Anomalous Scattering of Polarized X-Rays

1988 ◽  
Vol 143 ◽  
Author(s):  
David H. Templeton ◽  
Lieselotte K. Templeton
Keyword(s):  
Amorphous Materials ◽  
Incident Radiation ◽  
Single Element ◽  
Anomalous Scattering ◽  
X Rays ◽  
Single Chemical ◽  
Chemical States ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
X Ray Absorption

AbstractSome elements in some chemical states exhibit strong dichroism and birefringence near x-ray absorption edges. The atomic scattering factor is a complex tensor. This polarization anisotropy has profound effects on the transmission and scattering of x-rays even when the incident radiation is unpolarized. The linear polarization of synchrotron radiation makes it easier to study the effects and to use them for new methods of structure determination. Several of these anomalous scattering tensors have been measured by absorption spectroscopy and in diffraction experiments. New polarization terms enter the calculation of diffraction intensities, with interesting consequences. Reflections forbidden by a screw-axis rule are observed in sodium bromate near the Br K edge and permit direct observation of the structure factor phases of their second order reflections. This technique is a method of selective diffraction in which atoms of single element in a single chemical state contribute to the signal, and it can reveal their positions with precision. These effects can be a handicap for some applications of near-edge anomalous scattering in the study structures of crystals and amorphous materials.

scholarly journals Long-wavelength native-SAD phasing: opportunities and challenges

IUCrJ ◽  
2019 ◽  
Vol 6 (3) ◽  
pp. 373-386 ◽  
Author(s):  
Shibom Basu ◽  
Vincent Olieric ◽  
Filip Leonarski ◽  
Naohiro Matsugaki ◽  
Yoshiaki Kawano ◽  
...  
Keyword(s):  
Anomalous Scattering ◽  
X Rays ◽  
X Ray ◽  
Long Wavelength ◽  
Experimental Phasing ◽  
Sad Phasing ◽  
Anomalous Signal ◽  
Scattering Factor ◽  
X Ray Absorption

Native single-wavelength anomalous dispersion (SAD) is an attractive experimental phasing technique as it exploits weak anomalous signals from intrinsic light scatterers (Z < 20). The anomalous signal of sulfur in particular, is enhanced at long wavelengths, however the absorption of diffracted X-rays owing to the crystal, the sample support and air affects the recorded intensities. Thereby, the optimal measurable anomalous signals primarily depend on the counterplay of the absorption and the anomalous scattering factor at a given X-ray wavelength. Here, the benefit of using a wavelength of 2.7 over 1.9 Å is demonstrated for native-SAD phasing on a 266 kDa multiprotein-ligand tubulin complex (T2R-TTL) and is applied in the structure determination of an 86 kDa helicase Sen1 protein at beamline BL-1A of the KEK Photon Factory, Japan. Furthermore, X-ray absorption at long wavelengths was controlled by shaping a lysozyme crystal into spheres of defined thicknesses using a deep-UV laser, and a systematic comparison between wavelengths of 2.7 and 3.3 Å is reported for native SAD. The potential of laser-shaping technology and other challenges for an optimized native-SAD experiment at wavelengths >3 Å are discussed.

Determination of the anomalous scattering factors for Cu, Ni and Ti using the dispersion relation

1984 ◽  
Vol 17 (5) ◽  
pp. 344-351 ◽  
Author(s):  
J. J. Hoyt ◽  
D. de Fontaine ◽  
W. K. Warburton
Keyword(s):  
Dispersion Relation ◽  
Optical Theorem ◽  
Anomalous Scattering ◽  
X Ray ◽  
Atomic Scattering ◽  
Experimental Errors ◽  
Scattering Factor ◽  
Radiation Laboratory ◽  
X Ray Absorption

X-ray absorption spectra about the K edges of Ni, Cu and Ti have been measured at the Stanford Synchrotron Radiation Laboratory. The imaginary part of the atomic scattering factor f′′ was determined using the optical theorem and the real part f′ computed by the Kramers–Kronig dispersion relation. Methods for evaluating this integral as well as the effects on f′ of various experimental errors are investigated. The f′ results for Cu and Ni are compared to data from interferometry experiments.

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

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.

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.

Valence-contrast studies by resonant diffraction with synchrotron radiation; the rôle of X-ray absorption measurements

1992 ◽  
Vol 25 (5) ◽  
pp. 654-657 ◽  
Author(s):  
A. P. Wilkinson ◽  
A. K. Cheetham
Keyword(s):  
Optical Theorem ◽  
Anomalous Scattering ◽  
X Rays ◽  
Acta Cryst ◽  
X Ray ◽  
X Ray Absorption ◽  
Kronig Relation ◽  
Absorption Measurements ◽  
Good Agreement

The X-ray absorption spectra of GaCl2, GaAlCl4 and GaCl3 have been measured in the vicinity of the Ga K edge and values of f′′ and f′ estimated for GaI and GaIII from the latter two spectra by using the optical theorem and the Kramers–Kronig relation. The resulting f′ values are compared with those previously determined from anomalous-scattering measurements with synchrotron X-rays on the compound GaCl2 [Wilkinson, Cheetham & Cox (1991). Acta Cryst. B47, 155–161] and found to be in good agreement. The use of anomalous scattering methods for distinguishing oxidation states is discussed in the light of these results and others found in the literature.

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.

Determination of the Anomalous Scattering Factors in the Soft-X-ray Range using Diffraction from a Multilayer

1998 ◽  
Vol 31 (5) ◽  
pp. 700-707 ◽  
Author(s):  
L. Sève ◽  
J. M. Tonnerre ◽  
D. Raoux
Keyword(s):  
Fluorescence Yield ◽  
Bragg Diffraction ◽  
Anomalous Scattering ◽  
Total Electron Yield ◽  
Total Electron ◽  
X Ray ◽  
Scattering Factor ◽  
X Ray Absorption ◽  
Kronig Relation

Bragg diffraction from an Ag/Ni multilayer was used to determine independently both the real and imaginary parts of the anomalous scattering factor (ASF) around the NiLIIIandLIIedges in the soft-X-ray range. Huge resonant variations were observed with f'' reaching 55\,r_o and f' decreasing to −63 r_o at the NiLIIIedge. The independent measurements of f' and f'' are tested for coherency using the Kramers–Kronig relation. The f'' values are also compared with those derived from X-ray absorption methods such as total electron yield and fluorescence yield measurements.

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