Solving the generalized indirect Fourier transformation (GIFT) by Boltzmann simplex simulated annealing (BSSA)

2000 ◽  
Vol 33 (5) ◽  
pp. 1212-1216 ◽  
Author(s):  
A. Bergmann ◽  
G. Fritz ◽  
O. Glatter
Keyword(s):  
Simulated Annealing ◽  
Fourier Transformation ◽  
Global Minimum ◽  
Colloidal Particles ◽  
Form Factors ◽  
Real Space ◽  
Mean Deviation ◽  
Model Free ◽  
Information Interaction ◽  
Structure Factors

The structure of colloidal particles can be studied with small-angle X-ray and neutron scattering (SAXS and SANS). In the case of randomly oriented systems, the indirect Fourier transformation (IFT) is a well established technique for the calculation of model-free real-space information. Interaction leads to an overlap of inter- and intraparticle scattering effects, preventing most detailed interpretations. The recently developed generalized indirect Fourier transformation (GIFT) technique allows these effects to be separated by assuming various models for the interaction,i.e.the so-called structure factors. The different analytical behaviour of these structure factors from that of the form factors, describing the intraparticle scattering, allows this separation. The mean-deviation surface is defined by the quality of the fit for different parameter sets of the structure factor. Its global minimum represents the solution. The former non-linear least-squares approach has proved to be inefficient and not very reliable. In this paper, the incorporation of the completely different Boltzmann simplex simulated annealing (BSSA) algorithm for finding the global minimum of the hypersurface is presented. This new method increases not only the calculation speed but also the reliability of the evaluation.

Neutron diffraction investigation of copper tellurite glasses with high real-space resolution

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Navjot Kaur ◽  
Atul Khanna ◽  
Alex C. Hannon
Keyword(s):  
Neutron Diffraction ◽  
Coordination Number ◽  
Diffraction Data ◽  
Fourier Transformation ◽  
Short Range ◽  
Real Space ◽  
Tellurite Glasses ◽  
Space Resolution ◽  
Bond Lengths ◽  
Structure Factors

High real-space resolution neutron diffraction measurements up to 34 Å−1 were performed on a series of xCuO–(100 − x)TeO2 (x = 30, 40 and 50 mol%) glasses that were synthesized by the melt-quenching technique. The Fourier transformation of neutron diffraction structure factors was used to generate the pair distribution functions, with the first peak at 1.90 Å due to the overlapping Te–O and Cu–O atomic pairs. Reverse Monte Carlo (RMC) simulations were performed on the structure factors and the six partial atomic pair distributions of Cu–Cu, Cu–Te, Cu–O, Te–Te, Te–O and O–O were calculated. The Te–O and Cu–O distributions are very similar and asymmetrical, which revealed that there is a significant short-range disorder in the tellurite network due to the existence of a wide range of Te—O and Cu—O bond lengths. A high-Q (magnitude of momentum transfer function) neutron diffraction study revealed that the average Te–O coordination number decreases steadily from 3.45 to 3.18 with an increase in CuO concentration from 30 to 50 mol% in the glass network. Similar coordination number modifications were earlier found by the RMC analysis of neutron diffraction data sets of copper tellurite glasses that were performed up to lower Q maximum values of 9.5 Å−1. The comparison of high-Q and low-Q neutron diffraction studies reveals that RMC is a powerful and possibly the only technique that is available to elucidate the glass short-range and medium-range structural properties when diffraction data are available up to low Q values of, say, 9.5 Å−1, and when cation–oxygen bond lengths are strongly overlapping and cannot be resolved by Fourier transformation. In situ high-temperature (473 K) neutron diffraction studies of 50CuO–50TeO2 glass revealed that significant distortion of the tellurite network occurs with heating.

scholarly journals Interpreting SAXS data recorded on cellulose rich pulps

Cellulose ◽  
2021 ◽  
Author(s):  
Per Tomas Larsson ◽  
Jasna Stevanic-Srndovic ◽  
Stephan V. Roth ◽  
Daniel Söderberg
Keyword(s):  
Form Factors ◽  
Simulation Method ◽  
Real Space ◽  
Step Size ◽  
Saxs Data ◽  
Modelling Method ◽  
Saxs Intensity ◽  
Structure Factors ◽  
Separate Form ◽  
C Nmr

AbstractA simulation method was developed for modelling SAXS data recorded on cellulose rich pulps. The modelling method is independent of the establishment of separate form factors and structure factors and was used to model SAXS data recorded on dense samples. An advantage of the modelling method is that it made it possible to connect experimental SAXS data to apparent average sizes of particles and cavities at different sample solid contents. Experimental SAXS data could be modelled as a superposition of a limited number of simulated intensity components and gave results in qualitative agreement with CP/MAS 13C-NMR data recorded on the same samples. For the water swollen samples, results obtained by the SAXS modelling method and results obtained from CP/MAS 13C-NMR measurements, agreed on the ranking of particle sizes in the different samples. The SAXS modelling method is dependent on simulations of autocorrelation functions and the time needed for simulations could be reduced by rescaling of simulated correlation functions due to their independence of the choice of step size in real space. In this way an autocorrelation function simulated for a specific sample could be used to generate SAXS intensity profiles corresponding to all length scales for that sample and used for efficient modelling of the experimental data recorded on that sample. Graphical abstract

Two-dimensional indirect Fourier transformation for evaluation of small-angle scattering data of oriented samples

2013 ◽  
Vol 46 (5) ◽  
pp. 1447-1454 ◽  
Author(s):  
Gerhard Fritz-Popovski
Keyword(s):  
Small Angle ◽  
Fourier Transformation ◽  
Real Space ◽  
Small Angle Scattering ◽  
Basis Functions ◽  
Scattering Data ◽  
Normal Wood ◽  
Two Dimensional ◽  
Model Free ◽  
Angle Scattering

An extension of the indirect Fourier transformation method for two-dimensional small-angle scattering patterns is presented. This allows for a model-free investigation of real-space functions of oriented structures. The real-space function is built from two-dimensional basis functions. The Fourier transformed basis functions are approximated to the scattering pattern. The solution to this problem in reciprocal space can be used to compute the corresponding real-space functions. These real-space functions contain information on size, shape, internal structure and orientation of the structures studied. Information on structures that are oriented in different distinct directions can be partly separated. The applicability of the technique is demonstrated on simulated data of oriented cuboids and on two experimental data sets based on the nanostructure of spruce normal wood.

Scatter: software for the analysis of nano- and mesoscale small-angle scattering

2010 ◽  
Vol 43 (3) ◽  
pp. 639-646 ◽  
Author(s):  
S. Förster ◽  
L. Apostol ◽  
W. Bras
Keyword(s):  
Small Angle ◽  
Calculated Data ◽  
Form Factors ◽  
Real Space ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Mathematical Treatment ◽  
Mesoscale Structures ◽  
Structure Factors ◽  
Angle Scattering

Scatteris a new software for analysis, modeling and fitting of one- and two-dimensional small-angle scattering data of non-ordered, partially ordered or fully ordered nano- and mesoscale structures. The calculations are based on closed analytical expressions for the scattering intensity, enabling efficient evaluation of form factors and structure factors. The software allows one to sequentially fit large series of scattering curves and scattering patterns automatically. It provides further tools for data loading, beam centering, calibration, zooming, binning, lattice identification, calculation of density profiles and size distributions, and visualization of real-space structures. Presentations of experimental and calculated data can be saved as is for presentations or exported for further graphical or mathematical treatment.

scholarly journals Interpreting SAXS Data Recorded On Cellulose Rich Pulps

2021 ◽  
Author(s):  
Tomas Larsson ◽  
Jasna Stevanic-Srndo ◽  
Stephan V. Roth ◽  
Daniel Söderberg
Keyword(s):  
Form Factors ◽  
Simulation Method ◽  
Real Space ◽  
Step Size ◽  
Saxs Data ◽  
Modelling Method ◽  
Saxs Intensity ◽  
Structure Factors ◽  
Separate Form ◽  
C Nmr

Abstract A simulation method was developed for modelling SAXS data recorded on cellulose rich pulps. The modelling method is independent of the establishments of separate form factors and structure factors and was used to model SAXS data recorded on dense samples. An advantage of the modelling method was that it made it possible to connect experimental SAXS data to apparent average sizes of particles and cavities at different sample solid contents. Experimental SAXS data could be modelled as a superposition of a limited number of simulated intensity components and gave results in qualitative agreement with CP/MAS 13C-NMR data recorded on the same samples. For the water swollen samples, results obtained by the SAXS modelling method and results obtained from CP/MAS 13C-NMR measurements, agreed on the ranking of particle sizes in the different samples. The SAXS modelling method is dependent on simulations of autocorrelation functions. The time needed for simulations could be reduced by rescaling of simulated correlation functions, due to their independence of the choice of step size in real space. This way an autocorrelation function simulated for a specific sample could be used to generate SAXS intensity profiles corresponding to all length scales for that sample and used for efficient modelling of the experimental data recorded on that sample.

DASH: a program for crystal structure determination from powder diffraction data

2006 ◽  
Vol 39 (6) ◽  
pp. 910-915 ◽  
Author(s):  
William I. F. David ◽  
Kenneth Shankland ◽  
Jacco van de Streek ◽  
Elna Pidcock ◽  
W. D. Samuel Motherwell ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Global Minimum ◽  
Molecular Structures ◽  
Powder Diffraction Data ◽  
Peak Fitting ◽  
Structure Factors ◽  
Integrated Intensities ◽  
User Friendly

DASHis a user-friendly graphical-user-interface-driven computer program for solving crystal structures from X-ray powder diffraction data, optimized for molecular structures. Algorithms for multiple peak fitting, unit-cell indexing and space-group determination are included as part of the program. Molecular models can be read in a number of formats and automatically converted to Z-matrices in which flexible torsion angles are automatically identified. Simulated annealing is used to search for the global minimum in the space that describes the agreement between observed and calculated structure factors. The simulated annealing process is very fast, which in part is due to the use of correlated integrated intensities rather than the full powder pattern. Automatic minimization of the structures obtained by simulated annealing and automatic overlay of solutions assist in assessing the reproducibility of the best solution, and therefore in determining the likelihood that the global minimum has been obtained.

scholarly journals Structure factors for generalized grey Browinian motion

2019 ◽  
Vol 22 (2) ◽  
pp. 396-411
Author(s):  
José L. da Silva ◽  
Ludwig Streit
Keyword(s):  
Gaussian Processes ◽  
Form Factors ◽  
Analytic Form ◽  
Debye Function ◽  
Asymptotic Decay ◽  
Structure Factors ◽  
Closed Analytic Form ◽  
Non Gaussian

Abstract In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

scholarly journals A CHARGE FORM FACTOR (CFF) OF 5He NUCLEUS

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Piyush Sinha ◽  
Neelam Sinha
Keyword(s):  
Electron Scattering ◽  
Fourier Transforms ◽  
Form Factors ◽  
High Energy ◽  
Energy Electron ◽  
High Energy Electron ◽  
Structure Factors ◽  
Transition Matrix Elements ◽  
Current Densities ◽  
A Charge

High energy electron scattering is a very powerful tool for studying geometrical details of nuclear structure. The studies provide information on static distribution of charge and magnetization in nuclei. As the interaction is relatively weak so that in the scattering process the internal structure of the target nucleus is not significantly disturbed. Using electrons as projectile, we can study how transition matrix elements vary with q2 and map out the Fourier transforms of the transition charge and current densities called Form Factors or Structure factors. In the high energy electron scattering we can know the details of the spatial distribution of transition charge and current density. In this paper we have formulated CFF for 5He nucleus

Small-angle scattering of interacting particles. II. Generalized indirect Fourier transformation under consideration of the effective structure factor for polydisperse systems

1999 ◽  
Vol 32 (2) ◽  
pp. 197-209 ◽  
Author(s):  
B. Weyerich ◽  
J. Brunner-Popela ◽  
O. Glatter
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Structure Factor ◽  
Fourier Transformation ◽  
Hard Spheres ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Model Free ◽  
Angle Scattering ◽  
The Gift

The indirect Fourier transformation (IFT) is the method of choice for the model-free evaluation of small-angle scattering data. Unfortunately, this technique is only useful for dilute solutions because, for higher concentrations, particle interactions can no longer be neglected. Thus an advanced technique was developed as a generalized version, the so-called generalized indirect Fourier transformation (GIFT). It is based on the simultaneous determination of the form factor, representing the intraparticle contributions, and the structure factor, describing the interparticle contributions. The former can be determined absolutely free from model assumptions, whereas the latter has to be calculated according to an adequate model. In this paper, various models for the structure factor are compared,e.g.the effective structure factor for polydisperse hard spheres, the averaged structure factor, the local monodisperse approximation and the decoupling approximation. Furthermore, the structure factor for polydisperse rod-like particles is presented. As the model-free evaluation of small-angle scattering data is an essential point of the GIFT technique, the use of a structure factor without any influence of the form amplitude is advisable, at least during the first evaluation procedure. Therefore, a series of simulations are performed to check the possibility of the representation of various structure factors (such as the effective structure factor for hard spheres or the structure factor for rod-like particles) by the less exact but much simpler averaged structure factor. In all the observed cases, it was possible to recover the exact form factor with a free determined parameter set for the structure factor. The resulting parameters of the averaged structure factor have to be understood as apparent model parameters and therefore have only limited physical relevance. Thus the GIFT represents a technique for the model independent evaluation of scattering data with a minimum ofa prioriinformation.

FitGISAXS: software package for modelling and analysis of GISAXS data using IGOR Pro

2010 ◽  
Vol 43 (4) ◽  
pp. 929-936 ◽  
Author(s):  
David Babonneau
Keyword(s):  
Software Package ◽  
Form Factors ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Scattering Data ◽  
Stratified Medium ◽  
X Ray ◽  
X Ray Scattering ◽  
Structure Factors ◽  
Scripting Language

A software package for performing modelling and analysis of GISAXS (grazing-incidence small-angle X-ray scattering) data within the distorted-wave Born approximation has been developed using the IGOR Pro scripting language (http://www.wavemetrics.com). The tool suite uses a slab-model approach with the Abélès matrix method to calculate X-ray reflectivity curves, electric field intensity distributions and GISAXS intensities from supported or buried scatterers arranged in two or three dimensions in a stratified medium. Models are included to calculate the scattered intensity for monodisperse, polydisperse and interacting particles with various size distributions, form factors and structure factors. The source code for the entire package is freely available, allowing anyone to develop additional tools.

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