6.8 Some Examples
Here we illustrate the strengths and pitfalls of EXAFS analysis with three chemical
examples of progressively greater complexity. We will see that a phase-shiftcorrected EXAFS Fourier transform can give an approximate radial distribution
function but that artefacts persist due to (a) “truncation effects,” (b) imperfect
background subtraction, (c) missing shells of atoms, and in some cases (d) strong
multiple-scattering contributions. We then show how curve-fitting analysis can
complement and supersede the Fourier transform interpretations.
6.8.1 Molybdate: MoO 4
22
The EXAFS Fourier transform for Na 2 MoO 4 (H 2 O) 2 was shown to illustrate data
processing in Fig. 6.17. It is also useful as one of the simplest possible cases for
EXAFS analysis. In this structure, there is approximate tetrahedral symmetry for four
O ligands around Mo at 1.77 Æ 0.02 Å [246], and indeed the phase-shift-corrected
Fourier transform (FT) gets this average distance almost exactly right. However, this
phase-shift-corrected k
3 FT is still not a perfect representation of the true radial
distribution function. For example, there are small side lobes symmetrically displaced
from the main peak, at ~1.48 and 2.00 Å. These peaks come from the termination of
the transform over a finite range—in the FT literature, they are called truncation
effects. These very small features persist out to 7 Å and beyond.
Another type of artefact is seen at very short distances, ~1.16 Å and even at 0 Å.
These low-frequency features come from an imperfect spline subtraction of the
atomic background, leading to small residuals at short distances in the FT. Finally,
the FT is missing any evidence for the Na ions in the 3.7 Å range. These ions have a
very large thermal motion and also static disorder. Combined with the relatively low
Z for Na, their EXAFS contribution becomes invisible. To summarize, the main peak
in an EXAFS Fourier transform can do a good job at representing the first coordination sphere, but the FT will also have some peaks that are not real, and some real
features will be missing.
6.8.2 MoS 2
Molybdenum disulfide, MoS 2 , is a highly symmetrical layered solid with each Mo
surrounded by a trigonal prismatic array of 6 S ions at 2.37 Å. In this layered
structure, each Mo is bridged through S to 6 Mo neighbors with a Mo–Mo distance
of 3.16 Å. The symmetry and relatively high Z for these neighbors lead to strong
Mo–S and Mo–Mo interactions in the EXAFS, with a clear beat pattern in the kspace data and 2 large peaks in the EXAFS Fourier transform (Fig. 6.18).
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6 X-ray Absorption and EXAFS
Here we illustrate the strengths and pitfalls of EXAFS analysis with three chemical
examples of progressively greater complexity. We will see that a phase-shiftcorrected EXAFS Fourier transform can give an approximate radial distribution
function but that artefacts persist due to (a) “truncation effects,” (b) imperfect
background subtraction, (c) missing shells of atoms, and in some cases (d) strong
multiple-scattering contributions. We then show how curve-fitting analysis can
complement and supersede the Fourier transform interpretations.
6.8.1 Molybdate: MoO 4
22
The EXAFS Fourier transform for Na 2 MoO 4 (H 2 O) 2 was shown to illustrate data
processing in Fig. 6.17. It is also useful as one of the simplest possible cases for
EXAFS analysis. In this structure, there is approximate tetrahedral symmetry for four
O ligands around Mo at 1.77 Æ 0.02 Å [246], and indeed the phase-shift-corrected
Fourier transform (FT) gets this average distance almost exactly right. However, this
phase-shift-corrected k
3 FT is still not a perfect representation of the true radial
distribution function. For example, there are small side lobes symmetrically displaced
from the main peak, at ~1.48 and 2.00 Å. These peaks come from the termination of
the transform over a finite range—in the FT literature, they are called truncation
effects. These very small features persist out to 7 Å and beyond.
Another type of artefact is seen at very short distances, ~1.16 Å and even at 0 Å.
These low-frequency features come from an imperfect spline subtraction of the
atomic background, leading to small residuals at short distances in the FT. Finally,
the FT is missing any evidence for the Na ions in the 3.7 Å range. These ions have a
very large thermal motion and also static disorder. Combined with the relatively low
Z for Na, their EXAFS contribution becomes invisible. To summarize, the main peak
in an EXAFS Fourier transform can do a good job at representing the first coordination sphere, but the FT will also have some peaks that are not real, and some real
features will be missing.
6.8.2 MoS 2
Molybdenum disulfide, MoS 2 , is a highly symmetrical layered solid with each Mo
surrounded by a trigonal prismatic array of 6 S ions at 2.37 Å. In this layered
structure, each Mo is bridged through S to 6 Mo neighbors with a Mo–Mo distance
of 3.16 Å. The symmetry and relatively high Z for these neighbors lead to strong
Mo–S and Mo–Mo interactions in the EXAFS, with a clear beat pattern in the kspace data and 2 large peaks in the EXAFS Fourier transform (Fig. 6.18).
158
6 X-ray Absorption and EXAFS