scholarly journals Using the singular value decomposition to extract 2D correlation functions from scattering patterns

2019 ◽  
Vol 75 (5) ◽  
pp. 766-771 ◽  
Author(s):  
Philipp Bender ◽  
Dominika Zákutná ◽  
Sabrina Disch ◽  
Lourdes Marcano ◽  
Diego Alba Venero ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Small Angle ◽  
Correlation Functions ◽  
Simulated Data ◽  
Colloidal Dispersions ◽  
Singular Value ◽  
Model Free ◽  
X Ray Scattering ◽  
Angle Scattering ◽  
Value Decomposition

The truncated singular value decomposition (TSVD) is applied to extract the underlying 2D correlation functions from small-angle scattering patterns. The approach is tested by transforming the simulated data of ellipsoidal particles and it is shown that also in the case of anisotropic patterns (i.e. aligned ellipsoids) the derived correlation functions correspond to the theoretically predicted profiles. Furthermore, the TSVD is used to analyze the small-angle X-ray scattering patterns of colloidal dispersions of hematite spindles and magnetotactic bacteria in the presence of magnetic fields, to verify that this approach can be applied to extract model-free the scattering profiles of anisotropic scatterers from noisy data.

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.

Singular value decomposition analysis of time-resolved small-angle X-ray scattering during morphological transition in a block copolymer

2003 ◽  
Vol 36 (4) ◽  
pp. 982-985 ◽  
Author(s):  
Shigeru Okamoto ◽  
Shinichi Sakurai
Keyword(s):  
Block Copolymer ◽  
Singular Value Decomposition ◽  
Temperature Jump ◽  
Singular Value ◽  
Morphological Transition ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
Value Decomposition ◽  
Ray Scattering

Time-resolved small-angle X-ray scattering (TR-SAXS) studies of the structural changes in a block copolymer after a temperature jump are reported. The sample used was a polystyrene-block-poly(ethylene-alt-butylene)-block-polystyrene (SEBS) triblock copolymer, which has a number-average molecular weight of 54000 g mol−1and a volume fraction of polystyrene of 0.227. The film specimen was prepared by the solution-cast method using a selective solvent. The as-cast specimen with lamellar microdomains underwent the temperature jump from 363 to 403 K and the morphological transition from lamellae to cylinders was observed as a function of time by the TR-SAXS technique. The singular value decomposition (SVD) analysis was performed on the scattering profiles. This analysis strongly suggested the existence of a third basis component of the X-ray scattering profiles, thus supporting that there is an intermediate state during the transition from lamellae to cylinders.

Simple inversion formula for the small-angle X-ray scattering intensity from polydisperse systems of spheres

2012 ◽  
Vol 45 (3) ◽  
pp. 406-416 ◽  
Author(s):  
Robert Botet ◽  
Bernard Cabane
Keyword(s):  
Size Distribution ◽  
Small Angle ◽  
Inversion Formula ◽  
Colloidal Dispersions ◽  
Inversion Method ◽  
X Ray Scattering ◽  
Angle Scattering ◽  
Porod Law ◽  
Simple Inversion ◽  
Scattering Signal

A practical inversion method to calculate the size distribution of colloidal homogeneous particles from small-angle scattering experiments is presented. It is based on the analysis of the deviations of the scattering signal from the Porod law. The resulting inversion formula provides a reliable way to assess complex size distributions such as power-law, multimodal or very broad distributions. It is particularly suitable for colloidal dispersions that have a substantial fraction of very small particles. These cases correspond to large deviations from the Porod law over a broad range of scattering vector values,q. Shannon's theorem gives a way to obtain the maximum amount of information concerning the size distribution, without requiring an arbitrary extrapolation of the data beyond the availableqrange. It is demonstrated that this protocol yields a calculated distribution of particle sizes that is stable.

Indexing of powder diffraction patterns by iterative use of singular value decomposition

2003 ◽  
Vol 36 (1) ◽  
pp. 86-95 ◽  
Author(s):  
A. A. Coelho
Keyword(s):  
Singular Value Decomposition ◽  
Powder Diffraction ◽  
Present Method ◽  
Linear Equations ◽  
Noisy Data ◽  
Simulated Data ◽  
Singular Value ◽  
Fast Method ◽  
Diffraction Patterns ◽  
Value Decomposition

A fast method for indexing powder diffraction patterns has been developed for large and small lattices of all symmetries. The method is relatively insensitive to impurity peaks and missing highd-spacings: on simulated data, little effect in terms of successful indexing has been observed when one in threed-spacings are randomly removed. Comparison with three of the most popular indexing programs, namelyITO,DICVOL91andTREOR90, has shown that the present method as implemented in the programTOPASis more successful at indexing simulated data. Also significant is that the present method performs well on typically noisy data with large diffractometer zero errors. Critical to its success, the present method uses singular value decomposition in an iterative manner for solving linear equations relatinghklvalues tod-spacings.

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