scholarly journals Simplified tube form factor for analysis of small-angle scattering data from carbon nanotube filled systems

2007 ◽  
Vol 40 (s1) ◽  
pp. s88-s92 ◽  
Author(s):  
Ryan S. Justice ◽  
David H. Wang ◽  
Loon-Seng Tan ◽  
Dale W. Schaefer
Keyword(s):  
Form Factor ◽  
Carbon Nanotube ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Angle Scattering

Small-angle scattering of interacting particles. II. Generalized indirect Fourier transformation under consideration of the effective structure factor for polydisperse systems

1999 ◽  
Vol 32 (2) ◽  
pp. 197-209 ◽  
Author(s):  
B. Weyerich ◽  
J. Brunner-Popela ◽  
O. Glatter
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Structure Factor ◽  
Fourier Transformation ◽  
Hard Spheres ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Free ◽  
Angle Scattering ◽  
The Gift

The indirect Fourier transformation (IFT) is the method of choice for the model-free evaluation of small-angle scattering data. Unfortunately, this technique is only useful for dilute solutions because, for higher concentrations, particle interactions can no longer be neglected. Thus an advanced technique was developed as a generalized version, the so-called generalized indirect Fourier transformation (GIFT). It is based on the simultaneous determination of the form factor, representing the intraparticle contributions, and the structure factor, describing the interparticle contributions. The former can be determined absolutely free from model assumptions, whereas the latter has to be calculated according to an adequate model. In this paper, various models for the structure factor are compared,e.g.the effective structure factor for polydisperse hard spheres, the averaged structure factor, the local monodisperse approximation and the decoupling approximation. Furthermore, the structure factor for polydisperse rod-like particles is presented. As the model-free evaluation of small-angle scattering data is an essential point of the GIFT technique, the use of a structure factor without any influence of the form amplitude is advisable, at least during the first evaluation procedure. Therefore, a series of simulations are performed to check the possibility of the representation of various structure factors (such as the effective structure factor for hard spheres or the structure factor for rod-like particles) by the less exact but much simpler averaged structure factor. In all the observed cases, it was possible to recover the exact form factor with a free determined parameter set for the structure factor. The resulting parameters of the averaged structure factor have to be understood as apparent model parameters and therefore have only limited physical relevance. Thus the GIFT represents a technique for the model independent evaluation of scattering data with a minimum ofa prioriinformation.

scholarly journals Neither Sphere nor Cube - Analyzing the Particle Shape Using Small-Angle Scattering and the Superball Model

2021 ◽  
Author(s):  
Dominique Dresen ◽  
Asmaa Qdemat ◽  
Dominika Zákutná ◽  
Erik Wetterskog ◽  
Emmanuel Kentzinger ◽  
...  
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Particle Shape ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Monodisperse Nanoparticles ◽  
Statistical Relevance ◽  
Angle Scattering ◽  
Microscopy Data ◽  
User Friendly

<div>Accurate characterization of the nanocrystal shape with high statistical relevance is essential for exploiting the strongly shape-dependent properties of cuboidal nanoparticles towards applications. <br></div><div>This work presents the development of a new small-angle scattering form factor based on the superball geometry. The superball quantifies the characteristic rounding of corners and edges of cuboidalnanoparticles with a single parameter. Applied to small-angle scattering data of sufficiently monodisperse nanoparticles, the superball form factor enables differentiation between the effects of extended<br></div>particle size distribution and irregular particle shape. The quantitative application of the superball form factor is validated against microscopy data for a series of monodisperse nanoparticles and implemented into the user-friendly, open source software Sasview.

Structure and order in lamellar phases determined by small-angle scattering

2004 ◽  
Vol 37 (5) ◽  
pp. 703-710 ◽  
Author(s):  
Thomas Frühwirth ◽  
Gerhard Fritz ◽  
Norbert Freiberger ◽  
Otto Glatter
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Structure Factor ◽  
Scattering Length ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
X Rays ◽  
Model Free ◽  
Angle Scattering

Multilamellar phases can be identified and characterized by small-angle scattering of X-rays (SAXS) or neutrons (SANS). Equidistant peaks are the typical signature and their spacing allows the fast determination of the repeat distance,i.e.the mean distance between the midplane of neighbouring bilayers. The scattering function can be described as the product of a structure factor and a form factor. The structure factor is related to the ordering of the bilayers and is responsible for the typical equidistant peaks, but it also contains information about the bilayer flexibility and the number of coherently scattering bilayers. The form factor depends on the thickness and the internal structure (scattering length density distribution) of a single bilayer. The recently developed generalized indirect Fourier transformation (GIFT) method is extended to such systems. This method allows the simultaneous determination of the structure factor and the form factor of the system, including the correction of instrumental broadening effects. A few-parameter model is used for the structure factor, while the determination of the form factor is completely model-free. The method has been tested successfully with simulated scattering data and by application to experimental data sets.

scholarly journals Neither Sphere nor Cube - Analyzing the Particle Shape Using Small-Angle Scattering and the Superball Model

2021 ◽  
Author(s):  
Dominique Dresen ◽  
Asmaa Qdemat ◽  
Dominika Zákutná ◽  
Erik Wetterskog ◽  
Emmanuel Kentzinger ◽  
...  
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Particle Shape ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Monodisperse Nanoparticles ◽  
Statistical Relevance ◽  
Angle Scattering ◽  
Microscopy Data ◽  
User Friendly

<div>Accurate characterization of the nanocrystal shape with high statistical relevance is essential for exploiting the strongly shape-dependent properties of cuboidal nanoparticles towards applications. <br></div><div>This work presents the development of a new small-angle scattering form factor based on the superball geometry. The superball quantifies the characteristic rounding of corners and edges of cuboidalnanoparticles with a single parameter. Applied to small-angle scattering data of sufficiently monodisperse nanoparticles, the superball form factor enables differentiation between the effects of extended<br></div>particle size distribution and irregular particle shape. The quantitative application of the superball form factor is validated against microscopy data for a series of monodisperse nanoparticles and implemented into the user-friendly, open source software Sasview.

scholarly journals 2017 publication guidelines for structural modelling of small-angle scattering data from biomolecules in solution: an update

2017 ◽  
Vol 73 (9) ◽  
pp. 710-728 ◽  
Author(s):  
Jill Trewhella ◽  
Anthony P. Duff ◽  
Dominique Durand ◽  
Frank Gabel ◽  
J. Mitchell Guss ◽  
...  
Keyword(s):  
Small Angle ◽  
Task Force ◽  
Data Bank ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Quality Data ◽  
Angle Scattering ◽  
Publication Guidelines ◽  
Guidelines And Recommendations

In 2012, preliminary guidelines were published addressing sample quality, data acquisition and reduction, presentation of scattering data and validation, and modelling for biomolecular small-angle scattering (SAS) experiments. Biomolecular SAS has since continued to grow and authors have increasingly adopted the preliminary guidelines. In parallel, integrative/hybrid determination of biomolecular structures is a rapidly growing field that is expanding the scope of structural biology. For SAS to contribute maximally to this field, it is essential to ensure open access to the information required for evaluation of the quality of SAS samples and data, as well as the validity of SAS-based structural models. To this end, the preliminary guidelines for data presentation in a publication are reviewed and updated, and the deposition of data and associated models in a public archive is recommended. These guidelines and recommendations have been prepared in consultation with the members of the International Union of Crystallography (IUCr) Small-Angle Scattering and Journals Commissions, the Worldwide Protein Data Bank (wwPDB) Small-Angle Scattering Validation Task Force and additional experts in the field.

A Study of Beryllium-Based Materials and Comparison of Their X-Ray Homogeneities According to Small-Angle Scattering Data

2018 ◽  
Vol 63 (6) ◽  
pp. 874-882 ◽  
Author(s):  
A. A. Semenov ◽  
V. V. Volkov ◽  
A. V. Zabrodin ◽  
V. V. Gorlevskii ◽  
M. S. Sheverdyaev ◽  
...  
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
X Ray ◽  
Angle Scattering

scholarly journals Small-angle scattering data representation in SASCIF and integrative/hybrid methods dictionary

2017 ◽  
Vol 73 (a2) ◽  
pp. C1441-C1441
Author(s):  
Brinda Vallat ◽  
Benjamin Webb ◽  
John Westbrook ◽  
Andrej Sali ◽  
Helen Berman
Keyword(s):  
Small Angle ◽  
Hybrid Methods ◽  
Data Representation ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Angle Scattering

scholarly journals Numerically stable form factor of any polygon and polyhedron

2021 ◽  
Vol 54 (2) ◽  
pp. 580-587
Author(s):  
Joachim Wuttke
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Form Factors ◽  
Small Angle Scattering ◽  
Important Application ◽  
Divergence Theorem ◽  
Series Expansions ◽  
Stable Form ◽  
Application Domain ◽  
Angle Scattering

Coordinate-free expressions for the form factors of arbitrary polygons and polyhedra are derived using the divergence theorem and Stokes's theorem. Apparent singularities, all removable, are discussed in detail. Cancellation near the singularities causes a loss of precision that can be avoided by using series expansions. An important application domain is small-angle scattering by nanocrystals.

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