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

1992 ◽  
Author(s):  
P.R. Jemian ◽  
A.J. Allen
Keyword(s):  
Maximum Entropy ◽  
Small Angle ◽  
Maximum Entropy Method ◽  
Shape Function ◽  
Small Angle Scattering ◽  
Entropy 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.

Maximum-entropy method as a routine tool for determination of particle size distributions by small-angle scattering

2004 ◽  
Vol 37 (1) ◽  
pp. 32-39 ◽  
Author(s):  
Dragomir Tatchev ◽  
Rainer Kranold
Keyword(s):  
Particle Size ◽  
Fourier Transform ◽  
Small Angle ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Angle Scattering ◽  
The Fourier Transform

Several aspects of the application of the maximum-entropy method (MEM) to the determination of particle size distributions by small-angle scattering (SAS) are discussed. The `historic' version of the MEM produces completely satisfying results. Limiting the data error from below (i.e.imposing a minimal relative error) is proposed as a solution of some convergence problems. The MEM is tested against the Fourier transform technique. The size distribution of Pb particles in an Al–Pb alloy is determined by the MEM and the Fourier transform technique. The size distributions obtained by transmission electron microscopy (TEM) and SAXS show partial agreement.

A model-independent maximum-entropy method for the inversion of small-angle X-ray diffraction patterns

1999 ◽  
Vol 32 (6) ◽  
pp. 1069-1083 ◽  
Author(s):  
J. A. Elliott ◽  
S. Hanna
Keyword(s):  
Maximum Entropy ◽  
Small Angle ◽  
Disordered Systems ◽  
Maximum Entropy Method ◽  
Structural Model ◽  
Entropy Method ◽  
X Ray Diffraction ◽  
X Ray ◽  
Model Independent ◽  
Diffraction Patterns

A model-independent maximum-entropy method is presented which will produce a structural model from small-angle X-ray diffraction data of disordered systems using no other prior information. In this respect, it differs from conventional maximum-entropy methods which assume the form of scattering entitiesa priori. The method is demonstrated using a number of different simulated diffraction patterns, and applied to real data obtained from perfluorinated ionomer membranes, in particular Nafion™, and a liquid crystalline copolymer of 1,4-oxybenzoate and 2,6-oxynaphthoate (B–N).

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