Resonant scattering (see §2.4), also called anomolous dispersion, is in my opinion an underutilized technique in powder diffraction. Part of the reason for this is that these experiments are hard to perform, as it is usually quite difficult to make wavelength changes at powder diffraction beamlines. This is not because wavelength changes are inherently difficult at synchrotrons. Spectroscopy beamlines routinely run scans of wavelengths. The difficulty is that no facility has designed an instrument that is dedicated to performing resonant scattering powder diffraction experiments. GSAS-II includes a program for computing the scattering factor curves for selected elements that is useful for planning resonant scattering measurements called Fprime. It is also useful for determining elements that would be problematic for a measurement at a particular x-ray wavelength. One always wants to avoid wavelengths that are slightly shorter than the edge, as this is where both absorption and fluorescence is most problematic.
Program Fprime. It uses the same computation method as GSAS-II does for estimation of \(f^\prime \) and \(f^{\prime \prime }\) values, which are taken from a compilation made in 1981 by D. T. Cromer and D. A. Liberman.. Note that these curves are approximate and the exact values will depend on the exact chemical environment of each atom. If the exact \(f^\prime \) and \(f^{\prime \prime }\) curves need to be known for some reason, one should perform a wavelength scan of absorption or fluorescence and then perform a Kramers-Kronig inversion, but resonant scattering experiments are typically performed 50-100 eV below the edge, where the \(f^\prime \) and \(f^{\prime \prime }\) values are not much affected by chemical shifts so the values from this program are accurate enough for these experiments.
To access program Fprime, use the Calculate/“Run Fprime” menu command. This will open a window that is somewhat similar to the initial window in program Absorb (Fig. 19.1.) The next step in use is to designate the element(s) that will be used in the computation. Use the Fprime/“New Element” menu command to add the elements that will be needed. After entering the menu command, a periodic table is shown. This window is exactly the same as the periodic table used in Absorb, shown in Fig. 19.2. Click on one or more elements in the table; note the color of the selected elements change as selected. Click on OK to close the periodic table window and return to the previous window for the Fprime program, which now lists the selected elements and their \(f^\prime \) and \(f^{\prime \prime }\) values at the default wavelength, as seen in Fig. 19.4. The wavelength dependence of the \(f^\prime \) and \(f^{\prime \prime }\) values, as well as the form factors, are plotted in the graphics window, as shown in Fig. 19.5. Note that the plot x-axes can be changed from the main Fprime window.
The wavelength/energy that is used to compute the \(f^\prime \) and \(f^{\prime \prime }\) values can be changed in several ways. On the main window, the slider can by dragged or a value can be typed into either box. Also, the value is shown as a black vertical line on the \(f^\prime \) and \(f^{\prime \prime }\) plot; this black line can be dragged. Fig. 19.6 shows the change to the main window and Fig. 19.7 shows the change to the plot after the energy has been changed close to the Zr absorption edge. If the wavelength were just below (the energy just above) the Zr absorption edge, the \(\mu \) value would be much higher. Note that due to the shift, relative to well away from the edge, the effective scattering power of Zr has been changed by a few electrons. This is not a large change, but the ability to measure both close to the edge and away from the edge would provide much greater sensitivity to Zr atom positions, if both datasets are used in a single refinement.
To close the Fprime window, use the Fprime/Quit manu command. This will also close the tab on the plot window.
