As mentioned previously, scattering from an atom involves components in the real and complex planes. This becomes of particular importance when considering scattering at resonant edges, meaning where the energy of an x-ray photon is close to that for an absorption edge for a particular element. When x-rays are scattered near an atom’s absorption edge, the scattering can be described by adding two additional components for scattering in the real and imaginary planes, so the total form factor ftot(\(\lambda \),Q) is written as f tot(\(\lambda \),Q) = f (Q) + f ’(\(\lambda \)) + if ’’(\(\lambda \)). This effect of wavelength on scattering is usually called anomalous dispersion in chemical crystallography and resonant scattering in physics. I think that resonant scattering seems a much better term to use. The values of f ’ and f ’’ are normally quite small, but can reach an electron or two close to absorption edges, which means they are still not large, but do become experimentally significant.
In a resonant scattering experiment, one collects two datasets, one at a wavelength close to (but still somewhat below) an absorption edge for an element and another at a similar wavelength, but well away from an absorption edge. Since the only significant change between the two patterns will be the scattering from the element at this selected edge. This “tweaking” of the scattering for a particular element can be thought of as akin to the derivative of the diffraction pattern with respect to the element in question, but in GSAS-II one analyzes the data by fitting both datasets against a single model. Note that the values for f’ and f’’ and in particular the exact location of the absorption edge will be dependent on the chemical environment for the selected element, but 100 eV below the edge, the values are pretty much independent of the bonding details. Prior to synchrotrons, resonant scattering diffraction experiments were nearly impossible, now they are possible, but are still uncommon as few if any synchrotron diffraction beamlines are designed to change x-ray wavelengths easily.
In GSAS-II the values for f ’ and f ’’ are computed using the tabulation of D.T. Cromer and D. A. Liberman and are automatically computed for every appropriate element based on the supplied x-ray wavelength. The GSAS-II program Fprime (in the Calculate menu) shows the values computed with this tabulation as a function of x-ray wavelength. As noted, these values are only approximate near the edge, but where resonant scattering measurements are normally made, circa 100 eV below the resonant scattering edge, the values are largely not highly dependent on the species’ chemical environment and should be reasonable approximations. If greater accuracy is needed, when a resonant scattering experiment is done, one should consider collecting a wavelength-dependent fluorescence or absorption measurement. From this using a Kramers-Kronig inversion one can compute the f ’ and f ’’ curves for the specific material being studied as a function of wavelength. This would need to be done outside of GSAS-II.
A similar resonant scattering effect can also occur when neutron energies that match absorption edges for particular isotopes, but this is far less common and typically occurs at relatively high neutron energies that are seldom accessible in diffraction experiments, but there are a small number of elements that offer exceptions. GSAS-II uses tables computed by Lynn and Seeger to compute nuclear resonant scattering. The values generated from those tables can be also viewed in program PlotXNFF, as shown in Fig. 2.2. Nuclear resonant scattering is usually an issue only with the higher energy neutrons available at spallation sources, but that can pose a problem since some TOF instruments sum together data acquired over a wide of range of detector angles. This mixes together diffraction from different wavelengths making treatment of resonance in the form factor impossible.
