SMALL ANGLE SCATTERING AND STRUCTURE FACTOR NEUTRON MEASUREMENTS OF AN AMORPHOUS Al70Si17Fe13 ALLOY

1985 ◽  
Vol 46 (C8) ◽  
pp. C8-461-C8-466 ◽  
Author(s):  
J. M. Dubois ◽  
K. Dehghan ◽  
C. Janot ◽  
P. Chieux ◽  
B. Chenal
Keyword(s):  
Small Angle ◽  
Structure Factor ◽  
Small Angle Scattering ◽  
Angle Scattering

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.

Assessment of structure factors for analysis of small-angle scattering data from desired or undesired aggregates

2020 ◽  
Vol 53 (4) ◽  
pp. 991-1005
Author(s):  
Andreas Haahr Larsen ◽  
Jan Skov Pedersen ◽  
Lise Arleth
Keyword(s):  
Small Angle ◽  
Structure Factor ◽  
Protein Structures ◽  
Simulated Data ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
Spherical Cluster ◽  
Structure Factors ◽  
Angle Scattering ◽  
Aggregation Processes

Aggregation processes are central features of many systems ranging from colloids and polymers to inorganic nanoparticles and biological systems. Some aggregated structures are controlled and desirable, e.g. in the design of size-controlled clustered nanoparticles or some protein-based drugs. In other cases, the aggregates are undesirable, e.g. protein aggregation involved in neurodegenerative diseases or in vitro studies of single protein structures. In either case, experimental and analytical tools are needed to cast light on the aggregation processes. Aggregation processes can be studied with small-angle scattering, but analytical descriptions of the aggregates are needed for detailed structural analysis. This paper presents a list of useful small-angle scattering structure factors, including a novel structure factor for a spherical cluster with local correlations between the constituent particles. Several of the structure factors were renormalized to get correct limit values in both the high-q and low-q limit, where q is the modulus of the scattering vector. The structure factors were critically evaluated against simulated data. Structure factors describing fractal aggregates provided approximate descriptions of the simulated data for all tested structures, from linear to globular aggregates. The addition of a correlation hole for the constituent particles in the fractal structure factors significantly improved the fits in all cases. Linear aggregates were best described by a linear structure factor and globular aggregates by the newly derived spherical cluster structure factor. As a central point, it is shown that the structure factors could be used to take aggregation contributions into account for samples of monomeric protein containing a minor fraction of aggregated protein. After applying structure factors in the analysis, the correct structure and oligomeric state of the protein were determined. Thus, by careful use of the presented structure factors, important structural information can be retrieved from small-angle scattering data, both when aggregates are desired and when they are undesired.

scholarly journals Microscale Fragmentation and Small-Angle Scattering from Mass Fractals

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
E. M. Anitas
Keyword(s):  
Power Law ◽  
Small Angle ◽  
Structure Factor ◽  
Structural Information ◽  
Small Angle Scattering ◽  
Fragmentation Model ◽  
Scattering Method ◽  
Power Law Decay ◽  
Angle Scattering ◽  
Polydisperse Structure

Using the small-angle scattering method, we calculate here the mono- and polydisperse structure factor from an idealized fragmentation model based on the concept of renormalization. The system consists of a large number of fractal microobjects which are randomly oriented and whose positions are uncorrelated. It is shown that, in the fractal region, the monodisperse form factor is characterized by a generalized power-law decay (i.e., a succession of maxima and minima superimposed on a simple power-law decay) and whose scattering exponent coincides with the fractal dimension of the scatterer. The present analysis of the scattering structure factor allows us to obtain the number of fragments resulted at a given iteration. The results could be used to obtain additional structural information about systems obtained through microscale fragmentation processes.

Structure and order in lamellar phases determined by small-angle scattering

2004 ◽  
Vol 37 (5) ◽  
pp. 703-710 ◽  
Author(s):  
Thomas Frühwirth ◽  
Gerhard Fritz ◽  
Norbert Freiberger ◽  
Otto Glatter
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Structure Factor ◽  
Scattering Length ◽  
Small Angle Scattering ◽  
Scattering Data ◽  
X Rays ◽  
Model Free ◽  
Angle Scattering

Multilamellar phases can be identified and characterized by small-angle scattering of X-rays (SAXS) or neutrons (SANS). Equidistant peaks are the typical signature and their spacing allows the fast determination of the repeat distance,i.e.the mean distance between the midplane of neighbouring bilayers. The scattering function can be described as the product of a structure factor and a form factor. The structure factor is related to the ordering of the bilayers and is responsible for the typical equidistant peaks, but it also contains information about the bilayer flexibility and the number of coherently scattering bilayers. The form factor depends on the thickness and the internal structure (scattering length density distribution) of a single bilayer. The recently developed generalized indirect Fourier transformation (GIFT) method is extended to such systems. This method allows the simultaneous determination of the structure factor and the form factor of the system, including the correction of instrumental broadening effects. A few-parameter model is used for the structure factor, while the determination of the form factor is completely model-free. The method has been tested successfully with simulated scattering data and by application to experimental data sets.

Small-angle scattering: the Guinier technique underestimates the size of hard globular particles due to the structure-factor effect

2015 ◽  
Vol 48 (4) ◽  
pp. 1089-1093 ◽  
Author(s):  
Alexander V. Smirnov ◽  
Ivan N. Deryabin ◽  
Boris A. Fedorov
Keyword(s):  
Small Angle ◽  
Structure Factor ◽  
Hard Spheres ◽  
Small Angle Scattering ◽  
Radius Of Gyration ◽  
Concentration Effects ◽  
Factor Effect ◽  
Calculated Correction ◽  
Angle Scattering ◽  
Guinier Plot

The straightforward calculation of small-angle scattering intensity by hard spheres at different concentrations is performed. For the same system of hard spheres, the scattering intensities were found both using the product of the form factor and the structure factor {based on the work of Kinning & Thomas [Macromolecules, (1984),17, 1712–1718]} and using the correlation function {based on the work of Kruglov [J. Appl. Cryst.(2005),38, 716–720] and Hansen [J. Appl. Cryst.(2011),44, 265–271;J. Appl. Cryst.(2012),45, 381–388]}. All three intensities are in agreement at every concentration. The values of the radii of gyration found from the Guinier plot are shown to be noticeably underestimated compared to the true radius of gyration of a single sphere. Presented are the calculated correction factors that should be applied to the experimentally found radius of gyration of spheres. Also, the concentration effects are shown to have an even greater impact on the radius of gyration of prolate particles that is found from the Guinier plot.

Small angle scattering study of silica gels and zeolites

1993 ◽  
Vol 03 (C8) ◽  
pp. C8-393-C8-396
Author(s):  
T. P.M. BEELEN ◽  
W. H. DOKTER ◽  
H. F. VAN GARDEREN ◽  
R. A. VAN SANTEN ◽  
E. PANTOS
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Silica Gels ◽  
Angle Scattering ◽  
Scattering Study
Sign in / Sign up

Export Citation Format

Share Document