Incommensurate magnetism in FeAs strips: neutron scattering from CaFe(4)As(3)

Magnetism in the orthorhombic metal CaFe(4)As(3) was examined through neutron diffraction for powder and single crystalline samples. Incommensurate [q(m) ≈ (0.37-0.39) × b*] and predominantly longitudinally (|| b) modulated order develops through a 2nd order phase transition at TN = 89.63(6) K with a 3D Heisenberg-like critical exponent β = 0.365(6). A 1st order transition at T2 = 25.6(9) K is associated with the development of a transverse component, locking q(m) to 0.375(2)b*, and increasing the moments from 2.1(1) to 2.2(3) μ B for Fe2+ and from 1.3(3) to 2.4(4) μB for Fe+. The ab initio Fermi surface is consistent with a nesting instability in cross-linked FeAs strips.     

Monte Carlo simulation code for confocal 3D micro‐beam X‐ray fluorescence analysis of stratified materials

Stratified materials are of great importance for many branches of modern industry, e.g. electronics or optics and for biomedical applications. Examination of chemical composition of individual layers and determination of their thickness helps to get information on their properties and function. A confocal 3D micro X‐ray fluorescence (3D µXRF) spectroscopy is an analytical method giving the possibility to investigate 3D distribution of chemical elements in a sample with spatial resolution in the micrometer regime in a non‐destructive way. Thin foils of Ti, Cu and Au, a bulk sample of Cu and a three‐layered sandwich sample, made of two thin Fe/Ni alloy foils, separated by polypropylene, were used as test samples. A Monte Carlo (MC) simulation code for the determination of elemental concentrations and thickness of individual layers in stratified materials with the use of confocal 3D µXRF spectroscopy was developed. The X‐ray intensity profiles versus the depth below surface, obtained from 3D µXRF experiments, MC simulation and an analytical approach were compared. Correlation coefficients between experimental versus simulated, and experimental versus analytical model X‐ray profiles were calculated. The correlation coefficients were comparable for both methods and exceeded 99%. The experimental X‐ray intensity profiles were deconvoluted with iterative MC simulation and by using analytical expression. The MC method produced slightly more accurate elemental concentrations and thickness of successive layers as compared to the results of the analytical approach. This MC code is a robust tool for simulation of scanning confocal 3D µXRF experiments on stratified materials and for quantitative interpretation of experimental results. Copyright © 2011 John Wiley & Sons, Ltd.     

Hexagonal nanorods of tungsten trioxide: Synthesis, structure, electrochemical properties and activity as supporting material in electrocatalysis

Tungsten trioxide, unhydrated with hexagonal structure (h-WO₃), has been prepared by hydrothermal method at a temperature of 180 °C in acidified sodium tungstate solution. Thus prepared h-WO₃ has been characterized by X-ray diffraction (XRD) method and using electrochemical techniques. The morphology has been examined by scanning and transmission electron microscopies (SEM and TEM) and it is consistent with existence of nanorods of 50-70 nm diameter and up to 5 μm length. Cyclic voltammetric characterization of thin films of h-WO₃ nanorods has revealed reversible redox behaviour with charge-discharge cycling corresponding to the reversible lithium intercalation/deintercalation into the crystal lattice of the h-WO₃ nanorods. In propylene carbonate containing LiClO₄, two successive redox processes of hexagonal WO₃ nanorods are observed at the scan rate of 50 mV/s. Such behaviour shall be attributed to the presence of at least two W atoms of different surroundings in the lattice structure of h-WO₃ nanorods. On the other hand, in aqueous LiClO₄ solution, only one redox process is observed at the scan rate of 10 mV/s. The above observations can be explained in terms of differences in the diffusion of ions inside two types of channel cavities existing in the structure of the h-WO₃ nanorods. Moreover, the material can be applied as active support for the catalytic bi-metallic Pt-Ru nanoparticles during electrooxidation of ethanol in acid medium (0.5 mol dm⁻³ H₂SO₄).     

Scalar Extensions of Triangulated Categories

Given a triangulated category ${{\mathcal T}}$ over a field K and a field extension L/K, we investigate how one can construct a triangulated category ${{\mathcal T}}_L$ over L. Our approach produces the derived category of the base change scheme X _L if ${{\mathcal T}}$ is the bounded derived category of a smooth projective variety over K and the field extension is finite and Galois. We also investigate how the dimension of a triangulated category behaves under scalar extensions.     

Comparison theorems for diffusion processes

We prove comparison theorems for diffusion processes onR ^d. From these theorems we derive lower and upper bounds for the transition probabilities of a diffusion process. In contrast to the known estimates for fundamental solutions of parabolic equations our bounds do not depend on the moduli of continuity of the coefficients of the differential operator.     

The E(4) Πu state in K2 and its perturbations

The E(4) ¹Π_u←X ¹Σ⁺_g band system of the K₂ molecule is investigated by the technique of Doppler-free optical–optical double resonance polarization spectroscopy. The observed vibrational levels v=0 to 9 of the E state are subject to numerous rotational perturbations by the neighboring 4 ³Π_u, 4 ¹Σ⁺_u, and 5 ³Σ⁺_u electronic states. By using deperturbation methods, the potential curves of the 4 ¹Π_u and 4 ³Π_u states are determined as well as some properties of the 4 ¹Σ⁺_u and 5 ³Σ⁺_u state potentials. The results are compared with predictions of ab initio calculations.     

Structure and morphology of the aliphatic polyester poly(δ‐valerolactone) in solution‐grown,chain‐folded lamellar crystals

Poly(δ‐valerolactone) (PVL) crystals in the form of chain‐folded lamellae were prepared by isothermal crystallization from a 2‐methylbutane‐2‐ol solution. Wide‐angle and small‐angle X‐ray diffraction data, obtained from PVL lamellae sedimented to form oriented mats, were supplemented with morphological and structural data from electron microscopy, both imaging and diffraction. The diffraction signals index on an orthorhombic unit cell with the parameters a = 0.747 ± 0.002 nm, b = 0.502 ± 0.002 nm, and c (chain axis) = 0.742 ± 0.002 nm. Similar unit cell parameters were obtained from crystals grown from 1‐octanol and also from drawn melt‐pressed films. The evidence supports a model containing two antiparallel chain segments in the unit cell. The c value of 0.742 nm is appropriate for an all‐trans or onefold helical backbone conformation for the straight stems. Possible slight perturbations at the ester units from the all‐trans backbone conformation are discussed. Computerized modeling was used to optimize the adjacent‐reentry folded structure. The setting angles, with respect to the a axis, are ±58° for the corner and center chains. The lamellae are 7.26 ± 0.05 nm thick, and the chains run orthogonal to the lamellar surface. The chains fold in the diagonal (110) and (11¯0) planes in an alternating fashion. The X‐ray diffraction data suggest that a proportion of adjacent paired antiparallel entities, or hairpin units, are c‐axis‐sheared, and a relationship to the results obtained from drawn films is discussed. A brief comparison is also made with related polymer structures. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2622–2634, 2001     

Distribution of the strength of acid sites in mildly steamed HZSM-5 studied by IR spectroscopy

Steaming resulted in modification of the distribution of acid strength of OH groups. The contribution of less acidic sites increased and new, very strongly acidic hydroxyls characterized by IR band at 3590 cm^-1 appeared.     

The continuous grey pattern problem

A new location problem is formulated and solved. It is the continuous version of the grey pattern problem which is a special case of the Quadratic Assignment Problem. The problem is a minimization of a convex function subject to non-convex constraints and has infinitely many optimal solutions. We propose several mathematical programming formulations that are suitable for a multi-start heuristic algorithm. In addition to solving these formulations by the Solver in Excel and Mathematica, a special Nelder–Mead algorithm is proposed. This special algorithm provided the best results. One suggested modification may improve the performance of the Nelder–Mead algorithm for other optimization problems as well.