Analysis of the Initial Slope of the Small-Angle Scattering Correlation Function of a Particle

2005 ◽  
Vol 22 (4) ◽  
pp. 254-260 ◽  
Author(s):  
Wilfried Gille ◽  
Alain Mazzolo ◽  
Benoit Roesslinger
Keyword(s):  
Correlation Function ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Initial Slope ◽  
Angle Scattering

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.

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 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.

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