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

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.

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.

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 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

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.

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.

Validation of carbohydrate structures: not just nomenclature

2014 ◽  
Vol 70 (a1) ◽  
pp. C1481-C1481
Author(s):  
Jon Agirre ◽  
Kevin Cowtan
Keyword(s):  
Protein Data Bank ◽  
Correlation Coefficient ◽  
Electron Density ◽  
Systematic Study ◽  
Data Bank ◽  
Real Space ◽  
Space Correlation ◽  
Structure Factors ◽  
Ring Distortion ◽  
Experimental Electron Density

Despite the key implications carbohydrates have in a multitude of pathological processes, a large number of the sugar-containing structures deposited into the Protein Data Bank (PDB) show nomenclature errors [1] that persist even after the remediation of the PDB archive [2]. Here we present the results from a systematic study of the conformation and ring distortion of cyclic carbohydrate models for which structure factors have been deposited into the PDB. These models have also been scored using a real-space correlation coefficient calculated between model and experimental electron density. The results have enabled us to produce a database of well-refined carbohydrate structures for use in the framework of an automated sugar-detecting software, to be announced shortly.

scholarly journals A Comparison between Electron Crystal Scattering Potentials derived from X-ray Electron Densities and from Atom Muffin Tin Potentials

1985 ◽  
Vol 38 (3) ◽  
pp. 487 ◽  
Author(s):  
Andrew E Smith ◽  
DF Lynch
Keyword(s):  
Fourier Coefficients ◽  
Real Space ◽  
Space Representation ◽  
Natural Representation ◽  
X Ray ◽  
Low Energy Electron Diffraction ◽  
Structure Factors ◽  
Structure Determinations ◽  
Low Energy Electron ◽  
Electron Crystal

Two different forms of electron crystal potential are compared for the particular cases of aluminium and niobium diselenide. One of these is the solid-state muffin tin potential frequently used for band structure and low energy electron diffraction problems, and with its natural representation in real space. The other potential, derived from X-ray structure factors, is that most commonly used in electron microscopy structure determinations. It is expressed in terms of its Fourier coefficients and is accordingly a reciprocal space representation. Comparisons are carried out in both spaces. It is concluded that differences between the potentials are only minor and are mainly due to details in truncation and superposition.

Dynamical scaling in fractal structures in the aggregation of tetraethoxysilane-derived sonogels

2010 ◽  
Vol 43 (5) ◽  
pp. 949-954 ◽  
Author(s):  
Dimas R. Vollet ◽  
Dario A. Donatti ◽  
Alberto Ibañez Ruiz ◽  
Fabio S. de Vicente
Keyword(s):  
Factor Model ◽  
Fractal Structures ◽  
Saxs Data ◽  
Scaling Properties ◽  
Dynamical Scaling ◽  
X Ray Scattering ◽  
Linear Chains ◽  
Saxs Intensity ◽  
Scattering Factor ◽  
Kinetics Of

Dynamical scaling properties in fractal structures were investigated from small-angle X-ray scattering (SAXS) data of the kinetics of aggregation in silica-based gelling systems. For lack of a maximum in the SAXS intensity curves, a characteristic correlation distance ξ was evaluated by fitting a particle scattering factor model valid for polydisperse coils of linear chains andf-functional branched polycondensates in solution, so the intensity atq= ξ−1,I(ξ−1,t), was considered to probe dynamical scaling properties. The following properties have been found: (i) the SAXS intensities corresponding to different timest,I(q,t), are given by a time-independent functionF(qξ) =I(q,t)ξ−D/Q, where the scattering invariantQhas been found to be time-independent; (ii) ξ exhibited a power-law behavior with time as ξ ≃tα, the exponent α being close to 1 but diminishing with temperature; (iii)I(ξ−1,t) exhibited a time dependence given byI(ξ−1,t) ≃tβ, with the exponent β found to be around 2 but diminishing with temperature, following the same behavior as the exponent α. In all cases, β/α was quite close to the fractal dimensionDat the end of the studied process. This set of findings is in notable agreement with the dynamical scaling properties.

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