How Is DAFS Data Analyzed?

The real and imaginary parts of the anomalous scattering factor for an atom or a crystal are related by a Kramers-Krönig dispersion relation

f'(E) equals (2/pi) times the principle part of the integral dE of (E f"(E)) / (E^2-E0^2)

Using the atomic form of f"(E) as a starting function, the intensity

I(E,Q) ~= | sum over sites f(E,Q) * exp(i Q.R) |^2

is compared to the data to extract a first guess for f"(E) for each reflection. A new f'(E) is then obtained using the Kramers-Krönig relation. This procedure is iterated [6] until a stable f"(E) is found for each reflection.

Each resonant crystallographic site contributes to the diffraction intensity differently at each reflection due to the exp(i Q.R) term, thus linear combinations of the f"(E) from different reflections are made to isolate contributions from the different sites.

 

In this way, an XAFS-like function for the Ti K edge can be extracted from the DAFS spectrum and analyzed quantitatively.

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Bruce Ravel

Last modified: Wed Feb 18 15:56:11 EST 1998