X-ray induced fluorescence spectrometry at grazing incidence for quantitative surface and layer analysis

Summary Single layers and layer systems on diverse substrates were measured by Total Reflection X-Ray Fluorescence (TXRF) spectrometry. The angular dependence of the fluorescence intensities at grazing incidence allows the elemental composition, density and thickness of the layers to be evaluated using model calculations.     

Theoretical and experimental investigation of the linear optical response of YBa2Cu4O8 The relevance of LDA calculations

We report results of ellipsometric measurements of the dielectric tensor of YBa₂Cu₄O₈ as well as calculations employing density functional theory in the local density approximation (LDA). For the computation of the one-electron eigenvalues and states the linear-muffin-tin-orbital method (LMTO) was used. Measured and calculated results show good agreement. In particular, the calculation predicts different band structures for YBa₂Cu₃O₇ and YBa₂Cu₄O₈ in the vicinity of the Fermi energy which lead to significant differences in the optical spectra. One such difference is a region of small ε₂ in the near infrared which is a fingerprint of the high (relative to the top of the highest fully occupied band) Fermi energy as compared to the situation in YBa₂Cu₃O₇. Our experimental results confirm the theoretical findings.     

Input control in nonnegative matrix equations

In this paper we consider the nonnegative matrix system c_iA+u_iB=c_i+1 where the nonnegative matrix A is allowed to vary, within bounds. The cone control problem is to find a nonnegative matrix B such that if C_i is a nonnegative vector in a specified cone, then there is a nonnegative vector u_i such that c_i+1 is in that cone. We extend this problem to input control by finding a B such that the cone, generated by the rows of B, is as small as possible. Thus, the percent distribution of ∣u_iB∣ through the states of the sustem by u_iB is either constant or varies little.     

Flow and reactive transport in porous media induced by well injection: Similarity solution

The authors study concentration profiles of solutes undergoingequilibrium absorption in the vicinity of a water well. Forthe case of a contamination event, the limit problem of vanishingwell radius, which is of self-similar nature, is analysed indetail. Existence, uniqueness, and qualitative properties ofsolutions of the corresponding ordinary differential equationsare shown. Some numerical examples are also presented.     

Dense Monolayers of Monodisperse Opaque Spheres: Transmission and diffraction in the fraunhofer domain

The transmission and diffraction of radiation through dense monolayers of monodisperse opaque spheres were studied for the Fraunhofer domain. Theoretical considerations, numerical calculations and experiments on ultrasonic transmission and on laser light transmission and diffraction yielded corresponding results. Complementary studies included the cases of sterically non-interacting particles (by numerical simulation) and of small particle size parameters (by ultrasonic extinction). Transmission was found to be, in general, a non-linear function of the monolayer density. Secondary effects on the transmission can be attributed to the effect of the monolayer structure (characterized by the pair correlation function) on the angular distribution of diffracted intensity. The results were found to be in accordance with experimental results on extinction in three-dimensional systems.     

Liquid crystal properties of some substituted pyrazines

A number of biphenyl, terphenyl analogues and ethynes which contain a pyrazine ring have been made and their liquid crystal transition temperatures, together with examples of birefringence measurements, are reported. All the 2,5-disubstituted pyrazine systems are liquid crystalline showing high birefringence values for the biphenyl and terphenyl analogues, whereas the 1,5-disubstituted systems are not liquid crystalline. The pyrazine ethyne systems exhibit very high birefringence values. X-ray diffraction has been used to identify the liquid crystal phases of 2-n-nonyloxy-5-(4'-propylbiphenyl-4-yl)pyrazine.