Analysis of Small-Angle Scattering Data from Spherical Particles by both the Indirect Transform Method and the Maximum-Entropy Method

1997 ◽  
Vol 30 (3) ◽  
pp. 353-361 ◽  
Author(s):  
C. S. Tsao ◽  
T. L. Lin
Keyword(s):  
Maximum Entropy ◽  
Small Angle ◽  
Maximum Entropy Method ◽  
Small Angle Scattering ◽  
Entropy Method ◽  
Spherical Particles ◽  
Scattering Data ◽  
Transform Method ◽  
Angle Scattering

The effect of the shape function on small-angle scattering analysis by the maximum-entropy method

1994 ◽  
Vol 27 (5) ◽  
pp. 693-702 ◽  
Author(s):  
P. R. Jemian ◽  
A. J. Allen
Keyword(s):  
Maximum Entropy ◽  
Size Distribution ◽  
Small Angle ◽  
Shape Function ◽  
Small Angle Scattering ◽  
Entropy Method ◽  
Scattering Data ◽  
Shape Functions ◽  
Incident Wavelength ◽  
Angle Scattering

Analysis of small-angle scattering data to obtain a particle-size distribution is dependent upon the shape function used to model the scattering. From a maximum-entropy analysis of small-angle scattering data, the effect of shape-function selection on the obtained size distribution is demonstrated using three different shape functions to describe the same scattering data from each of two alloys. The alloys have been revealed by electron microscopy to contain a distribution of randomly oriented and mainly noninteracting irregular ellipsoidal precipitates. A comparison is made between the different forms of the shape function. The effect of an incident-wavelength distribution is also shown. The importance of testing appropriate shape functions and validating these against other microstructural studies is discussed.

Determination of particle size distributions by small-angle scattering with polarized neutrons using maximum-entropy method

2004 ◽  
Vol 37 (1) ◽  
pp. 40-47 ◽  
Author(s):  
Dragomir Tatchev ◽  
Andre Heinemann ◽  
Albrecht Wiedenmann ◽  
Armin Hoell
Keyword(s):  
Particle Size ◽  
Maximum Entropy ◽  
Small Angle ◽  
Maximum Entropy Method ◽  
Small Angle Scattering ◽  
Entropy Method ◽  
Single Experiment ◽  
Polarized Neutrons ◽  
Angle Scattering ◽  
Particle Form

The extension of the small-angle scattering technique with polarized neutrons invokes the necessity of new tools for data analysis. Up to five scattering curves can be derived from a single experiment. It is shown that for the case of a dilute system of particles in a matrix, the maximum-entropy method can be modified to analyse any combination of these curves in order to find the underlying particle size distribution. An additional step of simplex or simulated-annealing optimization is introduced in order to determine the particle form-factor parameters. Computer simulations demonstrate the functionality of this method.

Estimation and fingerprinting of the size distribution of non-interacting spherical particles from small-angle scattering data

2021 ◽  
Vol 54 (5) ◽  
Author(s):  
Debasis Sen ◽  
Ashwani Kumar ◽  
Avik Das ◽  
Jitendra Bahadur
Keyword(s):  
Size Distribution ◽  
Small Angle ◽  
Colloidal Particles ◽  
Nonlinear Least Squares ◽  
Small Angle Scattering ◽  
Spherical Particles ◽  
Scattering Data ◽  
Fitting Procedure ◽  
Angle Scattering ◽  
Log Normal

A new method to estimate the size distribution of non-interacting colloidal particles from small-angle scattering data is presented. The method demonstrates that the distribution can be efficiently retrieved through features of the scattering data when plotted in the Porod representation, thus avoiding the standard fitting procedure of nonlinear least squares. The present approach is elaborated using log-normal and Weibull distributions. The method can differentiate whether the distribution actually follows the functionality of either of these two distributions, unlike the standard fitting procedure which requires a prior assumption of the functionality of the distribution. After validation with various simulated scattering profiles, the formalism is used to estimate the size distribution from experimental small-angle X-ray scattering data from two different dilute dispersions of silica. At present the method is limited to monomodal distributions of dilute spherical particles only.

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.

Update for BayesApp: a web site for analysis of small-angle scattering data

2014 ◽  
Vol 47 (4) ◽  
pp. 1469-1471 ◽  
Author(s):  
Steen Hansen
Keyword(s):  
Maximum Entropy ◽  
Bayesian Methods ◽  
Small Angle ◽  
Web Site ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Structure Factors ◽  
Angle Scattering ◽  
Ellipsoid Of Revolution ◽  
The Web

An update for BayesApp, a web site for analysis of small-angle scattering data, is presented. The indirect transformation of the scattering data now includes an option for a maximum-entropy constraint in addition to the conventional smoothness constraint. The maximum-entropy constraint uses an ellipsoid of revolution as a prior, and the dimensions of the ellipsoid as well as the overall noise level of the experimental data are estimated using Bayesian methods. Furthermore, a correction for slit smearing has been added. The web site also includes options for calculation of the scattering intensity from simple models as well as the estimation of structure factors for polydisperse spheres and nonspherical objects of axial ratios between 0.4 and 2.5.

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