The Journal of
Physical Chemistry
0 Copyright, 1988, by the American Chemical Society
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VOLUME 92, NUMBER 3 FEBRUARY 11,1988
ARTICLES Scaling Extended X-ray Absorption Fine Structure to Debye-Scherrer Diffraction Data. 1 N-S. Chiu and S . H.Bauer* Department of Chemistry, Baker Laboratory, Cornel1 University, Ithaca, New York 14853- 1301 (Received: February 9, 1987; In Final Form: June 8, 1987)
Specific atom-centered radial distribution functions, which can be derived from Debye-Scherrer difference patterns recorded at two wavelengths within the anomalous dispersion region of the element of interest, can be used to calibrate the phase-shifted radial distributions derived from EXAFS spectra thus obviating the need to record the spectra of similar but known structures for estimating phase shifts. At the same time, the amplitude levels of the EXAFS patterns can be normalized to correspond to the atomic numbers of the back scatterers, rather than to their atomic form factors. From the combined sets of adjusted data the normalized radial distribution functions have high resolution and peak areas that are quantitatively related to the scattering species. (Because the requisite diffraction patterns are not yet available, computed values were used in developing the computer codes.)
Introduction There is an evident need for detailed structural data of amorphous materials and submicroscopic clusters of metals, metal oxides, or alloys, prepared for use as catalysts, by sputtering or by pyrolysis of precursors. Not only is the molecular geometry of any sample of matter an essential fingerprint which uniquely identifies it, but also knowledge of its structure provides the basis for classification, and an initial guide toward an explanation of its physical and chemical properties. At present three techniques have been developed for evaluating partial structure factors for materials which consists of two or more elements. Radial distribution functions centered at specific elements can be derived from (I) neutron diffraction patterns of samples that have two levels of isotopic enrichment of the element of interest;' (11) extended X-ray absorption fine structure, recorded as a function of photon energy just past the characteristic edge;* (111) differences
between X-ray diffraction patterns recorded at several wavelengths in the anomalous dispersion region of the element of i n t e r e ~ t . ~ Each technique has advantages and limitations. The neutron diffraction technique (I) has proved most successful in providing high-resolution data, which particularly illuminated liquid structures. Its obvious limitations are the need for high-flux beams of monochromatized neutrons, and for each element-centered radial distribution curve the preparation of two sufficiently large samples, each adequately enriched with an isotope that has a distinctive coherent scattering length. The advantages and limitations of EXAFS (11) for structure determination are ~ e l l - k n o w n . ~Briefly, they are as follows. (a) (3) (a) Fukamachi, T.; Hososa, S.; Kawamura, T. J . Appl. Crysrallogr. 1977, 10, 321. (b) Shevchik, N. J. Philos. Mag. 1977, 35, 805, 1289. (c) Fuoss, P. H.; Eisenberger, P.; Warburton, W. K.; Bienenstock, A. Phys. Rev. Lett. 1981, 46, 1537. Also refer to SSRL report 80/06 by the same author. (d) Waseda, Y. Novel Applications of Anomalous X-ray Scattering; Springer-Verlag: New York, 1984. (4) Good reviews: Gurman, S. J. J . Mater. Sci. 1982, 17, 1541. Lee, P. A,; Citrin, P. H.; Eisenberger, P.; Kincaid, B. M. Rev. Mod Phys. 1981, 53, 169.
(1) Enderby, J. E. J . Phys. C 1982, 15, 4609. (2) Teo, B. K. EXAFS: Basic Principles and Data Analysis; SpringerVerlag: Berlin, 1985.
0022-3654188 , ,12092-0565$01SO10 I
0 1988 American Chemical Societv -
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566
The RD curves are centered about the selected atomic species (j). (b) The experimental procedures are simple and are readily performed; spectra can be obtained over a wide range of sample temperatures and ambient atmospheres. The data reduction (in first instance) is well developed, and refined computer codes are avai1able.j (c) Potentially the resolution is high, since the upper (sk) limit is at least 30, and often reaches 40; [ k 27r/A; s 2 sin 6; 26 is the scattering angle]. (d) Due to the presence of the 1/R2 factor (atomic dimension) under the integral (see eq 1 below), the radial distribution curves derived from EXAFS data appear like those from gas-phase X-ray or electron diffraction patterns, rather than from X-ray diffraction patterns for condensed phases. The reason: the effective coherence length is short because the amplitudes are damped by the 1/R2factors. (e) As for other X-ray, neutron, or electron diffraction scattering probes, EXAFS measures a bulk property. Nonetheless, one can arrange to study systems wherein the surface structure is greatly emphasized by dispersing the elements of interest over a high-area substrate with a low atomic number, or by investigating highly dispersed particulates, in which a large fraction of the interesting constituents are either on the surface or adjacent to it. However, there are difficulties: (a) The recorded oscillations in absorption coefficient (or fluorescence yield) above the background are related to the radial distribution of atomic species [D(R)] through an integral with a phase-shifted argument:
kx(k)
Chiu and Bauer
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988
exp[2(u2)k2] (Lf(k;r)I) L m d R y e - 2 R / ( A sin ) [2kR
+ $ ( k ) ] (1)
lncoh.
x
” 00
I
‘ 20
I
40
60
80
100
120
140
160
sk(A-’)
Figure 1. The atomic incoherent and coherent scattering factors for Mo, for X = 0.621 and 0.630 A.
density, andf’and j” are the real and imaginary components of dispersion; these are essentially independent of sk but are function of A]. The limitation imposed by the superposed structure-insensitive scattered radiation (Compton) does not appear since that is eliminated during the subtraction step. The maximum value of sk is set by the location of the j absorption edge; hence the range in sk is limited [=O.l?r/Adge h/&dge]. Consequently the resulting radial distribution peaks have low resolution. This is an intrinsic limitation that cannot be obviated by a deconvolution procedure. From the above general discussion it is clear that EXAFS and G(XRD) provide complementary portions of diffraction data. Were it possible to combine these patterns with appropriate scaling, the following significant improvements would be achieved. (1) By correlating Fourier transforms of EXAFS spectra with RD functions derived from G(XRD), the magnitudes of phase shifts of the peak positions derived from the former can be evaluated, thus eliminating the need to transfer phase shifts from spectra of known, “similar” structures. (2) After appropriate normalization of both the ( A p / p ) and G(XRD) patterns, scaling of the former to the latter can be achieved by equating them in the region of overlap. [This proved to be a nontrivial operation; four procedures were tested in the course of developing the proposed sequence of steps.] One can then derive a combined intensity curve over the extended range: O . l ~ / h , d ~ , 2k,,,(EXAFS). (3) The Fourier transform of the extended intensity function has high resolution, due to the large range in sk, and quantitative structural information that extends from short to long R. To develop a protocol for recording the necessary scans and converting these data into a format suitable for scaling we undertook the computer simulation described below.
-
x(k) is the experimentally measured function, x(k) = ( p - pLbg)/pLbg; the essential atomic back-scattering factors [ f ( k ; 7 r ) ] are not known with sufficient precision; neither are the phase shifts [$(IC)] that appear in the argument of the sine term.6 It is therefore essential that absorption curves for very similar structures be available for calibration. At best, the areas under the RD curves obtained by using adjusted functions have semiquantitative reliability. (b) No structurally useful data are available over the range 0 < ( 2 k ) < 8. This leads to a loss of structural information for interatomic distances beyond the second (or third) coordination sphere, particularly for amorphous materials. (c) Due to the large background absorption from overlapping wings of L,M edges of a high Z component in a sample, the desired absorption curves at the K edge for a low Z component must be recorded with exceptional care to maximize the signal/noise ratio. In procedure I11 Debye-Scherrer diffraction patterns are recorded at two wavelengths (A,; A,) in the anomalous dispersion region of atomic species j; high fluxes of tunable monochromatized X-rays are needed, as are currently available at synchrotron radiation facilities. Since the magnitudes of the dispersion corrections have been t a b ~ l a t e dFourier ,~ inversion of the difference [I,(&) - I,(sk)] = G(XRD) for identical sk values leads to D(R,,). Thus, the overlapping radial distribution functions in a multiThe Data Manipulation Sequence component sample can be unscrambled. One of the obvious X-ray Diffraction. Each of the following steps is represented limitations is the enhanced relative magnitude of the noise resulting by a quantitative relation for which an algorithm was written and from such a subtraction process for small differences in the atomic programmed on an IBM-XT compatible system. scattering factors: (i) In our laboratory many EXAFS data sets, recorded at the Mo K edge of well-crystallized and amorphous materials, are available. Analyses of these have been p ~ b l i s h e d .However, ~ no [here Lo(&)is the Fourier transform of the electronic charge adequate Debye-Scherrer patterns of the same materials have been recorded in the anomalous dispersion region. Hence, for two ( 5 ) (a) Chiu, N.-S.; Bauer, S.H.; Johnson, M. F. L. J . Catal. 1984, 89, test materials [MoS, and Moo3], total diffracted densities were 226; ( b ) Acta Crystallogr. 1984, C40, 1646; (c) J . Catal. 1986, 98, 32; (d) calculated as functions of sk at A, = 0.621 8, and A, = 0.630 8,, J . Catal. 1986, 98, 51. Studies at the Co K edge, submitted for publication both on the low-energy side of the Mo K edge; complete atom in J . Catal. form factors were used.’ Figure 1 shows the relative magnitudes (6) However, see: (a) Lee, R. A,; Beri, G. Phys. Reu. B 1977, IS, 2862. (b) Teo, B.-K.; Lee, P.A J . A m . Chem. Soc. 1979, 101, 2816. of the atomic scattering factors for Mo, at two wavelengths close (7) (a) Hubbell, J. H.; Veigele, W. J.; Briggs, E.A.; Brown, R. T.; Cromer, to the steeply rising K edge. For S and 0 atoms there is no D. T.; Howerton, R. J. J . Phys. Chem. Ref. Data 1975.4, 471. (b) Hubbell, discernible difference between 0.621 and 0.630 A. [No temJ. H.; Overbo, I. J . Phys. Chem. Ref.Data 1979,8, 69. (c) Cromer, D. T.; perature factor was included in the calculated patterns. For a Lieberman, D. J . Chem. Phys. 1970, 53, 1891; Acta Crystallogr., Sect. A macroscopic powder sample the peaks would be somewhat sharper, 1981, A37, 267. ( d ) Jensen, M. S. Phys. Lett. 1979, 7 4 4 41.
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Scaling EXAFS to Debye-Scherrer Diffraction Data
The Journal of Physical Chemistry, Vol. 92, No. 3, I988 567 0
but located at the same sk values.] The coherent and incoherent atomic terms were also incorporated to simulate experimental scans. The range covered was sk = 0 to 16. No polarization factor was inserted since the synchrotron beam is 90% polarized in the plane of the diffraction circle. Designate these computed intensities [which simulate experimentally determined scans] Il(sk) and Z2(sk);all atoms other than j are identified with the subscript 1. Then I(sk) =
(1#1‘)
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v;12 = V;O(sk) +fy’ + V{I2
‘0.0
Vfil V;O(sk) + f i l v ; O ( s k )+f:l +f’if”, (3a) [For the simulations we tabulated all distances of atom pairs that were =lo A, or shorter, centered about j and 1 atoms.] Were the diffraction patterns experimentally recorded, their intensities would have to be individually scaled with respect to the intensities recorded at the highest (extrapolated) sk, using calculated values for the dominant atomic incoherent scattering plus small corrections for the background level of the atomic coherently scatter radiation. [The elementary composition of the sample under study is presumed known.] (ii) From Zl(sk)and Z2(sk)subtract the corresponding calculated coherent atomic scattering function of center atoms, j. Ji(sk) E Ii(sk) - CV;(sk)12
2.0
4.0
6.0
8.0 sk(A-’)
10.0
12.0
14.0
16.0
2 :: (b)
A
(4)
(coherent) J
(iii) Compute (Jl(sk)- J2(sk)}.This is the desired atom-center diffraction function, Figure 2a. (J,(sk)- Jz(sk)) G(XRD)I =
0
a
I
W
700
20
40
60
80 sk(A-’)
100
120
140
160
Figure 2. (a) The difference curve is G(XRD)f for X 0.630-0.621 %., which corresponds to eq 5. (b) The difference curve normalized to atomic numbers. 6(XRD)Z. This corresponds to eq 7 The complete pattern 0 < ( s k ) < 16 must be included for proper inversion If the section sk < 2 is not experimentally available, a computed curve should be added, based on an approximated structure.
All contributions from atom pairs that are independent of the j species and incoherent scattering function cancel.* (iv) An atomic number scaled intensity function G(XRD)Z is then obtained by dividing b(XRD)f by an mean product of atomic form factors. Define $j(sk) = J / Z J ;$l(sk) = f ; / Z l ;etc. Then
Since the $l’s differ little from each other, we have introduced a composition-weighted mean function: (+) Clxl$l.Then G(XRD), e
-
(sk)wRD)/
{+j(Xl)
+ $ j ( U I { $ j ( X l ) - 4 j ( ~ 2 ) 1-
1 -2 .., [ Z j z / R i , ]sin skRjjt JJ
+
Refer to Figures 2b, which is the Z-scaled intensity function. To is independent an acceptable approximation, ( +)/(4J(XJ+ dJ(X2)) of sk, and is readily calculated. (v) The Fourier transform of 6(XRD)Z yields a j-elementcentered radial distribution [ D o ( R ) / R ] Figure , 3a, but with relatively low resolution due to the restricted upper limit of sk. It does include structural information for large R . The peak areas are proportional to (NJZJ2/R,,,) and (NIZIZJ/RIJ) for each type of atom (1) around the central atom j. Comment, for later reference: eq 7 does not show Debye-Waller factors. However, in computing the sine transform a damping factor was inserted of the form exp[-a(sk)’], with a set so that exp[-a(sk),,,2] = 7%. We shall refer to this term as the 7% modulating function.
Preparation of EXAFS Radial Function Consider now the reduction of EXAFS spectra to a stage comparable to G(XRD),. (vi) The initially approximated background function ( M , , ~ ) must be corrected; for this step we developed an objective procedure? Also, we found that the conventional replacement in (1) of
dk) = (lf7k;r)l)exp[-2(az)k21
(8) The magnitude of the difference function is greatly enhanced and the relative noise levels reduced, when I , is recorded below the edge, and I , above it. Preliminary experiments with an energy dispersive detector (energy resolution of approximately 150 V) indicate that the recorded levels of fluorescence radiation may be sufficiently reduced to give useful diffraction scans. Scintillation counters do not have adequate energy resolution.
(8) by kW2is a poor approximation. A qualitatively better approximation is achieved by dividing the initially evaluated x l ( k ) by a computed q ( k ) , using an atom-weighted average of back33.
(9) Chiu, N.-S.; Bauer, s.H.; Johnson, M. F. L. J . Mol. Srruct. 1985,125,
568
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The Journal of Physical Chemistry, Vol. 92, No. 3, 1988 a
‘0.0
1.0
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5.0 R
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7.0
8.0
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9.0
(4
80
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sk(A-’)
Figure 5. The background-adjustedand normalized EXAFS function, skx2(sk)/q(sk),with ( a ) = 0.05 A.
4 (b)
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‘ 4 0
of the structure, which would be recycled. The Fourier transform of [kxi(k)/q(k)] is thus a first approximation to a radial distribution function, designated pi(rt,)/R$; [ R, is the phase-shifted distance from the central atom]. (vii) By suitable manipulation9 one can then derive a better approximation for the intensity function (Figure 5), from which we derive [p2(R+)/R:]; Figure 3b. This radial function should be relatively free of spurious peaks and show no negative values. However, it still incorporates phase shifts in the peak positions, and the amplitudes are not scaled to the corresponding products of atomic numbers.
00
10
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R (A)
Figure 3. (a) The Fourier transform of Figure 2b, computed with y = 10%. This has been designated @ ( R ) / R . (b) The Fourier transform of k x , ( k ) / q ( k ) , illustrated in Figure 5 . This FT was designated [ P ~ ( R + ) / R and + ~ ] is , the radial distribution derived from the back-
ground-corrected EXAFS spectrum.
0 0
0 0
\
0
.-.
; 0
/
,’--I,
/
\
% S I J’
0
l
a
‘ \
1
0 0
40
BO
120
Scaling Whereas correcting the peak positions in p2(RJ,)/Rii.fis straightforward, scaling the corresponding amplitudes requires a more extended sequence of steps. (viii) A narrow window is placed about each peak in the EXAFS radial function, and the peak is displaced to the position at which the corresponding peak appears in the 10% modulated transform of G(XRD)=. Generally, the magnitudes of the shifts for the various coordination shells differ little from each other; all are positive. The shifted p 2 ( R ) / R 2is then multiplied by R, so that the “synthesized” function represents p2(R)/R; this corresponds to Do(R)/R. The inversion process in (ix) converts EXAFS peak shapes to near-Gaussian; then their areas are scaled to corresponding peaks derived from G(XRD)= (ix) A scaling factor must be obtained individually for each p2(R)/R peak. [Peak-by-peak inversion and individual scaling proved essential for developing correct peak areas in the final RD curve (demonstrated in Table I).] Upon inversion, the corresponding intensity function is plotted vs sk (s = 2), to match the scale of the XRD intensity function. Shift to lower sk the sinusoidal EXAFS function so that it overlaps that from XRD at the closest maximum. Multiply the EXAFS amplitude‘by ae-fl(sk-skw), where a is such that the mean amplitude of EXAFS in the overlap region [sk,] equals the mean intensity of the XRD function, and (3 is such that at skmanthe amplitude of EXAFS is about 0.2 of that at sk,,; illustrated in Figure 6a. Sum the separate, scaled EXAFS intensities and meld the resulting function with the 6(XRD)= pattern, shown in Figure 6b. (x) The final radial distribution, D(R)/R, is the Fourier transform of the combined amplitude functions. For this step [as for (v)] a sine transform, with modulation functions as required for resolution of adjacent peaks, is used. The desired D(R) is N,Z,Z,weighted; it has good resolution and extends to large values of R. For MoS2 we illustrated in Figure 6a the scaling of the sinusoidal EXAFS intensity function to that from G(XRD)= for a single radial distribution peak, at 5.02 A. Figure 6b is the total melded intensity pattern that is range-extended and Z-weighted. Figure 7a,b is the corresponding sine transforms, computed with y = 0%
160
200
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280
320
360
sk(A-’)
Figure 4. (a) Theoretical back-scattered amplitude for Mo. (b) Theoretical back-scattered amplitude for MoS, (using composition-weighted contributions). For clarity they scales for curves (a) and (b) were placed on the right and left, respectively.
scattered atom-form factors. Theoretical values for the amplitude functions have been tabulated.6b To underscore the importance of amplitude scale conversion of x(k) by dividing by q ( k ) rather than (k)-2,we show the calculated back-scattered amplitudes for Mo (Figure 4a) and for MoS, (Figure 4b); their functional dependence on k is clearly not (-2) power. For unknown structures this step will have to follow an initial preliminary approximation
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988 569
Scaling EXAFS to Debye-Scherrer Diffraction Data TABLE I: Peak Area Ratios [Derived from D ( R ) Curves] MoS~
Deak no.
(XWZ
theor
r = O
MOO,
combined Y
= 0%
Y
= 10%
(XWZ
theor
r - 0
Y
combined = 10% Y = 20%
~
1 2.63 1 .oo 1.50 1.88 3.46 2.96 3.46 1.67 1.38 1.21
1" 2" 3 4" 5" 6" 7 8 9 10 11 av dev
1 2.42 0.99 1.31 1.74 2.69 2.76 3.24 1.35 1.32 0.84 0.25
1 2.54 1.08 1.38 1.76 2.86 3.03 3.36 1.49 1.34 0.74 0.19
1
1 4.70 4.12 7.52 6.96b
'1
2.4 1.03 1.36 1.86 2.99 3.02 3.41 1.48 1.38 0.71 0.17
4.17" 3.42" 6.58' 4.17" 3.42 3.04 10.38 12.63 3.08 6.21
1
1 3.53 4.97 7.24 4.65 2.90 3.38 10.58 14.23 4.77 8.63 1.02
3.52 5.03 7.25 4.72 2.91 3.42 10.61 14.29 4.79 8.64 1.04
5.06 11.27 14.16 5.82 8.47 1.24
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" EXAFS augmented. Combination of peaks 5 and 6;resolved when EXAFS augmented.
d
I
0.0
4.0
8.0
12.0
16.0
20.0
24.0
28.0
32.0
7 0.0
1.0
2.0
i 3.0
4.0
5.0
6.0
7.0
(1.0
0.0
10.0
R (A)
sk(A-')
ll
2 N
1
(b)
21
zI 0.0
-,I 4.0
8.0
, 12.0
7 0.0 16.0 sk(A-')
20.0
24.0
28.0
1.0
32.0
F i e 6. (a) Melding of the sinusoidal amplitude function for the 5.02-A
peak that appears in Figure 3b (after phase shift), shown dashed, with that for the corresponding calibrating peak (Figure 3a). The scaling factor a! = 740. (b) The melded intensity function for MoS,. and 10% modulating functions. These should be compared with Figure 3a,b for the two criteria of merit: fwhm, and 27,weighted peak areas. The significant improvement in spacial resolution is obvious; quantitative checks of peak areas are presented in Table
I. A similar set was computed for Moo3,which consists of highly distorted Os octahedra about Mo atoms. In this case, the spatial resolution, provided by the P ~ ( R Jcurves, / ~ ~is not so favorable. In the simulations, the XRD patterns were terminated at sk = 10, which is generally a practical limit. Figure 8a is the sine transform of the difference pattern with y = 0%; this corresponds
2.0
3.0
4.0
5.0 R (A)
8.0
7.0
1.0
0.0
-
10.0
Figure 7. (a) The sine transform of curve 6b (0% modulated): D ( R ) / Rabout Mo. (b) The sine transform of curve 6b, 10% modulated. Because of the higher resolution developed when lower modulation is used, truncation of the Fourier transform generates small lobes and negative spike-s adjacent to the intense peaks.
to Figure 3a. The reduced, background-adjusted intensity function derived from experimental absorption spectra of Moo3 was inverted to give the radial function shown in Figure 8b; it corresponds to Figure 3b. Finally, Figure 9 is the scaled and melded intensity pattern for MOO, (corresponding to Figure 6b). Figure 10a is the sine transforms of Figure 9 with y = 20% and lo%, respectively. These correspond to Figure 7a,b.
Comments Based on computed XRD difference patterns we developed a routine for scaling EXAFS spectra with XRD patterns (pro-
Chiu and Bauer
The Journal of Physical Chemistry, Vol. 92, No. 3, 1988
578
'0.0
3.0
2.0
1.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
d
10.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
6.0
7.0
8.0
9.0
10.0
R (A)
R (A)
; Downloaded by GEORGETOWN UNIV on September 3, 2015 | http://pubs.acs.org Publication Date: February 1, 1988 | doi: 10.1021/j100314a001
(b)
0.0
1.0
3.0
2.0
4.0
5.0
6.0
7.0
1.0
R (A)
9.0
-
10.0
=)
0 0
.(0
x x
1
t
I
1 8
7 0 0
40
80
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280
1.0
2.0
3.0
5.0
4.0
R
Figure 8. (a) The sine transform of the computed difference curve [a(XRD),] for MOO,, for X = 6.30 and 0.621 A; y = 0% @ ( R ) / R . (b) The Fourier transform of the background-adjusted EXAFS intensity function for MOO, p2(R,)/R+*.
9
(0.0
32.0
sk(A-')
Figure 9. The melded intensity pattern for MOO, grammed for an IBM-XT compatible), and thereby developed one-dimensional radial distribution functions that have enhanced resolution, an extended range in detectable interatomic spacings, and quantitatively correct peak areas. This procedure eliminates the need for calibrating radial functions derived from EXAFS
(A)
Figure 10. (a) The sine transform of Figure 9, y = 20% =+ D ( R ) / R about Mo. (b) The sine transform of Figure 9, y = 10%. spectra for an unknown by reference to closely similar known structures. Now calibrations can be achieved by recording XRD patterns for the same substance at two wavelengths within the anomalous dispersion region of the central element. Clearly, a one-dimensional radial distribution function merely provides a constraint on a three-dimensional model that must be developed; its parameters can be further refined by least-squares fitting of computed to observed EXAFS and XRD patterns. The proposed data manipulation sequence is no more extended than the sum of what is in general practice for two sets of experiments, but has the added advantage that it is fully programmed and essentially objective. Recorded XRD difference patterns (after corrections for absorption and angle dependent apparatus sensitivity) may have rather large S/N ratios. This remains to be determined experimentally. Finally, it should be noted that the procedure described in this report is restricted to the case where the distribution of 1 atoms about the central element (j)is of one type. The treatment of mixtures (Le., two or more structure types, such as MX, + MY,,,), either mechanical or as solid solutions, is more complicated and requires additional data for distinctive structure resolution.
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administrated by the American Chemical Society, for support of this research. The EXAFS spectra were recorded at the Cornel1 High Energy Synchrotron Source, supported by NSF grant No. DMF-780/267. Registry No. Mo, 7439-98-7; MoS2, 1317-33-5; MOO,, 1313-27-5.
