Evidence for Cluster Orbital Formation in CsSn2X5 Compounds (X=Cl, Br)

The formation of cluster orbitals in CsSn₂Br₅ is discussed and related more generally to tetragonal compounds of the type AB₂X₅ (A=monovalent cation; B=Sn, Pb; X=Cl, Br, I). The crystal structures of CsSn₂Cl₅ and CsSn₂Br₅ have been solved by single-crystal X-ray diffraction. These compounds are isostructural with each other and a range of AB₂X₅ structural analogues. In many AB₂X₅ compounds where B is a subvalent main group metal a tetragonal cell is observed with space group I4/mcm. The structures of CsSn₂Br₅ and CsSn₂Cl₅ are layered with polymeric sheets of [Sn₂X₅]ⁿ⁻_n separated by the Cs⁺ cations. Stereochemical considerations suggest that stabilization of this structural form, rather than the more ionic NH₄Pb₂Cl₅ or NaSn₂Cl₅ structures, is through interaction of the “nonbonding” valence electron pairs on tin with low-lying empty d-orbitals on neighboring X atoms. Electronic structure calculations based on the structural data confirm the likelihood of cluster orbital formation. Crystal data: CsSn₂Cl₅, tetragonal, I4/mcm, a=8.153(1) Å, c=14.882(4) Å, Z=4, R₁=0.0215, wR₂=0.0503 [I>2σ(I)], R₁=0.0393, wR₂=0.0536 (all data); CsSn₂Br₅, tetragonal, I4/mcm, a=8.483(6) Å, c=15.28(2) Å, Z=4, R₁=0.0607, wR₂=0.1411 [(I>2σ(I)], R₁=0.1579, wR₂=0.1677 (all data).     

Thermal Analysis Characterization of a Commercial Thermoplastic/Thermoset Adhesive

DSC, TGA and DMA thermal analysis techniques are used to characterize a complex adhesive blend. The chemical and thermomechanical property development shown to follow a two-stage process. Beneficial synergy between these analysis tools is demonstrated in this study.This revised version was published online in November 2005 with corrections to the Cover Date.     

Comparative performance study of ICP mass spectrometers by means of U “isotopic measurements”

The performance of four commercially available ICPMS instruments of three different types was compared by means of uranium “isotopic measurements”. Examined were two quadrupole sector (different generation, different manufacturer), one single detector double focusing magnetic sector and one multiple collector double focusing magnetic sector instruments. The same samples of the IRMM-072 series were used under routine conditions to measure the ²³³U/²³⁵U and the ²³³U/²³⁸U ratios which, in these samples, vary over almost three orders of magnitude from ～ 1 to ～ 2 · 10^–3. Within expanded (k = 2) uncertainties, good agreement was observed between the certified values and the data internally corrected for mass-discrimination effects. The magnitude of the evaluated uncertainties was different for each type of instrument. With the multiple collector instrument, expanded uncertainties varied from ± 0.04% to± 0.24% for the ²³³U/²³⁵U ratio, and from ± 0.08% to ± 0.27% for the ²³³U/²³⁸U ratio. They were ～ 1 to 5 times larger with the single detector magnetic sector instrument, and ～ 10 to 25 times larger with both quadrupole sector instruments. With the multiple collector instrument, repeatability of the measurements seemed to be limited by the difficulty of correcting properly for instrumental background, whereas with the single detector magnetic sector instrument the counting statistics was the only limitation (on smallest ratios). Apparent mass-discrimination was clearly found to be larger but more reproducible (and hence easier to correct for) in the case of magnetic sector instruments than for both quadrupole sector instruments. If space charge effects were the main source of mass-discrimination for all instruments, these results are in contradiction with the hypothesis of the size of mass-discrimination decreasing with the acceleration voltage. With the single detector magnetic sector instrument in particular (when operated by changing the ion energy only), our results pointed at more than only one major source of mass-discrimination, with variable size depending on the ratios measured.     

Exploiting a powerful science base

Europe is striving to become the world's leading knowledge‐based economy but those in the corridors of power do not recognise the contribution chemistry can make.     

A new 11 point degree 6 cubature formula for the triangle

We present a new cubature formula in the triangle which exactly integrates polynomials up to degree 6, using only 11 points. The formula was computed by starting with a 12 point cubature formula and applying the reduced basis method to drive one of the weights to zero, resulting in an 11 point formula with positive weights and no points outside the triangle. This improves upon the previously best known positive inside formulas, which have 12 or more points. The lower bound on the number of points for a degree 6 cubature formula in the triangle is 10, which to date has only been obtained by allowing some of the points to be outside the triangle. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis of Silsesquioxane Cages from Phenyl-cis-tetrol,1,3-Divinyltetraethoxydisiloxane and Cyclopentyl Resins

The synthesis of T8, T10 and T12 silsesquioxane cages from a range of starting materials: phenyl-cis-tetrol, 1,3-divinyltetraethoxydisiloxane and cyclopentyl T resins by using tetra n-butylammonium fluoride (TBAF) as the catalyst is described in this paper. The reaction yields obtained via the current route are bet-ter compared to those via the literature routes. Some of the cage compounds have been characterized by X-ray crystallography.     

State-dependent Coupling of Quasireversible Nodes

The seminal paper of Jackson began a chain of research on queueing networks with product-form stationary distributions which continues strongly to this day. Hard on the heels of the early results on queueing networks followed a series of papers which discussed the relationship between product-form stationary distributions and the quasireversibility of network nodes. More recently, the definition of quasireversibility and the coupling mechanism between nodes have been extended so that they apply to some of the later product-form queueing networks incorporating negative customers, signals, and batch movements.In parallel with this research, it has been shown that some special queueing networks can have arrival and service parameters which depend upon the network state, rather than just the node state, and still retain a generalised product-form stationary distribution.In this paper we begin by offering an alternative proof of a product-form result of Chao and Miyazawa and then build on this proof by postulating a state-dependent coupling mechanism for a quasireversible network. Our main theorem is that the resultant network has a generalised product form stationary distribution. We conclude the paper with some examples.     

State-Dependent Coupling in General Networks

In this paper we extend a result which holds for the class of networks of quasireversible nodes to a class of networks constructed by coupling Markov chains. We begin with a network in which the transition rates governing the stochastic behaviour of the individual nodes depend only on the state of the node. Assuming that the network has an invariant measure, we construct another network with transition rates at each node depending on the state of the entire network, and obtain its invariant measure.