Determination of volume fraction and size distribution by use of a stochastical model from small-angle scattering

1997 ◽  
Author(s):  
Wilfried Gille
1988 ◽  
Vol 132 ◽  
Author(s):  
G. Wallner ◽  
E. Jorra ◽  
H. Franz ◽  
J. Peisl ◽  
R. Birringer ◽  
...  

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.


2006 ◽  
Vol 39 (5) ◽  
pp. 676-682 ◽  
Author(s):  
M. Paskevicius ◽  
C. E. Buckley

The characterization of hydrogen defects in an aluminium–hydrogen system was performed previously [Buckleyet al.(2001).J. Appl. Cryst.34, 119–129] using small-angle scattering, inelastic neutron scattering and electron microscopy techniques. This analysis resulted in the determination of the relative change in lattice parameter as a result of hydrogen introduction into the Al matrix. However, this method relied on the average volume of the bubbles of hydrogen and also the pressure in a bubble of average volume. The characterization of the Al–H system has been improved by considering the size polydispersity of the hydrogen bubbles. The determination of a volume-fraction size distribution of the bubbles from small-angle scattering data has allowed a polydispersity analysis to be undertaken. A size-dependent contrast has been utilized in the modification of the volume-fraction size distribution into a more accurate form that accounts for varying concentrations of hydrogen within bubbles of different sizes. The determination of the size-dependent contrast is based upon an equation of state for molecular hydrogen which incorporates the compressibility of hydrogen under high pressures. The formation of alane (AlH3) is also investigated, as it can be formed by the chemisorption of hydrogen in aluminium under high pressures. The polydispersity analysis has allowed a more accurate description of the Al–H system and can be applied to similar scattering systems where the scattering length density is not constant over the whole scattering size regime.


2017 ◽  
Vol 73 (9) ◽  
pp. 710-728 ◽  
Author(s):  
Jill Trewhella ◽  
Anthony P. Duff ◽  
Dominique Durand ◽  
Frank Gabel ◽  
J. Mitchell Guss ◽  
...  

In 2012, preliminary guidelines were published addressing sample quality, data acquisition and reduction, presentation of scattering data and validation, and modelling for biomolecular small-angle scattering (SAS) experiments. Biomolecular SAS has since continued to grow and authors have increasingly adopted the preliminary guidelines. In parallel, integrative/hybrid determination of biomolecular structures is a rapidly growing field that is expanding the scope of structural biology. For SAS to contribute maximally to this field, it is essential to ensure open access to the information required for evaluation of the quality of SAS samples and data, as well as the validity of SAS-based structural models. To this end, the preliminary guidelines for data presentation in a publication are reviewed and updated, and the deposition of data and associated models in a public archive is recommended. These guidelines and recommendations have been prepared in consultation with the members of the International Union of Crystallography (IUCr) Small-Angle Scattering and Journals Commissions, the Worldwide Protein Data Bank (wwPDB) Small-Angle Scattering Validation Task Force and additional experts in the field.


2017 ◽  
Vol 750 ◽  
pp. 53-66
Author(s):  
Fabrizio Fiori ◽  
Emmanuelle Girardin ◽  
Alessandra Giuliani ◽  
Adrian Manescu ◽  
Serena Mazzoni ◽  
...  

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.


2021 ◽  
Vol 54 (5) ◽  
Author(s):  
Debasis Sen ◽  
Ashwani Kumar ◽  
Avik Das ◽  
Jitendra Bahadur

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.


Sign in / Sign up

Export Citation Format

Share Document