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 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 Recently, however, it has been shown both theoretically and experimentally that the last assumption is no longer valid, when the scattered frequency is in the neighbourhood of one of the characteristic frequencies of the scattering element.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 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 standing wave as a result of only the imaginary part of the atomic scattering factor

1999 ◽  
Vol 55 (2) ◽  
pp. 267-273 ◽  
Author(s):  
Riichirou Negishi ◽  
Tomoe Fukamachi ◽  
Takaaki Kawamura
Keyword(s):  
Standing Wave ◽  
Accurate Method ◽  
Anomalous Absorption ◽  
Acta Cryst ◽  
X Ray ◽  
The Real ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

The X-ray standing wave has been studied when the real part of the scattering factor is zero. In the symmetric Laue case, the phase of the standing wave advances by π when the deviation parameter W changes from −1 to 1, which is the same variation as in the usual symmetric Bragg case when only the real part of the scattering factor exists. However, the phase in the former case is different from that in the latter by \pi/2. By using the standing waves, the origins of the anomalous transmission and anomalous absorption effects reported by Fukamachi & Kawamura [Acta Cryst. (1993), A49, 384–388] have been analysed. The standing wave in the Laue case can give rise to a more accurate method of site determination of a specified impurity atom as well as a wider range of applications than a conventional standing-wave approach.

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

Effect of Dispersion and of Lattice Distortion on the Atomic Scattering Factor of Copper for X-Rays

Nature ◽  
1934 ◽  
Vol 134 (3396) ◽  
pp. 850-850
Author(s):  
G. W. BRINDLEY ◽  
F. W. SPIERS
Keyword(s):  
Lattice Distortion ◽  
X Rays ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

Solid-state effect on the anomalous x-ray atomic scattering factor

1988 ◽  
Vol 37 (8) ◽  
pp. 2968-2969 ◽  
Author(s):  
M. S. Wang ◽  
Sheau-Huey Chia
Keyword(s):  
Solid State ◽  
X Ray ◽  
Atomic Scattering Factor ◽  
State Effect ◽  
Atomic Scattering ◽  
Scattering Factor

scholarly journals Divergent-beam X-ray photography of crystals

1947 ◽  
Vol 240 (817) ◽  
pp. 219-250 ◽  
Keyword(s):  
Wave Length ◽  
Impurity Content ◽  
Type I ◽  
X Rays ◽  
Divergent Beam ◽  
X Ray ◽  
Air Temperatures ◽  
High Degree ◽  
Good Agreement

Divergent-beam X-ray photography of single crystals by transmission can be used to study the ‘extinction’, that is, the diminution of the transmitted radiation that takes place at the Bragg reflexion angles. The intensity and geometry of the absorption lines observed give useful information about the texture of the crystal. Divergent beam photographs have shown that many crystals of organic compounds are unexpectedly perfect, and that sudden cooling to liquid-air temperatures will increase the mosaic character of their structure by an important factor and make them more suitable for structural analysis by the usual methods. Type I diamonds, and natural ice even near to its melting-point, are also found to possess a high degree of perfection, which cannot be removed by liquid-air treatment. The divergent beam method may be used for the determination of orientation, but it is important that the wave-length of X-rays employed should be correctly related to the size and nature of the crystal. In certain favourable cases it is possible to make precision measurements of lattice constant or of wave-length from divergent beam photographs, without the use of any kind of precision apparatus. By such means it has been shown that the C—C distance in individual diamonds varies from 1541.53(± 0-02) to 1541.27X, (1.54465-1-54440A), a difference presumably due to varying impurity content. Using diamond and a brass anticathode, the Zn Ka 1 wave-length, relative to Cu K Ka 1 as 1537.40X, is found to be 1432.21 ( ± 0-04) X. Temperature control would improve the accuracy of this measurement, which is, however, in good agreement with the latest value obtained by orthodox precision methods.

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