Neue Alkalioxoarsenate (V) Zur Kenntnis von Rb2Li[AsO4] und Cs2Li[AsO4]

New Alkalioxoarsenates (V). On Rb₂Li[AsO₄] and Cs₂Li[AsO₄] By heating of well-grounded mixtures of the binary oxides (A₂O, Li₂O₂, and As₂O₃; A : Li : As = 2 : 1 : 1; Ni-tube, 550°C, 21 d; A = Rb, Cs) colourless single crystals of Rb₂Li[AsO₄] and Cs₂Li[AsO₄] were obtained for the first time. These new orthoarsenates(V) crystalize orthorhombic (space group C mc2₁? C, No. 36) with Z = 4. As expected they are isotypic with the according orthovanadates(V) [2] A₂Li[VO₄], A = Rb, Cs. The lattice constants of Rb₂Li[AsO₄]: a = 582.1(4) pm, b = 1171.1(7) pm, c = 792.4(5) pm and Cs₂Li[AsO₄]: a = 596.4(2) pm, b = 1223.4(2) pm, c = 819.7(3) pm were taken from Guinier-Simon powder data. The structure was determined by four-circle-diffractometer data [Siemens AED II, MoKα , 6290 I₀ (hkl), R = 3.5%, R_w = 3.2% to Rb₂Li[AsO₄]; 3518 I₀ (hkl), R = 2.8%, R_w = 2.6% to Cs₂Li[AsO₄]; parameters see text]. The Madelung Part of Lattice Energy, MAPLE, and Effective Coordination Numbers, ECoN, these calculated via Mean Fictive Ionic Radii, MEFIR, as well as charge distribution CHARDI are calculated and discussed.     

Cs4[IrO4], ein neues Iridat mit planarem Anion [IrO4]4−

Cs₄[IrO₄], a New Iridate with Planar Anion [IrO₄]^4? For the first time we obtained black single crystals of Cs₄[IrO₄] by heating intimate mixtures of CsO_0.52 and IrO₂ (molar ratio Cs : Ir = 4.30 : 1.00; “Ag-bomb”, 740°C/86 d). Cs₄[IrO₄] crystallizes monocline, C 2/m, with a = 1031.66(8) pm, b = 671.61(4) pm, c = 660.44(6) pm, b? = 108.118(7)° and Z = 2 in the K₄[IrO₄]-type. The structure has been determined by four-circle-diffractometer data (PW 1100 from Phillips, Ag? Kα , graphite) with 841 I₀(hkl) with I ≥ 3s?(F) (from 947 I₀(hkl) out of 3529 measured reflexes). The Madelung Part of Lattice Energy, MAPLE, Effective Coordination Numbers, ECoN, these via Mean Fictive Ionic Radii, MEFIR, are calculated and discussed.     

Über Oxide mit dem “Butterfly-Motiv”: Rb6[Fe2O5] und K6[Fe2O5]

New Oxides with the “Butterfly-Motive”: Rb₆[Fe₂O₅] and K₆[Fe₂O₅] Rb₆[Fe₂O₅] and K₆[Fe₂O₅] were obtained for the first time by annealing intimate mixtures of “Rb₆CdO₄” with CdO (molar ratio 1 : 1.1) and KO_0.48 with CdO (molar ratio 5.9 : 1) respectively in closed Fe-cylinders. Determination and refinement of the crystalstructure confirms the space group C2/m (four-circle-diffractometer data). Rb₆[Fe₂O₅]: Ag Kα , 720 out of 1220 Io(hkl), R = 9.68%, R_w = 6.09%; a = 718.9pm, b = 1183.1 pm, c = 695.4pm, β = 95.05°, Z = 2; K₆[Fe₂O₅]: MoKα , 1214 Out of 12141_o(hkl), R = 3.20070, R_w = 2.48%, a = 691.21 pm, b = 1142.78pm, c = 665.50pm, β = 93.82°, Z = 2. The binuclear unit [O₂FeOFeO₂]^6? already known to be planar with oxoferrates(II) now was observed to be angular here and closely related to Na₆[Be₂O₅].     

Neue Oxoterbate(IV) mit Lithium Rb2Li14[Tb3O14] und Li6Tb2O7

New Oxoterbates(IV) with Lithium: On Rb₂Li₁₄[Tb₃O₁₄] and Li₆Tb₂O₇ For the first time we prepared Rb₂Li₁₄[Tb₃O₁₄] as yellow single crystals from Li₈TbO₆ and Rb₂O (Tb:Rb = 1:2) [Ag-cylinder, 500°C, 30 d, then Au-tube, 700°C, 27 d]. The structure refinement [652 I₀ (h kl), four circle diffractometer Philips PW 1100, ω-scan, MoKα, R = 4.69%, R_w = 3.24%, absorption considered, Immm with a = 1 283.07(10), b = 790.87(7), c = 736.87(7)pm, Z = 2, d_x = 4.30 g · cm^?3] confirms that it is isotypic with K₂Li₁₄[Pb₃O₁₄]. Furthermore we got for the first time Li₆Tb₂O₇ as a bright yellow compound from Li₂O₂ and “Tb₄O₇*” [(Li:Tb = 3.4:1), Au-ube, 750°C, 13 d (powder), 850°C 22 d (single crystals)] and by thermal decomposition of Rb₂Li₁₄[Tb₃O₁₄] (Au-tube, 850°C, 25 d). Powder and single crystal data [1 327 I₀ (h kl), four circle diffractometer PW 1100, ω-scan, AgKα, R = 9.38%, R_w = 5.23%, absorption not considered, P2₁/a, a = 1 056.30(10), b = 613.50(4), c = 546.56(5) pm, β = 109.668(7)°, Z = 2, d_x = 4.67 g · cm^?3 d_pyc = 4.53 g · cm^?3] reveal a new type of structure that may be deduced by the NaCl-type of structure. The Madelung Part of Lattice Energy, MAPLE, Effective Coordination Numbers, ECoN, these via Mean Fictive Ionic Radii, MEFIR, are calculated and discussed.     

Das erste Diniobat mit ‚isolierten’︁ Anionen: KLi4[NbO5]=K2Li8[Nb2O10]

The First Diniobate with ‘Isolated’ Anions: KLi₄[NbO₅]=K₂Li₈[Nb₂O₁₀] [1] . By heating of well ground mixtures of the binary oxides [K₂O, Li₂O, Nb₂O₅, K:Li:Nb=1.1:4.4:1, Pt-tube, 1100°C, 3d] colourless, triclinic single crystals of KLi₄NbO₅ have been prepared for the first time: space group P1 (Nr. 2) with a=816.9(2) pm, b=592.2(2) pm, c=589.7(2) pm, α=121.00(2)º, β=91.78(2)°, γ=99.23(2)°, Z=2. The crystal structure was solved by four-cycle diffractometer data [Mo-Kα , 1386 from 1386 I_o(hkl), R=3.4%, R_w=2.6%], parameters see text. Characteristic for this structure are “isolated” groups of [Nb₂O₁₀] and the tetrahedral coordination of Li(1), Li(2), and Li(3). Li(4) has a tetragonal-pyramidal coordination. The structural relations are deduced by Schlegel Diagrams. The Madelung Part of Lattice Energy, MAPLE, the Effective Coordination Numbers, ECoN and the charge distribution have been calculated and discussed.     

Neue Oxogallate der Alkalimetalle: Über K6[Ga2O6] und Rb6[Ga2O6], sowie Na3GaO3 und Cs6[Ga2O6]

New Oxogallates of Alkaline Metals: On K₆[Ga₂O₆] and Rb₆[Ga₂O₆] as well as Na₃GaO₃ and Cs₆[Ga₂O₆] Due to powder and single crystal data K₆[Ga₂O₆] a = 7.09₉; b = 11.11₆; c = 6.48₄ Å; ß = 101.6₆° and Rb₆[Ga₂O₆] a = 7.39₃; b = 11.47₅; c = 6.79₈ Å; ß = 103.5° crystallize isotypic with K₆[Fe₂O₆]; space group C2/m-C₃^2h; As well has been prepared the hitherto unknown Na₃GaO₃ a = 11.48, b = 10.82, c = 6.13 Å, space-group Imcm or I2cm Z = 8; and Cs₆[Ga₂O₆] a = 7.2₆, b = 12.1, c = 7.6₈ Å, ß = 105°, Z = 4, space-group P2₁/a.     

Das erste quaternäre Oxostannat mit „Inselstruktur”︁: RbNa3[SnO4]

The First Quaternary Oxostannate with Isolated Anion Structure: RbNa₃[SnO₄] For the first time colourless single crystals of RbNa₃SnO₄ which are isotypic with NaLi₃SiO₄ and NaLi₃GeO₄ [2] have been prepared by heating e.g. a well ground mixture of RbSn and Na₂O₂ [Rb : Na = 1 : 4.0; 750°C; 21 d; Ni-tube]. The crystal structure was solved by four-cycle-diffractometer data [Siemens AED2; 1801 I₀(hkl); space group I4₁/a; Z = 16; a = 1279.57, c = 1510.85 pm; R = 5.7%; R_w = 4.4%]. Mean Fictive Ionic Radii, MEFIR, Effective Coordination Numbers, ECoN, and the Madelung Part of Lattice Energy, MAPLE, are calculated. The isotypism of the compounds mentioned above is compared graphically.     

Necessary conditions for normed convergence of critical multitype Bienaymé-Galton-Watson processes without variance

The condition on the offspring distribution in the critical multitype Bienaymé-Galton-Watson process without variance, which was previously shown to be sufficient for the existence of the analogue of the exponential limit law, is now shown also to be necessary. This completely extends previous one-type work of R. S. Slack.     

Neue Oxoferrate(III). Zur Kenntnis von Na14[Fe6O16]

New Oxoferrates(III). On the Knowledge of Na₁₄[Fe₆O₁₆] Na₁₄Fe₆O₁₆ crystallizes triclinic (P1 ) with a = 11.42₇, b = 8,27₁, c = 5.95₃ Å, α = 109.3, β = 87.7, γ = 111.4°, Z = 1, 2166 independent reflexions, R = 0.051. FeO₄ tetrahedra are connected by common cornes forming ?Zweier-Doppel-Ketten”? Effektive Coordination Numbers, ECoN, and the Madelung Part of Lattive Energy, MAPLE, are calculated and discussed.