scholarly journals The atomic scattering factor for X-rays in the region of anomalous dispersion

1933 ◽  
Vol 139 (838) ◽  
pp. 459-466 ◽  
Keyword(s):  
Free Electron ◽  
Scattered Radiation ◽  
Wave Length ◽  
Anomalous Dispersion ◽  
X Rays ◽  
Characteristic Frequencies ◽  
X Ray ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

The atomic scattering factor ( f -factor) for X-rays is the ratio of the amplitude of the X-rays scattered by a given atom and that scattered according to the classical theory by one single free electron. It is given as a function of sin ϑ/λ, λ being the wave-length of the X-rays, 2ϑ the angle between the primary and the scattered radiation. It is assumed to be independent of the wave-length so long as sin ϑ/λ remains constant. Recently, however, it has been shown both theoretically and experimentally that the last assumption is no longer valid, when the scattered frequency is in the neighbourhood of one of the characteristic frequencies of the scattering element. The first to show the influence of the anomalous dispersion on the f factor were Mark and Szilard, who reflected strontium and bromine radiations by a rubidium bromide crystal. Theoretically the problem was dealt with by Coster, Knol and Prins in their investigation of the influence of the polarity of zincblende on the intensity of X-ray reflection and later on once more by Gloeker and Schäfer.

scholarly journals the atomic scattering power of iron for various X-ray wave-lengths

1932 ◽  
Vol 136 (829) ◽  
pp. 272-288 ◽  
Keyword(s):  
Energy Levels ◽  
Wave Length ◽  
X Rays ◽  
X Ray ◽  
Atomic Scattering Factor ◽  
Hard Radiation ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Dispersion Terms

Calculations of f , the atomic scattering factor of an element for X-rays, have hitherto been made on the assumption that the value of f for a given value of sin θ/λ is independent of wave-length. This assumption is only justified when the frequency of the X-rays is much greater than the characteristic frequency of any of the energy levels in the scattering atom. This condition is realised when a hard radiation such as Mo Kα is used in order to investigate crystals containing only light elements, such as aluminium. Under these conditions it has been found that absolute determination of f made experimentally give results in excellent agreement with theory. In many investigations, however, we are dealing with an entirely different set of conditions. For example, investigations of alloys are usually carried out with Cr, Fe or Cu radiation. Often the alloys contain Cr, Mn, Fe, Co, Ni, Cu or Zn, and the K absorption edge for each of these elements is near the wave-length of the radiation employed. Under these circumstances the conditions postulated by the simple theory no longer hold. Dispersion terms must now be introduced into the scattering formula, and we get an effect which may in some degree be compared with the anomalous dispersion of light.

scholarly journals On the reflection and refraction of X-Rays by perfect crystals

1933 ◽  
Vol 140 (841) ◽  
pp. 301-313 ◽  
Keyword(s):  
Point Of View ◽  
Theoretical Treatment ◽  
X Rays ◽  
X Ray ◽  
Reflection And Refraction ◽  
Atomic Scattering Factor ◽  
Mosaic Crystals ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
The Subject

It is now well established that from the point of view of the theory of X-ray reflection, the majority of crystals can be divided into those which are relatively perfect and those which are relatively imperfect or mosaic. The intensity of reflection of X-rays by the former has been much less extensively studied than by the latter and hitherto no really satisfactory agreement appears to have been found between the observed intensities of reflection from highly perfect crystals such as diamond and the results predicted by the theoretical treatment of the subject. It will be shown in what follows that this lack of agreement is very largely removed when the atomic scattering factor, f , which plays such an important part in the theory of reflection by mosaic crystals, is taken into account for perfect crystals.

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.

Bragg reflection and transmission of X-rays induced by the imaginary part of the atomic scattering factor

1995 ◽  
Vol 7 (42) ◽  
pp. 8089-8098 ◽  
Author(s):  
Xu Zhangcheng ◽  
Zhao Zongyan ◽  
Guo Changlin ◽  
Zhou Shengming ◽  
Tomoe Fukamachi ◽  
...  
Keyword(s):  
Imaginary Part ◽  
Bragg Reflection ◽  
X Rays ◽  
Reflection And Transmission ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

Anomalous x-ray atomic scattering factor for Zr, Nb, and Mo

1989 ◽  
Vol 40 (9) ◽  
pp. 5420-5421
Author(s):  
M. S. Wang ◽  
Sheau-Huey Chia
Keyword(s):  
X Ray ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

scholarly journals Calculation of The Imaginary Part of Atomic Form Factor For X-ray In Nickel

2019 ◽  
Vol 23 (10) ◽  
pp. 66
Author(s):  
Ahmed Raheem Ahmed ◽  
, Muhsin Hasan Ali
Keyword(s):  
Imaginary Part ◽  
High Energy ◽  
Approximate Methods ◽  
X Ray ◽  
X Ray Scattering ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Atomic Form Factor ◽  
Good Agreement

In the present study, we calculated the imaginary part of the x-ray scattering factor of nickel based on the principles of quantum mechanics to find a wave function that describes the electronic state of atoms by approximate methods, observed the study suggested that in both low energy values , and at high energy values , the imaginary part is approximately zero, this means that the electrons are intensely connected to the atom, where in the spectrum the photon energies are approximately equal to the electron bonding energy  we note the study pointed out that the imaginary part of the atomic scattering factor become  prominent and the electron becomes highly absorbent, the relative accuracy varies within range (0.03-0.22)%, and there was also a good agreement between the behavior we obtained for the imaginary part of the atomic scattering factor and the behavior that was calculated using other models.    http://dx.doi.org/10.25130/tjps.23.2018.171

6.—Electron Diffraction and Electron Mobility in Non-polar Crystals

1972 ◽  
Vol 70 ◽  
pp. 63-66
Author(s):  
W. Cochran
Keyword(s):  
Electron Diffraction ◽  
Conduction Band ◽  
Satisfactory Agreement ◽  
Electron Mobility ◽  
X Rays ◽  
Deformation Potential ◽  
Simple Manner ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

SynopsisIt is shown that the mobility of electrons in silicon or germanium can be estimated in a relatively simple manner. The scattering scross-section of a ’beam’ of electrons in the conduction band is evaluated in the same way as for a beam of X-rays or of slow neutrons which is scattered by phonons. It therefore involves the atomic scattering factor for electrons rather than the deformation potential introduced by Bardeen and Shockley. Predicted mobilities are in satisfactory agreement with observation.

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