EXAFS as a tool for catalyst characterization: a review of the ... - INT
EXAFS as a tool for catalyst characterization: a review of the ... - INT
EXAFS as a tool for catalyst characterization: a review of the ... - INT
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
<strong>EXAFS</strong> <strong>as</strong> a <strong>tool</strong> <strong>for</strong> <strong>catalyst</strong><br />
<strong>characterization</strong>: a <strong>review</strong> <strong>of</strong> <strong>the</strong> data<br />
analysis methods<br />
F. B. NORONHA<br />
Instituto Nacional de Tecnologia, Av. Venezuela 82, CEP 20081-310,<br />
Rio de Janeiro - RJ, Brazil, Fax (55-21) 206-1051 E-mail -<br />
bellot@peq.coppe.ufrj.br.<br />
Abstract - A <strong>review</strong> <strong>of</strong> <strong>the</strong> <strong>EXAFS</strong> data analysis methods is<br />
presented. A detailed description <strong>of</strong> <strong>the</strong> <strong>EXAFS</strong> signal extraction and<br />
<strong>the</strong> Fourier trans<strong>for</strong>m <strong>of</strong> <strong>the</strong> data are discussed. The procedure <strong>for</strong><br />
determining interatomic distances, coordination numbers and<br />
disorder effects from <strong>EXAFS</strong> data is described. This paper also<br />
discusses <strong>the</strong> data analysis statistics. Finally, one example <strong>of</strong> <strong>catalyst</strong><br />
<strong>characterization</strong> by <strong>the</strong> <strong>EXAFS</strong> technique is reported.<br />
Keywords: <strong>EXAFS</strong>, <strong>catalyst</strong> <strong>characterization</strong>, structure <strong>of</strong> <strong>catalyst</strong>s.<br />
<strong>INT</strong>RODUCTION<br />
During <strong>the</strong> p<strong>as</strong>t years, <strong>the</strong> extended X-ray absorption fine structure<br />
(<strong>EXAFS</strong>) technique h<strong>as</strong> been incre<strong>as</strong>ingly used <strong>as</strong> a valuable <strong>tool</strong> <strong>for</strong><br />
<strong>catalyst</strong> <strong>characterization</strong>. The <strong>EXAFS</strong> analysis is particularly<br />
interesting in <strong>the</strong> c<strong>as</strong>e <strong>of</strong> both highly dispersed and bimetallic<br />
<strong>catalyst</strong>s where it is usually difficult or impossible to obtain<br />
in<strong>for</strong>mation about <strong>the</strong> structure from o<strong>the</strong>r techniques, such <strong>as</strong> X-ray<br />
diffraction. There<strong>for</strong>e, <strong>EXAFS</strong> me<strong>as</strong>urements have been used to<br />
determine <strong>the</strong> metal particle size <strong>of</strong> highly dispersed <strong>catalyst</strong>s (Kip et<br />
al., 1987; Pandya et al., 1996) to locate noble metal particles in a<br />
zeolite matrix in function <strong>of</strong> <strong>the</strong> pretreatment (Tzou et al., 1988;<br />
Reifsnyder et al., 1998) to study <strong>the</strong> alloy <strong>for</strong>mation (Noronha, 1994;<br />
Sinfelt et al., 1984).<br />
THE <strong>EXAFS</strong> PHENOMENON
The X-ray absorption coefficient <strong>for</strong> an atom decre<strong>as</strong>es <strong>as</strong> <strong>the</strong> X-ray<br />
energy incre<strong>as</strong>es. It displays discontinuities (absorption edges) <strong>as</strong> an<br />
incident photon is absorbed by <strong>the</strong> atom and electronic transitions<br />
from a core atomic level to unoccupied conduction states above <strong>the</strong><br />
Fermi level take place.<br />
The photoelectron emitted in this process can be represented <strong>as</strong> a<br />
wave. If <strong>the</strong> excited atom is surrounded by o<strong>the</strong>r atoms, <strong>the</strong> outgoing<br />
wave scatters from <strong>the</strong> surrounding atoms, producing ingoing waves.<br />
These ingoing waves can constructively or destructively interfere with<br />
<strong>the</strong> outgoing waves. This interference produces <strong>the</strong> oscillatory<br />
behavior <strong>of</strong> <strong>the</strong> fine structure.<br />
The extended X-ray absorption fine structure (<strong>EXAFS</strong>) is <strong>the</strong><br />
oscillation in <strong>the</strong> absorption coefficient on <strong>the</strong> high-energy side <strong>of</strong> X-<br />
ray absorption edges, ranging from 30 to about 1000eV above <strong>the</strong><br />
edge. Stern, Sayers and Lytle related <strong>the</strong>se fluctuations <strong>of</strong> <strong>the</strong><br />
absorption coefficient to <strong>the</strong> atomic arrangement surrounding <strong>the</strong><br />
absorbing atom (Stern, 1974; Stern et al., 1975; Lytle et al., 1975).<br />
In this paper, we will be concerned with nei<strong>the</strong>r <strong>the</strong> <strong>the</strong>ory <strong>of</strong> <strong>EXAFS</strong><br />
(Stern, 1974) nor <strong>the</strong> experimental techniques used to me<strong>as</strong>ure<br />
<strong>EXAFS</strong> (Lytle et al., 1975; Meitzner, 1998). The aim <strong>of</strong> this work is to<br />
<strong>review</strong> <strong>the</strong> ma<strong>the</strong>matical procedure <strong>for</strong> treating <strong>the</strong> <strong>EXAFS</strong> spectrum<br />
in order to calculate <strong>the</strong> physical parameters. A final section presents<br />
one example <strong>of</strong> <strong>EXAFS</strong> application to catalysis.<br />
Data Analysis<br />
An X-ray absorption experiment involves <strong>the</strong> me<strong>as</strong>urement <strong>of</strong> <strong>the</strong><br />
total linear absorption coefficient, µ, <strong>as</strong> <strong>the</strong> photon energy is varied.<br />
In <strong>the</strong> c<strong>as</strong>e <strong>of</strong> a transmission experiment,<br />
ln I 0 /I = µ x (1)<br />
where I 0 and I are <strong>the</strong> photon intensities be<strong>for</strong>e and after <strong>the</strong><br />
absorber <strong>of</strong> thickness x.<br />
A typical X-ray absorption spectrum can be separated into four parts<br />
(Bart and Vlaic, 1987) (Figure 1):<br />
a- pre-edge region;<br />
b- edge region;<br />
c- X-ray absorption near edge structure (XANES) region;<br />
d- extended X-ray absorption fine structure (<strong>EXAFS</strong>) region.
Figure 1: Regions <strong>of</strong> <strong>the</strong> X-ray absorption spectrum <strong>of</strong> metallic cobalt.<br />
In <strong>the</strong> first region, <strong>the</strong> absorption coefficient decre<strong>as</strong>es <strong>as</strong> <strong>the</strong> energy<br />
incre<strong>as</strong>es due to transitions from o<strong>the</strong>r occupied levels <strong>of</strong> <strong>the</strong> same<br />
atom and <strong>of</strong> o<strong>the</strong>r atoms. A Victoreen law, µ(E) = C E -3 + D E -4 , or<br />
linear relation, µ(E) = A E + B, is used be<strong>for</strong>e <strong>the</strong> absorption edge to<br />
determine <strong>the</strong> constants. The absorption coefficient rises sharply at<br />
<strong>the</strong> edge, corresponding to <strong>the</strong> electron transitions to higher<br />
unoccupied levels. This region (b) is <strong>the</strong> absorption edge (within a<br />
range <strong>of</strong> a few electronvolts). Finally, <strong>the</strong> XANES and <strong>EXAFS</strong> zones<br />
are at <strong>the</strong> high-energy side <strong>of</strong> <strong>the</strong> absorption edge (c and d). XANES
and <strong>EXAFS</strong> stem from <strong>the</strong> same phenomenon. The difference between<br />
<strong>the</strong>m is due to <strong>the</strong> kinetic energy <strong>of</strong> <strong>the</strong> photoelectron in each c<strong>as</strong>e.<br />
At a low energy, <strong>the</strong> mean free path is high, which induces an<br />
important multiple scattering effect. On <strong>the</strong> o<strong>the</strong>r hand, at <strong>the</strong> <strong>EXAFS</strong><br />
region, <strong>the</strong> mean free path <strong>of</strong> <strong>the</strong> photoelectrons is limited.<br />
There<strong>for</strong>e, single scattering is <strong>the</strong> major process.<br />
The fine structure χ(E) <strong>as</strong>sociated to a particular absorption edge is<br />
thus:<br />
where µ(E) is <strong>the</strong> me<strong>as</strong>ured absorption coefficient, µ 1 (E) is <strong>the</strong><br />
absorption coefficient <strong>of</strong> <strong>the</strong> isolated atom and µ 0 (E) is <strong>the</strong> smooth<br />
background absorption be<strong>for</strong>e <strong>the</strong> edge. µ 0 (E) andµ 1 (E) can not be<br />
obtained directly and must be estimated.<br />
The advantage <strong>of</strong> this procedure is b<strong>as</strong>ed on <strong>the</strong> fact that µ 0 (E) is<br />
determined directly from <strong>the</strong> pre-edge region be<strong>for</strong>e <strong>the</strong> calculations<br />
<strong>for</strong> <strong>the</strong> <strong>EXAFS</strong> region. However, <strong>the</strong> µ 0 (E) extrapolation can produce<br />
anomalous behavior <strong>for</strong> µ 1 (E) - µ 0 (E), since it is highly sensitive to <strong>the</strong><br />
energy range <strong>of</strong> <strong>the</strong> pre-edge chosen. There<strong>for</strong>e, generally, <strong>the</strong><br />
Lengeler-Eisenberger method is used to calculate µ 0 (E) (Lengeler and<br />
Eisenberger, 1980). This method is b<strong>as</strong>ed on <strong>the</strong> following <strong>for</strong>mula:<br />
(2)<br />
First µ 1 (E) is calculated after <strong>the</strong> edge by a polynomial <strong>of</strong> degree n (n<br />
= 4, 5 or 6) or cubic splines. Then µ 0 (E) is determined from equation<br />
(3).<br />
In order to relate χ (E) to structural parameters, it is convenient to<br />
per<strong>for</strong>m a trans<strong>for</strong>mation to χ (κ) in <strong>the</strong> photoelectron<br />
wavevector κ space, where<br />
(3)<br />
(4)<br />
After conversion <strong>of</strong> energy to <strong>the</strong> k scale using eq. (4), <strong>the</strong><br />
normalized <strong>EXAFS</strong> function χ (κ ) is obtained <strong>as</strong> follows:<br />
(5)
The normalized <strong>EXAFS</strong> spectrum <strong>as</strong>sociated with <strong>the</strong> K-edge <strong>of</strong><br />
metallic cobalt at 298K is shown in Figure 2.<br />
Figure 2: Normalized K-edge <strong>EXAFS</strong> spectrum <strong>of</strong> metallic cobalt.<br />
For excitation <strong>of</strong> a s shell, <strong>the</strong> normalized <strong>EXAFS</strong> oscillations can be<br />
described by<br />
Where Rj is <strong>the</strong> distance from <strong>the</strong> central absorbing atom to atoms in<br />
<strong>the</strong> j th coordination shell, N j is <strong>the</strong> number <strong>of</strong> atoms in <strong>the</strong> j th shell, σj<br />
is <strong>the</strong> Debye-Waller factor due to static disorder and <strong>the</strong>rmal<br />
vibrations, λ (κ ) is <strong>the</strong> mean free path <strong>of</strong> <strong>the</strong> ejected photoelectron<br />
(6)
from <strong>the</strong> absorber atom and Σ <strong>the</strong> summation extends over j<br />
coordination shells, <strong>the</strong> term e -2rj/λ is due to inel<strong>as</strong>tic losses, Aj(κ ) is<br />
<strong>the</strong> backscattering amplitude from each <strong>of</strong> <strong>the</strong> N j neighboring atoms<br />
and φ j(κ ) is <strong>the</strong> ph<strong>as</strong>e shift between <strong>the</strong> incident and backscattering<br />
wave given by<br />
φ (κ ) = φ a(κ ) + φ b(κ ) (7)<br />
where φ a(κ ) is <strong>the</strong> ph<strong>as</strong>e shift due to <strong>the</strong> central atom and φ b(κ ) is<br />
<strong>the</strong> ph<strong>as</strong>e <strong>of</strong> <strong>the</strong> backscattering amplitude from <strong>the</strong> neighbor.<br />
Multiple scattering effects have been ignored in <strong>the</strong> derivation <strong>of</strong> eq.<br />
6. Fur<strong>the</strong>rmore, since <strong>the</strong> intensity <strong>of</strong> <strong>the</strong> outgoing wave decre<strong>as</strong>es<br />
very f<strong>as</strong>t with incre<strong>as</strong>ing R, <strong>the</strong>re is very little contribution to <strong>the</strong> fine<br />
structure <strong>of</strong> <strong>the</strong> distant atoms.<br />
The raw <strong>EXAFS</strong> signal obtained with <strong>the</strong> procedure described above is<br />
made <strong>of</strong> many sinusoidal waves. The Fourier trans<strong>for</strong>m is <strong>the</strong><br />
standard <strong>tool</strong> used <strong>for</strong> frequency separation. The Fourier trans<strong>for</strong>m<br />
<strong>of</strong> χ(κ ) yields <strong>the</strong> following radial distribution function (RDF):<br />
Since at high κ values, <strong>the</strong> χ(κ ) is low, function χ(κ ) is multiplied by<br />
<strong>the</strong> factor κ n be<strong>for</strong>e <strong>the</strong> trans<strong>for</strong>m is per<strong>for</strong>med in order to obtain<br />
more in<strong>for</strong>mation at those values (Vlaic et al., 1998). Factor κ n is<br />
used to weight <strong>the</strong> data according to <strong>the</strong> value <strong>of</strong> κ . Generally,<br />
values <strong>of</strong> n= 1, 2 or 3 are used. The limits <strong>of</strong> <strong>the</strong> integral, kmin and<br />
kmax, are <strong>the</strong> experimental minimum and maximum values<br />
<strong>of</strong> κ obtained. Ano<strong>the</strong>r problem related to FT is that <strong>the</strong> <strong>EXAFS</strong> signal<br />
h<strong>as</strong> a limited number <strong>of</strong> points. There<strong>for</strong>e, <strong>the</strong> Fourier integral is<br />
truncated. W(κ ) is a window function, where <strong>the</strong> function is Fourier<br />
trans<strong>for</strong>med in a limited range (kmin, kmax). Three types <strong>of</strong> windows<br />
have been used in <strong>the</strong> literature: HAMMING, HANNING and KAISER<br />
(Michalowicz, 1990).<br />
HAMMING<br />
HANNING<br />
KAISER<br />
(8)<br />
κ min < κ < κ max (9)<br />
κ min < κ < κ max (10)
(11)<br />
I 0 - modified BESSEL function, degree 0;<br />
τ - <strong>the</strong> shape <strong>of</strong> <strong>the</strong> window;<br />
κ 1 and κ 2 - window limits.<br />
Only <strong>the</strong> magnitude <strong>of</strong> <strong>the</strong> trans<strong>for</strong>m is considered (eq.12). It shows<br />
a series <strong>of</strong> peaks, which corresponds to <strong>the</strong> different coordination<br />
shells (Figure 3). Because <strong>of</strong> <strong>the</strong> ph<strong>as</strong>e shift, φ j (κ ), interatomic<br />
distances derived from <strong>the</strong> peaks <strong>of</strong> FT(R) have to be properly<br />
corrected to coincide with those <strong>of</strong> X-ray diffraction.<br />
(12)
Figure 3: Fourier trans<strong>for</strong>m corresponding to <strong>EXAFS</strong> spectrum <strong>of</strong><br />
metallic cobalt.<br />
When <strong>the</strong> contribution <strong>of</strong> two shells is not resolved in <strong>the</strong> Fourier<br />
spectrum, Fourier filtering can be used. By means <strong>of</strong> a filter function,<br />
specific peaks in <strong>the</strong> Fourier spectrum are separated from <strong>the</strong> rest <strong>of</strong><br />
<strong>the</strong> spectrum. The product <strong>of</strong> <strong>the</strong> spectrum with this filter function is<br />
Fourier backtrans<strong>for</strong>med into k space. This procedure separates <strong>the</strong><br />
contribution <strong>of</strong> adjacent coordination shells so that <strong>the</strong> effect <strong>of</strong> only<br />
<strong>the</strong> coordination shell <strong>of</strong> interest is maintained.<br />
In fact, <strong>the</strong> Fourier backtrans<strong>for</strong>m is calculated by<br />
(13)<br />
where W(κ) is <strong>the</strong> window <strong>of</strong> <strong>the</strong> Fourier trans<strong>for</strong>m and W’(κ) is <strong>the</strong><br />
window <strong>of</strong> <strong>the</strong> Fourier backtrans<strong>for</strong>m which separate <strong>the</strong> specific<br />
peak.
Thus, <strong>the</strong> resulting curves are fitted with <strong>the</strong> <strong>EXAFS</strong> <strong>for</strong>mula to<br />
determine R, N and σ . In order to extract in<strong>for</strong>mation about <strong>the</strong> local<br />
environment <strong>of</strong> <strong>the</strong> absorber, <strong>the</strong> backscattering amplitude and ph<strong>as</strong>e<br />
shift functions must be known. These functions can be obtained<br />
experimentally from <strong>EXAFS</strong> spectra <strong>of</strong> model compounds or calculated<br />
<strong>the</strong>oretically (Teo and Lee, 1979; McKale et al., 1988; Rehr, 1989).<br />
Experimental functions are extracted from reference compounds with<br />
known structures. However, it is not always possible to obtain<br />
experimental functions since <strong>the</strong> reference compounds do not exist or<br />
it is not possible to extract <strong>the</strong>m (Vlaic et al., 1998). Fur<strong>the</strong>rmore,<br />
experimental ph<strong>as</strong>e and amplitude functions must be extracted by<br />
using <strong>the</strong> same integration limits and <strong>the</strong> same windows to <strong>the</strong><br />
unknown sample in order to introduce <strong>the</strong> same truncation errors.<br />
In general, <strong>the</strong> accuracy <strong>of</strong> <strong>the</strong> analysis is about 0.01-0.02Å <strong>for</strong> <strong>the</strong><br />
interatomic distances, 5 to 15% <strong>for</strong> <strong>the</strong> coordination numbers and<br />
20% <strong>for</strong> σ (Lengeler and Eisenberger, 1980).<br />
The minimization procedure is carried over into <strong>the</strong> following function<br />
(Michalowicz, 1990):<br />
(14)<br />
where p i are <strong>the</strong> fitting parameters and W(k) is a weighting function.<br />
A residual factor is also defined by <strong>the</strong> following expression:<br />
(15)<br />
The number <strong>of</strong> parameters that can be determined from <strong>the</strong> <strong>EXAFS</strong><br />
signal is related to <strong>the</strong> number <strong>of</strong> independent points, N ind , by<br />
N par = N ind – 1 (16)<br />
There is some uncertainty in <strong>the</strong> literature on how to calculate N ind .<br />
According to Stern (1993), <strong>the</strong> correct expression is given by<br />
(17)<br />
The fit quality is given by <strong>the</strong> chi-square function. Particularly in<br />
<strong>EXAFS</strong> this function is defined <strong>as</strong> follows:<br />
(18)
where s(κ i ) is <strong>the</strong> standard deviation given by<br />
(19)<br />
The quality <strong>of</strong> <strong>the</strong> fit can also be expressed by a merit factor defined<br />
<strong>as</strong> (Faudon et at., 1993)<br />
(20)<br />
Evidence <strong>of</strong> Alloy Formation <strong>of</strong> Graphite-Supported Palladium-<br />
Cobalt Catalysts<br />
It h<strong>as</strong> been reported that <strong>the</strong> addition <strong>of</strong> a noble metal to a supported<br />
cobalt <strong>catalyst</strong> creates important changes in <strong>the</strong> selectivity <strong>of</strong> <strong>the</strong> CO<br />
+ H 2 reaction (Noronha et al., 1996; Idriss et al., 1992). In general,<br />
<strong>the</strong>se results are attributed to alloy <strong>for</strong>mation. However, no clear<br />
evidence <strong>of</strong> alloying is presented.<br />
Recently, <strong>EXAFS</strong> w<strong>as</strong> used to obtain both fur<strong>the</strong>r evidence <strong>of</strong> Pd-Co<br />
interaction and <strong>the</strong> mean composition <strong>of</strong> bimetallic particles<br />
(Noronha, 1994). Pd/G (2.26 wt.%), Co/G (3.61 wt.%) and<br />
Pd 16 Co 84 /G (3.37 Pd wt.% and 9.96 Co wt.%) <strong>catalyst</strong>s were<br />
prepared by <strong>the</strong> incipient wetness impregnation <strong>of</strong> <strong>the</strong> graphite.<br />
As shown in Figure 4, <strong>the</strong> radial distribution function (RDF) <strong>of</strong> <strong>the</strong><br />
bimetallic <strong>catalyst</strong> is different from <strong>the</strong> RDF <strong>of</strong> both Pd/G <strong>catalyst</strong> and<br />
reference sample (Pd foil). The first coordination shell consists <strong>of</strong><br />
palladium atoms alone in <strong>the</strong> Pd/G and in <strong>the</strong> reference. On <strong>the</strong> o<strong>the</strong>r<br />
hand, data analysis revealed <strong>the</strong> presence <strong>of</strong> both Pd and Co atoms in<br />
<strong>the</strong> first coordination shell <strong>of</strong> Pd (Table 1). The local atomic<br />
concentration <strong>of</strong> palladium, obtained by <strong>the</strong> n 1 /n 1 +n 2 ratio, w<strong>as</strong><br />
61.5% suggesting that <strong>the</strong> first shell around Pd atoms is clearly<br />
palladium-enriched.
Figure 4: Amplitude <strong>of</strong> <strong>the</strong> Radial Distribution Function at <strong>the</strong> Pd K-edge <strong>for</strong><br />
palladium foil (solid line) and Pd/G (dotted line) and Pd 16 Co 84 /G (d<strong>as</strong>hed line).<br />
Table 1: <strong>EXAFS</strong> parameters at <strong>the</strong> Pd K-edge<br />
Pd - Pd pair<br />
Pd - Co pair<br />
Sample n 1 R 1 (Å) σ 2 (Å 2 ) n 2 R 2 (Å) σ 2 (Å 2 ) Q (%) n 1 +n 2<br />
Pd foil 12.0 2.75 - - - - - -<br />
Pd/G 9.1 2.74 0.0000 - - - 5 -<br />
Pd 16 Co 84 /G 6.7 2.73 0.0310 4.2 2.61 0.0050 8 10.9<br />
The RDF <strong>of</strong> <strong>the</strong> bimetallic <strong>catalyst</strong> is not so different from <strong>the</strong> RDF <strong>of</strong><br />
both Co/G <strong>catalyst</strong> and reference (Figure 5). This suggests that <strong>the</strong><br />
environment <strong>of</strong> cobalt atoms in <strong>the</strong> Pd 16 Co 84 /G and in <strong>the</strong> reference<br />
sample is similar. However, since a fairly good fit cannot be obtained<br />
only with Co atoms in <strong>the</strong> first coordination sphere <strong>of</strong> cobalt, it w<strong>as</strong>
necessary to per<strong>for</strong>m <strong>the</strong> fit with Pd and Co atoms (Table 2). This<br />
results in a mean palladium concentration <strong>of</strong> only 7.7% around a Co<br />
atom, which is much lower than that expected from chemical<br />
analysis, indicating that Co atoms tend to be preferentially<br />
surrounded by Co atoms.<br />
Figure 5: Amplitude <strong>of</strong> <strong>the</strong> Radial Distribution Function at <strong>the</strong> Co K-edge <strong>for</strong> cobalt<br />
foil (solid line) and Co/G (dotted line) and Pd 16 Co 84 /G (d<strong>as</strong>hed line).<br />
Table 2: <strong>EXAFS</strong> parameters at <strong>the</strong> Co K-edge<br />
Co - Co pair<br />
Co - Pd pair<br />
Sample n 1 R 1 (Å) σ 2 (Å 2 ) n 2 R 2 (Å) σ 2 (Å 2 ) Q<br />
(%)<br />
n 1 +n 2<br />
Co foil 12.0 2.51 - - - - - -<br />
Co/G 11.5 2.50 0.0020 - - - 3 11.5<br />
Pd 16 Co 84 /G 8.0 2.50 0.0060 3.7 2.61 0.0080 9 11.7
There<strong>for</strong>e, <strong>the</strong> <strong>EXAFS</strong> analysis demonstrated that <strong>the</strong> alloy ph<strong>as</strong>e w<strong>as</strong><br />
<strong>for</strong>med during reduction, <strong>as</strong> already shown by magnetic and X-ray<br />
diffraction me<strong>as</strong>urements (Noronha, 1994). The bimetallic particles<br />
consist <strong>of</strong> both palladium and cobalt rich ph<strong>as</strong>es.<br />
CONCLUSIONS<br />
A <strong>review</strong> <strong>of</strong> <strong>the</strong> <strong>EXAFS</strong> data analysis methods w<strong>as</strong> presented. A<br />
detailed description <strong>of</strong> <strong>the</strong> <strong>EXAFS</strong> signal extraction and <strong>the</strong> Fourier<br />
trans<strong>for</strong>m <strong>of</strong> <strong>the</strong> data were discussed. The procedure <strong>for</strong> determining<br />
interatomic distances, coordination numbers and disorder effects<br />
from <strong>EXAFS</strong> data w<strong>as</strong> described. These parameters were calculated in<br />
order to obtain both fur<strong>the</strong>r evidence <strong>of</strong> Pd-Co interaction and <strong>the</strong><br />
mean composition <strong>of</strong> bimetallic particles.<br />
NOMENCLATURE<br />
Aj(κ ) <strong>the</strong> backscattering amplitude from each <strong>of</strong> <strong>the</strong> N j neighboring<br />
atoms<br />
E photoelectron energy<br />
E 0 energy <strong>of</strong> <strong>the</strong> absorption edge<br />
Planck`s constant divided by 2π<br />
h.ν energy <strong>of</strong> <strong>the</strong> X-ray photon<br />
I 0 photon intensities be<strong>for</strong>e <strong>the</strong> absorber<br />
I photon intensities after <strong>the</strong> absorber<br />
m m<strong>as</strong>s <strong>of</strong> <strong>the</strong> electron<br />
N j number <strong>of</strong> atoms in <strong>the</strong> j th shell<br />
N ind number <strong>of</strong> independent points<br />
N par number <strong>of</strong> parameters<br />
p i fitting parameters
Rj distance from <strong>the</strong> central absorbing atom to atoms in <strong>the</strong><br />
j th coordination shell<br />
s standard deviation<br />
x thickness <strong>of</strong> <strong>the</strong> sample<br />
X 2 chi-square function<br />
W window <strong>of</strong> <strong>the</strong> Fourier trans<strong>for</strong>m<br />
W’ window <strong>of</strong> <strong>the</strong> Fourier backtrans<strong>for</strong>m<br />
Greek letters<br />
κ photoelectron wavevector<br />
λ mean free path <strong>of</strong> <strong>the</strong> ejected photoelectron from <strong>the</strong> absorber<br />
atom absorption coefficient<br />
µ 1 absorption coefficient <strong>of</strong> <strong>the</strong> isolated atom<br />
µ 0 absorption coefficient be<strong>for</strong>e <strong>the</strong> edge<br />
σ Debye-Waller factor due to static disorder and <strong>the</strong>rmal vibrations<br />
φ ph<strong>as</strong>e shift between <strong>the</strong> incident and backscattering wave<br />
χ <strong>EXAFS</strong> function<br />
Super/subscripts<br />
e experimental<br />
c calculated<br />
exp experimental<br />
<strong>the</strong> <strong>the</strong>oretical<br />
REFERENCES
Bart, J.C.J. and Vlaic, G., Adv.Catal. 35, 1 (1987). [ Links ]<br />
Faudon, J.F., Senocq, F., Bergeret, G., Moraweck, B., Clugnet, G.,<br />
Nicot, C. and Renouprez, A., J.Catal. 144, 460 (1993). [ Links ]<br />
Idriss, H., Diagne, C., Hindermann, J.P., Kinnemann, A. and Barteau,<br />
M.A., Proceedings <strong>of</strong> <strong>the</strong> 10th Int. Cong. on Catal. (Guczi, L.,<br />
Solymosi, F. and Tetenyi, P., Eds.), part C, p. 2119, Elsevier,<br />
Budapest, 1992. [ Links ]<br />
Kip, B.J., Duivenvoorden, F.B.M., Koningsberger, D.C. and Prins,<br />
R., J.Catal. 105, 26 (1987). [ Links ]<br />
Lengeler, B. and Eisenberger, P., Phys.Rev.B 21, 4507<br />
(1980). [ Links ]<br />
Lytle, F.W., Sayers, D.E. and Stern, E.A., Physical Review B 11, 4825<br />
(1975). [ Links ]<br />
McKale, A.G., Veal, B.W., Paulik<strong>as</strong>, A.P., Chan, S.K. and Knapp,<br />
G.S., J.Am.Chem.Soc. 110, 3763 (1988). [ Links ]<br />
Meitzner, G., Catal. Today 39, 281 (1998). [ Links ]<br />
Michalowicz, A., Ph.D. diss., Paris Val de Marne (1990). [ Links ]<br />
Noronha, F.B., Ph.D. diss., COPPE/UFRJ, Rio de Janeiro<br />
(1994). [ Links ]<br />
Noronha, F.B., Frydman, A., Aranda, D.A.G., Perez, C.A., Soares,<br />
R.R., Moraweck, B., C<strong>as</strong>tner, D., Campbell, C.T., Frety, R. and<br />
Schmal, M., Catalysis Today 28 (1-2), 147 (1996). [ Links ]<br />
Pandya, K.I., Heald, S.M., Hriljac, J.A., Petrakis, L. and Fraissard,<br />
J., J.Phys.Chem. 100, 5070 (1996). [ Links ]<br />
Rehr, J.J., Physica B 158, 1 (1989). [ Links ]<br />
Reifsnyder, S.N., Otten, M.M. and Lamb, H.H., Catal.Today 39, 317<br />
(1998). [ Links ]<br />
Sinfelt, J.H., Via, G.H. and Lytle, F.W., Catal.Rev.Sci.Eng. 26, 81<br />
(1984). [ Links ]<br />
Stern, E.A., Physical Review B 10, 3027 (1974). [ Links ]<br />
Stern, E.A., Physical Review B 48, 9825 (1993). [ Links ]
Stern, E.A., Sayers, D.E. and Lytle, F.W., Physical Review B 11, 4836<br />
(1975). [ Links ]<br />
Teo, B.K. and Lee, P.A., J.Am.Chem.Soc. 101, 2815<br />
(1979). [ Links ]<br />
Tzou, M.S., Teo, B.K. and Sachtler, W.M.H., J.Catal. 113, 220<br />
(1988). [ Links ]<br />
Vlaic, G., Andreatta, D. and Colavita, P.E., Catal.Today 41, 261<br />
(1998). [ Links ]