Pr(BO2)3 und PrCl(BO2)2: Zwei meta‐Borate des Praseodyms im Vergleich

Pr(BO₂)₃ and PrCl(BO₂)₂: Two Praseodymium meta‐Borates in Comparison Single‐crystalline PrCl(BO₂)₂ can be obtained by the reaction of praseodymium, Pr₆O₁₁ and PrCl₃ with a small excess of B₂O₃ in evacuated silica tubes after seven days at 850 °C. If NaCl is additionally used as flux, single crystals of Pr(BO₂)₃ dominate the main product. Both praseodymium(III) meta‐borates are air and water stable. The crystals of PrCl(BO₂)₂ emerge as long, thin, pale green needles which tend to severe twinning due to their fibrous habit. The crystal structure (triclinic, P1¯; a = 420.56(4), b = 655.42(7), c = 808.34(8) pm, α = 82.361(8), β = 89.173(9), γ = 71.980(7)°, Z = 2) exhibits zigzag chains {[(B1)o^t_1/1O^e_2/2(B2)O^t_1/1O^e_2/2]²⁻} (≡ {[BO₂]⁻}) of corner‐linked [BO₃]³⁻ triangles with syndiotactic orientation of the terminal oxygen atoms which are running parallel to the [100] direction. The Pr³⁺ cations are surrounded by three Cl⁻ and seven O²⁻ anions with the shape of a tetracapped trigonal prism. The green, transparent crystals of Pr(BO₂)₃ (monoclinic, C2/c; a= 984.98(9), b = 809.57(8), c = 641.02(6) pm, β = 126.783(9)°, Z = 4) appear either lath‐shaped or rather spherical. In the crystal structure the B³⁺ cations reside both in trigonal planar as well as in tetrahedral coordination of oxygen atoms. Both types of borate polyhedra ([BO₃]³⁻ and [BO₄]⁵⁻) are linked via corners to form chains of the composition {[(B2)‐O^t_1/1O^e_2/2(B1)O^e_4/2(B2)O^t_1/1O^e_2/2]³⁻} (≡ {[BO₂]⁻}) which run parallel [101]. The coordination sphere of the Pr³⁺ cations consists of ten oxide anions which build up a bicapped square antiprism.     

Sm4S3[Si2O7] und NaSm9S2[SiO4]6: Zwei Sulfidsilicate mit dreiwertigem Samarium

Sm₄S₃[Si₂O₇] and NaSm₉S₂[SiO₄]₆: Two Sulfide Silicates with Trivalent Samarium The sulfide silicates Sm₄S₃[Si₂O₇] and NaSm₉S₂[SiO₄]₆ are obtained as light yellow transparent crystals by the reaction of Sm, Sm₂O₃, S, and SiO₂ with fluxing SmCl₃ or NaCl, respectively, in suitable molar ratios in fused evacuated silica tubes (850 °C, 7 d). Tetragonal crystals of Sm₄S₃[Si₂O₇] (I4₁/amd; Z = 8; a = 1186.4(1); c = 1387.0(2) pm) with ecliptically conformed [Si₂O₇]^6–‐groups of corner sharing [SiO₄]‐tetrahedra are formed. These double tetrahedra as well the sulfide anions (S^2–) coordinate two crystallographically independent metal cations. They provide coordination numbers of 8 + 1 (5 S^2– and 3 + 1 O^2–) for Sm1 and 9 (3 S^2– and 6 O^2–) for Sm2. NaSm₉S₂[SiO₄]₆ crystallizes hexagonally (P6₃/m; Z = 1; a = 975.32(9); c = 676.46(7) pm) in a modified bromapatite‐type structure. The coordination spheres about the two crystallographically different Sm³⁺ cations are built up by oxygen atoms of the orthosilicate units ([SiO₄]^4–) and sulfide anions (S^2–). As a result, Sm1 and Sm2 have coordination numbers of 9 and 8, respectively. Na⁺ and (Sm1)³⁺ occupy the position 4 f in a molar ratio of 1 : 3 whereas the lower coordinated (Sm2)³⁺ occupies the 6 h position.     

Sm3Cl[SiO4]2: Ein chlorarmes Chloridorthosilicat des Samariums

Sm₃Cl[SiO₄]₂: A Chlorine‐poor Chloride Orthosilicate of Samarium Pale yellow, plate‐like single crystals of Sm₃Cl[SiO₄]₂ (orthorhombic, Pnma; a = 701.74(8), b = 1800.8(2), c = 626.63(7) pm; Z = 4) are obtained upon the reaction of SmCl₃, Sm₂O₃ and SiO₂ (”︁Kieselgel”︁”︁) in 1 : 4 : 6 molar ratios, most advantageously in the presence of substantial amounts of NaCl as fluxing agent, after seven days at 850 °C in evacuated silica ampoules. The B‐type crystal structure (isotypic with e. g. Yb₃Cl[SiO₄]₂) contains discrete orthosilicate tetrahedra [SiO₄]^4– which form anionic double layers ({(Sm1)₂[SiO₄]₂}^2–) with (Sm1)³⁺. These are alternatingly sheethed along [010] with cationic monolayers ({(Sm2)Cl}²⁺) consisting of (Sm2)³⁺ and Cl^–. Both crystallographically independent Sm³⁺ cations exhibit coordination numbers of eight (Sm1: 1 Cl + 7 O; Sm2: 2 Cl + 6 O) with respect to the involved electronegative particles.     

On the pollution effect of quasi‐compressibility methods in magneto‐hydrodynamics and reactive flows

The study of the asymptotics of quasi‐compressibility methods is an essential tool to construct and improve numerical schemes in hydrodynamics, like e.g., stabilized finite element methods or time‐splitting projection methods. The goal of this work is to illustrate different asymptotical solution behaviour for equations in magneto‐hydrodynamics and those that describe reactive flows for standard quasi‐compressibility methods that influences the design of numerical algorithms. Copyright © 1999 John Wiley & Sons, Ltd.     

Energy surfaces of rare-earth silicide films on Si(1 1 1)

We report on angle-resolved photoelectron spectroscopy results of thin dysprosium-silicide layers formed on Si(1 1 1), taken with a toroidal analyzer allowing to image the energy surfaces in k_||-space. At monolayer dysprosium coverages, where hexagonal DySi₂ grows with a 1×1 superstructure, electron pockets are observed at the points with highly anisotropic effective masses, and around a hole pocket at the point also an anisotropic dispersion is found. The band filling of these two bands amounts to one, indicating an even number of electrons assigned to the surface unit cell. Similar features are found for multilayer coverages, where hexagonal Dy₃Si₅ layers are formed with a superstructure. Here, the influence of zone folding effects due to the reconstructed layers in the bulk silicide is only weak because of the high surface sensitivity of the experiments.     

Modelling issues of a holistic finite element approach in the virtual engineering design process

In the paper methods for the coupling of different meshed local domains of a product model, which occur in an adaptivity process are compared. The properties of the applied coupling methods are demonstrated on finite element models from structural mechanics to point out the advantages and disadvantages of the methods in a model adaptivity process in the field of automotive engineering. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergent discretizations for the Nernst–Planck–Poisson system

We propose and compare two classes of convergent finite element based approximations of the nonstationary Nernst–Planck–Poisson equations, whose constructions are motivated from energy versus entropy decay properties for the limiting system. Solutions of both schemes converge to weak solutions of the limiting problem for discretization parameters tending to zero. Our main focus is to study qualitative properties for the different approaches at finite discretization scales, like conservation of mass, non-negativity, discrete maximum principle, decay of discrete energies, and entropies to study long-time asymptotics.     

Pathway for the stereocontrolled Z and E production of alpha,alpha-difluorine-substituted phenyl butenoates

An efficient preparation of pure ethyl Z- and E-alpha,alpha-difluoro-4-phenyl-3-butenoate 1a and 1b together with the corresponding acids 2a and 2b is described. The procedures involve stereocontrolled additions of *CF2CO2Et to phenylacetylene or beta-bromostyrene. Compound 1a is easily obtained by addition of *CF2CO2Et to phenylacetylene via a mechanism where the stereochemistry is controlled by an electron-transfer process to produce predominantly the Z vinyl anion. The product 1b is obtained by *CF2CO2Et addition-elimination to Z- or E-beta-bromostyrenes via a mechanism where the stereochemistry is controlled by steric factors in the conformational equilibration of the intermediates.     

A poroplastic model of structural reorganisation in porous media of biomechanical interest

We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of “plastic” distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.     

Ergodic Directions for Billiards in a Strip with Periodically Located Obstacles

We study the size of the set of ergodic directions for the directional billiard flows on the infinite band ${\mathbb{R}\times [0,h]}$ with periodically placed linear barriers of length 0 < λ < h. We prove that the set of ergodic directions is always uncountable. Moreover, if λ/h ∈ (0, 1) is rational, the Hausdorff dimension of the set of ergodic directions is greater than 1/2. In both cases (rational and irrational) we construct explicitly some sets of ergodic directions.