Phases anomalous scattering

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

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. 

SOLVE/RESOLVE is a program system that permits automation of all the steps between processed data and interpretation of phased maps. These include scaling of data measured at multiple wavelengths, location of anomalous scatterers. 

Fan, H. E, et al. (1990). Combining direct methods with isomorphous replacement or anomalous scattering data. VII. Ab initio phasing of one-wavelength anomalous scattering data from a small protein. Acta Crystallogr. A 46, 935-939. 

Fanchon, E. and Hendrickson, W. A. (1990). Effect of the anisotropy of anomalous scattering on the MAD phasing method. Acta Crystallogr. A 46, 809-820. 

The anomalous components of the total scattering are wavelength dependent and the use of radiation close to an absorption edge may increase or optimise the contribution due to the anomalously scattering atoms. Ramaseshan (1962) pointed out that data collected at multiple wavelengths optimising the anomalous dispersion effects would improve the quality of phase determination. 

The resulting increase in data quality is illustrated in Fig. 5, which shows a comparison of ADX and EDX data from the same sample of InSb. The quality achieved was such that more sophisticated techniques could be applied, such as the use of anomalous scattering to distinguish similarly-scattering elements, like In (Z = 49) and Sb (Z = 51) [164, 165]. And the combination of the high-resolu-tion 2D data and the GUI software made it possible to distinguish mixed phases simply from the difference in appearance of the diffraction rings [164, 245]. 

Fig. 146. Anomalous scattering in a non-centrosymmetrie crystal. Effect on -f and — reflections. Left representation of amplitudes and phases of waves. Right corresponding vector diagrams (scale of amplitudes doubled), a and b 002 and 002 reflections of structure of Fig. 145, when scattering is normal for both atoms, c and d the same reflections when scattering is anomalous for atom giving wave E.

Fig. 21S. Determination of the absolute configuration of a non-centrosymmetric structure by using anomalous scattering. Left—Scattering by anomalously scattering atom JP and by the rest of the molecule, E. Centre—Representation of amplitudes and phases ot waves. Right—Corresponding vector representation (scale of amplitudes doubled).

The determination of absolute configurations in these investigations was based on a qualitative use of the anomalous scattering effects—on simple observations of which of two opposite reflections, hkl or hkl, was the stronger. It is, however, possible in principle to make quantitative use of the differences between Fhkl and Fjm to determine phase angles directly. The difference between Fhkl and depends on the phase relations of the waves from the anomalously scattering atom and from the rest of the molecule when these two waves are nearly in phase,... 

Fig. 219. o. The difference between Fhkl and Fjfci is small when wave from the anomalously scattering atom and the rest of the molecule are nearly in phase, b. The difference is greater when the two components are at about 90° to each other. 

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