S. V. Borisov

Crystal Chemistry of Dichalcogenides MX2

Crystal-chemical analysis of the structures of metal (other than REE) dichalcogenides of composition X:M = 2:1 has been carried out. It is shown that there are two types of structure depending on the formal degree of metal oxidation. The first group are compounds M(X2) containing metals in the oxidation state 2+ and covalently bonded pairs of chalcogen elements; the main structural types here are cubic (pyrite) and orthorhombic (marcasite) FeS2. The second group involves the compounds MX2 with metals in the formal oxidation state 4+ and chalcogenide ions X2-; the main structural types in this group are CdI2, CdCl2, MoS2. The bond lengths M–X, X–X, and X...X are analyzed; it is shown that the high polarizability of the chalcogenide ions is reflected in shortened X...X distances. In the covalently bonded pairs X–X, the bond lengths change within the following limits: 2.03-2.30, 2.35-2.55, and 2.70-2.83 Å for X...X ion contacts, the minimal values are 3.07, 3.10, and 3.20 Å (X = S, Se, and Te, respectively).

Algorithms, software, and examples of pseudotranslational sublattice analysis for crystal structures

Software for analyzing pseudotranslational sublattices (PTSs) in crystal structures is described. This software makes it possible to enumerate triads of reflections, sort them out with respect to different characteristics, calculate linear and angular subcell parameters, and express the sublattice vectors in terms of the initial lattice vectors. The solution to the most widespread problems is illustrated by the example of the well-known [Ru(NH3)6]Cl3 and [CuL](NO3)(ReO4) crystal structures (L is 4,6,6-trimethyl-1,9-diamino-3,7-diazanon-3-en) and the structure of mineral iltisite, which is still unknown. In all cases we observed a tendency of crystal structures to have a higher symmetry, which was noted by Academician Belov in his time. “A material that in fact crystallizes in a lower system is nevertheless rather close (in its crystalline form) to numerical relations characteristic of a higher system.” (Belov [1, p. 227])

Analysis of atomic structures as the development of Belov’s “lattice” crystallography

The theorems of lattice crystallography, which was developed by N.V. Belov, and the wave-mechanical concept of the crystalline state lie in the basis of the crystallographic analysis of structures, which determines the results of atomic ordering by sets of crystallographic planes with the formation of pseudotranslational sublattices (force skeletons of structures). The role of cationic and anionic sublattices is shown by the example of structures of natural sulfides: heyrovskyite Pb6Bi2S9 and cannizzarite (Pb,Cd)5(Bi,In)6(S,Se)14.

Crystallographic analysis of a series of inorganic compounds

The method of crystallographic analysis relies on the mechanical-wave concept that treats the crystalline state as the result of ordering of atomic positions by families of parallel equidistant planes. Using this method, a large set of fluoride, oxide and sulfide structures was analyzed. The pseudo-translational ordering of various atomic groups (including the presence of cation and anion sublattices) in the structures of various classes of inorganic compounds was established. The crucial role of local ordering of heavy cations (coherent assembly) in the structures comprising large cluster fragments (Keggin polyanions, polyoxoniobates, etc.) is discussed. The role of symmetry and the regular distribution of heavy atoms in the formation of stable crystal structures, which is to be taken into account in the targeted design, is considered. The universality of configurations of atomic positions in the structures of various classes of inorganic compounds resulting from the ordering mechanism organized by mechanical (elastic) forces is demonstrated. The bibliography includes 158 references.

Crystal chemistry of mercury(I) and mercury(I, II) minerals

The crystal structures of 16 mercury(I)- and mercury(I, II)-containing minerals having (Hg-Hg)2+ groups are considered. The Hg-Hg and Hg-X bond lengths and the HgHgX angles (X = Cl, Br, I, O, S) are analyzed. A comparative crystal chemical analysis of the environment of Hg atoms is carried out. The Hg-Hg and Hg-X distances vary within 2.43-2.60 and 1.93-2.43 å, respectively; the angles defining the deviation of the X-Hg-Hg-X groups from linearity are from 146 to 177‡. In most cases, the coordination environment of the mercury atoms involves the metal atom of the (Hg-Hg)2+ dumbbell and the X atom, but in several compounds the coordination number of the mercury atoms increases due to the additional atoms lying 2.5–3.5 å away. In terlinguaite and kuznetsovite, the Hg3 triangle is rather unusual; in the latter mineral, the Hg-Hg bonds are lengthened to 2.64-2.70 å. The review covers structural data up to May 1997.

Crystal chemistry of mercury oxo- and chalcohalides

The features of mercury oxo- and chalcohalide crystal structure, including Hg3 Y 2 X 2 (Y = O, S, Se, Te; X = Cl, Br, I), chromates, phosphates and related compounds, are analyzed in terms of building blocks, their symmetry and stability. Building blocks are found, which are rigid atomic groups, namely, oxo-centered [Hg4O] tetrahedra, [Hg6O2] r-octahedra, [Hg2]2+, [Hg3]4+, [Hg3O]2+, [Ag3Hg]4+ cluster cations, etc. Bonded by the strongest chemical bonds, these groups keep their geometry unchanged in crystal structures of different composition. Thus cluster cations can be considered as single large cations, while their environment may be described by pseudo-coordination polyhedra, constructed around the centroid of each cation. This tendency was found for the example of atoms joined to pairs of [CrO4] tetrahedra, according to which the geometry of mutual arrangement of rigid atomic groups tends not to change. It is shown that the symmetry of the rigid atomic groups is a subgroup of the space group symmetry, and partly predetermines it. In crystal structures of some Hg3 Y 2 X 2 chalcohalides, the structure-forming role of packing of halogen atoms is revealed.

Experimental Crystallography from Atomic to Supramolecular Scale

Results of crystal structure analysis for various types of compounds are discussed in terms of a new concept of crystal formation. The effect of ordering “rigid” atomic groups ([Hg2]2+, [H2As · W18O60]7-, etc.) by families of crystallographic planes with interplanar distances comparable to the sizes of the groups is considered. The wide occurrence of symmetrical packings of atoms and/or centers of rigid atomic groups in structures is explained by a tendency toward maximum reduction in the number of degrees of freedom and, hence, a tendency toward minimum energy of the system.

Oxocentered polycationic complexes — An alternative approach to crystal-chemical investigation of the structure of natural and synthetic mercury oxosalts

The crystal structures of mercury oxosalts are described with isolation of oxocentered tetrahedrul groups [OHg4]. The bond topology of the oxocentered polycations is more diversified and rich than the motifs of canonic polyhedra in “classical” crystal chemistry and often is a more striking illustration of the unique nature of the structure of compounds from this class. The relative stability of the oxocentered polyions indicates that they play an important role in structure formation and possibly exist in various natuml media, making it appropriate to consider these groups in analysis of mercury transfer processes occurring in nature. The oxocentered approach proved to be useful for establishing structure-property type correlations and promotes the understanding and predicting the anisotropy of physical properties.

Coherence assembly phenomenon in the typical structures of heteropolyniobates

Crystallographic analysis has provided evidence for single cation frameworks formed from preordered cation positions in the individual building blocks (modules) constituting the basis of structures. We propose to call this phenomenon coherence assembly. According to the mechanical wave concept of the crystalline state, coherence assembly dictates the rules of mutual packing of “rigid” structural fragments. This study investigates the typical structures of heteropolyniobates: Na12[Ti2O2][SiNb12O40]·4H2O (I), menezesite Ba2MgZr4[BaNb12O42]·12H2O (II), and the menezesite-isostructural aspedamite □12(Fe3+,Fe2+)3Nb4·[Th(Nb,Fe3+)12O42]·(H2O,OH)12 (III).

Structure of dysprosium polysulfide DyS1.83 (Dy6S11) according to x-ray diffraction analysis

The crystal structure of a single crystal of dysprosium polysulfide DyS1.83 = Dy6S11 is determined. The unit cell parameters are similar to those established for DyS1.76 = Dy4S7, but the composition is different. The unit cell is monoclinic, space group P21/m, a = 11.009(2), b = 11.531(2), c = 11.023(1) Å, β = 91.152(8)∘, V= 1398.1(4) Å3; for Z = 4 this gives the composition Dy6S11, regarding the experimental values of the partial statistic of the S atoms and dcalc = 6.303 g/cm3 (EnrafNonius CAD-4 automatic diffractometer, γMoKα, Raniso = 0.0349 for 6381 unique Ihkl > 2σI of 9804 measured ones). An empirical absorption correction was applied based on transmission curves and habit data. The polysulfide is a PbFCl type structure; the monoclinic unit cell parameters are related to a0 and c0 of the tetragonal cell of PbFCl as [101] ≅ 4a0, [010] ≅3a0, [101] ≅2c0. The crystal is a twin with the ratio of components k2 = 1-k1 = 0.243(2) and a transition matrix 001/010/100. The composition DyS1.83±0.02 agrees with the chemical analysis data and the experimental value dexp = 6.30±0.08 g/cm3. The phase individuality of the polysulfide is confirmed by the form of the P-T projection of the P-T-X diagram of the Dy-S system.