Versatile application of indirect Fourier transformation to structure factor analysis: from X-ray diffraction of molecular liquids to small angle scattering of protein solutions

2011 ◽  
Vol 13 (8) ◽  
pp. 3187 ◽  
Author(s):  
Toshiko Fukasawa ◽  
Takaaki Sato
Keyword(s):  
Factor Analysis ◽  
Small Angle ◽  
Structure Factor ◽  
Fourier Transformation ◽  
Small Angle Scattering ◽  
Protein Solutions ◽  
X Ray Diffraction ◽  
Molecular Liquids ◽  
X Ray ◽  
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.

An X-Ray Small-Angle Scattering Instrument

1967 ◽  
Vol 11 ◽  
pp. 332-338 ◽  
Author(s):  
Donald M. Koffman
Keyword(s):  
Small Angle ◽  
Scintillation Counter ◽  
Small Angle Scattering ◽  
High Angular Resolution ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
Double Crystal ◽  
X Ray ◽  
Angle Scattering ◽  
Diffraction Patterns

AbstractAn X-ray small-angle scattering instrument is described which is used for recording X-ray diffraction patterns or small-angle X-ray scattering curves in an angular region very close to the direct beam. The measurement of X-ray intensity is accomplished with standard geiger or scintillation counter techniques. The instrument is designed for use with a spot-focus or vertical-line X-ray source, In essence, it is a multiple-reflection double-crystal diffractometer, based on a concept developed by Bonse and Hart, employing two grooved perfect germanium crystals arranged in the parallel position. Multiple diffraction from these crystals produces a monochromated X-ray beam which can be several millimeters wide while still exhibiting extremely high angular resolution. As a result, effective sample volumes can be employed with maximum volume-to-thickness ratios. The principal features of the instrument are discussed with emphasis on the advantages of this device over those employing complex slit systems and film-re cording techniques, Data are presented to illustrate the operation, intensity, and resolution of the unit.

Effect of finite spatial coherence length on small-angle scattering

2015 ◽  
Vol 48 (6) ◽  
pp. 1660-1664 ◽  
Author(s):  
Yuya Shinohara ◽  
Yoshiyuki Amemiya
Keyword(s):  
Small Angle ◽  
Coherence Length ◽  
Spatial Coherence ◽  
Small Angle Scattering ◽  
Forward Scattering ◽  
X Ray Diffraction ◽  
X Ray ◽  
X Ray Imaging ◽  
Angle Scattering ◽  
Diffraction Imaging

This study shows that forward scattering at the origin of reciprocal space contributes to the scattering intensity profiles of ultra-small-angle scattering. The forward scattering corresponds to a Fourier transform of the X-ray coherent volume on a sample. This contribution is usually ignored in the study of small-angle scattering, while it is fully considered in the fields of X-ray imaging, such as coherent X-ray diffraction imaging and X-ray ptychography. This effect is explicitly illustrated in the context of small-angle scattering, and the effect of a finite spatial coherence length on small-angle scattering is discussed.

Neutron and X-ray small-angle scattering with Fe-based metallic glasses

1988 ◽  
Vol 97 ◽  
pp. 227-230 ◽  
Author(s):  
P. Lamparter ◽  
S. Steeb ◽  
D.M. Kroeger ◽  
S. Spooner
Keyword(s):  
Metallic Glasses ◽  
Small Angle ◽  
Small Angle Scattering ◽  
X Ray ◽  
Angle Scattering

Dimensions de micelles mixtes de p-alkylbenzènesulfonates par diffusion central des rayons X

1977 ◽  
Vol 10 (1) ◽  
pp. 37-44 ◽  
Author(s):  
C. Cabos ◽  
P. Delord ◽  
J. Rouviere
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Micellar Solutions ◽  
Probable Structure ◽  
X Ray ◽  
Absolute Scale ◽  
Angle Scattering ◽  
Scattering Measurements ◽  
Two Component ◽  
Most Probable Structure

The structure of micellar solutions is determined from X-ray small-angle scattering measurements on an absolute scale. The most probable structure is chosen by comparison with spherical cylindrical and lamellar models. This method is applied to two-component micelles and it is possible to follow the variation of micellar dimensions when the concentration of each component is varying.

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