X-ray Scattering Factors of Ions in Crystals

1979 ◽  
Vol 34 (12) ◽  
pp. 1471-1481 ◽  
Author(s):  
P. C. Schmidt ◽  
Alarich Weiss
Keyword(s):  
Gaseous Phase ◽  
Form Factors ◽  
Negative Ions ◽  
X Rays ◽  
Charged Sphere ◽  
Sphere Model ◽  
X Ray ◽  
Hartree Fock ◽  
X Ray Scattering ◽  
Atomic Scattering

AbstractThe atomic scattering factors for X - Rays are given for the ions Li⊕, Be2⊕, B3⊕, C4⊕, N5⊕, N3⊖, O2⊖, F⊖, Na⊕, Mg2⊕, Al3⊕, S2⊖, Cl⊖, K⊕, Ca2⊕, Sc3⊕, Ti4⊕, V5⊕, Ni, Cu⊕, Zn2⊕, Ga3⊕, Se2⊖, Br⊖, Rb⊕, Sr2⊕, Y3⊕, Pd, Ag⊕, Cd2⊕, I⊖, Cs⊕, and Ba2⊕ in the crystal. The crystal potential is simulated by a hollow charged sphere (Watson sphere model). The Hartree-Fock-Roothaan-method was used for the calculation. The crystal field affects most strongly the atomic form factors of the negative ions, especially the twofold and threefold ionized negative ions, which are unstable in the gaseous phase.

X-ray scattering factors for O2− and N3−

1978 ◽  
Vol 34 (6) ◽  
pp. 994-999 ◽  
Author(s):  
K. Schwarz ◽  
H. Schulz
Keyword(s):  
Neutral Atom ◽  
Form Factors ◽  
Theoretical Models ◽  
Wave Functions ◽  
Radial Variation ◽  
Sphere Model ◽  
X Ray ◽  
X Ray Scattering ◽  
First Approximation ◽  
Ray Scattering

Form factors calculated from several theoretical models show that the Xα method is accurate to about 1%. With the latter scheme and the Watson-sphere model the atomic form factors for O2- and N3- are computed for varying sphere radii. To a first approximation this radial variation accounts for the different environments of such ions. Deviations of up to 25% in the scattering factors occur when compared with the results obtained from the wave functions of the corresponding neutral atom.

scholarly journals Coherent X-ray Scattering by Co III

1985 ◽  
Vol 38 (4) ◽  
pp. 609
Author(s):  
R Glass
Keyword(s):  
Ground State ◽  
Open Shell ◽  
Sufficient Accuracy ◽  
X Ray ◽  
Hartree Fock ◽  
X Ray Scattering ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
State Configuration

The atomic scattering factor for the ground state of the cobalt ion, 3d7 4F, has been evaluated using nonrelativistic and 'relativistic-corrected' wavefunctions of varying accuracy. The importance of incorporating all types of electron correlation systematically within the valence subshell while keeping a fixed argon core is discussed. From the results presented, it appears that atomic scattering factors evaluated using Hartree-Fock wavefunctions are of sufficient accuracy for an atomic ion with an open-shell ground-state configuration.

Mesoscopic structure of SiC fibers by neutron and x-ray scattering

1996 ◽  
Vol 11 (5) ◽  
pp. 1169-1178 ◽  
Author(s):  
Kentaro Suzuya ◽  
Michihiro Furusaka ◽  
Noboru Watanabe ◽  
Makoto Osawa ◽  
Kiyohito Okamura ◽  
...  
Keyword(s):  
Neutron Scattering ◽  
Volume Fraction ◽  
X Rays ◽  
X Ray ◽  
Sic Fibers ◽  
X Ray Scattering ◽  
Mesoscopic Structure ◽  
Angle Scattering ◽  
Momentum Transfer Range ◽  
First Time

Mesoscopic structures of SiC fibers produced from polycarbosilane by different methods were studied by diffraction and small-angle scattering of neutrons and x-rays. Microvoids of a size of 4–10 Å in diameter have been observed for the first time by neutron scattering in a medium momentum transfer range (Q = 0.1–1.0 Å−1). The size and the volume fraction of β–SiC particles were determined for fibers prepared at different heat-treatment temperatures. The results show that wide-angle neutron scattering measurements are especially useful for the study of the mesoscopic structure of multicomponent materials.

Resonant Inelastic X-ray Scattering at the ESRF: Hard and Soft X-rays

2012 ◽  
Vol 25 (4) ◽  
pp. 9-15 ◽  
Author(s):  
L. Braicovich ◽  
N. B. Brookes ◽  
G. Ghiringhelli ◽  
M. Minola ◽  
G. Monaco ◽  
...  
Keyword(s):  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

A multi-length-scale USAXS/SAXS facility: 10–50 keV small-angle X-ray scattering instrument

2013 ◽  
Vol 46 (5) ◽  
pp. 1508-1512 ◽  
Author(s):  
Byron Freelon ◽  
Kamlesh Suthar ◽  
Jan Ilavsky
Keyword(s):  
Small Angle ◽  
Soft Matter ◽  
High Energy ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Wide Range ◽  
And Performance ◽  
New Facility ◽  
Ray Scattering

Coupling small-angle X-ray scattering (SAXS) and ultra-small-angle X-ray scattering (USAXS) provides a powerful system of techniques for determining the structural organization of nanostructured materials that exhibit a wide range of characteristic length scales. A new facility that combines high-energy (HE) SAXS and USAXS has been developed at the Advanced Photon Source (APS). The application of X-rays across a range of energies, from 10 to 50 keV, offers opportunities to probe structural behavior at the nano- and microscale. An X-ray setup that can characterize both soft matter or hard matter and high-Zsamples in the solid or solution forms is described. Recent upgrades to the Sector 15ID beamline allow an extension of the X-ray energy range and improved beam intensity. The function and performance of the dedicated USAXS/HE-SAXS ChemMatCARS-APS facility is described.

scholarly journals Studying the x- ray atomic Scattering form Factor and Nuclear Magnetic Shielding Constant for Be atom in its Excited state (1s2 2s 3s) and the Be - like ions

2015 ◽  
Vol 12 (1) ◽  
pp. 204-209
Author(s):  
Baghdad Science Journal
Keyword(s):  
Form Factor ◽  
Excited State ◽  
Computer Software ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Electron Systems ◽  
X Ray ◽  
Hartree Fock ◽  
Atomic Scattering ◽  
Nuclear Magnetic

The division partitioning technique has been used to analyze the four electron systems into six-pairs electronic wave functions for ( for the Beryllium atom in its excited state (1s2 2s 3s ) and like ions ( B+1 ,C+2 ) using Hartree-Fock wave functions . The aim of this work is to study atomic scattering form factor f(s) for and nuclear magnetic shielding constant. The results are obtained numerically by using the computer software (Mathcad).

FitGISAXS: software package for modelling and analysis of GISAXS data using IGOR Pro

2010 ◽  
Vol 43 (4) ◽  
pp. 929-936 ◽  
Author(s):  
David Babonneau
Keyword(s):  
Software Package ◽  
Form Factors ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Scattering Data ◽  
Stratified Medium ◽  
X Ray ◽  
X Ray Scattering ◽  
Structure Factors ◽  
Scripting Language

A software package for performing modelling and analysis of GISAXS (grazing-incidence small-angle X-ray scattering) data within the distorted-wave Born approximation has been developed using the IGOR Pro scripting language (http://www.wavemetrics.com). The tool suite uses a slab-model approach with the Abélès matrix method to calculate X-ray reflectivity curves, electric field intensity distributions and GISAXS intensities from supported or buried scatterers arranged in two or three dimensions in a stratified medium. Models are included to calculate the scattered intensity for monodisperse, polydisperse and interacting particles with various size distributions, form factors and structure factors. The source code for the entire package is freely available, allowing anyone to develop additional tools.

X-Ray Determination of Site Occupation Parameters in Ordered Ternaries Cu(Aux.M1x.)M = Ni,Pd

1990 ◽  
Vol 213 ◽  
Author(s):  
R. Kumar ◽  
C. J. Sparks ◽  
T. Shiraishi ◽  
E.D. Specht ◽  
P. Zschack ◽  
...  
Keyword(s):  
Rietveld Method ◽  
Scattering Data ◽  
X Rays ◽  
X Ray ◽  
Site Occupation ◽  
Intensity Measurements ◽  
X Ray Scattering ◽  
Chemical Phase ◽  
Multiple Wavelengths ◽  
Scattering Factor

ABSTRACTX-ray scattering data obtained for multiple wavelengths with synchrotron radiation were analyzed by the Rietveld method to determine Ni and Pd distributions on the Cu(000) and Au(½½½) sites in the CuAuI tetragonal P4/mmm structure. Alloys of CuAuxM1-x containing 6 at. % Ni or 10 and 25 at. % Pd were processed to obtain maximum ordering. Nickel is predominantly found on the Cu site and most all the Pd is found on the Au site. The uncertainty in site occupation parameters is discussed for various contributions which affect powder intensity measurements. For highly absorbing materials, an observed powder roughness effect decreases the low angle (2θ) intensities relative to the high 2θ intensities. This effect reduces the reliability of the thermal parameters and obscures a proper description of the thermal motion of the two sublattices. Corrections to the X-ray intensity data for surface roughness/porosity effects reduce uncertainties to about ±1 at. % on the refined value of the site occupations. This use of variable wavelength X-rays with simultaneous refinement of the corresponding data is capable of distinguishing site occupations even between two elements of almost equal scattering factor as, for example, Cu and Ni atoms in this investigation. Chemical phase stability is related to the site occupation parameters.

X-Ray Diffraction

2021 ◽  
pp. 408-480
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Point Group ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Symmetry Point Group ◽  
X Ray ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Diffraction Patterns ◽  
Lattice Planes

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

A new high-resolution small-angle X-ray scattering apparatus using a fine-focus rotating anode, point-focusing collimation and a position-sensitive proportional counter

1984 ◽  
Vol 17 (5) ◽  
pp. 337-343 ◽  
Author(s):  
O. Yoda
Keyword(s):  
High Resolution ◽  
Small Angle ◽  
Proportional Counter ◽  
Anisotropic Scattering ◽  
Photon Flux ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Position Sensitive ◽  
Ray Scattering

A high-resolution small-angle X-ray scattering camera has been built, which has the following features. (i) The point collimation optics employed allows the scattering cross section of the sample to be directly measured without corrections for desmearing. (ii) A small-angle resolution better than 0.5 mrad is achieved with a camera length of 1.6 m. (iii) A high photon flux of 0.9 photons μs−1 is obtained on the sample with the rotating-anode X-ray generator operated at 40 kV–30 mA. (iv) Incident X-rays are monochromated by a bent quartz crystal, which makes the determination of the incident X-ray intensity simple and unambiguous. (v) By rotation of the position-sensitive proportional counter around the direct beam, anisotropic scattering patterns can be observed without adjusting the sample. Details of the design and performance are presented with some applications.

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