Synthesis and Characterization of Three Multi‐Shell Metalloid Gold Clusters Au32(R3P)12Cl8

Three multi‐shell metalloid gold clusters of the composition Au₃₂(R₃P)₁₂Cl₈ (R=Et, ⁿPr, ⁿBu) were synthesized in a straightforward fashion by reducing R₃PAuCl with NaBH₄ in ethanol. The Au₃₂ core comprises two shells, with the inner one constituting a tilted icosahedron and the outer one showing a distorted dodecahedral arrangement. The outer shell is completed by eight chloride atoms and twelve R₃P groups. The inner icosahedron shows bond lengths typical for elemental gold while the distances of the gold atoms in the dodecahedral arrangement are in the region of aurophilic interactions. Quantum‐chemical calculations illustrate that the Jahn–Teller effect observed within the cluster core can be attributed to the electronic shell filling. The easily reproducible synthesis, good solubility, and high yields of these clusters render them perfect starting points for further research.     

Picosecond laser for performance of efficient nonlinear spectroscopy from 10 to 21 microm

Laser tunability from 10 to 21 microm is obtained by use of an optical parametric oscillator based on a KTP crystal followed by a difference-frequency stage with a CdSe crystal. An all-solid-state picosecond Nd:YAG oscillator mode locked by a frequency-doubling nonlinear mirror is used for synchronous pumping.     

Electrochemically programmed, spatially selective biofunctionalization of silicon wires

A method for the spatially selective biofunctionalization of silicon micro- and nanostructures is reported, and results are presented for both single-crystal silicon (111) or (100) surfaces. An electroactive monolayer of hydroquinone was formed on the surface of H-terminated silicon working electrodes via an olefin reaction with UV-generated surface radicals. Molecules presenting either cyclopentadiene or a thiol group can be immobilized onto the regions where the hydroquinone has been oxidized. Molecular size and crystal orientation are evaluated as important factors that dictate the electrode stability in aqueous solution under anodic potentials. Monolayers composed of smaller molecules on (111) surfaces exhibit the highest packing density and are more effective in preventing anodic oxidation of the underlying substrate. Voltammetry, X-ray photoelectron spectroscopy, and atomic force and fluorescence microscopy are utilized to interrogate the kinetic rates of biofunctionalization, the extent of surface coverage, monolayer quality, and the spatial selectivity of the process.     

Preparation and characterization of novel inorganic-organic hybrid materials containing rare, mixed-halide anions of bismuth(III)

Three new hybrid inorganic-organic salts containing novel mixed haloanions of bismuth were synthesized by the solvothermal reaction of bismuth iodide with a haloacid, HX (X = Cl or Br), and the alkylamine 4,4'-trimethylenedipiperidine (TMDP). All three compounds were structurally characterized by single-crystal X-ray diffraction. Reaction of TMDP and BiI(3) with HCl yielded two crystalline products: [H(2)TMDP](2)[(Bi(2)I(9))(BiCl(2)I(2))] (1, major yield) and [H(2)TMDP](2)[Bi(2)Cl(10-x)I(x)] (2, x = 3.83, minor yield). Compound 1 crystallizes in the monoclinic space group Cc (a = 22.8586(11) A, b = 15.5878(7) A, c = 17.6793(9) A, beta = 118.7010(10) degrees , Z = 4) and contains the mononuclear mixed-halide anion BiCl(2)I(2)(-) in addition to a face-sharing bioctahedral Bi(2)I(9)(3)(-) anion and two independent H(2)TMDP(2+) cations. The BiCl(2)I(2)(-) anion has a sawhorse geometry (equatorially vacant trigonal bipyramidal geometry) that is not commonly observed in bismuth chemistry. Compound 2 crystallizes in the monoclinic space group P2(1)/c (a = 14.9471(7) A, b = 12.7622(6) A, c = 13.3381(7) A, beta = 116.1030(10) degrees , Z = 2) and contains an edge-sharing bioctahedral mixed-halide anion in which iodide occupies one and chloride occupies two of the five crystallographically independent halide sites. The remaining two sites have mixed-chloride and -iodide occupancy. Reaction of TMDP and BiI(3) with HBr yielded the crystalline product [H(2)TMDP][BiBr(5-x)I(x)] (3, x = 0.99), which contains, in addition to the organic cation, a polymeric, mixed-haloanion of bismuth(III). Compound 3 crystallizes in the chiral, orthorhombic space group P2(1)2(1)2(1) (a = 8.5189(5) A, b = 14.8988(9) A, c = 17.9984(11) A, Z = 4) and consists of an H(2)TMDP(2+) cation in addition to the anion, which is built up of corner-sharing BiX(6) octahedra. Of the five crystallographically independent halide sites in this anion, two are occupied solely by Br and the remaining three have mixed-bromide and -iodide occupancy. Other anion stoichiometries have been observed crystallographically for 3, as the specific stoichiometry is dependent on the relative concentration of the haloacid starting material used.     

The -theory of is undecidable

The three quantifier theory of , the recursively enumerable degrees under Turing reducibility, was proven undecidable by Lempp, Nies and Slaman (1998). The two quantifier theory includes the lattice embedding problem and its decidability is a long-standing open question. A negative solution to this problem seems out of reach of the standard methods of interpretation of theories because the language is relational. We prove the undecidability of a fragment of the theory of that lies between the two and three quantifier theories with but includes function symbols.

Theorem. The two quantifier theory of , the r.e. degrees with Turing reducibility, supremum and infimum (taken to be any total function extending the infimum relation on ) is undecidable.

The same result holds for various lattices of ideals of which are natural extensions of preserving join and infimum when it exits.

     

Classical Yang-Baxter equation and left invariant affine geometry on lie groups

Let G be a Lie group, T*G=Lie(G)*G its cotangent bundle considered as a Lie group, where G acts on Lie(G)* via the coadjoint action. Each solution r of the Classical Yang Baxter Equation on G, corresponds to a connected Lie subgroup H of T*G such that Lie(H) is a Lagrangian graph in Lie(G)Lie(G)* and H carries a left invariant affine structure. If r is invertible, the Poisson Lie tensor given by r on G is polynomial of degree at most 2 and every double Lie group of (G,) is endowed with an affine and a complex structures and J, both left invariant and given by r, such that J=0.Mathematics Subject Classification (2000): 53D17, 53A15, 17B62Acknowledgements. The first author was partially supported by Enterprise Ireland. He wishes to thank the mathematical department of NUI Maynooth for their kind welcome, during his stay.Revised version: 5 April 2004     

On the influence of fatigue on ultrasonic polar scans of fiber reinforced composites

Ultrasonic polar scans have already proved to be well-suited as a practical means of characterizing fiber reinforced composite plates. The method consists of registering the reflected or transmitted sound amplitude as a function of each possible angle of incidence. It is hence an amplitude measurement by which it differs from more common 'time of flight' measurements. Ultrasonic polar scans are actually a fingerprint of a composite laminate. One of the many promising applications of the ultrasonic polar scan is the monitoring of fiber reinforced composites in service. Especially the progress of fatigue damage can be monitored easily and nondestructively. This paper presents numerical simulations of the influence of fatigue on ultrasonic polar scans as well as some experimental results.     

Secondary coordination sphere controlled reversible geometry reorganisations in copper(II) complexes

Reversible geometry reorganisations are demonstrated by cis-3,5-diamino-trans-hydroxycyclohexane (cis,trans-DAHC) copper(ii) fluoride complexes, with the concentration of water in the mother liquor controlling interconversion between blue crystals of 5-coordinate syn-[Cu(DAHC)(2)F](F).2CH(3)OH.H(2)O and red crystals of 4-coordinate anti-[Cu(DAHC)(2)](F)(2).2H(2)O.