One term used in scattering theory is the scattering contrast, which refers to the difference in electron density between different phases within the sample. The contrast, however, is dependent on energy with a correction factor necessary when using energies near x-ray absorption edges of elements within the sample.
By using the energy corrected scattering factor we would obtain a scattered intensity of the form:
Thus, the scattering pattern has three components,
the normal SAXS signal,
the scattering cross term,
and the resonant scattering term.
One can now see that it is necessary to have a minimum of three scattering patterns, obtained at three different energies, to deconvolute the scattering patterns into their constituent partial scattering functions. It is usual for the three energies to be selected below the absorption edge to avoid the influence of fluorescence on the scattering patterns.
The diagram to the left shows the change in f ′ and f ′′ with increasing energy. One can see from the diagram that f ′ and f ′′ are linked. f ′ and f ′′ can be obtained from each other by using the Kramers-Kronig relationship.
he L (2 keV) and K (18 keV) absorption edges are clearly visible. Due to the inability of low energy x-rays to penetrate solid-state samples it is necessary to conduct ASAXS at edges whose position is at higher energies.
Whilst conducting ASAXS it is important to note any chemical shift between the theoretical values given by Cromer and Liberman and the sample. This shift will have consequences on the values given for f ′ and f ′′ , especially at energies near the edge. Since the edge is very narrow (typically less than an electron volt) small errors in the edge position will have huge errors in the values of f ′ and f ′′. One feature which is not shown in the theoretical values for f ′′ in the diagram below, are the “wiggles” clearly visible above the edge in the experimental data. These wiggles are known as the extended x-ray absorption fine structure (EXAFS).
Taking the shift in edge position into account, it is possible to obtain corrected values for the scattering factors, f ′ and f ′′ . These corrected values can then be used in conjunction with the three scattering patterns obtained at associated energies, to obtain the normal scattering, cross scattering and resonant scattering patterns.
ASAXS - In Depth -Part 2 - creating a contrast
