scholarly journals Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

Open Physics ◽  
2014 ◽  
Vol 12 (5) ◽  
Author(s):  
Amélie Juhin ◽  
Christian Brouder ◽  
Frank Groot
Keyword(s):  
Inelastic Scattering ◽  
Cross Section ◽  
Electric Dipole ◽  
Electric Quadrupole ◽  
Absorption Process ◽  
X Ray ◽  
X Ray Scattering ◽  
Powder Samples ◽  
Sum Of Products ◽  
Scattered Beam

AbstractA spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit interference terms between electric dipole and quadrupole contributions when coupling each photon to itself. Some specific cases of the spherical tensor expansion are discussed. For example the case of isotropic samples is considered and the cross-section is expressed as a combination of only three fundamental spectra for the situation where electric dipole or electric quadrupole transitions in the absorption process are followed by electric dipole transitions in the emission. This situation includes the case of untextured powder samples, which corresponds to the most frequent situation met experimentally. Finally, it is predicted that some circular dichroism may be observed on isotropic samples provided that the circular polarization of the scattered beam can be detected.

The non-resonant magnetic X-ray scattering cross-section for photon energies up to 500 keV

1997 ◽  
Vol 40 (5) ◽  
pp. 569-574 ◽  
Author(s):  
J Strempfer ◽  
Th Brückel ◽  
D Hupfeld ◽  
J. R Schneider ◽  
K.-D Liss ◽  
...  
Keyword(s):  
Cross Section ◽  
Scattering Cross Section ◽  
X Ray ◽  
Scattering Cross ◽  
X Ray Scattering ◽  
Ray Scattering

Time-Resolved Small Angle X-Ray Scattering and Dynamic Light Scattering Studies of Sol-Gel Transition in Gelatin

1988 ◽  
Vol 143 ◽  
Author(s):  
Dan Q. Wu ◽  
Benjamin Chu
Keyword(s):  
Light Scattering ◽  
Cross Section ◽  
Sol Gel ◽  
Slow Mode ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
Saxs Intensity ◽  
Sol Gel Transition ◽  
Gel Transition

AbstractStructural and dynamical properties of an aqueous gelatin solution (5 wt%, 0.1M NaCi, pH=7) in a sol-gel transition were studied by time-resolved small angle x-ray scattering (SAXS) and dynamic light scattering (DLS) after quenching the gelatin sol at ∼45”C to 11°C. SAXS intensity measurements suggested the presence of gel fibrils which grew initially in cross-section. The average cross-section of the gel fibrils reached a constant value after an initial growth period of ∼800 sec. Further increase in SAXS intensity could be attributed to the increase in the length of the gel fibrils. Photon correlation, on the other hand, clearly showed two relaxation modes in both the sol and the gel (∼1 hr after the quenching process) states: a fast cooperative diffusion mode which remained constant from the sol to the gel state after correction for the temperature dependence of solvent viscosity; and a slow mode that could be attributed to the self-diffusion of the “free” gelatin chains and aggregates. The slow mode contribution to the time correlation function was reduced from ∼40% in sol to ∼20% in gel signaling a decrease but not the elimination of “free” particles in the gel network. The decrease in the intensity contribution by the slow mode is, however, accompanied by a large increase in the characteristic line-width distribution.

scholarly journals Pore shape and sorption behaviour in mesoporous ordered silica films

2016 ◽  
Vol 49 (5) ◽  
pp. 1713-1720 ◽  
Author(s):  
Gerhard Fritz-Popovski ◽  
Roland Morak ◽  
Parvin Sharifi ◽  
Heinz Amenitsch ◽  
Oskar Paris
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Grazing Incidence ◽  
Dip Coating ◽  
Silica Films ◽  
Elliptical Cross ◽  
Sorption Behaviour ◽  
X Ray ◽  
Pluronic P123 ◽  
X Ray Scattering

Mesoporous silica films templated by pluronic P123 were prepared using spin and dip coating. The ordered cylindrical structure within the films deforms due to shrinkage during calcination. Grazing-incidence small-angle X-ray scattering (GISAXS) measurements reveal that both the unit cell and the cross section of the pores decrease in size, mainly normal to the surface of the substrate, leading to elliptical cross sections of the pores with axis ratios of about 1:2. Water take-up by the pores upon changing the relative humidity can be monitored quantitatively by the shift in the critical angle of X-ray reflection as seen by the Yoneda peak.

scholarly journals Resonant x-ray scattering study of magnetic-dipole and electric-quadrupole order inU0.75Np0.25O2

2004 ◽  
Vol 70 (21) ◽  
Author(s):  
S. B. Wilkins ◽  
J. A. Paixão ◽  
R. Caciuffo ◽  
P. Javorsky ◽  
F. Wastin ◽  
...  
Keyword(s):  
Magnetic Dipole ◽  
Electric Quadrupole ◽  
X Ray ◽  
X Ray Scattering ◽  
Scattering Study ◽  
Ray Scattering

FiXR: a framework to reconstruct fiber cross-sections from X-ray fiber diffraction experiments

2020 ◽  
Vol 76 (2) ◽  
pp. 102-117
Author(s):  
Biel Roig-Solvas ◽  
Dana H. Brooks ◽  
Lee Makowski
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Amyloid Β ◽  
Diffraction Theory ◽  
Saxs Data ◽  
Molecular Conformations ◽  
X Ray ◽  
X Ray Scattering ◽  
Reconstruction Methods ◽  
Optimization Heuristics

Ab initio reconstruction methods have revolutionized the capabilities of small-angle X-ray scattering (SAXS), allowing the data-driven discovery of previously unknown molecular conformations, exploiting optimization heuristics and assumptions behind the composition of globular molecules. While these methods have been successful for the analysis of small particles, their impact on fibrillar assemblies has been more limited. The micrometre-range size of these assemblies and the complex interaction of their periodicities in their scattering profiles indicate that the discovery of fibril structures from SAXS measurements requires novel approaches beyond extending existing tools for molecular discovery. In this work, it is proposed to use SAXS measurements, together with diffraction theory, to infer the electron distribution of the average cross-section of a fiber. This cross-section is modeled as a discrete electron density with continuous support, allowing representations beyond binary distributions. Additional constraints, such as non-negativity or smoothness/connectedness, can also be added to the framework. The proposed approach is tested using simulated SAXS data from amyloid β fibril models and using measured data of Tobacco mosaic virus from SAXS experiments, recovering the geometry and density of the cross-sections in all cases. The approach is further tested by analyzing SAXS data from different amyloid β fibril assemblies, with results that are in agreement with previously proposed models from cryo-EM measurements. The limitations of the proposed method, together with an analysis of the robustness of the method and the combination with different experimental sources, are also discussed.

Temperature dependence of the thermal diffuse X-ray scattering from sodium single crystals

1990 ◽  
Vol 68 (11) ◽  
pp. 1279-1290
Author(s):  
W. Mayr ◽  
G. Fritsch ◽  
E. Lüscher
Keyword(s):  
Temperature Dependence ◽  
Single Crystals ◽  
Cross Section ◽  
Reciprocal Lattice ◽  
Scattering Cross Section ◽  
X Ray ◽  
Scattering Cross ◽  
X Ray Scattering ◽  
Thermal Diffuse ◽  
Ray Scattering

We report on experimental results for the thermal diffuse X-ray-scattering cross section from Na single crystals. Data are presented for the [100], [110], and [111] directions taken in the temperature range from 38 K to the melting point. In addition we present a numerical calculation of the harmonic diffuse-scattering cross section including all orders of multiphonon contributions using a realistic phonon-dispersion relation. The results of this model are compared with a simpler approximation for the higher order multiphonon terms. The differences between the calculations and the experimental data show a distinct asymmetrical behaviour with respect to the reciprocal lattice points. Owing to this fact and their temperature dependence they can be related to anharmonic scattering. The contributions of the four lowest order terms are derived from the data. The lowest order antisymmetric contribution agrees quite well with available theoretical calculations.

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