Extraction of domain structure information from small-angle scattering patterns of bulk materials

2001 ◽  
Vol 34 (4) ◽  
pp. 496-503 ◽  
Author(s):  
Norbert Stribeck
Keyword(s):  
Domain Structure ◽  
Small Angle ◽  
Real Space ◽  
Small Angle Scattering ◽  
Short Exposure ◽  
Raw Data ◽  
Short Exposure Time ◽  
Structure Information ◽  
Spatial Frequencies ◽  
Angle Scattering

A method is presented that permits the extraction and visualization of topological domain structure information contained in small-angle scattering (SAS) patterns without complex pretreatment. Multi-dimensional noisy raw data can be processed. Such data are, for instance, accumulated in the field of materials research from short-exposure-timein situsmall-angle X-ray scattering (SAXS) experiments with synchrotron radiation. The result is a multi-dimensional intersect or chord distribution, which is defined as the Laplacian of the correlation function. Moreover, it is equivalent to the autocorrelation of the gradient of the electron density. The procedure is, in particular, adapted to the analysis of the nanoscale structure of samples with fibre symmetry, such as polymer fibres or strained elastomers. Multi-dimensional relations among morphological components become apparent in real space and help to elucidate the nature of the processes governing formation and change of structure on the nanometre scale. Utilizing digital signal processing tools, the algorithm is based on spatial frequency filtering of the raw data. The background to be subtracted from the small-angle scattering pattern is formed from its own low spatial frequencies. Noise may be removed by suppressing high spatial frequencies. In the frequency band between these low and high spatial frequencies, the domain structure information of the studied nanocomposite appears.

SLADS: a parallel code for direct simulations of scattering of large anisotropic dense nanoparticle systems

2017 ◽  
Vol 50 (3) ◽  
pp. 951-958 ◽  
Author(s):  
Sen Chen ◽  
Juncheng E ◽  
Sheng-Nian Luo
Keyword(s):  
Analytical Solutions ◽  
Small Angle ◽  
Real Space ◽  
Small Angle Scattering ◽  
Two Dimensional ◽  
X Ray ◽  
X Ray Scattering ◽  
Angle Scattering ◽  
Parallel Code ◽  
Diffraction Patterns

SLADS(http://www.pims.ac.cn/Resources.html), a parallel code for direct simulations of X-ray scattering of large anisotropic dense nanoparticle systems of arbitrary species and atomic configurations, is presented. Particles can be of arbitrary shapes and dispersities, and interactions between particles are considered. Parallelization is achieved in real space for the sake of memory limitation. The system sizes attempted are up to one billion atoms, and particle concentrations in dense systems up to 0.36. Anisotropy is explored in terms of superlattices. One- and two-dimensional small-angle scattering or diffraction patterns are obtained.SLADSis validated self-consistently or against cases with analytical solutions.

Real space functions from experimental small angle scattering data

2011 ◽  
Vol 13 (13) ◽  
pp. 5872 ◽  
Author(s):  
Gerhard Fritz-Popovski ◽  
Alexander Bergmann ◽  
Otto Glatter
Keyword(s):  
Small Angle ◽  
Real Space ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Angle Scattering

An iterative method to extract the size distribution of non-interacting polydisperse spherical particles from small-angle scattering data

2014 ◽  
Vol 47 (2) ◽  
pp. 712-718 ◽  
Author(s):  
D. Sen ◽  
Avik Das ◽  
S. Mazumder
Keyword(s):  
Iterative Method ◽  
Size Distribution ◽  
Small Angle ◽  
Real Space ◽  
Colloidal Dispersions ◽  
Small Angle Scattering ◽  
Spherical Particles ◽  
Scattering Data ◽  
X Ray Scattering ◽  
Angle Scattering

In this article, an iterative method for estimating the size distribution of non-interacting polydisperse spherical particles from small-angle scattering data is presented. It utilizes the iterative addition of relevant contributions to an instantaneous size distribution, as obtained from the fractional difference between the experimental data and the simulated profile. An inverse relation between scattering vector and real space is assumed. This method does not demand the consideration of any basis function set together with an imposed constraint such as a Lagrange multiplier, nor does it depend on the Titchmarsh transform. It is demonstrated that the method works quite well in extracting several forms of distribution. The robustness of the present method is examined through the successful retrieval of several forms of distribution, namely monomodal, bimodal, trimodal, triangular and bitriangular distributions. Finally, the method has also been employed to extract the particle size distribution from experimental small-angle X-ray scattering data obtained from colloidal dispersions of silica.

Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures

2015 ◽  
Vol 48 (1) ◽  
pp. 44-51 ◽  
Author(s):  
Gerhard Fritz-Popovski
Keyword(s):  
Small Angle ◽  
Fourier Transformation ◽  
Real Space ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Two Dimensional ◽  
Spruce Wood ◽  
Angle Scattering ◽  
Nanostructured Silica ◽  
Internal Architecture

The new two-dimensional indirect Fourier transformation converts small-angle scattering patterns obtained by means of area detectors into two-dimensional real-space functions. These functions contain identical information to the scattering patterns, but many parameters related to the microstructure can be obtained directly from them. The size and shape of the microstructures are mainly reflected in the contours of the real-space functions. Their height can be used to get information on the internal architecture of the microstructures. The principles are demonstrated on nanostructured silica biotemplated by spruce wood.

Two-dimensional indirect Fourier transformation for evaluation of small-angle scattering data of oriented samples

2013 ◽  
Vol 46 (5) ◽  
pp. 1447-1454 ◽  
Author(s):  
Gerhard Fritz-Popovski
Keyword(s):  
Small Angle ◽  
Fourier Transformation ◽  
Real Space ◽  
Small Angle Scattering ◽  
Basis Functions ◽  
Scattering Data ◽  
Normal Wood ◽  
Two Dimensional ◽  
Model Free ◽  
Angle Scattering

An extension of the indirect Fourier transformation method for two-dimensional small-angle scattering patterns is presented. This allows for a model-free investigation of real-space functions of oriented structures. The real-space function is built from two-dimensional basis functions. The Fourier transformed basis functions are approximated to the scattering pattern. The solution to this problem in reciprocal space can be used to compute the corresponding real-space functions. These real-space functions contain information on size, shape, internal structure and orientation of the structures studied. Information on structures that are oriented in different distinct directions can be partly separated. The applicability of the technique is demonstrated on simulated data of oriented cuboids and on two experimental data sets based on the nanostructure of spruce normal wood.

scholarly journals Simultaneous high-resolution scanning Bragg contrast and ptychographic imaging of a single solar cell nanowire

2015 ◽  
Vol 48 (6) ◽  
pp. 1818-1826 ◽  
Author(s):  
Jesper Wallentin ◽  
Robin N. Wilke ◽  
Markus Osterhoff ◽  
Tim Salditt
Keyword(s):  
Solar Cell ◽  
High Resolution ◽  
Single Crystal ◽  
Small Angle ◽  
Indium Tin Oxide ◽  
Real Space ◽  
Small Angle Scattering ◽  
Bragg Diffraction ◽  
X Ray ◽  
Angle Scattering

Simultaneous scanning Bragg contrast and small-angle ptychographic imaging of a single solar cell nanowire are demonstrated, using a nanofocused hard X-ray beam and two detectors. The 2.5 µm-long nanowire consists of a single-crystal InP core of 190 nm diameter, coated with amorphous SiO2and polycrystalline indium tin oxide. The nanowire was selected and aligned in real space using the small-angle scattering of the 140 × 210 nm X-ray beam. The orientation of the nanowire, as observed in small-angle scattering, was used to find the correct rotation for the Bragg condition. After alignment in real space and rotation, high-resolution (50 nm step) raster scans were performed to simultaneously measure the distribution of small-angle scattering and Bragg diffraction in the nanowire. Ptychographic reconstruction of the coherent small-angle scattering was used to achieve sub-beam spatial resolution. The small-angle scattering images, which are sensitive to the shape and the electron density of all parts of the nanowire, showed a homogeneous profile along the nanowire axis except at the thicker head region. In contrast, the scanning Bragg diffraction microscopy, which probes only the single-crystal InP core, revealed bending and crystalline inhomogeneity. Both systematic and non-systematic real-space movement of the nanowire were observed as it was rotated, which would have been difficult to reveal only from the Bragg scattering. These results demonstrate the advantages of simultaneously collecting and analyzing the small-angle scattering in Bragg diffraction experiments.

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