scholarly journals Small-angle scattering and scale-dependent heterogeneity

2016 ◽  
Vol 49 (4) ◽  
pp. 1162-1176 ◽  
Author(s):  
Cedric J. Gommes
Keyword(s):  
Correlation Function ◽  
Data Analysis ◽  
Small Angle ◽  
Average Density ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Material Surface ◽  
Probe Volume ◽  
Angle Scattering ◽  
Local Average

Although small-angle scattering is often discussed qualitatively in terms of material heterogeneity, when it comes to quantitative data analysis this notion becomes somehow hidden behind the concept of correlation function. In the present contribution, a quantitative measure of heterogeneity is defined, it is shown how it can be calculated from scattering data, and its structural significance for the purpose of material characterization is discussed. Conceptually, the procedure consists of using a finite probe volume to define a local average density at any point of the material; the heterogeneity is then quantitatively defined as the fluctuations of the local average density when the probe volume is moved systematically through the sample. Experimentally, it is shown that the so-defined heterogeneity can be estimated by projecting the small-angle scattering intensity onto the form factor of the chosen probe volume. Choosing probe volumes of various sizes and shapes enables one to comprehensively characterize the heterogeneity of a material over all its relevant length scales. General results are derived for asymptotically small and large probes in relation to the material surface area and integral range. It is also shown that the correlation function is equivalent to a heterogeneity calculated with a probe volume consisting of two points only. The interest of scale-dependent heterogeneity for practical data analysis is illustrated with experimental small-angle X-ray scattering patterns measured on a micro- and mesoporous material, on a gel, and on a semi-crystalline polyethylene sample. Using different types of probes to analyse a given scattering pattern enables one to focus on different structural characteristics of the material, which is particularly useful in the case of hierarchical structures.

scholarly journals Small Angle Scattering Data Analysis Assisted by Machine Learning Methods

MRS Advances ◽  
2020 ◽  
Vol 5 (29-30) ◽  
pp. 1577-1584
Author(s):  
Changwoo Do ◽  
Wei-Ren Chen ◽  
Sangkeun Lee
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Small Angle ◽  
Confusion Matrix ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Search Spaces ◽  
Angle Scattering ◽  
Analysis Workflow ◽  
The Right

ABSTRACTSmall angle scattering (SAS) is a widely used technique for characterizing structures of wide ranges of materials. For such wide ranges of applications of SAS, there exist a large number of ways to model the scattering data. While such analysis models are often available from various suites of SAS data analysis software packages, selecting the right model to start with poses a big challenge for beginners to SAS data analysis. Here, we present machine learning (ML) methods that can assist users by suggesting scattering models for data analysis. A series of one-dimensional scattering curves have been generated by using different models to train the algorithms. The performance of the ML method is studied for various types of ML algorithms, resolution of the dataset, and the number of the dataset. The degree of similarities among selected scattering models is presented in terms of the confusion matrix. The scattering model suggestions with prediction scores provide a list of scattering models that are likely to succeed. Therefore, if implemented with extensive libraries of scattering models, this method can speed up the data analysis workflow by reducing search spaces for appropriate scattering models.

Small-angle scattering data analysis for dense polydisperse systems: the FLAC program

2000 ◽  
Vol 133 (1) ◽  
pp. 66-75 ◽  
Author(s):  
Flavio Carsughi ◽  
Achille Giacometti ◽  
Domenico Gazzillo
Keyword(s):  
Data Analysis ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Angle Scattering

scholarly journals ATSAS 2.1 – towards automated and web-supported small-angle scattering data analysis

2007 ◽  
Vol 40 (s1) ◽  
pp. s223-s228 ◽  
Author(s):  
Maxim V. Petoukhov ◽  
Peter V. Konarev ◽  
Alexey G. Kikhney ◽  
Dmitri I. Svergun
Keyword(s):  
Data Analysis ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Angle Scattering

Quantification of the information in small-angle scattering data

2014 ◽  
Vol 47 (6) ◽  
pp. 2000-2010 ◽  
Author(s):  
Martin Cramer Pedersen ◽  
Steen Laugesen Hansen ◽  
Bo Markussen ◽  
Lise Arleth ◽  
Kell Mortensen
Keyword(s):  
Data Analysis ◽  
Neutron Scattering ◽  
Ray Tracing ◽  
Information Content ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
X Ray ◽  
Angle Scattering ◽  
Wide Range

Small-angle X-ray and neutron scattering have become increasingly popular owing to improvements in instrumentation and developments in data analysis, sample handling and sample preparation. For some time, it has been suggested that a more systematic approach to the quantification of the information content in small-angle scattering data would allow for a more optimal experiment planning and a more reliable data analysis. In the present article, it is shown how ray-tracing techniques in combination with a statistically rigorous data analysis provide an appropriate platform for such a systematic quantification of the information content in scattering data. As examples of applications, it is shown how the exposure time at different instrumental settings or contrast situations can be optimally prioritized in an experiment. Also, the gain in information by combining small-angle X-ray and neutron scattering is assessed. While solution small-angle scattering data of proteins and protein–lipid complexes are used as examples in the present case study, the approach is generalizable to a wide range of other samples and experimental techniques. The source code for the algorithms and ray-tracing components developed for this study has been made available on-line.

scholarly journals SASfit: a tool for small-angle scattering data analysis using a library of analytical expressions

2015 ◽  
Vol 48 (5) ◽  
pp. 1587-1598 ◽  
Author(s):  
Ingo Breßler ◽  
Joachim Kohlbrecher ◽  
Andreas F. Thünemann
Keyword(s):  
Data Analysis ◽  
Reference Material ◽  
Small Angle ◽  
Fractal Model ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Parameters ◽  
Angle Scattering ◽  
Confidence Assessment ◽  
Analysis Workflow

SASfitis one of the mature programs for small-angle scattering data analysis and has been available for many years. This article describes the basic data processing and analysis workflow along with recent developments in theSASfitprogram package (version 0.94.6). They include (i) advanced algorithms for reduction of oversampled data sets, (ii) improved confidence assessment in the optimized model parameters and (iii) a flexible plug-in system for custom user-provided models. A scattering function of a mass fractal model of branched polymers in solution is provided as an example for implementing a plug-in. The newSASfitrelease is available for major platforms such as Windows, Linux and MacOS. To facilitate usage, it includes comprehensive indexed documentation as well as a web-based wiki for peer collaboration and online videos demonstrating basic usage. The use ofSASfitis illustrated by interpretation of the small-angle X-ray scattering curves of monomodal gold nanoparticles (NIST reference material 8011) and bimodal silica nanoparticles (EU reference material ERM-FD-102).

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