Diffraction anomalous dispersion effects

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... 

Because part of the anomalous dispersion component is jt/2 out of phase with the isomorphous, real component, the net observable effect is a breakdown of Friedel s law regarding the perfect equality of the magnitudes of and If-h-k-i- That is, the two need not be absolutely equivalent but can demonstrate some slight difference A I anom = fhki — f-h-k-i- This difference will normally be imperceptible and within the expected statistical error of most X-ray diffraction intensity measurements, but with care in data collection, and judicious choice of X-ray wavelength, it can be measured and used to obtain phase information in conjunction with isomorphous replacement phase determination, or even independently, as described in Chapter 8. 

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... 

The X-ray intensity diffraction data of the given crystal do not allow one to specify which of the two sets describes the actual crystal structure and thus the absolute configuration of the molecule when there is no effect of anomalous X-ray dispersion. Under such conditions Friedel s law holds, which states that the X-ray intensity diffraction pattern of a crystal is centrosymmetric whether the crystal structure is centrosymmetric or not. This does not mean that a false crystal structure containing a center of symmetry is obtained as the solution of the structural problem, but rather that the X-ray analysis cannot differentiate between the two enantiomeric structures. A simple mathematical analogy is provided by the two possible square roots of a number Vj = x. 

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