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.

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 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.

Influence of neglected small-angle scattering in radial distribution function analysis

1971 ◽  
Vol 4 (4) ◽  
pp. 277-283 ◽  
Author(s):  
G. S. Cargill
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Small Angle ◽  
Function Analysis ◽  
Small Angle Scattering ◽  
Density Fluctuations ◽  
Atomic Density ◽  
X Ray ◽  
Angle Scattering

Materials containing inhomogeneities (density-fluctuations) of much greater than atomic size produce scattering at very small angles, which may go unobserved in many X-ray, electron, and neutron scattering experiments. For liquids and for amorphous and polycrystalline solids composed of one atomic species, an approximate expression for the reduced radial distribution function obtained from intensity measurements which neglect the small-angle scattering is shown to be Gexp(r) = 4πr{ρ(r) − ρ0[1 + (\overline {\eta^2}η2(ω)/ρ0 2)γ(ω, r)]} where ρ(r) is the atomic distribution function, ρ0 is the average atomic density, \overline {\eta^2}(ω) is the average square of atomic density fluctuations, γ(ω,r) is the density fluctuation correlation function, and ω is a volume element larger than the average atomic volume but smaller than the scale of long-range density fluctuations. This expression is also valid for systems composed of more than one type of atom where ρ(r) is a weighted average of pair distribution functions and [\overline {\eta^2}(ω)/ρ0 2]γ(ω,r) for X-ray scattering describes electron density fluctuations The neglect of small-angle scattering gives rise to a G exp(r) which appears, from its slope at small r, to correspond to a material of greater average atomic density ρ0,exp than that of the sample being studied. These results are illustrated by application to fluid argon (ρ0,exp/ρ0 = 1.17 near the critical point), to amorphous silicon (ρ0,exp/ρ0 = 1.13), and to phase separated PbO–B2O3 glasses (ρ0,exp/ρ0 = 1.07 for 24 wt. % PbO).

Sign in / Sign up

Export Citation Format

Share Document