INTERFERENCE EFFECTS IN THE SMALL ANGLE SCATTERING OF X RAYS BY SMALL PARTICLES

1953 ◽  
Vol 31 (1) ◽  
pp. 40-48 ◽  
Author(s):  
G. E. Noakes ◽  
Elizabeth J. Allin
Keyword(s):  
Small Angle ◽  
Particle Distribution ◽  
Spherical Particles ◽  
Unique Determination ◽  
X Rays ◽  
Interference Effects ◽  
Uniform Size ◽  
Gold Colloids ◽  
Interference Maximum ◽  
Angle Scattering

Interparticle interference effects have been observed in the small angle X-ray-scattering from 30 samples prepared by the evaporation of gold colloids containing spherical particles of uniform size. The position of the interference maximum was found not to be the same for all samples containing particles of the same size. Calculation verifies that the position of this maximum is dependent on the radial distribution of the particles. It cannot be used for size determinations unless this distribution is known. The predicted variation of the slope at small angles of the In I vs. k2 curve with particle distribution was confirmed experimentally. This method of size determination is unsatisfactory whenever interference effects are present. It is suggested that size determinations based on the positions of the form function maxima are almost independent of particle distribution even in concentrated samples. A unique determination of the particle distribution from the position and shape of the interference maximum would appear to be impossible even if the size were known.

Small-angle scattering of polychromatic X-rays: effects of bandwidth, spectral shape and high harmonics

2018 ◽  
Vol 25 (2) ◽  
pp. 496-504 ◽  
Author(s):  
Sen Chen ◽  
Sheng-Nian Luo
Keyword(s):  
Small Angle ◽  
Spectral Shape ◽  
Spherical Particles ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
High Harmonics ◽  
Angle Scattering ◽  
Particle Size Determination ◽  
Photon Source

Polychromatic X-ray sources can be useful for photon-starved small-angle X-ray scattering given their high spectral fluxes. Their bandwidths, however, are 10–100 times larger than those using monochromators. To explore the feasibility, ideal scattering curves of homogeneous spherical particles for polychromatic X-rays are calculated and analyzed using the Guinier approach, maximum entropy and regularization methods. Monodisperse and polydisperse systems are explored. The influence of bandwidth and asymmetric spectra shape are exploredviaGaussian and half-Gaussian spectra. Synchrotron undulator spectra represented by two undulator sources of the Advanced Photon Source are examined as an example, as regards the influence of asymmetric harmonic shape, fundamental harmonic bandwidth and high harmonics. The effects of bandwidth, spectral shape and high harmonics on particle size determination are evaluated quantitatively.

Advanced Synchrotron Radiation and Neutron Scattering Techniques for Microstructural Characterization in Industrial Research

2017 ◽  
Vol 750 ◽  
pp. 53-66
Author(s):  
Fabrizio Fiori ◽  
Emmanuelle Girardin ◽  
Alessandra Giuliani ◽  
Adrian Manescu ◽  
Serena Mazzoni ◽  
...  
Keyword(s):  
Residual Stresses ◽  
Spatial Resolution ◽  
Small Angle ◽  
3D Imaging ◽  
Volume Fraction ◽  
Rapid Development ◽  
Small Angle Scattering ◽  
Bragg Diffraction ◽  
X Rays ◽  
Angle Scattering

The rapid development of new materials and their application in an extremely wide variety of research and technological fields has lead to the request of increasingly sophisticated characterization methods. In particular residual stress measurements by neutron diffraction, small angle scattering of X-rays and neutrons, as well as 3D imaging techniques with spatial resolution at the micron or even sub-micron scale, like micro-and nano-computerized tomography, have gained a great relevance in recent years.Residual stresses are autobalancing stresses existing in a free body not submitted to any external surface force. Several manufacturing processes, as well as thermal and mechanical treatments, leave residual stresses within the components. Bragg diffraction of X-rays and neutrons can be used to determine residual elastic strains (and then residual stresses by knowing the material elastic constants) in a non-destructive way. Small Angle Scattering of neutrons or X-rays, complementary to Transmission Electron Microscopy, allows the determination of structural features such as volume fraction, specific surface and size distribution of inhomogeneities embedded in a matrix, in a huge variety of materials of industrial interest. X-ray microtomography is similar to conventional Computed Tomography employed in Medicine, allowing 3D imaging of the investigated samples, but with a much higher spatial resolution, down to the sub-micron scale. Some examples of applications of the experimental techniques mentioned above are described and discussed.

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 of Neutrons and X-Rays

2015 ◽  
pp. 1-11
Author(s):  
Naveed A Nadvi ◽  
John YH Chow ◽  
Jill Trewhella
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
X Rays ◽  
Angle Scattering

scholarly journals Small Angle Scattering of X-Rays

1968 ◽  
Vol 8 (2) ◽  
pp. 72-80
Author(s):  
Masao KAKUDO
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
X Rays ◽  
Angle Scattering
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