Numerical approximation of AR‐XPS spectra for rough surfaces considering the effect of electron shadowing

A computational scheme is presented that takes into account the topography, i.e. the shadowing and hence the local emission angle of the electrons when evaluating AR‐XPS data of macroscopic rough surfaces. The topography of the sample surface is supposed to be recorded by atomic force microscopy and/or optical microscopy. The emitted photoelectrons are simulated based on an extension of the Beer–Lambert law that includes the shadowing, the current local emission angle, and the geometrical instrument setup. The obtained angle‐resolved XPS spectra are optimized in accordance with experimental ones via a self‐consistent minimization algorithm that also allows one to determine the layer thicknesses of the corrugated sample. In order to validate the proposed numerical scheme, the simulation program simulation of electron spectra for surface analysis is used. An additional analysis is then performed considering only experimental data. The numerical scheme gives good agreement in simulation–simulation as well as simulation–experiment comparisons and permits a comprehensible interpretation of the measured data. Copyright © 2014 John Wiley & Sons, Ltd.     

Compressing strongly connected subgroups in social networks: An entropy-based approach

To detect and study cohesive subgroups of actors is a main objective in social network analysis. What are the respective relations inside such groups and what separates them from the outside. Entropy-based analysis of network structures is an up-and-coming approach. It turns out to be a powerful instrument to detect certain forms of cohesive subgroups and to compress them to superactors without loss of information about their embeddedness in the net: Compressing strongly connected subgroups leaves the whole net’s and the (super-)actors’ information theoretical indices unchanged; i.e., such compression is information-invariant. The actual article relates on the reduction of networks with hundreds of actors. All entropy-based calculations are realized in an expert system shell.     

A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.     

trans-[Pt(BCat')Me(PCy3)2]: an experimental case study of reductive elimination processes in Pt-Boryls through associative mechanisms

A stable trans‐(alkyl)(boryl) platinum complex trans‐[Pt(BCat′)Me(PCy₃)₂] (Cat′=Cat‐4‐tBu; Cy=cyclohexyl=C₆H₁₁) was synthesised by salt metathesis reaction of trans‐[Pt(BCat′)Br(PCy₃)₂] with LiMe and was fully characterised. Investigation of the reactivity of the title compound showed complete reductive elimination of Cat′BMe at 80 °C within four weeks. This process may be accelerated by the addition of a variety of alkynes, thereby leading to the formation of the corresponding η²‐alkyne platinum complexes, of which [Pt(η²‐MeCCMe)(PCy₃)₂] was characterised by X‐ray crystallography. Conversion of the trans‐configured title compound to a cis derivative remained unsuccessful due to an instantaneous reductive elimination process during the reaction with chelating phosphines. Treatment of trans‐[Pt(BCat′)Me(PCy₃)₂] with Cat₂B₂ led to the formation of CatBMe and Cat′BMe. In the course of further investigations into this reaction, indications for two indistinguishable reaction mechanisms were found: 1) associative formation of a six‐coordinate platinum centre prior to reductive elimination and 2) σ‐bond metathesis of B? B and C? Pt bonds. Mechanism 1 provides a straightforward explanation for the formation of both methylboranes. Scrambling of diboranes(4) Cat₂B₂ and Cat′₂B₂ in the presence of [Pt(PCy₃)₂], fully reductive elimination of CatBMe or Cat′BMe from trans‐[Pt(BCat′)Me(PCy₃)₂] in the presence of sub‐stoichiometric amounts of Cat₂B₂, and evidence for the reversibility of the oxidative addition of Cat₂B₂ to [Pt(PCy₃)₂] all support mechanism 2, which consists of sequential equilibria reactions. Furthermore, the solid‐state molecular structure of cis‐[Pt(BCat)₂(PCy₃)₂] and cis‐[Pt(BCat′)₂(PCy₃)₂] were investigated. The remarkably short B? B separations in both bis(boryl) complexes suggest that the two boryl ligands in each case are more loosely bound to the Pt^II centre than in related bis(boryl) species.     

Optimization of the collocation inversion method for the linear viscoelastic homogenization

The effective behaviour of linear viscoelastic heterogeneous material can be derived from the correspondence principle and the inversion of the obtained symbolic homogenized behavior. Various numerical methods were proposed to carry out this inversion. The collocation method, widely used, within this framework rests on a discretization of the characteristic spectrum in a sum of discrete lines for which it is necessary to determine the intensities and the positions by the minimization of the difference between the exact temporal function and its approximation. The classical method is based on a priori choice of the lines positions and on the optimization of their intensities. It is shown here that the combined optimization of the positions and the (positive) intensities lead to a minimization problem under constraints. In the simple case of an incompressible isotropic two-phase material, the assessment of the effective relaxation function with a continuum spectra or made up of discrete lines proves that the proposed method improves the predictions of the classical approach.     

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