclinic, C2/m, Z = 16, a = 16.786(2), b = 22.731(2), c = 6.9969(7) Å, β = 90.051(3)°, V = 2669.8(5) Å3) has been solved by direct methods and refined to R1 = 0.065, calculated for 6702 unique observed reflections (|Fo| ≥ 4σF). The crystal structure of [(UO2)(CrO4)(H2O)2](H2O) (monoclinic, P21, Z = 4, a = 9.7206(14), b = 7.1617(10), c = 11.0909(16) Å, β = 92.388(3)°, V = 771.43(19) Å3) has been solved by direct methods and refined to R1 = 0.052, calculated for 4879 unique observed reflections (|Fo| ≥ 4σF). The crystal structure of [(UO2)(CrO4)(H2O)2]4(H2O)9 (monoclinic, P21/c, Z = 4, a = 31.397(1), b = 7.1701(3), c = 16.2480(7) Å, β = 97.515(1)°, V = 3626.3(3) Å3) has been solved by direct methods and refined to R1 = 0.051, calculated for 8164 unique observed reflections (|Fo| ≥ 4σF). Each structure contains chains of composition [(UO2)(CrO4)(H2O)2]. Within the chains, (UO2)O3(H2O)2 pentagonal bipyramids share three equatorial O atoms with CrO4 tetrahedra. The CrO4 tetrahedra in the [(UO2)(CrO4)(H2O)2] chains each share three corners with uranyl polyhedra, and contain one non-shared (terminal) ligand pointing either up or down relative to the plane of the chain. This results in a geometrical isomerism of the uranyl chromate chains that can be described as a sequence of tetrahedra orientations along the chain extension, e.g. ... up-down-up-down ... or ... ududud .... [or (ud)∞]. The structures of (UO2)(CrO4)(H2O)2 and [(UO2)(CrO4)(H2O)2](H2O) are based upon the chains of the (ud)∞ type, whereas [(UO2)(CrO4)(H2O)2]4(H2O)9 contains two types of chains: (ud)∞ and (u)∞. The [(UO2)(CrO4)(H2O)2] chains extend in the same direction in each structure and are linked via hydrogen bonds involving H2O molecules.