Low-contrast Systems Research Articles

Non-destructive determination of functionalized polyelectrolyte placement in layer-by-layer films by IR ellipsometry.

Layer-by-layer (LbL) assembly facilitates controlled coatings on a variety of surfaces with the ability to manipulate the composition through the thickness by selection of the complementary pairs. However, the characterization of these composition profiles tends to be destructive and requires significant compositional differences that can limit their utility. Here, we demonstrate the ability to non-destructively quantify the depth dependence of the allyl content associated with the selective incorporation of poly(sodium acrylate-co-allylacrylamide) (84 : 16 mol : mol) (allyl-PAA) in LbL films based on the assembly of poly(diallyldimethylammonium chloride) (PDAC)/poly(acrylic acid) (PAA) and PDAC/allyl-PAA. Although the atomic composition of the film is not dramatically influenced by the change between PAA and allyl-PAA, the absorption in the IR near 1645 cm-1 by the allyl group provides sufficient optical contrast to distinguish the LbL components with spectroscopic ellipsometry. The use of IR spectroscopic ellipsometry can determine the thickness of layers that contain allyl-PAA and also gradients that develop due to re-arrangements during the LbL process. With multiple films fabricated simultaneously, the location of the gradient between the 1st and 2nd series of multilayers (e.g., first PDAC/PAA bilayers and then PDAC/allyl-PAA bilayers) can be readily assessed. The results from a variety of different multilayer architectures indicate that the gradient is located within the thickness expected for the 1st deposited bilayer stack (PDAC/PAA or PDAC/allyl-PAA). These results are indicative of a dynamic dissolution-deposition process (in- and out- diffusion) during the fabrication of these LbL films. These results provide additional evidence into the mechanisms for exponential growth in LbL assemblies. The ability to quantify a gradient with the low contrast system examined indicates that spectroscopic IR ellipsometry should be able to non-destructively determine compositional gradients for most polymer films where such gradients exist.

Which Resolution can be Achieved in Practice in Neutron Imaging Experiments? – A General View and Application on the Zr - ZrH2 and ZrO2 - ZrN Systems

Current methodical developments improve the spatial resolution of neutron imaging facilities. Objects with dimensions down to several microns should be detectable. However, the minimum object size detectable depends not only on the facility hardware like detector resolution or neutron optics, but also on the attenuation contrast. In this paper the relation between illumination time needed, neutron contrast of the objects and their minimal size detectable is derived and an analysis of the minimal dimension of an object can be detected in neutron radiography and tomography is discussed at two examples: zirconium hydride ZrH2 in Zircaloy-4 as a high contrast system and zirconium nitride ZrN in zirconium oxide ZrO2 as a low contrast system. It is concluded which minimal sizes of the precipitates can be detected in realistic times.

Modelless approach in X-ray reflectivity of multilayer nanoheterostructure Fe/Cr

A new modelless method of determining the element concentration profile of metallic multilayer nanoheterostructures for low-contrast systems is applied to study periodical and aperiodical multilayer Fe/Cr system by X-ray reflectivity. As a special case, we discuss a cluster-layered Fe/Cr film with Kondo-like behavior of the resistance. The method does not require any a priori information on the structure of the multilayer nanostructures, such as position and width of interfaces, as well as, their shape. The method is based on solution of the Fredholm integral equation of the first kind, which relates the reflection coefficient and the concentration profile of the chemical elements of the sample. The ill-posed inverse problem of determination of the element concentration profile is solved by the regularization method. Efficiency of the method is confirmed by model calculations.

Structural characterization of Cr/Gd/Cr and Cr/Gd/Fe/Cr multilayer nanostructures by X-ray reflectometry

It is shown that the new approach to low-contrast systems upon the interpretation of X-ray reflectivity data can be applied to multilayer samples such as Cr/Gd/Fe/Cr/Si. The method is based on solving the Fredholm integral equation of the first kind, which connects the reflectivity with the concentration profiles of elements that enter into the sample composition. The inverse ill-posed problem of the determination of the concentration profile is solved using the regularization method. The efficiency of the method proposed is verified by model calculations fulfilled for a Cr/Gd/Fe/Cr/Si four-layer structure, where there are both high-contrast pairs of layers (Cr/Gd) and pairs with a low contrast (Fe/Cr). Experimental data for Cr/Gd/Cr and Cr/Gd/Fe/Cr multilayer nanoheterostructures have been obtained under laboratory conditions. The thicknesses of all layers of all the elements and of the Cr/Gd, Gd/Fe, and Fe/Cr interfaces have been determined.

Diagnostics of the atomic structure of multilayer metallic nanoheterostructures from reflectometry data: A new approach to low-contrast systems

A new method for determining the concentration profiles of chemical elements in multilayer metallic nanoheterostructures from X-ray reflectometry data has been developed as applied to low-contrast systems. The method is based on the solution of the Fredholm integral equation of the first kind, which relates the reflection coefficient and the concentration profile of the chemical elements involved in the composition of the sample. The ill-posed inverse problem of the determination of the concentration profile is solved by the regularization method. The efficiency of the proposed method is confirmed by model calculations performed for a four-layer Cr/Gd/Fe/Cr//Si structure with high-contrast Cr/Gd pairs and low-contrast Fe/Cr pairs. The experimental results on the determination of the concentration profile of the surface layer of the epitaxial thin Cr films and three-layer Cr/Fe/Cr structure deposited on the Al2O3 substrate are presented.

X-ray tomography using the full complex index of refraction

We report on x-ray tomography using the full complex index of refraction recorded with a grating-based x-ray phase-contrast setup. Combining simultaneous absorption and phase-contrast information, the distribution of the full complex index of refraction is determined and depicted in a bivariate graph. A simple multivariable threshold segmentation can be applied offering higher accuracy than with a single-variable threshold segmentation as well as new possibilities for the partial volume analysis and edge detection. It is particularly beneficial for low-contrast systems. In this paper, this concept is demonstrated by experimental results.

Effective dielectric constant of two phase systems: Application to mixed conducting systems

Theoretical approaches to electrical characterization of two phase systems are mostly limited to the systems where the individual components exhibit the same type of conductivity (pure dielectric or pure conductive systems). In this article, the brick wall geometry is extended to the mixed conductive systems with percolation. Impedance spectroscopy techniques were used for experimental investigation of slurries. Various metal oxide powders and host liquids were analyzed using a wide range of solids loadings. Comparison of experimental results with theoretical predictions shows good fitting of the experimental data. Parameters (the values of permittivity for both phases and percolation threshold) calculated from this fitting match the corresponding values of components of two phase systems. Analysis of both low frequency (less than 10 kHz) as well as high frequency (10 kHz to 1 MHz) responses of impedance spectra allows determining of permittivity of dielectric powders suspended in various liquids. Low frequency response provides better accuracy for systems with high dielectric contrast between components, while high frequency response is more accurate for low contrast systems.

Diffusion on grain boundary networks: Percolation theory and effective medium approximations

Grain boundary networks in polycrystalline materials are heterogeneous and comprise a spectrum of local boundary diffusivities. Although it is desirable to ascribe a single “effective” grain boundary diffusivity to a polycrystal, this quantity is a complex average over the grain boundary character distribution, in view of the network topology and connectivity among boundaries of different character. Here we evaluate the macroscopic diffusivity of grain boundary networks with both randomly distributed and crystallographically correlated grain boundary character. In high-contrast networks, where the local diffusivity varies by more than four orders of magnitude between grain boundaries of different character, the macroscopic diffusivity is governed by the development of a percolating path of high-diffusivity boundaries. In low-contrast systems, the effective network diffusivity is less sensitive to topology and can be described by composite averaging schemes. We quantitatively delineate high- and low-contrast regimes, and discuss a generalized effective medium approximation that quantitatively links the network structure to effective macroscopic transport properties at all levels of contrast. We also illustrate how effective medium theory can be adapted to capture crystallographic correlations among boundary types, and expanded to include a broader spectrum of boundary character.

X‐Ray Galaxy Clusters in NoSOCS: Substructure and the Correlation of Optical and X‐Ray Properties

We present a comparison of optical and X-ray properties of galaxy clusters in the northern sky. We determine the recovery rate of X-ray detected clusters in the optical as a function of richness, redshift and X-ray luminosity, showing that the missed clusters are typically low contrast systems when observed optically. We employ four different statistical tests to test for the presence of substructure using optical two-dimensional data, finding that approximately 35% of the clusters show strong signs of substructure. However, the results are test-dependent, with variations also due to the magnitude range and radius utilized.We have also performed a comparison of X-ray luminosity and temperature with optical galaxy counts (richness). We find that the slope and scatter of the relations between richness and the X-ray properties are heavily dependent on the density contrast of the clusters. The selection of substructure-free systems does not improve the correlation between X-ray luminosity and richness, but this comparison also shows much larger scatter than one obtained using the X-ray temperature. In the latter case, the sample is significantly reduced because temperature measurements are available only for the most massive (and thus high contrast) systems. However, the comparison between temperature and richness is very sensitive to the exclusion of clusters showing signs of substructure. The correlation of X-ray luminosity and richness is based on the largest sample to date ($\sim$ 750 clusters), while tests involving temperature use a similar number of objects as previous works ($\lsim$100). The results presented here are in good agreement with existing literature.