New Molybdenyl Iodates: Hydrothermal Preparation and Structures of Molecular K2MoO2(IO3)4 and Two-Dimensional β-KMoO3(IO3)

Two new molybdenyl iodates, K₂MoO₂(IO₃)₄ (1) and β-KMoO₃(IO₃) (2), have been prepared from the reactions of MoO₃ with KIO₄ and NH₄Cl at 180°C in aqueous media. The structure of 1 consists of molecular [MoO₂(IO₃)₄]²⁻ anions separated by K⁺ cations. The Mo(VI) centers are ligated by two cis-oxo ligands and four monodentate iodate anions. Both terminal and bridging oxygen atoms of the iodate anions form long ionic contacts with the K⁺ cations. β-KMoO₃(IO₃) (2) displays a two-dimensional layered structure constructed from ²_∞[(MoO₃(IO₃)]¹⁻ anionic sheets separated by K⁺ cations. These sheets are built from one-dimensional chains formed from corner-sharing MoO₆ octahedra that run along the b-axis that are linked together through bridging iodate groups. K⁺ cations separate the layers from one another and form long contacts with oxygen atoms from both the iodate anions and molybdenyl moieties. Crystallographic data: 1, monoclinic, space group C2/c, a=12.8973(9) Å, b=6.0587(4) Å, c=17.694(1) Å, β=102.451(1)°, Z=4, MoKα, λ=0.71073, R(F)=2.64% for 97 parameters with 1584 reflections with I>2σ(I); 2, monoclinic, space group P2₁/n, a=7.4999(6) Å, b=7.4737(6) Å, c=10.5269(8) Å, β=109.023(1)°, Z=4, MoKα, λ=0.71073, R(F)=2.73% for 83 parameters with 1334 reflections with I>2σ(I).     

Mixed-metal uranium(VI) iodates: hydrothermal syntheses,structures, and reactivity of Rb[UO(2)(CrO(4))(IO(3))(H(2)O)], A(2)[UO(2)(CrO(4))(IO(3))(2)] (A = K,Rb, Cs), and K(2)[UO(2)(MoO(4))(IO(3))(2)

The reactions of the molecular transition metal iodates A[CrO(3)(IO(3))] (A = K, Rb, Cs) with UO(3) under mild hydrothermal conditions provide access to four new, one-dimensional, uranyl chromatoiodates, Rb[UO(2)(CrO(4))(IO(3))(H(2)O)] (1) and A(2)[UO(2)(CrO(4))(IO(3))(2)] (A = K (2), Rb (3), Cs (4)). Under basic conditions, MoO(3), UO(3), and KIO(4) can be reacted to form K(2)[UO(2)(MoO(4))(IO(3))(2)] (5), which is isostructural with 2 and 3. The structure of 1 consists of one-dimensional[UO(2)(CrO(4))(IO(3))(H(2)O)](-) ribbons that contain uranyl moieties bound by bridging chromate and iodate anions as well as a terminal water molecule to create [UO(7)] pentagonal bipyramidal environments around the U(VI) centers. These ribbons are separated from one another by Rb(+) cations. When the iodate content is increased in the hydrothermal reactions, the terminal water molecule is replaced by a monodentate iodate anion to yield 2-4. These ribbons can be further modified by replacing tetrahedral chromate anions with MoO(4)(2)(-) anions to yield isostructural, one-dimensional [UO(2)(MoO(4))(IO(3))(2)](2)(-) ribbons. Crystallographic data: 1, triclinic, space group P(-)1, a = 7.3133(5) A, b = 8.0561(6) A, c = 8.4870(6) A, alpha = 88.740(1) degrees, beta = 87.075(1) degrees, gamma = 71.672(1) degrees, Z = 2; 2, monoclinic, space group P2(1)/c, a = 11.1337(5) A, b = 7.2884(4) A, c = 15.5661(7) A, beta = 107.977(1) degrees, Z = 4; 3, monoclinic, space group P2(1)/c, a = 11.3463(6) A, b = 7.3263(4) A, c = 15.9332(8) A, beta = 108.173(1) degrees, Z = 4; 4, monoclinic, space group P2(1)/n, a = 7.3929(5) A, b = 8.1346(6) A, c = 22.126(2) A, beta = 90.647(1) degrees, Z = 4; 5, monoclinic, space group P2(1)/c, a = 11.3717(6) A, b = 7.2903(4) A, c = 15.7122(8) A, beta = 108.167(1) degrees, Z = 4.     

Syntheses, structures, and ion-exchange properties of the three-dimensional framework uranyl gallium phosphates, Cs4[(UO2)2(GaOH)2(PO4)4].H2O and Cs[UO2Ga(PO4)2

The reaction of UO(2)(NO(3))(2).6H(2)O with Cs(2)CO(3) or CsCl, H(3)PO(4), and Ga(2)O(3) under mild hydrothermal conditions results in the formation of Cs(4)[(UO(2))(2)(GaOH)(2)(PO(4))(4)].H(2)O (UGaP-1) or Cs[UO(2)Ga(PO(4))(2)] (UGaP-2). The structure of UGaP-1 was solved from a twinned crystal revealing a three-dimensional framework structure consisting of one-dimensional (1)(infinity)[Ga(OH)(PO(4))(2)](4-) chains composed of corner-sharing GaO(6) octahedra and bridging PO(4) tetrahedra that extend along the c axis. The phosphate anions bind the UO(2)(2+) cations to form UO(7) pentagonal bipyramids. The UO(7) moieties edge-share to create dimers that link the gallium phosphate substructure into a three-dimensional (3)(infinity)[(UO(2))(2)(GaOH)(2)(PO(4))(4)](4-) anionic lattice that has intersecting channels running down the b and c axes. Cs(+) cations and water molecules occupy these channels. The structure of UGaP-2 is also three-dimensional and contains one-dimensional (1)(infinity)[Ga(PO(4))(2)](3-) gallium phosphate chains that extend down the a axis. These chains are formed from fused eight-membered rings of corner-sharing GaO(4) and PO(4) tetrahedra. The chains are in turn linked together into a three-dimensional (3)(infinity)[UO(2)Ga(PO(4))(2)](1-) framework by edge-sharing UO(7) dimers as occurs in UGaP-1. There are channels that run down the a and b axes through the framework. These channels contain the Cs(+) cations. Ion-exchange studies indicate that the Cs(+) cations in UGaP-1 and UGaP-2 can be exchanged for Ca(2+) and Ba(2+). Crystallographic data: UGaP-1, monoclinic, space group P2(1)/c, a = 18.872(1), b = 9.5105(7), c = 14.007(1) A, beta = 109.65(3)(o) , Z = 4 (T = 295 K); UGaP-2, triclinic, space group P, a = 7.7765(6), b = 8.5043(7), c = 8.9115(7) A, alpha = 66.642(1)(o), beta = 70.563(1)(o), gamma = 84.003(2)(o), Z = 2 (T = 193 K).     

Cation-cation interactions between uranyl cations in a polar open-framework uranyl periodate

Novel open-framework alkali metal uranyl periodates, having the formula A[(UO2)3(HIO6)(OH)(O)(H2O)].1.5H2O (A = Li, Na, K, Rb, Cs), have been prepared through mild hydrothermal synthesis. These isostructural compounds contain distorted UO7 pentagonal bipyramids that are linked through a uranyl (UO22+) to uranyl cation-cation interaction. This interaction arises from a single axial uranyl oxygen coordinating at an equatorial site of an adjacent uranyl unit. These uranium oxide polyhedra are further bound by IO6 distorted octahedra creating an open-framework structure whose channels contain the alkali metal cations.     

Syntheses, structures, and vibrational spectroscopy of the two-dimensional iodates Ln(IO3)3 and Ln(IO3)3(H2O) (LnYb, Lu)

The reaction of Lu³⁺ or Yb³⁺ and H₅IO₆ in aqueous media at 180 °C leads to the formation of Yb(IO₃)₃(H₂O) or Lu(IO₃)₃(H₂O), respectively, while the reaction of Yb metal with H₅IO₆ under similar reaction conditions gives rise to the anhydrous iodate, Yb(IO₃)₃. Under supercritical conditions Lu³⁺ reacts with HIO₃ and KIO₄ to yield the isostructural Lu(IO₃)₃. The structures have been determined by single-crystal X-ray diffraction. Crystallographic data are (MoKα, λ=0.71073 Å): Yb(IO₃)₃, monoclinic, space group P2₁/n, a=8.6664(9) Å, b=5.9904(6) Å, c=14.8826(15) Å, β=96.931(2)°, V=766.99(13), Z=4, R(F)=4.23% for 114 parameters with 1880 reflections with I>2σ(I); Lu(IO₃)₃, monoclinic, space group P2₁/n, a=8.6410(9), b=5.9961(6), c=14.8782(16) Å, β=97.028(2)°, V=765.08(14), Z=4, R(F)=2.65% for 119 parameters with 1756 reflections with I>2σ(I); Yb(IO₃)₃(H₂O), monoclinic, space group C2/c, a=27.2476(15), b=5.6296(3), c=12.0157(7) Å, β=98.636(1)°, V=1822.2(2), Z=8, R(F)=1.51% for 128 parameters with 2250 reflections with I>2σ(I); Lu(IO₃)₃(H₂O), monoclinic, space group C2/c, a=27.258(4), b=5.6251(7), c=12.0006(16) Å, β=98.704(2)°, V=1818.8(4), Z=8, R(F)=1.98% for 128 parameters with 2242 reflections with I>2σ(I). The f elements in all of the compounds are found in seven-coordinate environments and bridged with monodentate, bidentate, or tridentate iodate anions. Both Lu(IO₃)₃(H₂O) and Yb(IO₃)₃(H₂O) display distinctively different vibrational profiles from their respective anhydrous analogs. Hence, the Raman profile can be used as a complementary diagnostic tool to discern the different structural motifs of the compounds.     

New one-dimensional uranyl and neptunyl iodates: crystal structures of K3[(UO2)2(IO3)6](IO3)·H2O and K[NpO2(IO3)3]·1.5H2O

The uranyl and neptunyl(VI) iodates, K₃[(UO₂)₂(IO₃)₆](IO₃)·H₂O (1) and K[NpO₂(IO₃)₃]·1.5H₂O (2), have been prepared and crystallized under mild hydrothermal conditions. The structures of 1 and 2 both contain one-dimensional _∞¹[AnO₂(IO₃)₃]¹⁻(An=U,Np) ribbons that consist of approximately linear actinyl(VI) cations bound by iodate anions to yield AnO₇ pentagonal bipyramids. The AnO₇ units are linked by bridging iodate anions to yield chains that are in turn coupled by additional iodate anions to yield ribbons. The edges of the ribbons are terminated by monodentate iodate anions. For 1 and 2, K⁺ cations and water molecules separate the ribbons from one another. In addition, isolated iodate anions are also found between _∞¹[UO₂(IO₃)₃]¹⁻ ribbons in 1. In order to aid in the assignment of oxidation states in neptunyl containing compounds, a bond-valence sum parameter of 2.018 Å for Np(VI) bound exclusively to oxygen has been developed with b=0.37 Å. Crystallographic data (193 K, MoKα, λ=0.71073): 1, triclinic, , a=7.0609(4) Å, b=14.5686(8)  Å, c=14.7047(8)  Å, α=119.547(1)°, β=95.256(1)°, γ=93.206(1)°, Z=2, R(F)=2.49% for 353 parameters with 6414 reflections with I>2σ(I); (203 K, MoKα, λ=0.71073): 2, monoclinic, P2₁/c, a=7.796(4)  Å, b=7.151(3)  Å, c=21.79(1)  Å, β=97.399(7)°, Z=4, R(F)=6.33% for 183 parameters with 2451 reflections with I>2σ(I).     

Excision of uranium oxide chains and ribbons in the novel one-dimensional uranyl iodates K(2)[(UO(2))3(IO(3))(4)O(2)] and Ba[(UO(2)2(IO(3))(2)O(2)](H(2)O)

The alkali metal and alkaline-earth metal uranyl iodates K(2)[(UO(2))(3)(IO(3))(4)O(2)] and Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O) have been prepared from the hydrothermal reactions of KCl or BaCl(2) with UO(3) and I(2)O(5) at 425 and 180 degrees C, respectively. While K(2)[(UO(2))(3)(IO(3))(4)O(2)] can be synthesized under both mild and supercritical conditions, the yield increases from <5% to 73% as the temperature is raised from 180 to 425 degrees C. Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O), however, has only been isolated from reactions performed in the mild temperature regime. Thermal measurements (DSC) indicate that K(2)[(UO(2))(3)(IO(3))(4)O(2)] is more stable than Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O) and that both compounds decompose through thermal disproportionation at 579 and 575 degrees C, respectively. The difference in the thermal behavior of these compounds provides a basis for the divergence of their preparation temperatures. The structure of K(2)[(UO(2))(3)(IO(3))(4)O(2)] is composed of [(UO(2))(3)(IO(3))(4)O(2)](2)(-) chains built from the edge-sharing UO(7) pentagonal bipyramids and UO(6) octahedra. Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O) consists of one-dimensional [(UO(2))(2)(IO(3))(2)O(2)](2)(-) ribbons formed from the edge sharing of distorted UO(7) pentagonal bipyramids. In both compounds the iodate groups occur in both bridging and monodentate binding modes and further serve to terminate the edges of the uranium oxide chains. The K(+) or Ba(2+) cations separate the chains or ribbons in these compounds forming bonds with terminal oxygen atoms from the iodate ligands. Crystallographic data: K(2)[(UO(2))(3)(IO(3))(4)O(2)], triclinic, space group P_1, a = 7.0372(5) A, b = 7.7727(5) A, c = 8.9851(6) A, alpha = 93.386(1) degrees, beta = 105.668(1) degrees, gamma = 91.339(1) degrees, Z = 1; Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O), monoclinic, space group P2(1)/c, a = 8.062(4) A, b = 6.940(3) A, c = 21.67(1), beta= 98.05(1) degrees, Z = 4.     

Hydrothermal synthesis and crystal structure of Cs6[(UO2)4(W5O21)(OH)2(H2O)2]: a new polar uranyl tungstate

The hydrothermal reaction of UO₃, WO₃, and CsIO₄ leads to the formation of Cs₆[(UO₂)₄(W₅O₂₁)(OH)₂(H₂O)₂] and UO₂(IO₃)₂(H₂O). Cs₆[(UO₂)₄(W₅O₂₁)(OH)₂(H₂O)₂] is the first example of a hydrothermally synthesized uranyl tungstate. It's structure has been determined by single-crystal X-ray diffraction. Crystallographic data: tetragonal, space group I4 cm, , , Z=4, MoKα, , R(F)=2.84% for 135 parameters with 2300 reflections with I>2σ(I). The structure is comprised of two-dimensional anionic layers that are separated by Cs⁺ cations. The coordination polyhedra found in the novel layers consist of UO₇ pentagonal bipyramids, WO₆ distorted octahedra, and WO₅ square pyramids. The UO₇ polyhedra are formed from the binding of five equatorial oxygen atoms around a central uranyl, UO₂²⁺, unit. Both bridging and terminal oxo ligands are employed in forming the WO₅ square pyramidal units, while oxo, hydroxo, and aqua ligands are found in the WO₆ distorted octahedra. In the layers, four (UO₂)O₅ polyhedra corner share with equatorial oxygen atoms to form a U₄O₂₄ tetramer entity with a square site in the center; a tungsten atom populates the center of each of these sites to form a U₄WO₂₅ pentamer unit. The pentamer units that result are connected in two dimensions by edge-shared dimers of WO₆ octahedra to form the two-dimensional [(UO₂)₄(W₅O₂₁)(OH)₂(H₂O)₂]^6- layers. The lack of inversion symmetry in Cs₆[(UO₂)₄(W₅O₂₁)(OH)₂(H₂O)₂] can be directly contributed to the WO₅ square pyramids found in the pentamer units. In the structure, all of these polar polyhedra align their terminal oxygens in the same orientation, along the c axis, thus resulting in a polar compound.     

Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.