Measurements of Absolute Concentration and Size Distribution of Particles by Laser Small Angle Scattering

1988 ◽  
pp. 549-558
Author(s):  
Shigeru Hayashi
Keyword(s):  
Size Distribution ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Absolute Concentration ◽  
Angle Scattering ◽  
Size Distribution Of Particles

Estimation and fingerprinting of the size distribution of non-interacting spherical particles from small-angle scattering data

2021 ◽  
Vol 54 (5) ◽  
Author(s):  
Debasis Sen ◽  
Ashwani Kumar ◽  
Avik Das ◽  
Jitendra Bahadur
Keyword(s):  
Size Distribution ◽  
Small Angle ◽  
Colloidal Particles ◽  
Nonlinear Least Squares ◽  
Small Angle Scattering ◽  
Spherical Particles ◽  
Scattering Data ◽  
Fitting Procedure ◽  
Angle Scattering ◽  
Log Normal

A new method to estimate the size distribution of non-interacting colloidal particles from small-angle scattering data is presented. The method demonstrates that the distribution can be efficiently retrieved through features of the scattering data when plotted in the Porod representation, thus avoiding the standard fitting procedure of nonlinear least squares. The present approach is elaborated using log-normal and Weibull distributions. The method can differentiate whether the distribution actually follows the functionality of either of these two distributions, unlike the standard fitting procedure which requires a prior assumption of the functionality of the distribution. After validation with various simulated scattering profiles, the formalism is used to estimate the size distribution from experimental small-angle X-ray scattering data from two different dilute dispersions of silica. At present the method is limited to monomodal distributions of dilute spherical particles only.

Small Angle Scattering from Nanocrystalline Pd

1988 ◽  
Vol 132 ◽  
Author(s):  
G. Wallner ◽  
E. Jorra ◽  
H. Franz ◽  
J. Peisl ◽  
R. Birringer ◽  
...  
Keyword(s):  
Crystallite Size ◽  
Size Distribution ◽  
Small Angle ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Spatial Arrangement ◽  
Small Angle Scattering ◽  
X Rays ◽  
Angle Scattering ◽  
Log Normal

ABSTRACTThe microstructure of nanocrystalline Pd was investigated by small angle scattering of neutrons and X-rays. The samples were prepared by compacting small crystallites produced by evaporation and condensation in an inert gas atmosphere. The strong scattering signal is interpreted to arise from crystallites embedded in a matrix of incoherent interfaces. Size distributions were deduced from the scattering curves. They consist of two parts: the crystallite size distribution dictated by the production process, and a structureless contribution due to the correlation in the spatial arrangement of the crystallites. The crystallite size distribution may be described by a log-normal distribution centred at R=2nm. The characteristic form of the correlation contribution arises from the dense packing of non-spherical crystallites. From the scattering cross-section in absolute units the volume fraction vc of crystallites was obtained as vc≈0.3, and the mean atomic density ρi in the interfaces as ρi≈0.52. The change of structural parameters during thermal annealing of the samples was studied. Up to high temperatures an appreciable volume fraction of crystallites with nearly unchanged size remains along with large particles.

Characterization of components of nano-energetics by small-angle scattering techniques

2007 ◽  
Vol 22 (7) ◽  
pp. 1907-1920 ◽  
Author(s):  
Joseph T. Mang ◽  
Rex P. Hjelm ◽  
Steven F. Son ◽  
Paul D. Peterson ◽  
Betty S. Jorgensen
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Small Angle ◽  
Particle Morphology ◽  
Small Angle Scattering ◽  
Nanoparticle Size ◽  
X Rays ◽  
Angle Scattering

Small-angle scattering (SAS) and ultra small-angle scattering techniques, employing x-rays and neutrons, were used to characterize six different aluminum nanopowders and nanopowders composed of molybdenum trioxide and tungsten trioxide nanoparticles. Each material has different primary particle morphology and aggregate and agglomerate geometry, and each is important to the development of nano-energetic materials. The combination of small-angle and ultra small-angle techniques allowed a wide range of length scales to be probed, providing a more complete characterization of the materials. For the aluminum-based materials, differences in the scattering of x-rays and neutrons from aluminum and aluminum oxide provided sensitivity to the metal core and metal oxide shell structure of the primary nanoparticles. Small-angle scattering was able to discriminate between particle size and shape and agglomerate and aggregate geometry, allowing analysis of both aspects of the structure. Using the results of these analyses and guided by scanning electron microscopy (SEM) images, physical models were developed, allowing for a quantitative determination of particle morphology, mean nanoparticle size, nanoparticle size distribution, surface layer thickness, and aggregate and agglomerate fractal dimension. Particle size distributions calculated using a maximum entropy algorithm or by assuming a log-normal particle size distribution function were comparable. Surface area and density determinations from the small-angle scattering measurements were comparable to those obtained from other, more commonly used analytical techniques: gas sorption using Brunauer–Emmett–Teller analysis, thermogravimetric analysis, and helium pycnometry. Particle size distribution functions derived from the SAS measurements agreed well with those obtained from SEM.

An iterative method to extract the size distribution of non-interacting polydisperse spherical particles from small-angle scattering data

2014 ◽  
Vol 47 (2) ◽  
pp. 712-718 ◽  
Author(s):  
D. Sen ◽  
Avik Das ◽  
S. Mazumder
Keyword(s):  
Iterative Method ◽  
Size Distribution ◽  
Small Angle ◽  
Real Space ◽  
Colloidal Dispersions ◽  
Small Angle Scattering ◽  
Spherical Particles ◽  
Scattering Data ◽  
X Ray Scattering ◽  
Angle Scattering

In this article, an iterative method for estimating the size distribution of non-interacting polydisperse spherical particles from small-angle scattering data is presented. It utilizes the iterative addition of relevant contributions to an instantaneous size distribution, as obtained from the fractional difference between the experimental data and the simulated profile. An inverse relation between scattering vector and real space is assumed. This method does not demand the consideration of any basis function set together with an imposed constraint such as a Lagrange multiplier, nor does it depend on the Titchmarsh transform. It is demonstrated that the method works quite well in extracting several forms of distribution. The robustness of the present method is examined through the successful retrieval of several forms of distribution, namely monomodal, bimodal, trimodal, triangular and bitriangular distributions. Finally, the method has also been employed to extract the particle size distribution from experimental small-angle X-ray scattering data obtained from colloidal dispersions of silica.

The effect of the shape function on small-angle scattering analysis by the maximum-entropy method

1994 ◽  
Vol 27 (5) ◽  
pp. 693-702 ◽  
Author(s):  
P. R. Jemian ◽  
A. J. Allen
Keyword(s):  
Maximum Entropy ◽  
Size Distribution ◽  
Small Angle ◽  
Shape Function ◽  
Small Angle Scattering ◽  
Entropy Method ◽  
Scattering Data ◽  
Shape Functions ◽  
Incident Wavelength ◽  
Angle Scattering

Analysis of small-angle scattering data to obtain a particle-size distribution is dependent upon the shape function used to model the scattering. From a maximum-entropy analysis of small-angle scattering data, the effect of shape-function selection on the obtained size distribution is demonstrated using three different shape functions to describe the same scattering data from each of two alloys. The alloys have been revealed by electron microscopy to contain a distribution of randomly oriented and mainly noninteracting irregular ellipsoidal precipitates. A comparison is made between the different forms of the shape function. The effect of an incident-wavelength distribution is also shown. The importance of testing appropriate shape functions and validating these against other microstructural studies is discussed.

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