Scattering power of atoms

When x-ray or electron diffraction methods are used to study the nature of the binding forces in a crystal, it is desirable to know the influence on the scattering power of atoms of those changes in the spatial distribution of electrons which are due to the interaction between the particles forming the crystal lattice. 

In a sense, a superconductor is an insulator that has been doped (contains random defects in the metal oxide lattice). Some of the defects observed via neutron diffraction experiments include metal site substitutions or vacancies, and oxygen vacancies or interstituals (atomic locations between normal atom positions). Neutron diffraction experiments have been an indispensable tool for probing the presence of vacancies, substitutions, or interstituals because of the approximately equal scattering power of all atoms. 

CuZn would be expected, because the scattering powers of the two atoms for slow electrons in the lattice are probably considerably different, even though the scattering powers for fast electrons and for x-rays are very nearly the same. 

The reliability factor B was 0276 after the first refinement and 0-211 after the fourth refinement. The parameters from the third and fourth refinements differed very little from one another. The final values are given in Table 1. As large systematic errors were introduced in the refinement process by the unavoidable use of very poor atomic form factors, the probable errors in the parameters as obtained in the refinement were considered to be of questionable significance. For this reason they are not given in the table. The average error was, however, estimated to be 0-001 for the positional parameters and 5% for the compositional parameters. The scattering power of the two atoms of type A was given by the least-squares refinement as only 0-8 times that of aluminum (the fraction... 

This is the most useful quantitative intensity formula that may be derived from kinematical theory, since it is applicable to thin layers and mosaic blocks. We add up the scattering from each unit cell in the same way that we added up the scattering from each atom to obtain the stractme factor, or the scattering power of the unit cell. That is, we make allowance for the phase difference r, . Q between waves scattered from unit cells located at different vectors ri from the origin. Quantitatively, this results in an interference function J, describing the interference of waves scattered from all the unit cells in the crystal, where... 

X-ray diffraction studies yield radial distribution function data which are dominated by the much greater scattering power of the more electron-rich oxygen atoms in water. These diffraction results tell us something about... 

In the opposite sitnation, when the carbon is exposed to D O at RH=0.87 in association with a 1 1 (v/v) mixtnre of TH and TD (THD), a large difference is observed with respect to the case where the tolnene is fnlly deuterated (Fig. 6.4, curve 4). I. shows a substantial increase, to 0.11 cm , and the contrast factor also increases as a result of the replacement of deuterium atoms in the toluene (fep=H-0.66 X10 cm) by protons (b -0.37 x 10 cm). It is also noticeable that the accumulated intensity at the peak around 1.7 A is much weaker owing to the reduced scattering power of the TH molecules. 

Before this information can be used, the data set has to undergo some routine corrections, this process is known as data reduction. The Lorentz correction, L, relates to the geometry of the collection mode the polarization correction, p, allows for the fact that the nonpolarized X-ray beam, may become partly polarized on reflection, and an absorption correction is often applied to data, particularly for inorganic structures, because the heavier atoms absorb some of the X-ray beam, rather than just scatter it. Corrections can also be made for anomalous dispersion, which affects the scattering power of an atom when the wavelength of the incident X-ray is close to its absorption edge. These corrections are applied to the scattering factor, 4 of the atom. 

One slight disadvantage of neutron diffraction comes from the independence of scattering power of sin 0 (which is otherwise quite useful). Disregarding positional disorder, all nuclear density peaks are shaped by thermal vibration only and therefore contain no information about the nature of the atom (besides the trivial fact that the peak cannot be attributed to a nucleus of lower scattering cross section). 

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