EXAFS as a tool for catalyst characterization: a review of the data analysis methods

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 [phone] E-mail - [e-mail].

(Received: January 15, 1999; Accepted: July 5, 1999)

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, m, as the photon energy is varied. In the case of a transmission experiment,

ln I₀/I = m x (1)

where I₀ 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, m(E) = C E^-3 + D E^-4, or linear relation, m(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 c(E) associated to a particular absorption edge is thus:

(2)

where m(E) is the measured absorption coefficient, m₁(E) is the absorption coefficient of the isolated atom and m₀(E) is the smooth background absorption before the edge. m₀(E) and m₁(E) can not be obtained directly and must be estimated.

The advantage of this procedure is based on the fact that m₀(E) is determined directly from the pre-edge region before the calculations for the EXAFS region. However, the m₀(E) extrapolation can produce anomalous behavior for m₁(E) - m₀(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 m₀(E) (Lengeler and Eisenberger, 1980). This method is based on the following formula:

(3)

First m₁(E) is calculated after the edge by a polynomial of degree n (n = 4, 5 or 6) or cubic splines. Then m₀(E) is determined from equation (3).

In order to relate c (E) to structural parameters, it is convenient to perform a transformation to c (k) in the photoelectron wavevector k space, where

(4)

After conversion of energy to the k scale using eq. (4), the normalized EXAFS function c (k ) 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

(6)

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, sj is the Debye-Waller factor due to static disorder and thermal vibrations, l (k ) is the mean free path of the ejected photoelectron from the absorber atom and S the summation extends over j coordination shells, the term e^-2rj/l is due to inelastic losses, Aj(k ) is the backscattering amplitude from each of the N_j neighboring atoms and f j(k ) is the phase shift between the incident and backscattering wave given by

f (k ) = f a(k ) + f b(k ) (7)

where f a(k ) is the phase shift due to the central atom and f b(k ) 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 c(k ) yields the following radial distribution function (RDF):

(8)

Since at high k values, the c(k ) is low, function c(k ) is multiplied by the factor k n before the transform is performed in order to obtain more information at those values (Vlaic et al., 1998). Factor k n is used to weight the data according to the value of k . 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 k obtained. Another problem related to FT is that the EXAFS signal has a limited number of points. Therefore, the Fourier integral is truncated. W(k ) 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

k min < k < k max (9)

HANNING

k min < k < k max (10)

KAISER

(11)

I₀- modified BESSEL function, degree 0;

t - the shape of the window;

k₁ and k₂- 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, f_j(k ), 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(k) is the window of the Fourier transform and W’(k) 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 s . 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 s (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(k_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 + H₂ 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 Pd₁₆Co₈₄/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 n₁/n₁+n₂ 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 Pd₁₆Co₈₄/G (dashed line).

Table 1:
EXAFS parameters at the Pd K-edge

	Pd - Pd pair			Pd - Co pair
Sample	n1	R1 (Å)	s 2(Å2)	n2	R2 (Å)	s 2(Å2)	Q (%)	n1+n2
Pd foil	12.0	2.75	-	-	-	-	-	-
Pd/G	9.1	2.74	0.0000	-	-	-	5	-
Pd16Co84/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 Pd₁₆Co₈₄/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 Pd₁₆Co₈₄/G (dashed line).

Table 2:
EXAFS parameters at the Co K-edge

	Co - Co pair			Co - Pd pair
Sample	n1	R1 (Å)	s 2(Å2)	n2	R2 (Å)	s 2(Å2)	Q (%)	n1+n2
Co foil	12.0	2.51	-	-	-	-	-	-
Co/G	11.5	2.50	0.0020	-	-	-	3	11.5
Pd16Co84/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(k ) the backscattering amplitude from each of the N_j neighboring atoms

E photoelectron energy

E₀ energy of the absorption edge

Planck`s constant divided by 2p

h.n energy of the X-ray photon

I₀ 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

X² chi-square function

W window of the Fourier transform

W’ window of the Fourier backtransform

Greek letters

k photoelectron wavevector

l mean free path of the ejected photoelectron from the absorber atom absorption coefficient

m₁ absorption coefficient of the isolated atom

m₀ absorption coefficient before the edge

s Debye-Waller factor due to static disorder and thermal vibrations

f phase shift between the incident and backscattering wave

c EXAFS function

Super/subscripts

e experimental

c calculated

exp experimental

the theoretical

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Publication Dates

• Publication in this collection
  16 Dec 1999
• Date of issue
  Sept 1999

History

• Accepted
  05 July 1999
• Received
  15 Jan 1999