X-ray Absorption Edges (theory vs reality)

Theory isn't good enough - measure it yourself

The Cromer/Liberman theoretical values for scattering factors are not accurate for energies very near an absorption edge. Here the interaction of the scattering atom with its chemical neighbors complicates the scattering behaviour considerably. Shown below is a comparison of the theoretical values of f' and f" with the values determined experimentally for the Cu site in single crystal of a blue copper protein [Guss et al, 1989]. In both cases the f' values were derived from the corresponding f" spectra via the Kramers-Kronig equation.

Note in particular:

• The actual absorption edge is shifted relative to the idealized edge for an isolated Cu atom. The largest part of this shift is due to the oxidation state of the Cu atom in the protein.
• The local chemical environment introduces "ripples" (EXAFS) into the scattering spectrum.
• The maximum achievable f" is actually larger than the edge jump from theory. (The effect isn't very large in this particular example, but sometimes it is substantial).
• The maximum achievable |f'|, however, is smaller than the theoretical value. This is largely limited by the energy bandwidth of the x-ray source.

Breaking Friedel's Law