Scattering anomalous dispersion effects

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. 

Our IBM 7040 least-squares programme was modified to cope with this situation. After several cycles of refinement of the gold atomic parameter, a c-axis difference electron-density projection was computed. On the resulting map it WM possible to locate the fluorine atoms there are only two independent fluorines, one in the general position x, y, z), 12(c), and the other in the special position (J, 0, 0), 6(o). Structure factors were calculated by use of the scattering factors of the International Tables for Au and F, that for gold being corrected for the real part of the anomalous dispersion effect B was taken as 2-0 A. ... 

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... 

The anomalous dispersion effect is associated with the ejection of photoelectrons from inner shell electrons in an atom. The normal scattering describes the interaction of all the electrons in the atom with the X-ray beam. The radial distribution of the electrons in an atom can be calculated using quantum mechanics, originally by Hartree s self-consistent field method (Hartree 1933). In figure 9.12 this distribution is given for rubidium, which has a K edge at 0.8155 A the mean radius for... 

In recent papers we have shown that small-angle X-ray scattering (SAXS) is a highly suitable method to investigate stiff-chain polyelectrolytes [71]. In particular, it has been demonstrated there that the effect of anomalous dispersion [72] can be applied to discern the contribution of the counterions to the measured scattering intensity I(q). Here the main points of this analysis that is based on earlier work by small-angle neutron scattering (SANS [73-76]) and by SAXS [77, 78] are presented and discussed. 

Strictly, the scattering factors / tabulated in Appendix 12 apply only when the scattered radiation has a wavelength much shorter than that of an absorption edge of the scattering atom. When these two wavelengths are nearly the same, a small correction to /must be applied in precise work. An example is given in Sec. 13-4. Ordinarily we neglect this effect, called anomalous dispersion. 

In the past 10 years, anomalous dispersion (AD) effects have been used more and more frequently to solve the phase problem. All elements display an AD effect in x-ray diffraction. However, the elements in the first and second row of the periodic table, for example, C, N, O, and so on, have negligible AD effects. For heavier elements, especially when the x-ray wavelength approaches an atomic absorption edge of the element, these AD effects can be very large. The scattering power of an atom exhibiting AD effects is... 

Because of the effects of anomalous dispersion for certain electrons (Section 3.2.2), the scattering power is only approximately given by the electron density function p(r). Equation (3.20) is still correct if p(r) is replaced by a complex function that describes the distribution of scattering power. 

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