On the determination of resonant curves in anomalous small-angle X-ray scattering

Data interpretation in anomalous small-angle X-ray scattering (ASAXS) relies on the atomic scattering factors of the resonant element near its X-ray absorption edge. The standard approach has been to use tabulated atomic scattering factors. However, these refer to free isolated atoms, while ASAXS typically probes condensed matter systems such as solids, liquids or soft matter. This discrepancy is addressed by measuring the X-ray absorption spectrum near the absorption edge and applying the Kramers–Kronig relations (Hilbert transform) to extract the atomic scattering factors of the resonant element. A related issue is the frequent occurrence of partially or fully negative resonant scattering curves, which is resolved by revisiting the assumptions of the data analysis. Two example experiments are presented to demonstrate our improved interpretation: ASAXS measurements of Xe physisorption in a nanoporous Si membrane near the Xe absorption edge, and the precipitation of magnetite/hematite in an Fe-doped soda-lime silicate glass.