Common mistakes in XAS manuscripts

Referring to the Magnitude of the Fourier transform as a radial structural function

The Fourier transform (FT) of the EXAFS data is sometimes referred to as a radial distribution/structural function (RDF). This a confusing over-simplification of the XAFS signal. Here is a list of some of the reasons why the magnitude of the FT of the EXAFS data is NOT a RDF.

  1. The peak position in the FT of the EXAFS data doesn’t correspond to the distance between the absorbing atom and it’s neighboring atoms as they do in a RDF. The shift of the peaks in the FT depends on both the absorbing atom and the neighboring atoms types. Therefore peaks corresponding to scattering paths from Fe atoms are shifted less than peaks corresponding to O atoms.
  2. Multiple scattering paths can correspond to strong signals in FT of the EXAFS data and are not part of a RDF.
  3. The interference between two scattering paths of the photo-electron may result in a minimum rather than a peak in the FT of the EXAFS data. This does not occur in a RDF.
  4. The amplitude of the peaks in the FT of the EXAFS data depends on photo-electron scattering factors as well as the radial distribution of atomic distances. An RDF does not depend on photo-electron scattering factors.

Referring to sigma2 as a Debye-Waller Factor

Strictly speaking, σ2 is not a Debye-Waller Factor. A Debye-Waller Factor is a term commonly used in diffraction to describe the attenuation of the scattered intensity due to the displacement of atoms away from a lattice point. For XAFS, the analogous Debye-Waller factor would describe the attenuation of χ(k) due to the thermal and static disorder in the bond length.

It would be reasonable to call $e{-2k2\sigma^2}$ the XAFS Debye-Waller factor. That misses a few subtleties in how the distribution of atoms at different bond lengths, including anharmonicity in the distribution of interatomic distances, but it does capture the same idea that disorder (such as from thermal motion of atoms) attenuates the measured signal.

It is common to refer to σ2 as the XAFS Debye-Waller factor, just as for diffraction it is common to refer to $\langle u2 \rangle$ as the Debye-Waller factor. More properly, the XAFS σ2 is the mean-square disorder in the distribution of interatomic distances, and the diffraction $\langle u2\rangle$ is the mean-square disorder in the distribution of atomic displacements from a lattice point.

Not reporting error bars

That seems like a fairly obvious mistake, but a remarkable number of manuscripts go out for review without proper consideration of uncertainties in the text, tables, and/or figures. The rule of thumb is simple -- it's not a measurement if there is no report of uncertainty.

But, let's be reasonable about this too: In general, and in casual conversations, implied uncertainties are OK (that is, I'll be there in 5 minutes does not imply that I will arrive in exactly 300,000 milliseconds).

For most scientific measurements, however, an implied uncertainty is not good enough, and error bars should be reported. Sometimes implied error bars are good enough, as in This XANES spectra is consistent with all Fe3+ . The implied error bar should probably be stated somewhere in the manuscript -- XANES spectral fitting is generally accurate only to 5% , but does not need to appear as This XANES spectra implies 98+/-3% Fe3+ . Similarly, if it turns out that all distances refined from EXAFS analysis are 0.01Å, it should be acceptable to state this once, as in a table caption.

Common_Mistakes (last edited 2009-10-09 19:50:56 by localhost)