scholarly journals Chord length distribution density and small-angle scattering correlation function of the right circular cone

1999 ◽  
Vol 30 (9-10) ◽  
pp. 107-130 ◽  
Author(s):  
W. Gille ◽  
H. Handschug
Keyword(s):  
Correlation Function ◽  
Small Angle ◽  
Distribution Density ◽  
Length Distribution ◽  
Small Angle Scattering ◽  
Circular Cone ◽  
Chord Length ◽  
Chord Length Distribution ◽  
Angle Scattering ◽  
The Right

Chord length distribution of pentagonal and hexagonal rods: relation to small-angle scattering

2009 ◽  
Vol 42 (2) ◽  
pp. 326-328 ◽  
Author(s):  
Wilfried Gille ◽  
Narine G. Aharonyan ◽  
Hrachya S. Harutyunyan
Keyword(s):  
Small Angle ◽  
Length Distribution ◽  
Small Angle Scattering ◽  
Chord Length ◽  
Density Functions ◽  
Explicit Formulas ◽  
Chord Length Distribution ◽  
Regular Pentagon ◽  
Angle Scattering

Based on explicit formulas of chord length density functions (CLDs) for a regular pentagon and a hexagon, the CLDs of infinitely long regular homogeneous pentagonal/hexagonal cylinders are discussed. Characteristic properties of the small-angle scattering of these cylinders are studied.

The small-angle scattering correlation function of the cuboid

1999 ◽  
Vol 32 (6) ◽  
pp. 1100-1104 ◽  
Author(s):  
Wilfried Gille
Keyword(s):  
Correlation Function ◽  
Asymptotic Behaviour ◽  
Small Angle ◽  
Length Distribution ◽  
Chord Length ◽  
Scattering Intensity ◽  
Chord Length Distribution ◽  
Angle Scattering ◽  
Higher Derivatives ◽  
Derivatives Of

The analytical expression of the correlation function γ(r) for the cuboid with edgesa,bandcis established. The calculation is based on the chord-length distribution. Details of these structure functions at essentialrpositions are analysed, including higher derivatives of the correlation function at the maximum chord length. The result was checked on closer analysis of the corresponding scattering intensityI(h) and its asymptotic behaviourI∞(h).

Small-angle scattering analysis of the spherical half-shell

2007 ◽  
Vol 40 (2) ◽  
pp. 302-304 ◽  
Author(s):  
Wilfried Gille
Keyword(s):  
Correlation Function ◽  
Small Angle ◽  
Pair Correlation ◽  
Length Distribution ◽  
Small Angle Scattering ◽  
Scattering Intensity ◽  
Chord Length Distribution ◽  
Angle Scattering ◽  
Analytic Expressions

For a spherical half-shell (SHS) of diameter D, analytic expressions of the small-angle scattering correlation function \gamma_0(r), the chord length distribution (CLD) and the scattering intensity are analyzed. The spherically averaged pair correlation function p_0(r)\simeq r^2\gamma_0(r) of the SHS is identical to the cap part of the CLD of a solid hemisphere of the same diameter. The surprisingly simple analytic terms in principle allow the determination of the size distribution of an isotropic diluted SHS collection from its scattering intensity.

Estimation of chord length distributions from small-angle scattering using indirect Fourier transformation

2003 ◽  
Vol 36 (5) ◽  
pp. 1190-1196 ◽  
Author(s):  
Steen Hansen
Keyword(s):  
Small Angle ◽  
Fourier Transformation ◽  
Length Distribution ◽  
Small Angle Scattering ◽  
Chord Length ◽  
Scattering Data ◽  
Additional Tool ◽  
Additional Information ◽  
Chord Length Distribution ◽  
Angle Scattering

It is shown that it is possible to estimate the chord length distribution from small-angle scattering data by indirect Fourier transformation. This is done for several examples of scatterers varying in structure from globular to elongated as well as scatterers consisting of separated parts. The presented examples suggest that the chord length distribution may give additional information about the scatterer. Therefore it may be relevant to consider estimation of the chord length distribution as an additional tool for analysis of small-angle scattering data.

Characteristics of the SAS correlation function of long cylinders with oval right section

2010 ◽  
Vol 43 (2) ◽  
pp. 347-349 ◽  
Author(s):  
Wilfried Gille
Keyword(s):  
Correlation Function ◽  
Surface Area ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Chord Length ◽  
Angle Scattering ◽  
The Mean ◽  
Two Parameters

An approximation for the small-angle scattering (SAS) correlation function (CF) β0(r) of a plane oval domainXis discussed. The approach is based on two parameters, the perimeteruand the surface areaSRS, ofX. The function β0(r) fixes the correlation function γ0(r) of the oval homogeneous rod with constant right sectionX. The mean chord lengthl1of such a rod is the root of the equation γ0(l1) = 1 − 8/(3π). For a dilute rod arrangement, the Porod lengthlpand γ′(l1), the value of the derivative of the sample CF atr=l1, are related by γ′(l1) = −4/(3πlp).

SMALL-ANGLE SCATTERING OF FAST POLARIZED NEUTRONS BY HEAVY NUCLEI

1956 ◽  
Vol 34 (1) ◽  
pp. 36-42 ◽  
Author(s):  
J. T. Sample
Keyword(s):  
Small Angle ◽  
Intensity Ratio ◽  
Horizontal Plane ◽  
Small Angle Scattering ◽  
Fast Neutrons ◽  
Heavy Nuclei ◽  
Spin Orientation ◽  
Scattering Angle ◽  
Angle Scattering ◽  
The Right

Detailed calculations have been carried out which indicate that the small-angle scattering of fast neutrons by lead depends on the polarization, or spin orientation, of the neutrons. When the scattering of neutrons whose spin vectors point upward is observed in the horizontal plane, more neutrons should be found scattered to the right than to the left. For completely polarized 3.1 Mev. neutrons, the theory predicts a maximum "right to left" intensity ratio of 14.5:1 at a scattering angle of 0.5°, the ratio decreasing to 1.6:1 at 5°, and approaching unity rapidly as the scattering angle increases.

scholarly journals Small Angle Scattering Data Analysis Assisted by Machine Learning Methods

MRS Advances ◽  
2020 ◽  
Vol 5 (29-30) ◽  
pp. 1577-1584
Author(s):  
Changwoo Do ◽  
Wei-Ren Chen ◽  
Sangkeun Lee
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Small Angle ◽  
Confusion Matrix ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Search Spaces ◽  
Angle Scattering ◽  
Analysis Workflow ◽  
The Right

ABSTRACTSmall angle scattering (SAS) is a widely used technique for characterizing structures of wide ranges of materials. For such wide ranges of applications of SAS, there exist a large number of ways to model the scattering data. While such analysis models are often available from various suites of SAS data analysis software packages, selecting the right model to start with poses a big challenge for beginners to SAS data analysis. Here, we present machine learning (ML) methods that can assist users by suggesting scattering models for data analysis. A series of one-dimensional scattering curves have been generated by using different models to train the algorithms. The performance of the ML method is studied for various types of ML algorithms, resolution of the dataset, and the number of the dataset. The degree of similarities among selected scattering models is presented in terms of the confusion matrix. The scattering model suggestions with prediction scores provide a list of scattering models that are likely to succeed. Therefore, if implemented with extensive libraries of scattering models, this method can speed up the data analysis workflow by reducing search spaces for appropriate scattering models.

Small-angle scattering of particle assemblies

2015 ◽  
Vol 48 (4) ◽  
pp. 1172-1182 ◽  
Author(s):  
Andrew J. Senesi ◽  
Byeongdu Lee
Keyword(s):  
Correlation Function ◽  
Small Angle ◽  
Diffuse Scattering ◽  
Diffraction Theory ◽  
Small Angle Scattering ◽  
Orientational Disorder ◽  
Angle Scattering ◽  
Decoupling Approximation ◽  
Particle Assemblies ◽  
Do So

Small-angle scattering formulae for crystalline assemblies of arbitrary particles are derived from powder diffraction theory using the decoupling approximation. To do so, the pseudo-lattice factor is defined, and methods to overcome the limitations of the decoupling approximation are investigated. Further, approximated equations are suggested for the diffuse scattering from various defects of the first kind due to non-ideal particles, including size polydispersity, orientational disorder and positional fluctuation about their ideal positions. Calculated curves using the formalism developed herein are compared with numerical simulations computed without any approximation. For a finite-sized assembly, the scattering from the whole domain of the assembly must also be included, and this is derived using the correlation function approach.

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