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Specific stereochemical features of silicon in oxygen-containing compounds, including hybrid silicates with all oxygen atoms of SiOn groups (n = 4, 5, or 6) entering into the composition of organic anions or molecules, are described by characteristics of Voronoi—Dirichlet polyhedra. It is found that in rutile-like stishovite and post-stishovite phases with the structures similar to those of СаСl2, α-PbO2, or pyrite FeS2, the volume of Voronoi—Dirichlet polyhedra of silicon and oxygen atoms decreases linearly with pressure increasing to 268 GPa. Based on these results, the possibility of formation of new post-stishovite phases is shown, namely, the fluorite-like structure (transition predicted at ~400 GPa) and a body-centered cubic lattice with statistical arrangement of silicon and oxygen atoms (~900 GPa).

Mechanisms of radiation damages in minerals promising for the utilization of highly active radioactive waste (zircon ZrSiO4, monazite LaPO4, orthophosphate YbPO4, lakargiite CaZr0,8Sn0,1Ti0,1O, and Gd2Zr2O7 and Gd2Ti2O7 compounds with the pyrochlore structure) are studied by the computer simulation using the molecular dynamics method. The formation of a damaged region in the structures under study is considered along with the recovery (relaxation) processes in these structures. The number of Frenkel pairs and antistructural defects that form in the structure of these minerals after the pass of the knocked out thorium atom is calculated by the molecular dynamics method. A parameter is proposed that characterizes the mineral tendency to amorphization under the effect of the radiation damage. The obtained results show that one of the main factors determining the radiation stability of minerals is the crystal structure type, compounds with the monazite structure being more radiationally stable than compounds with the zircon structure. It is found that the Gd2Zr2O7 compound and lakargiite have a weaker tendency to amorphization than other minerals such as zircon, monazite, and orthophosphate YbPO4. A high radiation stability of the studied Gd2Zr2O7 compound as well as a solid solution of the composition CaZr0.8Sn0.1Ti0.1O3 makes it possible to propose them as a possible matrix for the utilization of highly active radioactive waste.

The possibilities of studying the local structure in isomorphic systems by methods based on the minimization of the interatomic interaction energy are considered in the work. The original procedure for the theoretical analysis of the local structure, which the authors have been developing for a number of years and have implemented in four computer programs, is discussed in detail. The practical implementation of this procedure is exemplified by the following solid substitution solutions: halite–sylvin (Na,K)Cl, corundum–eskolaite (Al,Cr)2O3, spinel–magnesiochromite Mg(Al,Cr)2O4, chrysoberyl–mariinskite Be(Al,Сr)2O4, grossular–uvarovite Ca3(Al,Cr)2[SiO4]3. Calculations are performed on a SKIF MGU Chebyshev supercomputer for supercells containing several thousands of atoms. The performed analysis of the behavior of changes in the geometric characteristics of CrO6 octahedra in various isomorphic systems makes it possible to reveal the main reasons affecting the alteration of the relaxation parameter. It is found that the key factor is the size of the common structural unit of an isomorphic mixture. Thus, the behavior of the relaxation parameter obeys the isomorphism assistance rule.

In connection with the 100th anniversary of the discovery of the phenomenon of the diffraction of X-rays by crystals (Max von Laue, 1912) and the basics of X-ray crystallographic analysis (Lawrence Bragg, 1913), the article marks the major milestones in this outstanding event in the history of science. Special emphasis is given to the role of Russian scientists (E. S. Fedorov, G. V. Vulf) in the emergence and early steps in the establishment of this discovery being one of the pillars of the scientific revolution of the first half of the past century.

The thermodynamics of mixing is computed for eight different distributions of Sr and Ca over the M1 and M2 cation sites in the fluorapatite solid solution. Calculations are carried out for a 4×4×4 supercell via the semi-empirical approach using the GULP package. In the solid solution with the most energetically favorable distribution, Sr tends to occupy the M2 site rather than the M1 site and the x (Sr1): x (Sr2) ratio varies as a function of the Sr content. These structures are used for further investigation of the effect of mixing on the lattice parameters, local structure and elasticity of the Ca-Sr fluorapatite solid solution. Changes in the Sr2-F bond lengths as the Sr content increases turn out not to comply with Vegard’s rule. However, this deviation occurs in order to keep the linear dependence of the polyhedral volumes with the solid-solution composition. The obtained data allow us to estimate the structural relaxation parameters for both independent cation positions. Analysis of the bond sums also backs up the preference of Sr cations for the M2 site.

The crystal structure of the new mineral magnesioneptunite (K0.8Na0.1−0.1)Na2Li(Ti0.39Mg0.34Fe0.27)2(Ti0.59Mg0.22Fe0.19)2[Si4O11]2(O,OH) from the xenolith of Verkhnechegemskaya caldera (Lakarga Mountain, North Caucasus) has been investigated by X-ray diffraction (XCalibur-S diffractometer, R = 0.0244): a = 16.3271(7) A, b = 12.4788(4) A, c = 9.9666(4) A β = 115.651(5), V = 1830.5(1) A3, sp. gr. C2/c, Z = 4, and ρcalcd = 3.152 g/cm3. The disordered distribution of Ti, Mg, and Fe atoms in the octahedra forming the basis of the cationic framework is established. It is shown that the isomorphic occupation of octahedral positions by cations of three types corresponds to the centrosymmetric crystal structure and is likely caused by the high-temperature crystallization of the mineral.

Synthetic analogues of murataite, a very rare mineral—a complex oxide of REE, actinide, Ti, Fe, and other elements,—are of great interest as confinement matrices of radioactive wastes. They are produced by sintering (1200–1300°C) and melting (1500–1600°C) with subsequent crystallization of the melt. Four structural varieties of murataite distinguished by unit-cell parameters have been established by TEM study. All these varieties are derivatives of the fluorite structure designated as murataite 3C, 5C, 7C, and 8C depending on repetition factor of a parameter of the fluorite subcell. The structural features of the synthetic murataite varieties are analyzed in this paper based on data obtained from high-resolution electron microscopy, microdiffraction, and X-ray refinement. The hypothesis of a modular structure of the members of polysomatic pyrochlore-murataite series has been confirmed. At the same time, the structural modules are zero-dimensional rather than two-dimensional as had previously been suggested. The combinations of zero-dimensional modules in 3D space create the entire structural diversity of the polysomatic series.

The thermodynamic and elastic properties of mixing have been calculated and the local structure of Be(Al,Cr,FeIII)2O4 solid solutions has been analyzed using a previously elaborated set of interatomic potentials for atomistic modeling of simple and complex beryllium oxides, which almost exactly reproduced their structural, elastic, and thermodynamic properties. Calculations have been performed for a (4a × 2b × 2c) supercell of the olivine structural type with the relieved nontranslational symmetry (space group P1), which has made it possible to specify the distribution of trivalent atoms over nonequivalent positions and to provide relaxation of the local structure. The mixing properties have been calculated over the entire range of compositions, the changes in the Gibbs free energy with variations in temperature and the regions of stability of the solid solutions have been estimated, and the critical values of the temperature and composition have been determined. The histograms of the distributions of M-M, M-O, and O-O interatomic distances, as well as MO6 octahedron volumes, have been constructed; the compliances of cation positions have been evaluated; and the groups of atoms that are most readily shiftable from their ideal positions have been established. The performed analysis has demonstrated that two different octahedral positions M1 and M2 in the olivine-type structure, namely, chrysoberyl, are extremely sensitive to their own atomic environment. This leads to a preferable incorporation of Al3+ cations into the M1 octahedral position, whereas larger-sized Cr3+ (Fe3+) cations preferentially occupy the M2 octahedral position.

Standard enthalpies of formation of GdBaCo2−xMxO5.5 (M = Fe, Mn; x = 0, 0.2) from constituent oxides, Δ o x H i ∘ , and elements, Δ f H i ∘ , at 298 K were calculated using dissolution enthalpies of corresponding double perovskites. Both Δ o x H i ∘ and Δ f H i ∘ were found to decrease in the sequence of GdBaCo2O5.5, GdBaCo1.8Fe0.2O5.5 and GdBaCo1.8Mn0.2O5.5 indicating growth of relative thermodynamic stability of GdBaCo2O5.5 caused by the substitution of Fe or Mn for Co.

Data on the structural and valence distribution of Cr and Fe in chrysoberyl and in alexandrite, its gem variety, are given. It is shown that the Cr3+ line in the natural Ural and Tanzania samples is the strongest in the M1 site and for the synthetic stones, in the M2 site. During the annealing of the alexandrite crystals, Cr3+ passes from the smaller M1 site into the larger M2 site. The Mossbauer spectroscopy quantitatively determined the distribution of different valence Fe ions. The various proportions of both Fe2+ and Fe3+ ions isomorphically entering the octahedral sites in the BeAl2O4 crystal structure were established.

Statistical analysis of modern structural databases on inorganic crystals and minerals is carried out to elucidate the classification of crystal structure distributions over space groups. The known fact about extremely uneven occupation of space groups is confirmed; the relative abundance of all and, in particular, 24 most frequent groups (>1%) is derived, and the latter are noted to belong to holohedral and centrosymmetric classes. The data on occupation of extremely rare and empty space groups are analyzed and refined separately, which allows the reduction of a number of unreliable structural data. The theoretical analysis of empirical regularities is performed from the standpoint of filling rules for special structural positions (Wyckoff positions) and the symmetry of lattice complexes. It is shown that only combined consideration of different symmetry rules and restrictions provides an explanation for most regularities observed in occupation of symmetry point groups.

A set of partially covalent interatomic potentials has been developed with the aim of reproducing the experimentally known crystal structures and predicting the unknown crystal structures and the thermodynamic and elastic properties of bromellite BeO, chrysoberyl BeAl2O4, and its isostructural analogs BeCr2O4 and BeFe2O4. The calculated structural, elastic, and thermodynamic properties of these minerals are in good agreement with the available experimental data. This gives grounds to believe that the prediction of a number of unknown properties of these compounds and the model crystal structure of Fe chrysoberyl are sufficiently reliable. A theoretical analysis of the energy characteristics of the Schottky and Frenkel point defects is carried out for all the substances under investigation.

Using Voronoi-Dirichlet (VD) polyhedra and the method of overlapping spheres, we analyze the coordination of 714 crystallographically different vanadium atoms in the structure of compounds containing VO n polyhedra. Vanadium atoms are found to be bonded to 4, 5, 6, or 7 oxygen atoms. The effect of the valence state and coordination number of vanadium atoms on the main parameters of their VD polyhedra is considered. A unified linear dependence between the solid angles of VD polyhedron faces corresponding to V-O bonds and the respective interatomic distances varying in a range of 1.55 A to 2.79 A is stated to exist. It is shown that the parameters of VD polyhedra can be used to determine the valence state of vanadium atoms.

A detailed historical review is presented and the difficulties arising when defining such a fundamental concept as structural type in crystal chemistry are analyzed. Particular attention is paid to the genetic relationship between different structural types and to the criteria of choosing between them. Many other terms and concepts of modern crystal chemistry defined for completeness.

The dependences of average V-O distances in inorganic compounds of vanadium of different valence on the degree of distortion of coordination polyhedra have been obtained by careful statistical treatment of modern structural data banks. Values of bond lengths in undistorted (regular) polyhedra are recommended. Theoretical analysis of the statistical data made it possible to calculate the most likely values of the parameters of the bond valence model: the interatomic distance for the single (two-electron) bond, corresponding to the single valence, and the bond softness parameter. Calculations of the sums of bond valences for some complicated cases (different coordination numbers, mixed vanadium valence) confirmed reliability of the recommended parameters.

The structural, elastic, and thermodynamic properties of halite NaCl and sylvine KCl and the miscibility properties of the NaCl-KCl solid solution found by computer simulation are in good agreement with the experimental data. Analysis of the relaxation of the solid solution structure suggests that both anion and cation sublattices are distorted; however, the anion sublattice is distorted much more strongly. Calculations of the local bond valence at all types of ions in the solid solution show opposite deviations from the balance at cations, whereas the general balance is retained. The values of the electrostatic potential in the ion positions reflect weakening of bonding in the solid solution with respect to its pure components. In addition, with an increase in the average interatomic distance in the first coordination sphere around cations, the modulus of the electrostatic potential at cations decreases.

Knowledge of the high-pressure and high-temperature elasticity of Fe–Ni alloy with low (5–25%) Ni content is crucial for geosciences since it is probably the major component of the cores of the terrestrial planets and the Moon. Here we present a study of a FeNi alloy with 22 at.% of Ni to 72 GPa and 715 K, using inelastic X-ray scattering (IXS) and X-ray powder diffraction from polycrystalline material. The X-ray diffraction (XRD) study revealed stability of the face centred cubic (fcc) over the hexagonal close packed (hcp) phase in the whole investigated pressure–temperature range. The study presents first investigations of elasticity of fcc phase of iron–nickel Fe0.78Ni0.22 alloy. The isothermal equations of state were derived at room temperature and at 715 K (K300 = 162(1) GPa, K ′ 300 = 4.97 ( 1 ) , V300 = 6.89(1) cm3/mol; K715 = 160(1) GPa, K ′ 715 = 4.97 ( 2 ) , V715 = 6.96(1) cm3/mol). Inelastic X-ray measurements allow the determination of the longitudinal acoustic wave velocity VP, and provide, combined with the measured equations of state, the full isotropic elasticity of the material. We found that within experimental errors our data follow the Birch's law. We did not observe any significant deviations for fcc Fe0.78Ni0.22 from elastic properties of pure ɛ-iron.

This paper reports on the results of a structural investigation of an important group of synthetic compounds with derivative structures of the mineral murataite, a potential matrix for immobilization of radioactive wastes. A model describing the structure of the entire group of compounds is proposed on the basis of analyzing the results obtained using chemical (electron microprobe) analysis methods, high-resolution transmission electron microscopy (high-resolution electron images and microdiffraction patterns), and X-ray diffractometry of a large array of artificial murataite ceramics. In essence, the proposed structural model is as follows: in the structure, layers of two (pyrochlore and murataite) packing types alternate along the [111] direction of the cubic supercell, so that the resulting structures can undergo substitutional and displacive modulations. Experiments on irradiation of different murataite modifications with heavy ions demonstrate that these modifications have close values of the radiation resistance, which is higher than that of the pyrochlore coexisting with them.

The synthetic mineral urusovite $\mathrm{CuAl}(\mathrm{As}{\mathrm{O}}_{4})\mathrm{O}$ was prepared through the wet chemistry route and characterized over a wide temperature range in terms of studies of magnetization, specific heat, and X-band electron spin resonance. The basic structural units of the compound are distorted square pyramids $\mathrm{Cu}{\mathrm{O}}_{5}$ assembled into corrugated honeycomb layers separated by $\mathrm{As}{\mathrm{O}}_{4}$ and $\mathrm{Al}{\mathrm{O}}_{4}$ tetrahedrons. Both thermodynamic and resonant measurements indicate that $\mathrm{CuAl}(\mathrm{As}{\mathrm{O}}_{4})\mathrm{O}$ is a spin gap system with a gap of $\ensuremath{\sim}350\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The electronic structure calculations performed within the framework of density functional theory suggest a weakly interacting dimer model with antiferromagnetic signs for both intradimer and interdimer superexchange interactions. This establishes the valence bond solid as the quantum ground state of the title compound. The pronounced discrepancy between experimental data and calculations within the weakly interacting dimer model at elevated temperatures is ascribed in part to the steep increase of the intradimer exchange interaction parameter driven by the thermal expansion effects.

Structure simulation is performed for molybdophates of variable composition A1−x Zr2(PO4)3−x (MoO4)x, where A is Na (0≤x≤0.6), K (0≤x≤0.6), K (0≤x≤0.3), Rb (0≤x≤0.2), or Cs (0≤x≤0.1), using the minimization of the interatomic interaction energy; these molybdophosphates crystallize in the NaZr2(PO4)3 (NZP) structure type. The results of the computer-assisted structure simulation are verified by the synthesis of the molybdophosphates and their characterization by X-ray powder diffraction and IR spectroscopy. The crystallization field of the NZP molybdophosphate shrinks as the alkali cation size increases. The key factors that govern the stability of the NZP structure in alkali zirconium molybdophosphates are determined.

The crystal structure of a synthetic analog of the mineral lipscombite (Fe2.32+Fe4.73+)[PO4]4O2.7(OH)1.3 obtained under hydrothermal conditions in the LiF-Fe2O3-(NH4)2HPO4-H2O system is resolved (R = 0.040) by X-ray diffraction analysis (Bruker Smart diffractometer with a highly sensitive CCD detector, MoKα radiation): a = 14.776(3) A, b = 14.959(3) A, c = 7.394(1) A, β = 119.188(4)°, sp. gr. C2/c, Z = 4, ρexp = 3.8 g/cm3, ρcalcd = 3.9 g/cm3. Fe2+ and Fe3+ cations are statistically distributed in each of four crystallographically independent positions, while occupying the corresponding octahedra with probabilities of 60, 90, 100, and 91%. The ratio Fe2+/Fe3+ in the composition of the crystals was established by Mossbauer spectroscopy. Lipscombite is interpreted as a mineral of variable composition described by the formula (Fex2+Fen−x3+)[PO4]4Oy(OH)4−y. The field of stability is determined as a function of the iron content and the ratio Fe2+/Fe3+. It is shown that at n = 6 iron cations are ordered in octahedra and barbosalite structure is formed. An interpretation of genetically and structurally related members of the lipscombite family within a unified polysomatic series is proposed.

Combined X-ray powder diffraction, Mossbauer, and XANES spectroscopy in situ experiments revealed the transformation of cubic (Mg0.8Fe0.2)O ferropericlase to a rhombohedrally distorted phase at 35(1) GPa and room temperature. The Mossbauer spectroscopy results show that the rhombohedral distortion does not involve magnetic ordering. Combined with data from the literature, our results imply that the cubic to rhombodedral transition occurs in (Mg,Fe)O under conditions of non-hydrostatic stress over a wide range of composition (0.2≤x Fe≤1).

Partition coefficients (K) between forsterite crystal and melt are experimentally determined for many univalent, bivalent, trivalent, and tetravalent trace elements. Using numerical modeling, we calculated the energies of intrinsic and impurity defects in forsterite (Edf) and the energies of dissolution of univalent, bivalent, trivalent, and tetravalent impurities (Eds). These results are compared with literature data. A linear dependence is established for the energy of defects on the charge of the impurity ion and the relative difference in the radii of the impurity and matrix ions Δr/d, where d is the average interatomic distance in the matrix. Partition coefficients are described by parabolic dependences on Δr/d and charge of the impurity ion using literature data on K of impurity elements in olivines and impurity ion dissolution energies. Linear dependences-RTlnK-(Δr/d)2 and Eds-(Δr/d)2 pass through the origin for isovalent substitutions and are well apart from it for heterovalent substitutions. Linear dependence (Δr/d)2 has a free term of about 200 kJ/mol, which is approximately equal to a half of the energy of formation of the Frenkel defect in forsterite; this defect maintains electroneutrality. If valency is compensated due to addition into the melt of an ion with another charge (than that of the impurity ion), Eds-(Δr/d)2 and-RTlnK-(Δr/d)2 lines at low (Δr/d)2 shift to the origin. This means that energy consumption for coupled isomorphism is lower than that for the formation of intrinsic structural defects. Correlation dependences are proposed for the distribution of impurities and the energy of their dissolution. They indicate the increasing contribution of the entropy components of impurity ion dissolution energy during heterovalent isomorphism.

The forsterite-melt partition coefficients K are determined experimentally for a large number of mono-, di-, tri-, and tetravalent impurities. The energies of native defects and impurities (E d) and the solution energies (E s) of impurities in forsterite are evaluated using computer simulation. The defect energy is shown to vary linearly with the difference in ionic radius between the host and substituent atoms (Δr) and with the impurity cation charge, while the partition coefficient and solution energy of impurities are quadratic functions of these parameters. The plots of lnK versus (Δr)2 and E s versus (Δr)2 for isovalent substitutions and Me Mg x and Me Si x ) pass close to the origin, in contrast to the plots for heterovalent substitutions (Me Mg ′ and Me Si ⋅ ). The significant y intercept of the latter plots is interpreted as evidence for the formation of extra defects maintaining electroneutrality. The y intercept of the plot of E s versus (Δr)2 is 2 eV, which is about half the formation energy of Frenkel defects in forsterite. The best fit equations representing the correlation between the partition coefficients and solution energies of impurities demonstrate that heterovalent substitutions increase the entropy contribution to the free energy of solution of impurities.

The crystal structure of mineral sakhaite Ca48[Mg13.2(Fe, Mn)2.8](CO3)16{ Al[SiO3.75(OH)0.25]4}(BO3)28[(H2O)3.3(HCl)3.3] from the Solongo deposit, Zabaykalye, is established (R 0.047) by X-ray diffraction analysis (Bruker Smart CCD diffractometer, 2θ: θ scan, λMoK α radiation, graphite monochromator): a = 14.679(2) A, sp. gr. Fd3m, Z = 1, ρcalcd = 2.99 g/cm3. It is shown that some part of BO3 triangles in the structure of sakhaite from Solongo is replaced with five-member complexes {Al[SiO3(O,OH)]4}, established previously in the harkerite structure. Three schemes of isomorphism, which are characteristic of the sakhaite-harkerite mineral series, are selected and the general formula is proposed: Ca48(Mg,Fe,Mn)16(CO3)16{Al[SiO3(O, OH)]4}y(B3)32−y · n(H2O,HCl) (Z = 1), y max = 8, n max = 16 − y. The structural relationship of sakhaite-harkerite minerals with borate-sulfates of the tychite family Na6(Mg,Fe,Mn)2(BO3)4(SO4) is revealed. The correlation between the number of harkerite fragments forming the mineral structure, the structural symmetry, and the degree of imperfection is ascertained.

A hierarchical approach to the choice of the most probable structural models of a compound with a specified chemical composition and to the subsequent refinement of these models with the use of different methods is analyzed. Most attention is given to one of the first stages of the choice of the starting model (on the basis of the principles of total and local crystal electroneutrality) and to the solution of the problem of construction and determination of the bond graphs and connectivity matrices. Simple criteria for the most stable configurations of chemical bonds are introduced reasoning from the principles of minimum dissymmetrization and maximum informational entropy.

The distortion theorem is analyzed by the use of the Bond Valence Model for the case of an isolated coordination polyhedron with bonds of different lengths. It is shown that a correlation should exist between the average bond length increase and the mean-square deviation of individual bond lengths from the average one, at least for nonstrained crystal structures. It is proved that the correlation parameters are strongly dependent on a mode of distortion (symmetry of coordination environment). These conclusions are in general and sometimes in quantitative agreement with available experimental data, although in most cases the distortion of coordination polyhedra results from a variety of factors of chemical, geometric and electronic origin. It is assumed that an observed correlation between the average bond distance and the distortion degree may be taken as a measure of relative role of intrinsic bond strengths and influence of crystalline environment.

Investigations of the last decade significantly extended the list of known zeolite-like compounds, whose crystal structure is based on mixed frameworks composed of various anion polyhedra. In addition to the well-known natural and artificial zeolites with the Al and Si tetrahedron frameworks, a large number of microporous phases with three-dimensional anion constructions based on Zn‐P, Be‐P, Zn‐As, Al‐P, and other cation matrices were found [1‐6]. Oxygen complexes of amphoteric metals in combination with [ PO 4 ] 3— acid complex anions form mixed anion frameworks containing pores or channels, where either alkaline or organic cations are located. In this group of compounds, which are often used as molecular sieves as an alternative to aluminum silicates, aluminum phosphates are most studied. Systematically investigating aluminum phosphates, we synthesized one more such compound. In this work, we study colorless transparent isometric well-cut crystals up to 5 mm in size, which were produced in standard Teflon-lined 4-cm 3 autoclaves by the method of soft hydrothermal synthesis ( T = 250i C and P = 100 atm). A mechanical mixture of Na 2 O‐ Al 2 O 3 ‐P 2 O 5 ‐B 2 O 3 components prepared in equal weight amounts was introduced into a water-filled autoclave. Experiments continued for 18‐20 days. The diffraction pattern recorded from a powder sample by a DRON UM diffractometer indicated that the synthesized compound is original. The X-ray analysis (CanScan 4DV) showed that this phase include Na, Al, and P atoms. Investigating a single crystal with a SYNTEX P four-circle autodiffractometer, we found that the parameters of a rhombic (pseudotetragonal) unit cell are a = 8.475(2) A , b = 8.471(2) A, and c = 14.319(3) A. Experimental data needed to interpret the structure were obtained with the same diffractometer (Mo K α radia1 tion) by the 2 θ : θ -scanning method. The intensities of reflexes were adjusted with allowance for the Lorenz factor and polarization effect. Calculations were made with the SHELX program package [7, 8] by using the curves of atomic scattering and the corrections for anomalous dispersion taken from [9]. We could not find a structural model in the framework of the tetragonal symmetry ( P 4 2 2 1 2 space group). For this reason, we supposed that the crystal has rhombic symmetry, and the pseudotetragonal symmetry results from merohedric or pseudomerohedric microtwinning. The structure was determined by direct methods and refined in the anisotropic full-matrix approximation with allowance for absorption and secondary isotropic extinction. In the absence of chemical analysis, atoms were identified by taking into account the composition of the system in the process of crystal synthesis, interatomic spacings, temperature factors, and the character of ellipsoids of thermal vibrations. Allowance for pseudotetragonal twinning showed that the samples under investigation contain two kinds of objects with different orientations in a ratio of 0.440(3) : 0.560(3). The Flack parameter [10] testified to the proper choice of an “absolute” acentric configuration ( P 2 1 2 1 2 1 space group). The structure is described by the formula

The structure and some physical properties of malayaite CaSnOSiO4 have been studied by the precision X-ray diffraction, Mossbauer spectroscopy, and computer simulation of the structure. The unit-cell parameters a = 7.152(2) A, b = 8.888(2) A, c = 6.667(2) A, β = 113.37(2)°, V = 389.0(3) A3, and μr = 0.68 are refined on a synthetic impurity-free sample. The distribution of the deformation electron density is analyzed in the basic fragments of the crystal structure forming an anionic framework. The constructed potentials of pair and three-particle interaction reproduced quite well the elastic, dielectric, and energy characteristics and allowed us to predict their numerical values, which are in good agreement with the limited available experimental data.

The structure of KDP crystals doped with trivalent (Al3+, Fe3+, Mn3+, V3+, and La3+) and divalent (Ni2+, Co2+, Fe2+, Mn2+, Ca2+, Sr2+, and Ba2+) cations was simulated by minimizing the energy of atomic interactions. Three types of defects were revealed: isolated defect centers formed by M3+ and Ni2+ ions, cluster chain centers formed by M2+ ions with ionic radii exceeding 0.9 A, and complex centers formed via the replacement of potassium ions by large Ba2+ dopants with the simultaneous replacement of some of the phosphorus atoms by silicon ones. The corresponding energies of defect formation are calculated. The surface morphology of the crystal faces is studied. The changes in morphology in the presence of M3+ dopants are caused by their adsorption, whereas for M2+ dopants, these changes are caused mainly by their incorporation into the crystal structure.

The crystal structure of FeII-doped KDP crystals was simulated with the use of specially developed partly covalent potentials. Different variants of introduction of impurity into the structure were analyzed. The M1 position was found to be more favorable for both isolated divalent and trivalent metal ions. Upon optimization, the coordinates of the FeII ion are (0.25, 0.44, 0.125). The FeII ions can aggregate to form “clusters” energetically more favorable than isolated defects. It seems that FeIII ions cannot form aggregates.

The program is a computer realization of the bond valence method (BVM), used to predict bond lengths in crystal structures from topological data. Using object-oriented programming made it possible to analyze structures of any complexity (up to 6480 crystal chemical positions). Hardware and software requirements: i486DX processor, operating system Windows 3.1/95, 4M RAM, and about 2M disk space. The program was developed at the Crystallography and Crystal Chemistry Department, Geological Faculty, Moscow State University.

Maximum solubility of Sn 4+ ions in the spin glass Fe 2 Ti 1- x Sn x O 5 (pseudobrookite) corresponds to x = 0.22(3) at T = 1250°C, and Sn 4+ ions appear to occupy only 4c octahedral sites amongst the 4c and 8f sites. According to EPR data, the observed spin glass transition temperature T g depends on tin concentrations nonmonotonically. The T g values correlate with the measurement times typical of EPR and some other methods. This correlation is well approximated by the empirical Vogel-Fulcher law.

The mixed valence compound Na2Fe2F7 crystallizes in the monoclinic weberite structure of the Na2CuFeF7-II type (M-II), space group C2/c, Z = 16, a = 12.676, b = 7.422, c = 24.710 A, β = 99.97°. Refinement on F2 led to wR(F2) = 0.117 for all 2 645 reflections, R = 0.057 for 1 258 refl. with Fo > 4σ(F). On the basis of this and other recent single crystal investigations the structures of weberites Na2MIIMIIIF7 are classified in four main structure types: O-I is the ‘classical’ orthorhombic weberite type (S.G. Imma) encountered e.g. in the mineral Na2MgAlF7, from which two lower symmetric variants O-II (Na2CuCrF7 type) and O-III (Na2NiInF7) are deriving. The second M-I and third M-II basic type are monoclinic (e. g. Na2CuFeF7-I and -II), the fourth type T is trigonal (Na2MnFeF7). The structural relations within the weberite family are discussed and the connections established, which allow to regard these weberites as well as the pyrochlores as subtraction derivatives of the fluorite type. Struktur von Na2Fe2F7 und Strukturbeziehungen in der Weberitfamilie Na2MIIMIIIF7 Die gemischtvalente Verbindung Na2Fe2F7 kristallisiert im monoklinen Weberit-Typ von Na2CuFeF7-II (M-II), Raumgruppe C2/c, Z = 16, a = 12,676, b = 7,422, c = 24,710 A, β = 99,97°. Die Verfeinerung mit F2-Daten ergab wR(F2) = 0,117 fur alle 2 645 Reflexe, R = 0,057 fur 1 258 Reflexe mit Fo > 4σ(F). Auf der Grundlage dieser und anderer neuer Einkristalluntersuchungen werden die Strukturen der Weberite Na2MIIMIIIF7 in vier Haupttypen eingeteilt: O-I ist der „klassische” orthorhombische Weberit (RG Imma), wie er im Mineral Na2MgAlF7 auftritt, und von dem sich zwei niedriger symmetrische Varianten, O-II (Na2CuCrF7-Typ) und O-III (Na2NiInF7), ableiten. Der zweite M-I und dritte M-II Typ sind monoklin (z. B. Na2CuFeF7-I and -II), der vierte Typ T ist trigonal (Na2MnFeF7). Die strukturellen Verwandtschaften innerhalb der Weberitfamilie werden diskutiert und die Zusammenhange aufgezeigt, die es erlauben, diese Weberite ebenso wie die Pyrochlore als Subtraktionsabkommlinge des Fluorittyps zu betrachten.

Recently, the Hy-2a hydrous olivine (MgH2 SiO4)·3(Mg2SiO4) occurring as nanometre-sized inclusions in mantle olivines has been found by TEM, and has been suggested to be a new DHMS phase (Khisina et al. 2001). A model of the crystal structure of Hy-2a has been proposed as a 2a-superstructure of olivine with one Me2+ -vacant octahedral layer in the (1 0 0) plane per Hy-2a unit cell (Khisina and Wirth 2002). In the present study the crystal structure of Hy-2a hydrous olivine is optimized by ab initio calculations. The aims of this study are: (1) verification of the suggested models of Hy-2a hydrous olivine structure; (2) calculation of the most stable configurations for Hy-2a structure with minimum static lattice energy, by assuming a possible formation of Me2+ vacancies in either M1 or M2 octahedral sites; (3) determination of the position of protons and hydrogen bonds in the Hy-2a structure. Several different possible configurations of the Hy-2a structure are optimized. The results support the idea of a stable olivine structure with ordered planar-segregated OH-bearing defects oriented parallel to (1 0 0). The data obtained indicate a preferred stability of the Hy-2a structure with the protons associated with M1 vacancies and bonded with O1 and O2 oxygen sites. The relative energy values of the optimized Hy-2a structure configurations correlate as a rule with the average shifts of atoms from their positions in pure forsterite structure.