scholarly journals Transformation cycle between the spherically symmetric correlation function, projected correlation function and differential cross section as implemented inSASfit

2017 ◽  
Vol 50 (5) ◽  
pp. 1395-1403 ◽  
Author(s):  
J. Kohlbrecher ◽  
A. Studer

Spin-echo-based small-angle neutron scattering techniques like spin-echo SANS (SESANS) or spin-echo modulated SANS (SEMSANS) as well as dark-field (DF) imaging are directly sensitive to \tilde{G}(\delta), which is the projection of the scattering length density autocorrelation function \tilde{\gamma}(r). Here, a simplified transformation cycle relating the spherically symmetric correlation function \tilde{\gamma}(r), the projected correlation function \tilde{G}(\delta) and the macroscopic small-angle scattering cross section dΣ/dΩ is introduced. The suggested changes to the cycle make it easier to include size distribution on an absolute scale if the data from the different techniques are fitted simultaneously. As up to now only very few analytical expressions for the projected correlation function are known, a numerical transformation of known scattering functions into the projected correlation function in theSASfitsoftware package is supplied. Furthermore, a new analytical expression for the projected correlation function for polymers that can be described by the generalized Gaussian coil model is provided. For this polymer model, the Hankel transform used to calculate \tilde{G}(0) from the SANS signal is divergent for a certain parameter range describing a polymer in a good solvent and finite in the case of a poor solvent. It is therefore a suitable example of how the experimentally availableqrange can strongly influence the obtained results.

2003 ◽  
Vol 36 (1) ◽  
pp. 109-116 ◽  
Author(s):  
Oktay Uca ◽  
Wim G. Bouwman ◽  
M. Theo Rekveldt

Spin-echo small-angle neutron scattering (SESANS) is a new kind of SANS technique enabling measurements to be made directly in real space from a range of a few nanometres up to micrometres. In this paper it is shown by calculations on models that SESANS measures correlations directly. Furthermore, the effect of polydispersity and structure factor has been studied. An exact expression for the correlation function has been derived in the case of random systems, such as fractal systems.


2008 ◽  
Vol 41 (5) ◽  
pp. 868-885 ◽  
Author(s):  
Robert Andersson ◽  
Léon F. van Heijkamp ◽  
Ignatz M. de Schepper ◽  
Wim G. Bouwman

Spin-echo small-angle neutron scattering (SESANS) is, in contrast to conventional small-angle neutron scattering (SANS), a real-space technique. SESANS measures the projection of the density–density correlation function of a sample, rather than, as in SANS, its Fourier transform. This paper introduces a toolkit for interpretion and analysis of a SESANS measurement. Models that are used in SANS are discussed and translated into a SESANS formalism. These models can be used to analyse and fit the data obtained by SESANS. Dilute, concentrated, random, fractal and anisotropic density distributions are considered. Numerical methods used to calculate the projection from numerical data are presented, either by using Fourier transformation orviathe real-space pair correlation function.


2001 ◽  
Vol 34 (5) ◽  
pp. 639-645 ◽  
Author(s):  
Jinkui Zhao

Two-dimensional spin echo small-angle neutron scattering experiments that measure the vector-length distribution function, or pair-distance distribution function, in real space are discussed. The proposed diffractometer uses two cylindrically symmetric magnetic fields with conically shaped front and end faces to enable experiments in two dimensions. It also features a π/2 neutron spin flipper to make the effective analyzing direction of the analyzer perpendicular to the polarizing direction of the polarizer. The theoretical aspect of one-dimensional spin echo small-angle neutron scattering experiments is also explored. The relationship between the correlation function from one-dimensional experiments and the vector-length distribution function is established, and interpretation of this correlation function in real space is presented.


2003 ◽  
Vol 36 (1) ◽  
pp. 117-124 ◽  
Author(s):  
Timofei Krouglov ◽  
Ignatz M. de Schepper ◽  
Wim G. Bouwman ◽  
M. Theo Rekveldt

Spin-echo small-angle neutron scattering (SESANS) is a novel real-space scattering technique. SESANS measures a correlation-like functionG(Z), the meaning of which was unknown until now. Here a direct real-space interpretation ofG(Z) through the particle scattering density and pair correlation function is given. One-dimensional and two-dimensional SESANS are compared. The case of non-interacting particles is considered in detail with an explicit geometrical interpretation. General methods for the calculation of structural parameters, such as the total scattering length and the radius of gyration, are developed. Analytical expressions ofG(Z) for non-interacting solid spheres, hollow spheres and Gaussian coils are derived. The case of solid spheres is compared with experimental data.


2003 ◽  
Vol 36 (5) ◽  
pp. 1177-1181
Author(s):  
Jinkui Zhao

Following previous works on data interpretation in the case of a one-dimensionally encoded spin-echo small-angle neutron scattering instrument when the scattering data are collected along a single direction, further studies for the more general case of data collection in two dimensions are presented. A mathematical relationship between the correlation function measured in two dimensions and the pair-distance distribution function of the scattering sample is established. The relationship between the correlation function measured in one and two dimensions is also examined.


Author(s):  
J. Langmore ◽  
M. Isaacson ◽  
J. Wall ◽  
A. V. Crewe

High resolution dark field microscopy is becoming an important tool for the investigation of unstained and specifically stained biological molecules. Of primary consideration to the microscopist is the interpretation of image Intensities and the effects of radiation damage to the specimen. Ignoring inelastic scattering, the image intensity is directly related to the collected elastic scattering cross section, σɳ, which is the product of the total elastic cross section, σ and the eficiency of the microscope system at imaging these electrons, η. The number of potentially bond damaging events resulting from the beam exposure required to reduce the effect of quantum noise in the image to a given level is proportional to 1/η. We wish to compare η in three dark field systems.


2014 ◽  
Vol 47 (1) ◽  
pp. 237-244 ◽  
Author(s):  
Karsten Vogtt ◽  
Miriam Siebenbürger ◽  
Daniel Clemens ◽  
Christian Rabe ◽  
Peter Lindner ◽  
...  

Small-angle scattering methods have become routine techniques for the structural characterization of macromolecules and macromolecular assemblies like polymers, (block) copolymers or micelles in the spatial range from a few to hundreds of nanometres. Neutrons are valuable scattering probes, because they offer freedom with respect to scattering length density contrast and isotopic labelling of samples. In order to gain maximum benefit from the allotted experiment time, the instrumental setup must be optimized in terms of statistics of scattered intensity, resolution and accessible range in momentum transferQ. The new small-angle neutron scattering instrument V16/VSANS at the Helmholtz-Zentrum in Berlin, Germany, augments neutron guide collimation and pinhole optics with time-of-flight data recording and flexible chopper configuration. Thus, the availableQrange and the respective instrumental resolution in the intermediate and high momentum transfer regions can be adjusted and balanced to the individual experimental requirements. This renders V16/VSANS a flexible and versatile instrument for soft-matter research.


Sign in / Sign up

Export Citation Format

Share Document