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EXTENDED X-RAY ABSORPTION FINE
STRUCTURE : RECENT DEVELOPMENTS
P. Lee
To cite this version:
JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 7 , Tome 39, Juillet 1978, page C4-120
EXTENDED X-RAY ABSORPTION FINE STRUCTURE
:
RECENT DEVELOPMENTS
P. A. LEE Bell Laboratories,
Murray Hill, New Jersey 07974, U.S.A.
Rksumk. - L'EXAFS (Structure Fine dlAbsorption X) est l'ttude des oscillations du coefficient d'absorption X, en fonction de l'tnergie du photon X au-dessus du seuil. 11 est depuis longtemps admis que ce phtnomene est lie aux modifications de 1'Ctat electronique final resultant de la presence des atomes voisins. Dans les dernieres annees, I'EXAFS est, de plus en plus, apparu comme un nouvel outil dans l'ttude des structures ; la mise en service de sources de rayonnement synchrotron, multipliant par un facteur 106 les intensites disponibles dans un large domaine d'energie, a permis l'obtention, en quelques minutes, de spectres EXAFS ayant un excellent rapport signal sur bruit. Plus recemment, enfin, des progres ont ete realises dans les methodes d'analyse des resultats. En effet, avant d'extraire des distances exactes d'un spectre EXAFS, on doit connaitre les dephasages associes aux propriites de retrodiffusion des atomes ; ces derniers peuvent Etre obtenus par analyse de systemes modeles connus ou par des calculs ab initio. Si la couche des premiers voisins est suffisamment isolee, les d e w mirthodes ont demontre la possibilitk de mesurer des distances avec une precision de 0,01
A.
Des systemes, oh plusieurs distances interviennent, ont ete aussi analyses avec succes.L'intensite du rayonnement synchrotron permet de s'interesser i des expkriences jusqu'a present impossibles, par exemple I'EXAFS de surface. I1 a ete demontre qu'en mesurant l'intensite d'une transition Auger en fonction de I'knergie du photon incident, on pouvait detecter un signal EXAFS dQ a une monocouche d'atomes absorbes. Les recentes experiences, sur ce sujet, faites par Citrin, Eisenberger et Hewltt seront presentees.
Abstract. -Extended X-ray Absorption Fine Structure (EXAFS) refers to the oscillation of the X-ray absorption coefficient as a function of X-ray energy above threshold. It has long been recognized that this phenomenon is caused by modifications of the final electronic state due to the presence of the surrounding atoms. In the past few years there has been growing appreciation of the possibility of using EXAFS as a new structural tool. At the same time synchrotron radiation in this energy range has become available. The 106 increase in tunable X-ray intensities available over a broad spectral region means that EXAFS spectra with excellent signal-to-noise can be obtained in a matter of minutes. More recently progress has also been made in the ability to analyze these data. Before one can extract distances from the EXAFS data, it is necessary to have information on phase shifts associated with the scattering properties of the photoelectrons. Such phase shifts can be obtained either by analysis of model systems with known distances or by ab initio calculations. In cases where the nearest neighbour shell is sufficiently isolated, both methods have been demonstrated to yield nearest neighbour distances to an accuracy of 0.01
a.
Multiple distance systems have also been analyzed with good results.The availability of an intense X-ray radiation from the synchrotron source naturally leads one to consider experiments that were previously impossible. One such example is surface EXAFS. It has been pointed out that by measuring the intensity of a single Auger transition as a function of photon frequency, it is possible to obtain EXAFS signal from a monoiayer of adsorbed atoms. The recent experimental observation of surface EXAFS by Citrin, E~senberger and Hewitt will be reviewed.
Extended X-ray Absorption Fine Structure half a century and the basic physical explanation has (EXAFS) refers to oscillations of the X-ray absorp- been provided by Kronig [l] as being due to modifi- tion coefficient on the high energy side of an absorp- cation of the final state of the photoelectron by tion edge. Such oscillations can extend up to 1 000 eV atoms surrounding the excited atom. As we shall above the edge and may have a magnitude of 10 "/, see in greater detail later, more recent work has or more. This phenomenon has been known for established that a single scattering short-range order
EXTENDED X-RAY ABSORPTION FINE STRUCTURE C4-121
theory is adequate under most circumstances. The atomic shells. The advantages of EXAFS versus oscillatory part of the absorption coefficient AX conventional X-ray diffraction are obvious and indeed normalized to the background X , is given by [2-41 some of the features were already appreciated by Hartree et al. [ 5 ] . EXAFS permits the determination
Ax
- - - -
C
3(E^.fi)' 2 N. A(k) sin X of the local structure of each individual atomicXo i kr? species. Single crystals are not required,. The appli- cations that immediately come to mind are compli-
X (2 kr,
+
2 6;(k)+
I9(k)) e-2"fk2 e-2yrz (l) cated biological molecules, alloys and amorphousfor excitations of an S state in a system by X-ray
polarized in the E^ direction. Equation (1) describes the modification of the electron wave function at the origin due to scattering by
N i
neighbours located at a radial distance ri away. The scattering amplitude is given by, f (z) r A (k) eiB(k)
where 6, are the scattering phase shifts. The electron wave vector k is defined as
where SZ is the X-ray frequency and E, is some choice of the threshold energy. It is clear that the electron wave will be phase shifted by 2 kr, by the time it makes the return trip to the neighbour. To this we must add the phase change in the backscattering process 8(k) and also twice the central atom phase shift 6; (the prime denotes the fact that the central atom is photoexcited and is in general different from the neighbour) to account for the potential of the central atom that the I = 1 photoelectron wave has traversed. The wave function at the origin is therefore modulated according to this total phase factor and this accounts for the sinusoidal term in equation (1). In addition we have to account for the fact that the atoms are not stationary. Thermal vibration will smear out the EXAFS oscillation and in the harmonic approximation this can be accounted for by a Debye-Waller type term exp(- 2 a: k2). Finally electrons that have suffered inelastic losses will not have the right wave vector to contribute to the interference process. This is crudely accounted for by an exponential damping term exp(- yr,). It is the limited range of the photoelectrons in the energy region of interest (50-1 000 eV) that permits a short-range order description of EXAFS even in crystalline materials.
The recent revival of interest in EXAFS began with the work of Sayers, Stern and Lytle [2]. They emphasized that if EXAFS can be described by equation (l), it should be possible to invert the problem and obtain the distances ri from an analysis of EXAFS data. In particular, they performed a Fourier transform in k space of EXAFS data for crystalline and amorphous germanium and showed that peaks in the transform correspond to various
-
materials, solution chemistry, catalysis, etc. [8-111. At the same time it is also clear that certain problems need to be overcome before EXAFS can be esta- blished as a new structural tool. We see from equa- tion (1) that in order to go from the data to distances r,, it is necessary to have information on the k depen- dence of the phase 2 6:
+
19 and, to a lesser extent, information i n the amplitude A(k) and the Debye- Waller factor. Furthermore, there is the important question of the extent to which different distances can be resolved by EXAFS analysis. In this paper we review the recent progress toward answering these equations.So far we have discussed only the theoretical question of data analysis. In the past few years there has also been a dramatic improvement in the experi- mental arena. EXAFS requires a continuously tunable X-ray source. The conventional source has been the bremstralung background from X-ray tubes and an EXAFS spectrum may require several weeks to produce. Synchrotron radiation in the X-ray range has become available and proves to be the ideal source for EXAFS experiments. As demonstrated by Kincaid and Eisenberger [l21 the 106 increase in intensity means that spectra can be taken in a matter of minutes. Since that time there has been an explosion in the amount of data available in both simple and complicated systems. In particular, detailed studies of simple systems with known distances have enabled the phases 2 6;
+
I9 to be extracted experi- mentally which are then used to predict distances with an accuracy of 0.01A
[13]. Such data have also inspired considerable theoretical work so that finally quantitative comparison of theory and experiment can be made [14].C4- 122 P. A. LEE
bution in k-space which tend to cancel out. Alter- nately if we perform Fourier transform of the data, multiple scattering will make contributions peaked at re,, which is certainly far removed from the first shell. Beyond the first shell it has been found that for open structure like germanium that multiple scattering corrections are small whereas for close- packed structure like copper, it is a much more serious problem [14].
Using equation (1) to analyze EXAFS data on single distance systems with known bond length like Br, Citrin, Eisenberger and Kincaid [l31 have extracted the k-dependence of the phase function q(k) = 2 6 ;
+
8. They then demonstrated that this phase function can be used to analyze a different system consisting of the same atom pair (the Br-Br distance in CBr, for instance) and determining the bond length with an accuracy of 0.01 to 0.02a.
Since that time the transfer of phase shifts has been extended to multidistance systems [IS]. If the shell s are sufficiently far apart, it is possible to filter out the nearest neighbour distance in the Fourier spectrum of EXAFS and transform the first shell contribution back to k-space. Numerous systems have been analyzed in this way with good results, some of which are summarized in table I. Several other groups [16, 171 have performed analyses working either in k-space or Fourier transformed r-space with comparable results.There have also been various attempts at ab initio
calculations of the phase functions. The recent work by Lee and Beni [l41 uses an energy dependent complex potential to account for exchange and correlation effects and obtains good agreement with experiment. Figure 1 shows the comparison of theory with experiment for Br,. The distance and Debye- Waller factors are taken from independent measure- ments. The only adjustable parameters are the overall magnitude and the location of the threshold Eo. The good agreement indicates that both the phase function and the amplitude function are in good shape. The calculated phase shift and amplitude are then used to best fit the data and extract a distance. Tests on a variety of systems show that the nearest neighbour distances are obtained with an accuracy of 0.01 to 0.02
A.
At this point we should pause and examine why it is possible to do so well. The basic reason is that in EXAFS the photoelectron is relatively energetic (100 eV to 1 000 eV) and the scattering is mainly due to core electrons. Let us suppose that different chemical environment or approximations in the theory give rise to an error in the atomic potential of 10 eV. The difference in phase shift Acp can be estimated by making an E, change of 10 eV. It is easy to see that A q = 0.2 rd for k = 16
a-'
(870 eV). Now if we use only the data at k = 16A-'
to extract a distance, the error in that distance is only Ar = 0.212 k = 0.006W.
Clearly the error is more serious for small k. However, by making E, anDistance determination by EXAFS
A. Using empirically determined phase shifts
Bond - Br-Br Ge-C Ge-Br Ge-Ge Ge-Ge Fe-N Br-Br Ge-Cl Ge-Ge Cu-Cu Fe-S Compound CBr, GeCH, GeBrH, GeO, Ge,H, Iron porphyrin model I Iron porphyrin model 2 K,NaFeF, K,Fe(CN), Known EXAFS distance
B. Using calculated phase shifts
EXTENDED X-RAY ABSORPTION FINE STRUCTURE
k (atomic units)
FIG. 1. - Comparison of EXAFS data on Br, (circles joined by lined) with theory (solid line). The absolute magnitude and the threshold
energy E,, are the only adjustable parameters.
adjustable parameter, we can compensate for errors in the potential and make the phase shift error small for a large range in k. The important point is that changes in E, produce a change in cp that decreases like llk whereas an error in the distance causes a ichange in cp that increases linearly with k. Thus by adjusting E, it is not possible to produce an artifi- cially good fit of the data with the wrong distance. In more complicated systems where shells are too close together to perform Fourier filtering it is still possible to analyze the data by fitting, especially by using amplitude and phase information that are either empirically determined [l01 or calculated [18]. This is particularly feasible if the atoms in the diffe- rent shells have very different atomic number. Then the difference in the amplitude and phase function permits unambiguous identification of the distances even though the accuracy is not as good as single distance systems. If the atomic species in different shells are the same, it becomes difficult to resolve the distances beyond the limit imposed by the uncer- tainty principle, i.e., Ar = n/2 km,, when km,, is the
maximal range in k-space where data is available. The analysis of EXAFS spectra is now relatively routine. Application of EXAFS ranging from macro- molecules to superionic conductors [l91 and adsorbed gases on grafoil [20] have been made and we will see more and more applications in the future. Theo- retical phase shifts and amplitudes have been para- metrized as a function of atomic number for atoms up to bromine [21], thereby greatly simplifying data analysis. Work is also in progress to study to
what extent coordination number and atomic species can be reliably' identified using the amplitude infor- mation in EXAFS. I would like to discuss one parti- cularly exciting development : the use of EXAFS for adsorbate structure determination.
The difficulty with surface EXAFS (SEXAFS) is of course that absorption by one monolayer of adsor- bate will be impossible to detect. One solution that comes to mind is to monitor the photoelectron yield. While it is clear that angular integration over 4 n steradians of all the elastic photoelectrons must be proportional to the absorption, in practice the photoelectron can be collected only over 2 n steradians
C4- 124 P. A. LEE
Adam [25], even though I do not believe EXAFS will be useful in the situation that they considered, namely a clean surface.
The first SEXAFS experiment was performed by Citrin, Eisenberger and Hewitt [26] for the system iodine adsorbed on the (l 11) surface of silver. By comparing the SEXAFS spectrum with the spectrum of silver iodide, Citrin et al. have been able to deter- mine the bond length with an accuracy of 0.02
W.
The adsorbed site can also be determined by exploiting the polarization dependence of EXAFS. At present this technique is limited to a few adsorbed atomswith absorption edges in the right energy range. Extension to lighter atom (down to oxygen or carbon) will be difficult because the width of the Auger line will increase and the absorption coefficient decreases more rapidly above threshold. However, EXAFS in principle still exists and with improved sources and monochrometers such possibilities should not be discounted.
In conclusion EXAFS is well on its way toward becoming a routine structural tool to complement other conventional probes such as X-ray diffraction, LEED, spin resonance, etc.
References
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