EXAFS as a tool for catalyst characterization: a review of the ... - INT

EXAFS as a tool for catalyst
characterization: a review of the data
analysis methods
F. B. NORONHA
Instituto Nacional de Tecnologia, Av. Venezuela 82, CEP 20081-310,
Rio de Janeiro - RJ, Brazil, Fax (55-21) 206-1051 E-mail -
bellot@peq.coppe.ufrj.br.
Abstract - A review of the EXAFS data analysis methods is
presented. A detailed description of the EXAFS signal extraction and
the Fourier transform of the data are discussed. The procedure for
determining interatomic distances, coordination numbers and
disorder effects from EXAFS data is described. This paper also
discusses the data analysis statistics. Finally, one example of catalyst
characterization by the EXAFS technique is reported.
Keywords: EXAFS, catalyst characterization, structure of catalysts.
INTRODUCTION
During the past years, the extended X-ray absorption fine structure
(EXAFS) technique has been increasingly used as a valuable tool for
catalyst characterization. The EXAFS analysis is particularly
interesting in the case of both highly dispersed and bimetallic
catalysts where it is usually difficult or impossible to obtain
information about the structure from other techniques, such as X-ray
diffraction. Therefore, EXAFS measurements have been used to
determine the metal particle size of highly dispersed catalysts (Kip et
al., 1987; Pandya et al., 1996) to locate noble metal particles in a
zeolite matrix in function of the pretreatment (Tzou et al., 1988;
Reifsnyder et al., 1998) to study the alloy formation (Noronha, 1994;
Sinfelt et al., 1984).
THE EXAFS PHENOMENON

The X-ray absorption coefficient for an atom decreases as the X-ray
energy increases. It displays discontinuities (absorption edges) as an
incident photon is absorbed by the atom and electronic transitions
from a core atomic level to unoccupied conduction states above the
Fermi level take place.
The photoelectron emitted in this process can be represented as a
wave. If the excited atom is surrounded by other atoms, the outgoing
wave scatters from the surrounding atoms, producing ingoing waves.
These ingoing waves can constructively or destructively interfere with
the outgoing waves. This interference produces the oscillatory
behavior of the fine structure.
The extended X-ray absorption fine structure (EXAFS) is the
oscillation in the absorption coefficient on the high-energy side of X-
ray absorption edges, ranging from 30 to about 1000eV above the
edge. Stern, Sayers and Lytle related these fluctuations of the
absorption coefficient to the atomic arrangement surrounding the
absorbing atom (Stern, 1974; Stern et al., 1975; Lytle et al., 1975).
In this paper, we will be concerned with neither the theory of EXAFS
(Stern, 1974) nor the experimental techniques used to measure
EXAFS (Lytle et al., 1975; Meitzner, 1998). The aim of this work is to
review the mathematical procedure for treating the EXAFS spectrum
in order to calculate the physical parameters. A final section presents
one example of EXAFS application to catalysis.
Data Analysis
An X-ray absorption experiment involves the measurement of the
total linear absorption coefficient, µ, as the photon energy is varied.
In the case of a transmission experiment,
ln I 0 /I = µ x (1)
where I 0 and I are the photon intensities before and after the
absorber of thickness x.
A typical X-ray absorption spectrum can be separated into four parts
(Bart and Vlaic, 1987) (Figure 1):
a- pre-edge region;
b- edge region;
c- X-ray absorption near edge structure (XANES) region;
d- extended X-ray absorption fine structure (EXAFS) region.

Figure 1: Regions of the X-ray absorption spectrum of metallic cobalt.
In the first region, the absorption coefficient decreases as the energy
increases due to transitions from other occupied levels of the same
atom and of other atoms. A Victoreen law, µ(E) = C E -3 + D E -4 , or
linear relation, µ(E) = A E + B, is used before the absorption edge to
determine the constants. The absorption coefficient rises sharply at
the edge, corresponding to the electron transitions to higher
unoccupied levels. This region (b) is the absorption edge (within a
range of a few electronvolts). Finally, the XANES and EXAFS zones
are at the high-energy side of the absorption edge (c and d). XANES

and EXAFS stem from the same phenomenon. The difference between
them is due to the kinetic energy of the photoelectron in each case.
At a low energy, the mean free path is high, which induces an
important multiple scattering effect. On the other hand, at the EXAFS
region, the mean free path of the photoelectrons is limited.
Therefore, single scattering is the major process.
The fine structure χ(E) associated to a particular absorption edge is
thus:
where µ(E) is the measured absorption coefficient, µ 1 (E) is the
absorption coefficient of the isolated atom and µ 0 (E) is the smooth
background absorption before the edge. µ 0 (E) andµ 1 (E) can not be
obtained directly and must be estimated.
The advantage of this procedure is based on the fact that µ 0 (E) is
determined directly from the pre-edge region before the calculations
for the EXAFS region. However, the µ 0 (E) extrapolation can produce
anomalous behavior for µ 1 (E) - µ 0 (E), since it is highly sensitive to the
energy range of the pre-edge chosen. Therefore, generally, the
Lengeler-Eisenberger method is used to calculate µ 0 (E) (Lengeler and
Eisenberger, 1980). This method is based on the following formula:
(2)
First µ 1 (E) is calculated after the edge by a polynomial of degree n (n
= 4, 5 or 6) or cubic splines. Then µ 0 (E) is determined from equation
(3).
In order to relate χ (E) to structural parameters, it is convenient to
perform a transformation to χ (κ) in the photoelectron
wavevector κ space, where
(3)
(4)
After conversion of energy to the k scale using eq. (4), the
normalized EXAFS function χ (κ ) is obtained as follows:
(5)

The normalized EXAFS spectrum associated with the K-edge of
metallic cobalt at 298K is shown in Figure 2.
Figure 2: Normalized K-edge EXAFS spectrum of metallic cobalt.
For excitation of a s shell, the normalized EXAFS oscillations can be
described by
Where Rj is the distance from the central absorbing atom to atoms in
the j th coordination shell, N j is the number of atoms in the j th shell, σj
is the Debye-Waller factor due to static disorder and thermal
vibrations, λ (κ ) is the mean free path of the ejected photoelectron
(6)

from the absorber atom and Σ the summation extends over j
coordination shells, the term e -2rj/λ is due to inelastic losses, Aj(κ ) is
the backscattering amplitude from each of the N j neighboring atoms
and φ j(κ ) is the phase shift between the incident and backscattering
wave given by
φ (κ ) = φ a(κ ) + φ b(κ ) (7)
where φ a(κ ) is the phase shift due to the central atom and φ b(κ ) is
the phase of the backscattering amplitude from the neighbor.
Multiple scattering effects have been ignored in the derivation of eq.
6. Furthermore, since the intensity of the outgoing wave decreases
very fast with increasing R, there is very little contribution to the fine
structure of the distant atoms.
The raw EXAFS signal obtained with the procedure described above is
made of many sinusoidal waves. The Fourier transform is the
standard tool used for frequency separation. The Fourier transform
of χ(κ ) yields the following radial distribution function (RDF):
Since at high κ values, the χ(κ ) is low, function χ(κ ) is multiplied by
the factor κ n before the transform is performed in order to obtain
more information at those values (Vlaic et al., 1998). Factor κ n is
used to weight the data according to the value of κ . Generally,
values of n= 1, 2 or 3 are used. The limits of the integral, kmin and
kmax, are the experimental minimum and maximum values
of κ obtained. Another problem related to FT is that the EXAFS signal
has a limited number of points. Therefore, the Fourier integral is
truncated. W(κ ) is a window function, where the function is Fourier
transformed in a limited range (kmin, kmax). Three types of windows
have been used in the literature: HAMMING, HANNING and KAISER
(Michalowicz, 1990).
HAMMING
HANNING
KAISER
(8)
κ min < κ < κ max (9)
κ min < κ < κ max (10)

(11)
I 0 - modified BESSEL function, degree 0;
τ - the shape of the window;
κ 1 and κ 2 - window limits.
Only the magnitude of the transform is considered (eq.12). It shows
a series of peaks, which corresponds to the different coordination
shells (Figure 3). Because of the phase shift, φ j (κ ), interatomic
distances derived from the peaks of FT(R) have to be properly
corrected to coincide with those of X-ray diffraction.
(12)

Figure 3: Fourier transform corresponding to EXAFS spectrum of
metallic cobalt.
When the contribution of two shells is not resolved in the Fourier
spectrum, Fourier filtering can be used. By means of a filter function,
specific peaks in the Fourier spectrum are separated from the rest of
the spectrum. The product of the spectrum with this filter function is
Fourier backtransformed into k space. This procedure separates the
contribution of adjacent coordination shells so that the effect of only
the coordination shell of interest is maintained.
In fact, the Fourier backtransform is calculated by
(13)
where W(κ) is the window of the Fourier transform and W’(κ) is the
window of the Fourier backtransform which separate the specific
peak.

Thus, the resulting curves are fitted with the EXAFS formula to
determine R, N and σ . In order to extract information about the local
environment of the absorber, the backscattering amplitude and phase
shift functions must be known. These functions can be obtained
experimentally from EXAFS spectra of model compounds or calculated
theoretically (Teo and Lee, 1979; McKale et al., 1988; Rehr, 1989).
Experimental functions are extracted from reference compounds with
known structures. However, it is not always possible to obtain
experimental functions since the reference compounds do not exist or
it is not possible to extract them (Vlaic et al., 1998). Furthermore,
experimental phase and amplitude functions must be extracted by
using the same integration limits and the same windows to the
unknown sample in order to introduce the same truncation errors.
In general, the accuracy of the analysis is about 0.01-0.02Å for the
interatomic distances, 5 to 15% for the coordination numbers and
20% for σ (Lengeler and Eisenberger, 1980).
The minimization procedure is carried over into the following function
(Michalowicz, 1990):
(14)
where p i are the fitting parameters and W(k) is a weighting function.
A residual factor is also defined by the following expression:
(15)
The number of parameters that can be determined from the EXAFS
signal is related to the number of independent points, N ind , by
N par = N ind – 1 (16)
There is some uncertainty in the literature on how to calculate N ind .
According to Stern (1993), the correct expression is given by
(17)
The fit quality is given by the chi-square function. Particularly in
EXAFS this function is defined as follows:
(18)

where s(κ i ) is the standard deviation given by
(19)
The quality of the fit can also be expressed by a merit factor defined
as (Faudon et at., 1993)
(20)
Evidence of Alloy Formation of Graphite-Supported Palladium-
Cobalt Catalysts
It has been reported that the addition of a noble metal to a supported
cobalt catalyst creates important changes in the selectivity of the CO
+ H 2 reaction (Noronha et al., 1996; Idriss et al., 1992). In general,
these results are attributed to alloy formation. However, no clear
evidence of alloying is presented.
Recently, EXAFS was used to obtain both further evidence of Pd-Co
interaction and the mean composition of bimetallic particles
(Noronha, 1994). Pd/G (2.26 wt.%), Co/G (3.61 wt.%) and
Pd 16 Co 84 /G (3.37 Pd wt.% and 9.96 Co wt.%) catalysts were
prepared by the incipient wetness impregnation of the graphite.
As shown in Figure 4, the radial distribution function (RDF) of the
bimetallic catalyst is different from the RDF of both Pd/G catalyst and
reference sample (Pd foil). The first coordination shell consists of
palladium atoms alone in the Pd/G and in the reference. On the other
hand, data analysis revealed the presence of both Pd and Co atoms in
the first coordination shell of Pd (Table 1). The local atomic
concentration of palladium, obtained by the n 1 /n 1 +n 2 ratio, was
61.5% suggesting that the first shell around Pd atoms is clearly
palladium-enriched.

Figure 4: Amplitude of the Radial Distribution Function at the Pd K-edge for
palladium foil (solid line) and Pd/G (dotted line) and Pd 16 Co 84 /G (dashed line).
Table 1: EXAFS parameters at the Pd K-edge
Pd - Pd pair
Pd - Co pair
Sample n 1 R 1 (Å) σ 2 (Å 2 ) n 2 R 2 (Å) σ 2 (Å 2 ) Q (%) n 1 +n 2
Pd foil 12.0 2.75 - - - - - -
Pd/G 9.1 2.74 0.0000 - - - 5 -
Pd 16 Co 84 /G 6.7 2.73 0.0310 4.2 2.61 0.0050 8 10.9
The RDF of the bimetallic catalyst is not so different from the RDF of
both Co/G catalyst and reference (Figure 5). This suggests that the
environment of cobalt atoms in the Pd 16 Co 84 /G and in the reference
sample is similar. However, since a fairly good fit cannot be obtained
only with Co atoms in the first coordination sphere of cobalt, it was

necessary to perform the fit with Pd and Co atoms (Table 2). This
results in a mean palladium concentration of only 7.7% around a Co
atom, which is much lower than that expected from chemical
analysis, indicating that Co atoms tend to be preferentially
surrounded by Co atoms.
Figure 5: Amplitude of the Radial Distribution Function at the Co K-edge for cobalt
foil (solid line) and Co/G (dotted line) and Pd 16 Co 84 /G (dashed line).
Table 2: EXAFS parameters at the Co K-edge
Co - Co pair
Co - Pd pair
Sample n 1 R 1 (Å) σ 2 (Å 2 ) n 2 R 2 (Å) σ 2 (Å 2 ) Q
(%)
n 1 +n 2
Co foil 12.0 2.51 - - - - - -
Co/G 11.5 2.50 0.0020 - - - 3 11.5
Pd 16 Co 84 /G 8.0 2.50 0.0060 3.7 2.61 0.0080 9 11.7

Therefore, the EXAFS analysis demonstrated that the alloy phase was
formed during reduction, as already shown by magnetic and X-ray
diffraction measurements (Noronha, 1994). The bimetallic particles
consist of both palladium and cobalt rich phases.
CONCLUSIONS
A review of the EXAFS data analysis methods was presented. A
detailed description of the EXAFS signal extraction and the Fourier
transform of the data were discussed. The procedure for determining
interatomic distances, coordination numbers and disorder effects
from EXAFS data was described. These parameters were calculated in
order to obtain both further evidence of Pd-Co interaction and the
mean composition of bimetallic particles.
NOMENCLATURE
Aj(κ ) the backscattering amplitude from each of the N j neighboring
atoms
E photoelectron energy
E 0 energy of the absorption edge
Planck`s constant divided by 2π
h.ν energy of the X-ray photon
I 0 photon intensities before the absorber
I photon intensities after the absorber
m mass of the electron
N j number of atoms in the j th shell
N ind number of independent points
N par number of parameters
p i fitting parameters

Rj distance from the central absorbing atom to atoms in the
j th coordination shell
s standard deviation
x thickness of the sample
X 2 chi-square function
W window of the Fourier transform
W’ window of the Fourier backtransform
Greek letters
κ photoelectron wavevector
λ mean free path of the ejected photoelectron from the absorber
atom absorption coefficient
µ 1 absorption coefficient of the isolated atom
µ 0 absorption coefficient before the edge
σ Debye-Waller factor due to static disorder and thermal vibrations
φ phase shift between the incident and backscattering wave
χ EXAFS function
Super/subscripts
e experimental
c calculated
exp experimental
the theoretical
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