[en] The crystallographic analysis of the recently determined structures of LaBiI₆·13H₂O and NdBiI₆·13H₂O reveals that their common basis is a sublattice of iodine anions built of coherently assembled octahedral I₆ fragments. The relationship between the parameters of orthorhombic and monoclinic unit cells of these structures is shown and their symmetry features are discussed.

[en] The crystallographic analysis of five compositionally similar structures shows that the $R\stackrel{¯<!--\; ??\; -->}{3}$-symmetrical trigonal structure and two monoclinic (C2/c) structures with the ratio M:S = 3:2 that is the same for all three have identical cation sublattices and similar real configurations of atomic positions. Two structures with M:S = 9:8, with the orthorhombic symmetry (Pcan) and with its monoclinic distortion (P2₁/c), have identical cation sublattices. In the first group of the structures the symmetry and pseudosymmetry are determined by the SO₄ template symmetry, namely, axis 3. In the second group the symmetry of cation frameworks and structures in general is partially formed by three mutually perpendicular axes $\stackrel{¯<!--\; ??\; -->}{4}$ of the SO₄ tetrahedra.

[en] The crystallographic analysis of the orthorhombic (Pnma) structure of Sr₃B₂SiO₈ ≈ (Sr(B,Si)O_2.67) shows that its experimentally found symmetry is determined by the geometry of the Sr sublattice where the anion radical without this symmetry simulates it by the statistical averaging of four variants of real configurations. With a reduced fraction of heavy atoms in the triclinic (Р1) structure of Ba₃B₆Si₂O₁₆, the Ba and Si cations whose sublattice determines the presence of additional pseudosymmetry form the skeleton of the structure.

[en] 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.

[en] 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

[en] The role of symmetry in the formation of stable crystal structures is considered on the examples of cubic (Fe,Ni)₈AgS₈ ($Fm\stackrel{¯<!--\; ??\; -->}{3}m$), KTb₃F₁₀ ($Fm\stackrel{¯<!--\; ??\; -->}{3}m$), (Ba,Pb)6(Cu,Fe,Ni)₂₅S₂₇ ($Fm\stackrel{¯<!--\; ??\; -->}{3}m$), and spinel Al₂MgO₄ ($Fm\stackrel{¯<!--\; ??\; -->}{3}m$). The variants of atomic arrangement in a standard lattice of symmetrically related sites that are often “uncomfortable” for the atoms falling into them, but satisfying a given stoichiometry are shown. The symmetry phenomenon significantly reducing the information space volume determining the structure is the main factor in crystal dynamics (order dynamics) in understanding the essence of crystallization processes.

[en] The common “template” of datolite and okayamalite structures is a column-ribbon formed by alternating empty and Si occupied oxygen tetrahedra interconnected by common edges. The columns consolidate with their environment into crystalline structures largely due to the influence of the local symmetry of SiO₄ and BO₄ tetrahedra. As a result, mirror symmetry pseudo-planes of monoclinic datolite transform into okayamalite m planes; the pseudo-axis $\stackrel{¯<!--\; ??\; -->}{4}$ becomes the principal axis, whereas both structures contain glide planes and cation sublattices close in size.

[en] The structure of KHgI_3 · H_2O is assigned to the family of crystal structures having the three-layer cubic packing of iodine anions with cations in the tetrahedral voids (the structures of α-HgI_2, β-Ag_2HgI_4, and β-Cu_2HgI_4 among them). Crystallographic analysis shows that the nodes of the three-layer close packing are populated by iodine anions and K cations in the ratio 3/4: 1/4. Transformation of the structure of α-HgI_2 into the structure of KHgI_3 · H_2O can be formally represented as the replacement of (HgI)_n"+ fragments by (KH_2O)_n"+ fragments: (Hg_2I_4)–(HgI)"+ + (KH_2O)_n"+ = KHgI_3 · H_2O. Perforated layers of vertex-sharing HgI_4 tetrahedra break down into parallel isolated chains. Channels formed in place of I–Hg–I–Hg–fragments are occupied by–H_2O–K–-H_2-O-K-H_2O-chains weakly bound to neighbors.

[en] Crystallization proceeds by ordering atomic positions by translational and point symmetry operations. By fixing the symmetrical atomic configuration, this process removes the degrees of freedom from the atoms and thereby minimizes their energy and space volume V* characterizing this configuration. The structure of corundum (Al₂O₃) is crystallographically analyzed and its parameters are compared with those for the other prevalent structures (spinel, garnet, apatite, tourmaline, etc.). The phenomenon of crystallographic symmetry in the space of three coordinates and energy minimizes the number of degrees of freedom, and hence, the energy of atomic systems, unifies their configuration by packing it into a minimum volume-an information cell. An “ideal” construction (stencil) stable with respect to variations in external conditions and atomic compositions forms.

[en] The effect of symmetry ordering of sites of material particles (atoms, chemically strong atomic groups) is shown on characteristic examples. This ordering leads to reduction of the degrees of their freedom and, therefore, minimizes the energy of a system during crystallization. The geometry of Fedorov groups, supplemented with the symmetry energy function, determines the processes occurring in condensed atomic medium (“Kingdom of crystals,” according to E.S. Fedorov). Criteria are proposed for comparative estimation of the stability of structures, including the structural stencils (structure types of tourmaline, apatite, et al.) abundant in nature.