The evaluation of the small-angle scattering of lamellar two-phase systems by means of interface distribution functions

1977 ◽  
Vol 255 (5) ◽  
pp. 417-427 ◽  
Author(s):  
W. Ruland
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Distribution Functions ◽  
Two Phase ◽  
Angle Scattering ◽  
Phase Systems

Multiphase approximation for small-angle scattering

2009 ◽  
Vol 43 (1) ◽  
pp. 8-11 ◽  
Author(s):  
Dragomir Tatchev
Keyword(s):  
Small Angle ◽  
Small Angle Scattering ◽  
Multiphase System ◽  
Contrast Variation ◽  
Two Phase ◽  
Angle Scattering ◽  
Multiphase Systems ◽  
Phase Systems ◽  
The Difference ◽  
Two Phases

The two-phase approximation in small-angle scattering is well known and is still the dominant approach to data analysis. The intensity scattered at small angles is proportional to the second power of the difference between the scattering densities of the two phases. Nevertheless, scattering contrast variation techniques are widely used, and they are obviously suitable for multiphase systems or systems with gradually varying scattering density, since if no parasitic scattering contributions are present the scattering contrast variation would only change a proportionality coefficient. It is shown here that the scattered intensity at small angles of a multiphase system can be represented as a sum of the scattering of two-phase systems and terms describing interference between all pairs of phases. Extracting two-phase scattering patterns from multiphase samples by contrast variation is possible. These two-phase patterns can be treated with the usual small-angle scattering formalism. The case of gradually varying scattering density is also discussed.

scholarly journals Small-Angle Scattering from Fractional Brownian Surfaces

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2042
Author(s):  
Eugen Mircea Anitas
Keyword(s):  
Small Angle ◽  
Structural Parameters ◽  
Small Angle Scattering ◽  
Distribution Functions ◽  
Advanced Materials ◽  
Two Phase ◽  
Amorphous Phases ◽  
Angle Scattering ◽  
Recent Developments ◽  
New Generation

Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in dilute particulate systems (e.g., colloids) or the interfaces in non-particulate two-phase systems (e.g., semicrystalline polymers with crystalline and amorphous phases). However, for such systems, a realistic simulation involves parameters averaged over a macroscopic volume. Here, a method based on small-angle scattering technique is proposed to extract the main structural parameters of surfaces/interfaces from experimental data. It involves the analysis of scattering intensities and the corresponding pair distance distribution functions. This allows the extraction of information with respect to the overall size, fractal dimension, Hurst and spectral exponents. The method is applied to several classes of fBs, and it is shown that the obtained numerical values of the structural parameters are in very good agreement with theoretical ones.

Interpretation of small-angle scattering data of inhomogeneous ellipsoids

2004 ◽  
Vol 37 (5) ◽  
pp. 815-822 ◽  
Author(s):  
Gerhard Fritz ◽  
Alexander Bergmann
Keyword(s):  
Cross Sections ◽  
Small Angle ◽  
Theoretical Calculations ◽  
Negative Contrast ◽  
Small Angle Scattering ◽  
Distribution Functions ◽  
Distance Distribution ◽  
Scattering Data ◽  
Elliptical Cross ◽  
Angle Scattering

Small-angle scattering data of inhomogeneous ellipsoidal particles are discussed in terms of their pair distance distribution functionsp(r). Special attention is given to the determination of core and shell thicknesses and axis ratios as well as to large distances within the particles, since cross terms between parts of positive and negative contrast within the particle can produce misleading results, similar to homogeneous particles or Janus particles. Cross-section pair distance distribution functionspc(r) of cylinders with elliptical cross sections show similar behaviour. Theoretical calculations are compared with small-angle X-ray and neutron scattering (SAXS and SANS) data of cetyltrimethylammonium bromide in aqueous KCl solutions.

scholarly journals Small-angle scattering from multiphase fractals

2014 ◽  
Vol 47 (1) ◽  
pp. 198-206 ◽  
Author(s):  
A. Yu. Cherny ◽  
E. M. Anitas ◽  
V. A. Osipov ◽  
A. I. Kuklin
Keyword(s):  
Power Law ◽  
Small Angle ◽  
Small Angle Scattering ◽  
Variation Method ◽  
Multiphase System ◽  
Model Parameters ◽  
Contrast Variation ◽  
Crossover Point ◽  
Two Phase ◽  
Angle Scattering

Small-angle scattering (SAS) intensities observed experimentally are often characterized by the presence of successive power-law regimes with various scattering exponents whose values vary from −4 to −1. This usually indicates multiple fractal structures of the sample characterized by different size scales. The existing models explaining the crossover positions (that is, the points where the power-law scattering exponent changes) involve only one contrast parameter, which depends solely on the ratio of the fractal sizes. Here, a model that describes SAS from a multiphase system with a few contrast parameters is described, and it is shown that the crossover position depends on the scattering length density of each phase. The Stuhrmann contrast variation method is generalized and applied to experimental curves in the vicinity of the crossover point beyond the Guinier region. The contrast variation is applied not to the intensity itself but to the model parameters, which can be found by fitting the experimental data with the suggested interpolation formula. The model supplements the existing two-phase models and gives the simple condition of their inapplicability: if the crossover point depends on the contrast then a two-phase model is not relevant. The developed analysis allows one to answer the qualitative question of whether one fractal `absorbs' another one or they are both immersed in a surrounding homogeneous medium like a solvent or solid matrix. The models can be applied to experimental SAS data where the absolute value of the scattering exponent of the first power-law regime is higher than that of the subsequent second power-law regime, that is, the scattering curve is `convex' near the crossover point. As is shown, the crossover position can be very sensitive to contrast variation, which influences significantly the length of the fractal range.

Struktur von Aluminium-Indium-Schmelzen mittels Röntgen-Weitwinkelbeugung

1975 ◽  
Vol 30 (6-7) ◽  
pp. 771-774 ◽  
Author(s):  
Jochen Hoehler ◽  
Siegfried Steeb
Keyword(s):  
Radial Distribution ◽  
Small Angle ◽  
Radiation Intensity ◽  
Small Angle Scattering ◽  
Distribution Functions ◽  
Subsequent Paper ◽  
Radial Distribution Functions ◽  
Angle Scattering ◽  
Nearest Neighbours ◽  
Concentration Dependency

Abstract Structure By transmission of Mo-Kα-radiation, intensity curves were obtained from molten Al and molten In as well as from Al-In alloys containing 10, 20, 30, 40, 70, 80, 90, and 95.3 a/o Al. Radial distribution functions were calculated from these experimental curves. From the RDF's the con-centration dependency of the number NI and the distance rI of nearest neighbours was obtained. The concentration dependency of nearest neighbours reveals the segregation tendency of molten Al-In alloys. The small angle scattering observed in the intensity curves is in agreement with this result and will be treated in a subsequent paper.

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