XAFS
techniques
The prevailing rule
of an x-ray absorption spectrum is the monotonic dependence of the x-ray
absorption with the photon energy, interspersed with sharp edges (Fig.
4). However, the detailed shape of the edge and of the x-ray absorption
spectrum above it contains useful structural information. In the dominant
absorption process of photoeffect, an electron is ejected from the core,
mostly from the deepest level accessible to the photon energy. The photoelectron
is emitted in the form of a simple spherical wave when the atom is free,
i.e. in a monatomic gas sample. If the atom is incorporated in dense
matter, or even in a molecule, the outgoing wave and, consequently,
the probability of the photoeffect, is modified by the surroundings.
The problem of calculating the outgoing waves in the strong field of
adjacent atoms in a solid or liquid sample is notoriously difficult:
it has to be tackled in full for slow photoelectrons, i.e. when the
incident photon energy is just above the threshold. This region of the
absorption spectrum, so called XANES ( = X-ray Absorption Near-Edge
Structure) contains valuable information on chemical bonds and the site
symmetry [5,6].
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Fig.
4. X-ray absorption coefficient of copper in the
region of L and K edges. The box area is expanded in the inset
to show EXAFS and XANES signal. |
Further out from
the absorption edge, in the EXAFS ( = Extended X-ray Absorption Fine
Structure) spectral region, the problem of the photoelectron wave is
considerably simplified [6,7]. With the shorter
photoelectron wavelength, the adjacent atoms scatter the photoelectron
as point obstacles, each contributing a tiny wavelet (Fig. 5). The interference
pattern of the photoelectron wavelets modifies the probability of the
photoeffect. When the absorption spectrum is scanned by changing the
photon energy, the energy of the photoelectron changes. Consequently,
its wavelength varies, and the interference of the wavelets changes
from constructive to destructive and back again. Each atom scatterer
contributes a harmonic oscillatory mode, together they form a complex
quasiperiodic EXAFS signal: Fourier analysis of the signal resolves
the harmonic components into a probability vs distance diagram (Figs.
6, 7). Its peaks occur at rather accurate values of the neighbor atom
distances. In addition, the coordination number and chemical species
of the neighbor atoms, as well as the statistical spread of their distances
due thermal motion or static disorder can be deduced from the size and
shape of the peaks.
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Fig.
5. Interference of photoelectron waves scattered
from neighbor atoms and the resulting oscillation in x-ray photoabsorption
probability. |
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Fig.
6. EXAFS signal of rhodium metal at 80 K above the
K-edge (a) and its Fourier transform magnitude (b). |
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Fig.
7. The contributions of the nearest four shells of
neighbors to the Rh EXAFS signal from Fig 6, recovered from the
largest peaks in the Fourier transform. |
The basic EXAFS
experimental method is the standard absorption spectrometry of a thin
homogeneous sample of the investigated material above the absorption
edge of the element under study. Optimum thickness of the sample is
of the order of 10 microns for pure elements (metal foils) and accordingly
larger when other (lighter) elements are present. Powdered samples are
conveniently attached to layers of adhesive tape or mixed with a light
matrix and pressed into thin pellets. The sample must be at least locally
homogeneous: if not, the unavoidable small deviations of the x-ray beam
position on the sample are translated into spurious intensity variations
mimicking the EXAFS signal.
The sensitivity of the basic EXAFS experiment is not very high: the
measured element must contribute at least a few percent to the beam
absorption to produce a meaningful structural signal. Weaker signals
tend to be drowned in the statistical noise of the beam. In an alternative
method the fluorescence photons from the sample are monitored instead
of the transmitted beam, whereby the sensitivity is improved by one
or two orders of magnitude. In TEY ( = Total Electron Yield) detection
mode the emitted electrons from the sample are registered [8].
Another order of magnitude may be gained in sensitivity; the smaller
penetration
depth of the electrons, however, limits the sensitivity to a thin layer
at the surface of the sample. A good surface sensitivity is provided
also by measuring the intensity of the totally reflected x-ray beam:
the method requires a perfectly flat surface, though, which precludes
it for routine analysis [9]. A
specific variant of EXAFS, x-ray magnetic circular dichroism (XMCD)
has been developed for investigation of magnetic
materials [10,11].
The scan of a standard EXAFS spectrum requires about 20 minutes on a
synchrotron beamline – and several hours on a conventional laboratory
x-ray generator. On modern synchrotron x-ray sources with high brilliance
much faster detection modes have been developed for studying chemical
reactions in real time (Quick EXAFS = QEXAFS 12). Currently, 100 ms
for a scan is available, with a promise of a hundredfold improvement
with the next generation of coherent x-ray sources (TESLA in Hamburg).
The range of the elements amenable to a routine EXAFS analysis depends
on the x-ray monochromator. The low-energy limit of the most widely
used Si(111) monochromators is around 3 keV, translating to Z = 16 (K
edge of sulfur). With special monochromators, the technique can be extended
to about 2 keV (K edge of aluminium). For the lightest elements (C,
O, N) diffraction gratings are used instead of crystals for beam monochromatization:
in this low-energy region (200 - 600 eV), the typical span of the EXAFS
signal (1 keV) requires or exceeds the entire monochromator range, so
that only XANES spectra are studied [5].
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At
the high-energy end, the limit is defined by the large-scale
parameters
of the x-ray source: the storage-ring energy and radius define
the critical photon energy above which the intensity of the synchrotron
radiation decreases exponentially [4]. Consequently,
L3 edge EXAFS instead of K edge is exploited for heavier elements.
The switch
to L3 is not recommended for elements below antimony (L3 edge 4132
eV, K edge 30491 eV), since the range of the L3 EXAFS signal,
cut
off by the subsequent L2 edge, is too short so that the spatial
resolution of the method is seriously impaired. In the schematic
overview of accessible EXAFS intervals in Fig. 8, the relative
position of the limiting L2 edge is shown by the thick gray
line. However,
modern insertion devices (wigglers) generate the high-energy photons
much more abundantly and the switch to the L3 EXAFS is practised
at higher energies (and atomic numbers) depending on the monochromator
resolution. Mostly, L3 edge is exploited for lanthanides and
heavier
elements. |
Fig.
8. The useful interval of EXAFS signals (horizontal
dotted lines) as a function of the atomic number. With K-edge
energy out of the range of standard monochromators, L3 edge EXAFS
is measured for heavier elements. The thick gray line shows the
relative position of L2 edge truncating the L3 EXAFS signal. The
relative excitation energies of sharp multielectron photoexcitation
features in the EXAFS interval are shown by dots. |
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