Introduction

Since its development in the early 1970's, synchrotron-based x-ray absorption spectroscopy (XAS) has proven to be a versatile structural probe for studying the local environments of cations in a variety of materials ranging from crystalline solids, glasses, and high-temperature liquids to aqueous sorption systems which involve metal complexes associated with (or sorbed at) solid/water interfaces. The structural information provided by XAS includes average interatomic distances and the number and chemical identities of neighbors within 5 to 6 Å of a selected atom species. In many cases including short-range ordering of cations in crystalline solids, cation environments in poorly ordered materials such as gels, glasses, melts, and metamict or radiation damaged materials, and the structure and composition of sorbed species at solid/water interfaces of environmental importance, XAS provides unique structural data not duplicated by other methods.

An x-ray absorption spectrum is typically divided into two energy regions: the X-ray Absorption Near-Edge Structure or XANES region, which extends from a few eV below an element's absorption edge to about 50 eV above the edge, and the Extended X-ray Absorption Fine Structure or EXAFS region, which extends from about 50 eV to as much as 1000 eV above the edge (Fig. 1). The XANES region is also sometimes referred to as the Near-Edge X-ray Absorption Fine Structure or NEXAFS region. As will be explained later, the physics of the processes responsible for XANES and EXAFS spectral features is different, thus these spectral regions provide different types of information about an element and its local environment.

XAS generally requires a synchrotron x-ray source for several important reasons: (1) A high x-ray flux is required in an XAS experiment in order to obtain high signal-to-noise data in a reasonable time frame (of the order of 30-40 minutes per spectrum). This requirement is particularly critical if the element of interest is at low concentration in a sample. Synchrotron sources provide x-rays of five or more orders of magnitude greater flux than conventional laboratory x-ray sources. (2) A broad spectral range at uniformly high flux is required because a typical x-ray absorption spectrum covers about 1000 eV. Tunable monochromators with appropriate d-spacings can be used to scan through a broad range of energy; thus one can choose the most appropriate energy range for an experiment. (3) High stability in flux, energy, and beam position is required in an XAS experiment and can be achieved with a synchrotron x-ray source such as a storage ring.

The primary purpose of this chapter is to provide some of the backgound and useful hints necessary for an inexperienced scientist with some knowledge of x-ray diffraction and/or x-ray fluorescence to carry out a successful XAS experiment at a synchrotron radiation laboratory. Because the primary participants in this workshop are earth, environmental, or soil scientists, the examples chosen to illustrate the attributes and limitations of XAS are mostly from these research specialities.

An XAS experiment, including analysis of the EXAFS spectrum, is a complicated undertaking. Furthermore, synchrotron radiation laboratories are large, complicated, and impersonal places that can be daunting for new users. Performing an experiment in these laboratories requires the normal user to learn something of the culture of large physics laboratories as well as many of the operational details required to successfully perform an experiment. Fortunately at laboratories like the Stanford Synchrotron Radiation Laboratory (SSRL) and the National Synchrotron Light Source (NSLS), its possible for a new user to talk with staff scientists, participating research team members, or experienced users about experimental design and to receive some level of help in performing their studies. Therefore, the knowledge barrier that many potential synchrotron users perceive need not be an overwhelming one. On the other hand, new users must have a serious need for the data provided by synchrotron radiation experiments and must make a significant commitment of time and energy if they hope to be successful.

We make no attempt in this chapter to cover all of the information necessary for an inexperienced scientist to understand all aspects of the design and execution of an XAS experiment, EXAFS data analysis, and data interpretation. Instead, we have focused on some of the basics required to design and carry out an XAS study of elements with K- or L-edge energies greater than about 3000 eV. We have included references to a number of useful monographs and papers which provide much more detailed accounts of XAS as well as its applications in various fields of science and engineering, including the earth sciences. The reader is referred to these for full accounts of the theory, techniques, and applications of XAS.
 

Guide to the XAS literature

During the past 15 years, a number of papers and monographs have appeared which present the theory, techniques, and applications of XAS. Among the best sources for the theory of EXAFS and XANES spectroscopies in relatively brief form are in Stern (1988) and Durham (1988). More detailed accounts of the theory of EXAFS are found in Stern and Heald (1983) and in Hayes and Boyce(1982). Applications of XAS in materials science are summarized by Wong (1986), and applications in the earth sciences are summarized by Brown et al. (1988) and Brown (1990). An excellent account of EXAFS experimental techniques is found in Lytle (1989). EXAFS data analysis procedures are discussed by Sayers and Bunker (1988). Relatively recent reviews of the applications of XAS to catalysis, amorphous and liquid systems, and biochemistry are in Koningsberger and Prins (1988). An excellent source of information on a wide range of applications of XAS are the proceedings volumes of biennial meetings on EXAFS and Near Edge Structure. Six such meetings have been held during the past 12 years, the most recent being in York, England, in July 1990 (Hasnain, 1991).
 

Information obtainable from an XAS experiment

XAS is an atom-specific, local structure probe. Both physical and electronic structure are probed, but the probe range is generally only the first two shells of atoms around the absorber atom, which is generally less than 5-6Å. In some special cases (e.g., when the sample is highly crystalline and the second and more distant shells around the absorbing atom contain atoms that backscatter photoelectrons well), information about more distant shells can be obtained, usually with greater uncertainty than in the near-shell cases.

A XANES or NEXAFS spectrum contains information on bound-state electronic transitions and multiple-scattering resonances associated with a given absorption edge. The former give information similar to optical electronic spectra: valence, coordination number, relative site distortion, and so on. The latter are sensitive to the details of the atomic geometry of the first few neighbor atom shells, i.e., the multiple-scattering resonances in the XANES region often serve as a "fingerprint" of a particular structural arrangement of atoms in the vicinity of the absorber.

An EXAFS spectrum is produced by electron scattering in the vicinity of the absorber, and thus holds information similar to that recovered from an x-ray scattering experiment, although the scattering is much more local for electrons. Bond distances involving the absorber can be determined for the first two shells with a precision of 0.01 Å or so, and an accuracy of 0.02-0.04 Å. Coordination numbers in the best case are accurate to 5%, and in general to 10-20%. Thermal and static disorder are also convoluted into the EXAFS signal. These are usually more of a problem than a source of information but can be used, in favorable cases, to determine vibrational amplitudes and details of site populations.

The main advantages of XAS are its element specificity and the fact that it can be used with practically any atom in any state of organization (solid, liquid, or gas). In addition, the sensitivity of XAS can be at the hundreds of ppm level of an element, thus it can be used to study the structural environment of an element at trace levels (<2000 ppm) in a chemically complex matrix. These attributes coupled with its ability to provide quantitative information on interatomic distances and the number and identities of atoms in the first and, in favorable cases, the second shell around an absorber, make XAS an extremely versatile and often unique probe of an atom's local environment. The local nature of the XAS probe is both an advantage (e.g., XAS is particularly useful in studying the environment of atoms in amorphous materials where there is no long-range order and where x-ray scattering methods suffer from lack of element specificity) and a disadvantage (e.g., XAS provides essentially no information on long-range order in a solid, including cation order-disorder among non-equivalent sites in a crystal structure). Disadvantages of XAS relative to x-ray diffraction include limited resolution for sets of similar bond lengths and high sensitivity to disorder. By going through the following sections and the references cited above, one can judge if XAS is suitable for a particular problem and how it might be solved and ascertain the necessary conditions for applying the technique.

When planning an XAS experiment, the experimentalist has a number of choices to make including which technique to use (XANES, EXAFS, polarized EXAFS, grazing incidence EXAFS, SEXAFS), which absorption edge of an element to study (K, LIII, MV, etc.), what monochromator crystal to choose, what type of detection to employ (transmission, fluorescence, electron-yield, etc.), and what type of sample is needed (dry powders, wet powders, liquids, what sample thickness, single crystals, crystal surfaces, etc.). In the following sections, we will discuss some of these topics based on our experiences over the past decade.
 

Components of an XAS experiment

A schematic illustration of the experimental arrangements required for two types of XAS experiments is shown in Figure 2. Figure 2a shows the typical setup needed for conducting a fluorescence-yield experiment on a hard x-ray beamline. As will be discussed in more detail later, this is the desired setup for studying elements at low concentrations in a sample. It differs from a transmission experiment, which is commonly used for samples with high element concentrations, only in the placement of the second ion chamber, labeled If, and the orientation of the sample. In the transmission experiment, the second detector is placed directly behind the sample and in line with the direct x-ray beam. Also in this case, the sample is aligned perpendicular to the x-ray beam. Critical variables of this experimental arrangement are the vertical spacing of slits in the monochromator chamber and in front of the I0 or first ion chamber (labeled mask), the type of monochromator crystals employed (typically the (111), (220), and (400) cuts of silicon), the types of gas used in the ion chambers, and the type and configuration of the sample. Other types of detectors may be used in place of If and will be discussed later.

Figure 2b show a possible arrangement of sample and detector components for an UHV experiment. In this case, both a channeltron electron multiplier and a cylindrical mirror analyzer (CMA) are shown. The channeltron collects all electrons emitted by the sample whereas the CMA can be used to discriminate against electrons above and below chosen energy limits. This experimental arrangement is commonly used to study the local environment of atoms at or near a single-crystal surface using the XAS technique known as SEXAFS (Surface EXAFS) spectroscopy. Monochromators used to access the soft x-ray energy range include a-quartz (100) (useful for Mg and Al EXAFS), InSb (111) (useful for Si EXAFS), and beryl (100) (useful for Na EXAFS). Ruled diffraction gratings are commonly used in place of monochromators for EXAFS studies of lower Z elements such as oxygen.
 

Elements accessible using synchrotron-based XAS

In theory, almost all elements of the periodic table can be studied using synchrotron-based XAS methods. However, there are some practical limitations to the energy ranges accessible to the experimentalist caused by the flux distribution of synchrotron sources, the availability of appropriate monochromator crystals, and by the fact that x-rays softer than about 2500 eV are strongly absorbed by air and by the thin Be windows placed between the storage ring, operating under UHV conditions (>10-9 Torr), and the experiment on most hard x-ray synchrotron beamlines. Many of the elements of interest to earth, environmental, or soil scientists have edge energies greater than 3000 eV, including the first-row transition elements, with K-edge energies ranging from 4492 eV (Sc) to 9659 eV (Zn), the rare earths, with LIII-edge energies ranging from 5483 eV (La) to 8944 eV (Yb), and the actinides with LIII-edge energies above 15871 eV (Ac). Elements with K- or L-edge energies lower than about 2500 eV, including C (284 eV), N (410 eV), O (543 eV), F (697 eV), Na (1071 eV), Mg (1303 eV), Al (1559 eV), Si (1839 eV), and P (2149 eV), cannot be accessed using standard x-ray beamlines at synchrotron sources for the reasons mentioned above. However, they can be accessed using soft x-ray-VUV beamlines. Such experiments require that the samples be placed in UHV chambers which are directly coupled to the storage ring, thus they are considerably more complicated than a hard x-ray EXAFS experiment conducted in air.
 

Choice of XAS experimental technique

The type of information desired from a sample dictates the type of XAS technique to be utilized. For example, XANES spectroscopy is the appropriate technique for determining an atom's valence as there can be shifts of 1 to 3 eV in edge position for each valence unit change as well as significant changes in the energy of electronic transitions (Fig. 3). Edge features shift to higher energies with increasing oxidation state of an element because the decrease in valence electrons reduces the shielding of core electrons from the nucleus. The positions of XANES resonance features are related to different interatomic distances from the absorber to other atoms by the relationship R²= c/(E_r - E_b), where R is the interatomic distance, c is a constant, E_r is the energy of the resonance feature, and E_b is the energy of a bound state transition (e.g., the 1s to 3d pre-edge transition of a first-row transition element K edge) (Bianconi, 1988). Distances determined in this way are less accurate than those derived by detailed analysis and fitting of the EXAFS spectrum. However, they are typically within 0.05 Å of the EXAFS-derived distance in our experience.

If the location of a given atom in a crystal structure is to be determined, EXAFS spectroscopy is typically more appropriate than XANES spectroscopy. For example, suppose we wish to know if a given impurity atom substitutes for Ti in rutile, which contains only octahedral cation sites. The K-edge EXAFS from Ti in rutile can be compared with EXAFS from impurity atoms in rutile. Allowing for small displacements in atomic position to compensate for variations in the sizes of impurity atoms versus Ti, the EXAFS and Fourier transformed EXAFS (the radial structure function) of Ti and the impurity atoms should be identical if the impurities are substituting for Ti. Refined interatomic distances and coordination numbers from analysis of the EXAFS data should confirm the site occupied by the impurity atom.

A more complex problem commonly encountered in mineralogy and materials science involves determining the location of a given atom in a crystalline or amorphous material which has more than one type of cation site. If the possible sites are relatively different in geometry (e.g., tetrahedral vs. octahedral), EXAFS spectroscopy can provide a definitive answer, subject to certain experimental limitations discussed below. However, if the sites are relatively similar such as six-coordinated sites with similar average metal-oxygen distances (e.g., the M1, M2, and M3 sites of amphiboles), EXAFS spectroscopy may be of limited value, and single crystal x-ray or neutron diffraction methods are more likely to provide a definitive answer.

How dissimilar do the sites have to be for XAS to be of use? The resolution in an EXAFS experiment for determination of interatomic distance is related to the useable data range collected (not the data range scanned, which may include regions at high wavevector value (k = [0.2625(E-E₀)^½) with no observable EXAFS). For example, assume useable data in an EXAFS scan is collected up to 1000 eV above the edge. The maximum k-value is then approximately (.2625*1000)^½, and the maximum k-range is 0-16.2 Å^-1. Because the k-range 0-3 Å^-1 is unusable due to overlap with the XANES, we have a useful Dk range of 13.2 Å^-1. In the Fourier transform (FT) the peaks will then have widths of about 2p/Dk = 0.47 Å (or perhaps better). We thus need bond distances differing by this much or larger to be clearly resolved in the FT, but in practice distances differing by about half this width are separable by curve fitting. Otherwise an average distance for bonds within these ranges is obtained. If much is known about the host structure, geometric models can be devised to simulate atom occupation in various sites to differing degrees and can be used to generate model EXAFS functions for several shells of neighboring atoms. These model functions can then be compared to the observed EXAFS to obtain a best match.

In addition to the limitation in distance resolution, there is also a limit on the information content of EXAFS, which may be expressed as degrees of freedom or number of independent variables determinable by 2DRDk/p, where DR is the backtransform range in Å and Dk is the k-range in Å-1. If we were using the k-range assumed above and had a DR of 1.0 Å for the first FT peak (usually metal-oxygen bonds), the number of degrees of freedom is 8.4 (a fairly large value in general). This means we can fit up to 8 independent variables when fitting the first shell data. For each shell of atoms around an absorber we must fit interatomic distance, coordination number, and a disorder parameter. E0, which is defined as the energy at which the electron's momentum is zero (i.e., the energy above which the electron is considered to be in a continuum state), is another variable. Thus we would be able to fit two complete shells with one extra parameter (which could be a third bond length). From this exercise one can determine whether the occupation of a given atom among a number of similar sites can be differentiated.

A difficult problem for EXAFS is illustrated by the substitution of an element at trace levels, say V, in forsterite, which has two 6-coordinated sites (M1 and M2). Can we determine how much V is in each site? First we must assume that the sites do not change much from their sizes in the same forsterite without V. We can then examine the known M-O distances for each site from XRD refinements. For forsterite the M-O distances are: M1 2@2.088, 2@2.075, 2@2.141; M2 1@2.176, 1@2.057, 2@2.221, 2@2.067 Å. The range of bond lengths is such that only a single peak will be seen in the structure function for the first shell. If we average the longer and shorter bonds we get: M1 4 short @2.081, 2 long @2.141; M2 3 short @2.063, 3 long @2.206 Å. Because the relative numbers of longer and shorter bonds differ between the sites, and there is some change in average distance, our eight degrees of freedom in the refinement should give us enough information to determine qualitative site partitioning. But quantitative determination is unlikely due to the difficulty of measuring highly accurate EXAFS amplitudes. Note that we need to know the disorder parameters independently of site occupancies, which is not trivial, and errors in these will affect partitioning ratios.

Obviously, for a mineral with more than two different six coordinated sites, the task is progressively more difficult. However, for one with sites that are rather distinct, like, e.g., the M1, M2, and M3 sites in epidote, the results from EXAFS analysis can be quite good.

Coordination numbers (CN) can be determined to about 10% accuracy in the best situations, but how good is this? To distinguish between 4-fold and 6-fold coordination with this size error we must be able to differentiate in the worst case a CN of 4.4 from 5.4. That should be possible. But if the experiment is poor and we have a 20% error, then in the worst case no difference will be observed via EXAFS analysis. Fortunately the differentiation of octahedral vs. tetrahedral coordination for a first-row transition element is frequently made easier by a dramatic change in the XANES pre-edge and edge structure. For example, when these elements are present in sites tht lack a center of symmetry (e.g., a tetrahedron), their K-XANES spectrum often shows a distinct pre-edge feature, located several eV below the absorption edge, which is due to a 1s to 3d electronic transition. This feature is very weak or absent when the transition element is present in sites with a center of symmetry (e.g., an undistorted octahedron) (Fig. 4). Thus XANES together with EXAFS may allow detection of different coordination environments.

Site distortion in crystalline materials contributes to increased numbers of separate bond lengths at a given site. With several such sites the numbers of differing bond lengths can be very large, e.g., the M1, M2, and M3 sites in the amphibole structure. The range of bond lengths produces the effect of "static disorder", i.e., it is equivalent to a single bond disordered over a range of lengths similar to the range produced by thermal vibrations. If the distribution of bond lengths is Gaussian-like, then the disorder is very similar to harmonic thermal vibrations and can be handled as such. The refinement will yield true average bond lengths. If the range is very non-Gaussian, standard refinement will yield non-accurate bond length averages. For the worst cases with very unusual distance distributions, the coordination number and interatomic distance can be substantially off. As EXAFS is made up of a finite wave train of sinusoidal oscillations, it is easy to see that with enough different bond lengths, and hence frequencies, eventually all signal can be canceled out. Thus EXAFS analysis is poor for systems with very large numbers of different sites that can be occupied by the element of interest, or for structures with unusual distributions of site sizes. Obviously this produces problems for EXAFS studies of glasses and melts, and special modelling techniques must be used in those cases.

These considerations lead us to questions such as: How complex is the sample? Is it too complex for XAS to be of any use? How many elements are to be examined? Are there a large number of possible valence states? How much static disorder is associated with the sites? Before starting an XAS experiment, all of these questions must be considered in light of the technique's inherent limitations.

Other XAS techniques which provide the same type of information as transmission or fluorescence-yield EXAFS but with additional attributes include grazing incidence or reflection EXAFS, SEXAFS, and polarized EXAFS. These techniques are commonly used on single-crystal samples. The first two provide structural information about atoms at or near a surface, whereas the last utilizes the strong polarization of the electric vector of synchrotron light parallel to the electron orbit of the storage ring and provides information about the orientation of bonds in single-crystal samples. Grazing-incidence methods are discussed by Heald et al. (1984) and SEXAFS spectroscopy is reviewed by Stohr (1988). Several examples of polarized EXAFS spectroscopy applied to mineralogical problems can be found in Waychunas and Brown (1989).
 

Choice of which absorption edge to study

K-edge spectra show the largest net absorption, and also the largest emission of fluorescent photons per photon absorbed. Hence K-edge spectroscopy is generally the most sensitive. However the K edges of elements with Z>50 (and possibly less) are too high to be reached on most beam lines available today. Also higher energies are on the decreasing side of the synchrotron flux curve, so that the sensitivity afforded by using the K edge is reduced, in part, by lower synchrotron flux.

L-edge spectra occur in triplets compared to the single K edge. The fluorescence photon efficiency is relatively low, but many more elements are accessible because of the low L-edge energies. The lowest energy LIII edge is the one of choice, but this edge may have a relatively small separation from the LII edge for elements with intermediate Z values and thus shorten the collectable data range. For example, Cd has a K-edge of 26.711 KeV. If this energy is out of range of the available beam lines or monochromators, then the LIII edge at 3.538 KeV must be used. However, the LII edge is at 3.727 KeV, allowing EXAFS only up to about a k of 7.0. L-edge spectra have potentially greater sensitivity to valence and electronic structure than do K edge spectra due to differences in selection rules for l-edge bound-state transitions relative to those for K edges. Hence L-edge XANES structure may be particularly rich and informative.

M edge spectra are more complex still (five edges), and usually not used for XAS studies except when L-edge energies are too high to be easily accessible for a given monochromator. The fluorescence yields and relative absorption are still smaller than for L edges. However the various M edges for high Z elements in a sample may interfere with L- and K-edge measurements for elements of interest. Similarly, L edges can interfere with K-edge measurements. The authors noted this effect years ago when examining the spectrum of Ti4+ in benitoite (BaTiSi3O9). The K-edge Ti spectrum contained all three L-edges of Ba, the first close enough to the Ti edge to reduce the k-range to about 8 Å-1.
 

Element concentration and choice of XAS detection method

We next need to consider how concentrated the element of interest must be in order to obtain a useable EXAFS signal and how this affects the choice of EXAFS detectors. In addition, we need to know something about the overall composition of the sample in order to optimize experimental design. Neglecting the host structure, transmission EXAFS measurements can be used on samples with element concentrations as low as a few tenths of an atom percent, though transmission spectra provide more accurate structural information for samples with higher atom concentrations. Fluorescence EXAFS data collection has difficulties for higher concentrations and is most useful below 1 atom percent.

The effect of a matrix that has an average Z equivalent to or higher than the element of interest is to contribute a significant amount of absorption to the XAS spectrum. This reduces S/N, and thus the sensitivity. In the case of fluorescence techniques, the matrix will stop the incident beam from exciting much of the element being studied, as well as impede fluorescence emission. Thus again the sensitivity is markedly reduced. Finally, the higher Z matrix will also create additional main beam scattering into the fluorescent detector, which further lowers the S/N of the fluorescence experiment. Hence XAS experiments work best when the element of interest has a larger Z than the average Z of the matrix. Fortunately most minerals have oxygen and silicon matrices with a low average Z compared to transition metals and other elements of interest.

As already noted, transmission data collection is often less sensitive than other methods. However, the transmission method is simple to use, and provided that samples are not too thick (see below), it gives excellent results for many elements. The main considerations are: Is there enough of the element of interest to get high quality data? Is the host matrix too absorbing for transmission work? Is it possible to make a thin, uniform sample? This last question is very important, as the grain size in a powder should be such that a single uniform particle layer yields an edge-step of about mx = 1.0, where m is the atomic absorption coefficient in cm-1 and x is the thickness in cm. To understand what this means consider a layer of particles of the mineral fayalite, Fe2SiO4. The mass absorption coefficient-density product (m/r*r) is about 1145 at the Fe edge. This yields a layer that is 8.7 microns thick for mx = 1.0. As typical ground powder grains might be 10 microns in diameter, the thinnest, uniform, mechanically produced powder has a mx of about 1.15. Several such layers are needed for uniformity. Thus the typical sample would have a mx of about 3.5, which is thicker than the ideal sample (mx=2.6) from the statistical view, and much thicker than a sample which minimizes thickness effects (mx=1.0). However, if made carefully and uniformly and if beam harmonics are eliminated, a fayalite sample made from a ground powder should work acceptably. Should one be working with a sample with a higher Fe content than fayalite, things get difficult. A worst case is pure iron foil. For mx=1, we need a foil of thickness 2.8 microns. This could never be made from grains any larger than about 0.7 microns, but fortunately metal foils can be made very thin by mechanical rolling or by vapor deposition methods.

Another difficult case arises if the matrix of the mineral has high mx. In order to reduce this mx to sufficiently low values where thickness effects do not plague transmission experiments, we must thin the sample significantly. This then reduces the amount of the element of interest in the sample. As noted above, a high average Z of the sample creates other problems as well.

Transmission experiments thus require the ability to make a uniform sample with acceptable mx and acceptable concentration of the element to be studied. But satisfactory data can be obtained for a wide variety of element/host matrix combinations. In cases where the grain size cannot be reduced properly, or the overall mx is too large for some reason, the experimenter can consider fluorescence- or electron-yield detection.

In the fluorescence-yield mode, fluorescence photons emitted by the excited absorbing atoms are detected. It is unnecessary to have a uniform sample, as the transmitted beam is not used to normalize or contribute to the data signal. Hence a single layer of powdered sample can be used. This gets around the thickness problem for many samples, but self-absorption effects (not seen in the transmission experiment) occur if the sample has mx significantly larger than 1.0. This sets a limit on the absorption of individual sample grains. Dilution of a sample with sugar or some other medium of low average absorption cannot solve the self absorption problem if the individual grains are too large. Dilution of the sample does help in handling highly absorbing samples with small grains having small mx values. Fluorescence detection is particularly useful with dilute samples of concentrations less than an atom percent. If the host matrix is not too absorbing, then very thick samples (several mm) can be used. This large sample volume enables very dilute aqueous solutions and adsorption samples to be studied, even where element concentration may be as low as 0.0001 M. Fluorescence detection is described in more detail below.

Another way to get around highly absorbing samples is the use of electron-yield detection. In this case the detector senses only ejected Auger electrons associated with the decay of the excited absorber atoms. Such electrons have small path lengths in the sample, so small, in fact, that self absorption effects are eliminated. Hence thick, highly absorbing samples can be studied readily with this method. Another benefit of electron-yield is its sensitivity. It is 100 to 1000 times as sensitive as fluorescence-yield due to the large solid angle aperture of the detector, the amplifying effects of the carrier gas (He if present), and the high efficiency of producing ejected electrons.

There are two problems associated with this mode of data collection. First, the yield electrons cannot be detected in air as their mean free path is very short. One needs either a vacuum chamber or a chamber that can be filled with flowing He or H2. He works adequately down to sulfur according to Lytle (1989). For very low Z elements, a vacuum chamber is required. Second, any thin coating of a second phase can dramatically alter the XAS signal as this surface phase is the signal comes from. Hence great care must be taken to keep samples unoxidized, unhydrated, or in whatever pristine state is necessary. For most silicates this is not a problem if samples are prepared shortly before the experiment.

Useful concentration ranges for each detection method.

For transmission EXAFS studies, the example of fayalite discussed above shows that this material (28 atom % Fe) has enough Fe to make it difficult to prepare optimal samples. However, samples with less Fe are relatively easy to prepare from ground powders. Note that the absorption change across the edge is somewhat different for every element or edge, and one must make appropriate absorption calculations rather than compare every case to Fe.

On a statistical basis, the point where equivalent S/N is produced for transmission and fluorescence experiments is mx=0.18. Thus, if the sample mx is lower than this value, fluorescence detection will yield a better spectrum. To determine the atom concentration equivalent to this absorption value, we use an example of Fe3+ in corundum. Using the absorption coefficients at 7.2 KeV, just above the Fe K-edge, we find that at 1 wt % Fe m=1911, and the "changeover" thickness is 0.94 microns. For 0.5 wt % Fe the thickness is 1.7 microns and for 0.2 wt % Fe it is 5.1 microns. As samples for fluorescence do not have to be uniform, it is clear from the mechanical considerations above that a workable powder sample concentration range is < 0.2 wt %.

For materials with high element concentrations, powdered samples will be difficult or impossible to make unless sputtering or precipitation processes can be used. The best alternative is then electron-yield detection, provided that the surface phase problem can be overcome. This technique probes only the top 30 Å or so of the sample.
 

Sample optimization for the chosen XAS experiment

From a statistical point of view it is necessary to have enough counts from the reference detector (incident beam detector I0) so that this signal is measured as precisely as possible. At the same time the beam exiting this detector must be maximized to provide the largest transmission or fluorescence signal. Similarly, a sample that is too absorbing limits the counts detected by the transmission detector, and also reduces the precision of the mx determination. Analysis of this problem leads to an ideal transmission sample thickness of 2.6 mx, and an ideal I0 detector absorption of about mx=1.0. However, this assumes a perfectly homogeneous sample. If holes are present in the sample, or even if it is somewhat inhomogeneous, then the change in absorption over an edge will be greatly attenuated. The data may still be useable, but the S/N would be reduced at the cost of later uncertainties in the fitted parameters.

The ideal thickness calculation also assumes that no beam harmonics are present. Harmonics are the Bragg reflected beams from higher-order planes in the monochromator crystals (recall that synchrotron radiation covers a large energy range). These can be reduced by strategies detailed below, but complete elimination is difficult. In the case of a sample with mx=2.6, even if it is perfectly uniform, the presence of higher energy harmonics will cause a large drop in S/N. The reason is that mx for the higher energy harmonic is very much smaller than 2.6, and the incident beam will excite the transmission detector over the full edge scan. This "dilutes" the effect of the absorption of the element of interest. In the fluorescence experiment harmonics will excite fluorescence at all energies of a data scan, and thus also reduces S/N.

For these reasons the ideal transmission mx is more like 1.0, but reduction of harmonics is necessary for any kind of XAS experiment. Any effort to reduce harmonics does so at the cost of intensity over the energy range of the spectral scan. Thus there is some optimum harmonic rejection where the best S/N is produced. This is usually determined empirically.
 

Effects of temperature on EXAFS spectra

Another question is whether or not the sample should be cooled. Temperature affects EXAFS amplitudes through the Debye-Waller or disorder parameter. Amplitudes can be increased by as much as 300% in going from room to liquid nitrogen temperatures. More importantly, higher frequency EXAFS oscillations are obtainable at increasingly higher k values as the temperature of the sample is reduced. Hence both S/N and data range improve at reduced temperatures (Fig. 5).

Moderating the use of lower temperatures is the difficulty of configuring Dewar systems, especially at low x-ray energies, where the Dewar windows can be highly absorbing. Each case should be evaluated by examining the thermal vibration parameters from an x-ray refinement of the analogous crystalline material, if available. From such refined thermal parameters it is possible to estimate the effects of temperature on the EXAFS amplitudes.
 

Beam line selection and hardware requirements

XAS beamlines often differ in a number of components. Because the type of beamline and its components help determine what type of XAS experiment can be done and place limits on sample geometry and element concentration, they must be understood at some level.

Type of source device: bending magnet, wiggler magnet or undulator.

Bending magnets are magnet assemblies that provide for angular acceleration of the synchrotron electron or positron beam. As the acceleration generates synchrotron radiation, a port associated with the bending magnet allows the radiation to travel out to a beam line. The total x-ray flux is characteristic of the ring parameters and the magnetic field. Brilliance of bending magnets is much less than for wigglers and undulators.

Wigglers are sets of magnets which bend the electron or positron beam back and forth, returning the original beam to the same direction at the end of the device. They are thus inserted into straight sections of a storage ring. Intensity and brilliance are related to the number of wiggles such that the wiggler is essentially a sum of bending magnet synchrotron sources. Intensity is one to two orders of magnitude higher than from bending magnets.

Undulators are wiggler-like devices with the magnet spacing and gap tuned to invoke interference in the synchrotron radiation. The exiting radiation is therefore not continuous as from a wiggler or bending magnet but is peaked at several specific energy ranges. The undulator thus produces still more intense x-rays in these regions compared to the wiggler. It can yield intensities more than three orders of magnitude higher than a bending magnet.

The differences in these devices and associated lines matter most in terms of the required sensitivity. Simplistically, one requires two or more orders of magnitude increase in beam intensity in order to measure samples with an order of magnitude less element of interest.

Mirrors which deflect and/or focus the x-rays.

Mirrors may be located any place in the beam line, e.g., between monochromator and source, post monochromator, or pre- and post-monochromator and are commonly used to focus the x-ray beam. This focusing increases the beam intensity, but reduces energy resolution in the monochromator due to enhanced beam divergence. For EXAFS experiments requiring fairly low resolution (3-4 eV at best), mirrors do not affect results. For XANES work, this level of resolution would obliterate fine details in any of the first row transition element K-edge spectra.

Mirrors are also used to reject monochromator harmonics, which is useful for EXAFS experiments. The critical angle of reflection decreases with x-ray energy. Thus one can set up a curved mirror to reflect a range of energies down the beam line, but stop any radiation above a certain energy cutoff. Provided this is consistent with the energy range scanned in XAS experiments, complete harmonic rejection can be obtained. Many beam lines have mirrors which can be removed easily, sometimes even by automatic control, and thus provide the user with more options.

Monochromators which sort the incoming x-ray energies.

Monochromators vary greatly in design and operating parameters. They can be of several types, having distinctly different energy ranges, as well as greatly different energy or angular resolutions.

At SSRL most XAS beamlines have a two-crystal monochromator with about 10-4 energy resolution (DE/E). (Table 1). Both crystals rotate to vary the reflected beam energy, but there is no translation. Thus the exit beam moves vertically as a function of angular setting. To accommodate this, SSRL beamlines have a computer- controlled table which move the entire experimental setup up and down to follow the beam. SSRL monochromators are under He, so that relatively little time is needed to change crystals if such a change is needed.

At the NSLS many XAS beamlines have two crystal monochromators which rotate and translate. This yields a fixed exit beam but usually a more limited angular range (energy range). NSLS monochromators are under moderate vacuum, thus crystal changes are more time consuming.

Usually Si (111), (220) or (400) crystals are used in XAS monochromators. The smaller the d-spacing, the more efficient the monochromator crystal for progressively higher energy x-ray reflection. For low energy work, crystals with larger d-spacings are necessary. Sometimes ruled gratings are used for the largest x-ray wavelengths! The rocking curve of crystals decreases with d-spacing, hence these crystals have the highest energy resolution capabilities. This fact is made use of in "detuning" monochromators to remove harmonics. When the (111) reflection is being used, higher energy x-rays will also be reflecting from the parallel (333) planes (Fig. 6). But as Si(333) planes have narrower rocking curves, slight rotation of one crystal with respect to the other will move the crystals out of the Bragg condition for the higher energy harmonic, without removing the Bragg condition for the fundamental (lowest) energy radiation.

Glitch avoidance.

Glitches are double diffractions occurring in the monochromator crystals, i.e., the Bragg condition is geometrically obtained for two crystal planes simultaneously. When this occurs at an occasional energy position, there is a net loss in the beam delivered to the experiment and the I0 detector. On passing the double diffraction region, the intensity climbs back up to its regular condition. This usually occurs in a single monochromator step, and if the electronics do not ratio the count intensity correctly, a "glitch" in the spectrum is detected (Fig. 7). Glitches can be moved in energy, if not eliminated, by azimuthal (axis of rotation normal to crystal face) rotation of one of the crystals in the monochromator. Some monochromators allow for this operation. Other beam lines have a choice of Si crystals cut with different azimuthal orientations. One set of glitches on one crystal my disturb the energy range of Fe, but the Fe K-EXAFS spectrum be relatively glitchless over other energy ranges. These crystals are then exchanged as needed to alleviate glitch problems over a wide range of energies, however, crystal changes typically take several hours so should be avoided if not essential for obtaining useable spectral scans.

Crystal reflectivity, tilt angle, absorption, and other factors contribute to a "reflectivity function". This function often varies more than an order of magnitude over the useful energy range of a monochromator crystal. Hence users should consult such curves before choosing crystals, and crystal settings. For example, Si(111) and Si(220) can be used for the energy range of 3-20 KeV, but the Si(220) crystal has much better reflectivity at the upper end of this energy range.

Other important beamline considerations are the complement of detectors and electronics, the availability of appropriate gases, and the computer system. There are too many choices to cover in this brief chapter, but the following lists provide some idea of the various possibilities:

Detectors

Several different types of detectors may be employed in XAS experiments and are discussed below.

(a) Gas-filled ion chambers - They provide no energy resolution and are used for I0 and I1 detectors in transmission and fluorescence XAS experiments. They are usually attached to gas mixing racks whereby the total absorption for any energy range can be adjusted. Table 2 from Lytle (1989) provides useful information of choice of detector gases for different energy ranges.

(b) "Lytle" detectors - These are special type of ion chamber that affords some energy resolution in fluorescence detection mode (Fig. 8). The window of the detector is fronted with a soller slit assembly and a filter holder. The filter is chosen to have an absorption edge between the edge of the element of interest, and this element's fluorescence emission line energy. The filter thus preferentially passes the fluorescence, but absorbs the scattered radiation from the sample during a scan. The soller slit is so configured as to allow fluorescence radiation from the small sample to pass, but it blocks most of the stray fluorescence from the filter excited by the scattered main beam. The S/N is thus greatly enhanced over a simple ion chamber.

(c) Si and PIN diodes - These are single semiconductor devices which may have large spatial extent. They operate as the solid state analogue of ion chambers. There is no energy resolution, but like the ion chamber, these detectors can tolerate any count rate. The advantage over ion chambers is the small size (very thin), and high efficiency. The disadvantage is the inability to use these in a partly transmitting mode, such as for I0. Hence they find application in fluorescence-yield detection.

(d) SiLi and intrinsic Ge diodes - These detectors, though similar to the simple Si diode, are used in the slow count mode for fluorescence detection, but are able to descriminate individual photon count energies. The playoff is between energy resolution and speed of counting. Typically, count rates of 50,000 counts per second give the best energy resolution, on the order of 200 eV, which is quite good enough to descriminate scattered radiation and other "noise" from the fluorescence signal. Several individual diodes can be used to allow aggregate count rates of up to several million counts per second. For very dilute samples and a lot of scattered radiation which must be filtered out, these detectors are the best choice. The greatest problem is the "dead time", or the time spent while the electronics determines the energy (actually pulse height) of a given photon-absorption event. During this time the detector is dead to the processing of other counts, and thus misses some portion. This limits contemporary designs to speeds of about 100,000 counts per second at best, even with reduced energy resolution.

(e) Electron-yield detectors - These can be quite simple, such as a simple collection grid with a slight bias to collect electrons. Or they can be as elaborate as a CMA (cylindrical mirror analyzer), which can measure both the energy and number of ejected electrons. Other detectors can measure both electron-emission angle and energy.

Electronics

Beamline electronics covers a wide range of components, but we are mostly concerned with the data channels and monochromator positioning (energy). Most beamlines utilize a CAMAC crate controller interfaced to a minicomputer. The crate has 24 or more subaddresses that are used to directly send and receive signals to and from assorted operational modules. One set of these will be the data channels, usually with quad or hex scaling crate modules. The data stream, in the form of current from an ion chamber, is converted to a voltage, then sent to a voltage-to-frequency converter. This converter generates pulses at a rate proportional to the initial current, and hence an integrated count of these pulses over a step interval of a scan is proportional to the integrated intensity measured by the ion chamber. The computer reads out the subaddresses of the scalers and records the intensities of all detectors in this way. It then resets the scalers, advances the monochromator to the next energy position in the scan, and repeats the cycle. Important to this operation are the following:

(a) Dwell time of the monochromator before counting is initiated. The system must be set so that any vibrations in the monochromator do not continue once intensity measurement has begun at a step. This may take 0.5 seconds or longer.

(b) Operating range of the V to F convertors and current to voltage convertors. This is dependent on the particular electronics used. If not known, the computer could be recording above the overflow count rate (all the same) over much of a data scan.

(c) Integrating time of any current amplifiers used to amplify the ion chamber signal. The amplifiers will add noise to the system, rather than average it out if this time is not correctly set.

(d) System linearity. The more nonlinear the entire data channel system is, the larger are glitches.
 

Data Collection

Prior to data collection, a number of adjustments of beamline components is necessary to optimize a particular experiment. Some of these adjustments are discussed below.

Detuning of monochromator to reduce harmonics. How and why?

Monochromator detuning has been mentioned above. The usual method for determining the degree of detuning is based on fluorescence detection. The monochromator is set to an energybelow the edge of interest and the detector is set up to detect the fluorescence emission from the sample. As the fluorescence can only originate from higher energy beam harmonics, their presence can be identified. The monochromator is detuned with a piezoelectric transducer that pushes one crystal slightly away from its ideal Bragg position. As this is done step by step, the ratio of the incident beam intensity [I0/I0(max)] and the intensity measured by the fluorescence detector is plotted versus the degree of detuning. Detuning will result in a loss of incident beam intensity to I0, but the part of the fluorescent detector signal due to scattered main beam will drop off proportionally. Hence the ratio will be constant if only scattered beam is detected. However, the fluorescent signal due to sample fluorescence will fall dramatically with detuning, thus the plot will show a downward trend to a constant baseline. The start of the baseline indicate the minimal detuning to effectively eliminate harmonics, and thus the position with highest overall beam intensity (Fig. 9).

Slit settings to get proper resolution and to center on the "hot" part of the monochromatized beam.

Slits are ordinarily placed before the monochromator and between the I0 chamber and the monochromator to improve energy resolution. Decreasing the slit spacings allows a smaller range of angles and thus energies to be accepted from the second monochromator crystal. It is vital to set both the slit spacings and overall position accurately. Too high a resolution when maximum intensity is required is a waste of photons. Likewise too low a resolution reduces the quality of XANES data. Positioning which is off will not be sampling the "hot" or most intense part of the beam from the monochromator. Such considerations are mainly a job for those setting up an experiment. Beam line scientists can usually advise experimenters on the optimum settings for these slits. (Table 3)

Proper I0 and I1 level for optimum ratioing.

As noted above in the discussion of statistical considerations affecting sample thickness, the optimum detector absorption is about mx = 1.0 for I0 and I1. Note that if this amount of absorption generates voltages in the electronics which are grossly different, optimum ratios will not be obtained. Hence both absorption and gain in the electronics needs to be set correctly.

Choice of energy range and step size in scans.

For XAS work it is important to collect data points well away from the region of interest, so that appropriate background fitting can be done later in the data reduction. Particularly for EXAFS, data collection should start about 200 eV below an edge, and continue to at least 1000 eV above it. The choice of step sizes depends on monochromator/slit resolution. Steps much smaller than this resolution limit accomplish nothing. Longer integration times are better. For EXAFS scans, because of the quadratic dependence of wavevector k on energy, the steps in energy can be progressively larger past the edge. Some computer data collection systems allow EXAFS scans to be set up in units of fixed Dk (commonly 0.05 Å-1), so that the energy step size is automatically increased over a scan.

Edge vs. EXAFS scans; inherent resolution limits.

Energy resolution for features on the edge for a given element is related to the lifetime of the excited state core hole created by photon absorption. The lifetime is longer for lower Z elements, thus the energy uncertainty of absorption is smaller, yielding better resolved edge features. (Fig. 10) For Fe the lifetime suggests a resolution of about 1.0 eV at the K-edge. This must be convoluted with the monochromator/slit resolution. For a Si (111) monochromator crystal with a 1 mm slit, the energy resolution is about 2.0 eV. Hence the peaks in the Fe XANES measured with this arrangement will be about 2.2 eV in width. For Si (220) crystal and a 1 mm slit, the minimum peak width decreases to about 1.5 eV.

Data averaging--How much is enough?

How much data need to be collected? How many scans need to be run? These questions are difficult to answer from ab initio calculations, as too many experimental factors are involved, many of which will not be known until set up on the beam line. Statistically, the S/N of the data improves as the square of the number of data scans. Hence an improvement of five times in the S/N over a single scan requires 25 scans.

Determination of the required S/N, and thus of the tractability of a particular (usually low concentration) experiment requires some degree of data reduction capability at the beamline. For example, if good next-nearest neighbor data are needed, it is essential that a good FT of the data can be made which shows a well defined second FT peak with minimal side ripples.

A second consideration is the length of step integration periods in individual data scans versus the total number of scans. Traditionally there has been enough instability in storage ring operation (beam losses, beam shifts, electronic anomalies) such that it has been inadvisable to collect single scans of more than 30-35 minutes. The situation has changed for the better, and longer scans are now possible at most synchrotron sources. However the relative improvement in time economy is limited by the inability to perform some data reduction promptly. Hence short scan times are preferred by most experimenters.

Model compounds--what is required in general.

One of the most important elements of an XAS experiment is the recovery of good data for "model" compounds. These are samples of well-known crystal structure and composition, carefully selected and prepared, which most closely provide the type of sites of the elements of interest. For example, we may wish to study trace Sr in carbonates. Sr would probably reside on the Ca site, hence pure Sr carbonate is an appropriate model compound. The information we need (the Sr-O, Sr-C and Sr-Sr phase and amplitude parameters) can be extracted from this model compound provided that good XRD structure refinements are known.

We may also wish to evaluate Sr clustering in the carbonates we study. We then need Sr-Ca phase and amplitude parameters. Where do we get these? We would need to find the most similar compound (possibly not a carbonate but at least an oxide) which might have all Sr next-nearest neighbors about a Ca or vice versa. Given failure in this area, we might turn to theoretical calculations, such as those produced by John Rehr's program FeFF. Fortunately, FeFF works well enough to give us many parameters not available with models. It does not, however, yield any information about Debye-Waller disorder parameters. These can be estimated from the XRD refinements of similar crystalline materials, or extracted from structurally related (not necessarily the same composition) model compounds.

In some cases model compounds can be synthesized. For example, doping Fe2+ into MgO allows for an excellent Fe-Mg parameter model. Obviously, if model compounds must be selected and synthesized, EXAFS experiments can be considerably complicated.
 

Data reduction

The steps required for data analysis are discussed reasonably thoroughly in Sayers and Bunker (1988) and include the following:

Background shape and removal.

Normalization

FT analysis (optimizing peak shape, width, # of fittable parameters; decreasing FT ripples and termination errors)

References for curve fitting; ratio method; etc.