Extended Xray absorption fine structure EXAFS and Xray absorption nearedge

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Extended X-ray absorption fine structure (EXAFS)
and X-ray absorption near-edge structure (XANES)
Fred Mosselmans
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Whats an X-ray absorption spectrum? Some
theoretical background How you do a XAFS
experiment? Practical considerations What you do
with the EXAFS data then? Analysis methods What
else is there? The edge region - XANES
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The basis of an X-ray absorption spectrum In the
interaction of X-rays with matter, there are
three main processes elastic
scattering, inelastic scattering (Compton)
absorption due to ionisation. The absorption
can be characterised by the following equation I1
I0exp(-µx) I0 is incident intensity I1 is the
exiting intensity x is the distance travelled
through the material µ is the x-ray absorption
coefficient of the material
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µ The coefficient is energy dependent and
generally decreases smoothly but it has certain
discontinuities in its values. These are known
as absorption edges. They are caused when the
incident X-ray is energetic enough to eject one
of the core electrons (1s, 2s, 2p etc) to the
continuum. The shell the electron is ejected from
gives rise to the edges name. 1s K etc. If
the excited atom is a monatomic gas, the
absorption coefficient also varies smoothly after
the edge.
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However in condensed matter or (multi-atomic gas
molecules) the ejected photo-electron (wave) will
be scattered by neighbouring atoms. It is
the interference between the outgoing electron
and the back-scattered ones which leads to
oscillations visible in the absorption spectrum
above the edge. These can extend to up to 1000 eV
past the edge. These oscillations are the EXAFS.
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The EXAFS signal is denoted by ? and is defined
as ? µ(E) - µ0(E)/µo(E)
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The EXAFS equation This is obtained through
treating the scattering process in a
semi-classical way. ( Use quantum states but the
EM wave properties are treated classically). In
the equation Ri is the distance from the central
atom to a scattering atom i.
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k is the wave vector associated with the
photoelectron of energy E. k
(2me/hh2)(E-E0)1/2 E0 is the edge energy, me
is the mass of the electron Niis the no. of
scattering atoms of type i
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is a term to account for disorder in the solid.
A Gaussian distribution of mean distances from
the central atom is assumed. This is the
Debye-Waller term.

f(p,k) is the scattering amplitude at atom i. d1
is the phase shift undergone by the photoelectron
at the central atom f is the phase shift the
photoelectron undergoes when it bounces off the
scattering atom.
is an amplitude reduction factor, when the core
electron is ejected it leaves a hole. The
valence electron rearrange because of this. These
multielectron processes contribute to the edge
jump but not the EXAFS.
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• e (-2R/ ?(k)) is a term to account for the fact
  the photoelectron is only elastically scattered a
  short distance in solids (the mean free path).
  This is thus a damping factor depending on the
  ratio of the distance travelled, 2R, to the
  electron mean free path, ?(k).
• To get the equation the following assumptions are
  made
• The ejected electron is a K shell (initial state
  L0 final state L1)
• Only back scattering at the angle p is
  considered.
• Only single scattering events are considered.
• The plane wave approximation ( f(p ,k) is
  independent of R).
• Distances are distributed harmonically.

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Why you need a synchrotron? Here are two spectra
of MoS2 the laboratory source one took over 12
hours to collect, the synchrotron one took 25
minutes and could have been collected in about 3.
Lab
Synchrotron
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• EXAFS experiments
• The system
• The sample
• A synchrotron is useful (not essential). A broad
  continuous spectrum of X-radiation is required.
• For a standard experiment where discrete energy
  measurements are made a method of
  monochromating the input beam is needed.
• A method of measuring the intensity of the X-ray
  before and after the sample.
• A data acquisition system to control the
  experiment and record the data.
• Optional extras include focussing optics, high
  power detector systems.

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Monochromators These nowadays tend to be double
crystal at high energy (below 1keV gratings are
used). They rely on the Bragg law to define
the energy n?2dsin(?) This condition is
satisfied for more than one value of n, which can
lead to problems with so-called Harmonic
contamination. Normally made of Silicon with
popular cuts being the (111), (220) and (311)
planes. Most monochromators require cooling to
maintain an even temperature.
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?
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Ion Chambers These are used to measure the
intensity of the beam before and after the sample.
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To HT unit
sample
To amplifiers
They consist of two parallel plates, (one at high
potential) in an inert gas atmosphere. Current is
collected off the other plate and fed to an
amplifier before measurement to record the beam
intensity. The gas mixture is adjusted to absorb
about 20 of the beam in the 1st chamber and 80
in the second. Often a third chamber is used
after a metal foil to do in situ energy
calibration
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The amplifier feeds to a voltage to frequency
converter (V2F). The gain on the amplifier should
be set so that the V2F input is within its linear
range. At DL this is ca 0.1 -6 V. The V2F feeds
into the data acquisition computer (a VME
system). The VME is controlled via a Sun
workstation using the data acquisition program
EXAFS
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Harmonics These do not get absorbed in the same
way as the primary beam and thus distort the
EXAFS signal. Two main removal methods
exist. Mirrors Use of a vertical mirror in the
beam line. This is set at an angle above that
the critical angle of the higher harmonics but
below that of the desired beam energy. The beam
energy is then reflected of the mirror while the
higher harmonics are absorbed . This is the
preferred method giving a harmonic content below
0.1
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Rocking Off If the beam intensity is plotted
against the tilt off parallel for a DCM the
fraction of higher harmonic reduces much faster.
Thus by tilting the second crystal with respect
to the first to get only ca. 50 of the maximum
intensity harmonic content can be reduced to gt1
Intensity
First harmonic
Second harmonic
Tilt
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For samples with a reasonably high concentration
(gt3-5) of the element whose edge is being
measured, transmission mode scanning is used as
illustrated before, where the beam is fired
through the sample and intensity of the beam
measured before and after the sample. µ
Loge(Io/I1) The sample should be homogenous and
ideally give an edge step of 0.5-1.0. However
for less concentrated samples or thin films or
samples where the beam cannot be fired through
the sample, other means of detection must be
employed.
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• To obtain homogeneous solid samples, two
  techniques are commonly employed
• Grinding up the either the pure sample or more
  normally the sample mixed with an inert matrix
  of low Z (often BN) and using a press to produce
  a pellet.
• Grinding up the sample on its own and spreading
  it onto a layer of adhesive tape shaking off the
  excess and repeating the process to bulild up a
  sandwich of tape and substance of the required
  thickness.

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Fluorescence detection
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This is one of the decay processes by which the
core hole is filled. It involves an outer shell
electron dropping into the core hole giving off a
characteristic energy photon. The energy of
this photon is independent of the incoming photon
energy.
h?
It can be shown that the fluorescence signal is
proportional to the absorbance and thus the EXAFS
can be extracted from it. Fluorescence EXAFS
extends the minimum possible concentration
(Depending on sample and beamline) to about 1ppm
at best.
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For Fluorescence the sample is normally set at
45o to the incident beam. The fluorescence signal
is emitted spherically from the sample. The
detector should be placed to get as much solid
angle of the sphere as possible to maximise the
signal. Fluorescence detectors tend to be
cryogenically cooled solid state devices
now. They have energy resolution in the low
100s of eV .This is enough to separate the
fluorescence peak from the scatter peak, thus in
data collection only the signal of interest can
be collected.
fluorescence
scatter
Energy
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Solid state fluorescence detectors have maximum
count rates, beyond which they are not linear (or
cant be corrected for non-linearity). Other
fluorescence arrangements include using a
hemisphere of multilayers to select a certain
energy range and direct the photons to a
photo-multiplier. This gives much higher count
rate capability but is only about 10 efficient.
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Electron yield
Free state valence band K shell
The other principal detection method used is
electron yield (especially for light elements
where the fluorescence yield is low). This method
involves collecting the Auger electrons.
Normally this is achieved by biasing the sample
and collecting the drain current. (TEY) Can also
be done with a collector plate above a floating
sample (PEY) EY is surface sensitive (ca 100s Å)
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DEXAFS These are modes where the data is
collected on a point-by-point basis. There is
also (Energy) Dispersive EXAFS. Here a bent
polychromator focuses all the light onto a small
spot (ca. 100-200 microns) at the sample The
light then expands again onto a position
sensitive detector, which is effectively an
energy scale. Thus the spectrum is collected in a
single shot. Although data quality is not
generally as good it can be alright.
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Time A single step-scanning EXAFS scan will take
about 20-40 minutes.(perhaps longer for a very
dilute sample measured in Fluorescence.) With a
normal DCM the QEXAFS technique is also
available. Here the monochromator moves at a
constant speed and the data is collected over
fixed time intervals, which define the energy of
each point. This enables transition scans to be
done in minutes or less. DEXAFS scans can be
recorded in ms. Hence for studying fast
transitory processes DEXAFS offers a big
advantage which outweighs problems with lesser
data quality.
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Reflexafs Another way to get surface sensitivity
is to use Reflexafs. A very thin vertical beam
(ca 100 microns) is directed onto an optically
flat sample at well below the critical angle for
the incident radiation. At this angle most of the
light is not absorbed by the sample but reflected
off it. The fluorescence signal can be
collected off the sample. This gives a surface
sensitivity of ca. 50Å , depending on the edge
and energy and the sample.
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detector
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XAS accessible elements
XANES only EXAFS hardish K-edge EXAFS L3-edge
EXAFS L3/K-edge EXAFS
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Sample considerations Uniformity EXAFS samples
should be homogeneous and of small particle size.
Consider nickel oxide. The ideal thickness should
be about 10 microns. Thus for a powdered nickel
oxide sample to have a chance of uniformity, the
particles should be lt 1/10 of the sample
thickness i.e. 1 micron diameter. The beam may
not be uniform intensity all the way across its
profile thus if the sample is not uniform the
signal ratio between I1 and I0 will be distorted.
Thus pinholes should be avoided at all costs.
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Concentration in fluorescence samples If a
fluorescence sample is too concentrated an effect
called self-absorption will occur. This results
in a damped EXAFS signal and so lower than
expected coordination numbers when the data is
analysed. Self-absorption is caused by the fact
in a thick concentrated sample around the edge as
the energy of the incident X-ray goes up, the
absorption coefficient of the element of interest
goes up reducing the penetration depth of the
X-rays. This tends to compensate for the increase
in absorption and results in a non-linear
distortion of the measured spectrum.
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Sample environments Often if you have a
reasonably ordered sample you will want to do
your experiment at cryogenic temperatures. In
this case the biggest contributor to the
Debye-Waller factor may be thermal vibrations, by
cooling to 80K or 10K these can be considerably
reduced increasing the amplitude of the EXAFS and
the distance to which atoms can be seen. If your
sample has a lot of static disorder, cooling will
not improve the size of EXAFS signal much. If
the EXAFS is Fourier transformed you get a RDF
plot of neighbouring atoms shells.
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• Scanning
• In step scanning mode it is normal to have three
  regions
• Before the edge in large steps with low count
  times
• Over the edge with small steps and low count time
  (here the XAFS dominates the signal
• Past the edge in k-spaced steps with a gradually
  increasing time period (here the exafs signal is
  gradually decreasing as a part of the total
  signal)

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Noise Statistical (random noise) decreases with
where N scans are taken. In transmission
scans the noise source is normally electronic,
thus counting for longer does not decrease the
noise very much. Fluorescence noise is largely
photon related, hence collecting for longer at
each point is worthwhile. It is normally worth
taking two scans or more of a sample to get
better quality data. (Higher signal-to-noise). In
looking at very dilute samples, collecting 32 or
16 scans of a sample is fairly common, for
transmission samples normally 4 scans is
sufficient. (often less will do).
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Other environments One of the great powers of
EXAFS is its ability to be used in situ. Thus a
wide range of different sample environmental
cells . Hi-pressure cells such as HIPREXX (a
DAC) Furnaces for solid samples Ovens for liquids
and solution Cryostats (Nitrogen and Helium)
Matrix IR set-ups Catalytic cells for doing
reactions in. At DL we have EXAFS cells to take a
sample from 10 to 1300 K and from 0.00001 mbar to
100 kbar.
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• What do you with your data?
• There are three basic steps to analysing EXAFS.
• Converting the raw data into an absorption
  spectrum
• Extracting the EXAFS signal from the absorption
  spectrum
• Fitting the EXAFS spectrum with a model
  environment
• There are other things you may wish to do with a
  XAFS spectrum such as look at the edge position ,
  near-edge structure.

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Converting the Raw Data At DL we do this with a
program called EXCALIB. EXCALIB has three primary
functions It converts the raw data (a list of the
signal outputs at each point) into an absorbance
spectrum SRS SRSRUN87891,SRSDAT010617,SRSTIM
171443, SRSSTN'exf9',SRSPRJ'xrsws9p2',SRSEXP'e
xafs ', SRSTLE'CdAcThU (0.5,1.0), heating
from RT to 100C 2/c6 more60c ' SRSCN1'one
',SRSCN2'two ',SRSCN3'three ', END
6978.02 3479.50 1577790.00 96400.00
1.00 0.00 6974.88
3479.50 1573627.00 96444.00 1.00
0.00 6971.75 3479.50 1572506.00
96649.00 1.00 0.00
6968.62 3479.50 1569606.00 96684.00
1.00 0.00
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For a transmission file this involves taking the
natural log of the I0/I1 ratio and converting the
monochromator angle to energy. For a fluorescence
file this involves summing the useful individual
fluorescence chaneels, dividing the total by I0
and converting the monochromator angle to energy.
SRS SRSRUN85233,SRSDAT010329,SRSTIM224519,
SRSSTN'exf9',SRSPRJ'xrsws9p2',SRSEXP'exafs
', SRSTLE'Rusticyanin Hough sample ph4 oxy
green ' SRSCN1'one
',SRSCN2'two ',SRSCN3'three ', END
21400.00 1000.00 66765.00 19529.00
3900.00 1444686.00 0.00
441.00 342.00 389.00 386.00
314.00 330.00 299.00
336.00 266.00 303.00 216.00
278.00 0.00 0.00
0.00 0.00 13081.00 11023.00
12126.00 16529.00 13305.00
10911.00 11177.00 13079.00
15568.00 18412.00 13074.00
150.00 0.00 0.00 0.00
21390.00 1000.00 66567.00
19564.00 3798.00 1451272.00
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The next stage in EXCALIB is to add together all
the datasets of a sample in one state. This
produces a summed spectrum. Finally if there any
obvious glitches in the spectrum these can be
removed before the data is written out.
Glitches distort the background removal process
thus it is important to remove them before this
stage
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Glitches are not always easy to spot in the raw
data. Thus some time you need to begin the EXAFS
extraction process to see the glitch then remove
it and begin the background removal process again.
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EXAFS extraction Once the clean data is saved
you can begin the EXAFS extraction process in the
program EXSPLINE.
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Initially the pre-edge background is removed and
the EXAFS normalised to the edge step. This
polynomial is normally of order 1. This leaves a
normalised absorption spectrum ready for post
edge subtraction.
Edge step
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This spectrum is the one to use for Near-edge
comparisons. 41 Another of our background
removal programs (EXBROOK) is better for
producing normalised absorption spectra for
output and at measuring the edge position.
A number of smoothly joined linked polynomials
are used to subtract the post edge background.
This gives you the EXAFS and its Fourier
transform.
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The EXAFS is displayed with a k3 weighting this
gives the spectrum a more even amplitude across
its width. In general amplitude envelopes should
be smooth.
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The Fourier transform is a radial distribution
function of the atoms surrounding the excited
atom. There should be little intensity below 1Å.
The distances in the EXSPLINE FT are not
corrected for phase shifts so will be shorter
than the real
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ones, which are obtained during simulation.
Normally the first shell has the largest
amplitude in EXAFS. EXSPLINE shows the real,
imaginary and modulus parts of the FT
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EXCURVE Once you are happy with the background
removal process, you move on to the important
data simulation part of the analysis. At DL we do
this with the program EXCURVE. Other simulation
programs are available e.g. FEFFIT using the UW
code FEFF and GNXAS. In EXAFS simulation you
build a model environment for the material
studies then calculate the theoretical EXAFS
spectrum for that model. Then you refine the
model by comparing the theoretical spectrum with
the real one, until the simulated spectrum most
nearly matches the real experimental data with a
few constraints of course. Thus there is no
unique solution you are looking for a best-fit.
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• To create a simulated EXAFS spectrum from the
  model
• you have to define the model in terms of shells
  of the same atom type at the same distance from
  the central atom.
• calculate phase shifts for each of the atom types
  in the model
• Phase shifts are calculated from the atomic
  potentials of each atom.
• These are calculated using Hedin-Lundquist ground
  states and von Barth exchange potentials.
• Systematic errors in the former mean that they
  account for the S02 factor in the EXAFS (AFAC).

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An AB model is defined where A is the atom whose
potential is being calculated and B is its
nearest neighbour. The type of central atom is
selected The potential outside the muffin tin is
equalised. Then using the core hole width the
phase shifts are
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calculated. These theoretical phase shifts are
pretty good for most systems. They can be tweaked
a bit, using refinement to a known structural
model.
V
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• Parameters
• In each shell there are four principal
  parameters
• The distance from the central atom
• The type of atom in the shell
• The number of atoms in the shell
• The Debye-Waller factor for the shell
• The latter two parameters are closely correlated.
  Thus unless one is known obtaining an accurate
  value for the other is difficult.
• Another key parameter is
• Ef the energy offset between the theoretical E0
  and the one defined in EXSPLINE

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Refinement Initially you tend to fit one or two
shells and then add further ones after refining
those to a best fit. When building a model use
all the information you have about the system.
This cuts down the no. of parameters that
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need to be refined. When parameters are closely
correlated (gt0.8) such as the Debye-Waller
factor and the occupancy no. of a shell, you may
want to map them against each other to determine
the possible range of optimal values
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? k
EXAFS spectra contain a limited amount of
information. Statistical analysis implies there
are only Nind independent points where Nind
(2 ?r.? k/ p) You should not have more variables
than independent points and preferably much less.
?r
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You refine your model to a Fit Index, F.I. If you
add extra variables the fit is likely to improve,
however this is not always a good measure of
whether you have a better model. R gives a better
measure of the absolute fit quality as it does
not take account of the amplitude of the
EXAFS
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Another measure of goodness of fit is the reduced
chi squared value as this takes into account the
number of variables used in obtaining the fit.
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? is the no. of variables used, N the no of
points in the exafs and ? a weighting term to
estimate the error in the spectrum at each point.
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Multiple Scattering
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If you are looking at a linear system, e.g. M -
C- O , you may have to consider multiple
scattering in your fit, otherwise the second
shell will not give accurate parameters.
Multiple scattering can also be relevant in
structures with long range order, ring systems
and some square planar complexes.
Mo(CO)6
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End of Refinement When you added sufficient
shells to fit the data and have reached the
lowest reduced chi-squared value, you have
finished the refinement. You may well not be able
to fit all the shells you think are there
reliably. If a shell contributes less than 10
to the total EXAFS amplitude it will be hard to
fit, if it contributes less than 5 it almost
certainly cant be fitted meaningfully. Then you
need to think about errors.
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Errors Standard EXAFS gives a mean picture of
atomic environments, thus when looking at a
mixture of species the average picture may be
physically meaningless. In cases where you have
shells of similar or the same atom type, EXAFS
will have difficulty separating them reliably if
they are less than 0.15Å apart. Atomic
separations have an accuracy of 1 or better ,
shell occupancy numbers have an accuracy of about
15 normally. You can obtain a measure of error
in the program by varying a single parameter
manually and seeing what effect it has on the fit
index.
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The edge region Consider the cause of XAFS
again, the energy needed to
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eject the core shell elctron is dependent on the
charge experienced by it. Thus the position of
the absorption edge will be related to the charge
on the atom. Hence by measuring the edge position
and comparing it to
h?
Continuum
Empty bands
Valence band
Ef
standards of known valence state, information
about the valence state of the excited atom can
be obtained.
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• The edge region
• Edge fine structure associated with inner shell
  transitions, e.g. K edge shows fine detail due to
  1s? 3d, 1s ? 4s, 1s ?4p exact positions depend
  on oxidation state, site symmetry, surrounding
  ligands and nature of bonding.

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• Entire spectrum displaced to higher energies for
  CuCl2 due to higher oxidation state (2)

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What is the edge position? On a spectrum with a
clear peak on the edge e.g. Cu, it is generally
taken as the top of the peak, otherwise it is
often taken as the maximum slope point on the
edge. Occasionally it is taken as halfway up the
edge. Consistency is the key.
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However a linear relationship between edge
position and valence state does not normally
exist as the neighbouring atoms have an effect,
as the charge on the atom will depend on the
hardness/softness of neighbouring atoms, e.g. the
edge position of Mo K-edge in Mo2(AcO)4 is 20001
eV and in
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K4Mo2Cl8 it is 20007 eV. Both are Mo(II)
dimers. However in similar coordination
environments useful information can be obtained.
Mn(II)(acetylyacetonate)2(H2O)2 Mn(III)(acetylyace
tonate)3 Mn(IV)(salicylate)2bipyridine Yachanda
et al. Science 1993, 260 675-678
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In the pre-edge there are transitions to bound
states. These can be useful indicators of
geometrical configuration. This is because the
symmetry of the site may allow or forbid some of
these transitions. E.g. TM tetrahedral species
often show a peak on the edge, which is much
smaller or absent in octahedral ones. This is
because of p-d band mixing.
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MoO3 octahedral
Na2MoO4tetrahedral
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Band mapping
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Transitions to bound vacant states just above the
Fermi level can be seen thus Near-Edge XAS can be
used a probe of the unoccupied band structure of
a material. The selection rules (L 1) determine
which states can be seen at each edge. So a range
of edges can be collected for a full picture of
the bands which can then be compared with
theoretical calculations.
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White lines The white line is the bit on the edge
that goes above the edge step. The area of the
white line for TM L-edge is an indication of the
no of empty d states that exist. It has been used
to follow small changes in bulk valency that
occur during catalytic chemical reactions at
metal particles. The
edge shift may be very small and difficult to
measure accurately enough but the area under the
white line is easier to quantify.
WO3
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Advanced fingerprinting The near-edge structure
is thus characteristic of an environment and
valence state hence one of its more common uses
is in fingerprinting. Thus if you have a mixture
of sites/compounds in a sample you can fit with
linear combinations of XANES (X-ray absorption
near edge structure) or EXAFS spectra of known
species.
XANES spectrum of Pd/POM (circles), linear
combination XANES (thick solid line) and
component XANES spectra (thin solid line) (a)
for model 1 assuming PdO, PdCl and PdPd shells
and (b) for model 2 assuming PdN, PdCl and
PdPd shells. Sobczak et al. J Alloys Compounds
2004 362 162-166
Kim et al., J Synch Rad 1999 6 648-650
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• Summing up
• What gives rise to an XAFS spectrum?
• The ejection of a core hole electron
• How to obtain a XAFS spectrum?
• Use Homogeneous sample of the correct thickness
• What to do with the XAFS Spectrum?
• Analyse it to determine the local site structure