Scattering, anomalous

Now consider the effect of anomalous scattering on the relative intensities of the diffracted rays in Scheme 2a and b when atom Y scatters anomalously with an intrinsic phase lead A< >(Y), and atom W scatters normally. Under such circumstances, the wave scattered by atom Y in Scheme 2a would lead that of atom W by a phase difference of + A< >(Y), and the wave scattered by atom Y in Scheme 2b would lag behind that of atom W by - + A(Y). These two phase differences are unequal in magnitude, so the corresponding amplitudes of their resultant waves, and the subsequent intensities, will be different, leading to a breakdown of Friedel s law. 

Similar to an electromagnetic field (see Chapter 9), the total wavefield in the model described above can be represented as a sum of two parts, the incident p (background) field p r,w) and the scattered (anomalous) field p (r,cu),... 

If an atom absorbs X radiation in this way (even moderately), the result will be a phase change in the X rays scattered by that atom, relative to the X rays scattered by the other atoms in the structure (which do not scatter anomalously). This phase change is equivalent to a path length... 

Anomalous X-ray dispersion effects will cause intensity differences if the structure is noncentrosymmetric and contains an atom that scatters anomalously. Friedel s Law, which states that the X-ray diffraction pattern of a crystal is centrosymmetric even if the crystal structure is not, will not be obeyed. This means that, in the presence of anomalous dispersion effects, I hkl) If the structure is... 

Any reasonably heavy atom can serve as an anomalous scatterer if the appropriate wavelength of X rays is used. For neutrons, however, there are fewer atoms that scatter anomalously (for example, Li, B, Cd, Sm, Eu, Gd) and their high absorption may limit their use. If X-ray diffraction intensity data are sufficiently carefully measured, it is possible to determine absolute configurations even if there are no heavy atoms in the structure, although values of A/" are very small for the light elements. Results of determinations of absolute structure must come from laboratories with an excellent reputation for careful intensity measurement. For example, Hakon Hope has been able to assign absolute... 

Reciprocal lattices and therefore, diffraction patterns are generally centrosymmetric regardless of whether the corresponding direct lattices are centrosymmetric or not Thus, pairs of reflections with the opposite signs of indices, hkl) and hkl) -ihe so-called Friedel pairs - usually have equal intensity. Yet, they may be different in the presence of atoms that scatter anomalously (see section 2.11.4) and this phenomenon should be taken into account when multiplicity factors are evaluated comprehensively. Relevant details associated with the effects of anomalous scattering on the multiplicity factor will be considered below in section 2.12.2. 

The peaks marked H and H are not distinguishable in position and for regular scattering (anomalous scattering negligibly small) the Friedel law holds (Chapter 7), then / h (A ) = /r (Ai). As a consequence the measured intensity for the textured sample is ... 

Single crystal Laue diffiaction Enwgy-dispersive X-ray scattering Anomalous scattraing... 

A teclmique that employs principles similar to those of isomorphous replacement is multiple-wavelength anomalous diffraction (MAD) [27]. The expression for the atomic scattering factor in equation (B1.8.2h) is strictly accurate only if the x-ray wavelength is well away from any characteristic absorption edge of the element, in which case the atomic scattering factor is real and Filiki) = Fthkl V- Since the diffracted... 

Structure of the MoFe Protein. Extensive spectroscopic studies of the MoEe proteia, the appHcation of cluster extmsion techniques (84,151), x-ray anomalous scattering, and x-ray diffraction (10,135—137,152) have shown that the MoEe proteia contains two types of prosthetic groups, ie, protein-bound metal clusters, each of which contains about 50% of the Ee and content. Sixteen of the 30 Ee atoms and 14—16 of the 32—34... 

Because of anomalous scattering by H the results for the as-precipitated Ni(OH)2 could not be refined. Nevertheless, cell constants and the O-H bond distance could be determined. The results showed that the as-precipitated material was different from the well-crystallized material. The unit cell dimensions were aQ =3.119 and c0 =4.686 A. Also the... 

Hendrickson WA, Smith JL, Sheriff S. Direct phase determination based on anomalous scattering. Methods Enzymol 1985 115 44-55. 

According to anomalous small angle X-ray scattering (ASAXS), this compound slowly decomposes to release redispersible platinum nanoclusters with a mean diameter of 1.2 nm. The protective shell is formed on site by excess aluminium organics. 

Sehgal, A. and Seery, T.A.P., Anomalous dynamic light scattering from solutions of light absorbing polymers, Macromolecules, 32, 7807, 1999. 

P212121 Z = 4 D = 2.01 R = 0.04 for 1,611 intensities. The compound is a minor product in the synthesis of methyl tyveloside. The pyranose conformation is a distorted 4, with Q = 66 pm 6= 162° (p=H8a. The (methylthio)carbonyl side-chain is extended. The C-S bond-lengths are 174.8, 179.1 pm. The C-I bond-length is 215.2 pm. The absolute configuration was confirmed by using the anomalous-scattering factors of the iodine atoms. 

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