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Measurements in general are limited in accuracy by the presence of noise. This also holds true for highly sophisticated scintillation-based CCD cameras, as they are used in medical applications, astronomy or transmission electron microscopy. Further, signals measured with pixelated detectors are convolved with the inherent detector point spread function. The Poisson noise, arising from the quantized nature of the beam electrons, gets correlated by this convolution, which allows to reconstruct the detector PSF based on the Wiener–Khinchin theorem and the Pearson correlation coefficients under homogeneous illumination conditions. However, correlation also has a strong impact on the noise statistics of basic operations like the binning of signals, as it is usually done in electron energy-loss spectroscopy. Thus, this paper aims to give an insight into the different noise contributions occurring on such detectors, into their underlying statistics and their correlation. Detectors usually suffer from gain non-linearities and quantum efficiency deviations, which must be corrected for optimal results. All these operations influence the noise and are influenced by it, vice versa. In this work, we mathematically describe all these changes and show them experimentally. Methods on how to measure individual noise and correlation parameters are described allowing readers to implement routines for finding them. Sufficient knowledge on the noise of a measurement is not only crucial for classifying its quality and meaningfulness, but also allows for better post-processing operations like deconvolution, which is a common practice in spectroscopy to enhance signals.

A dark-field scanning transmission ion microscopy detector was designed for the helium ion microscope. The detection principle is based on a secondary electron conversion holder with an exchangeable aperture strip allowing its acceptance angle to be tuned from 3 to 98 mrad. The contrast mechanism and performance were investigated using freestanding nanometer-thin carbon membranes. The results demonstrate that the detector can be optimized either for most efficient signal collection or for maximum image contrast. The designed setup allows for the imaging of thin low-density materials that otherwise provide little signal or contrast and for a clear end-point detection in the fabrication of nanopores. In addition, the detector is able to determine the thickness of membranes with sub-nanometer precision by quantitatively evaluating the image signal and comparing the results with Monte Carlo simulations. The thickness determined by the dark-field transmission detector is compared to X-ray photoelectron spectroscopy and energy-filtered transmission electron microscopy measurements.

Dodecyl amine edge functionalized few-layer graphene oxide quantum dots were synthesized in good yields. The covalent functionalization was demonstrated with NMR and AFM-IR. The resulting structure and particle size was measured with AFM and HRTEM. The thermal stability of the compound was investigated and showed a stability of up to 220 °C. The modified graphene oxide quantum dots showed excellent solubility in various organic solvents, including ethers, methanol, toluene, n -hexane, heptane, xylene, dichloromethane and toluene. The stability of a resulting toluene solution was also proven by static light scattering measurements over several days. The excellent solubility gives the possibility of an efficient and fast spray application of the functionalized graphene oxide quantum dots to steel surfaces. Hence, the macroscopic friction behavior was investigated with a Thwing-Albert FP-2250 friction tester. A thin film of the dodecyl amine functionalized graphene oxide quantum dots on steel lowered the friction coefficient from 0.17 to 0.11 and revealed a significant corrosion inhibition effect.

Image restoration via alternating direction method of multipliers (ADMM) has gained large interest within the last decade. Solving standard problems of Gaussian and Poisson noise, the set of “Total Variation” (TV)-based regularizers proved to be efficient and versatile. In the last few years, the “Total Generalized Variation” (TGV) approach combined TV regularizers of different orders adaptively to better suit local regions in the image. This improved the technique significantly. The approach solved the staircase problem inherent of the first-order TV while keeping the beneficial edge preservation. The iterative minimization for the augmented Lagrangian of TGV problems requires four important parameters: two penalty parameters ρ and η and two regularization parameters λ 0 and λ 1 . The choice of penalty parameters decides on the convergence speed, and the regularization parameters decide on the impact of the respective regularizer and are determined by the noise level in the image. For scientific applications of such algorithms, an automated and thus objective method to determine these parameters is essential to receive unbiased results independent of the user. Obviously, both sets of parameters are to be well chosen to achieve optimal results, too. In this paper, a method is proposed to adaptively choose optimal ρ and η values for the iteration to converge faster, based on the primal and dual residuals arising from the optimality conditions of the augmented Lagrangian. Further, we show how to choose λ 0 and λ 1 based on the inherent noise in the image.

Block copolymer (BCP) self-assembly is a promising tool for next generation lithography as microphase separated polymer domains in thin films can act as templates for surface nanopatterning with sub-20 nm features. The replicated patterns can, however, only be as precise as their templates. Thus, the investigation of the morphology of polymer domains is of great importance. Commonly used analytical techniques (neutron scattering, scanning force microscopy) either lack spatial information or nanoscale resolution. Using advanced analytical (scanning) transmission electron microscopy ((S)TEM), we provide real space information on polymer domain morphology and interfaces between polystyrene (PS) and polymethylmethacrylate (PMMA) in cylinder- and lamellae-forming BCPs at highest resolution. This allows us to correlate the internal structure of polymer domains with line edge roughnesses, interface widths and domain sizes. STEM is employed for high-resolution imaging, electron energy loss spectroscopy and energy filtered TEM (EFTEM) spectroscopic imaging for material identification and EFTEM thickness mapping for visualisation of material densities at defects. The volume fraction of non-phase separated polymer species can be analysed by EFTEM. These methods give new insights into the morphology of polymer domains the exact knowledge of which will allow to improve pattern quality for nanolithography.

Colloidal nanosphere monolayers—used as a lithography mask for site-controlled material deposition or removal—offer the possibility of cost-effective patterning of large surface areas. In the present study, an automated analysis of scanning electron microscopy (SEM) images is described, which enables the recognition of the individual nanospheres in densely packed monolayers in order to perform a statistical quantification of the sphere size, mask opening size, and sphere-sphere separation distributions. Search algorithms based on Fourier transformation, cross-correlation, multiple-angle intensity profiling, and sphere edge point detection techniques allow for a sphere detection efficiency of at least 99.8%, even in the case of considerable sphere size variations. While the sphere positions and diameters are determined by fitting circles to the spheres edge points, the openings between sphere triples are detected by intensity thresholding. For the analyzed polystyrene sphere monolayers with sphere sizes between 220 and 600 nm and a diameter spread of around 3% coefficients of variation of 6.8–8.1% for the opening size are found. By correlating the mentioned size distributions, it is shown that, in this case, the dominant contribution to the opening size variation stems from nanometer-scale positional variations of the spheres.

The replacement of noble metal catalysts by abundant iron as an active compound in CO oxidation is of ecologic and economic interest. However, improvement of their catalytic performance to the same level as state-of-the-art noble metal catalysts requires an in depth understanding of their working principle on an atomic level. As a contribution to this aim, a series of iron oxide catalysts with varying Fe loadings from 1 to 20 wt% immobilized on a γ-Al2O3 support is presented here, and a multidimensional structure–activity correlation is established. The CO oxidation activity is correlated to structural details obtained by various spectroscopic, diffraction, and microscopic methods, such as PXRD, PDF analysis, DRUVS, Mössbauer spectroscopy, STEM-EDX, and XAS. Low Fe loadings lead to less agglomerated but high percentual amounts of isolated, tetrahedrally coordinated iron oxide species, while the absolute amount of isolated species reaches its maximum at high Fe loadings. Consequently, the highest CO oxidation activity in terms of turnover frequencies can be correlated to small, finely dispersed iron oxide species with a large amount of tetrahedrally oxygen coordinated iron sites, while the overall amount of isolated iron oxide species correlates with a lower light-off temperature.

The suitability of molecular statics (MS) simulations to model the structure of 90{\\deg} glide set partial dislocation cores in GaAs is analyzed. In the MS simulations the atomic positions are iteratively relaxed by energy minimization, for which a Tersoff potential parametrization appropriate for nanostructures has been used. We show that for the Ga terminated partial the resulting bond lengths of the atoms in the dislocation core agree within 5-10% with those of previous density functional theory studies, whereas a significant discrepancy appears in the case of the As terminated partial.

Most properties of solid materials are defined by their internal electric field and charge density distributions which so far are difficult to measure with high spatial resolution. Especially for 2D materials, the atomic electric fields influence the optoelectronic properties. In this study, the atomic-scale electric field and charge density distribution of WSe\\(_2\\) bi- and trilayers are revealed by using an emerging microscopy technique, differential phase contrast (DPC) imaging in the scanning transmission electron microscope (STEM). For pristine material, a higher positive charge density located at the selenium atomic columns compared to the tungsten atomic columns is obtained and tentatively explained by a coherent scattering effect. Furthermore, the change in the electric field distribution induced by a missing selenium atomic column is investigated. A characteristic electric field distribution in the vicinity of the defect with locally reduced magnitudes compared to the pristine lattice is observed. This effect is accompanied by a considerable inward relaxation of the surrounding lattice, which according to first principles DFT calculation is fully compatible with a missing column of Se atoms. This shows that DPC imaging, as an electric field sensitive technique, provides additional and remarkable information to the otherwise only structural analysis obtained with conventional STEM imaging.

Abstract The DARWIN observatory is a proposed next-generation experiment to search for particle dark matter and for the neutrinoless double beta decay of $$^{136}$$ 136 Xe. Out of its 50 t total natural xenon inventory, 40 t will be the active target of a time projection chamber which thus contains about 3.6 t of $$^{136}$$ 136 Xe. Here, we show that its projected half-life sensitivity is $$2.4\\times {10}^{27}\\,{\\hbox {year}}$$ 2.4×1027year , using a fiducial volume of 5 t of natural xenon and 10 year of operation with a background rate of less than 0.2 events/(t $$\\cdot $$ ·  year) in the energy region of interest. This sensitivity is based on a detailed Monte Carlo simulation study of the background and event topologies in the large, homogeneous target. DARWIN will be comparable in its science reach to dedicated double beta decay experiments using xenon enriched in $$^{136}$$ 136 Xe.