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Abstract

X-ray absorption spectroscopy has become a common technique in mineral studies only in fairly recent times. It is an element-specific method which is suited to extend structure determination down to the local environment of an atom, i.e. a volume some three orders of magnitude less than that inspected by methods based on X-ray diffraction. However, in line with many other modern techniques, X-ray absorption spectroscopy is neither simple as for the practical operations by which one records high-quality experimental results, nor it is straightforward in the interpretation of them, the more so as minerals are far more complex multi-atomic systems than most compounds investigated by other material scientists. Consequently the mineralogical literature related to X-ray absorption spectroscopy is full of misunderstandings, which may even become traps for a new user. A further motive for the poor interpretation of experimental results that are otherwise technically excellent arises from the bare fact that the theoretical framework of X-ray absorption spectroscopy lies well beyond the basic physics normally taught to mineral and material science students. Indeed, this is possibly why quite a few people have used this powerful technique as if it were a black box (e.g. the ominous “fingerprinting” practice!), or they have overextended the interpretation of spectra beyond what is their true potential content (cf. Stern, 2001).

In this chapter, I try to show all what is possible as well as all what is reasonable to obtain by the main absorption spectroscopy methods in use at the present time

Introduction

X-ray absorption spectroscopy has become a common technique in mineral studies only in fairly recent times. It is an element-specific method which is suited to extend structure determination down to the local environment of an atom, i.e. a volume some three orders of magnitude less than that inspected by methods based on X-ray diffraction. However, in line with many other modern techniques, X-ray absorption spectroscopy is neither simple as for the practical operations by which one records high-quality experimental results, nor it is straightforward in the interpretation of them, the more so as minerals are far more complex multi-atomic systems than most compounds investigated by other material scientists. Consequently the mineralogical literature related to X-ray absorption spectroscopy is full of misunderstandings, which may even become traps for a new user. A further motive for the poor interpretation of experimental results that are otherwise technically excellent arises from the bare fact that the theoretical framework of X-ray absorption spectroscopy lies well beyond the basic physics normally taught to mineral and material science students. Indeed, this is possibly why quite a few people have used this powerful technique as if it were a black box (e.g. the ominous “fingerprinting” practice!), or they have overextended the interpretation of spectra beyond what is their true potential content (cf. Stern, 2001).

In this chapter, I try to show all what is possible as well as all what is reasonable to obtain by the main absorption spectroscopy methods in use at the present time in the X-ray energy range, and for only the short portion of the spectra that is nearest to the absorption edge, namely XANES, the spectral region that is still hardest to interpret. My exposition will be finalised to better understanding the crystal chemistry of minerals, thus it will concern the major atoms occurring in the Earth's crust (Table 1). However, most spectroscopic studies performed using synchrotron radiation actually exploit the method's unique chemical selectivity properties that make it fit to detect and characterise even trace amounts of atoms that are dispersed within minerals; thus, X-ray absorption spectroscopy has become more a geochemical method than a mineralogical one. I too shall refer to certain trace elements, when useful, not only because the techniques in use for them are mostly the same as those for major atoms, but because I forecast an almost natural development of spectroscopic studies to this direction, where new important crystal chemical information will be discovered that will better explain the P–T–t reasons of atom distribution in the Earth (and planetary) materials, i.e., minerals, first of all (but also glasses and poorly crystalline compounds), which is the ultimate goal of geosciences (Hemley, 1999).

Table 1.

The 13 most widespread atoms occurring in the Earth crust, with their most commonly used absorption lines, and with a summary of XAS spectroscopy studies on the minerals containing them in essential amounts. Atoms listed in order of abundance in the Earth crust after Railsback (2003). K and L absorption edge energies [eV] after Williams (2001).

AtomZK 1sL1 2sL2 2p1/2L3 2p3/2Mineral groupReferences

O8543.141.6OxidesNakai et al. (1987b), de Groot et al. (1989), Räth et al. (2003)
Si141839149.799.8299.42Silica mineralsLi et al. (1993, 1994a, 1995a), Wu et al. (1996b)
PerovskitesAndrault et al. (1998)
Al131559.6117.872.9572.55OxidesMcKeown (1989), Cabaret et al. (1996), Ildefonse et al. (1998)
PerovskitesAndrault et al. (1998)
GarnetsWu et al. (1996a)
ClinopyroxenesMottana et al. (1999)
MicasMottana et al. (1997a, 2002)
Clay mineralsIldefonse et al. (1994, 1998)
FeldsparsLi et al. (1995b), Wu et al. (1997), Ildefonse et al. (1998)
Fe267112.92844.6719.9706.8miscellaneousWaychunas et al. (1983), Galoisy et al. (2001), Petit et al. (2001), Wilke et al. (2001)
OxidesBajt et al. (1994), Sutton et al. (1995), Berry et al. (2003)
OlivinesWu et al. (1996c, 2004)
GarnetsDyar et al. (1998)
ClinopyroxenesQuartieri et al. (1993b, 1997), Davoli et al. (1988), Mottana et al. (1991), Paris & Tyson (1994)
OrthopyroxenesClosmann et al. (1996), Giuli et al. (2002)
AmphibolesDelaney et al. (1996, 1998)
MicasGuttler et al. (1989), Manceau et al. (1990), Cruciani et al. (1995), Mottana et al. (2002), Dyar et al. (2001, 2002), Brigatti et al. (2001), Giuli et al. (2001), Tombolini et al. (2002a, 2002b, 2003)
Clay mineralsBonnin et al. (1985), Manceau & Calas (1986), Manceau et al. (1988, 1992, 1998, 2000), Drits et al. (1997)
CordieriteGeiger et al. (2000)
GrandidieritesFarges (2001)
PumpellyitesArtioli et al. (1991)
StaurolitesHenderson et al. (1993, 1997)
Ca204038.5438.4349.7346.2GarnetsChaboy & Quartieri (1995), Quartieri et al. (1995)
            ClinopyroxenesDavoli et al. (1987, 1988), Paris et al. (1995)
Na111070.863.530.8130.65Clinopyroxenes FeldsparsMcKeown et al. (1985), Mottana et al. (1997b), McKeown et al. (1985)
Mg121303.088.749.7849.50PerovskitesAndrault et al. (1998)
OlivinesWu et al. (1996c, 2004)
ClinopyroxenesCabaret et al. (1998), Mottana et al. (1999)
   
OrthopyroxenesAndrault et al. (1998), Giuli et al. (2002)
   
MicasMottana et al. (2002)
miscellaneousLi et al. (1999), Cibin et al. (2003)
K193608.4378.6297.3294.6HalidesLytle et al. (1984), Lavrentyev et al. (1999)
   
MicasMottana et al. (2002)
Ti224966560.9460.2453.8miscellaneousWaychunas (1987)
Oxidesde Groot et al. (1992), Farges et al. (1996), Farges (1997)
  
Garnetsde Groot et al. (1992), Locock et al. (1995)
  
Clinopyroxenesde Groot et al. (1992), Quartieri et al. (1993a)
  
AmphibolesParis et al. (1993)
StaurolitesHenderson et al. (1993, 1997)
Cl172822.4270202200HalidesLytle et al. (1984), Murata et al. (1992),
Lavrentyev et al. (1999)
P152145.5189136135PhosphatesFranke & Hormes (1995)
S162472230.9163.6162.5ThiospinelsCharnock et al. (1990)
SulphidesLi et al. (1994b, 1995b), Mosselmans
et al. (1995), Zajdel et al. (1999),
Farrell & Fleet (2001)
SulphatesLi et al. (1995b)
Mn256539769.1649.9638.7OxidesBelli et al. (1980), Manceau & Calas
(1986), Manceau et al. (1992),
McKeown & Post (2001)
CarbonatesLee et al. (2002)
StaurolitesHenderson et al. (1997)
AtomZK 1sL1 2sL2 2p1/2L3 2p3/2Mineral groupReferences

O8543.141.6OxidesNakai et al. (1987b), de Groot et al. (1989), Räth et al. (2003)
Si141839149.799.8299.42Silica mineralsLi et al. (1993, 1994a, 1995a), Wu et al. (1996b)
PerovskitesAndrault et al. (1998)
Al131559.6117.872.9572.55OxidesMcKeown (1989), Cabaret et al. (1996), Ildefonse et al. (1998)
PerovskitesAndrault et al. (1998)
GarnetsWu et al. (1996a)
ClinopyroxenesMottana et al. (1999)
MicasMottana et al. (1997a, 2002)
Clay mineralsIldefonse et al. (1994, 1998)
FeldsparsLi et al. (1995b), Wu et al. (1997), Ildefonse et al. (1998)
Fe267112.92844.6719.9706.8miscellaneousWaychunas et al. (1983), Galoisy et al. (2001), Petit et al. (2001), Wilke et al. (2001)
OxidesBajt et al. (1994), Sutton et al. (1995), Berry et al. (2003)
OlivinesWu et al. (1996c, 2004)
GarnetsDyar et al. (1998)
ClinopyroxenesQuartieri et al. (1993b, 1997), Davoli et al. (1988), Mottana et al. (1991), Paris & Tyson (1994)
OrthopyroxenesClosmann et al. (1996), Giuli et al. (2002)
AmphibolesDelaney et al. (1996, 1998)
MicasGuttler et al. (1989), Manceau et al. (1990), Cruciani et al. (1995), Mottana et al. (2002), Dyar et al. (2001, 2002), Brigatti et al. (2001), Giuli et al. (2001), Tombolini et al. (2002a, 2002b, 2003)
Clay mineralsBonnin et al. (1985), Manceau & Calas (1986), Manceau et al. (1988, 1992, 1998, 2000), Drits et al. (1997)
CordieriteGeiger et al. (2000)
GrandidieritesFarges (2001)
PumpellyitesArtioli et al. (1991)
StaurolitesHenderson et al. (1993, 1997)
Ca204038.5438.4349.7346.2GarnetsChaboy & Quartieri (1995), Quartieri et al. (1995)
            ClinopyroxenesDavoli et al. (1987, 1988), Paris et al. (1995)
Na111070.863.530.8130.65Clinopyroxenes FeldsparsMcKeown et al. (1985), Mottana et al. (1997b), McKeown et al. (1985)
Mg121303.088.749.7849.50PerovskitesAndrault et al. (1998)
OlivinesWu et al. (1996c, 2004)
ClinopyroxenesCabaret et al. (1998), Mottana et al. (1999)
   
OrthopyroxenesAndrault et al. (1998), Giuli et al. (2002)
   
MicasMottana et al. (2002)
miscellaneousLi et al. (1999), Cibin et al. (2003)
K193608.4378.6297.3294.6HalidesLytle et al. (1984), Lavrentyev et al. (1999)
   
MicasMottana et al. (2002)
Ti224966560.9460.2453.8miscellaneousWaychunas (1987)
Oxidesde Groot et al. (1992), Farges et al. (1996), Farges (1997)
  
Garnetsde Groot et al. (1992), Locock et al. (1995)
  
Clinopyroxenesde Groot et al. (1992), Quartieri et al. (1993a)
  
AmphibolesParis et al. (1993)
StaurolitesHenderson et al. (1993, 1997)
Cl172822.4270202200HalidesLytle et al. (1984), Murata et al. (1992),
Lavrentyev et al. (1999)
P152145.5189136135PhosphatesFranke & Hormes (1995)
S162472230.9163.6162.5ThiospinelsCharnock et al. (1990)
SulphidesLi et al. (1994b, 1995b), Mosselmans
et al. (1995), Zajdel et al. (1999),
Farrell & Fleet (2001)
SulphatesLi et al. (1995b)
Mn256539769.1649.9638.7OxidesBelli et al. (1980), Manceau & Calas
(1986), Manceau et al. (1992),
McKeown & Post (2001)
CarbonatesLee et al. (2002)
StaurolitesHenderson et al. (1997)
Table 2.

Absorption edges and corresponding electronic core levels.

EdgeM1L3L2L1K
Core level3s2p3/22p1/22s1s
EdgeM1L3L2L1K
Core level3s2p3/22p1/22s1s

Section 1 will sketch the historical development of the method. Readers interested in its immediate application may skip this section with no great loss of information. However, I am convinced that from knowing the long struggle by which pioneers made research to progress, the reader learns not only a better, more factual idea of some difficulties they are going to meet, but also of the reliability of the results they are going to obtain, and will avoid unduly overconfidence that might lead to unfortunate errors.

In section 2, I define what is XAS (“X-ray Absorption Structure”) or XAFS (“X-ray Absorption Fine Structure”): to my mind the two terms are synonyms, the latter merely emphasizing the well-resolved spectral structure of modern experimental X-ray absorption edge spectra that is unwise to forget and is, anyway, closely tied with the method ever since synchrotron became the source of the absorbed radiation. I also explain how and why XAFS spectra underwent and still undergo two distinct sorts of theoretical treatment for their low (XANES) and high (EXAFS) energy regions as if they were two different phenomena, while they are just two facets of the same physical phenomenon that should be addressed by the same theoretical approach. With this perspective, I feel to highly recommend giving XAFS the meaning of a general term referring to all fine structures occurring over the entire absorption spectrum (i.e., XAFS = XANES + EXAFS), as initially suggested by Rehr et al. (1986). This usage would merely anticipate a result that current theoretical research is struggling to achieve and is certainly going to attain in the long run.

In section 3 the multiple scattering (MS) theory is explained, in simple terms so as to make it understandable by non-physicists, but not in such a simplistic manner as to make the reader realise a wrong feeling of XAS potentials, which are great indeed because of the conceptual content it is based upon. Thus, I will insist on this theoretical approach by showing the calculation procedure to be followed to simulate the experimental spectra from known crystal structure data and ab initio concepts. As today's computational approaches are many, I shall detail the method I normally use and I am best acquainted of, but I will also make a point of describing other methods that are widespread among mineralogical users.

Section 4 deals with a description of various apparatus and methods used for experimental recording of XANES spectra, with an evaluation of the best conditions for their use, while section 5 is a description of the information that can be retrieved from the various XANES sub-regions of the XAFS spectrum. I shall deal with it in general terms, because detailed examples of spectral manipulation are given in the final section: an addendum (written in cooperation with A. Marcelli and G. Cibin) that shows step-by-step how to handle a genuine experimental spectrum and interpret it by comparison with spectra simulated theoretically on the basis of the known crystal structure parameters of the investigated mineral. This part is designed for beginners, and can be disregarded by those who feel to be already expert in handling XANES data.

A final warning: my aim is at showing how XAS can help in the study of minerals only, and not of all Earth materials; indeed, the present widespread application of XAS to low-temperature geochemistry and environmental science is also referred to cursorily, but it is beyond the scope of this work.

The historical development of XAS spectroscopy

The absorption of X-rays, i.e., the event that in that famous night of 8 November 1895 allowed W.K. Röntgen to notice the new form of radiation that shattered the world of physics (and medicine) of that time, was first investigated by C.G. Barkla from 1905 to 1912 in a series of pioneer studies. However, the first experimental detection of a fine structure at the absorption edge was apparently delayed for some years (de Broglie, 1913; Kossel, 1916; Stenström, 1918) and, at any rate, it occurred later than Moseley's genial intuition (1913) that the energies of the emitted X-rays are related to the atomic energy levels envisaged by Bohr (1913) and vary according to the square of atomic number Z. Systematic recording of absorption lines for the various atoms started even later (Fricke, 1920; Hertz, 1920), but it developed rapidly, at least during a short initial stage, because quantum mechanics, which was being introduced at that time (Heisenberg, 1925; Schrödinger, 1926), required better and better experimental information in order to reach a picture of even the simplest atomic structure. This early phase, when research on the absorption of X-rays contributed jointly with other basic electromagnetic concepts to the understanding of the electronic structure of matter and to the establishment of modern solid state physics, has been extensively reviewed and appraised by Stumm von Bordwehr (1989).

XAS spectra were first theoretically explained and experimentally verified for the part of the spectrum nearest to the edge (Kossel, 1920, referring also his previous experimental findings of 1914 and 1916; Wentzel, 1921) and, one decade later, for that extending to higher energies (Kronig, 1931, 1932a, 1932b; Hanawalt, 1931a, 1931b). Then, spectra started being used to derive information about the electronic structure of condensed matter, but they proved to be of such a difficult recording in their fine details as to distract most physicists from further insight; thus the practical aspects of the XAS method remained stagnant for nearly half a century.

Indeed, the method was revitalised only in the early 1970's, but even then mostly on theoretical grounds. It eventually became operational only after a breakthrough in the type of X-ray source took place, i.e., when conventional X-ray tubes were superseded by synchrotron radiation (SR) and the recorded spectra started to show their full wealth of fine details: no longer XAS, but XAFS! Yet, even now, when spectra are recorded by thousands each year with high energy resolution and great accuracy at numerous facilities, several aspects of the underlying theory are not completely worked out (Stern, 2001). The struggle to reach a unified, consistent physical theory that can interpret and explain at the same time all regions of the XAFS spectrum is still on, with only a fair perspective chance of reaching conclusion in a reasonable time (Natoli et al., 2003). Consequently, many accurate and well-resolved XAFS spectra are still interpreted approximately (when not simply by the “fingerprinting” rule of thumb!) and stored away for better times.

Basic knowledge

As previously mentioned, modern XAS research began a few years before SR entered into use for the physical community and at the beginning led to negative results, most probably because the spectra were not resolved enough. The old scattering theories, put forth to explain the absorption structures observed in solids and molecules in terms of “long-range order” (Kronig, 1931, 1932a) and “short-range order” (Kronig, 1932b; however, both terms have been introduced much later: cf. Azaroff, 1963), were shown not to work properly, despite some occasional success. It was easily demonstrated that the second approach included the first one (Kostarev, 1941), but it took a long time before such a fundamental theoretical result crept into the users' minds. Indeed, it was the entire XAS theory that had to be reconsidered starting from its basic assumptions. Lytle (1965) did so by first developing a calculation method that was able to explain the size of the first coordination shell (i.e., the “short range” around the absorbing atom) and contained the essential concepts that could interpret the “Extended X-ray Absorption

Fine Structure” (EXAFS: an acronym approved, if not invented, by J.A. Prins, cf. Lytle, 1999). In the following ten years he improved this approach by working in cooperation with others (Sayers et al., 1970, 1971; Lytle et al., 1974, 1975; Stern et al., 1975), to make it eventually reach a status very much like the present, familiar EXAFS theory based on Fermi's golden rule and with its Fourier transform mathematical analysis of oscillations to determine the radial distribution function (Teo, 1986; Stern et al., 1995; Fornasini, 2003; see Galoisy, 2004, in this volume).

Most of this theoretical upgrading was carried out over a time span of ten years before SR became widely used as the impinging X-ray radiation for solids. More precisely, it was later than the very first absorption experiments carried out at the earliest synchrotron linear sources (e.g. Axelrod & Givens, 1960), but it preceded the first ones attempted using soft X-ray radiation derived from 1st generation storage rings (e.g. Haensel et al., 1969, 1970; Sonntag et al., 1969) as well as those in the hard X-ray range (Eisenberger et al., 1974). Therefore SR, which we now consider inseparably linked with the XAS method, actually helped to perfect theory and data treatment by making it possible to demonstrate their validity for a greater number of oscillations and for an ever-increasing number of compounds; however, it did not substantially modify the basic theoretical understanding of XAS spectroscopy so as it had been developed for conventional sources.

By contrast, physical research met such a hard nut as not to have it cracked even now for the most conspicuous region of the XAFS spectrum closest to the absorption edge. This region had been originally explained by a theory conceived by Kossel (1920) and upgraded by Kronig (1931, 1932a) according to the “long-range order” model: indeed, that theory refers to the “X-ray Absorption Near-Edge Structure”, i.e., XANES (an acronym that is widely substituting for what was known in the past as the “Kossel structure” and was first used by Bianconi et al., 1978; alternatively, the acronym NEXAFS, i.e., “Near-edge X-ray Absorption Fine Structure”, has also been used, especially for organic compounds where absorption occurs in the very soft X-ray range, from below ca. 200 eV up to ca. 2500 eV: cf. Stöhr, 1992; Myneni, 2002).

Kossel is to be credited to have first detected many key properties of XANES, such as of being related to bound excited states, the effect of the ionisation state (“Hauptvalenzzahl”: Kossel, 1916) of the investigated atom on the energy position in a compound, the simple nature of the K edge in contrast to the more complex ones of the L, M etc. edges (Kossel, 1920) and, together with Sommerfeld (1920), the additive relationships for position and intensity of the structures in an edge series that satisfied the experimental evidence of his time. He also correctly interpreted the relationships existing between absorption and emission when excitation induces electron transitions to an atom. However, it was Hertz (1920) who first described the occurrence of fine structures at the L edge, and Kronig (1931) who introduced into XAS studies the useful “core hole” picture conceived by Bloch (1928), which relates the edge features with the scattering strength of the electron undergoing transitions from core levels to high-energy niveaux, so that the chemical bonding effect and the effective charge density around the absorbing atom become easy to understand. Moreover, it was Bergengren (1920) who generalised the concept that valence influences the energy at which absorption starts, and

Fajans (1928) who explained this effect with the outer electrons screening the atom core levels, while Veldkamp (1932) showed that the K-edge structures change with changing the structure of the examined compound: e.g., in a NiFe alloy, having face-centred cubic (fcc) structure, the Fe K-edge resembles the K-edge of Ni metal, which is also fcc, rather than that of α-Fe that is body-centred cubic (bcc). Although apparently simple, this is fundamental information by no means to be disregarded nor forgotten, because it proves that XANES is structure-dependent on the long range, too, rather then on the short (local) range only, as it is often reiterated even in recent papers.

The years 1930 to 1960 are scattered with small contributions by many who all contributed to a more detailed knowledge of the absorption near-edge fine structures of heavy atoms in a variety of simple compounds. Taken together, they certainly increased insight in the phenomenon; however, they could never shatter Kossel's or Kronig's early theories. Therefore, modern XANES spectroscopy started not only after the EXAFS region had already been theoretically reconsidered and reinterpreted (see above), but also after SR had become the normal X-ray source in the middle of the 1970s. Indeed, it was by building on experience accumulated following the relatively simple but successful one-electron single scattering (SS) theory, developed to explain EXAFS by Sayers, Lytle and Stern in the years 1965–1975, that Dill & Dehmer (1974), Dehmer & Dill (1975, 1976) and Lee & Pendry (1975) could formulate the theory that XANES structures are due to the multiple scattering (MS) of photoelectrons against atoms in the surrounding of the photoabsorber. As a matter of fact, they extended the one-electron single scattering process that had explained EXAFS as being due to reflection of the photoelectron by one of the neighbouring atoms directly back to the absorbing atom (Fig. 1a, b, d) to a more complex multiple scattering cascade process where the photoelectron is reflected onto two or more neighbouring atoms, which then reflect off still other atoms before the absorber is finally reached (Fig. 1c, e). Such a multiple back-reflection view of the process makes the XANES spectrum much easier to interpret and understand. Therefore, it is widely acknowledged now that XANES contains two kinds of information on the investigated atom: a) its electronic structure, and b) its geometric distribution within the structure.

Fig. 1.

Pictorial view of the events occurring when a strong-enough photon collides an atom (after Benfatto et al. 1986, modified). (a) Formation of a core hole by ejection of a photo-electron e from a deep level of the absorbing atom. (b) Propagation of an X-ray wave that collides with a B atom nearby; the particle is reflected back directly to the absorber A following a direct path and a single scattering event (d). (c) The propagating wave is shown to collide against many atoms nearby, one of which becomes a scattering centre producing many interferences which in (e) are depicted as the multiple pathways of a particle multiple scattering process. The (e) sequence of multiple scattering events (here limited to n < 4) gives rise to XANES features and the (d) single event to EXAFS oscillations, all together forming the XAFS spectrum of atom A in the environment of the ABC multiatomic compound.

Fig. 1.

Pictorial view of the events occurring when a strong-enough photon collides an atom (after Benfatto et al. 1986, modified). (a) Formation of a core hole by ejection of a photo-electron e from a deep level of the absorbing atom. (b) Propagation of an X-ray wave that collides with a B atom nearby; the particle is reflected back directly to the absorber A following a direct path and a single scattering event (d). (c) The propagating wave is shown to collide against many atoms nearby, one of which becomes a scattering centre producing many interferences which in (e) are depicted as the multiple pathways of a particle multiple scattering process. The (e) sequence of multiple scattering events (here limited to n < 4) gives rise to XANES features and the (d) single event to EXAFS oscillations, all together forming the XAFS spectrum of atom A in the environment of the ABC multiatomic compound.

In those years (and even now, as a matter of fact) XAS moved forward through a combination of new experimental findings and subtle theoretical modifications conceived under the constant pressure of developing improved computational software that would cope with the impetuous progress in the hardware. The spectra of simple molecular compounds, which were tackled first, were just a small step in the search for the solution of the much more complex task of deciphering condensed systems. Most theoretical research aimed at devising consistent sets of algorithms that could be translated into computer codes, while experimental research not only strove to add new, more accurate evidence (in this being supported by the technological innovations intervening at synchrotron facilities, which upgraded to present-day 3rd generation machines: cf. Winick, 1994; Norman, 2001; Sham & Rivers, 2002), but also to find new case studies that would pinpoint inadequacies still present in the theory, so that the relevant codes would be improved.

Indeed, the development of increasingly faster computers proved to be essential to improve both physical theory and mathematical calculation: e.g. McKeown (1989) was content with computing satisfactorily the spectra generated by the 1st shell neighbours of Al in minerals, i.e., the local XANES spectra of the [AlO6] 7-atom octahedral cluster and the [AlO4] 5-atom tetrahedral cluster; by contrast, only few years later, Wu et al. (1996c) could calculate satisfactorily the full MgO (periclase) XANES spectrum using a 147-atom cluster (later enhanced to more than 200 atoms), and demonstrate that the XANES spectrum of forsterite can be decomposed into two partial spectra for the M1 and M2 sites by adding up [MgO6] clusters to the 6th coordination shell that comprise as many as 89 atoms in their respective local neighbourhoods. Such a progress implies steady, parallel advancements in both theory and experiment, which in addition go hand in hand with gains in both software and hardware.

Mineral studies

Elsewhere I have recently reviewed the last 25 years of XAS advancement in mineralogy (Mottana, 2003) and I am not going to repeat it here, the more so as there have also been others who did the same at different times, often under different outlooks that complement my own, which is explicitly devoted to minerals and mineral analogues. The most relevant of such reviews, which deal with both K- and L-edge spectroscopy, are by Calas et al. (1987, 1990), Petiau et al. (1987), Brown et al. (1988), Brown & Parks (1989), Davoli & Paris (1990), Bianconi & Marcelli (1992), Cressey et al. (1993), Henderson et al. (1995), Schofield et al. (1995) and, very recent and mainly oriented to XAS applications in geochemistry, by Jiang (2002) and Brown & Sturchio (2002).

The first modern, SR-based XAS study of mineralogical interest was by Brown et al. (1978) at the Fe K edge, i.e., in the hard X-ray energy range. It was only four years after the very first experiment of physical interest had been carried out in a storage ring at that edge (Eisenberger et al., 1974) and less than a decade after those in the soft X-ray range, i.e., at the L edge of the gas and solid phases of noble gases (Haensel et al., 1969) and at the M and L edges of REE metals (Sonntag et al., 1969; Haensel et al., 1970). As a matter of fact, the material studied by Brown et al. (1978) was not a true mineral, but synthetic NaFe3+Si2O6 “acmite”, i.e., the analogue of aegirine, together with the glass starting material that had been used for its synthesis. The relative energy positions of their “white line” (i.e., first and most intense feature at the absorption threshold: Bradley et al., 1985) were compared to measure the shift in energy that marks the Fe3+ change in coordination number from four in glass to six in the crystal.

Indeed, the ability of XANES to infer the coordination number and to determine the oxidation state of the investigated atom have been the most investigated subjects during the 1980s (e.g. Calas et al., 1980; Calas & Petiau, 1983; Waychunas et al., 1983; Waychunas, 1987; Davoli et al., 1987, 1988; Guttler et al., 1989; etc.), with a distinct preference for transition elements that could be scanned in air and with good energy resolution at 2nd generation synchrotrons. However, pioneer studies using the strong linear polarisation character of SR that allows measuring X-ray absorption dichroism (Manceau et al., 1988; Waychunas & Brown, 1990) were also made. Furthermore, XAS unique properties of atom selectivity and independence upon the physical state of the sample were constantly exploited with special emphasis for very fine grained clays (Kaiser et al., 1989; Manceau et al., 1999), nearly amorphous manganates (Manceau et al., 1987, 1992; Combes et al., 1988) and allophanes (Ildefonse et al., 1994, 1998).

XANES spectroscopy started being used systematically to explore the local crystal chemistry of major and minor atoms in various mineral groups at different atomic edges after 1985. At present, there is good information for the most significant edges in various mineral groups and families for the major mineral forming atoms (Table 1) as well as for a variety of minor atoms, most of which were studied on model compounds for geochemical purposes (e.g. As: Foster et al., 1998; B: Fleet & Mathupari, 2000; Cd: Parkman et al., 1999; Ce: Quartieri et al., 2002; Co: Manceau et al., 1992; Cr: Brigatti et al., 2000, 2001; Cu: Parkman et al., 1999, Cheah et al., 2000; Eu: Rakovan et al., 2001; Nd: Quartieri et al., 2002; Ni: Manceau & Calas, 1987, Manceau et al., 1992, Giuli et al., 2000, Carvalho-e-Silva et al., 2003; Pb: Morin et al., 1999, 2001; U: Sturchio et al., 1998; Zn: Henderson et al., 1993, 1997; etc.). Furthermore, there is plenty of information on synthetic compound analogues of minerals. Unfortunately, the whole evidence is still grossly incomplete in comparison with that gathered by other methods, especially for the major atoms which determine the mineral formula: no more than 10% of the ca. 4000 known mineral species have been investigated, compared to ca. 90% of them having their structure determined by single-crystal or Rietveld XRD refinement.

The random distribution of the information is due to the fact that XAS research was mostly addressed towards minor to trace atoms that had not been properly located in the investigated structure, either because they could not be revealed by XRD refinement, or because they were ambiguous in their redox conditions. Nevertheless, novel information impossible by other methods has been gained, e.g., on metamict minerals (Greegor et al., 1984; Nakai et al., 1987a; Akimoto et al., 1988; Farges & Calas, 1991; Farges, 1997) and on amorphisation and crystallisation processes taking place at high temperature (Farges et al., 1995a, 1995b) and/or pressure, mainly using the diamond anvil cell (Itié, 1992; Itié et al., 1996, 1997; Petit et al., 1996; Bassett et al., 2000a, 2000b). The recent development of an XAS microprobe (SmX, or micro-XANES: cf. Baker, 2002) makes it possible to study quantitatively the oxidation state of atoms in even the smallest mineral grains (e.g. Sutton et al., 1995, 2002; Delaney et al., 1996, 1998; Mosbah et al., 1999), both in situ and oriented according to their structural and/or optical axes (Dyar et al., 2001, 2002). This will reflect positively on the study of a very large number of minerals (indeed, most of the 4000 species known!), which are unavailable as large crystals or in significant amounts.

XANES is now commonly used when aiming at solving practical environmental problems too, so that experimental XANES studies on minerals span over most elements of the periodic table using either the K or the L and even M edges; from B, which has its K edge at 194 eV (Li et al., 1996; Fleet & Muthupari, 2000), to U with its L2 edge at 21 keV (Morris et al., 1996; Thompson et al., 1997; Sturchio et al., 1998) and, recently (due to the increased brilliance of 3rd generation synchrotrons) even to the Nd K edge at 43 keV (Chaboy et al., 2002; Quartieri et al., 2002). The quality of the information is only hampered by the purity of the scanned grains, because the high detection power of XAS makes it inevitable to record spurious spectra when the examined mineral contains traces of nano-grained inclusions that escape optical or EMP detection.

The XANES region: Definition and limits

An absorption spectrum consists of a sequence of structures (or features, or peaks) having two characteristics: intensity (generally given in arbitrary units) and energy (eV). The “Kossel structure” was originally intended to be the portion of the spectrum extending from the absorption edge to ca. 20–25 eV above it, and the “Kronig structure” the part beyond it. This distinction was maintained for a long time (and is still maintained by some, e.g., Stern, 2001) because it proved useful to separate the low-energy range of the spectrum dominated by electronic effects from the high-energy one determined by the local geometric atomic structure. However, when Kronig's (1932b) theory was superseded by the one-electron single scattering theory, it became customary to refer to the broad oscillations that followed at a certain distance to the edge as the EXAFS region of the XAFS spectrum, and a few years later to the features at or near the edge itself as the XANES region. Moreover, since it had appeared rather early that more than one absorption edges could be recorded for the same atom (one only, i.e., K, up to Z = 6, plus two L up to Z = 17, then other three M for Z = 29 etc.; cf. Fuggle & Mårtensson, 1980; Williams, 2001 – see Table 1) and each one of them had its own near-edge and extended regions, it also became customary to use the names XANES and EXAFS with no further specification for the 1s absorption edge, or else K edge, as it will be always done throughout the following sections.

Each edge energy depends upon the binding energy of the corresponding core level, and its value increases monotonically with the atomic number Z. This is the reason why XAS is a chemically selective technique: each measured edge energy corresponds to a well-defined atomic species that can be identified because it remains constant (albeit with a very limited variation) whatever the environment is of the compound (solid, liquid, glass, gas) the absorbing atom is located in.

Even a visual evaluation of a full XAFS spectrum (Fig. 2) suggests that the strong and sharp XANES region with its discontinuities is different from the very weak EXAFS oscillations that follow and fade progressively away; however, establishing a boundary in the transition region between the two may be a matter of subjective opinion. A rationale was found in the past, when the two regions of the XAFS spectrum were interpreted using two different theoretical scattering approaches, but it seems not to hold now, with the continuous advances of the multiple scattering theory (see later).

Fig. 2.

The complete X-ray absorption cross section for argon (after Henke et al., 1993, simplified) showing the Cooper minimum (CM), the three L edges at 326.3, 250.6 and 248.4 eV and the very strong single K edge at 3205.9 eV. At this scale neither the strong XANES features nor the weak EXAFS oscillations can be seen.

Fig. 2.

The complete X-ray absorption cross section for argon (after Henke et al., 1993, simplified) showing the Cooper minimum (CM), the three L edges at 326.3, 250.6 and 248.4 eV and the very strong single K edge at 3205.9 eV. At this scale neither the strong XANES features nor the weak EXAFS oscillations can be seen.

Bianconi (1988), proposed a separation between XANES and EXAFS (Fig. 3) considering that the single scattering approximation inherent to EXAFS theory, as outlined by Sayers and co-workers, is expected to break down when the photoelectron wavelength is larger than the interatomic distance, i.e., 

formula
or, in energy terms:  
formula

Fig. 3.

Pictorial view of the final-state wave functions in the core excitation of a diatomic molecule showing the high energy hv2 transition to the EXAFS region and the low hv1 one to the XANES region. The dotted curves are the wave functions of the emitted photoelectron. Ec is the critical energy marking the passage from the high- to the low-energy regime, i.e. from the single scattering (SS) that generates EXAFS oscillations to the multiple scattering (MS) that gives rise to the XANES spectrum (from Bianconi, 1988, modified).

Fig. 3.

Pictorial view of the final-state wave functions in the core excitation of a diatomic molecule showing the high energy hv2 transition to the EXAFS region and the low hv1 one to the XANES region. The dotted curves are the wave functions of the emitted photoelectron. Ec is the critical energy marking the passage from the high- to the low-energy regime, i.e. from the single scattering (SS) that generates EXAFS oscillations to the multiple scattering (MS) that gives rise to the XANES spectrum (from Bianconi, 1988, modified).

In Equation 1, kc is the critical wave vector, which is defined as the reciprocal of the shortest interatomic distance d (multiplied by 2π) occurring in the cluster of atoms surrounding the photoabsorber. In Equation 2, Ec is the critical energy at which EXAFS is no longer valid and should be substituted by XANES; and ∇ is the interstitial potential, i.e., the electrostatic potential over the entire spherical volume around a charged metallic atom before it fades out as a result of screening (Natoli et al., 1986; Gunnella et al, 1990). In widespread minerals such as the silicates, which are insulators, the minimum interatomic distance is ca. 1.5 Å and the average electrostatic potential (energy) is ca. –180 eV (Smyth & Bish, 1988, both with large variations accounting for different coordinations), so that kc, the low-energy cut-off for EXAFS, is at ca. 4 Å−1. Conversely, then, the XANES energy range should extend to at least ca. 50 eV above the absorption threshold, which is defined as the lowest energy at which the absorption process begins, i.e., the energy of the first allowed transition, which in turn represents the lowest energy state reached by the core excitations.

This appraisal clearly shows that the XANES region is system-dependent, i.e., it varies with the crystal chemistry of the investigated material, and can extend over a fairly large range of energies, depending on the interatomic distance and the potential assumed for the compound under study. Moreover, one should take into account not only the transition from the MS regime to the SS one, but also many other subtle effects affecting the XAS spectra such as many-body relaxation and correlation, atomic vibration, potential changes etc., as well as various experimental uncertainties: cf. Bianconi (1988) for a detailed treatment and Natoli et al. (2003) for an update.

However, the energy cut-off notion (Eqn. 2) is basically invalid, because there are MS contributions even at high k (e.g. 3–12 k) that superimpose on EXAFS oscillations so as to create difficulties while retrieving the interatomic distances from them (see Galoisy, 2004, in this volume). Furthermore, recent calculations performed using MXAN (Benfatto et al., 2001; 2003; Benfatto & Della Longa, 2001), a code that is based on the MS theory, have shifted the energy region that can be computed by the full MS approach to ca. 200 eV above the threshold, thus implying that the XANES region may be conceived to extend well beyond the commonly accepted range. By contrast, however, there are also calculations that would show that a part at least of the XANES region can be modelled using the SS approach (Bugaev et al., 2001), or by combining molecular dynamics simulations with simple spectroscopic calculations (Merkling et al., 2001).

Summarising: for the sake of simplicity, in the description that follows I shall restrict the XANES region to its customary interpretation as the energy range of the absorption spectrum nearest to the edge, i.e., from a few eV below the absorption edge jump to ca. 50–(60–)80 eV above it (Fig. 3). In other words, I will assume as its lower boundary the point where in normalised and fitted spectra the absorption coefficient (in arbitrary units) starts to increase above the linear background because of the onset of the absorption features, and as its upper boundary the marked dip separating the weak, but well-structured XANES fine features from the wide, broad and structure-poor or structure-less EXAFS oscillations.

For practical as well as computational reasons, the XANES region conceived in this way (Fig. 4) has been further divided in three sub-regions (Natoli & Benfatto, 1986):

  1. The edge sub-region, or low-energy XANES region, from the absorption threshold up to ca. 8–10 eV above; the features just at or in the very first eV before the first intense absorption feature that marks the absorption jump are often singled out as the “pre-edge features”, first discovered by Rule (1945) at the Sm M4,5 edge, and the corresponding sub-region named pre-edge (PE) sub-region;

  2. The full multiple scattering (FMS) sub-region, up to ca. 20–30 eV above the absorption threshold, with the most intense features;

  3. The intermediate multiple scattering (IMS) sub-region, from ca. 20–30 eV above the threshold upwards to ca. 50–80 eV.

Fig. 4.

The XAFS spectrum of a high-Z atom in a silicate showing from left to right the base line (which in a Fe K-edge spectrum is located at < 7108 eV) the pre-edge (PE) sub-region (in Fe: 7108 to 7118 eV), the full multiple scattering (FMS) sub-region (in Fe: 7118 to 7138 eV), the intermediate multiple scattering (IMS) sub-region (in Fe: 7138 to 7160 eV) and, after the dotted vertical line, the region where single scattering (SS) dominates over multiple scattering (MS), i.e. the EXAFS region. In the insets the PE, FMS and IMS sub-regions are shown enlarged but at different energy scales. Note, however, that many oscillations up to 7200 eV (in Fe) may also be explained by the MS theory. In the PE inset, the broken vertical line is the absorption threshold, i.e., the zero point for the E–E0 abscissa; in a Fe K-edge XAFS spectrum this point is located at 7112.0 eV.

Fig. 4.

The XAFS spectrum of a high-Z atom in a silicate showing from left to right the base line (which in a Fe K-edge spectrum is located at < 7108 eV) the pre-edge (PE) sub-region (in Fe: 7108 to 7118 eV), the full multiple scattering (FMS) sub-region (in Fe: 7118 to 7138 eV), the intermediate multiple scattering (IMS) sub-region (in Fe: 7138 to 7160 eV) and, after the dotted vertical line, the region where single scattering (SS) dominates over multiple scattering (MS), i.e. the EXAFS region. In the insets the PE, FMS and IMS sub-regions are shown enlarged but at different energy scales. Note, however, that many oscillations up to 7200 eV (in Fe) may also be explained by the MS theory. In the PE inset, the broken vertical line is the absorption threshold, i.e., the zero point for the E–E0 abscissa; in a Fe K-edge XAFS spectrum this point is located at 7112.0 eV.

The broad oscillations that follow upwards to 700–1500 eV (for high-Z atoms) above the threshold belong to the EXAFS portion of the spectrum and are usually and conveniently interpreted using the SS approach (see Galoisy, 2004, in this volume).

It is clear that such a distinction accounts for both the traditional limit of the “Kossel structure” and the transitional sub-region where the SS and MS approaches seem to work equally well; in addition, it pin-points the lowest-energy sub-region before the edge jump, which, in fact, has been shown by the experiments to be extremely interesting for the information it contains.

The few features experimentally detected in this sub-region (PE features) are believed to be caused by electronic transitions to empty bound states; they may be either weak or strong depending upon (mainly) the atom coordination, and are bound upwards by the rising edge of the absorption jump inflection, i.e., the energy where the absorption intensity is half-height between the absorptions before and after the edge. The FMS sub-region that follows contains numerous (theoretically, an infinite number of) MS contributions, the first of which is the “white line” i.e., the first and usually (but not always) most intense and sharp feature of the spectrum. Finally, the IMS sub-region contains a small number (typically less than four) of features that in fact correspond to many superimposed MS contributions mainly related with the structural properties of the material. This sub-region is bound with and actually merges into the SS oscillations of the EXAFS region, i.e., of the former “Kronig structure”.

Theory of XANES spectroscopy

When dealing with theoretical matters, it is opportune to separate general theoretical concepts from their transformation into a practical calculation procedure that allows reproducing experimental results from known physical parameters. In the case of XAS, these two approaches are interwoven because they developed side-by-side, one affecting the other, for a rather long period (see above).

XAS theory is only a part of the well-established general scattering theory that studies the absorption of electromagnetic energy by the atoms (cf. Cowan, 1981; Fonda, 1992). In contrast, the theoretical calculations by which reproduction of the XAFS spectrum is attempted are mostly specific for the X-ray energy range. Moreover, they are still forced to incorporate a variety of simplistic models, the use of which is required by the available mathematical background and by the present computing resources.

General theory

The basic process promoting X-ray absorption is the excitation (ejection) of electrons from deep core levels of a selected atom (absorber) being hurt by a photon (Fig. 1a). Depending on the photon energy, a series of physical processes takes place, the first of which is the formation of a core hole (Bloch, 1928) by ejecting a deep-level photoelectron that escapes the atom potential well with emission of a characteristic energy in the X-ray range. This photoelectron acts as the probe in the entire process, because it collides with the atoms nearby: it may transfer all its energy in a single scattering event (Fig. 1d) or in a sequence of multiple events through several collisions against two or more atoms (Fig. 1e). All together, this cascade sequence of scattering events, which occurs in the time scale of electronic transitions (i.e., femtoseconds or n × 10−15 s) leads to the formation of a modulated absorption spectrum. Note that the entire process can also be described, according to de Broglie's equivalence, with a wave propagation formalism (Fig. 1b,c).

As all spectroscopic methods based on Lambert's law, XAS spectroscopy is basically a measurement of the variation of the linear X-ray absorption coefficient μ (with μ = μmρ [cm−1], where μm is the mass atomic absorption coefficient and ρ the electron density) as a function of energy E (with E = hv [eV], where h is Planck's constant and v the photon frequency) in the region across the characteristic absorption edge of the photoabsorbing atom and beyond, theoretically to infinity. XAS spectroscopy is particularly effective for the fine structures occurring in the region that immediately follows the absorption threshold, which is considered to be the energy of the lowest empty state reached by the core excitations. That is why (i.e., for the theoretical reasons briefly outlined before, but also for practical reasons of computation and interpretation) the XAFS spectrum has been divided in two distinct regions, XANES and EXAFS, and these were explained and quantitatively evaluated on the basis of two distinct theories and two distinct mathematical codes. Currently, however, one struggles to unify these two approaches into a unique, physically coherent theory. Apparently (or, better said, in the narrow limits of my own experience) the multi-channel one-electron multiple scattering theory or MMST (Natoli et al., 2003; Benfatto et al., 2003) is able to accomplish this task best (see later). The great advantage of the MMST formalism is that the absorption process is reconstructed in the real space, under theoretical constraints that allow adopting a mathematical approach that, although not simple at all, can be handled properly by the present computer performance.

The general MS theory was initially conceived and developed in nuclear physics to calculate nuclear scattering cross-sections (Rayleigh, 1892) and only much later was used in solid state physics to compute the electronic structure of solids (Korringa, 1947; cf. Cowan, 1981; Fonda, 1992). At the present stage of its development (well described in the differently addressed, but de facto converging, review papers by Rehr & Albers, 2000, and Natoli et al., 2003), this theory represents an extension of the bound-state molecular scattering method used by Johnson (1966, 1973) to determine the one-electron wave function for continuum states.

The cornerstones of the MMTS theory are:

  • the shape of the total potential of the system is represented by a cluster of non-overlapping spherical potentials that are centred on the atomic sites (typically three or four shells around the absorbing atom): this is the so-called “muffin-tin” approximation;

  • the Coulomb and exchange parts of the input potential are calculated on the basis of a total charge density obtained by superimposing the atomic charge densities of the individual atoms constituting the cluster, deduced from the Clementi & Roetti (1974) tables;

  • for the exchange potential, the energy-dependent Hedin-Lundqvist (HL) potential (Hedin & Lundqvist, 1969, 1971) is preferred because it incorporates the energy-dependent exchange and screening effects as well as extrinsic losses (local plasmon excitations); moreover, its imaginary part is able to reproduce accurately the observed mean free path length, or the length of the photoelectron propagation in the compound, which in this energy range is very short (0.5–1.5 nm: Müller et al., 1982; Penn, 1987). Indeed, although initially devised for Coulomb potentials, HL has been shown to hold valid even for the atomic core region (Lee & Beni, 1977) and to be best suited to account for the valence charge (Fujikawa et al., 2000). However, the energy-independent Slater (1979) approximation (X-α) and the Dirac-Hara (DH) potentials (Dirac, 1930; Hara, 1967) have also been used, and proved useful to explain certain parts of the XANES spectrum (e.g. Ankudinov, 1999, showed that the DH model fits better the experimental spectrum at energies very near the threshold such as the PE, whereas the HL model is much better for the FMS and IMS sub-regions). See the addendum for a comparison of calculations performed on the same cluster using different potential models.

In the MMTS theory, the absorption cross-section σ(E) for X-rays (assuming the dipole approximation, i.e., in the simple diatomic interaction model first devised by Kronig, 1932b, cf. Kutzler et al., 1980; Natoli et al., 1980, 2003; cf. Fig. 3) is given as:  

formula
where  
formula

In Equation 3, E is the photon energy in the initial (i) and final (f) states, α is a constant depending on the fine structure, δ is the Dirac constant and Mif the matrix element of the electronic transitions, which is made explicit in Equation 4, where ε is the polarisation vector of the electric field and rn the vector describing the position of the nth electron, all of them being integrated over the final (Ψf) and initial (Ψi) many-body radial wave functions. Therefore, being the initial state supposed to be known, the mathematical problem to solve is to calculate σ(E) when the final state of the system is reached and in accordance with the proper normalisation and boundary conditions.

Three alternative approaches have been proposed:

To clarify the physical implication of the cross-section of the photoabsorption process, it is better to use the Green's function approach with a generalised optical theorem (Natoli et al., 1986), and to rewrite the expression for the cross-section in the following way:  

formula
where mL(ε) is the matrix element that selects the final angular momentum L by the dipole selection rule, Im is the imaginary part of unit matrix I, Ta = forumla where forumla is the atomic t-matrix element of the atom at site i, describing its scattering power for an l spherical wave incident on it, and H = forumla is the free amplitude propagator of the photoelectron in the spherical wave state from site i with angular momentum L to site j with angular momentum L'.

All the geometrical information about the medium around the photoabsorber is contained in the inverse matrix (I + TaH)−1. When the modulus of the maximum eigenvalue ρ(TaH) of matrix TaH is less than one, it is possible to expand the inverse in series that are absolutely convergent relative to some matrix norm, so that the relationships for the cross section becomes:  

formula
where  
formula
The term n = 0 represents the smoothly varying “atomic” cross-section, whereas the generic n term is the contribution to the photoabsorption cross-section coming from processes in which the photoelectron has been scattered n – 1 times by the surrounding atoms before returning to the photoabsorbing site.

Thus, the unpolarised absorption coefficient, which is proportional to the total cross-section, is:  

formula
where l is the orbital angular momentum of the core initial state (l = 0 for the K level), Ml,l±1 is the atomic dipole transition matrix element for the photoabsorbing atom, and  
formula
is the quantity that contains the structural geometrical information. Here, forumla is the phase shift of the absorbing atom.

The total absorption coefficient can be expanded as a series:  

formula
where the first element α0 is the atomic absorption coefficient and the second term α1 is always zero because Hlm,lm = 0. For the K edge, in the plane-wave approximation, the expression for n = 2 is the usual back-scattering amplitude, i.e., the EXAFS signal multiplied by the atomic part.

Actually, the first MS contribution is the a3 term, which can be written (Benfatto et al., 1989) as follows:  

formula
where rij is the distance between atoms i and j, fi(ω) and fi(θ) are the relative scattering amplitudes, which now depend on the angles in the triangle that joins the absorbing atom to the neighbouring atoms located at sites rt and rj, and Rtot = ri + rij + rj. In this expression, P1(cosφ) are the Legendre polynomials with cosφ = –ri × rj, cosω = –ri × rij and cosθ = ri × rij. As a consequence, the n = 3 term and all terms with n > 2 contain information about the higher-order correlation function. In this framework, because P1(cosφ) = cosφ, there is a selection rule in the pathways; e.g., for the α3 term, whenever ri is perpendicular to rj, the corresponding MS term does not contribute to the total cross-section, since cosφ = 0. Neglecting multi-electron contributions, this description makes clear the distinction between the FMS and IMS sub-regions in a XANES spectrum, and assigns any differences to the local geometrical structure of the system. From the mathematical viewpoint, this total absorption formalism corresponds to considering the absorption signal as composed by an atomic smooth contribution α0 followed by an infinite series of oscillatory signals α1, α2, … that can be truncated at will (Benfatto & Natoli, 1986).

The MMST theory as outlined above is intrinsically consistent and essentially based on ab initio theoretical assumptions, with the only exception of the empirical choice of the potentials (see above, cf. Natoli et al., 2003). Unfortunately, despite being fundamental in all requirements up to this point of development, the MMST theory neither copes with the entire evidence that is contained in the experimental spectra nor it explains yet all the properties of the absorption process. Therefore, a number of additional concepts have been introduced that try to improve it; they are all based on empirical considerations in the pursuit of reaching the final goal of formulating a fully consistent and yet mostly a priori physical theory that accounts for all observed XAFS data. Obviously, these empirical constraints set limitations to the acceptance of the current MMST theory as a fundamental physical theory. They are:

  • The background atomic absorption coefficient μat(ω) needs an empirical definition, and the electronic and structural signals are to be extracted directly by fitting the experimental data for each material under study. As a matter of fact, the structural part of the photoabsorption cross-section σstr(ω) is proportional to the imaginary part of the product of the amplitude required to emit the photoelectron multiplied by the scattering amplitude required to propagate it from the absorber to the atom and back, times another amplitude that is needed to detect the photoelectron. During such a long process the photoelectron undergoes a damping that is related to the mean free path length, so that the total lengths of the possible MS pathways are not infinite but limited. In addition, the effect of the core hole lifetime is to be taken into consideration, and this is done by adding a Γh/2 term to Σ in Equation 10, where Γh is the full width at half maximum of the core hole, which in turn is related to its lifetime by the expression τ = h/Γh. The core hole has an exponential decay that adds to the damping of the mean free path and causes a sharp decrease of it.

  • The use of the muffin-tin approximation. This is a useful fiction that was devised to calculate the total potential. It consists of partitioning the space occupied by the cluster under study (by itself of difficult determination, actually to be found by trial and error until calculations reach convergence) into three regions (Fig. 5). Region I is made up of the atomic spheres around the physical atoms, their radii being determined by Norman (1974) prescription that is roughly proportional to Z, i.e., the atom position in the periodic table, reduced by 10–15% to account for an overlap that empirically simulates the covalent bond, and their potential being spherically symmetric. Region III is a region that lies outside the outer sphere circumscribing the cluster, with potential supposed to be constant, and can be disregarded. Region II is the space in between this outer sphere and the atomic spheres of region I. Any limitation in the interstitial volume or variation of the local potential is assumed to be located in region II and can be modulated simply by adding empty spheres to this region. The interstitial potential is calculated by expanding the potential around the centre of the cluster to the radius of the outer sphere, and this is either given as proportional to the Norman's radius or, following a suggestion by Wille et al. (1986) that seems to best account for a predominantly ionic bond, in such a way as to minimise the potential discontinuities at the boundaries of the various spheres included in the muffin-tin volume.

Fig. 5.

Pictorial view of the muffin-tin approximation seen from the top (a) and sideways (b). The atomic spheres of the cluster with their well-defined potentials represent region I; region III is outside the sphere circumscribing the cluster and does not contribute to the total potential; while region II does contribute, as it is the space in between this outer sphere and the atomic spheres of region I. The potential value for region II is chosen in a way that minimises the potential discontinuities at the boundaries of the various atomic spheres of region I.

Fig. 5.

Pictorial view of the muffin-tin approximation seen from the top (a) and sideways (b). The atomic spheres of the cluster with their well-defined potentials represent region I; region III is outside the sphere circumscribing the cluster and does not contribute to the total potential; while region II does contribute, as it is the space in between this outer sphere and the atomic spheres of region I. The potential value for region II is chosen in a way that minimises the potential discontinuities at the boundaries of the various atomic spheres of region I.

Obviously, this sequence of approximations implies a number of subjective decisions to be taken so as to reach the ultimate goal of calculating spectra that most closely match the experimental ones. In order to bypass such a bias, the ways proposed are many, and among them two are now preferred by theoretical physicists involved in this kind of studies: a) a self-consistent calculation (e.g. Ankudinov et al., 1998) and b) the elimination of the muffin-tin approximation, replaced by a finite difference calculation method (e.g. Joly, 2001). Both are mainly related to limitations in mathematical treatment and computer time and are beyond the scope of this paper. If of interest to the reader, they can be found in Appendix A of Natoli et al.'s (2003) review paper.

Theoretical calculations

As mentioned before, I am going to describe in detail the computer package I am acquainted with, and will only review cursorily other equally useful packages that are accessible to mineral-oriented users.

The CONTINUUM and MXAN computer codes

CONTINUUM is the computer package developed over the years at Frascati National Laboratories by C.R. Natoli's group (in cooperation with many other theoreticians). At the beginning it was conceived to test the potentials offered by the application to XAS of the one-electron multiple scattering theory conceived by Dill & Dehmer (1974) that had been developed in a series of studies by Dehmer & Dill (1975, 1976) and Lee & Pendry (1975). Then the computer code was steadily implemented with the aim of improving the theory itself by comparison with XAFS experiments on a variety of increasingly difficult systems (gas, metals and molecules), and eventually to complex structures such as minerals (Kutzler et al., 1980; Natoli et al., 1980, 1986, 1990; Durham et al., 1982; Natoli, 1983, 1984; Natoli & Benfatto, 1986; Wille et al., 1986; Durham, 1988; Filipponi et al., 1991; Tyson et al., 1992; etc.). As a matter of fact, the latest version of CONTINUUM (Tyson et al., 1992) goes well beyond the one-electron MS theory and is already based on the MMST as outlined above. CONTINUUM now copes with most needs of XAFS-based mineralogy, provided the crystal structure data of the mineral for which the XANES spectrum is to be calculated are approximately known (from XRD) and some allowance is given to the inevitable discrepancies that remain between experimental and calculated spectra. Excellent examples of calculations of complex silicate structures are to be found in Paris & Tyson (1994), Cabaret et al. (1996, 1998), Wu et al. (1996a, 1996b, 1996c, 2002, 2004) and Mottana et al. (1997b, 1999).

CONTINUUM is versatile and modular, so that its latest upgrade (Natoli et al., 2003) is equivalent not only to the band calculation method conceived by Müller et al. (1982) that accounts for a small cluster of atoms around the photoabsorber, but it also includes certain theoretical approaches able to better clarify some limited portions of the XAFS spectrum containing special information, e.g. the lowest energy sub-region with its PE features (Joly, 2001, 2003; Joly et al., 1999; Cabaret et al., 1999). Nevertheless, whilst CONTINUUM works well for the interpretation of the experimental spectra of known minerals, it cannot provide certain quantitative results on them such as the independent determination of their atomic positional parameters. Actually, its starting data themselves are long-range crystal structure data determined by SC-XRD refinement not necessarily on that very mineral, as the accuracy attained at the end of the calculation is not sufficient to characterise the individual mineral under study. To make it clear: in order to calculate the XANES spectrum of a natural augite, Cabaret et al. (1996) could make use as starting data of the crystal structure parameters of a synthetic diopside and reached very satisfactory results, yet without introducing new positional data that fit more closely the augite structural parameters. What CONTINUUM does is not only reproducing by calculation the experimental spectrum, thus giving information on the extent of the volume probed by the photoelectron, but also suggesting reliable information on the short- and intermediate-range structure around the probed atom. Note that, starting from the early 1990s, small modifications to the CONTINUUM code have been steadily introduced that simplify the number of passages required by the complete, but cumbersome full treatment without modifying its theoretical content. Most of these codes (and CONTINUUM itself, with some minor adaptation) now run on portable computers. They can be obtained by contacting directly Dr. C.R. Natoli at Frascati (calogero.natoli@lnf.infn.it).

The first of such new packages is GNXAS (Filipponi et al., 1991, 1995; Filipponi & Di Cicco, 1995a, 1995b, 2000), which is best oriented to EXAFS analysis and is based on a summation system that gives precise information on pair and higher-order correlations, such as bond distances and angles (Di Cicco, 2003). Instructions for downloading GNXAS can be found at http://www.aquila.infn.it/gnxas or, alternatively, http://camcnr.unicam.it/www/gnxas.htlm.

Another software derived from CONTINUUM is MXAN (Benfatto et al., 2001, 2003; Benfatto & Della Longa, 2001). It is designed to fit the XANES data based on a comparison of the experimental spectrum with several theoretical spectra individually generated by changing the geometrical parameters of the site around the absorbing atom. MXAN has been able to successfully reproduce (i.e., explain, since it starts from first principles) up to 200 eV above the measured absorption edge, thus bridging the gap between the original SS and MS theoretical treatments and almost reaching the final goal of establishing a unified scattering theory that explains the entire absorption spectrum by starting from ab initio physical and geometrical data.

The MXAN package makes use of a number of programs developed for CONTINUUM to calculate the full MS cross-section, but it follows an iterative method of comparison between the experimental spectrum and several calculated spectra, each one of them accounting for a well-defined initial geometrical configuration around the absorber, i.e., a set of selected structural parameters (usually those referring to the long-range order structure determined by SC-XRD refinement). Then, throughout the comparison cycle, certain structural parameters are being changed according to a strategy aiming at pointing out the most likely atomic distribution around the photoabsorber that is expected in the studied compound, i.e., its short-range ordered structure. The optimisation in the space of the parameters is obtained by the MINUIT package that minimises the square residual function  

formula
where n is the number of independent parameters to be determined in the fit, m the number of fitted data points, forumla and forumla the theoretical and the experimental values of the XANES spectrum absorption, εi are the individual errors in the experimental data set, and wi is a statistical weight. Note that for wi = const = 1 the square residual function S2 becomes the usual statistical χ2 function. The final calculated spectrum is convoluted with a Lorentzian function of constant width (directly fitted by the MXAN procedure) to account for the spectral broadening due to core hole lifetime and to experimental energy resolution, thus obtaining a calculated spectrum that visually mimics the experimental one.

MXAN needs three input files containing: a) the experimental data to be fitted; b) the starting atomic coordinates of the cluster to be calculated and c) the commands and the options necessary for the chosen minimisation strategy. The final best-fit solution has been found to be independent of both the starting conditions and the minimisation strategy, with no limitations either in the measured energy range or in the SR polarisation. However, different fitting strategies may lead to different solutions, so that a good deal of subjective evaluation and ingenuity is still needed. Indeed, in the analysis of XANES spectra of solid compounds, the first step to be pursued is the identification of the size of the relevant cluster of atoms (Benfatto et al., 1986), i.e., the cluster of atoms around the central absorbing atom that best represents the overall structure of the compound to be calculated and compared with its experimental spectrum. The size of this cluster may range from the smallest one, which includes only the nearest neighbours, to clusters including several high-order shells. Neither translation symmetry nor site symmetry of such clusters is required. The finite size of the cluster is determined only by the mean free path length for elastic scattering of the photoelectron and by the core hole lifetime. As a matter of fact, in the energy range 1–10 eV above the threshold, i.e., in the first part of the edge FMS sub-region where the most relevant features are, the mean free path length is longer than 1 nm, and the size limitation due to the core hole lifetime is the most important parameter to be considered, the more so because the contribution of further shells can be reduced or cancelled out by different degrees of structural (configurational) disorder. In most minerals such disordered structures are not to be forecasted, but they should be expected in other compounds of interest for Earth and environmental sciences (e.g. glasses, nanoparticles).

Other limitations of the MXAN package are the muffin-tin approximation, the complex potentials etc. All these limitations (which MXAN inherits from CONTINUUM) are underway to be overcome, so that soon structural parameters will be extracted from XANES spectra (or, better said, from extended XANES, i.e., up to ca. 200 eV above the threshold) with only a few percent error (ca. ± 0.04 Å), thus allowing a complete structural determination of the local geometry around the absorber with a higher spatial resolution than any XRD-based method (cf. Benfatto & Della Longa, 2001; Benfatto et al., 2003; Cardelli et al., 2003). The MXAN code may be obtained by contacting directly Dr. M. Benfatto at Frascati (maurizio.benfatto@lnf.infn.it).

The FEFF and FEFFIT codes

In the late 1980s and throughout the '90s, another computer code (FEFF), based on the MS theory but using different mathematical principles, was conceived and implemented (Rehr et al., 1986; Chou et al., 1987; Mustre de Leon et al., 1991; Rehr et al., 1991, 1992; Zabinsky et al., 1995; Vedrinskii et al., 1997; Ankudinov et al., 1998; Ankudinov, 1999; Rehr & Albers, 2000; Rehr & Ankudinov, 2003). Although not as rigorous as CONTINUUM in some aspects of its theoretical approach and in the extent of the truncation of certain algorithms, FEFF has become the calculation method preferred by most XAS researchers (Newville, 2001) because it is a “user-friendly” package that runs on desktop computers, separates its ab initio theory from analysis, and yet allows the theoretical evaluation to be introduced into an efficient analytical package so as to cope with most experimental needs for the study of ordered and disordered systems.

FEFF underlying approach is the real-space multiple scattering approach initially formulated by Beeby (1967) to study the electronic structure of disordered materials. Therefore, the early versions of FEFF were organised in such a way as to be definitively best suited to fit the EXAFS region of the XAFS spectrum (O'Day et al., 1994). Later, FEFF was implemented by including curved-wave effects that have been shown (Schaich, 1973) to lead to the same formula for both the long-range and short-range orders of atoms. Thus, the latest version (FEFF8: Ankudinov et al., 1998), although still especially suited for EXAFS, is able to simultaneously explain the full XAFS spectrum, i.e., both regions that are sensitive to order and disorder. Furthermore, by making use of the Green's function rather than the wave function to calculate the electron density, and of fast parallel methods of calculation, FEFF8 can explain at the same time the electronic structure and the atomic geometry of the investigated material, all this being carried out in rather short computing times. Finally, FEFF can calculate the polarisation dependence of EXAFS, while some latest improvements allow evaluating separately the dipolar vs. quadrupolar contributions to the XAFS spectrum.

As starting data, FEFF8 uses a list of atomic coordinates that is now most conveniently organised by ATOMS (Ravel, 2001), a computer code designed to convert the standard crystallographic data expressed according to the 230 space group into a set of coordinates relative to the atom chosen as the absorber and as the origin of the cluster in a sphere of defined radius. Then FEFF8 uses four different modules to first create atomic potentials based on the geometrical distribution of the selected atoms; secondly, it overlaps their wave functions and calculates the scattering phase shifts based on these potentials; and, finally, identifies all single and multiple scattering paths with the absorption contribution from each path to the overall absorption. Therefore, the final result of FEFF8 is not only a complete unravelling of the EXAFS region of the XAFS spectrum, but also a significant understanding of the XANES region, that remains challenging both to compute and interpret. A recent development, based on the use of fast parallel calculations (Rehr & Ankudinov, 2003), may make it possible a general treatment of the XAFS spectrum, and might even help in making the underlying theory more robust and reliable.

A derivation from the FEFF package is the FEFFIT code (Newville, 2001), again designed primarily for the analysis of the EXAFS region, but including some upgrade for the XANES region too. FEFFIT not only replaces some modules of the original FEFF package so as to expand the EXAFS interpretation, but it also Fourier transforms theoretical spectra into χ(R) and fits them by a method of non-linear least-squares minimization so as to reach a much higher level of precision. More information on all FEFF codes, which can be downloaded from site http://leonardo.phys.washington.edu/feff, will be given in Galoisy's (2004) chapter in this volume.

Other codes

To end up this matter, it is worth at least mentioning several codes, e.g. WIEN98 (Blaha et al., 1990), EXCURVE (Binsted et al., 1991), UWXAFS (Stern et al., 1995; Ressler, 1997) and others (Soldatov et al., 1994), which, although much less widespread than the two previously mentioned packages, have contributed to the understanding special aspects of the absorption process or to the unfolding of certain complex spectra, e.g., for biological compounds. Some of these codes, or at least certain sections of them, are now incorporated in the latest versions of both CONTINUUM and FEFF. A full catalogue of the software developed for XAFS evaluation can be found at http://ixs.csrri.iit.edu./IXS/catalog/XAFS_Programs.

In spite of all the development shown above, “much remains to be done”: this is the final conclusion that Natoli et al. (2003) were forced to come to in their recent state-of-the-art analysis of XAS. However, they also stated, “even with the present approximations structural analysis by full-spectrum fitting is possible”. This satisfies most requirements of current mineralogy, even though other important aspects for solid state physics such as “electronic analysis, like spin and charge state, electronic population analysis etc., should probably wait for further improvements”.

In particular, much has to be done to improve the atom spatial resolution that can be extracted from XAFS spectra. Theoretical considerations for two nearby atoms set the boundary condition to be ca. 0.1 Å for the standard EXAFS fitting method (Stern, 2001), and 0.04 Å for the much more time-consuming MXAN fit (Benfatto & Della Longa, 2001). The latter value compares well with the results of Rietveld refinement, but it is definitively much less accurate than the present value 0.0059 Å (2σ) attained by SC-XRD refinement (cf. Giacovazzo, 2002). However, it should be kept in mind that XAS records time-resolved events occurring at the local absorption site in the examined sample, whereas XRD averages them on a long time and space scale.

Experimental methods

The impetuous advance of XAS spectroscopy is mostly related with the development of SR sources. At the beginning, some 30 years ago, they overcame the limitations in energy range, intensity and stability that conventional X-ray tubes had, and made a strong, tuneable X-ray radiation available, the absorption of which by matter could be easily monitored using transmission mode detection systems (see later). Currently, 3rd generation storage rings with their new insertion devices offer a brilliant, tuneable and polarised radiation that spans over a wide range of energies, from IR to soft to hard X-rays, with an intensity much greater than was even expected 30 years ago, and opens an entire universe of opportunities to all types of condensed matter studies.

Synchrotron radiation is produced when a charged particle of mass m (normally an electron or a positron) accelerated to light velocity c by an energy Emc2 is being deflected in a magnetic field (Ivanenko & Pomeranchuk, 1944; McMillan, 1945; Veksler, 1945). The deflection of the electrons (or positrons) by a bending device generates an electromagnetic radiation (first observed at General Electric Research Laboratory in Schenectady, N.Y., U.S.A., on April 24, 1947: Elder et al., 1947), which is strongly linearly polarised in the plane of the orbiting electrons (i.e., horizontally, if the acceleration facility leads its particles into a storage ring), has a large, continuous range of energies (i.e., it is “white”), and is very intense (several orders of magnitude greater than conventional X-ray tubes: Fig. 6a).

Fig. 6.

. (a) The increase in the average brilliance of synchrotron storage rings of different generations compared with those of conventional X-ray tubes and future X-ray free-electron lasers (from Norman 2001, modified). (b) The intensity and energy distributions of synchrotron radiation emitted from a source by different insertion devices. Bending magnet and wiggler produce a continuous “white” radiation over a wide range of energies whereas undulators produce very intense harmonics (n = 1 to 7), each having a narrow energy range.

Fig. 6.

. (a) The increase in the average brilliance of synchrotron storage rings of different generations compared with those of conventional X-ray tubes and future X-ray free-electron lasers (from Norman 2001, modified). (b) The intensity and energy distributions of synchrotron radiation emitted from a source by different insertion devices. Bending magnet and wiggler produce a continuous “white” radiation over a wide range of energies whereas undulators produce very intense harmonics (n = 1 to 7), each having a narrow energy range.

Among the many properties of SR, two need to be carefully evaluated when planning XAS experiments:

  1. The flux, which is the number of delivered photons (ph) per second (s) per horizontal angle (θ) per bandwidth (BW) integrated over the entire vertical angle (Ψ). This angle is of the order of mrad and in high-energy storage rings may be significantly less for photon energy around or above Ec. The bandwidth is normally 0.1% so that, e.g., at 5 keV photon energy the transmitted photons are in a restricted energy range of ca. 5 eV. The SR flux increases continuously in intensity from a lower limiting value to a maximum, the critical energy, Ec, which is determined by the magnetic field applied and by the energy acquired by the electrons stored in the ring. At E > Ec the flux decreases exponentially to zero (Fig. 6b). A high flux is important for experiments on large samples (several mm2) that should intercept the beam in the vertical direction, or for experiments based on very small cross-sections such as studies of magnetic absorption, or for those using dispersive devices (e.g. D-XAS, T-XAS; see later) which collect a large fan of SR and focus it on a very small sample.

  2. The brightness, which is defined as the flux per vertical solid angle, or the closely related brilliance, i.e., the brightness per source area. Thus, brilliance is the number of photons per solid angle and size of the insertion device that delivers SR. A source can be made brighter either by increasing the flux, or by decreasing the size, or by enhancing the angular collimation (i.e., decreasing the angular spread). Brilliance is important when planning experiments on very small samples, typically for micro-XANES or SmX; in these set-ups, pinholes or specific optical devices (e.g. capillary or zone plates) are used to collimate SR on a focal spot (e.g. few μm). In these cases, the brilliance of a photon beam is reduced, but the photon intensity in the focal spot is conserved or it can even increase by several orders of magnitude.

SR started being used for its peculiar properties of flux, brilliance, collimation and polarisation (e.g. Bassett, 1988 and many others) and rapidly found a large variety of potential applications, thus priming the construction of larger and larger (i.e., stronger and stronger) storage rings to the present top represented by SPring8 (Table 3). Meanwhile, to bending magnets, i.e., the original insertion devices used to extract SR from the storage ring (Sham & Rivers, 2002), others have been added which are able to enhance certain aspects of the radiation in various ways (Fig. 6b), so that a great variety of experiments is now possible. In mineralogy most of these possibilities, now exploited by physicists, are still poorly used, except for very special experiments.

Table 3.

The major synchrotron facilities known to operate for the Earth science community.

LocationNameInstitutionEnergy (GeV)Max. beam current (mA)

Argonne, USAAPSArgonne National Laboratories7300
Beijing, ChinaBEPCInstitute of High Energy Physics1.5–2.8400
Berkeley, USAALSLawrence Berkeley National Laboratories1.5–1.9400
Berlin, GermanyBESSYIBerliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung1.0
(closed 31/12/99) 
BESSY II1.7–1.9700
Campinas, BrazilLNLSLaboratório Nacional de Luz Síncrotron1.37130
Daresbury, UKSRSDaresbury Laboratories2300
Frascati, ItalyDAΦNEIstituto Nazionale di Fisica Nucleare (INFN)0.511800
  
Grenoble, FranceESRFEuropean Synchrotron Radiation Facility6200
Hamburg, GermanyDORIS IIIHamburger Synchrotronstrahlungslabor4.5–5.3150
(HASYLAB) at Deutsches Elektronen-Synchrotron (DESY)
  
Lund, SwedenMAX IUniversity of Lund0.55250
MAX II1.5250
Moscow, RussiaSiberia IIKurchatov Institute2.5100
Nishi Harima, JapanSPring-8Japan Synchrotron Radiation Research Institute (JASRI)8100
  
Okazaki, JapanUVSORInstitute of Molecular Science0.75200
Orsay, FranceDCILaboratoire pour l'Utilisation du1.8
(closed 31/12/03)Rayonnement Electromagnétique (LURE)
  
Orsay, FranceSuperACOLaboratoire pour l'Utilisation du0.8
(closed 31/12/03)Rayonnement Electromagnétique (LURE)
  
Stanford, USASPEAR3Stanford Synchrotron Radiation3100
Laboratory (SSRL) at Stanford Linear
Accelerator Center (SLAC)
Stoughton, USAAladdinSynchrotron Radiation Center (SRC)0.8–1200
Trieste, ItalyELETTRASincrotrone Trieste1.5–2200
Tsukuba, JapanPhoton FactoryInstitute of Materials Structure Science at High Energy Accelerator Research Organization (KEK)2.5–3800
  
  
Upton, USANSLS IBrookhaven National Laboratories0.8350
NSLS II2.5–2.8
Villigen, SwitzerlandSLSPaul Scherrer Institut2.4400
LocationNameInstitutionEnergy (GeV)Max. beam current (mA)

Argonne, USAAPSArgonne National Laboratories7300
Beijing, ChinaBEPCInstitute of High Energy Physics1.5–2.8400
Berkeley, USAALSLawrence Berkeley National Laboratories1.5–1.9400
Berlin, GermanyBESSYIBerliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung1.0
(closed 31/12/99) 
BESSY II1.7–1.9700
Campinas, BrazilLNLSLaboratório Nacional de Luz Síncrotron1.37130
Daresbury, UKSRSDaresbury Laboratories2300
Frascati, ItalyDAΦNEIstituto Nazionale di Fisica Nucleare (INFN)0.511800
  
Grenoble, FranceESRFEuropean Synchrotron Radiation Facility6200
Hamburg, GermanyDORIS IIIHamburger Synchrotronstrahlungslabor4.5–5.3150
(HASYLAB) at Deutsches Elektronen-Synchrotron (DESY)
  
Lund, SwedenMAX IUniversity of Lund0.55250
MAX II1.5250
Moscow, RussiaSiberia IIKurchatov Institute2.5100
Nishi Harima, JapanSPring-8Japan Synchrotron Radiation Research Institute (JASRI)8100
  
Okazaki, JapanUVSORInstitute of Molecular Science0.75200
Orsay, FranceDCILaboratoire pour l'Utilisation du1.8
(closed 31/12/03)Rayonnement Electromagnétique (LURE)
  
Orsay, FranceSuperACOLaboratoire pour l'Utilisation du0.8
(closed 31/12/03)Rayonnement Electromagnétique (LURE)
  
Stanford, USASPEAR3Stanford Synchrotron Radiation3100
Laboratory (SSRL) at Stanford Linear
Accelerator Center (SLAC)
Stoughton, USAAladdinSynchrotron Radiation Center (SRC)0.8–1200
Trieste, ItalyELETTRASincrotrone Trieste1.5–2200
Tsukuba, JapanPhoton FactoryInstitute of Materials Structure Science at High Energy Accelerator Research Organization (KEK)2.5–3800
  
  
Upton, USANSLS IBrookhaven National Laboratories0.8350
NSLS II2.5–2.8
Villigen, SwitzerlandSLSPaul Scherrer Institut2.4400

Sources: Winick (1994), Sham & Rivers (2002) and the internet (all modified).

Beam line apparatus

In order to perform XAS experiments the availability of a SR source alone is not enough (Lytle, 1989). As a matter of fact the entire laboratory (i.e., the experimental line that leads SR extracted from the storage ring to the sample and to the absorption detector device) needs to be equipped with numerous components that perform such basic functions as collimation, monochromatisation etc.

Insertion devices

The bending and insertion devices (Fig. 7) are inaccessible to users, as they are located beyond the “front end” that separates the storage ring from the experimental beam line with its hutch. Yet, a few words about them are worthwhile, because certain experiments (especially on diluted atoms) may be hampered by not knowing their properties. More information can be found in Winick (1994) and Margaritondo et al. (2003).

Fig. 7.

Schematic view of the three major types of sources of synchrotron radiation with the characteristics of their spectral emissions: (a) bending magnet, (b) undulator and (c) wiggler.

Fig. 7.

Schematic view of the three major types of sources of synchrotron radiation with the characteristics of their spectral emissions: (a) bending magnet, (b) undulator and (c) wiggler.

Bending magnets (Fig. 7a) are magnetic devices that receive the electrons accelerated in the storage ring and deflect them from their straight path; thus, they generate SR. The SR total flux delivered by them depends on ring parameters and on the intensity of the applied magnetic field. Bending magnets were the first devices through which SR was easily extracted from the storage ring for operation, and are present in most SR facilities for both dedicated and parasitic use, although their flux no longer appears to be satisfactory for some current applications.

Wigglers (Fig. 7c) are also magnetic devices that bend the electrons back and forth several times (i.e., they wiggle them) to generate a SR beam that in principle has flux and brilliance two orders of magnitude greater than the beam delivered by bending magnets. Originally, they were built to extend the SR energy to higher values, because of their high magnetic field that has intensity proportional to the number of poles. Rather than being located at bends of the storage ring, they are inserted into the straight sections, so that the beam trajectory is significantly larger than the beam size. Wigglers produce a straight, fairly well-collimated SR beam. However, their definition is poor.

Undulators (Fig. 7b) are specially conceived wiggler-like units where the magnet spacings and gaps are tuned in such a way as to create SR interference. The beam displacement is comparable with the beam size and the photons emitted in different positions along the trajectory interfere coherently. Therefore, the resulting SR is discontinuous, but with a very high intensity: it is proportional to the square of the pole numbers and is 3 to 4 orders of magnitude greater than that from bending magnets. Undulators are best suited for XAS study of selected diluted atoms, and must be carefully planned to fit the problem: they may produce excellent XAFS spectra for few mg/g of an element diluted even in a high-Z matrix (e.g. Chaboy et al., 2002; Quartieri et al., 2002). In recent years, the increasing number of undulator devices inserted at SR sources has been justified with their unique possibility of tuning any kind of polarisation: linear horizontal, linear vertical, circular and elliptical.

Collimation devices

The collimation, deflection and focussing of SR are obtained by making use of a combination of slits (vertical and horizontal), mirrors (flat or curved) and bent crystals. Flat mirrors operate by total reflection of X-rays, whereas curved mirrors are in fact monochromators that take advantage of Bragg's law (2dhkl sinθ= nλ). Past a mirror, only a certain small range of X-ray energies passes into the beam line, but all unwanted ones are cut off, especially those high harmonics passing downstream the monochromatisation device that can create spurious absorption effects and, consequently, badly damage the recording of reliable XANES spectra. Inserting a mirror may either reduce or enhance the beam line performance, depending on the configuration; e.g., a collimating mirror limiting the beam horizontal and vertical divergence may improve the energy resolution; by contrast, a flat spherical mirror increasing aberrations may reduce the beam line performance.

Monochromatisation devices

The monochromator is possibly the most important device in a beam line, as its resolution is crucial for the success of the XAS experiment. Monochromators accomplish two assignments: a) they select a photon beam of defined energy E and with a ΔE width out of the continuous “white” SR delivered by the source; b) they scan over a predefined energy range (or ranges) across the selected absorption edge, thus giving rise to the absorption coefficient modulation, i.e., the XAFS spectrum. Therefore, a variety of different designs have been devised, the most efficient ones for the soft X-ray energy range still being the grating monochromators, and for the hard X-ray range the crystal monochromators.

Crystal monochromators consist of a crystal that transmits only the X-ray energy that satisfies the Bragg's equation for a given hkl plane and 0 incidence angle, and is slowly rotated, usually stepwise, so as to scan one step after the other over the entire range of energies required by the experiment. Actually, monochromators are real crystals; thus the SR beam is actually diffracted within a finite angular interval around the theoretical angle 0. The profile of the diffracted intensity as a function of the rotation angle is the so-called rocking curve, the width of which (Darwin width, measured as half width at half maximum, HWHM: Darwin, 1922) is usually small (ca. 5 · 10−6 rad), but it is always greater for the fundamental reflection than for the harmonics. In principle, in order to monochromatise the “white” SR beam delivered by the ring, only one crystal is needed, but most monochromators are of the double-crystal type, because the second crystal improves resolution. Moreover, if the monochromator is of the non-dispersive type, it also impresses a constant direction to the passed-through X-rays, thus transforming them from a divergent fan into a parallel beam that impinges the sample on a rectangular or circular area (spot), the position of which remains constant (or shifts only slightly on a constant direction) when the monochromator is rotated.

The energy range transmitted by double-crystal monochromators is defined by the lattice spacing dhkl of the crystal (a pair of parallel slices cut from the same crystal, for the double-crystal type proper, or a carving machined in one crystal, for the common “channel-cut” type). The former type is preferred because the two slices can be slightly rotated (detuned) to remove the harmonics, but the latter one is easy to manipulate for maintenance. Table 4 lists a series of commonly used crystals with their properties and the suggested ranges of application.

Table 4.

Monochromator crystals with their physical characteristics and best fields of application.

NameFormula(hkl)2d (Å)Reflectivity (%)Energy range (keV)Notes

α-quartzSiO250.21.62412.98–87shortest spacing of all used crystals: best for high-Z K edges
siliconSi3113.274216.56–40very stable for high-Z K edges: high resolution crystal
siliconSi2203.84031138 (±3 · 10−8)29.73.5–37defect-free and very stable: very high resolution due to a very accurate lattice spacing value
lithium fluorideLiF2004.0273.2–35best general-purpose crystal: highest intensity for most atoms
rock saltNaCl2005.6412.3–25best for S and Cl K edges, but unstable
siliconSi1116.271239.92–22.5defect-free and very stable: general-purpose crystal
germaniumGe1116.53285.92–21.5for intermediate- to low-Z atoms: best for P, S, and K K edges
indium antimonideInSb1117.48061.7–19very stable: best for Si, P, and S K edges
α-quartzSiO210.08.51218.81.5–16.5very stable: very high flux for Al K edge
KTPKTiOPO401110.95≈ 801.2–13for K edges from Mg to P
yttrium borideYB6640011.723.0–3.51.1–12best for Mg and Al K edges
berylBe3Al2Si6O1810.015.9543.5–140.8–8.9best for Na K edge
micaKAl2(OH)2[AlSi3O10]00219.840.65–7easy to obtain and to bend
KAPKHC8H4O410026.632≈ 800.5–5.3general-purpose for low-Z atoms down to the O K edge
NameFormula(hkl)2d (Å)Reflectivity (%)Energy range (keV)Notes

α-quartzSiO250.21.62412.98–87shortest spacing of all used crystals: best for high-Z K edges
siliconSi3113.274216.56–40very stable for high-Z K edges: high resolution crystal
siliconSi2203.84031138 (±3 · 10−8)29.73.5–37defect-free and very stable: very high resolution due to a very accurate lattice spacing value
lithium fluorideLiF2004.0273.2–35best general-purpose crystal: highest intensity for most atoms
rock saltNaCl2005.6412.3–25best for S and Cl K edges, but unstable
siliconSi1116.271239.92–22.5defect-free and very stable: general-purpose crystal
germaniumGe1116.53285.92–21.5for intermediate- to low-Z atoms: best for P, S, and K K edges
indium antimonideInSb1117.48061.7–19very stable: best for Si, P, and S K edges
α-quartzSiO210.08.51218.81.5–16.5very stable: very high flux for Al K edge
KTPKTiOPO401110.95≈ 801.2–13for K edges from Mg to P
yttrium borideYB6640011.723.0–3.51.1–12best for Mg and Al K edges
berylBe3Al2Si6O1810.015.9543.5–140.8–8.9best for Na K edge
micaKAl2(OH)2[AlSi3O10]00219.840.65–7easy to obtain and to bend
KAPKHC8H4O410026.632≈ 800.5–5.3general-purpose for low-Z atoms down to the O K edge

Note: The energy range has been calculated for a monochromator rotation θ from 5 to 70°.

High resolution is experimentally demanding in XANES spectroscopy because many important structural data are to be extracted from small intensity and/or energy variations of the absorption features. Resolution, ΔE, depends on the Darwin width of the crystal, and on the vertical angular divergence Δθ of the photon beam. The relative resolution, ΔE/E = ΔΘ cotgθ, where Θ [rad] is the convolution between Darwin width and beam divergence, is typically 10−4–10−5 (times the set edge energy). Therefore, such a resolution varies from ca. 0.3 to ca. 1.5 eV on going from the Na K edge at 1070.8 eV to the Fe one at 7112 eV (Schaefers et al., 1992). In other words, for a proficient XANES spectrum at the Na K edge a resolution of 0.25 eV is appropriate (e.g. Mottana et al., 1997b), but for another one at the Fe K edge a resolution of 1.5 eV (apparently a much greater value) is considered to be adequate even if the PE sub-region is studied (e.g. Galoisy et al., 2001; Wilke et al., 2001).

To reach such resolutions, a wise preliminary approach is the careful preparation of homogeneous pinhole-free samples (see later). Nevertheless, the first step always consists of choosing the monochromator most adequate for the energy range to be investigated (Table 4). With crystal monochromators, the energy bandwidth ΔE of the photon beam that is monochromatised using Bragg's law is determined by the horizontal angular divergence Δθ of the impinging beam (that depends upon the SR intrinsic vertical spread, in turn determined by the energy of the electron beam circulating in the storage ring and by the source size, and is reduced, but not entirely eliminated, by the slits upstream). More than on anything else, however, the energy bandwidth depends upon the crystal rocking curve, the width of which is a measure of the mosaic spread present in the irradiated area of the crystal, and decreases with its d spacing, so that reflecting planes with larger d spacings yield better energy resolutions than those with small spacings even in the same crystals; e.g., Si cut along 311 has a resolution by one order of magnitude lower than the same Si cut along 111 (1.9 · 10−5 vs. 1.33 · 10−4, respectively). Therefore, resolution can be improved by changing either the crystals, e.g. by substituting Si (111) with Ge (111), or else the crystal reflection planes, e.g. by using Si (331) instead of Si (111); refer to Table 4 for this choice.

In a double-crystal monochromator, the two reflections reduce tails of the rocking curve and consequently increase the resolution, but they let the entire content of high-order harmonic reflections pass, if any. Thus, as a second step, one should take all care of suppressing the high harmonics. Harmonics are nothing else but reflected X-rays, either by total reflection on a flat grazing incidence mirror or, in a curved monochromator, because Bragg's equation is satisfied for several nλ. If n = 1, the energy reflected is the fundamental one, but if n > 1 a number of other reflected X-rays arise – indeed, the harmonics – that may interfere in data collection. This interference has to be reduced either by using mirrors that behave as low-band passing filters, or by detuning one crystal (usually the first one) with respect to the other: when the two crystals are just slightly misaligned (min. 30%), the intensity of harmonics drops off much more rapidly than that of the fundamental radiation, which is just slightly attenuated. However, harmonics are sometimes looked for, e.g. to reach such extremely high energies that have recently allowed recording a very well-resolved XAFS spectrum on Au at the K edge (80.725 keV: D'Acapito et al., 2002).

Crystals for monochromators are real crystals, although mostly synthetic and very carefully grown. Therefore, they show defects that hamper their performances, i.e., reduce their resolution and stability (see above) or, as it is often seen, do not transmit some small range of the incident energy: in such a case a “glitch” occurs in the recorded XAFS spectrum. As a matter of fact, glitches are inevitable in crystal monochromators, because even in a perfect defect-free crystal the possibility exists that for a given angle of incidence two different hkl planes are in the condition of reflecting simultaneously according to Bragg's law, leading to a superimposition of reflections that creates interference with a net loss in the beam delivered downstream. Glitches of this kind can be eliminated by slightly rotating one crystal with respect to the other, but they are often kept as they are in the final spectrum because they provide a reference point of energy. Some other glitches are due to non-linear electronic responses, and can be corrected. Some other types of “glitches” (actually, they are unwanted absorption features) are unavoidable no matter which attempt is made of manipulating the monochromator setup (e.g. the glitch occurring at 1385.6 eV in the YB66 crystal monochromator is due to an anomalous scattering for the 006 reflection of the Y L2,3 edges; cf. Kinoshita et al. 1998; Wong et al. 1999).

The total reflectivity function of crystal monochromators is roughly the sum of the reflectivity of the crystals, their tilt angle, absorption, etc. This function may vary by more than one order of magnitude over the scanning range, and may induce a tilted background: a problem that is particularly felt in the EXAFS region (see Galoisy, this volume).

Crystal stability is related to the strength opposed by the compound to being disordered or damaged by the impinging SR (heating). Therefore, crystals that are damaged by the heat load are best used for low-energy 1st generation SR facilities. In order to withstand the very high heat loads delivered by the undulators in 3rd generation SR facilities, crystals are cryogenically cooled.

Consequently, at most facilities, there are different beam lines having monochromators optimised to investigate low-Z and high-Z atoms:

  • Very low-Z atoms such as O and F absorb in the ultra-soft X-ray energy range (hv < 1 keV): they need grating monochromators or, at most, crystal monochromators equipped with crystals having very large d spacings such as beryl, KAP and RAP (cf. Table 4);

  • Light atoms such as Na, Mg, Al, Si, P, S, K etc. absorb in the soft X-ray energy range (hv = 1–4 keV), so that they need large-spacing crystals such as quartz, KTP, YB66, InSb or beryl;

  • Heavy atoms (Z > 20), including transition elements, have their K-edge absorption lines in the hard X-ray energy range (hv > 4 keV) and require double-crystal monochromators with Si or Ge crystals, i.e., ones very stable under the heat produced by the SR beam, the reflecting crystal plane being properly chosen so as to achieve best resolution at high transmission intensity.

Detection modes

The detection system depends on the concentration of the absorbing atom, on the photon flux of the beam line and on the energy of the absorption edge to be investigated. For bulk experiments using hard X-rays on atoms with Z > 20 present with concentrations greater than 0.1% in the sample (atomic ratio), standard X-ray transmission techniques are used, under gas (He, N) or in air. By contrast, the soft and ultra-soft X-ray ranges require special beam lines and experimental chambers and, because of the strong absorption of radiation at these energies in air, high vacuum (HV) or ultra-high vacuum (UHV) conditions are compulsory. Furthermore, the strong photon absorption of gases prevents the use of photo-ionisation chambers; thus, in the HV or UHV conditions, electron detection systems are usually employed. Metal grids are typically used to monitor beam intensity, either by means of electron multipliers (channeltron) that collect all electrons extracted by the photon beam, or by directly measuring the drained photoelectron current (Stöhr et al., 1980).

Transmission mode.

This type of experiment not only is classical, as it was set up first and best fits Lambert's law, but also it is the preferred one when there are no experimental constraints that suggest another one. Indeed, it is very manageable, as one may operate in air. Limiting conditions are excessive thickness of the sample that forbids the beam to pass through, and diluteness of the absorber species (< 1 wt%), when the

XAS features become comparable with the statistical noise. In such cases another detection mode must be used. In the transmission mode method the flux of monochromatised SR is measured in a first ionisation chamber (I0) that is filled with a suitable gas mixture (N, Ar, He etc. in various amounts), which is empirically adjusted on the basis of the observed sample statistics so as to absorb a percentage of the impinging flux (usually 20 to 40%). The beam is then driven through the sample compartment, and eventually it is measured in a second ionisation chamber (I1) again filled with a gas mixture set to absorb another percentage that gives the best I1/I0 ratio. The ratio of transmitted flux  

formula
where μ is the absorption coefficient [cm2 g−1], ρ is the density of the gas mixture [g cm−3] and L is the thickness of the gas chamber [cm], is recorded for each energy [eV] and converted into the absorption vs. energy XANES spectrum. A schematic view of an experimental setup in the conventional transmission mode is shown in Figure 8 (Lytle, 1989).

Fig. 8.

Schematic representation of a modern experimental setup for XANES recording in the transmission mode (modified after Lytle, 1989, and Mottana et al., 2002).

Fig. 8.

Schematic representation of a modern experimental setup for XANES recording in the transmission mode (modified after Lytle, 1989, and Mottana et al., 2002).

Transmission through the sample assures that the whole bulk content of absorber present in the sample is probed, thus this is the standard experimental setup for hard X-rays which show no penetration problems even for fairly thick samples (> 0.1 mm), although best signal-to-noise (S/N) ratios are usually obtained from relatively thin samples, typically ca. 5–10 μm. Moreover, transmission is relatively independent upon the matrix effect, although the S/N ratio may be somewhat reduced in the case of matrices having an average Z close to that of the absorber. Furthermore, at hv > 4–6 keV there is no need for vacuum, and all experiments can be carried out most easily in air. However, one must carefully avoid the contamination of the beam by any harmonic, because this interference effect would be practically impossible to correct, the more so if the sample becomes badly damaged by the heat load the harmonics carry along with them. In any case, the sample must be uniform in thickness while containing a large enough amount of the absorber to produce a significant absorption jump, and the size of the single grains present in it must be small enough so that they can be evenly distributed over the entire surface (Stern & Kim, 1981). A rule of thumb for experimental reliability is to compare two spectra obtained with samples having different thickness. In the case diluted atoms are to be measured, it is often useful to mix the sample with light matrices such as borax or sugar, so as to fill the sample compartment with enough material without increasing its absorption, thus decreasing the S/N ratio.

Fluorescence mode.

Recording a spectrum in the fluorescence yield (FY) mode is a highly efficient experimental method for high-Z atoms, and particularly for K-XANES spectra, as these atoms constantly show significantly greater fluorescence yields for their K shells than for the L ones (Krause & Oliver, 1979). Such yields are directly proportional to the probability that the core hole is filled by a radiative de-excitation process, with emission of an X-ray photon of energy univocally determined by the involved electron level. An apparatus to record absorption spectra in the FY mode is schematically presented in Figure 9. Note that the best instrumental setting is when both the impinging and fluorescence beams form a 45° angle with the sample surface. Using appropriate filters, only the photons emitted by the excited absorbing atom are recorded, while the transmitted flux does not contribute to the signal, but only to the background noise, in the case that it undergoes some scattering. This detection mode crosscuts all problems of sample thickness that affect the transmission mode, thus even very thick samples (> 1 mm) can be probed, and is particularly effective when the absorber is diluted, as it increases detection by at least two orders of magnitude. However, it suffers from self-absorption effects, particularly if the matrix average Z is close to the Z of the absorber atom; self-absorption effects are particularly severe for very thick samples (see above). The detecting system normally consists of several semiconductor crystals (e.g. Ge, Li-doped Si) arranged in linear or circular arrays, the signals of which are amplified, cumulated and linearised by an electron analyser set in such a way as to let only the counts in the energy range of interest pass.

Fig. 9.

Schematic representation of an apparatus designed to record XANES spectra in the fluorescence mode using a 7-piece semiconductor detector (from Mottana et al., 2002, modified).

Fig. 9.

Schematic representation of an apparatus designed to record XANES spectra in the fluorescence mode using a 7-piece semiconductor detector (from Mottana et al., 2002, modified).

The Lytle detector is a special apparatus that solves most problems for samples where the absorber atom is moderately diluted (> 1000 mg/g) in an absorbing matrix. It is a special type of ionisation chamber originally devised by Stern & Heald (1979) and practically realised by Lytle et al. (1984). SR enters the chamber after having been collimated by a Soller slit assembly and filtered by a metal sheet chosen to have its absorption edge intermediate between the edge of the investigated atom and its fluorescence emission line i.e., with Z = Z – 1 of the absorber. Thus, the filter lets that fluorescence pass, but it absorbs any other scattered radiation, while the Soller slit allows the sample fluorescence to pass, but it blocks most fluorescence excited into the filter metal by the scattered main SR beam. Consequently, S/N ratio is enhanced by a factor 10–100 with respect to a conventional gas chamber, and XANES spectra on even very diluted heavy atoms can be measured proficiently (e.g. 50 ppm Cr in a matrix containing 12 wt% FeO: Brigatti et al., 2001), provided the appropriate gas mixture contains mostly N for hv < 3 keV, Ar for hv = 3–7 keV, and Kr for hv > 7 keV.

Alternatively, various solid state semiconductors (Si, Ge, SiLi etc.) can be used that operate in a similar way as chambers filled by ionised gas. Their instantaneous count rates and energy ranges are less restricted (and yet the latter ones are normally constrained by appropriate windows), but they show gaps in efficiency at energies near their absorption K edges; furthermore, they need cooling (usually by liquid nitrogen) and Be windows. However, they can be set as groups so as to aggregate count rates to several million counts per second (cps). Their largest intrinsic limitation is in the “dead time”, i.e., the time spent while electronics determines the energy of a given photon-absorption event. Thus, their energy resolution makes them suitable for hard X-ray edge absorption experiments (especially for hv > 6 keV). However, to record soft to ultra-soft edges, in recent years windowless detectors have been developed, and recently a Ge multi-element detector has been put into operation that can be used down to 300 eV.

FY is the most general method for bulk XAS study of materials of any type, because in any case its penetration depth is > 100 nm, i.e., it probes deep into the sample (Kawai et al., 1994; Kasrai et al., 1996), so that the spectrum obtained is very similar to that recorded in the transmission mode.

Electron yield mode.

In the soft and ultra-soft X-ray range, XAFS spectra are best measured by recording core hole decay products. Indeed, when the inner-shell photo-ionisation process is seen as a two-step process, then it may be guessed that during the first step the photon excites a core hole electron pair, and during the second step the recombination process of the core hole takes place. Among the various possible recombination channels, to record middle to hard X-ray XAFS spectra of dilute systems the direct radiative core hole decay that produces X-ray fluorescence is to be preferred, because at high photon energies this technique indeed probes the bulk (see above, and Baker, 2002). By contrast, in the soft X-ray range the non-radiative Auger recombination (see Galoisy, 2004, in this volume) has a higher probability than the fluorescence radiative recombination to fill the K and L core holes (Stöhr et al., 1984). This last method allows studying highly absorbing samples with a sensitivity that, although variable with penetration, is several orders of magnitudes greater than that of the fluorescence mode.

Because the energy of the Auger electrons is characteristic of a particular atom, the selective photoabsorption cross-section of that atom (in particular if chemi-adsorbed on the surface of the sample) can be measured by monitoring the intensity of its Auger electrons as a function of photon energy. An intense Auger line is selected by an electron analyser operating in the constant final state mode with an energy window of a few eV. However, because all Auger electrons arise from the uppermost-impinged layers of atoms, this type of measurement is essentially probing the surface of the sample down to less than ca. 2 nm, rather than its bulk (Seah & Dench, 1979). Moreover, UHV conditions (= 10−7 torr) are absolutely needed, as the mean free path length of electrons in air is very short.

For bulk measurements, the total electron yield (TEY), which measures the integral yield over the entire energy range of the emitted electrons, is normally used. TEY has been found to be proportional to the absorption coefficient (Gudat & Kunz, 1972), but it has a limited penetration into the sample (ca. 4 to 20 nm depending on the type of material and absorber: Erbil et al., 1988; Kasrai et al., 1996). A standard experimental set up for this type of XAS measurement is shown in Figure 10. The advantage of this method is that maximum counting rates are obtained, since by applying the appropriate positive voltage to the detector one can collect all electrons emitted by the sample over a large solid angle. However, spurious results particularly for peak intensity are commonplace, if the surface of the sample is not carefully cleaned, the more the softer the energy range of measurement (e.g. Kasrai et al., 1998).

Fig. 10.

Schematic representation of a standard experimental setup for surface XANES measurements using channeltrons or total electron yield detectors (from Mottana et al., 2002, modified).

Fig. 10.

Schematic representation of a standard experimental setup for surface XANES measurements using channeltrons or total electron yield detectors (from Mottana et al., 2002, modified).

Another detection method used is low-energy partial electron yield (PEY), which collects only the secondary electrons within a kinetic energy window around the maximum of the inelastic part of the electron energy distribution curve. Because of the long escape depth for low-energy electrons, bulk absorption recording with this method requires an electron analyser.

Dispersive mode.

There are other less widespread methods by which XANES spectra can be recorded. They have been developed mainly to reduce acquisition time or to decrease sample size while allowing non-ambient experimental conditions and the observation of fast reactions, but they generally involve some loss in resolution and/or accuracy.

In the dispersive mode (D-XAS), first proposed by Matsushita & Kaminaga (1980) (cf. Dartyge et al., 1986; Pascarelli et al., 1999a; Rakovan et al., 2001), the energy scan is performed by making a large white beam impinge on a polychromator, i.e., a cylindrically-curved crystal monochromator the range of Bragg's angles of which is large enough to cover the required energy interval. The radius of curvature, R, of the crystal is defined by the relationship: R = 2(ρ + q)/sinθ, where θ is the Bragg angle, and ρ and q are the polychromator distances from the source and the focal point, respectively. The band pass ΔE that is being opened by a Δθ change of the Bragg's angle along the surface of the crystal is ΔE = E cotθ Δθ, and is sensibly corresponding to resolution. The sample is located at the crystal focus, where a fan of beams containing all the selected energies simultaneously crosses it. After crossing the sample, each beam is dispersed on an array of photodiodes or on a position-sensitive detector in line with a CCD camera with a fast analogue buffer, so that the acquisition time is reduced to a few ms. The main advantages of D-XAS are in not having moving parts and in the possibility of studying very rapidly rather small samples (50 to 500 μm) with high S/N ratios (typically 105), thus of monitoring reaction kinetics. Furthermore, such high S/N ratios enhance the possibility of detecting and fitting weak absorption edges that would otherwise coalesce with the background using the normal FY mode (Rakovan et al., 2001). Thus, D-XAS is particularly suited for HP studies in the diamond anvil cell (DAC), where the sample is very small and pressure cannot be maintained for long, or for HT studies. In addition, it is commonly used for magnetic absorption. Unfortunately, SR beam instability may represent a problem when trying to quantify the changes observed in the XANES spectrum (Pascarelli et al., 1999a).

Another type of dispersive mode is Turbo-XAS (T-XAS), recently developed to overcome the difficulties inherent in the original D-XAS system (Pascarelli et al., 1999b) and to fully exploit the high brilliance of 3rd generation SR sources. It consists of a polychromator that disperses the SR beam over a large energy range (5 to 27 keV), a moving slit that rapidly scans such a energy-dispersed fan just after the polychromator and sequentially lets only one narrow, essentially monochromatic X-ray band pass at a time, a first ionisation chamber that records I0 before the beam reaches the sample located in the focal spot of the system, and a second ionisation chamber that simultaneously records I1. The experimental apparatus also has a position-sensitive detector that records the entire range of dispersed energies passed through the sample, and acts as a conventional D-XAS system (Fig. 11). The simultaneous recording of I0 and I1 is the essential improvement of T-XAS with respect to D-XAS, for it makes the instrumental setup less sensitive to beam instabilities while allowing acquisition times as short as 0.05 s for a XANES spectrum and 0.5 s for an EXAFS one (Pascarelli et al., 1999b). T-XAS has been tested for pure metals so far, but it will have a bright future in view of its promising applications in HP experiments and for micro-XANES, not to speak of studies on mineral reaction kinetics.

Fig. 11.

Schematic representation of a dispersive mode experimental setup for XANES measurements that combines the use of a position-sensitive detector (D-XAS) with that of two ionisation chambers (Turbo-XAS) on both sides of the sample lying in the focus (from Pascarelli et al., 1999b, modified).

Fig. 11.

Schematic representation of a dispersive mode experimental setup for XANES measurements that combines the use of a position-sensitive detector (D-XAS) with that of two ionisation chambers (Turbo-XAS) on both sides of the sample lying in the focus (from Pascarelli et al., 1999b, modified).

Sample preparation

There is no preferred method to prepare samples for XAS spectroscopy measurements, and indeed all possible methods have been used, with the only preliminary care that the sample must be homogeneous in thickness and absolutely free of pinholes, as these would transmit such an amount of incident SR as to choke the detection system. In the following, a little information will be given based on experience, but everybody has to do his/her own, often with a considerable effort and waste of time.

Powders

Normally, the samples to be investigated are powders; both for reasons of practical preparation and for a tradition that began with the first transmission experiments performed by physicists on simple chemicals, and that continues because it has some practical advantages. Indeed, in transmission mode XAS measurements the weight of material to be used for most effective I1/I0 recording, i.e., when 96% of the incident beam is absorbed, can be predetermined using the formula:  

formula
where ma is the mass [g] of the absorber atom to be contained in the sample, ms is the mass of the sample itself that is roughly related to the absorption coefficient, Vt is its total volume [cm3] for a thickness L [cm] of the compartment (or sample layer). In the case of an ideal sample thickness that would assure 96% transmission and the best S/N, the optimum ma × ms × L for counting statistics would be 2.6 (Stern & Heald, 1983), but this value is normally reduced to 2.3 to obtain a 90% transmission that accounts for various experimental losses, and occasionally much more, to reach performances down to 70–80% (see 4.1.4.1). Usual compartments are rectangular windows ca. 1 cm wide, 0.2 cm high and 0.1 cm thick. However, the lateral size may be reduced by letting the beam pass only through pinholes or slits carved into a thin screen made of Pb tape.

In normal practice, the above calculation is made only when the sample to be studied is so strongly absorbing as to require dilution. Samples for transmission experiments are prepared as very fine powders deposited on membranes or smeared on a kapton or graphite tape; these layers are made to adhere on the compartment window, several layers being superimposed till a satisfactory absorption jump is obtained.

It should always be kept in mind, in organising XAS experiments, that a powder XANES spectrum integrates the contributions of numberless minute crystals the surface of which may undergo alteration during the short time in between sample preparation and recording. Consequently, and particularly for light-atom XAS, the powder mounts are to be stored in a dessicator or even under vacuum.

Purity.

Most experimental XANES spectra on materials of mineralogical interest are recorded on powders obtained by grinding carefully separated and hand-picked grains that have been checked by optical microscopy and/or X-ray powder diffraction to be free of impurities, and especially of inclusions of other minerals that contain the absorber atom to be measured. Indeed, given XAS atomic selectivity, it is quite indifferent to record, e.g., the Fe K-edge spectrum of a garnet containing quartz and graphite grains, but it is not so at all if the examined garnet contains even the smallest blade of biotite or magnetite, as all Fe atoms contained in them would be excited too and produce their own Fe K-edge spectra. These would superimpose on the garnet Fe K-edge spectrum and give rise to a number of spurious fine features the interpretation of which would lead to wrong crystal chemical conclusions (in the above example: they are particularly dangerous for the evaluation of the PE sub-region). Thus, powders can be contaminated indeed, or even diluted on purpose with some other mineral, but never with any material that contains the absorber. Since minerals are mostly multi-atom compounds and the separation of them to be inclusion-free is a painstaking work, one is advised not to mix them with anything, or to use very light diluters such as sugar (that is soluble and can be easily removed) or borax or boron nitride.

Grain size.

For transmission mode experiments, powders are either pressed into the sample holder (see above) or smeared onto kapton tape (several tapes are prepared, so as to superimpose them to attain optimal thickness, i.e., the thickness that gives the most significant absorption jump without loss in the signal because of increased noise). For fluorescence and electron yield experiments, the powders are simply gently settled on a flat sample holder after dispersion in a liquid (ethanol, acetone). In all cases, the powder mounts should be uniform in grain size and, in particular, never contain grains the size of which exceeds the characteristic absorption length, i.e., 4 mm. Indeed, preferentially, mineral samples should be homogeneous in size, e.g. they should certainly pass the No. 400 mesh sieve (< 0.031 mm) and possibly be in the fine silt grain size range, i.e., 0.0156–0.0078 mm. Be careful, though, that grinding to such a size might induce damage into the crystals (Pettifer, 1990) that may go as far as to render them amorphous. For weak or layer minerals, only settling in liquids down to 0.0020 mm (clay size) assures constant grain size and undamaged sample at the same time, thus allowing reproducible experimental XAFS spectra (cf. Manceau et al., 1998). Unfortunately, uncontrolled grinding is one of the major sources of error for experimental XAFS. Too large grain size leads to large holes and to too thick samples; too small one brings to a (partial) amorphisation. There is no such recipe that satisfies all needs and the grain size and thickness for best recording often have to be looked for by trial and error.

Particle orientation.

Powder mounts are normally considered to be randomly oriented, and this is indeed the case with materials that do not exhibit cleavage. However, the incident SR beam is polarised with the electric field vector lying in the horizontal plane, so that the amplitude of the scattered photoelectron wave actually depends on the angle α between the impinging beam and the scattering pair inter-atomic vectors, which lie on a lattice plane of the structure (Heald & Stern, 1977). In most minerals, and especially in those of the cubic system, the structural effect is minor when compared to the cleavage effect, and yet it can be perceived even in the weak features of the PE sub-region (Poumellenc et al., 1990; Waychunas & Brown, 1990; Cabaret et al., 1999) or in XAFS spectra recorded in the very soft X-ray energy range (Räth et al., 2003). For minerals that cleave easily, experience gathered on clays and other layer silicates shows that, even with very fine powders, crystallite orientation strongly affects the shape of the XANES spectrum (e.g. Manceau, 1990; Manceau et al., 1988, 1990, 1998, 1999; Kaiser et al., 1989; Mottana et al., 2002; Tombolini et al., 2003): primarily, it changes peak intensity, which is a significant component of the information (Fig. 12). A theoretical study of the orientation effect (Pettifer, 1990; Pettifer et al., 1990) suggests that the isotropic average requested for powder mounts can always be attained by rotating the specimen by an angle with sin2θm = 1/3, i.e., by 35.26° (± 3°) around an axis that is perpendicular to both the beam direction and its polarisation axis. This value is complementary to the theoretical “magic angle” value 54.7° (Pettifer et al., 1990). A development of this theoretical result has been recently presented for self-supporting clay mineral thin films (Manceau et al., 1998). For these, a three-dimensional system of coordinates to record spectra in a standard setting for easy application has also been proposed (Manceau et al., 1999). However, most operators who record their spectra on powders in the FY mode use a 45° angle, which combines the magic one with the best setting of the detectors to record high S/N signals.

Fig. 12.

Spectral changes in the Si K-edge XANES spectrum of a muscovite crystal blade obtained by changing its orientation against the horizontally-polarised synchrotron radiation beam from orthogonal to almost vertical. The bottom spectrum is the Si K-edge XANES spectrum of the same muscovite recorded on a fine-grained powder mount (from Mottana et al., 2002, modified).

Fig. 12.

Spectral changes in the Si K-edge XANES spectrum of a muscovite crystal blade obtained by changing its orientation against the horizontally-polarised synchrotron radiation beam from orthogonal to almost vertical. The bottom spectrum is the Si K-edge XANES spectrum of the same muscovite recorded on a fine-grained powder mount (from Mottana et al., 2002, modified).

Single crystals

In the fluorescence and electron yield detection modes one can record the XANES spectrum directly by impinging SR on a face of a large enough crystal, provided it is inclusion-free. This allows studying the polarisation dependence of the absorption in the material, besides its bulk absorption that is better done with powders. It is advisable that the crystal face (or the cut and polished grain surface) is sufficiently flat (free of growth steps or cleavage traces) and certainly pollution-free (either by cleaving it afresh or simply by rinsing it with acetone; with the present sensitivity of XAS spectroscopy there is no need of sputtering).

The orientation dependence of XANES (named P-XAS) has been systematically studied only for the extreme case of minerals with an easy, perfect cleavage (Brown et al., 1977; Kutzler et al., 1981; Waychunas & Brown, 1990) and, in particular, for layer silicates such as micas and chlorites (Kaiser et al., 1989; Manceau, 1990; Manceau & Schlegel, 2001; Manceau et al., 1988, 1990, 1998, 1999, 2000). Mottana et al. (2002) recorded the XANES spectra at various K edges on single-crystal mica blades lying flat on the sample holder and optically oriented in such a way as to have their a ≅ b || Z, where Z is an axis orthogonal to the SR beam forward direction and parallel to the mica surface. The beam was first collimated to impinge the mica at right angle (α = 0°); then the blade was rotated on the Z axis and α increased up to 60–80°, this being the maximum angle allowed by the mechanics of the sample holder and the geometry of the detection system.

Consequently, the SR electric vector always lies on the horizontal plane, but it impinges two almost perpendicular sections of the mica structure, i.e., it is led to scan its atoms and bonds under different angles. Best agreement with the XANES spectrum of the same mica when settled on the sample holder as a homogeneous powder having a grain size of ca. 5 μm was obtained for α = 35–40°, i.e., the value complementary to the magic angle (Pettifer, 1990; Pettifer et al., 1990). Indeed, the rotation was found to induce displacements in the energy position of certain features by as much as 5 eV and variations in their intensity by as much as 50% (Fig. 12). Some features even disappeared or new ones appeared instead. These spectral changes affect all energy regions of the experimental XANES spectrum, thus showing not only their dependence upon the geometry of the section of the crystal that is being scanned, but also that the electronic properties of the absorbing atom are involved too. What is actually happening is a probability change of the MS path selection by the photoelectron due to the change of geometrical relationships in the crystal: the probability for some MS pathways is weakened, while others get stronger. Thus, with changing the MS contributions, the entire experimental peak appears to shift in energy. Polarised radiation increases the probability of observing scattering paths that are out of the plane of polarisation (e.g. intensity of the white line in non-centrosymmetric structures); in such a case, only theoretical simulation helps in correctly interpreting the spectral changes observed during the experiments.

Dyar et al. (2001, 2002) carried out an extensive investigation of the intensity variation of edge features in a number of Fe-bearing minerals using the micro-XANES probe that focus the beam size down to 10 × 15 μm. Single crystal grains on the order of 30 × 30 × 100 μm were studied, with no concern about their chemical homogeneity because of their small size. Spectra were recorded with the SR beam forward axis parallel to the three crystal directions. Changes in peak intensity and energy were observed for both the FMS and IMS sub-regions and studied in detail for the PE sub-region (Fig. 13). Such changes originate because different bonds having different orientations relative to the absorbing Fe sites are being probed. The purpose behind Dyar et al.'s study was to check the reliability of the method for quantitative determination of Fe3+/ΣFe ratio pursued for many years (cf. Bajt et al., 1994; etc.), as well as, more generally, of the PE method for measuring the oxidation state of transition elements. Their results show that the method can be reliably applied to isotropic materials such as glasses, but they warn against measurements carried out on powders uncontrolled for their grain size and particle orientation, including many cubic minerals which, although being optically isotropic, display easy cleavage, thus offering planes of preferential orientation to the impinging SR beam.

Fig. 13.

Spectral changes in the pre-edge sub-region of the Fe K-edge XANES spectrum of a biotite obtained by changing the angular orientation of the mica blade with respect to the strongly linearly polarised synchrotron radiation (from Dyar et al., 2001, modified).

Fig. 13.

Spectral changes in the pre-edge sub-region of the Fe K-edge XANES spectrum of a biotite obtained by changing the angular orientation of the mica blade with respect to the strongly linearly polarised synchrotron radiation (from Dyar et al., 2001, modified).

Another problem arising when using single crystal mounts lies in the choice of the suitable detection mode, this being often connected with the crystal surface condition. This effect is irrelevant in most XANES measurements in the hard X-ray energy range, but it may become exceedingly significant in the soft and ultra-soft X-ray ranges (Fig. 14; cf. Kasrai et al., 1998).

Fig. 14.

Effects of sample surface preparation (a) and of the detection mode (b) on the B K-edge spectrum of danburite and BPO4 respectively (from Kasrai et al., 1998, modified).

Fig. 14.

Effects of sample surface preparation (a) and of the detection mode (b) on the B K-edge spectrum of danburite and BPO4 respectively (from Kasrai et al., 1998, modified).

Spectrum optimisation

An experimental XANES spectrum recorded afresh displays a sequence of features (peaks or shoulders) differing in their intensity (normally given as a fraction of the maximum absorption or transmission of the incoming beam) and energy (eV, as determined by the monochromator) that superimpose on a (usually) down-sloping baseline. The intensity is related to the number of MS pathways that contribute to each feature (e.g. the white-line intensity is high because MS contributions in its region tend to infinity; however, in practice, even the white-line intensity is finite because in a real crystal the electron mean free path length is limited). The energy is set in such a way that the modulations of the absorption edge to be investigated are within a preset scanning range. Therefore, a raw experimental XANES spectrum is purposely made to start some 30–50 eV before the expected onset of the absorption process, and to finish some 100–150 eV after, or even at higher energy. However, in order to save time, the scanning range may also be made shorter after the preliminary spectra (e.g. in their study of the P K edge in 15 phosphates, Franke & Hormes, 1995, scanned from 2130 to 2190 eV, the observed absorption maximum being at 2152.4 eV vs. a theoretical P K-edge position expected to be 2149 eV). Indeed, although the general characteristics of the XANES spectrum are determined by the atomic distribution of the atoms neighbouring the absorber (local site symmetry), they are also system-dependent, particularly for their intensity, i.e., different model compounds exhibit different XANES spectra that may vary greatly with their crystal structure and, within isostructural series, with the extent of the chemical substitutions. Thus, it would be incorrect to cut off recording at too low an upper energy, for some information would be lost. By contrast, beginning a scan at an energy too close to the absorption edge may weaken the extrapolation of the base line (see later). Nevertheless, in order to decrease acquisition time, it may be opportune to set the experiment for different energy step-size scans in the various sub-regions, while preserving the need to reveal the related fine features with the highest possible resolution.

In addition to this organised sequence of instrumental operations, a series of other preliminary provisions is to be made that improve the quality of the raw experimental spectrum, and these are followed by a phase of fitting and debugging, to be carried out stepwise before reaching the final stage of a “clean” XANES spectrum worth to be evaluated in its scientific content. All this operational procedure will be described in detail in the Addendum, and just some preliminary remarks of general nature are made here.

Energy calibration

At all SR beam lines, the very first preliminary assignment consists of calibrating the energy positions of all observed features against a reference standard (usually metal foils, or minerals the XANES spectrum of which has been carefully studied and is well-known: cf. Waychunas & Rossman, 1983; Rehr et al., 1991; Li et al., 1995c; Newville et al., 1995). An alternative way is to calibrate them during the scan against a “glitch”, i.e., a spurious absorption at constant energy originating from the monochromator crystal (cf. 4.1.3).

Furthermore, when high thermal loads from the SR source heat the first monochromator crystal (or the entire “channel-cut” crystal monochromator), a systematic correction should be applied that takes into account the decrease of the ring current (and consequently of the heat load) with time. This correction consists in plotting the energy position of a selected sharp feature occurring in the spectra of a reference sample that are taken at regular time intervals against the ring current at that time, and determine for the reference material an energy vs. current function that is then extrapolated and applied to the sample or samples recorded during the same ring-filling period.

If the standard procedure is followed, the accuracy in energy that is achieved is ± 0.1 eV for the pre-edge sub-region and ± 0.03 eV for all other sub-regions of the XANES spectrum, both values being well within resolution (cf. 4.1.3). The accuracy in intensity measurement should be better than 1%, but in quite a few cases it is of the order of 5–10%.

Occasionally, either because of beam instability or for electronic anomalies or for other reasons intrinsic in the material such as the low concentration of the absorber, the S/N ratio of a single spectrum for a given mineral sample may be so poor as not to be worth considering. This trouble can be circumvented by recording additional spectra of the same sample in the same instrumental set up and by averaging them. There will be some time lost, as statistics shows that in order to double the S/N ratio one has to record at least four spectra (the S/N ratio of the data improves with the square of the number of scans). However, in this way a cumulative, trustworthy spectrum can be acquired on the long run, the more so as certain random defects that may be present in the individual spectra will be smoothed out during data averaging.

Spectrum fitting

The standard procedure of analysis for an energy-calibrated and yet still raw XANES spectrum follows several steps, just as standard XAFS analysis (Sayers & Bunker, 1988):

  1. The calibrated raw spectrum is corrected for background contributions from lower-energy absorption edges by fitting the base line (α = Cλ3 – Dλ2 + A, where λ is the photon wavelength and C, D are functions of the atomic number Z changing abruptly at the absorption edges; Victoreen, 1943). This polynomial fits better the base line than the flat photoelectric cross-section straight line to be expected on theoretical grounds (cf. Bianconi, 1988), but it is often neglected in XANES analysis in favour of a simple linear fit; by contrast, it is a must in EXAFS analysis.

  2. The background-corrected spectrum is normalised for intensity at high energy, i.e., close to the upper end of the XANES region at an energy position where no obvious features can be seen. As the extent of the XANES region is system-dependent (cf. section 2), this energy position cannot be predetermined; however, it is usually somewhere in the energy range intermediate between the FMS sub-region and the IMS one, in an energy range as smooth as possible.

  3. In addition, for PE analysis the contribution of the absorption jump is subtracted by a suitable mathematical function (e.g. an arctangent).

The entire procedure yields a profile of the absorption K-edge region that consists of a number of features, each one with its own energy, intensity and intrinsic width, even if occasionally partially superimposed (shoulders). Such a profile constitutes the (optimised) XANES spectrum that can either be evaluated visually or fit with Gaussian (or Lorentzian, or pseudo-Voigt) curves and standard peak-fitting algorithms. The numerical values of the fitted curves (energy and intensity, with errors and significance bars) can then be used as solid data to interpret the mineral absorption spectrum for crystal chemical considerations. This practice is already current from qualitative XANES analysis, but it is becoming more and more used in its quantitative aspects.

Information contained in XANES spectra

Bianconi (1988) summarised the scientific information to be extracted from XANES spectra as being of three types: a) “the local geometry of atomic arrangements in complex systems”, b) “effective charge on the absorbing atom” and c) “local electronic structure in metallic systems”.

From that time on, a great deal of progress has been made in the quantitative evaluation of XANES, and further advance is underway, so that:

  • not only the local, i.e., short-range, geometry around the probed atom can be determined, but also the atom medium-range order distribution in the structure (bond lengths and angles for clusters up to almost 1 nm in diameter) that complements its long-range order distribution best determined by SC-XRD refinement;

  • the “effective charge”, i.e., the time-averaged number of valence electrons on the atom, is now refined with an indication of their orientation and complemented with a rather precise evaluation of the coordination;

  • a quantitative evaluation of the electronic structure (charge distribution) may be carried out even for semiconductor and insulating systems.

However, in order to reach this stage, a more analytical study of XANES had to be carried out, not only by recording very well resolved experimental spectra on a number of structure prototypes, but by combining them with ab initio simulations starting from the known structure data determined on the same material by SC-XRD methods for the long-range, and progressively adapted to the short-range that is characteristic of XAS spectroscopy via a series of attempts often involving trials and errors. This analysis was found to need the separate evaluation of at least three separate sub-regions of the XANES spectrum (see Fig. 4), as they have been theoretically demonstrated to contain information of different type. However, such an analysis has dealt so far with only relatively few mineral structures (cf. 3.2.1) and needs to be continued, not only for sake of completeness, but also in order to stimulate the progress in XAS theory by submitting new case studies of increasing complexity, such as those nature generously provides.

Edge and pre-edge (PE) sub-region

The edge sub-region contains few features, normally weak but at times even stronger than the absorption jump, which are caused by electronic transitions to empty bound states that are controlled primarily by the selection rules for mainly electric dipolar (or, to a lesser extent, quadrupolar) electronic transitions. These transitions, first observed by Rule (1945) at the M4,5 edge of samarium, occur at energies that are lower than the absorption edge threshold; therefore, they are generally named pre-edge (PE) features, and the corresponding sub-region of the XANES spectrum is the PE sub-region. Although for a long time believed to occur only in (and mostly interpreted for) the spectra of atoms of the transition series, they have been shown to occur in spectra recorded for other atoms too, provided they have empty states available to which the core hole electron may leap to.

PE feature intensities are since long known to display a negative relationship with coordination numbers, thus they may represent an important indication of the local coordination of the absorber atom in the structure under investigation. However, such a relationship is not simple, because it also reflects intrinsic properties of the atom, such as the number of empty states, and/or of the atom environment, such as empty states available in the surrounding, coordinating atoms that can mix with those of the central coordinating absorber atom.

Most generally, all PE features can find an explanation in the molecular-orbital theory, so that the quantum mechanical selection rules that control the transition probabilities in the edge sub-region were at first considered to be the same as those that are valid for optical spectra (e.g. Brown et al., 1988). As a matter of fact, on the basis of the observation that Zn2+ (having 3d10 configuration, i.e., a filled final state configuration) does not exhibit PE features whereas cations of the other transition atoms (e.g. Fe2+ having 3d6 configuration) do, Shulman et al. (1976) had already suggested that the weak first absorption arises from a 1s → 3d transition. This finding was forgotten for a time, when it appeared that their following interpretation of the white line and edge top as due to 1s → 4s and 1s4p transitions, respectively, was untenable.

Causes of PE features

PE features are now known to arise from at least three major different electronic mechanisms:

  1. the quadrupole mechanism that is particularly significant for atoms located in centrosymmetric sites (Balzarotti et al., 1980; Hahn et al., 1982; Dräger et al., 1988);

  2. the mixture of the 4p states with the 3d ones in a transition metal, owing to the non-centrosymmetric symmetry of the coordination polyhedron around the absorbing atom (“pd mixture”: Roe et al., 1984; Ravel et al., 1993);

  3. the electric dipole allowed transitions of a transition metal ls electrons to the unoccupied 3d states of neighbouring transition metal atoms (“band effect”: Bianconi et al., 1985; Uozumi et al., 1992; Vedrinskii et al., 1997; Wu et al., 2002), which are also dominant for atoms located in sites that have no inversion centre. Note that this electronic mechanism is equivalent to the “intervalence charge transfer” (IVCT) mechanism between adjacent metal ions that is one, if not the most important colour cause in transition atom bearing minerals (Davoli et al., 1986; Burns, 1993).

The contribution of each mechanism is different and may be calculated (Westre et al., 1997). Moreover, several other additional factors have been suggested to contribute to determine intensity and energy of PE features (e.g. spin state, oxidation state, site geometry etc.) and still need to be properly evaluated. However, first of all, let us give a visual overlook of the PE sub-region (the acronym PEFS, for “Pre-Edge Fine Structure”, proposed by Vedrinskii et al., 1997, has not entered into use) for a number of atom species.

Transition elements

In the atoms of the first transition series (Fe, Cr, Co, Mn etc.), which have been investigated most carefully by mineralogists as they are of great geological and geochemical significance, the intensity of PE peaks is certainly related to transition probabilities: indeed, the 1snd transitions are formally dipole-forbidden, but they have a non-zero probability due to electric quadrupole transitions (i.e., mechanism 1 above). However, the quadrupolar coupling is extremely weak (Hahn et al., 1982), about two orders of magnitude smaller than the dipolar one (Bair et al., 1980; Brouder, 1990). Therefore, most PE intensity actually results from hybridisation between the 3d and 4p states (i.e., mechanism 2) that arises if the transition metal occupies a non-centrosymmetric site. In the particular case of Fe-bearing compounds, where the electric dipole mechanism is fundamentally intense, even a small amount of 4p → 3d mixing can have a very large effect on PE feature intensity (Roe et al., 1984; Randall et al., 1995; Westre et al., 1997). Therefore, the greater is the amount of 4p mixing into the 3d orbitals, the greater is the intensity of PE features. Immediate consequences are:

  • Symmetrical octahedral sites display very little electric dipole coupling, and indeed show extremely weak PE features or no PE features at all; however, as soon as the octahedral site increasingly distorts, the 4p mixing into 3d orbitals will increase too and PE features will appear and progressively increase in their intensity. This effect has been first verified and quantified for octahedral Ti-bearing minerals (Waychunas, 1987), and may apparently be extended to the cubic sites too (Heuman et al., 1997).

  • Tetrahedral sites have Td point symmetry that is perfectly cubic, but it has no inversion centre. Consequently, a transition element that is present in both the tetrahedral sites and in the octahedral ones of the same mineral has PE tetrahedral features that are far more intense than the PE octahedral ones, even if the cation concentration in each site is the same. Furthermore, smaller sites, such as the tetrahedral site is when compared with the octahedral one, attract small cations in a high oxidation state, and these have less-symmetric distributions of their outer electrons; this not only increases the number of possible empty states where the photoelectron may leap to, but also it increases the possibility of hybridisation, thus resulting in a greater intensity of the PE feature.

Brown et al. (1988) quantified the observed experimental evidence for iron and stated that the increase in PE feature intensity is 0.7–2.0% with respect to the intensity of the main K-edge jump for octahedral Fe2+, 5–7% for tetrahedral Fe2+, and up to 15% for tetrahedral Fe3+. More generally, Galoisy et al. (2001) established that PE intensity varies inversely with the coordination number for non-centrosymmetric environments, i.e., Ioct < I5–fold < Itet.

Finally, it has been noted for several atoms that the transition probability (and thus the relative intensity of the peak) is increased if the number of empty states in the d orbitals of the atom is large; e.g., the PE features at the V K edge of a mineral containing V, an atom that may show four valence states (V2+, V3+, V4+ and V5+, having the configurations 3d4, 3d3, 3d2 and 3d1, respectively), appear to be most intense for V5+ (Delaney et al., 1999).

The energy position of PE features is also important, because it has a first-order relationship to the oxidation state of the absorber atom; as a matter of fact, the first, conspicuous evidence of a change in the absorber oxidation state is always a shift in the absorption energy of the entire XANES spectrum. Shulman et al. (1976) had shown that PE transitions differ from their analogous optical transitions because the number of transitions present (i.e., the strong field many-electron states) must be modelled for the d(n + 1) excited state. This implies that the dominant effect due to a 1s core hole formation (which is spherically symmetrical) is an increase in the potential (Westre et al., 1997); in other words, this 1s hole is so close to the nucleus of the atom that the outer orbitals see a configuration equivalent to that of the atom next in the periodic chart, i.e., the atom having a fully occupied 1s shell. So, the final state of the ionised atom having atomic number Z, but with a 1s hole, is best approximated by that of a different nucleus having atomic number Z + 1 (Shulman et al., 1976; Lee & Beni, 1977); in other words, a Z atom XANES spectrum shows the energy level states predicted by the optical spectra for the Z + 1 atom (i.e., Co proxies for Fe).

Therefore, the following PE transitions for ionised Fe contained in different coordination polyhedra may be expected for isotropic materials (glasses) and may possibly be extrapolated to anisotropic compounds such as most minerals (Calas & Petiau, 1983; Westre et al., 1997; Heuman et al., 1997; Geiger et al., 2000; Galoisy et al., 2001; Wilke et al., 2001; etc.):

  1. The PE sub-region of a compound containing octahedral Fe2+ should show (at least) three peaks corresponding, in order of increasing energy, to the T1g (4F), T2g (4F), and T1g (4P) states; a fourth predicted transition, A2g, is not visible because it is a two-electron transition with low probability;

  2. For Fe3+ in octahedral coordination, two electronic transitions are expected, the one for octahedral Fe3+ in the 5T2g (5D) state being ca. 1.1–1.5 eV lower in energy than the transition for octahedral Fe3+ in the 5Eg (5D) state;

  3. For tetrahedral Fe3+, the states reverse in energy with respect to the octahedral situation, but their separation is only ca. 0.6 eV. Given the current resolution at the Fe K-edge energy, which, in the very best beam lines and under very special circumstances, is ca. 0.4 eV (Petit et al., 2001), but normally is ca. 1.5 eV (Galoisy et al., 2001; cf. 4.1.3), the two octahedral Fe3+ transitions in the PE sub-region can barely be resolved, and a compound with tetrahedral Fe3+ shows only one indistinct, but rather strong PE feature.

Unfortunately, studies of this type on minerals are still rare: e.g. only recently did Petit et al. (2001), claiming a ca. 0.4 eV resolution, determine in a series of Fe-bearing minerals the energy separation between the average PE centroid positions for Fe2+ and Fe3+ and found it to be 1.4 ± 0.1 eV. Furthermore, the energy separations of the PE features of other atoms in different oxidation states and coordinations have been precisely measured for glasses and a few model compounds, with just a little application to some more common minerals (Geiger et al., 2000; Farges, 2001).

As a final remark: one should always remember that there are other types of polyhedral distortions from the ideal octahedral symmetry, such as the 5-fold square pyramid observed in grandidierite (Farges, 2001) and in some glasses, which allow 3d → 4p mixing, and this affects both intensity and energy in the PE sub-region. Consequently, the evaluation of the PE sub-region is never straightforward, and yet it is fundamental to determine transition metal oxidation states and concentrations. Indeed, most current research struggles at using PE to determine the Fe oxidation state of minerals by such a non-destructive method.

Non-transition elements.

During a systematic study of Mg by XANES in minerals, Cibin et al. (2003) noticed the presence of a small feature on the lower energy limb of the first FMS feature that was detectable even in minerals where Mg was in six- and eight-fold coordination. Later checks on XANES spectra recorded for other atoms showed that such features occur, e.g., in some spectra for octahedral Al and eight-fold coordinated Ca. Neither Mg (electronic configuration [Ne]3s2) nor Ca ([Ar]4s2) etc. are transition atoms (i.e., contain electrons in the 3d shell); thus the observed small feature should not be equivalent to a PE generated by mechanisms 1 and 2 above. However, this feature occurs when the coordination polyhedra centred by the absorber are not symmetrical in their geometry (as determined by SC-XRD refinements), but deformed from their regular shape; furthermore, the anomalous feature increases in intensity the greater is the deformation (as determined by the quadratic elongation, QE: Robinson et al., 1971).

For Mg-bearing minerals, this effect is particularly easy to be seen in solid solution systems like garnets whenever the octahedral Al is partly substituted by a transition element (Ti, Cr, Fe etc.), thus producing a deformation in the Mg-centred cubic polyhedron nearby. Therefore, the anomalous feature may be interpreted as indication of ls → d transitions that are forbidden in a regular octahedron and cube, but that become allowed because of the non-centrosymmetric orbital character even of a non-transition atom if it is located in a deformed polyhedron (mechanism 2). In other words, it may be interpreted as being due to deformation of the first atomic cage where the photoelectron ejected from the Mg absorber undergoes its first multiple scattering interactions.

Alternatively, such a feature may be due to extra transitions towards 3p empty states mixed with the empty density states of Mg (mechanism 3), which only arise if the contributions from far-away atoms are significant. This interpretation is based on a calculation performed for garnets at the K edge of Al, i.e., another absorber that is a non-transition atom (Wu et al., 1996a). In that case, a “pre-edge” feature arose when large clusters, extending to the 4th to 5th shell around the photoabsorber, were included in the calculations. Such a calculated PE feature was interpreted as due not so much to a local site distortion from centrosymmetry, but to the existence of core transitions sensitive of long-range effects; indeed, it was generated not only when including in the calculation transition atoms such as Fe, but also non-transition atoms such as Ca, which has a large number of unfilled outer electronic states. This finding implies also that the final state reached in the core transitions is not really a simple atomic (or molecular) state, but it is sensitive to long-range order effects too: indeed, such anomalous “pre-edges” have been detected in well-ordered structures such as metamorphic olivines and orthopyroxenes. A further alternative interpretation for such anomalous “pre-edges” is that they arise in minerals when they contain many oxygen atoms, and are due to a metal-oxygen orbital overlap; however, evidence for this possibility is still scanty, and new, specific experimental studies need to be made.

Applications

Most applications of the PE features intensity ratios refer to the quantitative determination of the oxidation ratio of transition elements present in amorphous or semi-amorphous materials, but there is also a number of studies on the Fe redox state in oxides, phosphates, sulphates and carbonates (e.g. Galoisy et al., 2001; Petit et al., 2001; Wilke et al., 2001) characterised by a wide range of Fe coordination environments. These investigations showed that there are some very limited differences in the energies of the PE peaks related to the two Fe ionisation states, when their spectra are fit with two components and their average centroid positions are evaluated (ca. 7112 and ca. 7114 eV, for Fe2+ and Fe3+, respectively, or ΔE = 1.4 ± 0.1 eV: cf. Petit et al., 2001; Wilke et al., 2001). However, these differences are not only related to the oxidation state, but also to site coordination and distortion (Galoisy et al., 2001).

As a matter of fact, these two additional constraints have commonly been disregarded. Recently, significant work was carried out on silicate minerals by a group that systematically perfected initial suggestions by Bajt et al. (1994) and Sutton et al. (1995) to obtain quantitative Fe3+/Fetot ratios with an accuracy that is claimed to be from ±5 to ±15% as a function of coordination. Their regression lines refer to amphiboles (Delaney et al., 1996, 1998), olivines (Dyar et al., 1998), micas and garnets (Dyar et al., 2001, 2002). Furthermore, Farges (2001) not only decomposed the PE sub-regions of a series of grandidierites to unravel the effect of their Fe coordination from that of valence, but he calculated also the quadrupolar and dipolar transitions and confirmed the weak influence of the quadrupolar ones to shape the complete PE spectrum. Recently, Berry et al. (2003) reviewed the entire matter and found that coordination substantially affects the accuracy of the results, so that regression equations based on PE ratios are reasonable and consistent with Mössbauer data only as long as the Fe3+ and Fe2+ cations are in octahedral coordination, but they may deviate significantly and even become physically meaningless if Fe changes coordination. In particular, Berry et al. (2003) argue against the extrapolation of calibrations obtained for glasses to any mineral family (Fig. 15).

Fig. 15.

Dependence of the pre-edge main feature energy position for silicate glasses (•: after Berry et al., 2003) oxides (O: after Sutton et al., 1995) and several silicate mineral groups (after Delaney et al., 1998) as a function of their Fe3+/ΣFe ratios determined by Mössbauer spectroscopy.

Fig. 15.

Dependence of the pre-edge main feature energy position for silicate glasses (•: after Berry et al., 2003) oxides (O: after Sutton et al., 1995) and several silicate mineral groups (after Delaney et al., 1998) as a function of their Fe3+/ΣFe ratios determined by Mössbauer spectroscopy.

Among the transition metals different from Fe that have been investigated so far, a special interest was dedicated to Cr because of its environmental implications: the highly soluble Cr6+ is poisonous, whereas Cr3+ is both innocuous and very stable. The strong PE peak in Cr XANES spectra is normally assigned to the dipole-allowed transition of a 1s electron to an unoccupied antibonding 3d state that is forbidden in [CrO6] because the octahedron has inversion centre, but it is allowed in a [CrO4] tetrahedron due to the mixing between the 3d orbitals of chromium and the 2p orbitals of oxygen (Arcon et al., 1998). To support this assignment, a shoulder that follows at +10 eV above the PE onset is pointed out, which is ascribed to the simultaneous excitations of two electrons (one from the 1s core orbital and the other one from the valence t2 tetrahedral orbital) to the unoccupied forumla states (Arcon et al., 1998). By contrast, there is no such intense PE peak if Cr is located in an octahedron with inversion centre (e.g. in Cr2O3 or in uvarovite), but there are several weak PE peaks to be assigned to transitions of ls electrons to antibonding orbitals having their octahedral symmetry modified by local distortion. Following such a lead, Brigatti et al. (2000) could show that most Cr6+ contained in an aqueous solution in contact with ferroan smectites is drastically adsorbed by the minerals while being reduced to Cr3+ and fixed in the octahedral layer (Fig. 16), thus giving a crystal chemical explanation for a long-known environmental pollution problem needing beneficiation (cf. Peterson et al., 1997; Szulczewski et al., 1997). Moreover, Brigatti et al. (2001) could quantitatively disaggregate the PE features of a chromium muscovite and show not only that Cr is present only as Cr3+, but also that it occupies the M2 octahedral site by more than 99.5% of its total amount, as confirmed by Cardelli et al. (2003) by fitting the full XANES spectrum by the MXAN code (see the Addendum).

Fig. 16.

Changes in the Cr K-edge XANES spectrum of a corrensite before (untreated), during (treat. #1), and after (treat. #2) interaction with a solution rich in Cr6+ showing the initial high spectral noise due to the very small amount of Cr in the mineral (0.02 wt% Cr2O3) turning into well-resolved patterns with increasing interaction time while Cr6+ is progressively extracted from the solution and reduced to Cr3+ fixed in the octahedral layer (from Brigatti et al., 2000, modified).

Fig. 16.

Changes in the Cr K-edge XANES spectrum of a corrensite before (untreated), during (treat. #1), and after (treat. #2) interaction with a solution rich in Cr6+ showing the initial high spectral noise due to the very small amount of Cr in the mineral (0.02 wt% Cr2O3) turning into well-resolved patterns with increasing interaction time while Cr6+ is progressively extracted from the solution and reduced to Cr3+ fixed in the octahedral layer (from Brigatti et al., 2000, modified).

Full multiple-scattering (FMS) sub-region

The FMS sub-region extends from the absorption threshold, which is the energy of the lowest empty state reached by the core excitations, to ca. 30 eV above it, and contains a small number of fine features (ca. 4–6) due to at least two main phenomena: a) the very small mean free path length (0.5–1.0 nm) and the extremely short core hole lifetime (< 10−15 s) of the photoelectron, and b) the inelastic scattering contribution of the photoelectron at low kinetic energy, i.e., its MS interactions with nearby atoms, up to a certain distance that depends upon the energy of the photoelectron itself and the atom arrangement within the probed structure. In particular, the intense white-line feature, i.e., the most intense peak at the core-excitation threshold (Bradley et al., 1985) that marks the beginning of the FMS sub-region, arises from the superimposition of many MS contributions generated by the photoelectron along its pathways within the probed material, as well as from the atom electronic properties. Therefore, the FMS sub-region contains most information that arises from both the local (short-range) environment around the absorber, but also a number of MS pathways that originate from remote atoms, which are located in high-order shells. This is actually the case also for all parts of the XANES spectrum, but it is particularly noticed in the FMS sub-region owing to the fact that, over a relatively short energy range, there are superimpositions of MS contributions of different origins that enhance the intensity of the experimental features.

Unfortunately, all these contributions are interwoven in such a way as to never make interpretation straightforward, and occasionally impossible. As a matter of fact, until recently, the only effective method to unravel the information contained in the FMS sub-region was to compute ab initio the entire XANES spectrum of the compound, i.e., by starting from its crystal structure data determined by SC-XRD refinement, and then to compare the resulting theoretical spectrum with the experimental one (e.g. Cabaret et al., 1996; Wu et al., 1996b, 2004; Mottana et al., 1997b, 1999). Only recently the MXAN software (Benfatto et al., 2001), which is based on sound physical principles rather than being a mere mathematical peak-fitting procedure, started being applied to minerals (e.g. Cardelli et al., 2003), so that a less time-consuming, but still utterly reliable information on the electronic and structural properties of minerals is to be expected soon.

Spectral shape

The FMS sub-region (which corresponds to most if not all of the “Kossel structure”) is certainly the most interesting and conspicuous part of the entire XANES spectrum, the more so as experience gathered by recording XAS spectra at the K edges of the various atoms has shown that the spectral shapes of this region differ somewhat among compounds having different crystal structures, but they maintain their characteristic aspects for isostructural compounds, thus creating the conditions for a XAS systematics. In other words, while in general minerals belonging to different families or groups exhibit substantially different sequences of FMS features, those belonging to the same family or group have similar spectra, with the same number of features and with limited differences in both energy position and intensity of the individual features (e.g. clinopyroxenes: Davoli et al., 1988; Mottana et al., 1997b, 1999; orthopyroxenes: Giuli et al., 2002; etc.). This has just some limited significance in the identification of minerals that are too fine-grained to be identified optically, but can be identified by powder XRD methods; however, it is very important for minerals that are practically amorphous, and yet possess the short-range order that allows the X-rays to be absorbed according to the local atomic structural arrangement, i.e., by XAS spectroscopy. This possibility has been exploited at best, e.g., for allophanes at the Al K edge (Ildefonse et al., 1994, 1998) and for manganates at the Mn and Fe K edges (Combes et al., 1988; McKeown & Post, 2001; Refait et al., 2001; Scheinost et al., 2001), not to speak of santabarbaraite (Pratesi et al., 2003), the only mineral species accepted so far, although being amorphous, on the basis of the XAFS-determined singularity of its local structure.

At the moment, there is no atlas of XANES spectra available that may be used for the visual comparison of FMS sub-regions, thus for the identification of unknown minerals. Most likely, this is a consequence of the current investigation strategy, which privileges the “fingerprinting” use of XANES to determine oxidation ratio and coordination by comparison with model compounds against its full evaluation. However, some systematic spectra collections have already been made (e.g. Li et al., 1999 and Cibin et al., 2003 for Mg-bearing minerals) that help in pointing out differences and similarities for a limited number of related mineral species (cf. Table 1).

Energy shift

It is known since long that the entire FMS sub-region undergoes a positive shift in energy as a function of the ionisation condition of the absorber, the more so the greater its formal valence (Kossel, 1920; Bergengren, 1920). Such a “ chemical” shift is related to the fact that when a valence electron is removed the screening of the core electrons is reduced (Fajans, 1928); consequently, the core levels become more tightly bound and require a greater energy to participate in the absorption process. Normally, the amount of this shift is measured only for the white line, but the entire XANES spectrum is actually involved. For practical reasons, the amount of shift has been studied best for transition elements, i.e., the most common atoms to attain stable electronic configurations through a variety of ionisation potentials (e.g. Mn: Belli et al., 1980; Fe: Calas et al., 1980; Waychunas et al., 1983; V: Wong et al., 1984; Delaney et al., 1999; Cr: Sutton et al., 1993; etc.). Nevertheless, significant shifts have been observed for non-transition atoms that do also show multiple valence states, e.g. S (Li et al., 1994b), P (Franke & Hormes, 1995), As, Eu etc.

However, the chemical shift related to the valence of the absorber, which works well for most non-crystalline compounds, is often difficult to apply to minerals because of the interfering effect of another shift that is related to coordination (e.g. Berry et al., 2003), i.e., because type, size and symmetry of the cage of nearest neighbours around the absorber modify the shift according to laws of their own that interfere with that related to the ionisation potential. Such a “coordination” shift is related to the substantial change in bond length that occurs when the absorber moves from the old to the new first-neighbouring cage, thus it reflects the discontinuation of certain MS pathways and the development of new ones, different in length and orientation. In addition, it has been found to be clearly related with presence or absence of collinear atoms in the new ligand cage (Bunker & Stern, 1984): the same atom, when in a tetrahedral coordination that is intrinsically non-collinear, will absorb at lower energy than in an octahedral coordination, which is intrinsically collinear (e.g. Al: McKeown, 1989; Mottana et al., 1997a). The “coordination” shift occurring in the B K-edge spectra (Fleet & Mathupari, 2001) has been used to determine the ratio of tetrahedral vs. 3-fold-coordinated boron. By contrast, the magnitude of the “chemical” shift appears not to be significantly modified by the manner of octahedral linkage (Yoshiya et al., 1999).

The observed shifts in energy are not simply related to oxidation and/or coordination of the absorber atom only, but they may also depend on other reasons; e.g., in orthophosphates the observed P K-edge shift does not depend upon the cation oxidation (P is always +5) or coordination (always four-fold) states, but primarily upon the valence of the cation bound to the [PO4] tetrahedra via a corner oxygen (Franke & Hormes, 1995). Such a shift has been quantified to be +3.5–3.8 eV for trivalent cations, +4.2–4.8 eV for divalent cations and +5.1–5.3 eV for monovalent cations (Franke & Hormes, 1995). The little variations observed for isovalent cations are related to gradual differences in the ionic character of the cation-anion interaction; indeed, the shift has also been found to decrease with increasing electronegativity, i.e., with increasing covalent character of the outer cation involved in the bond with the oxygen that bridges with P in the tetrahedra.

Summarising: although, at a first approximation, in evaluating the FMS sub-region of atoms that exhibit multiple valence states the observed energy shift should be attributed to the oxidation state (indeed, this is a stronghold of the “fingerprinting” method!), it should always be maintained in the back of the mind that something may not fit because coordination too plays an important role. As a matter of fact, shifts have been observed also in the spectra for atoms that can be ionised to only one oxidation state (e.g. Si: Li et al., 1995a; Al: Mottana et al., 1997a; Mg: Cibin et al., 2003; etc.). Moreover, other factors, such as the ionic character of the bond outside the coordination polyhedron centred by the absorber, or its length, may modify the amount of shift and confuse the interpretation.

Bond length determination

The FMS sub-region may provide information about the average length of the bond between absorber and surrounding ligands, albeit with a rather large error (ca. 0.03 Å), which is only apparent because it reflects the local and time-resolved character of XAS analysis as opposed to XRD averaging over a rather long range. Indeed, the continuum part of the spectrum, where MS features can easily be resolved, is sensitive not only to ionisation state and coordination geometry, but also to interatomic distance d, according to a relationship that, in molecular compounds (Bianconi et al., 1983), is:  

formula
where kr is the wave vector of the photoelectron at resonance. In solid compounds this information is essentially based on the simplified relationships known as “Natoli's rule” (Natoli, 1983, 1984):  
formula
where Er and Eb are the energies of the resonance feature and of the electron bound state, respectively, and d(A–L) is the distance from absorber to ligand. This formula needs no determination of the average interstitial potential, and is certainly true for the bound states at the K edges of transition metals (e.g. ls → 4p transitions). Thus, at a given atom edge, the higher the energy of a resonance (peak) with respect to the white-line energy, the longer are the MS pathways of the photoelectron, i.e., the distance from the absorber to the involved coordination shell. In principle, this should apply to the first coordination shell (nearest neighbours) as well as to higher-order shells. However, Natoli's rule has been shown to be valid only for small variations of d (< ca. 10%, i.e., 0.015–0.025 nm) and for isostructural compounds: indeed, it does not work at all when the atom changes coordination (Bianconi et al., 1983, 1985).

A completely different method to quantitatively extract from a XANES spectrum the average nearest-neighbour (first shell) distance from the absorber and its coordination number at the same time has been proposed by Bugaev et al. (2001). Their procedure is said to solve the inverted problem of XANES, i.e., determining the structural parameters from the experimental XANES spectrum rather than calculating several spectra from slightly different structural parameters and compare them with the experimental one, with ≤ 1% inaccuracy for the interatomic distance and ≤ 3–5% for the absorber coordination number. The fitting procedure is derived from the SS approach, but it combines it with some little MS concept, and uses Fourier filtration (see Galoisy, 2004, in this volume) to perform the calculations. The method works only for light atoms with Z ≤ 20 and has been tested so far for a small group of Al- and Mg-bearing minerals only.

Applications

The energy shift of the white line has always been used to determine the oxidation state of the absorber atom, and/or its coordination; as a matter of fact, often the two effects were confused under the cumulative name “chemical shift”, thus leading to mistakes that were corrected only when understanding the origin of PE features made an alternative method available to cross-check the information (cf. 5.1.2). Remarkable studies using the FMS sub-region to identify valence and coordination are summarised by Brown et al. (1988).

Natoli's rule to determine bond lengths has rarely been applied, essentially because investigations on mineral families using consistent methods that allow reaching results with error bars smaller than the error intrinsic in the method have been rare so far. Moreover, better results can be obtained from the EXAFS region (see Galoisy, 2004, in this volume). The potential of such a method can be estimated from data contained in the papers by e.g. Davoli et al. (1987), Franke & Hormes (1995) or Andrault et al. (1998). Bugaev et al.'s (2001) method is still in a pioneer stage.

Recently, Giuli et al. (2002) made a successful attempt at using the normalised intensities of two prominent features in the FMS sub-regions of synthetic orthopyroxenes recorded at both the Fe and Mg K edges to quantitatively determine not only the composition of the intermediate members of the enstatite-ferrosilite solid solution series, but also, through the intensity ratio of those features, the distribution of the two cations between the M1 and M2 sites of the structure (Fig. 17). They could confirm in this way the orthopyroxene XANES geothermometer empirically conceived by Mottana et al. (1991) and perfected by Paris & Tyson (1994) on the basis of theoretical simulations of XANES spectra.

Fig. 17.

Experimental Fe (a) and Mg (b) K-edge XANES spectra of synthetic orthopyroxenes in the enstatite (En)–ferrosilite (Fs) join showing the correlation between the intensity ratio of the main features and the fractional Fe occupancy in the M2 site of En80Fs20 (top inset) as well as the total En% content (bottom inset). In the Mg XANES spectrum (b) note feature P that simulates a pre-edge, but which is actually due to the very high deformation of the M2 octahedral site (from Giuli et al., 2002, modified).

Fig. 17.

Experimental Fe (a) and Mg (b) K-edge XANES spectra of synthetic orthopyroxenes in the enstatite (En)–ferrosilite (Fs) join showing the correlation between the intensity ratio of the main features and the fractional Fe occupancy in the M2 site of En80Fs20 (top inset) as well as the total En% content (bottom inset). In the Mg XANES spectrum (b) note feature P that simulates a pre-edge, but which is actually due to the very high deformation of the M2 octahedral site (from Giuli et al., 2002, modified).

Indeed, fitting the entire FMS sub-region starting from theoretical assumptions has been repeatedly attempted with contrasting results, which in recent years tend to become better and better because of the improved mathematical treatment of the data and of the greater efficiency of the computer hardware. A first, still rather crude but successful result that did not entail any calculation was by Mottana et al. (1997a), who showed that the Al K-edge FMS sub-regions of the micas zinnwaldite and preiswerkite containing Al in both tetrahedral and octahedral coordination can be explained as being the weighed combination of the spectra of phlogopite and polylithionite, two micas having their Al only in the tetrahedral sites and in the octahedral ones, respectively, their contributions being shifted by some 2 eV. Similar conclusions, though related to valence, i.e., to “chemical shift”, were drawn by Brigatti et al. (2000) for a smectite and a chlorite, two trioctahedral layer silicates showing very similar Fe XANES spectra: they both contain Fe in the octahedral layer as a combination of Fe3+ and Fe2+, but the dominance of Fe3+ in smectite and that of Fe2+ in chlorite can be assessed via the energy positions and intensities of two distinct spectral features separated by ca. 7 eV that correspond to the respective white lines.

However, the most reliable way to extract information from the FMS sub-region lies in the comparison of it against computed FMS spectra based on ab initio structural parameters, such as those simulated by CONTINUUM and FEFF8 or by the new MXAN package (cf. 3.2.1). Given the time-consuming procedure involved, examples of this kind are still rather rare, but the information they convey is very interesting, particularly for complex structures such as most minerals. Wu et al. (1996c, 2004) reproduced the FMS sub-regions of forsterite (Fo) and fayalite (Fa), at the Mg and Fe K edge, respectively, and showed that they are the sum of the partial spectra generated by Mg and Fe in the M2 and M1 sites. Furthermore, Wu et al. (1996c, 2004) tried simulating the spectrum of an intermediate Fo–Fa solid solution in order to quantify its order-disorder Fe/Mg site distribution, but they did not reach indisputable results. In contrast, Cabaret et al. (1996) and Mottana et al. (1999) computed ab initio the FMS sub-regions of pyroxenes and not only were able to point out the individual contributions of Al and Mg, i.e., the two octahedrally coordinated cations, but also to show that the Mg and Al K edges, which are so dissimilar at visual examination, actually contain the same number of features, all generated by those two atoms as octahedrally coordinated absorbers, though along different pathways the lengths of which are influenced by the shrinking of the overall structure due to the heterovalent substitution of the small Al cation for the large Mg one. Finally, Cardelli et al. (2003) first evaluated the entire FMS sub-region of a Cr-bearing muscovite using MXAN and demonstrated that it is possible to gather complete structural information on the location of such an atom even when extremely diluted. Indeed, they not only determined that all Cr enters the M2 cis-octahedra, but also that it induces a significant distortion in the site by flattening it, in contrast to the nearby still Al-centred octahedral sites.

Intermediate multiple scattering (IMS) sub-region

The IMS sub-region features apparently inform only on the MS contributions deriving from atoms either at a very short distance from the absorber or from their arrangements at an intermediate range of distances, i.e., they give local information first, but also information on the crystal structure at a medium range of order. Indeed, the IMS sub-region usually contains a limited number (n < 4) of MS contributions (though sharper and stronger than the SS oscillations), which arise not only from interactions of the photoelectron with the nearest atoms in the first coordination shell, but also from far-away shells (up to the 4th or 6th shell: Wu et al. 1996c, 2004; Cabaret et al., 1996, 1998). In addition, under favourable structural conditions, certain IMS features arise (or, at least, they are affected) from contributions of very distant atoms the amplitude of which is emphasised because of collinear focussing (Kuzmin & Parent, 1994; Kuzmin et al., 1995). All this evidence implies that the IMS sub-region is related not only to the local geometry, but also to the overall structural properties (and symmetry) of the material and is affected by atomic orders that are not as long-range as those probed by XRD (at least ca. 30–50 unit cells, by itself a great improvement with respect to the n × 10−5 cm edge size of the original model crystallite: Darwin, 1922), but neither totally local, i.e., related to the first near-neighbours. Indeed, IMS features arise from a medium-range order that may extend over less than 6–8 unit cells, i.e., over a distance < 0.4–0.6 nm from the absorber (cf. Cabaret et al., 1998; Bugaev et al., 2001). Therefore, similarity in the IMS sub-regions (and EXAFS regions, of course; see Galoisy, 2004, in this volume) is a proof of the overall structure identity existing in the members of a complex solid solution series, even if the series undergoes a chemically-driven structural rearrangement (e.g. omphacite pyroxenes: Paris et al., 1995; Mottana et al., 1997b, 1999; trioctahedral micas: Tombolini et al., 2002a, 2003).

A major problem in evaluating this sub-region of the XANES spectrum, additionally to the difficulty of precisely locating and measuring features that are mostly weak and skew, is due to the fact that the upper boundary of the IMS sub-region is hard to define. As a matter of fact, the IMS sub-region merges into the EXAFS part of the XAFS spectrum. Some current work tends to shift such a boundary to energies above threshold absolutely unexpected only a few years ago: indeed, codes based on the MS theory are now able to reproduce and explain high-energy features that only few years ago could only be explained by the SS theory (see above). By contrast, however, there are other codes based on the SS theory that have been able to reproduce and explain the FMS features of some compounds, thus shifting the XANES/EXAFS boundary well down close to the absorption threshold. Fourier filtration (Bugaev et al., 2001), a mathematical tool typically associated with the SS theory, has shown itself to be able to extract quantitative information such as first near-neighbour distance and coordination of the absorber, thus including not only the IMS sub-region, but the entire XANES region back into the EXAFS one. The matter is still open to discussion, and there is a third tendency of thought (Solomon's judgement, perhaps, but certainly unproductive for the development of science) inclined at disregarding this sub-region in the experiments and at leaving it unexplained in the interpretation.

Applications

The weak features occurring in the IMS sub-region have rarely been exploited to gather information on minerals, partly for the same prejudice that favoured the “fingerprinting” use of the white line against that of the full FMS sub-region (see above) and partly for they were confused with EXAFS oscillations and were involved in their treatment by the SS approach, thus contributing to the occasionally wild scatter of that calculation. Only recently, Tombolini et al. (2002b) made a conscious, precise attempt at using features in the IMS sub-region to determine the size of the sites occupied by Si, Al, and Fe3+ in the tetrahedral sheet of Fe-bearing trioctahedral micas. Starting from the constant average <T–O> distance 1.68 Å measured by SC-XRD refinement and using the edge-top of the FMS sub-region as the reference bound state, they determined from the energy positions of two features in the IMS sub-region of different micas (Fig. 18), through a system of equations derived from Natoli's rule (cf. 5.2.3), that the tetrahedral site centred by Al is 1.78 Å in size, and that centred by Fe3+ is 1.86 Å (the Si-centred tetrahedron was confirmed to be 1.64 Å). Furthermore they were also able to confirm the XRD result that the tetrahedral sheet adapts itself via the reduction of the in-plane rotation angle (α), down to an almost regular hexagonal lattice (corresponding to α = 0°) that is almost reached in annite.

Fig. 18.

. (a) The Al (line) and Si (dots) K-XANES spectra of two trioctahedral micas normalised to their white-line centroids (B) showing the energy difference (EE0) in their D features. From similar comparisons carried out on numerous mica spectra, two relationships (b) can be deduced that allow determining from average <T–O> distances the individual atom to oxygen distances of the tetrahedra centred by Si (1.638 Å) and Al (1.778 Å), as well as tetrahedral rotation α (from Tombolini et al., 2002b, modified).

Fig. 18.

. (a) The Al (line) and Si (dots) K-XANES spectra of two trioctahedral micas normalised to their white-line centroids (B) showing the energy difference (EE0) in their D features. From similar comparisons carried out on numerous mica spectra, two relationships (b) can be deduced that allow determining from average <T–O> distances the individual atom to oxygen distances of the tetrahedra centred by Si (1.638 Å) and Al (1.778 Å), as well as tetrahedral rotation α (from Tombolini et al., 2002b, modified).

Addendum: A short manual on how to practically record, treat and interpret XANES spectra

in co-operation with Giannantonio CIBIN1 and Augusto MARCELLI2

1 State University Roma Tre, Department of Geological Sciences, Graduate School of Geodynamics, Largo S. Leonardo Murialdo 1, I-00146 Rome, Italy

2 National Institute of Nuclear Physics, Frascati National Laboratories, Via Enrico Fermi 40, I-00044 Frascati RM, Italy

A note of introduction, with some preliminary information

EXAFS gives a direct measurement of local structure properties (e.g. bond length and coordination number) around the selected absorber atom in a quantitative manner, and is also able to recognise the nature of the absorber nearest neighbours. However, the error on the coordination number is quite high (ca. 20%), so that determination of coordination higher than the octahedral one is a hard task. Moreover, EXAFS is not always applicable; e.g., in the case of an extremely low concentration of the atomic species under study, where the S/N ratio is not high enough to permit a reliable extraction of the above structural parameters by using the standard EXAFS data reduction techniques, or in the case of a low absorption signal, where the oscillations are very faint and too difficult to record with good quality over a long enough energy range (k > 12 Å−1). Furthermore, the selected atom may absorb in an energy range where the presence of other absorption edges related to different atomic species does not allow full EXAFS spectrum acquisition, e.g., at the K edges of light elements; or where the multiple edges of the same atom are too close in energy, e.g., the L edges of RE elements. By contrast, the XANES features are much more intense and restricted to a short energy window around the edge, thus their recording concerns only a short energy range; alternatively, over the same experimental time, one can choose to increase the number of XANES spectra to be recorded and/or to use longer acquisition times thus acquiring significant S/N ratios. As general characteristics: XANES is more demanding in terms of energy resolution, whilst EXAFS in terms of S/N ratio.

Thus, the best research strategy is to perform both types of experiments and fully characterise the atom properties using both techniques. As a matter of fact, although the two methods are different from the experimental point of view, some basic optimisation techniques (sample homogeneity, absence of high harmonics in the beam, detector saturation control) remain the same. However, in EXAFS, an absolute calibration of the incident beam energy is not always compulsory for the correct extraction of the EXAFS signal. By contrast, obtaining information on the oxidation state of the absorber from XANES is related to precise measurements of the absolute energy of some spectral structures, so that an accurate calibration procedure is crucial. The techniques usually adopted include both the control of the absolute energy position and of the monochromator stability through the systematic recording, even in the same experimental run, of reference spectra. Such references are either thin pure metal foils of the atomic species under investigation, or materials containing the absorber species in a structural setting having well-known geometrical characteristics and well-determined edge features.

Raw XANES data treatment

Energy calibration

The first step to be performed for experimental data reduction is energy calibration. This can be done by comparison with the energy position of reference spectra collected during the same experimental run. In the last generation beam lines, particular care is devoted to reducing the effects of the high-power white X-ray beam (up to several kW) impinging onto the monochromator crystals. The resulting heating, often concentrated on a small spot, locally changes the crystal temperature, modifies the plane d spacing and, consequently, changes the monochromatic beam energy. The effect may be significantly reduced by cooling the monochromator crystals at very low temperatures: indeed, Si and Ge, the most common monochromator crystals, have the beneficial property of having zero expansion at ca. 77 K: consequently, liquid nitrogen cooling favours maximum crystal stability.

Figure 19a shows the effect of heating the monochromator crystal on the absorption energy of MgO (periclase). The energy changes linearly (Fig. 19b) with the synchrotron ring electron current, which is steadily decreasing with time between two consecutive beam injections. In the data reduction procedure the spectrum energy is corrected using the linear fit calibration line obtained from the collected reference spectra. These reference spectra should be recorded at regular intervals during the experimental run, in between the measurements of the samples. In the transmission mode, when possible, one should measure reference foil spectra taken simultaneously with the sample spectrum using a third ionisation chamber (I2) located after the two ionisation chambers used for the sample transmission experiment. The reference foil should be placed after the second chamber (which measures I1), and the signal of this is used to monitor the incident beam intensity on the metal foil. The reference spectrum is calculated as ln (I1/I2). The experimental sample to be measured is not affected by the reference foil, and its absorption coefficient is calculated as ln (I0/I1), as usual.

Fig. 19.

. (a) Shift of the main peaks of different MgO spectra, taken at different storage ring current values that induced heating to the monochromator crystal. (b) Calibration chart reporting the MgO first absorption peak position as a function of the ring current (data at SSRL beam line 3-3 with (440) YB66 crystals) and linear fitting of the data.

Fig. 19.

. (a) Shift of the main peaks of different MgO spectra, taken at different storage ring current values that induced heating to the monochromator crystal. (b) Calibration chart reporting the MgO first absorption peak position as a function of the ring current (data at SSRL beam line 3-3 with (440) YB66 crystals) and linear fitting of the data.

Background subtraction

In XANES spectra, subtraction of the background signal from the raw data is performed by linear fit (Fig. 20), because the recorded energy range is usually short: a linear fit of the pre-edge region extrapolated to the post-edge region (Fig. 20a) works well in most cases. Exceptions depend on the experimental set up: e.g., in total electron yield measurements at low energy, an electrically insulating material may have poor ground contact and show an exponentially decreasing background. After background subtraction, the spectrum is normalised (Fig. 20b), usually at high energy: a recommended practice consists in averaging the spectrum oscillations at high energies to determine the absorption jump (i.e., the sample absorption coefficient).

Fig. 20.

Cr K-edge muscovite raw data background signal extraction and normalisation. A linear fit calculated in the region before the edge (top) is subtracted from the untreated spectrum. The resulting spectrum is normalised so that the high-energy part oscillations are set to 1.

Fig. 20.

Cr K-edge muscovite raw data background signal extraction and normalisation. A linear fit calculated in the region before the edge (top) is subtracted from the untreated spectrum. The resulting spectrum is normalised so that the high-energy part oscillations are set to 1.

“Fingerprinting”

Reference spectra are those taken on samples having the absorber in known site symmetry and oxidation state. Figure 21 shows the normalised and calibrated Cr K-edge experimental spectrum of a muscovite containing trace impurities of Cr. Comparison with the reference spectra (above) shows immediately that the Cr environment and symmetry in muscovite is similar to those of uvarovite and Cr2O3, and clearly differs from that of SrCO3. The “fingerprinting” rule of thumb says that Cr is in octahedral coordination and in the 3+ oxidation state. The reference standards should be chosen so as to have a chemical environment as similar as possible to the one expected in the sample under investigation: a direct comparison with a Cr metal foil spectrum would not be significant for a metallic sample has a different chemical state and electronic environment; conversely, mineral spectra with Cr in a first coordination shell made of oxygen atoms would be the obvious reference choice.

Fig. 21.

Comparison between the Cr K-edge experimental spectrum of muscovite and some reference standards. The standards are chosen in such a way as to have a known crystal structure and an environment for Cr as close as possible to that of muscovite.

Fig. 21.

Comparison between the Cr K-edge experimental spectrum of muscovite and some reference standards. The standards are chosen in such a way as to have a known crystal structure and an environment for Cr as close as possible to that of muscovite.

Pre-edge analysis

More accurate information on coordination and redox state of transition metals can be obtained by the analysis of the pre-edge features. A first step is to extract the pre-edge structure itself. There is no first-principles theory for this, and only experience can show the right method to follow. The main task is separating the usually small pre-edge peaks from the steeply rising main edge contribution. The subtraction of this contribution heavily affects the pre-edge shape; thus, for consistency, the same procedure should be followed for all experimental spectra. Fitting of the edge rise may be performed by pseudo-Voigt, arctangent or spline curves.

Figure 22 shows how to extract the pre-edge small structures of a Cr-muscovite. The edge rise is fitted by a pseudo-Voigt function, and then subtracted from the experimental spectrum. The resulting pre-edge shape (full dots) is then fitted with Gaussian peaks. In this case, the fit was performed by assigning to one of the structures (the first one at 5992 eV) the energy of the characteristic pre-peak of Cr in tetrahedral coordination, as in SrCrO4, so as to determine the muscovite maximum amount of tetrahedrally coordinated Cr from the intensity ratio of this peak to that of the reference compound (it turned out to be negligible: 0.05 a.p.f.u).

Fig. 22.

Pre-edge signal extraction from the Cr-bearing muscovite spectrum. The edge signal is fitted with a pseudo-Voigt function, and then subtracted from the normalised data. The resulting pre-edge structures are modelled using a two-component peak fitting.

Fig. 22.

Pre-edge signal extraction from the Cr-bearing muscovite spectrum. The edge signal is fitted with a pseudo-Voigt function, and then subtracted from the normalised data. The resulting pre-edge structures are modelled using a two-component peak fitting.

Simulation of XANES spectra

The final step to extract additional information from XANES is to perform simulations, such as those performed in the framework of the MS theory. Knowledge of the crystal structure of the material under study is the necessary starting point (atom positional parameters).

Figure 23 shows the Cr-muscovite optimised full XAFS spectrum and two plots of the muscovite structure as determined by SC-XRD refinement. After the first qualitative analysis that had essentially excluded a significant presence of Cr in tetrahedral coordination (cf. A.2.4), the second question concerns the kind of octahedral site taken by Cr, because in muscovite two octahedral sites occur (M1 and M2) that differ in size and in spatial relationship to the tetrahedral network. Simulations of the XANES region, to verify which the more plausible occupancy is, must start by the choice of the correct potential and cluster size.

Fig. 23.

Cr K-edge muscovite XAFS spectrum (top) and muscovite crystal structure as obtained by SC-XRD (bottom). The bottom panels show the main sites present in a muscovite crystal structure: T1 and T2 are the (Al,Si) tetrahedral sites; M1 and M2 the Al octahedral sites.

Fig. 23.

Cr K-edge muscovite XAFS spectrum (top) and muscovite crystal structure as obtained by SC-XRD (bottom). The bottom panels show the main sites present in a muscovite crystal structure: T1 and T2 are the (Al,Si) tetrahedral sites; M1 and M2 the Al octahedral sites.

The effect of adding increasingly higher-order shells of atoms around the Cr absorber in the calculation is summarised in Figure 24. Calculations have been performed using the atomic positions obtained by XRD crystal structure refinement, and with one Cr replacing one Al atom originally at the M2 site. Introduction of high coordination shells in the calculation induces the appearance and the definition of structures depending on the sum of the single and multiple scattering path contributions present in the clusters. The overall structure of the spectrum is almost the same for the smallest cluster (7 atoms, i.e., the Cr absorber plus 6 oxygen atoms of the octahedron), while changes in the spectral features are observed when crossing from an intermediate to long-range structure (48 and 70 atoms). Differences between the spectra simulated using 70 and 89 atoms are negligible; meaning that additional increase of atoms in the atomic cluster surrounding Cr does not improve the simulation.

Fig. 24.

Cr XANES calculation results obtained for muscovite after cluster size modification. The overall spectral shape is unmodified, but new fine structure details are generated by the introduction of atoms located in the medium- to long-range crystal structures. The similarity of the results obtained using clusters with 70 and 89 atoms suggests that convergence has been reached.

Fig. 24.

Cr XANES calculation results obtained for muscovite after cluster size modification. The overall spectral shape is unmodified, but new fine structure details are generated by the introduction of atoms located in the medium- to long-range crystal structures. The similarity of the results obtained using clusters with 70 and 89 atoms suggests that convergence has been reached.

As for the cluster size, the calculation results strongly depend on the choice of the potential parameters. Different kinds of correlation-exchange potential may be used. Figure 25 shows XANES simulations performed on two clusters, of 7 and 50 atoms respectively, using four different types of potentials. Calculations using the Dirac-Hara and X-α potentials show a more “expanded” spectral shape in the low-energy region than those using the Hedin-Lundqvist potential, but the Dirac-Hara potential seems to be less attractive then the X-α potential. The complex Hedin-Lunqvist energy dependent potential, which includes inelastic losses, produces a smoother spectrum than the real one.

Fig. 25.

Effect of the use of different exchange-correlation potentials in MS calculations, for different clusters (7 atoms, bottom group, and 50 atoms, top group). Note the different spectral contraction and the “smoothing” effect obtained when using Hedin-Lundqvist complex potentials in the calculation.

Fig. 25.

Effect of the use of different exchange-correlation potentials in MS calculations, for different clusters (7 atoms, bottom group, and 50 atoms, top group). Note the different spectral contraction and the “smoothing” effect obtained when using Hedin-Lundqvist complex potentials in the calculation.

Additional options are the choice of the muffin-tin radius, the maximum orbital momentum allowed for the basis functions for the electronic final state, and the intermediate region II constant potential. A maximum value of the orbital momentum lmax < 5 has to be selected, anyway, because calculation time increases quadratically with l. The muffin-tin region is usually restricted to a maximum distance from the atomic centre, with the neighbour atoms radii chosen using Norman's criterion and allowing for a small overlap of the muffin-tin spheres to reduce the size of the interstitial region, where the constant approximation of the potential is poorer. Often calculations are obtained with a “relaxed and screened” potential calculated in the Z + 1 approximation for the excited state. In this case the Z + 1 atomic orbital configuration is selected, then a 1s electron is removed (relaxation) for K edges, and an extra electron added on the outer orbital to mimic screening of the core hole.

Figure 26 shows the result of such a calculation for Cr in either the M1 or M2 site of muscovite, using the real part of the Hedin-Lundqvist potential, lmax = 3 and an overlap between the muffin-tin spheres of 5% in a clusters having 89 atoms. The comparison with the experimental spectrum clearly favours the M2 interpretation. However, agreement is not perfect.

Fig. 26.

MS calculation results for Cr in the M1 and M2 sites (cf. Fig. 23, bottom panels). The different site sizes and local structures determine completely different XANES spectral shapes.

Fig. 26.

MS calculation results for Cr in the M1 and M2 sites (cf. Fig. 23, bottom panels). The different site sizes and local structures determine completely different XANES spectral shapes.

A possible explanation is the deformation of the muscovite local site structure induced by the presence of Cr substituting Al in the M2 site, and a calculation in this direction is shown in Figure 27. We first selected simple deformations, and recalculated the XANES spectrum by scanning the related parameters. The calculated spectra were convoluted with a Lorentzian function having variable width, and every time the convolution parameters were fitted to minimise the difference with the experimental spectra. The deformation scan results show that a structural fitting is possible. Moreover, a variation of the elongation of the Cr-surrounding octahedron in the c* direction (shown in the upper spectra group of Fig. 27) has en effect mainly confined to structures up to ca. 40 eV above the edge. Changes in the radial direction of the octahedral cage (central group of spectra) results mainly in a different weight of the two main peaks at ca. +10 eV. The lower three spectra show the influence of small displacements of next nearest neighbours at intermediate distance, i.e., the Si-O and Al-O tetrahedra surrounding the octahedral layer: these effects are very small.

Fig. 27.

Comparison between the experimental Cr K-edge spectrum of muscovite and the MS calculation result obtained by putting Cr in the M2 site, and considering various small variations of the local Cr environment. Top spectra group: variations after displacement of the octahedral oxygen coordination cage in the c* axis direction. Central spectra group: variations after radial displacement of the oxygen atoms on the a–b plane. Bottom spectra group: effect of an intermediate distance structure deformation; in this case, displacement of the nearest tetrahedra in the radial direction.

Fig. 27.

Comparison between the experimental Cr K-edge spectrum of muscovite and the MS calculation result obtained by putting Cr in the M2 site, and considering various small variations of the local Cr environment. Top spectra group: variations after displacement of the octahedral oxygen coordination cage in the c* axis direction. Central spectra group: variations after radial displacement of the oxygen atoms on the a–b plane. Bottom spectra group: effect of an intermediate distance structure deformation; in this case, displacement of the nearest tetrahedra in the radial direction.

Figure 28 shows our final fit (Cardelli et al., 2003), performed using as free parameters only the vertical size and the radial size of the Cr octahedron. The agreement with the experimental spectrum is excellent, and the determined octahedral size is also in excellent agreement with the XRD values measured on muscovites having their octahedral layer fully occupied by Cr atoms.

Fig. 28.

Final result of the simulation and fitting of the Cr XANES spectrum of muscovite. Top: Comparison between the MS calculated Cr K-edge spectrum after the fitting procedure and the normalised experimental spectrum. Bottom: calculated XANES spectrum using the unmodified structure as obtained by SC-XRD, and used as a starting point for the structural fitting.

Fig. 28.

Final result of the simulation and fitting of the Cr XANES spectrum of muscovite. Top: Comparison between the MS calculated Cr K-edge spectrum after the fitting procedure and the normalised experimental spectrum. Bottom: calculated XANES spectrum using the unmodified structure as obtained by SC-XRD, and used as a starting point for the structural fitting.

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