Cluster self-organization of silicate and germanate systems: Suprapolyhedral precursor clusters and self-assembly of orthotetrahedral structures in Na,TR-germanates (silicates)

The geometrical and topological analysis of all known types of the orthotetrahedral structures of Na,TR-germanates and their silicon analogues has been carried out using computer methods (TOPOS 4.0 program package). The full 3D reconstruction of the self-assembly mechanism of crystal structures has been performed as follows: precursor cluster-primary chain-microlayer-microframework (supraprecursor). For Na₂HLaSiO₅, NaHo₄(GeO₄)₂O₂OH, NaScGeO₄, and NaSm₃Ge₂O₈(OH)₂, the same type of 2D TR, T-network has been recognized: 433334 + T 4433. For Na₂HScGeO₅, network TR 44444 + T 444 has been recognized. The coordination number (CN) of a precursor cluster in 2D networks is six. In all structures, the invariant type of cyclic four-polyhedral precursor clusters built of tetrahedron-linked TR-polyhedra has been identified with CNs being eight, seven, or six. In the Na₅Y₄Si₄O₁₆F structure, a tubular-type primary chain in which precursor clusters are tetrahedron-linked TR polyhedra with CN = 8 has been recognized. Their stacking in a layer is characterized by the network TR 8 8 4 + T 8 4 8, where 8 corresponds to the cross section of the primary chain. In a 3D network, the total number of neighboring tubular primary chains linked to the main chain is four. In the structures with TR: T = 1: 1 or 1.5: 1, the positions above and below the center of the precursor cluster are occupied by Na atoms; in NaHo₄(GeO₄)₂O₂(OH), where TR: T = 2: 1, these positions are occupied by an Na atom and a TR atom.     

Cluster self-organization of silicate and germanate systems: Suprapolyhedral precursor nanoclusters and self-assembly of tetrahedral structures of the family A2T2O5 (A = Li, Na; T = Si, Ge): Li2T2O5, Li4Ge3SiO10, Li2Si2O5, and A2Si2O5

Modeling of atomic species (An clusters in the form of atoms or Kn polyhedra, where n is the number of atoms or polyhedra) corresponding to the initial stage of evolution of a chemical system has been carried out. Three series of K4 clusters built of different T tetrahedra (L and T) have been recognized. For L₂T₂ clusters, six geometrically and symmetrically different types of suprapolyhedral clusters have been discovered. The model has been used to identify precursor clusters in A₂T₂O₅ (A = Li, Na; T = Si, Ge) framework structures: A-type Li₂T₂O₅ with space group Cc, B-type Li₄Ge₃SiO₁₀ with space group Abm2, C-type Li₂Si₂O₅ with space group Ccc2, and D-type A₂Si₂O₅ with space group Pbcn. Three (of the six possible) types of suprapolyhedral precursor nanoclusters K4 in the four structures have been identified. The full 3D reconstruction of the self-assembly scenario of crystal structures is as follows: precursor nanocluster ?? primary chain ?? microlayer ?? microframework ?? ?? framework. The bifurcation of structural evolution pathways (structural branching points) at the suprapolyhedral level for type A and B structures is found to occur only when a microframework is formed of equivalent microlayers.     

Cluster self-organization of TR-containing silicate and germanate systems: Suprapolyhedral precursors and self-assembly of A2HMTO5 (A = Li, Na; M = Sc, Lu, Yb) crystal structures with MTO5 frameworks

The combinatorial topological analysis is carried out using the coordination sequences method (the TOPOS 4.0 program package) and the matrix self-assembly is modeled for silicates Li₂HTRSiO₅ (TR = Lu, Yb; space group $P\bar 1$ ) and germanate Na₂HScGeO₅ (space group P2₁ ab). These compounds, having identical formulas, have different MT frameworks built of M octahedra (TRO₆) and T tetrahedra (SiO₄, GeO₄). New types of crystal-forming binodal nets are discovered: 4 4 6 6 + 4 4 6 for lutetium silicate and 44444(4⁵) + Ge 444(4³) for scandium germanate; the atom-site ratio in the nets is M: T = 1: 1. A ring invariant suprapolyhedral precursor cluster composed of four polyhedra is identified, with two (A = Li, Na) atoms lying one above and one below the center of the cluster. A₂M₂T₂ precursor clusters control the evolution of high-level crystal-forming clusters by means of the matrix assembly mechanism. The evolution routes of the suprapolyhedral precursor clusters bifurcate at the stage where topologically dissimilar layers are formed of equivalent chains. The cluster coordination numbers (CCNs) in a layer for the precursor clusters are four for lutetium silicate and six for scandium germanate.     

The Crystal Structure of Disodium Phosphonate,Na2HPO3

Anhydrous disodium phosphonate, Na₂HPO₃, was prepared by dehydration of its pentahydrate. The crystal structure of Na₂HPO₃ was solved from high resolution X‐ray powder diffraction data (P2₁/n; Z = 4; a = 9.6987(1), b = 6.9795(1), c = 5.0561(1) Å, β = 92.37(1)°; V = 341.97(1) ų). The crystal structure consists of two types of sodium‐oxygen polyhedra, which are connected via common edges and vertices forming layers perpendicular to [100]. These Na(1)‐ and Na(2)‐layers are interlinked via common edges, forming in a 3D‐framework. The resulting topology is providing oxygen arrangements that please the coordinative requirement of phosphorus(III).     

Modeling of self-organization processes in crystal-forming systems. Structural mechanism of self-assembly of zirconosilicate Na2ZrSi2O7 from suprapolyhedral clusters

Topological analysis of the crystal structure of Na₂ZrSi₂O₇ (parakeldyshite, space group P1^–) with an MT framework, where M are ZrO₆ octahedra and T are SiO₄ tetrahedra, was carried out by the method of coordination sequences (TOPOS.3.2 program package), and the self-organization of this structure was modeled. The cyclic-type suprapolyhedral cluster precursor Na₂M₂T₄ with the local symmetry 1^– was identified by bicolor decomposition of the 4646+664 net. The cluster is composed of six polyhedra with two Na atoms located in the center. The precursors control the evolution of high-level crystal-forming clusters. The cluster coordination number is six. The centers of eight cluster precursors in the superprecursor of the Na₂ZrSi₂O₇ structure are related by translation vectors.     

Synthese und Struktur neuer Natriumhydrogensulfate Na(H3O)(HSO4)2; Na2(HSO4)2(H2SO4) und Na(HSO4)(H2SO4)2

Synthesis and Structure of New Sodium Hydrogen Sulfates Na(H₃O)(HSO₄)₂, Na₂(HSO₄)₂(H₂SO₄), and Na(HSO₄)(H₂SO₄)₂ Three acidic sodium sulfates have been synthesized from the system sodium sulfate/sulfuric acid and have been crystallographically characterized. Na(H₃O)(HSO₄)₂ ( A ) crystallizes in the space group P2₁/c with the unit cell parameters a = 6.974(2), b = 13.086(2), c = 8.080(3) Å, α = 105.90(4)°, V = 709.1 Å3, Z = 4. Na₂(HSO₄)₂(H₂SO₄) ( B ) is orthorhombic (space group Pna2₁) with the unit cell parameters a = 9.970(2), b = 6.951(1), c = 13.949(3) Å, V = 966.7 ų and Z = 4. Na(HSO₄)(H₂SO₄)₂ ( C ) crystallizes in the triclinic space group P1 with the unit cell parameters a = 5.084(1), b = 8.746(1), c = 11.765(3) Å, α = 68.86(2)°, β = 88.44(2)°, γ = 88.97(2)°, V = 487.8 Å3 and Z = 2. All three compounds contain SO₄ tetrahedra as HSO₄^? anions and additionally in B and C in form of H₂SO₄ molecules. The ratio H:SO₄ determines the connectivity degree in the hydrogen bond system. In A , there are zigzag chains and dimers additionally connected via oxonium ions. Complex chains consisting of cyclic trimers (two HSO₄^? and one H₂SO₄) are present in B . In structure C , several parallel chains are connected to columns due to the greater content of H₂SO₄. Sodium cations show a distorted octahedral coordination by oxygen in all three structures, the NaO₆ octahedra being “isolated” (connected via SO₄ tetrahedra only) in A . Pairs of octahedra with common edge form Na₂O₁₀ dimeric units in C . Such double octahedra are connected via common corners forming zigzag chains in B .     

Modeling of self-organization of silicate systems: Precursor nanoclusters and self-assembly of Na<Subscript>3</Subscript>MSi<Subscript>3</Subscript>O<Subscript>9</Subscript> (M = Y,Eu-Lu; oP256) crystal structures producing two interpenetrating diamond-type frameworks

In the M-T-O model system (M is a polyvalent metal with CN ≥ 4; T is Si), cyclic clusters have been deduced as graphs in the T/M range from one to three. The case is considered when monocyclic cluster M₂T₂ is modified by T-tetrahedra that form diortho groups T₂. The M sites of the cluster have either topologically different local MT structures (four types) or identical local MT structures (two types). The cluster types for T/M = 3 obtained by modeling were used in analysis of one of the most complicated types of silicate crystal structures Na₃MSi₃O₉ (M = Y; Eu-Lu; T/M = 3) with the Pearson index oP256 and 64 independent atoms. The TOPOS program package was used to carry out the complete 3D reconstruction of the self-assembly of the crystal structure: suprapolyhedral precursor nanocluster → primary chain → microlayer → microframework (supraprecursor) → ... three-dimensional framework. The calculation of the coordination sequences of site atoms in the 3D network of the MT framework MT₃O₉ revealed topological symmetry related to a three-dimensional separation of the framework into two interpenetrating frameworks. Each framework structure is generated by topologically equivalent cyclic precursor clusters Na₂M₂T₆ consisting of two YO₆ octahedra comprising three diortho groups Si₂O₇ and two Na atoms located above and below the ring center. The 3D graphs characterizing the connectivity of the centers of crystallographically equivalent clusters in the frameworks correspond to diamond-type networks.     

Modeling of self-organization in crystal-forming MT systems: The structural mechanism of self-assembly from suprapolyhedral clusters for framework titanophosphates NaTiPO<Subscript>5</Subscript> (SYN), NaTiPO<Subscript>5</Subscript> (TIT), and KTiPO<Subscript>5</Subscript> (KTP)

Ring precursor clusters are derived for the MT-system containing two different polyhedra T and M, where T stands for a TO₄ tetrahedron and M is in the general case an MO_n polyhedron with the number of vertices n ≥ 5, i.e., a pyramid, octahedron, or others. The topological representation of the precursor cluster is given in the form of two-colored graphs. The model developed for describing the formation and evolution of clusters that form periodic structures is used to search for the precursor clusters of framework phosphate structures: NaTiPO₅ (SYN), NaTiPO₅ (TIT), and KTiPO₅ (KTP). Computer methods are used to perform the full 3D reconstruction of the self-assembly of phosphate crystal structures: precursor cluster—primary chain—micro-layer—microframework (supraprecursor). New eight-polyhedral ring precursor clusters are identified. The crystal-forming polynodal 2D nets with a hierarchic superstructure are recognized: M8833+T883 for SYN (NaTiPO₅), M84634+T843+M836+T864 for TIT (NaTiPO₅), M8939+2M8339+M839+3T893+T89 for KTP (KTiPO₅), and M8484+M88+2T848 for PNAT (Na₂TiSiO₅). The coordination numbers of the clusters in all 2D nets are four.     

Cluster self-organization of Na-TR-Ge-O-H (TR = La-Lu, Y, and Sc) germanate systems: Suprapolyhedral precursor clusters and self-assembly of Na2Pr6Ge8O26, Na4Sc2Ge4O13, and Na5ScGe4O12 crystal structures

In an M-T-O model system (M is a polyvalent metal; T = Ge or Si), we consider initial stages of formation of cyclic MT clusters and the mechanism of their modification by T tetrahedra. The polyhedron ratio T/M in clusters increases progressively during modeling from one in M₂T₂ to two (M₂T₂ + 2T = M₂T₄), three (M₂T₂ + 2T₂ = M₂T₆), and four (M₂T₂ + 2T + 2T₂ = M₂T₈). These types of clusters were used to find precursor clusters for T-condensed structures of Na₂Pr₆Ge₈O₂₆, Na₄Sc₂Ge₄O₁₃, and Na₅ScGe₄O₁₂. The TOPOS program package was used to carry out the complete 3D reconstruction of the self-assembly of Na,TR germanates: precursor cluster → primary chain → microlayer → microframework (supraprecursor) → ... framework. In all structures, as previously in six orthotetrahedral Na,TR germanate structures, the basic invariant type of four-polyhedral cyclic precursor cluster M₂T₂ was identified; this cluster is built of TR polyhedra, with CN = 6 or 7, linked via orthotetrahedra. The features of the generation of a Ge radical were considered in the form of a Ge₂O₇ chain and a Ge₄O₁₂ ring in various layers of the Na₂Pr₆Ge₈O₂₆ composite structure, a Ge₄O₁₃ chain in Na₄Sc₂Ge₄O₁₃, and a Ge₁₂O₃₆ ring in the Na₅ScGe₄O₁₂ superionic conductor. Original Russian Text ? G.D. Ilyushin, L.N. Dem’yanets, 2009, published in Zhurnal Neorganicheskoi Khimii, 2009, Vol. 54, No. 3, pp. 484–496.     

Crystal structures of sodium magnesium selenate decahydrate,Na2Mg(SeO4)2·10H2O,a new selenate salt,and sodium magnesium selenate dihydrate,Na2Mg(SeO4)2·2H2O

Metal selenates crystallize in many instances in isomorphic structures of the corresponding sulfates. Sodium magnesium selenate decahydrate, Na₂Mg(SeO₄)₂·10H₂O, and sodium magnesium selenate dihydrate, Na₂Mg(SeO₄)₂·2H₂O, were synthesized by preparing solutions of Na₂SeO₄ and MgSeO₄·6H₂O with different molar ratios. The structures contain different Mg octahedra, i.e. [Mg(H₂O)₆] octahedra in the decahydrate and [MgO₄(H₂O)₂] octahedra in the dihydrate. The sodium polyhedra are also different, i.e. [NaO₂(H₂O)₄] in the decahydrate and [NaO₆(H₂O)] in the dihydrate. The selenate tetrahedra are connected with the chains of Na polyhedra in the two structures. O—H…O hydrogen bonding is observed in both structures between the coordinating water molecules and selenate O atoms.     

The Rb analogue of grimselite,Rb6Na2[(UO2)(CO3)3]2(H2O)

The crystal structure of the Rb analogue of grimselite, rubidium sodium uranyl tricarbonate hydrate, Rb₆Na₂[(UO₂)(CO₃)₃]₂(H₂O), consists of a uranyl hexagonal bipyramid that shares three non‐adjacent equatorial edges with carbonate triangles, resulting in a uranyl tricarbonate cluster of composition [(UO₂)(CO₃)₃)]. These uranyl tricarbonate clusters form layers perpendicular to [001] and are interconnected by NaO₈ polyhedra. The title compound is isostructural with grimselite, with a reduced occupancy of the H₂O site (25% versus 50% in grimselite).     

Na3Al2Nb34O64 und Na (Si,Nb) Nb10O19: Clusterverbindungen mit isolierten Nb6-Oktaedern

Na₃Al₂Nb₃₄O₆₄ and Na (Si, Nb) Nb₁₀O₁₉. Cluster Compounds with Isolated Nb₆-Octahedra Hexagonal ormolu coloured plates of the new compounds Na₃Al₂Nb₃₄O₆₄ ( I ) and Na(Si, Nb)Nb₁₀O₁₉ ( II ) were prepared by heating pellets of NaF, Al₂O₃, NbO₂ and NbO (3:1:8:2) and NaF, NbO₂ and NbO (1:4:2), respectively, at approx. 850°C. I was contained in a sealed gold capsule, II in a silica tube. The Si incorporated in II originates from the container material. Both compounds crystallize in R 3 , I with a = 784.4(1), c = 7065(1) pm, Z = 3 and II with a = 784.1(1), c = 4221.8(5) pm, Z = 6. I and II represent new structure types. They contain the same characteristic structural units, namely discrete Nb₆O₁₂ clusters (d_Nb–Nb = 283 ± 4 pm) and Nb₂O₁₀ units with Nb–Nb dumbells (d_Nb–Nb ≈? 269 pm) in edgesharing coordination octahedra. In addition NbO₆ octahedra containing Nb in the oxidation state + 5 and NaO₁₂ cube-octahedra occur in both compounds besides AlO₄ and SiO₄ tetrahedra in I and II , respectively. The structures can be described in terms of a common closepacking of O and Na atoms together with Nb₆ octahedra.     

Über Na2PrO3 und Na2TbO3

On Na₂PrO₃ and Na₂TbO₃ Using an exchange reaction of Na₂O with Li₈TbO₆ (Na : Tb = 2.1 : 1; au-tube; 750°C, 30 d) yellow-orange colored single crystals of Na₂TbO₃ could be prepared for the first time. Na₂TbO₃ crystallizes monoclinic in C2/c (Z = 8; a = 576.92(6), b = 1001.27(9), c = 1117.91(14) pm, β = 99.98(1)°). According to four-circle data the Li₂SnO₃-type of structure is adopted (PW 1100, MoKα , 1935 I₀ (hkl), R = 4.86%, R_w = 3.63% for all 928 unique reflexions). By a similar exchange reaction of Na₂O with Li₈PrO₆ for the first time single crystals of Na₂PrO₃ could be prepared, too (Na : Pr = 2.2 : 1; au-tube; 700°C; 23 d). The structure determination reveils that there is a variant of the NaCl-type of structure, which ressembles to the Li₂SnO₃-type of structure (PW 1100, MoKα , 2199 I₀ (hkl)), R = 8.88%, R_w = 5.21% for all 947 unique reflexions; C2/c, Z = 8, a = 678.78(5), b = 977.47(7), c = 1080.38(9) pm, β = 108,4(1)°. In contrast to Na₂TbO₃ there are no layers according to NaO(Na_1/3Tb_2/3)O. All octahedral intersticies are occupied systematically with Pr⁴⁺ and Na⁺ : (Na_2/3Pr_1/3)O(Na_2/3Pr_1/3)O.     

A New Sodium Thioborate Fast Ion Conductor: Na3B5S9

We report a new sodium fast-ion conductor, Na₃B₅S₉, that exhibits a high Na ion total conductivity of 0.80 mS cm⁻¹ (sintered pellet; cold-pressed pellet=0.21 mS cm⁻¹). The structure consists of corner-sharing B₁₀S₂₀ supertetrahedral clusters, which create a framework that supports 3D Na ion diffusion channels. The Na ions are well-distributed in the channels and form a disordered sublattice spanning five Na crystallographic sites. The combination of structural elucidation via single crystal X-ray diffraction and powder synchrotron X-ray diffraction at variable temperatures, solid-state nuclear magnetic resonance spectra and ab initio molecular dynamics simulations reveal high Na-ion mobility (predicted conductivity: 0.96 mS cm⁻¹) and the nature of the 3D diffusion pathways. Notably, the Na ion sublattice orders at low temperatures, resulting in isolated Na polyhedra and thus much lower ionic conductivity. This highlights the importance of a disordered Na ion sublattice—and existence of well-connected Na ion migration pathways formed via face-sharing polyhedra—in dictating Na ion diffusion.     

Syntheses and Crystal Structures of Two Sodium Ruthenates: Na2RuO4 and Na2RuO3

Na₂RuO₄, prepared from Na₂O₂ and RuO₂ via high oxygen pressure synthesis, crystallises monoclinic in space group P2₁/c (a = 10.721(6), b = 7.033(4), c = 10.871(6) Å, β = 119.10(4)°, Z = 8, 2503 unique reflections, R₁ = 0.049). Structure determination from single crystal data shows that the compound consists of infinite chains of RuO₅ trigonal bipyramids connected through their axial vertices. The Na cations connect the pseudohexagonally packed equation/tex2gif-stack-1.gif[RuO₃O_2/2] chains and are coordinated by six or seven oxygen atoms, respectively. The compound exhibits an one‐dimensional spin system with μ = 2.80 μ_B and Θ = —222 K and a three‐dimensional antiferromagnetic ordering below 50 K. Na₂RuO₃ was obtained from Na₂RuO₄ at 850 °C under a flow of argon. The structure was determined from X‐ray powder diffraction. It is closely related to the α‐NaFeO₂ and the Li₂SnO₃ structure types, layered variants of the NaCl type. In Na₂RuO₃ the Na and Ru atoms are partially disordered. This partially disordered state was approximated by a Rietveld refinement of two superimposed structural models (model I: R 3¯ m, a = 3.12360(5), c = 16.0370(4) Å, Z = 2; model II: C2/c, a = 5.4141(4), b = 9.3663(6), c = 10.8481(4) Å, β = 99.636(9)°, Z = 8).     

First Mixed Alkaline Uranyl Molybdates: Synthesis and Crystal Structures of CsNa3[(UO2)4O4(Mo2O8)] and Cs2Na8[(UO2)8O8(Mo5O20)]

Two new mixed alkaline uranyl molybdates CsNa₃[(UO₂)₄O₄Mo₂O₈] ( 1 ) and Cs₂Na₈[(UO₂)₈O₈(Mo₅O₂₀)] ( 2 ) have been obtained by high‐temperature solid state reactions. Their crystal structures have been solved by direct methods: Compound 1 : triclinic, P , a = 6.46(1), b = 6.90(1), c = 11.381(2) Å, α = 84.3(1), β = 91.91(1), γ = 80.23(1)°, V = 488.6(2) ų, R₁ = 0.06 for 2865 unique reflections with |F_o| ≥ 4σ_F; Compound 2 : orthorhombic, Ibam, a = 6.8460(2), b = 23.3855(7), c = 12.3373(3) Å, V = 1975.2(1) ų, R₁ = 0.049 for 2120 unique reflections with |F_o| ≥ 4σ_F. The structure of 1 contains complex sheets of UrO₅ pentagonal bipyramids and molybdenum polyhedra. The sheets have [(UO₂)₂O₂(MoO₅)] composition. Natrium and cesium atoms are located in the interlayer space. Cesium atoms are situated between the molybdenum clusters, whereas natrium atoms are segregated between the uranyl complexes. The large Cs⁺ ions are localized between the Mo₂O₉ groups and force the molybdenum polyhedra to rotate relative to the [(UO₂)₂O₂(MoO₅)] sheets. Such rotation is impossible for U⁶⁺ polyhedra due to their rigid edge‐sharing complexes. The distance between the U⁶⁺ polyhedra vertices of neighboring layers is 3.8 Å, that allows the Na⁺ ion to be positioned between the uranyl groups. The crystal structure of 2 is based upon a framework consisting of [(UO₂)₂O₂(MoO₅)] sheets parallel to (010). The sheets are linked into a 3‐D framework by sharing vertices with the Mo(2)O₄ tetrahedra, located between the sheets. Each MoO₄ tetrahedron shares two of its corners with two MoO₆ octahedra in the sheet above, and the other two with MoO₆ octahedra of the sheet below. Thus four MoO₆ octahedra and one MoO₄ tetrahedron form chains of composition Mo₅O₁₈. The resulting framework has a system of channels occupied by the Cs⁺ and Na⁺ ions.     

Cluster self-organization of germanate systems: Suprapolyhedral precursor nanoclusters and self-assembly of CAN-Na8(Al6Ge6O24)Ge(OH)6(H2O)2 and CAN-Cs2Na6(Al6Ge6O24)Ge(OH)6) zeolite crystal structures re]20100419

Geometrical and topological analysis of zeolite crystal structures having a tetrahedral framework of the cancrinite (CAN) type, namely, (CAN) Na₈(Al₆Ge₆O₂₄)Ge(OH)₆(H₂O)₂ (acentric space group P6₃, hP64, Na-CAN) and Cs₂Na₆(Al₆Ge₆O₂₄)Ge(OH)₆ (P6₃, hP52, CsNa-CAN), is carried out with the use of computer techniques (the TOPOS 4.0 program package). An AT ₆ hexapolyhedral precursor nanocluster centered with a template cation A (Na, Cs) is identified. The topological type of a two-dimensional (2D) crystalforming T-net 4.6.12, which corresponds to a uninodal semiregular Shubnikov net, is recognized. The full 3D reconstruction of crystal structure self-assembly is performed as follows: precursor nanocluster → primary chain → microlayer → microframework → … framework. The symmetry of an AT6 precursor nanocluster is described by point group 3; the symmetry axis passes through the center of the nanocluster and cation A. The coordination number (CN) of a precursor nanocluster, which characterizes the nanocluster stacking in the macrostructure, is six. In both structures, six Na atoms and a Ge(OH)₆ polyhedral species are spacers filling the voids between AT ₆ precursor nanoclusters. The Ge(OH)₆ polyhedral species is characterized by four and two orientationally allowed positions in Na-CAN and CsNa-CAN, respectively. The minimal number of suprapolyhedral AT ₆ precursor nanoclusters required for the 3D microframework to form is 16; that is, 96 tetrahedra are involved in microframework self-assembly.     

Synthetic aenigmatite analog Na2(Mn5.26Na0.74)Ge6O20: structure and crystal chemical considerations

Disodium hexamanganese(II,III) germanate is the first aenigmatite‐type compound with significant amounts of manganese. Na₂(Mn_5.26Na_0.74)Ge₆O₂₀ is triclinic and contains two different Na positions, six Ge positions and 20 O positions (all with site symmetry 1 on general position 2i of space group P). Five out of the seven M positions are also on general position 2i, while the remaining two have site symmetry (Wyckoff positions 1f and 1c). The structure can be described in terms of two different layers, A and B, stacked along the [011] direction. Layer A contains pyroxene‐like chains and isolated octahedra, while layer B is built up by slabs of edge‐sharing octahedra connected to one another by bands of Na polyhedra. The GeO₄ tetrahedra show slight polyhedral distortion and are among the most regular found so far in germanate compounds. The M sites of layer A are occupied by highly charged (trivalent) cations, while in layer B a central pyroxene‐like zigzag chain can be identified, which contains divalent (or low‐charged) cations. This applies to the aenigmatite‐type compounds in general and to the title compound in particular.     

Cluster self-organization of Li-and TR-containing germanate systems: Suprapolyhedral precursors and self-assembly of LiScGeO4 and LiHo3(GeO4)2F2 crystal structures

The combinatorial and topologic analysis (the TOPOS 4.0 program package, the coordination sequences method) is carried out for the crystal structures of the orthogermanates Li^[6]Sc^[6]Ge^[4]O₄ (the olivine type, space group Pnuma) and Li^[6]Ho^[8]Ho ₂ ^[7] (GeO₄)₂F₂ (space group I2/c). The same type of 2D TR,Ge-net with the Schläfli index of 3⁴4² + 3²4² and the site ratio of TR: Ge = 1: 1 is discovered for both structures. Four-polyhedral ring precursor clusters (TR)₂T₂ are identified using the two-color decomposition of structural graphs. All the clusters have a symmetry center; they differ in the types of TR polyhedra (ScO₆ and HoO₆F), which are linked through GeO₄ orthotetrahedra into a ring. The Li atoms reside above and under the centers of the clusters. The Li₂(TR)₂T₂ clusters determine the formation of crystal-forming clusters of a higher level by means of matrix self-assembly. The coordination number of the precursor clusters in the 2D net is six, which is the highest possible value.     

Die kubischen Phasen Na16(ARb6)Sb7, Verbindungen mit den Anionen A = Rb−, Na−, Au−, I−

The Cubic Phases Na₁₆(ARb₆)Sb₇, Compounds with the Anions A = Rb^?, Na^?, Au^?, I^? The novel compounds Na₁₆(ARb₆)Sb₇ have been synthesized from the elements in sealed Nb ampoules at 873 K (A = Rb) and 823 K (A = I, Na, Au). They form brittle cuboctahedra (silver metallic; A = Rb) and irregular polyhedra (silver metallic lustre; A = Na, I; golden metallic lustre; A = Au). They rapidly decompose in moist air to gray products. Their crystal structures have been determined by single crystal X-ray crystallography (A = Rb: a = 1565.8(2) pm; A = I: a = 1563.3(2) pm; A = Na: a = 1562.6(2) pm; A = Au: a = 1560.7(2) pm). They crystallize cubically in the space group Fm3 m (no. 225) with Z = 4 formula units and are isotypic with Sc₁₁Ir₄. The compounds are ZINTL phases and their structures can be described as an eightfold defect variant of the Li₃Bi type of structure (cF128-8; a = 2a′(Li₃Bi)). The Sb atoms form a network of cuboctahedra, centered alternatingly by a SbNa₈ cube or a ARb₆ octahedron. Main structural features are the anions A^? within the Rb₆ octahedron. Supporting the existence of A^? are the isotypical compounds with the more common anion forming elements (A = Au, I), as well as electrostatic potential considerations together with calculations of the volume increments. The semiconducting properties (E_g = 0.33 eV) of Na₁₆(RbRb₆)Sb₇, as well as the diamagnetism χ_mol = ?508 × 10^?6 cm³ mol^?1, are in accordance with those to be expected from the Zintl concept.