Skip to Main Content

Abstract

Although absorption of X-rays by matter has been observed since a long time, it is the recent availability of synchrotron radiation sources that has established EXAFS spectroscopy as an important structural tool in geosciences. Nowadays, X-ray Absorption Fine Structure (XAFS, including both the EXAFS and XANES domains) has proven to be an unquestionably useful and powerful method to obtain information on the local and medium-range structural order around a chemical element in condensed matter (solids, liquids, interfaces etc.). This chapter provides basic information on EXAFS (Extended X-ray Absorption Fine Structure), including some recent experimental developments, both on data acquisition and on spectra reduction, and will be illustrated using recent applications in mineralogy, geochemistry, materials science and environmental science. XANES is separately discussed by Mottana (2004) in this volume.

The experimental and theoretical details of extended X-ray absorption fine structure, EXAFS, have been extensively described in the literature (e.g. Teo, 1986; Sayers & Bunker, 1987; Koningsberger & Prins, 1988; Lytle, 1989; Mustre de Leon et al., 1991; Lytle, 1999). Recently, the technique has gained wide popularity, due to major breakthroughs both in EXAFS theory and data analysis with (i) the availability of convenient software packages (www.esrf.fr/computing/scientific/exafs/links.html) and (ii) the development of the use of the ab initio multiple scattering code FEFF (Rehr & Albers, 1990; Zabinsky et al., 1995; Ankudinov et al., 1998; Ankudinov & Rehr, 2003).

Introduction

Although absorption of X-rays by matter has been observed since a long time, it is the recent availability of synchrotron radiation sources that has established EXAFS spectroscopy as an important structural tool in geosciences. Nowadays, X-ray Absorption Fine Structure (XAFS, including both the EXAFS and XANES domains) has proven to be an unquestionably useful and powerful method to obtain information on the local and medium-range structural order around a chemical element in condensed matter (solids, liquids, interfaces etc.). This chapter provides basic information on EXAFS (Extended X-ray Absorption Fine Structure), including some recent experimental developments, both on data acquisition and on spectra reduction, and will be illustrated using recent applications in mineralogy, geochemistry, materials science and environmental science. XANES is separately discussed by Mottana (2004) in this volume.

The experimental and theoretical details of extended X-ray absorption fine structure, EXAFS, have been extensively described in the literature (e.g. Teo, 1986; Sayers & Bunker, 1987; Koningsberger & Prins, 1988; Lytle, 1989; Mustre de Leon et al., 1991; Lytle, 1999). Recently, the technique has gained wide popularity, due to major breakthroughs both in EXAFS theory and data analysis with (i) the availability of convenient software packages (www.esrf.fr/computing/scientific/exafs/links.html) and (ii) the development of the use of the ab initio multiple scattering code FEFF (Rehr & Albers, 1990; Zabinsky et al., 1995; Ankudinov et al., 1998; Ankudinov & Rehr, 2003).

Importantly for geosciences, crystallinity is not required for XAFS measurements, making it one of the few structural probes available for determining interatomic distances, number of neighbours and disorder in non-crystalline materials including glasses (e.g. Galoisy et al., 2001; Cormier et al., 2001; Calas et al., 2002; Galoisy et al., 2003), aqueous solutions and mineral-water interfaces (e.g. Farges et al., 1993; Mosselmans et al., 1996; Kuzmin et al., 1997; Jalilehvand et al., 2001), melts (e.g. Farges et al., 1994; Brown et al., 1995; Farges et al., 2001) and natural materials from the environment (e.g. Morin et al., 1999, 2001, 2002).

XAFS spectra can be measured for each element of the periodic table, with some challenge for elements below sodium. This method is quite unique as it provides information on the local arrangement of atoms up to 6 Å around one given atom, either in the volume or at the surface of a specific material. The information obtained highly complement data from other spectroscopic (e.g. Mössbauer, optical or Raman spectroscopy) or scattering methods (diffraction of X-rays and neutron diffusion). The basic advantages of the XAFS method which are particularly relevant for Earth and environmental science research are: (i) chemical selectivity; (ii) high sensitivity, using fluorescence detection; (iii) the small sample volume analysed; (iv) the possibility to perform in situ measurements, including measurements of dynamic processes (e.g. phase transitions, coordination changes, chemical reactions) under both ambient and extreme conditions; (v) the possibility to use surface-sensitive detection (total yield electron mode) for e.g. the study of adsorption of atoms on surfaces or interfacial reactions (mineral/water).

Fundamentals of EXAFS

Synchrotron radiation

Over the last decades, synchrotron radiation has given major contributions to Earth and environmental sciences. For instance, XAFS has been extensively used to investigate the structure of Earth, planetary and environmental materials (see e.g. the reviews by Calas et al., 1984; Brown et al., 1988; Brown & Sturchio, 2002). The successive generations of synchrotron radiation facilities (see below) have opened new research domains, which would have not been accessible with classical sources (X-ray tubes). Synchrotron radiation provides continuum vacuum ultraviolet (VUV) and X-ray radiation five to ten orders of magnitude brighter than that from sealed or rotating-anode X-ray tubes (Altarelli et al., 1998).

In synchrotron X-ray experiments, the beam is at the same time highly collimated, quasi-parallel (with a divergence of a few mrad) and provides a high brilliance from the hard X-rays ≈ 0.1 Å to the infrared region (see the review by Bassett & Brown, 1990).

The first synchrotron light sources used to produce X-rays for EXAFS experiments were called “parasitic facilities” because the storage rings were primarily built for high-energy or nuclear physics; e.g. the 540 MeV ACO storage ring (Orsay, France) and the 2.5 GeV SPEAR ring (Stanford, USA) began working in 1971 and 1974, respectively. These sources were then updated to meet the standards of the new generation sources; e.g. the Stanford Synchrotron Radiation Laboratory (SSRL, USA) and the Hamburger Synchrotron-Strahlungslabor (HASYLAB, Germany).

The second-generation sources were dedicated to the specific production of synchrotron light (e.g. the Synchrotron Radiation Source, SRS, in Daresbury Laboratory, UK, since 1981). Others synchrotron sources were built at this time in several countries; e.g. in 1981 the National Synchrotron Light Source at the Brookhaven National Laboratory, Long Island, NY, USA; in 1982 the Photon Factory in Japan at the KEK Laboratory in Tsukuba, Japan, and BESSY (800 MeV) in Berlin, Germany; in 1984 the SUPERACO (800 MeV) at Laboratoire pour l'Utilisation du Rayonnement Electromagnétique (LURE), Orsay, France.

Today, insertion devices (e.g. wigglers and undulators) and third-generation sources provide optimised brilliance. In 1994, the European Synchrotron Radiation Facility (ESRF) in Grenoble (France) was the first of this generation of hard X-ray sources to operate with a 6 GeV storage ring. In 1997, the Advanced Photon Source (APS) was built with a 7 GeV source at Argonne National Laboratory (USA), as well as the Super Photon Ring-8 GeV (Spring-8) in Harima Science Garden City in Japan.

Since a decade, third-generation low-energy sources have been also built in several countries such as the Advanced Light Source (ALS) at Berkeley, USA, the Synchrotrone Trieste in Italy or Bessy II in Berlin, Germany, provide energies between 1.5 and 2.0 GeV since 1994 (Robinson, 2001).

Specifications of the third-generation facilities include higher brilliance and lower emittance than former generations, which is necessary for certain XAFS studies requiring high spatial resolution (e.g. element speciation at the microscale, high P–T studies, which require small volume samples). Some characteristics of synchrotron radiation are of major importance for EXAFS, mostly the high intensity over a broad energy range, the high degree of collimation, the polarised character and, to a lesser extent, the pulsed time structure (Winick, 1987; Bassett & Brown 1990).

The X-ray absorption phenomenon

Three main processes are at the origin of X-ray interaction with matter: elastic scattering, inelastic scattering (Compton effect) and absorption related to ionisation (Teo, 1986).

When X-ray photons interact with matter, the photoelectric excitation processes induce an absorption edge when the energy of the photons corresponds to the binding energy of electrons in atomic core levels (1s, 2s etc.). X-rays (wavelength 0.03 < λ < 12 Å or energy 1 < E < 500 keV) are absorbed by all matter through the photoelectric effect. An X-ray photon absorbed by an atom promotes a core-level electron (K, L, or M shell) out of the atom and into the continuum. The atom is left in an excited state with an empty electronic level (core hole). The electron ejected from the atom is called the photoelectron (Fig. 1).

Fig. 1.

Representation of the photoelectric effect: an X-ray photon is absorbed and a core level electron is promoted out of the atom.

Fig. 1.

Representation of the photoelectric effect: an X-ray photon is absorbed and a core level electron is promoted out of the atom.

Origin of EXAFS

After the absorption process, a photoelectron is emitted from a core level of the atom as an outgoing wave. In condensed matter and molecular gases, the emitted wave associated to the photoelectron will be backscattered by the surrounding atoms, giving rise to an interference signal (Fig. 2). XAFS theory took its definite form with the systematic use of synchrotron radiation sources because of the possibility of obtaining high-quality spectra (Stern et al., 1975; Lee et al., 1981; Hayes & Boyce, 1982).

Fig. 2.

A photoelectron wave emitted from the absorbing atom (A) is backscattered by a scattering atom (S). The backscattered wave modifies the final-state wavefunction at the absorber. If the emitted and backscattered waves are in phase, the wavefunction is increased. If the emitted and backscattered waves are out of phase, the wavefunction is decreased (modified after Ellis, 1995).

Fig. 2.

A photoelectron wave emitted from the absorbing atom (A) is backscattered by a scattering atom (S). The backscattered wave modifies the final-state wavefunction at the absorber. If the emitted and backscattered waves are in phase, the wavefunction is increased. If the emitted and backscattered waves are out of phase, the wavefunction is decreased (modified after Ellis, 1995).

X-ray absorption is characterised by the classical Beer-Lambert law:  

formula

in which I0 and I are the intensity of the incident and transmitted beam, respectively, x is the sample thickness and μ the absorption coefficient, which is dependent on incident X-ray energy. This coefficient decreases smoothly with increasing photon energy and exhibits discontinuities which constitute the absorption edges. At the vicinity of the absorption threshold, transitions to bound states may be observed such as the so-called “pre-edge”, which is observed on the low-energy side of the absorption K edge of transition elements. This feature is associated to transitions toward partly empty d states.

The value of the energy of the absorption edge for a given element (E0) can vary by as much as ± 10 eV because the electronic structure can be modified by the local environment and the oxidation state of the absorbing element (Brown et al., 1988).

The EXAFS part of the spectrum is the modulation of the X-ray absorption coefficient related to the above-mentioned interferences of photoelectron waves at photon energies larger than E0 (from 50–70 eV to as much as 1000 eV above the edge). The absorption features observed in the edge region are referred to as X-ray Absorption Near Edge Structure (XANES) and are discussed elsewhere (Mottana, 2004).

EXAFS theory

A theoretical treatment of the EXAFS signal implies three major simplifying assumptions:

  1. the photoelectron is considered to have a large enough kinetic energy to be regarded as a free electron in the interatomic potential;

  2. the process inducing EXAFS oscillations is assumed to be a single-electron process;

  3. in the majority of systems, only simple scattering is considered. However, multiple scattering effects can be important in specific surroundings and will be discussed in a further section.

Figure 3 shows the X-ray absorption spectrum of ZnO at the Zn K edge. The sharp rise of the absorbance is due to a Zn 1s core level electron promoted to the continuum. After this increase, the EXAFS oscillations may be described as a sum of damped sine waves. The modulation of the X-ray absorption coefficient χ(E), is given by:  

formula
where μ(E) is the measured absorption coefficient and μ0(E) is the “background” absorption, a smooth function representing the absorption of an isolated atom. Division by μ0(E), which is proportional to the number of atoms per unit volume, normalises the EXAFS data to a per atom basis.

Fig. 3.

XAFS spectrum of Zn at the Zn K edge in ZnO, showing the XANES and EXAFS domains.

Fig. 3.

XAFS spectrum of Zn at the Zn K edge in ZnO, showing the XANES and EXAFS domains.

To link χ(E) to structural parameters, the X-ray energy E is converted into the photoelectron wavevector, k, defined as:  

formula

E0 is the energy of the threshold and m the mass of the electron. The EXAFS oscillations χ(k) are rapidly damped with increasing k. To enhance these oscillations, χ(k) is multiplied by a power of k (k2 or k3) depending on the mass of the central atom.

The XANES part of the spectrum gives more information on the oxidation state of the element and on the coordination with the neighbours, while the EXAFS part is more specifically used to determine geometrical parameters such as interatomic distances between the investigated absorbing atom and the neighbours in its immediate surroundings, coordination numbers with the nearest and next-nearest neighbours and also the nature of the neighbours.

All this information is obtained through the modelling of the contributions of the successive coordination shells to EXAFS (Calas et al., 1984).  

formula

The index j refers to the jth atomic shell, Rj is the distance between the absorbing atom and the neighbouring atom in the jth shell, ϕj(k) is a phase function related to both central and backscattering atoms. Aj(k) is an intensity term defined as following:  

formula

Nj is the coordination number on the jth shell, fj(k) the backscattering amplitude function corresponding to the atomic species on this shell, σj is the standard deviation associated to the Rj distances and λ is the mean free path length of the photoelectron (typically 4 to 6 Å for electrons with an energy comprised between 100 to 500 eV).

As these equations describing the EXAFS phenomenon do not rely on the periodicity of a lattice, this technique can be used in amorphous as well as crystalline materials, including low-dimensionality systems such as mineral-water interfaces. The single backscattering approximation cannot be used to extract information in the first 50 eV above the absorption edge, corresponding to the XANES region, where multiple scattering is the dominating process. Inelastic processes are responsible for the limited mean free path of the photoelectrons. This process and the Debye-Waller type factor (including both thermal and radial contributions) σ, are responsible for the damping of the EXAFS function at higher photoelectron energy.

The backscattering amplitude function is related to the nature of the backscatterer element. This function decreases monotonously as k increases, more rapidly for light elements (e.g. B or O) than for heavier elements such as sulphur. This amplitude presents a broad maximum in the 5–10 Å–1 region for atoms such as 3d transition elements. Thus, it appears in most silicate minerals that the contribution of the first coordination shell (mostly oxygen) disappears after 300 to 400 eV above the absorption edge and that only cations contribute at higher energy.

Data collection

Monochromator

The polychromatic incident beam delivered by the storage ring is monochromatised by a single crystal, which selects one photon energy for one incident angle, according to the Bragg law. Two parallel crystals are used in order to keep a constant position to the outgoing monochromatic beam. Delivering higher energy harmonics is the major drawback of this technique. Mirrors are used to reject these harmonics: a vertical mirror is set at an incident angle above the critical angle of the higher harmonics but below that of the desired beam energy (Signorato et al., 1999). As this latter is reflected by the mirror, higher harmonics are absorbed, with typical rejection values of 99.9%. Spectral resolution depends on source and beamline geometry but also on the d values of the crystal used as monochromator. However, in contrast with XANES, spectral resolution is not a major concern in EXAFS spectroscopy, as the experimental modulations are usually broad. On modern synchrotron sources, most monochromators require efficient cooling due to beam absorption by the crystals.

Detection

Transmission mode

This detection mode is used for samples with a reasonably high concentration of the investigated elements (> 1%). In this experimental setting, the X-ray beam I0 is getting through the sample. A part of it is absorbed through the photoelectric effect with the probability related to the absorption coefficient μ according to Equation 1.

The absorption coefficient μ is, at most energies, a smooth function of energy, with a value related to the density of the sample ρ, the atomic number Z, the atomic mass A and the energy of the X-ray:  

formula

An EXAFS measurement is thus a measure of the variations of the absorption coefficient μ above the absorption edge as a function of the energy of the X-ray photons getting through the sample. Since each atom has a well-defined core level with a well-defined binding energy, it is possible to select the element to probe by tuning the X-ray energy to an appropriate absorption edge, the values of which are tabulated (e.g. Newville, 2002, at http://cars.uchicago.edu/xafs/).

Fluorescence detection

For diluted samples (from a few ppm to around 10000 ppm), X-ray fluorescence detection is used. The fluorescence signal is proportional to the absorbance (Stern & Heald, 1979).

In the fluorescence mechanism, a high-energy core-level electron fills the deeper core hole, ejecting an X-ray photon of well-defined energy (Fig. 4a, b). For instance, an electron from the M level dropping into a core hole of the K level gives the Kβ fluorescence line. The fluorescence energy is characteristic of the atom: X-ray fluorescence is a common method for quantitative geochemical analysis. In the fluorescence detection scheme, the fluorescence energy characteristic of a given element is selected, and the intensity of the fluorescence is scanned as a function of the incident X-ray beam energy. Various fluorescence lines may be selected, depending on the possible interferences, which may exist in multicomponent systems. In this experimental setting, the sample is set at 45° to the incident beam, and the fluorescence signal is generally measured with a solid-state detector (Derbyshire et al., 1999). The energy dependence of the absorption coefficient μ is proportional to If/I0 where If is the monitored intensity of a fluorescence line. If is directly proportional to the number of absorption events for diluted samples. For more concentrated samples, this proportionality is not maintained and transmission mode must be used instead. The process of fluorescence is not an efficient process and the background is dominated by the Compton effect and elastic scattering, which may be more intense than the fluorescence signal but are filtered out.

Fig. 4.

Representations of the fluorescence and Auger effects. When X-rays are absorbed through the photoelectric effect, the excited core-hole will relax back to a “ground state” of the atom. This will not affect the absorption process. A higher level core electron drops into the core hole, and a fluorescent X-ray (a, b) or an Auger electron (c) is emitted.

Fig. 4.

Representations of the fluorescence and Auger effects. When X-rays are absorbed through the photoelectric effect, the excited core-hole will relax back to a “ground state” of the atom. This will not affect the absorption process. A higher level core electron drops into the core hole, and a fluorescent X-ray (a, b) or an Auger electron (c) is emitted.

Electron yield detection

The second possible process of decay, following the X-ray absorption, is the Auger effect. A core hole in this case is filled by an outer-shell electron from the same atom, and the energy associated with the transition is imparted to a second outer-shell electron which is ejected to the continuum (Fig. 4c). In the hard X-ray regime (> 2 keV) the more likely event is fluorescence, whereas in the soft X-ray regime the Auger effect dominates.

Electrons emitted through the absorption process (primary photoelectrons) and the Auger effect (Auger electrons) can be detected under vacuum; their strong absorption by condensed matter makes this total yield electron detection a surface-sensitive method, which delivers structural information from 20 to 50 Å below the sample surface (Brown & Sturchio, 2002). It is an efficient method for elements with absorption edges at low energies (usually below 3 keV).

ReflEXAFS

Below a critical angle, incident photons are reflected by the surface of the sample. The fluorescence signal may be collected off the sample. Using a thin vertical beam (typically 100 microns), this technique, also called “grazing-incidence”, provides selective information on the surface of a sample, with a depth sensitivity of about 30–50 Å (e.g. Trainor et al., 2002).

Energy dispersive EXAFS

By contrast to the above mentioned experimental settings, in which the spectra are obtained by scanning the incident energy, energy dispersive EXAFS uses a bent crystal monochromator, which at the same time produces a continuous variation of the Bragg angle (and hence of the energy) and focuses the X-ray beam on a small spot at the sample position (e.g. Itié et al., 1989; Comez et al., 2002). The whole spectrum is recorded simultaneously in transmission mode by an energy dispersive detector. A convenient signal-to-noise ratio is obtained by averaging several spectra. As spectra may be recorded in milliseconds, transient processes may be investigated.

Micro-EXAFS

By combining collimation and focusing, a beam spot as small as 10 μm may be obtained. Two devices are used to reduce beam size in manageable increments. The first collimator defines the aperture of the optical system, and consists of a fixed width, horizontal slit and a vertical V-slit, which can be moved independently to produce a beam of about 1 mm size. The second collimation system, a tantalum four-jaw slit assembly, can then reduce this beam, either as white or monochromatic radiation down to 30 μm (white beam). Collimation is at the expense of beam intensity. Higher fluxes can be obtained by using a large variety of focusing optics devices, including Kirkpatrick-Baez mirrors, Fresnel zone plates, tapered glass capillaries, refractive lenses and critical-reflection focusing mirrors. A new device designed by Peter Eng (CARS) consists of two separated mirrors which focus the beam horizontally and vertically. These Rh–coated silica mirrors are dynamically bent to ellipsoid shapes using a mechanical bender. These mirrors can focus a 350 × 350 μm monochromatic beam down to 10 (vertical) × 14 (horizontal) μm resulting in a gain (flux/mm2) of about 1000 over a pinhole (Eng et al., 1995).

The focused beam is then directed to a microscope. A 9-element array detector is used for high count rate work such as microbeam XAFS. A few studies have been done nowadays using this new promising technique developed on different synchrotron sources (e.g.: X26A beam line at NSLS and GeosoilEnvironCARS station at APS) (Mayanovic et al., 1995; Duff et al., 1999; Davenport et al., 2001).

Polarised EXAFS studies

Usually, the information derived from EXAFS analysis is one-dimensional, averaged over all directions. Thus, it is not easy to elucidate 3-dimensional information, e.g. particle morphology, orientation or symmetry. K-edge EXAFS oscillation has a polarisation dependence which is given by the equation:  

formula
where χ(k), k, θ, χi(k) are the total EXAFS signal, the wavevector of the photoelectron, the angle between the ith bond and the X-ray polarisation vector, and the partial EXAFS oscillation associated with the ith bond, respectively.

As synchrotron radiation provides horizontally polarised X-rays, polarisation-dependent experiments can be achieved by altering the orientation of the sample against the polarisation vector of the X-ray (Asakura & Ijima, 2001). Many studies have been devoted to this method in various compounds, especially in clay mineralogy (e.g. Schlegel et al., 1999; Richard-Plouet et al., 2003; Dähn et al., 2003).

Sample environment

Most modern EXAFS stations provide versatile sample environments:

  1. low temperature: As thermal vibrations give a major contribution to the Debye-Waller factor, there is great advantage in collecting data at low temperature, typically 10–20 K using a He cryostat, especially for disordered materials such as glasses (e.g. Galoisy & Calas, 1993a, 1993b).

  2. high temperature: Heating devices allow investigation of reactions up to 1300–1500 °C. Their geometries depend on the recording mode, either transmission (e.g. Seifert et al., 1993; Filipponi & Di Cicco, 1994; Farges et al., 1995) or fluorescence (Farges et al., 1994).

  3. high pressure: Diamond anvil cells may be used with an energy dispersive EXAFS setting to record EXAFS spectra at high pressure (Itié et al., 1997; San Miguel et al., 2000; Ohtaka et al., 2002; Miyauchi et al., 2002).

EXAFS data reduction

Extraction of structural information from the EXAFS signal

The general aspects of EXAFS spectroscopy and data reduction have been presented in a number of review papers and books (see above) and guides to experimental XAFS procedures can be found at the following web sites:

http://cars9.uchicago.edu/xafs/xas_fun/, from M. Newville of the Argonne National Laboratory, Chicago, Illinois;

http://gbxafs.iit.edu/training/tutorials.html, from G. Bunker of the Department of Physics, Illinois Institute of Technology;

http://srs.dl.ac.uk/XRS/Theory/theory.html, from F. Mosselmans and P. Stephenson of the SRS, Daresbury Laboratory, UK.

The EXAFS signal is a simple sum of waves due to the contributions of various types of neighbouring atoms. Data reduction refers to the extraction of the EXAFS signal from the raw absorption data. An oxide glass containing Zr recorded at the Zr K edge is used as an example and the raw absorption spectrum is presented in Figure 5a. The analysis of the extracted signal allows then to derive structural parameters (number of neighbours, N, interatomic distances, d, Debye-Waller factor, σ, mean free path, λ).

The data reduction procedure involves eight basic steps:

  1. subtraction of the pre-edge function;

  2. identification of the threshold energy E0;

  3. normalisation of μ(E) by μ0(E);

  4. removal of a smooth post-edge function;

  5. conversion of μ(E) to μ(k);

  6. Fourier transform (FT) into R space of the k-weighted χ(k) EXAFS signal;

  7. back Fourier transform of a specific peak of the FT to isolate the contribution of specific neighbouring atoms;

  8. least-square refinement of the EXAFS signal to obtain average distance, coordination number, Debye-Waller factor and mean free path.

Fig. 5.

(a)Absorption spectrum of an oxide glass at the Zr K edge. (b) Fit of the pre-edge absorption curve using a Victoreen function. (c) Normalisation of the spectrum. (d) Identification of the threshold energy. (e) Example of a spline function used to model μ0(k) that will be removed from the μ(k) signal.

Fig. 5.

(a)Absorption spectrum of an oxide glass at the Zr K edge. (b) Fit of the pre-edge absorption curve using a Victoreen function. (c) Normalisation of the spectrum. (d) Identification of the threshold energy. (e) Example of a spline function used to model μ0(k) that will be removed from the μ(k) signal.

Subtraction of the pre-edge background

A pre-edge function is subtracted from μ(E) to get rid of instrumental background or absorption from other edges. Before the edge, the background absorbance is estimated by fitting a polynomial function to the absorbance curve using a least-square procedure and extrapolating it to the high-energy end of the spectrum. A polynomial function, a straight line or simply a constant can be used to represent this background (Ellis, 1995). In Figure 5b, a Victoreen function (Cλ3Dλ4) has been used.

Identification of the threshold energy E0

The position of the edge is calculated as the maximum of the derivative of μ(E) or the half-height of the jump (Fig. 5c).

Normalisation to μ0

To normalise the spectrum, the jump at the threshold (Δμ0) is estimated and the spectrum is normalised between 0 and 1 by this value (Fig. 5d).

Removal of a smooth post-edge background approximating μ0(k)

The post edge background is removed from μ(E) by calculating Δμ(E) = μ(E) – μ0(E). As μ0(E) is generally not known, the smooth part of the measured μ(E) after the edge without wiggles or oscillations is assumed to represent μ0(E). The conversion of μ(E) to μ(k) is done using Equation 3.

A smooth curve that best fits μ(k) is taken as μ0(k). Usually, a spline function is used (Fig. 5e). A spline function is a function defined over a series of intervals with each interval containing a polynomial of some order (Teo, 1986). The resulting function is highly flexible as adjacent intervals are constrained to have the same derivative. A least-square procedure is used to fit the spline to the normalised absorbance. However, this function should not match the whole μ(k) signal to avoid removing the entire EXAFS signal but only the low-frequency components of μ(k).

Extraction of the EXAFS signal

After the removal of the post-edge function μ0(k), the final EXAFS function χ(k) is calculated as presented in Equation 2 after conversion from E to k (3).The chi;(k) function is then plotted as a function of k and weighted by k2 or k3 depending of the element investigated to compensate for the rapid attenuation with increasing energy (Fig. 6a).

Fourier transform of the weighted chi;(k) EXAFS signal

In order to isolate the contribution of each atomic shell, a Fourier transform of the experimental EXAFS signal is calculated (Fig. 6b). This FT in the real space has the significance of a partial distribution function relative to the target atom. Each pair of neighbouring atoms relative to the studied element and contributing to the EXAFS signal corresponds to a definite peak (e.g. Zr–O, Zr–Si, Zr–Zr etc.). Before the Fourier transform, a window function is applied that allows selection of the k range to be transformed. This window function can be either a square window or, rather, a smooth window which sets the data to zero at kmin and kmax (e.g. Kaiser or Hanning window).

Fig. 6.

(a) k3χ(k) EXAFS signal for a glass at the Zr K edge. Weighting by k3 amplifies the oscillations at high k values. (b) Fourier transform of the k3chi;(k) EXAFS signal in a glass at the Zr K edge showing two distinct major contributions of neighbours around 1.7 Å and 3 Å without phase correction. (c) Back Fourier transform of the first peak of the FT in (b) of a glass at the Zr K edge and best fit for the first neighbours oxygen shell, (d) best fit for the second neighbours silicon shell.

Fig. 6.

(a) k3χ(k) EXAFS signal for a glass at the Zr K edge. Weighting by k3 amplifies the oscillations at high k values. (b) Fourier transform of the k3chi;(k) EXAFS signal in a glass at the Zr K edge showing two distinct major contributions of neighbours around 1.7 Å and 3 Å without phase correction. (c) Back Fourier transform of the first peak of the FT in (b) of a glass at the Zr K edge and best fit for the first neighbours oxygen shell, (d) best fit for the second neighbours silicon shell.

Fourier filtering

A peak of the FT is isolated with an appropriate window. By a back Fourier transform, the contribution of the corresponding (absorber-neighbour) pair (when Δr > 0.15 Å) can be separated and isolated. The back Fourier transformed curve of each peak is a typical damped sinusoid (Fig. 6c, d). The zeros of this function are obtained when 2kRj + φj(k) = nπ. The analysis of EXAFS data relies on knowledge of the phase-shift φj(k) and scattering amplitude functions Aj(k) (see 4 and 5). If the function φj(k) is known, an experimental value of R can be derived. Many solutions are possible to obtain these two scattering factors: (i) the use of tabulated functions for the various elements (e.g. Teo & Lee, 1979; McKale et al., 1986, 1988), (ii) the determination of the functions from the EXAFS data of reference compounds, (iii) the use of codes that give calculated functions, which in turn can be tested against the EXAFS spectra of suitable model compounds of known structure. One of the most commonly used codes for such analyses is the FEFF suite of ab initio codes (Rehr et al., 1992). Developed at the University of Washington, FEFF is an automated program for ab initio multiple scattering calculations of X-ray Absorption Fine Structure (XAFS) and X-ray Absorption Near-Edge Structure (XANES) spectra for clusters of atoms. The code yields scattering amplitudes and phases used in many modern XAFS analysis ab initio packages. The development of these codes is particularly suited for crystalline compounds (Rehr & Albers, 1990; Zabinsky et al., 1995; Rehr & Albers, 2000; Ankudinov et al., 2002). Once these two scattering factors (phase shift function φj(k) and amplitude function Aj(k)) are obtained, they can be used in EXAFS refinement to derive the structural parameters (interatomic distance R, number of neigbhours N, mean free path λ and Debye-Waller factor σ). Fourier filtering has the advantage of simultaneous removal of the high-frequency noise and the residual background as well as providing equally-spaced data points in k space. The latter is important since the raw data μ(E) with equally-spaced data points in energy space will give, after conversion of E to k, a χ(k) function with increasing density of data points as k increases, because k increases with E1/2.

Two sets of variables are highly correlated in EXAFS refinement: Ai(k), σ, λ, N and φj(k), E0, R. For example, to best fit the data, N and σ values must be increased accordingly. Similarly, an increase of ΔE0 by about 3 eV will cause an increase in R by approximately 0.01 Å. The resolution of EXAFS data can also be calculated using the relation ΔRΔk = 1, where ΔR is the spread of distances and Δk = kmaxkmin is the data length. Thus, an increase in Δk induces a decrease in ΔR. To resolve a distance spread of 0.1 Å, the data length should be > 10 Å–1 in k space. The number of degrees of freedom that correspond to the maximum number of parameters allowed to vary in a least-square fit is given by the relation Nfree = 2ΔRfitΔk/π, e.g. for a filtering window width of 1 Å and a Δk of 12 Å–1, Nftee= 7.

Recent programs for EXAFS data reduction

A catalog of about 40 EXAFS and XANES data reduction programs is available through the International XAFS Society web site (http://ixs.iit.edu/) maintained by Matt Newville and Julie Cross (http://ixs.csrri.iit.edu/catalog/XAFS_Programs). A number of other computer programs are available for analysis of XAFS data on the WEB site http://cars9.uchicago.edu/IXS-cgi/XAFS_Programs. These programs propose many different routines of XAFS data analysis and can work using PC, some of them being also available for Mac, UNIX and LINUX computing systems.

Pratically all of these programs use the FEFF codes to calculate the phase shift and backscattering amplitude functions. These codes are well suited for the analysis of crystalline compounds. However, the interpretations are more difficult in complex systems (i.e., aperiodic structures, adsorption mechanisms, samples under extreme conditions etc.).

FEFFIT

FEFFIT is a data reduction program for the analysis of XAFS spectra. It fits experimental XAFS spectra to theoretical calculations from FEFF analysis (Newville et al., 1995).

Fitting may be done in k or R space, and error analysis is automatically done. A wide range of options are given for modelling XAFS data. A complete description of the program is given on the web site http://cars9.uchicago.edu/ifeffit/feffit.html.

One of the advantages of the calculations made using the FEFF code is that they readily provide multiple-scattering calculations, with an analytical procedure that uses a sum over scattering paths (as opposed to the classical “shells” approach presented above), with no distinction between single- and multiple-scattering paths. The χ(k) model used is an extension of the single scattering form of the XAFS equation which includes a description of the atomic distribution function and corrections to the energy references used in FEFF calculation. In addition to ΔE0, various parameters (N, σ, etc.) are adjustable for each path and are the usual quantities describing the atomic distribution function. C3 and C4 are the third and fourth cumulants used to describe the non-Gaussian distribution of atoms (see below).

EXCURVE

The purpose of EXCURVE (Binsted et al., 1991) is to find a structural model of a material which agrees with the available EXAFS experimental spectra. The user defines the model in terms of atomic types and positions. The program refines the model by calculating a theoretical spectrum for comparison with experiment. EXAFS is calculated using the curved wave theory of Gurman et al. (1984, 1986), the small atom approximation of Gurman (1988) or the Rehr & Albers (1990) scattering matrix formulation. A muffin-tin potential is constructed from atomic potentials calculated within the program. The formulations of von Barth & Hedin (1972) are used for exchange and correlation terms. Parameters of the model are refined by the program to produce the best fit between theory and experiment (http://srs.dl.ac.uk/xrs/computing/UsefulTips/main.html).

SixPACK

SixPACK is a computer package developed by Sam Webb at Stanford University, which encompasses the entire range of XAS analysis (http://www-ssrl.slac.stanford.edu/~swebb/sixpack.htm). The package guides the user through data averaging and calibration, background removal and fitting. This program is based on the IFEFFIT subroutine developed by Matt Newville.

The interface contains six basic modules:

  1. the “SamView” program reads raw data with different formats and allows the user to visualise raw data, average scans, calibrate energy, and perform deadtime corrections for solid state detectors;

  2. a background subtraction module to create normalised μ(E) and χ(k) functions;

  3. a FEFF periodic table interface to create single scattering phase and amplitude paths, compatible with FEFF6 through FEFF8;

  4. a program for the fitting of experimental EXAFS to theoretically derived phase and amplitude files;

  5. a program for linear combination fitting to experimentally obtained reference spectra;

  6. a principal component analysis routine that decomposes data into a set of orthogonal components.

Recent progress in data reduction

In geosciences, materials of mineralogical, geochemical and environmental interest are often chemically and structurally complex. The analytical power of the above-mentioned technique might be greatly diminished in disordered systems, such as glasses or melts, heterogeneous mineral associations or under extreme P–T conditions. XAFS analysis tools have been recently proposed, such as wavelet analysis (Munoz et al., 2003), principal component analysis (Wasserman, 1997; Wasserman et al., 1999), as well as specific codes for the treatment of multiple-scattering interferences or anharmonic effects.

Continuous Cauchy wavelet transform (CCWT) analysis of EXAFS

While classical EXAFS data reduction gives a one-dimensional visualisation of the data, the Continuous Cauchy Wavelet Transform analysis (CCWT) allows information to be obtained in the three following dimensions: the wavevector (k), the interatomic distance uncorrected for phase shift (R') and the CCWT modulus which represents the continuous decomposition of the EXAFS amplitude terms. This method, first applied to petroleum exploration, has been applied recently to EXAFS data reduction, including the removal of the atomic background and the reconstruction of the radial distribution functions (Yamaguchi et al., 1999). A detailed numerical description has been given by Munoz et al. (2003). The various contributions to EXAFS can be determined in detail in both reciprocal and real space. Each component of EXAFS can be visualised through their above-mentioned 3D dependency.

Teo (1986) has shown that the backscattering amplitude functions of the neighbouring atoms often affect the variation in amplitude of a normalised EXAFS spectrum. Thus, atoms with high atomic numbers are more efficient backscatterers at high k values than atoms with low atomic numbers, for which backscattering is more efficient at low k values. As a consequence, the CCWT modulus, being a decomposition of each jth EXAFS amplitude terms, is interpreted based on the graphical analysis of this modulus. In their study, Munoz et al. (2003) gave a very interesting example of the determination of a thorite mineral structure through the CCWT method. The 8 nearest oxygen neighbours of the investigated thorium atom (around 2.0 Å on the FT plot for an effective distance of Th–O = 2.41 Å) are visualised as the first ridge on the CCWT modulus. The extension of the ridge shows that the contribution of the neighbouring oxygen atoms to the EXAFS spectrum cannot be restricted to the isolated FT first peak but are largely more extended, with a k domain ranging from 2 to 14 Å–1 and centred around 6 Å–1. From ab initio EXAFS calculations using the FEFF 7.0 package, this result appears coherent with the maximum of the theoretical amplitude term of the contribution of the 8 oxygen neighbours of the investigated Th atom. Another example shows that the FT at the Mo K edge in a sulphur bearing silicate glass consists mainly of two associated peaks centred at 1.4 Å and 1.8 Å. From classical EXAFS data reduction it was not possible to distinguish between the contributions of two oxygen shells, two sulphur shells, or one oxygen shell and one sulphur shell because the two peaks were too close together (ΔR' = 0.4 Å). Using the CCWT calculation the authors show clearly two distinct shapes for both contributions on the CCWT modulus in accordance with two distinct types of atoms surrounding the central Mo atom. The closest contribution being centred at low k values was more relevant to oxygen atoms whereas the second contribution was more likely associated to sulphur. From this study, it appears that Mo tends to form oxy-sulphur complexes in sodium trisilicate glasses, a form that can help understand its transport properties in magmas. This new technique appears promising in complex systems.

EXAFS data reduction through principal components analysis

The above mentioned data reduction methods are not sufficiently efficient however, when the system under investigation is a heterogeneous mineral mixture. Each of the species may present different local environment around the absorbing element (Frenkel et al., 2002). Principal component analysis (PCA) is a method that gives access to the number of chemically distinct species in the investigated system. In studies of complex systems such as those encountered in Earth sciences, environmental sciences or life sciences, principal component analysis (PCA) has been used recently to investigate series of EXAFS or XANES spectra of samples that exhibit changes in structure or composition (Coulston et al., 1997; Fernandez-Garcia et al., 1995; Wasserman et al., 1996, 1997). PCA allows to analyse systematically such series and simplify the process of extraction of the information from the various spectra (Wasserman et al., 1999).

The standard PCA scheme represents each experimental spectrum as a vector xi (i = 1, …, M) in the N-dimensional space, where N is the number of data points in each spectrum and M is the number of spectra. The data matrix D, of the dimension M × N, is constructed from all the datasets. It is then possible to construct an ordered orthogonal basis by finding the M eigenvectors and eigenvalues of D, and by arranging the eigenvectors in the descending order of eigenvalues. Each original spectrum is represented as a linear combination of M basic vectors (components). By selecting the eigenvectors having the largest eigenvalues, all the datasets can be represented by using a linear combination of just a few (Mc) principal components. As Mc < M < N, the PCA provides a convenient way to reduce the dimension of the representation. The first component, which is essentially the average of all the sample data, commonly dominates the analysis.

The EXAFS oscillations, once normalised and background-subtracted, represent the PCA vectors xi. The dimension N is the number of energy points in the EXAFS spectrum. The Mc principal components necessary to reconstruct the original data correspond to Mc distinct species in the original EXAFS spectra. Thus, it is possible to determine the species present in the sample without any assumption. At subsequent stages of analysis, the species are identified by comparison of suitable experimental (or theoretical) standards with a linear combination of the obtained components. The mixing fractions of different species in all samples are then obtained by a linear least-square fitting procedure. Furthermore, the PCA method allows the detection of changes in the data that would normally be considered below the sensitivity level of traditional EXAFS analysis methods. This approach has been recently used to analyse heavy metal speciation in contaminated systems (Isaure et al., 2002).

An example of program allowing the principal component analysis is EXAFSPACK, a suite of programs for XAFS data analysis which was developed by Dr. G. N. George (SSRL, USA).

Anharmonicity effects

EXAFS data reduction may be influenced by thermal disorder effects, through a reduction of the amplitude of EXAFS oscillations and a modification of the phase-shift function (Fornasini, 2001). The standard treatment of thermal disorder in EXAFS through a harmonic Debye-Waller factor (Lee et al., 1981) has proved to be inadequate for measurements of solid materials or melts at high temperature or pressure. Anharmonic effects cannot be neglected in such systems (Farges et al., 1995). Data analysis may use a cumulant expansion approach, which facilitates both the theoretical interpretation and the experimental analysis of anharmonicity (Dalba et al., 1993).

Let us consider a Gaussian isotropic three-dimensional distribution of distances between the absorber atom and one atom of a given coordination shell ρ(r) with a Debye-Waller factor σ. For σ << R, the one-dimensional real distribution can be expressed as:  

formula

while the effective distribution of distances P(r, λ) is expressed by:  

formula

The EXAFS signal can be expanded in a series of cumulants, Ci, of the effective distribution P(r,λ):  

formula
with even and odd cumulants determining the amplitude and the phase of the EXAFS signal, respectively. By comparison with a reference sample, the Cn cumulants can be obtained.

The difference between the phases of the EXAFS signal is given by:  

formula

The logarithm of the amplitude ratio is given by:  

formula
with forumla, s being the label of the unknown sample and r the label of the reference. The phase difference and the logarithm of the amplitude ratio are then fitted by finite polynomials of relatively low degree and the ratio of coordination number Ns/Nr is obtained (Dalba et al., 1993).

The mean interatomic distance Rs can be obtained through the expression of the first cumulant:  

formula

The SEDEM package (http://www.esrf.fr/computing/scientific/exafs/sedem.html) is an example of a code which performs a phenomenological analysis of EXAFS data by the cumulant method.

Multiple scattering interferences

Multiple scattering effects (MS) do not affect, generally, the single scattering EXAFS signal. However, if atoms (including the absorbing atom and its neighbours) are arranged in a collinear array, EXAFS contributions from neighbouring atoms can be observed as far as 6–7 Å. The scattering of the electron is strongly focussed in the forward direction (θ = 180°) and falls off rapidly for θ = 150° and smaller angles. MS affects both the amplitude and the phase but the amplitude is greatly enhanced due to strong forward scattering of the outgoing wave – the so-called “focusing effect”. The short-range single scattering theory of EXAFS is no longer relevant in this case and MS processes involving the intervening atoms must be taken into account. Since the EXAFS formulation of Teo (1986), which takes into account the effect of MS, many papers dealing with this phenomenon have been published (Westre et al., 1994; Rossano et al., 1999; Rossano et al., 2000).

There are specific codes for data treatments dealing with MS interferences; one example is GNXAS (http://www.aquila.infn.it/gnxas/). This software package is composed of a series of FORTRAN programs for EXAFS data analysis (Crymol, Phagen, Gnpeak, Gnxas, and Fitheo) together with several programs for sample optimisation, automatic background subtraction, and edge analysis (Di Cicco, 1995, 1997). This package allows accurate MS EXAFS calculations, achieving a reliable refinement of the structural models in the short range. It is possible to treat liquid phases or disordered systems and extract reliable g(r) functions in the short-range limit (5 Å).

EXAFS studies in geosciences

X-ray diffraction and microscopic analysis (SEM or TEM) are essential to obtain information on mineralogically complex systems, dilute elements or heterogeneous matrix. Due to the specifics mentioned above, XAFS highly complements these methods in the analysis of such complex systems. Important applications in geosciences include:

  1. structural environment and chemical bonding of trace elements in minerals, including site relaxation;

  2. environments of minor and trace components in disordered mineralogical systems: gels, glasses, melts and supercritical fluids;

  3. speciation of heavy metals in sediments and soils;

  4. speciation of elements in aqueous solutions;

  5. crystal chemistry at mineral-aqueous solution interfaces;

  6. intersite distribution of minor and trace elements;

  7. local structure of nanocrystalline minerals, gels and colloids;

  8. sorption of aqueous metal ions on high surface area minerals;

  9. nucleation and crystallisation processes;

  10. structural modifications during phase transformations in minerals, glasses and melts;

  11. in situ high P/T studies;

  12. kinetic processes.

Using examples from geochemical, mineralogical and environmental sciences, we will illustrate recent applications of EXAFS spectroscopy, which take advantage of specific experimental devices and recent data reduction codes.

Structural environment and chemical bonding of trace elements in minerals

Intracrystalline distribution of a minor amount of Ni in San Carlos olivine has been determined (Galoisy et al., 1995) using Ni K-edge fluorescence EXAFS spectroscopy. The mean Ni–O distance dNi–O = 2.08 å suggests a preferential location of Ni in the M1 site of the structure. This distance is smaller than the Mg–O distance in the M1 site of α-Mg2SiO4 (mean dM1–O = 2.10 å) and is similar to the average M1 cation-oxygen distance in olivines close to the San Carlos composition (mean dM1–O = 2.09 å). The Ni for Mg substitution induces an important relaxation effect resulting in a smaller mean M1–O distance (Fig. 7). The medium-range distribution of Ni in this natural olivine structure was estimated by modelling EXAFS spectra, considering various M1 and M2 cation distributions around M1 (Ni) sites (Fig. 8). These models suggest medium-range ordering of Ni and Fe in adjacent M1 and M2 sites of the olivine structure and non-ideal behaviour of Ni in San Carlos olivine. These findings emphasize that actual distortions at imperfectly sized impurities are not represented well by X-ray diffraction studies, which average over different atom types at a given site. As a consequence, Vegard's law-type behaviour for interatomic distances in a solid solution does not hold at a microscopic scale.

The coprecipitation of trace elements during crystal growth is one of the most studied water-mineral interactions. Aspects such as distortion and site relaxation and the possible existence of clustering of trace elements or short range order are fundamental to understand the partitioning behaviour and stability of dilute solid solutions, and the sequestering of toxic metals in minerals. The direct determination of these structural parameters has been done for individual divalent heavy metals (Co, Zn, Pb, and Ba) coprecipitated in synthetic and natural calcite using X-ray absorption fine structure (XAFS) spectroscopy (Reeder et al., 1999). XAFS spectra were collected at beamline X-11A of NSLS, BNL (USA). Spectra were collected at ∼ 77 K to minimise anharmonicity and to improve signal/noise ratio. Similar environment was found around Co2+ in natural and synthetic calcite with a mean dCo–O = 2.15å showing that Co occupies the unique

Fig. 7.

Linear relationship between and d(Ni–O) in various Mg-Ni olivines. The San Carlos sample in this study deviates from the general trend. Samples: A – Fujino et al. (1981), B, C, D, G, H, J – Boström (1987), E – Rajamani et al. (1975), F, I – Bish (1981), L– San Carlos olivine.

Fig. 7.

Linear relationship between and d(Ni–O) in various Mg-Ni olivines. The San Carlos sample in this study deviates from the general trend. Samples: A – Fujino et al. (1981), B, C, D, G, H, J – Boström (1987), E – Rajamani et al. (1975), F, I – Bish (1981), L– San Carlos olivine.

Fig. 8.

(a)Simulation of the Fourier transform of the environment of Ni in San Carlos olivine using the (Mg)2SiO4 structure; only Mg atoms are assumed in M1 and M2 around Ni. (b) Mg and Ni atoms are assumed in M1 and M2 around Ni. (c) Ni, Mg and Fe atoms are assumed in M1 and M2 around Ni.

Fig. 8.

(a)Simulation of the Fourier transform of the environment of Ni in San Carlos olivine using the (Mg)2SiO4 structure; only Mg atoms are assumed in M1 and M2 around Ni. (b) Mg and Ni atoms are assumed in M1 and M2 around Ni. (c) Ni, Mg and Fe atoms are assumed in M1 and M2 around Ni.

octahedral Ca site. Similar environment is found for Zn2+ with a dZn–O = 2.14 å typical of an octahedral coordination. Neither Co–Co nor Zn–Zn distances were identified, indicating no clustering of these elements in the calcite structure. For Ba2+, the longer dBa–O = 2.68 å indicates a dilation of the Ca octahedral site consistent with the larger size of Ba. Pb2+ occupies also the 6-fold site and no Pb–Pb backscattering was identified. The investigated heavy metals all substitute in the unique Ca site with varying degrees of local distortion. Analysis of the local distortion and relaxation around the impurities shows a contraction of the structure around Co2+ and Zn2+ with a relaxation largely confined within 6–7 å of the impurity. Relaxation around Pb and Ba also appears to be restricted, but extending further for Ba than for Pb. However, the substitution complies with the structure of calcite. This may be understood through the corner-sharing topology of the structure. The strain around an impurity may not be determined solely by the size of the substituting ion; rather the adaptation of the site and its immediate surrounding also plays a significant role.

The substitution of Sr for Ca in aragonite depends on temperature, and different authors use Sr/Ca ratios in coral aragonite as an indicator of local sea surface temperature (SST) in present and past seawaters. However, Sr concentration of coral aragonite is above the thermodynamic solubility of Sr in aragonite. Microanalytical studies have effectively indicated that Sr is more heterogeneously distributed in some coral skeletons than expected from SST data. Variations in the size and/or quantity of these domains may account for Sr heterogeneity at small scale and may explain the deviation of some corals from the expected relationship. In situ application of the X-ray microprobe (5 μm resolution) was used to map Sr/Ca variations (Allison et al., 2001). EXAFS measurements were made with a 5 μm diameter X-ray beam on individual spots corresponding to Sr-high and Sr-low areas. No difference was evidenced between these areas, indicating that Sr is in the same structural state. The differences in the peaks between 3 and 4 å are diagnostic and clearly show that Sr substitutes for a Ca atom in the aragonite structure and that domains of Sr carbonate (strontianite) are absent or in minor abundance. Strontium heterogeneity may reflect nonequilibrium processes of calcification. The interpretation of Sr/Ca ratios in terms of SST may be complicated, especially when attempting to extend the temporal resolution of the technique. The micro-EXAFS technique may be interesting in the push to higher temporal resolution, because this technique allows the selection of coral microvolumes for Sr/Ca measurement where strontium is incorporated in a known structural environment.

The horizontal polarisation of synchrotron radiation allows polarisation-dependent studies of oriented single crystals. An interesting illustration of the kind of information polarised EXAFS can provide in compositionally complex minerals is given in a recent study by Dähn et al. (2003) on smectites used as geochemical barriers in nuclear waste repositories.

In montmorillonite, X-ray absorbing atoms in the octahedral sheet are surrounded by neighbouring cations at R = 3.00 å in the octahedral sheet and R = 3.15 to 3.23 å in tetrahedral sheets. This local structure results in a strong overlap of scattering contributions from the octahedral and tetrahedral cations. In preceding papers, Manceau and coworkers have shown that this limitation can be easily overcome by polarised EXAFS (P-EXAFS) spectroscopy (Manceau et al., 1988; Manceau, 1990; Manceau et al., 1998; Schlegel et al., 1999). In the study by Dähn et al. (2003), the uptake mechanism of nickel (a fission product in nuclear waste materials) on montmorillonite was investigated with P-EXAFS.

Ni K-edge XAFS spectra were recorded on the ID26 beamline at the European Synchrotron Radiation Facility, Grenoble, France. P-EXAFS spectra were recorded with the electric field vector e at 10, 35, 55, and 80° with respect to the film plane. Data reduction was carried out with the WinXAS 97 2.1 software package (Ressler, 1998). Amplitude and phase shift functions were calculated using the FEFF 8.0 code (Rehr et al., 1991). The P-EXAFS data show angular dependence that allows in-plane and out-of plane contributions to be distinguished. Spectral analysis leads to the identification of three nearest cationic subshells with distances characteristic of edge-sharing linkages between Al and Ni octahedra and of corner-sharing linkages between Ni octahedra and Si tetrahedra, as in clay structures. The angular dependence of the Ni-Al and Ni-Si contributions indicates that Ni-Al pairs are oriented parallel to the film plane. The study reveals the formation of Ni inner-sphere mononuclear surface complexes located at the edges of montmorillonite platelets and, thus, that heavy metals binding to edge sites is a possible sorption mechanism. The attachment of metal ions specifically bound to clay mineral surfaces can severely reduce their bioavailability and mobility in soil and water environments. Thus molecular-level structural information from P-EXAFS measurements has proved to be essential for improving models on the fate of heavy metals in the geosphere.

Environments of trace elements in disordered mineralogical systems

Gels are an important class of disordered Earth materials from low-temperature sedimentary environments known as intermediate stage in the formation of supergene minerals (Brown et al., 1988). Natural gels represent reactive components with large specific areas.

The trapping mechanisms of uranium by natural gels during the oxidation of solutions percolating in a uranium mine have been investigated by Allard et al. (1999). EXAFS spectra were collected at LURE (Orsay, France) at the U LIII edge. Spectra were recorded at 10 K to minimise thermal disorder effects. EXAFS data were analysed using computer software written by Michalowicz (1991). Backscattering amplitude and phase functions were calculated using the FEFF6 code.

The U-bearing Si/Al-rich gels exhibit a local structure consisting of edge-sharing uranyl polymers. The contribution of uranyl groups (UO2)2+ prevails in the EXAFS spectra. Their geometry is characterised by two axial oxygen atoms at d(U–Oax)= 1.80 å and four equatorial oxygen atoms, at two distinct distances d(U–Oeq1) = 2.33 å and d(U–Oeq2) = 2.48 å (Fig. 9). A weak contribution near 5.5 å was assigned to a multiple scattering effect within the linear uranyl O–U–O bonds (Fig. 10). EXAFS data are consistent with uranophane-like local structure, indicating a coprecipitation process of U, Si and Al. In contrast, no U–Fe, U–Si/Al nor U–U contributions are evidenced in the Fe-rich gels. EXAFS data suggest that U is sorbed or complexed, the distinct U–Oeq distances are not consistent with outer-sphere complex species. This natural case study gives constraints on the modelling of uranium sorption and coprecipitation mechanisms in a quaternary system U–Si–Al–Fe. Relevance of such geochemical systems is emphasized, as the mobility of uranium at the Earth's surface may be reduced by the scavenging properties and independence on redox processes of the (Si,Al) gels.

Fig. 9.

U L-edge uranyl EXAFS, for cluster structure as in soddyite: FEFF6 calculation of Fourier transform including multiple scattering (MS) or without multiple scattering (no MS). Owing to the practical linearity of O–U–O, multiple scattering mostly concerns axial oxygen Oax and contributes at twice the U–O distance.

Fig. 9.

U L-edge uranyl EXAFS, for cluster structure as in soddyite: FEFF6 calculation of Fourier transform including multiple scattering (MS) or without multiple scattering (no MS). Owing to the practical linearity of O–U–O, multiple scattering mostly concerns axial oxygen Oax and contributes at twice the U–O distance.

Fig. 10.

Model showing the main contributions arising from 1–2–3–4, 3–4–3–4, 1–5–4 and symmetric legs.

Fig. 10.

Model showing the main contributions arising from 1–2–3–4, 3–4–3–4, 1–5–4 and symmetric legs.

EXAFS provides original information on the local atomic arrangements and more extended topologies (up to 6 å) in oxide glasses (e.g. Greaves, 1985; Calas et al., 1995; Calas et al., 2002). Glass structure consists of the coexistence of a polymeric network (silicate, borate etc. units) and of cations which act either as modifying elements by breaking the connectivity of the polymeric network, or as charge-compensating cations (Greaves, 2000; Galoisy et al., 2000). The cationic arrangement is difficult to investigate because of the chemical complexity of oxide glasses. By contrast to polyanions, in which the local geometry is generally well determined, cations may occur in a wide diversity of local surroundings which may have different influence on the properties of the glass/melts systems (colouration processes, crystal/liquid element partitioning, nucleating behaviour etc.).

Recent spectroscopic data on transition elements show that specific site geometries prevail in silicate glasses. Nickel usually occupies octahedral sites in crystalline phases due to its high crystal-field stabilisation energy at this site (Burns, 1993). However, Galoisy & Calas (1993a) have shown that nickel occurs in oxide glasses in unusual five- and four-fold coordinations, the proportion of which depends on the chemical composition. Ni K-edge EXAFS data on vitreous and crystalline CaNi2SiO6 show that the Ni–O distances and numbers of oxygen nearest neighbours are smaller in the vitreous state than in the crystalline one, i.e. dNi–O = 1.98 å and 2.07 å and N = 4.5 and 6, respectively. These EXAFS results together with the data from crystal field spectroscopy (Galoisy & Calas, 1993a, 1993b) are in accordance with a predominance of 5-fold coordinated Ni (Fig. 11).

Fig. 11.

Model of the environment of [5]Ni in glasses, reconstructed from the EXAFS-derived Ni–O distances.

Fig. 11.

Model of the environment of [5]Ni in glasses, reconstructed from the EXAFS-derived Ni–O distances.

If 5-fold coordination is unusual in crystalline solids, several other transition elements, such as divalent iron or tetravalent titanium, were found to be located at this site in oxide glasses (Rossano et al., 1999; Cormier et al., 1996).

Transition elements can also occur in a network-forming position, as observed for Ni in glasses containing potassium (Galoisy & Calas, 1992). The mean EXAFS-derived dNi–O = 1.95å is a typical value for tetrahedral Ni. Ni-Si contributions are consistent with NiO4 tetrahedra sharing corners with SiO4 tetrahedra (Fig. 12). The [4]Ni–O–Si inter-tetrahedral angle indicates that corner-sharing NiO4 and SiO4 tetrahedra belong to 4- or 5-membered rings or strongly distorted 6-membered rings, whatever the charge of the charge-compensating cation. [4]Ni may be stabilised in a silicate framework, however, the probability that three-dimensional silicate networks can accommodate divalent network-forming cations is higher if charge compensation is realised by large, low field strength cations. We have used the Pauling rules, which indicate how the electrical neutrality of the glass components is locally ensured, to propose the above mentioned simple models for the local structure of oxide glasses, around Ni.

Fig. 12.

Model of the [4]Ni surroundings in the K2NiSi3O8 glass showing the connection of the NiO4 tetrahedron with the SiO4 glassy network.

Fig. 12.

Model of the [4]Ni surroundings in the K2NiSi3O8 glass showing the connection of the NiO4 tetrahedron with the SiO4 glassy network.

Spectroscopic techniques such as EXAFS show clear evidence that cation-oxygen distances in oxide glasses are often smaller than in compositionally equivalent crystals. These small coordination numbers may be related to the statistical position of atoms in a liquid which does not allow the simultaneous presence of charge compensating cations around oxygen atoms made necessary by high coordination numbers. A major recent finding is that cations such as transition elements are not spread uniformly throughout the glass structure. Cation ordering in oxide glasses at both short range order (SRO) and medium range order (MRO) scales shows the inconsistency of the principle of randomness, that all possible structures are equally probable.

These data bear some similarity with the modified random network (MRN) proposed by Greaves (1985), in which alkalis form clusters which can percolate in channels. The MRN provides a simple representation of the MRO in glasses and suggests explanations for physical properties such as ionic transport by the diffusion of the mobile species through the pathways offered by these channels (Greaves & Ngai, 1995). Further progress will include a better incorporation of numerical simulation of glasses as well as the structural modifications induced by high temperature/pressure, in relation with the evolution of physical and chemical properties.

Energy dispersive X-ray absorption spectroscopy (EDXAS) is a major mark of advance in the X-ray absorption domain to study time-resolved structural changes (e.g. Charnock et al., 2003) or the structural evolution of glasses under extreme conditions, when coupled to a diamond anvil cell (DAC). Majerus et al. (2004, in print) have recorded the pressure-induced coordination change of Ge from [4]Ge to [6]Ge through in situ high-pressure EDXAS measurements at the Ge K edge, in SiO2–GeO2 tetrahedral framework glasses. xSiO2–(1 – x)GeO2 glasses with x = 30, 50, 65 and 80 were prepared and XAS experiments were performed at the D11 beamline (LURE, Orsay, France). The experimental dispersive set-up using a bent Si(220) crystal is shown in Figure 13. This experimental set-up will be soon available at SOLEIL (Orsay, France). The use of a bent monochromator offers the advantage of eliminating the stepwise scanning of the X-ray energy. An energy range is opened in the reflected beam by the continuous change of the Bragg incidence along the bent crystal. A position-sensitive detector allows using the correlation between position and energy of the X-ray. The most important advantages of EDXAS are the focusing optics, the short acquisition time (a few ms) and the great stability during the measurements because of the absence of any mechanical movement. These three advantages allow the study of small samples (40 μm in the future SOLEIL), to follow kinetics and to perform experiments demanding a low signal to noise ratio.

Fig. 13.

Scheme of the EDXAS setup coupled with a diamond anvil cell showing the bent mirror and the focusing of the X-ray beam on a small spot on the sample. The whole spectrum is then collected by an energy dispersive detector.

Fig. 13.

Scheme of the EDXAS setup coupled with a diamond anvil cell showing the bent mirror and the focusing of the X-ray beam on a small spot on the sample. The whole spectrum is then collected by an energy dispersive detector.

The EXAFS signals in the SG30 glass containing 4-fold Ge at 0.7 GPa and 6-fold Ge at 26.8 GPa are shown in Figure 14 (a and b, respectively) along with the SG80 glass at 25.1 GPa (Fig. 14c). The FT-filtered oscillations of the Ge–O peak were fitted with one Gaussian shell. The mean Ge–O distances and Debye Waller (σ) factors obtained for the SG30 sample were dGe–O = 1.73 ± 0.01 å (σ = 0.055 ± 0.005 å) at 0.7 GPa, and dGe–O = 1.81 ± 0.02 å (σ = 0.092 ± 0.005 å) at 26.8 GPa. The fit for the SG80 sample at 25 GPa gives a mean Ge–O distance of about 1.78 ± 0.02 å with σ = 0.09 ± 0.01 å. This indicates that the Ge coordination change is not completely achieved in this sample at this pressure. The Ge coordination change shows that the Ge local structure is strongly affected by Si and extends over a higher pressure range when the SiO2 content increases. The decompression is characterised by a hysteresis, which amplitude decreases with increasing SiO2 content (Fig. 15).

Fig. 14.

k3χ(k) EXAFS signal in the SG30 glass at 0.7 GPa (a), at 26.8 GPa (b) and in the SG80 glass at 25.1 GPa (c).

Fig. 14.

k3χ(k) EXAFS signal in the SG30 glass at 0.7 GPa (a), at 26.8 GPa (b) and in the SG80 glass at 25.1 GPa (c).

Fig. 15.

Compression and decompression in SG30 and SG80 glasses showing hysteresis (data from both EXAFS and XANES spectra reduction). The amplitude of the hysteresis decreases as the SiO2 content increases.

Fig. 15.

Compression and decompression in SG30 and SG80 glasses showing hysteresis (data from both EXAFS and XANES spectra reduction). The amplitude of the hysteresis decreases as the SiO2 content increases.

Figure 16 shows the pressure–composition diagram presenting three domains with distinct short-range structures. At low pressure, a tetrahedral framework structure (T) prevails, then, an intermediate domain with a mixture of [4]Ge and [6]Ge appears, and at higher pressure, the Oc domain corresponds to a structure with [6]Ge. The notion of polyamorphism would apply to the tetrahedral (T) and octahedral (Oc) framework domains. Since this polyamorphism is observed in the non-ergodic glassy regime, the question of its thermodynamic nature is challenging and different possibilities may be proposed. The T and Oc local structures could refer to: (i) two distinct amorphous phases, with their own metastability domains, separated by an activation energy barrier (this behaviour implies a first-order type transformation process involving coexistence of both local structures); (ii) the relaxation of the glass, from T toward Oc local structures, through continuous configurational rearrangement involving an intermediate fivefold coordination state. The data analysis supports the hypothesis of a kinetically hindered first-order polyamorphism in the entire SiO2–GeO2 binary.

Fig. 16.

Pressure-composition domains: T domain with only tetrahedral Ge, T + Oc domain with both [4]Ge and [6]Ge and Oc domain with only octahedral Ge.

Fig. 16.

Pressure-composition domains: T domain with only tetrahedral Ge, T + Oc domain with both [4]Ge and [6]Ge and Oc domain with only octahedral Ge.

Environmental mineralogy

Soils are known to be effective sinks for heavy metals released in the environment. The knowledge of the chemical form adopted by toxic metals, often at trace levels, allows a better understanding of their mobility, toxicity and bioavailability for the assessment of the environmental risk and for developing effective remediation methods for their removal. Juillot et al. (2003) showed that EXAFS is particularly well suited when associated with chemical analytical techniques to distinguish between many environments for the same element in complex multiphase systems. In their study, these authors investigated Zn speciation in two smelter-impacted soils located near a Pb and Zn processing plant in Northern France.

Zn K-edge EXAFS data were recorded on the high-flux wiggler beamline (BLIV-3) at SSRL (USA). X-ray fluorescence spectra were collected with a 13-element Ge-array detector. EXAFS data reduction was performed using the XAFS 2.6 PPC program of Winterer (1997). Phase shift and amplitude functions were calculated using the ab initio FEFF 8 code.

Ten well-characterised reference model compounds were recorded and analysed. For both soils, chemical analysis of the dense coarse fraction shows the presence of about 1% of crystalline ZnS (sphalerite and wurtzite). In this fraction, EXAFS data reduction indicates the localisation of Zn in the tetrahedral sites of a magnetite-franklinite solid solution, likely inherited from high-temperature smelting operations. This spinel form is considered to be a stable form of zinc in soils. The fraction < 2 μm (clay fraction) contains the highest concentration of Zn in both samples (77 and 62% of total Zn in the tilled and wooded soils, respectively). In this fraction, Zn is present in many forms: Zn outer-sphere complexes, Zn inner-sphere complexed with organic matter, Zn/Al hydrotalcite (a phyllosilicate in which Zn is present in the dioctahedral layer) and also in magnetite-franklinite. EXAFS is the most direct approach to determine the occurrence of the specific form in which heavy metals occur on the Earth's surface. For instance, the presence of Zn/Al hydrotalcite in Na4P2O7-treated soil samples is demonstrated by the persistence of a Zn–Zn pair correlation at 3.10 ± 0.04 å in EXAFS data, representing edge-sharing ZnO6 octahedra in the trioctahedral layer structure. This feature disappears after chemical treatment of the samples with 0.45 M HNO3. This study demonstrates the ability of EXAFS to identify multiple zinc phases in a heterogeneous sample, with a quantitative accuracy of about 25% for the zinc-containing phases considered.

EXAFS presents many advantages to characterise the nature of the species formed by a metal in solution: its chemical selectivity and high sensitivity to the weak signal of the complexes as compared to the large background contribution of the solvents and its possible use for determining element speciation in situ at elevated temperatures and pressures. Mosselmans et al. (1996) analysed the speciation of metals in hydrothermal fluids to understand better the metal transport and the formation of hydrothermal ore deposits. The structural information obtained is more direct than e.g. using solubility studies or fluid-inclusion techniques.

Three systems have been investigated in this study, Co(II)–Cl, Na2MoO4 and Cd(II)–Cl in aqueous solutions. The XAS study was performed on stations 8.1 (Co K edge) and 9.2 (Mo and Cd K edges) of the S.R.S. at the CCLRC Daresbury Laboratory. Experiments on Mo and Cd solutions were performed in quartz tubes, sealed under argon. Quartz being too absorbing at the Co K edge, a special titanium cell was designed. The temperature was controlled using an aluminium oven. The XAS data were collected in fluorescence mode using a 13-element Canberra detector. XAS data reduction was performed using the EXCURVE90 program (Binsted et al., 1990) with ab initio phase shifts (Gurman et al., 1986).

The Co–O interatomic distances in the 0.1 M solution of CoCl2 are compatible with an octahedrally coordinated Co (two chlorine dCo–Cl = 2.47 å and four oxygen atoms dCo–O = 2.06 å) as in CoCl2(OH)6 from 298 to 423 K. However, at both 323 and 373 K a small amount of cobalt tetrahedrally coordinated to both Cl (dCo–Cl = 2.27å) and O was also evidenced. The Mo–O distance (dMo–O = 1.75 å) found over the entire range of temperature showed that Mo is present as [MoO4]2– species. This well-ordered molybdate complex appears not to be affected by the increase of temperature. In the case of Cd(II) in chloride solutions, the more abundant complexes are hexa-aquo and tetra-chloro ions.

The presence of mixed chloro-aquo tetrahedral complexes of Co in significant concentration demonstrated using EXAFS is important as it will affect the activity coefficient previously calculated using optical absorption spectroscopy on a basis of only octahedrally coordinated Co.

References

Allard
,
T.
Ildefonse
,
P.
Beaucaire
,
C.
Calas
,
G.
(
1999
):
Structural chemistry of uranium associated with Si, Al, Fe gels in a granitic uranium mine
.
Chem. Geol.
 ,
158
:
81
103
.
Allison
,
N.
Finch
,
A.
Sutton
,
S.V.
Newville
,
M.
(
2001
):
Sr-heterogeneity in coral aragonite
.
Geochim. Cosmochim. Acta
 ,
65
:
2669
2676
.
Altarelli
,
M.
Schlacter
,
F.
Cross
,
J.
(
1998
):
Making ultrabright X-rays
.
Sci. Am.
 ,
268
:
66
73
.
Ankudinov
,
A.L.
Rehr
,
J.J.
(
2003
):
Development of XAFS theory
.
J. Synchrotron Radiat.
 ,
10
:
366
368
.
Ankudinov
,
A.L.
Ravel
,
B.
Rehr
,
J.J.
Conradson
,
S.D.
(
1998
):
Real space multiple scattering calculation of XANES
.
Phys. Rev.
 ,
B58
:
7565
.
Ankudinov
,
A.L.
Rehr
,
J.J.
Bouldin
,
C.
Sims
,
J.
Hung
,
H.
(
2002
):
Parallel calculation of electron multiple scattering using Lanczos algorithms
.
Phys. Rev.
 ,
B65
:
104107
.
Asakura
,
K.
Ijima
,
K.
(
2001
):
Polarization-dependent EXAFS studies on the structures of Mo oxides dispersed on single crystals
.
J. Electron Spectrosc. Relat. Phenom.
 ,
119
:
185
192
.
Bassett
,
W.A.
Brown
,
G. E.
(
1990
):
Synchrotron radiation: applications in the Earth sciences
.
Annu. Rev. Earth Planet. Sci.
 ,
18
:
387
447
.
Binsted
,
N.
Campbell
,
J.W.
Gurman
,
S.J.
Stephenson
,
P.C.
(
1990
):
SERC Daresbury Laboratory EXCURV90 program.
 
Warrington
:
Daresbury Laboratory
.
Binsted
,
N.
Campbell
,
J.W.
Gurman
,
S.J.
Stephenson
,
P.C.
(
1991
):
SERC Daresbury Laboratory EXCURV92 program.
 
Washington
:
Daresbury Laboratory
.
Bish
,
D.L.
(
1981
):
Cation ordering in synthetic and natural Ni-Mg olivines
.
Am. Mineral.
 ,
66
:
770
776
.
Boström
,
D.
(
1987
):
Single crystal X-ray diffraction studies of synthetic Ni-Mg olivine solid solutions
.
Am. Mineral.
 ,
72
:
965
972
.
Brown
,
G.E.
Jr.
Calas
,
G.
Waychunas
,
G.A.
Petiau
,
J.
(
1988
):
X-ray absorption spectroscopy and its applications in mineralogy and geochemistry
.
In
Hawthorne
,
F.C.
(ed.):
Spectroscopic methods in mineralogy and geology /Rev. Mineral.
 ,
18/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
431
-
512
–.
Brown
,
G.E.
Jr.
Farges
,
F.
Calas
,
G.
(
1995
):
X-ray scattering and X-ray spectroscopy studies of silicate melts
.
In
Stebbins
,
J.F.
McMillan
,
P.F.
Dingwall
,
D.B.
(eds.):
Structure, dynamics and properties of silicate melts /Rev. Mineral.
 ,
32/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
317
410
.
Brown
,
G.E.
Jr.
Sturchio
,
N.C.
(
2002
):
An overview of synchrotron radiation applications to low temperature geochemistry and environmental science
.
In
Fenter
,
P.
Rivers
,
M.
Sturchio
,
N.
Sutton
,
S.
(eds.):
Applications of synchrotron radiation in low-temperature geochemistry and environmental science./Rev. Mineral. Geochem.
 ,
49/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
1
115
.
Burns
,
R.G.
(
1993
):
Mineralogical applications of crystal field theory.
 
New York (N.Y.)
:
Cambridge Univ. Press
.
Calas
,
G.
Bassett
,
W. A.
Petiau
,
J.
Steinberg
,
D.
Tchoubar
,
D.
Zarka
,
A.
(
1984
):
Mineralogical applications of synchrotron radiation
.
Phys. Chem. Miner.
 ,
121
:
17
36
.
Calas
,
G.
Brown
,
G.E.
Jr.
Farges
,
F.
Galoisy
,
L.
Itié
,
J.P.
Polian
,
A.
(
1995
):
Cations in glasses under ambient and non-ambient conditions
.
Nucl. Instrum. Methods
 ,
B97
:
155
161
.
Calas
,
G.
Cormier
,
L.
Galoisy
,
L.
Jollivet
,
P.
(
2002
):
Structure properties relationships in multicomponent oxide glasses
.
C.R. Chimie
 ,
5
:
831
843
.
Charnock
,
J.M.
Moyes
,
L.N.
Pattrick
,
R.A.D.
Mosselmans
,
J.F.W.
Vaughan
,
D.J.
Livens
,
R.
(
2003
):
The structural evolution of mercury sulfide precipitate: an XAS and XRD study Am. Mineral.
 ,
88
:
1197
1203
.
Comez
,
L.
Cicco Di
,
A.
Itié
,
J.P.
Polian
,
A.
(
2002
):
High-pressure and high-temperature X-ray absorption study of liquid and solid gallium
.
Phys. Rev.
 ,
B65
:
14114
.
Cormier
,
L.
Creux
,
S.
Galoisy
,
L.
Calas
,
G.
Gaskell
,
P.
(
1996
):
Medium range order around cations in silicate glasses
.
Chem. Geol.
 ,
128
:
77
91
.
Cormier
,
L.
Galoisy
,
L.
Delaye
,
J.M.
Ghaleb
,
D.
Calas
,
G.
(
2001
):
Short- and medium – range structural order around cations in glasses: a multidisciplinary approach
.
C.R. Acad. Sci., Sér. IV
 ,
2:
249
262
.
Coulston
,
G.W.
Bare
,
S.R.
Kung
,
H.
Birkeland
,
K.
Bethke
,
G.K.
Harlow
,
R.
Herron
,
N.
Lee
,
P.L.
(
1997
):
The kinetic significance of V5+ in n-butane oxidation catalyzed by vanadium phosphates
.
Science
 ,
275
:
191
193
.
Dähn
,
R.
Scheidegger
,
A.M.
Manceau
,
A.
Curti
,
E.
Baeyens
,
B.
Bradbury
,
M.H.
Chateigner
,
D.
(
2003
):
Structural evidence for the sorption of Ni(II) atoms on the edges of montmorillonite clay minerals. A polarized X-ray absorption fine structure study
.
Geochim. Cosmochim. Acta
 ,
67
:
1
15
.
Dalba
,
G.
Fornasini
,
P.
Rocca
,
F.
(
1993
):
Cumulant analysis of the extended X-ray absorption fine structure of β-AgI
.
Phys. Rev.
 ,
B47
:
8502
8514
.
Davenport
,
A. J.
Ryan
,
M.P.
Simmonds
,
M.C.
Ernst
,
P.
Newman
,
R. C.
Sutton
,
S.R.
Colligon
,
J.S.
(
2001
):
In Situ Synchrotron X-ray Microprobe Studies of Passivation Thresholds in Fe-Cr alloys
.
J. Electrochem. Soc.
 ,
148
:
B217
B221
Derbyshire
,
G.
Cheung
,
K.-C.
Sangsingkeow
,
P.
Hasnain
,
S.S.
(
1999
):
A low-profile monolithic multi-element Ge detector for X-ray fluorescence applications
.
J. Synchrotron Radiat.
 ,
6
:
62
63
.
Di Cicco
,
A.
(
1995
):
EXAFS multiple-scattering data-analysis: GNXAS methodology and applications
.
Physica B
 ,
208
209
:
125
.
Di Cicco
,
A.
(
1997
):
Short-range structure in solid and liquid matter using multiple-edge EXAFS refinement
.
J. de Physique IV. Colloque C2
 ,
171
.
Duff
,
M.C.
Hunter
,
D.B.
Triay
,
I.R.
Bertsch
,
P.M.
Reed
,
D.T.
Sutton
,
S.R.
Shea-McCarthy
,
G.
Kitten
,
J.
Eng
,
P.
Chipera
,
S.J.
Vaniman
,
D.T.
(
1999
):
Mineral associations and average oxidation states of sorbed Pu on tuff
.
Environ. Sci. Technol.
 ,
33
:
2163
2169
.
Ellis
,
J.P.
(
1995
):
Structural studies of metalloproteins using X-ray absorption spectroscopy and X-ray diffraction.
Ph.D. Thesis
 ,
Univ. of Sydney
,
Australia
.
Eng
,
P.J.
Rivers
,
M.
Yang
,
B.X.
Schildkamp
,
W.
(
1995
):
Micro-focusing 4 keV to 65 keV X-rays with bent Kirkpatrick-Baez mirrors
.
In
Yun
,
W.
(ed.):
X-ray microbeam technology and applications /Proc. SPIE
 ,
2516/
,
Bellingham (Wash.)
:
SPIE
,
41
51
.
Farges
,
F.
Sharps
,
J.A.
Brown
,
G.E.
Jr.
(
1993
):
Local environment around gold(III) in aqueous chloride solutions: an EXAFS spectroscopy study
.
Geochim. Cosmochim. Acta
 ,
57
:
1243
1252
.
Farges
,
F.
Brown
,
G.E.
Jr.
Calas
,
G.
Galoisy
,
L.
Waychunas
,
G.A.
(
1994
):
Structural transformation in Ni-bearing Na2Si2O5 glass and melt
.
Geophys. Res. Lett.
 ,
21
:
1931
1934
.
Farges
,
F.
Fiquet
,
G.
Andrault
,
D.
Itié
,
J.-P.
(
1995
):
In situ high-temperature (?2100 K): XAFS and anharmonicity
.
Physica B
 ,
208
209
:
263–264
.
Farges
,
F.
Brown
,
G.E.
Jr.
Petit
,
P.E.
Munoz
,
M.
(
2001
):
Transition elements in water-bearing silicate glasses/melts. Part I. a high-resolution and anharmonic analysis of Ni coordination environments in crystals, glasses, and melts
.
Geochim. Cosmochim. Acta
 ,
65
:
1665
1678
.
Fernandez-Garcia
,
M.
Marquez-Alvarez
,
C.
Halle
,
G.L.
, (
1995
):
XANES-TPR study of Cu-Pd bimetallic catalysts: Application of factor analysis
.
J. Phys. Chem.
 ,
99
:
12565
12569
.
Filipponi
,
A.
Di Cicco
,
A.
(
1994
):
Development of an oven for X-ray absorption measurements under extremely high temperature conditions
.
Nucl. Instrum. Methods Phys. Res.
 ,
B93
:
302
310
.
Fornasini
,
P.
(
2001
):
Study of lattice dynamics via extended X-ray absorption-fine structure
.
J. Phys., Condens. Matter
 ,
13
:
7859
7872
.
Frenkel
,
A.I.
Kleifeld
,
O.
Wasserman
,
S.R.
Sagib
,
I.
(
2002
):
Phase speciation by extended X-ray absorption fine structure spectroscopy
.
J. Chem. Phys.
 ,
116
:
9449
9456
.
Fujino
,
K.
Sasaki
,
S.
Takeuchi
,
Y.
Sadanaga
,
R.
(
1981
):
X-ray determination of electron distributions in forsterite
.
Acta Crystallogr.
 ,
B37
:
513
518
.
Galoisy
,
L.
Calas
,
G.
(
1992
):
Network forming nickel in silicate glasses
.
Am. Mineral.
 ,
77
:
677
680
.
Galoisy
,
L.
Calas
,
G.
(
1993
a
):
Structural environment of nickel in silicate glass/melt systems. I. Spectroscopic determination of coordination states
.
Geochim. Cosmochim. Acta
 ,
57
:
3613
3626
.
Galoisy
,
L.
Calas
,
G.
(
1993
b
):
Structural environment of nickel in silicate glass/melt systems. II. Geochemical implications
.
Geochim. Cosmochim. Acta
 ,
57
:
3627
3633
.
Galoisy
,
L.
Calas
,
G.
Brown
,
G.B.
Jr.
(
1995
):
Intracrystalline distribution of Ni in San Carlos olivine: An EXAFS study
.
Am. Mineral.
 ,
80
:
1089
1092
.
Galoisy
,
L.
Cormier
,
L.
Rossano
,
S.
Ramos
,
A.
Le Grand
,
M.
Calas
,
G.
Gaskell
,
Ph.
(
2000
):
Cationic ordering in oxide glasses: the example of transition elements
.
Mineral. Mag.
 ,
64
:
207
222
.
Galoisy
,
L.
Calas
,
G.
Arrio
,
M.A.
(
2001
):
High-resolution XANES spectra of iron in minerals and glasses: structural information from the pre-edge region
.
Chem. Geol.
 ,
174
:
307
319
.
Galoisy
,
L.
Calas
,
G.
Cormier
,
L.
(
2003
):
Chemical stability of Ni-enriched nanodomains in alkali borate glasses
.
J. Non-Cryst. Solids
 ,
321
:
197
203
.
Greaves
,
G.N.
(
1985
):
EXAFS and the structure of glass
.
J. Non-Cryst. Solids
 ,
71
:
203
217
.
Greaves
,
G.N.
(
2000
):
Structure and ionic transport in disordered silicates
.
Mineral. Mag.
 ,
64
:
441
446
.
Greaves
,
G.N.
Ngai
,
K.L.
(
1995
):
Reconciling ionic transport properties with atomic structure in oxide glasses
.
Phys. Rev.
 ,
B52
:
6358
6380
.
Gurman
,
S.J.
(
1988
):
The small atom approximation theory
:
J. Phys. C: Solid State Phys.
 ,
21
:
3699
3717
.
Gurman
,
S.J.
Binsted
,
N.
Ross
,
I.
(
1984
):
A rapid, exact curved-wave theory for EXAFS calculations
.
J. Phys. C: Solid State Phys.
 ,
17
:
143
151
.
Gurman
,
S.
Binsted
,
N.
Ross
,
I.
(
1986
):
A rapid, exact, curved-wave theory for EXAFS calculations: II. The multiple-scattering contributions
.
J. Phys. C.
 ,
19
:
1845
1861
Hayes
,
T.M.
Boyce
,
J.B.
(
1982
):
Extended X-ray absorption fine structure spectroscopy
.
Solid State Phys.
 ,
37
:
173
365
.
Isaure
,
M-P.
Laboudigue
,
A.
Manceau
,
A.
Sarret
,
G.
Tiffreau
,
C.
Trocellier
,
P.
Lamble
,
G.
Hazemann
,
J.-L.
Chateignier
,
D.
(
2002
):
Quantitative Zn speciation in a contaminated dredged sediment by μ-PIXE, μ-SXRF, EXAFS spectroscopy and principal component analysis
.
Geochim. Cosmochim. Acta
 ,
66
:
1549
1567
.
Itié
,
J.P.
Polian
,
A.
Calas
,
G.
Petiau
,
J.
Fontaine
,
A.
Tolentino
,
H.
(
1989
):
Pressure-induced coordination changes in crystalline and vitreous GeO2
.
Phys. Rev. Lett.
 ,
63
:
398
401
.
Itié
,
J.P.
Polian
,
A.
Martinez-Garcia
,
D.
Briois
,
V.
Di Cicco
,
A.
Filipponi
,
A.
San Miguel
,
A.
(
1997
):
X-ray absorption spectroscopy under extreme conditions
.
J. Phys. IV
 ,
7
:C
2
31
.
Jalilehvand
,
F.
Spandberg
,
D.
Lindqvist-Reis
,
P.
Hermansson
,
K.
Persson
,
I.
Sandstrom
,
M.
(
2001
):
Hydration of the calcium ion. An EXAFS, large angle X-ray scattering and molecular dynamics simulation study
.
J. Am. Chem. Soc.
 ,
123
:
431
441
.
Juillot
,
F.
Morin
,
G.
Ildefonse
,
Ph.
Trainor
,
T.P.
Benedetti
,
M.
Galoisy
,
L.
Calas
,
G.
Brown
,
G.E.
Jr.
(
2003
):
Ocurrence of Zn/Al hydrotalcite in smelter-impacted soils from Northern France: Evidence from EXAFS spectroscopy and chemical extractions
.
Am. Mineral.
 ,
88
:
509
526
.
Koningsberger
,
D. C.
Prins
,
R.
(
1988
):
X-ray absorption: Principles, applications, techniques of EXAFS, SEXAFS, and XANES
 .
New York (N.Y.)
:
Wiley
.
Kuzmin
,
A.
Obst
,
S.
Purans
,
J.
(
1997
):
X-ray absorption spectroscopy and molecular dynamics studies of Zn2+ in aqueous solutions
.
J. Phys., Condens. Matter
 ,
9
:
10065
10078
.
Lee
,
P.A.
Citrin
,
P.H.
Eisenberger
,
P.
Kincaid
,
B.M.
(
1981
):
Extended X-ray absorption fine structure – its strengths and limitations as a structural tool
.
Rev. Mod. Phys.
 ,
53
:
769
806
Lytle
,
F.W.
(
1989
):
Applications of synchrotron radiation.
 
New York (N.Y.)
:
Gordon & Breach
.
Lytle
,
F.W.
(
1999
):
The EXAFS family tree: a personal history of the development of extended X-ray absorption fine structure
.
J. Synchrotron Radiat.
 ,
6
:
123
134
.
Majérus
,
O.
Cormier
,
L.
Itié
,
J.-P.
Galoisy
,
L.
Neuville
,
D.R.
Calas
,
G.
(
2004
):
Pressure-induced Ge coordination change and polyamorphism in SiO2–GeO2 glasses
.
J. Non-Cryst. Solids
 ,
in print
.
Manceau
,
A.
Bonnin
,
D.
Kaiser
,
P.
Frétigny
,
C.
(
1988
):
Polarized EXAFS of biotite and chlorite
.
Phys. Chem. Miner.
 ,
16
:
180
185
.
Manceau
,
A.
(
1990
):
Distribution of cations among the octahedra of phyllosilicates: insight from EXAFS
.
Can. Mineral.
 ,
28
:
321
328
.
Manceau
,
A.
Chateigner
,
D.
Gates
,
W.P.
(
1998
):
Polarized EXAFS, distance-valence least-squares modeling (DVLS), and quantitative texture analysis approaches to the structural refinement of Garfield nontronite
.
Phys. Chem. Miner.
 ,
25
:
347
365
.
Mayanovic
,
R.A.
Anderson
,
A.J.
Bajt
,
S.
(
1995
):
Development of micro-XAFS: applications to studies of single fluid inclusions
.
Physica
 ,
B208
209
:
239-240
.
McKale
,
A.G.
Knapp
,
G.S.
Chan
,
S.-K.
(
1986
):
Practical method for full curve wave theory analysis of experimental extended X-ray absorption fine structure
.
Phys. Rev.
 ,
B33
:
841
846
.
McKale
,
A.G.
Veal
,
V.W.
Paulikas
,
A.P.
Chan
,
S.K.
Knapp
,
G.S.
(
1988
):
Improved ab initio calculations of amplitude and phase functions for extended X-ray absorption fine structure spectroscopy
.
J. Amer. Chem. Soc.
 ,
110
:
1255
1265
.
Michalowicz
,
A.
(
1991
):
EXAFS pour le MAC. In Logiciels pour la Chimie
.
Paris: Soc. Fr. Chim.
 ,
102
103
.
Miyauchi
,
K.
Qiu
,
J.
Shojiya
,
M.
Kawamoto
,
Y.
Kitamura
,
N.
Fukumi
,
K.
Katayama
,
Y.
Nishihata
,
Y.
(
2002
):
In situ EXAFS study on GeS2 glass under high-pressure
.
Solid State Commun.
 ,
124
:
189
193
.
Morin
,
G.
Ostergren
,
J. D.
Juillot
,
F.
Ildefonse
,
Ph.
Calas
,
G.
Brown
,
G.E.
Jr.
(
1999
):
XAFS determination of the chemical form of lead in smelter-contaminated soils and mine tailings: Importance of adsorption processes
.
Am. Mineral.
 ,
84
:
420
434
Morin
,
G.
Juillot
,
F.
Ildefonse
,
Ph.
Samama
,
J. C.
Brown
,
G. E.
Jr.
Chevallier
,
P.
Calas
,
G.
(
2001
):
Mineralogy of lead in a Pb-mineralized sandstone (Ardèche, France)
.
Am. Mineral.
 ,
86
:
92
104
.
Morin
,
G.
Lecocq
,
D.
Juillot
,
F.
Ildefonse
,
Ph.
Calas
,
G.
Bellin
,
S.
Briois
,
V.
Dillmann
,
Ph.
Chevallier
,
P.
Gauthier
,
Ch.
Sole
,
A.
Petit
,
P-E.
Borensztajn
,
S.
(
2002
):
EXAFS evidence of sorbed arsenic (V) and pharmacosiderite in a soil overlying the Echassiere geochemical anomaly, Allier, France
.
Bull. Soc. Géol. Fr
 .,
173
:
281
291
.
Mosselmans
,
J.F.W
Schofield
,
P.F.
Charnock
,
J.M.
Garner
,
C.D.
Pattrick
,
R.A.D.
Vaughan
,
D.J.
(
1996
):
X-ray absorption studies of metal complexes in aqueous solution at elevated temperatures
.
Chem. Geol.
 ,
127
:
339
350
.
Mottana
,
A.
(
2004
):
X-ray absorption spectroscopy in mineralogy: Theory and experiment in the XANES region
. In
Beran
,
A.
Libowitzky
,
E.
(eds.):
Spectroscopic methods in mineralogy/EMU Notes Mineral.
 ,
6/.
Budapest: Eötvös Univ. Press
,
465
552
.
Munoz
,
M.
Argoul
,
P.
Farges
,
F.
(
2003
):
Continuous Cauchy wavelet transform analyses of EXAFS spectra: a qualitative approach
.
Am. Mineral.
 ,
88
:
694
700
.
Mustre de Leon
,
J.
Rehr
,
J.J.
Zabinsky
,
S.I.
Albers
,
R.C.
(
1991
):
Ab initio curved-wave X-ray-absorption fine structure
.
Phys. Rev.
 ,
B44
:4146.
Newville
,
M.
(
2002
):
XAFS: X-ray absorption fine structure.
 
http://cars.uchicago.edu/xafs/
.
Newville
,
M.
Ravel
,
B.
Haskel
,
D.
Stern
,
E.A.
(
1995
):
Analysis of multiple-scattering XAFS data using theoretical standards
.
Physica B., Condens. Matter
 ,
208–209
:
154
156
.
Ohtaka
,
O.
Yoshiasa
,
A.
Fukui
,
H.
Murai
,
K.
Okube
,
M.
Takebe
,
H.
Katayama
,
Y.
Utsumi
,
W.
(
2002
):
XAFS study of GeO2 glass under pressure
.
J. Phys., Condens. Matter
 ,
14
:
10521
10524
.
Rajamani
,
V.
Brown
,
G.E.
Jr.
Prewitt
,
C.T.
(
1975
):
Cation ordering in Ni-Mg olivine
.
Am. Mineral.
 ,
60
:
292
299
.
Reeder
,
R.J.
Lamble
,
G.M.
Northrup
,
P.A.
(
1999
):
XAFS study of the coordination and local relaxation around Co2+, Zn2+, Pb2+, and Ba2+ trace elements in calcite
.
Am. Mineral.
 ,
84:
1049
1060
.
Rehr
,
J.J.
Albers
,
R.C.
(
1990
):
Scattering-matrix formulation of curved-wave multiple-scattering theory: Application to X-ray-absorption fine structure
.
Phys. Rev.
 ,
B41
:
8139
49
.
Rehr
,
J.J.
Albers
,
R. C.
(
2000
):
Theoretical approaches to X-ray absorption fine structure
.
Rev. Mod. Phys.
 ,
72
:
621
654
.
Rehr
,
J.J.
Mustre de Leon
,
J.
Zabinsky
,
S.I.
Albers
,
R.C.
(
1991
):
Theoretical X-ray absorption fine structure standards
.
J. Am. Chem. Soc.
 ,
113:
5135
.
Rehr
,
J.J.
Zabinsky
,
Z.I.
Albers
,
R.C.
(
1992
):
High order multiple scattering calculations of X-ray K absorption fine structure
.
Phys. Rev. Lett.
 ,
69
:
3397
3400
.
Ressler
,
T.
(
1998
):
WinXAS: a program for X-ray absorption spectroscopy data analysis under MS-Windows
.
J. Synchrotron. Radiat.
 ,
5:
118
122
.
Richard-Plouet
,
M.
Guillot
,
M.
Chateigner
,
D.
Traverse
,
A.
Vilminot
,
S.
(
2003
):
Polarised EXAFS as a characterisation tool for new hybrid organic-inorganic nickel phyllosilicates
.
Nucl. Instrum. Methods Phys. Res.
 ,
B200
:
148
154
.
Robinson
,
A.L.
(
2001
):
History of synchrotron radiation
. In
Thompson
,
A.C.
Vaughan
,
D.
(eds.):
X-ray data booklet.
 2nd ed.
Berkeley (Cal.)
:
Lawrence Berkeley Nat. Lab., Univ. of California
,
2
17
.
Rossano
,
S.
Ramos
,
A.
Delaye
,
J.M.
Filipponi
,
A.
Creux
,
S.
Brouder
,
C.
Calas
,
G.
(
1999
):
Iron surrounding in CaO-FeO-2SiO2 glass: EXAFS and molecular dynamics simulation
.
J. Synchrotron Radiat.
 ,
6
:247.
Rossano
,
S.
Ramos
,
A.
Delaye
,
J.M.
Creux
,
S.
Filipponi
,
A.
Brouder
,
Ch.
Calas
,
G.
(
2000
):
EXAFS and molecular dynamics combined study of CaO-FeO-2SiO2 glass. New insight into site significance in silicate glasses
.
Europhys. Lett.
 ,
49
:597.
San Miguel
,
A.
Pellicer-Porres
,
J.
Itié
,
J.P.
Polian
,
A.
Gauthier
,
M.
(
2000
):
Single crystal EXAFS at high pressure
.
High Press. Res.
 ,
19
:
335
340
.
Sayers
,
D.E.
Bunker
,
B.A.
(
1987
):
Extended X-ray absorption fine structure.
 
New York (N.Y.)
:
Wiley
.
Schlegel
,
M.L.
Manceau
,
A.
Chateigner
,
D.
Charlet
,
L.
(
1999
):
Sorption of metal ions on clay minerals: I. Polarized EXAFS evidence for the adsorption of Co on the edges of Hectorite particles
,
J. Colloid Interface Sci.
 ,
215
:
140
158
.
Seifert
,
F.
Paris
,
E.
Dingwell
,
D.B.
Davoli
,
I.
Mottana
,
A.
(
1993
):
In situ X-ray absorption spectroscopy to 1500 °C: cell design, operation and first results
.
Terra Abstr.
 ,
1
:366.
Signorato
,
R.
Sole
,
V.A.
Gauthier
,
C.
(
1999
):
Performance of the ESRF ID26 beamline reflective optics
.
J. Synchrotron Radiat.
 ,
6
:
176
177
.
Stern
,
E.A.
Heald
,
S.M.
(
1979
):
X-ray filter assembly for fluorescence measurements of X-ray absorption fine structure
.
Rev. Sci. Instrum.
 ,
50
:
1579
1585
.
Stern
,
E.A.
Sayers
,
D.E.
Lytle
,
F.W.
(
1975
):
Extended X-ray fine structure technique. III. Determination of physical parameters
.
Phys. Rev.
 ,
B11
:
4836
4846
.
Teo
,
B.K.
(
1986
):
EXAFS: Basic principles and data analysis.
 
Berlin
:
Springer-Verlag
.
Teo
,
B.K.
Lee
,
P.A.
(
1979
):
Ab initio calculations of amplitude and phase functions for extended X-ray absorption fine structure spectroscopy
J. Am. Chem. Soc.
 ,
101
:
2815
2832
.
Trainor
,
T.P.
Fitts
,
J.P.
Templeton
,
A.S.
Grolimund
,
D.
Brown
,
G.E.
Jr.
(
2002
):
Grazing-incidence XAFS studies of aqueous Zn (II) sorption in α-Al2O3 single crystals
.
J. Colloid Interface Sci.
 ,
244
:
239
244
.
Von Barth
,
G.
Hedin
,
A.
(
1972
):
A local exchange-correlation potential for the spin polarized case: I
.
J. Phys. C. Solid State Phys.
 ,
5
:
1629
1642
Wasserman
,
S.R.
(
1997
):
The analysis of mixtures: Application of principal component analysis to XAS spectra
.
J. Phys. IV
 ,
7
:
C2–203
C2–205
.
Wasserman
,
S.R.
Winans
,
R.E.
McBeth
,
R.
(
1996
):
Iron species in Argonne Premium coal samples: An investigation using X-ray absorption spectroscopy
.
Energy Fuels
 ,
10
:
392
400
.
Wasserman
,
S.R.
Allen
,
P.G.
Shuh
,
D.K.
Bucher
,
J.J.
Edelstein
,
N.M.
(
1999
):
EXAFS and principal component analysis: a new shell game
J. Synchrotron Radiat.
 ,
6
:
284
286
.
Westre
,
T.E.
Di Cicco
,
A.
Filipponi
,
A.
Natoli
,
C.R.
Hedman
,
B.
Solomon
,
E.I.
Hodgson
,
K.O.
(
1994
):
Determination of the Fe-N-O angle in FeNO7 complexes using multiple scattering EXAFS analysis by GNXAS
.
J. Am. Chem. Soc.
 ,
116
:
6757
.
Winick
,
H.
(
1987
):
Synchrotron radiation
.
Sci. Am.
 ,
275:
88
99
.
Winterer
,
M.
(
1997
):
XAFS – A data analysis program for materials science
.
J. Phys IV.
 ,
7
:243.
Yamaguchi
,
K.
Ito
,
Y.
Mukoyama
,
T.
(
1999
):
The regularization of the basic X-ray absorption spectrum fine structure equation via the wavelet-Galerkin method
.
J. Phys. B, At. Mol. Opt. Phys.
 ,
32
:
1393
1408
.
Zabinsky
,
S.I.
Rehr
,
J.J.
Ankudinov
,
A.L.
Albers
,
R.C.
Eller
,
M. J.
(
1995
):
Multiple scattering calculations of X-ray absorption spectra
.
Phys. Rev.
 ,
B52
:
2995
3009
.

Figures & Tables

Fig. 1.

Representation of the photoelectric effect: an X-ray photon is absorbed and a core level electron is promoted out of the atom.

Fig. 1.

Representation of the photoelectric effect: an X-ray photon is absorbed and a core level electron is promoted out of the atom.

Fig. 2.

A photoelectron wave emitted from the absorbing atom (A) is backscattered by a scattering atom (S). The backscattered wave modifies the final-state wavefunction at the absorber. If the emitted and backscattered waves are in phase, the wavefunction is increased. If the emitted and backscattered waves are out of phase, the wavefunction is decreased (modified after Ellis, 1995).

Fig. 2.

A photoelectron wave emitted from the absorbing atom (A) is backscattered by a scattering atom (S). The backscattered wave modifies the final-state wavefunction at the absorber. If the emitted and backscattered waves are in phase, the wavefunction is increased. If the emitted and backscattered waves are out of phase, the wavefunction is decreased (modified after Ellis, 1995).

Fig. 3.

XAFS spectrum of Zn at the Zn K edge in ZnO, showing the XANES and EXAFS domains.

Fig. 3.

XAFS spectrum of Zn at the Zn K edge in ZnO, showing the XANES and EXAFS domains.

Fig. 4.

Representations of the fluorescence and Auger effects. When X-rays are absorbed through the photoelectric effect, the excited core-hole will relax back to a “ground state” of the atom. This will not affect the absorption process. A higher level core electron drops into the core hole, and a fluorescent X-ray (a, b) or an Auger electron (c) is emitted.

Fig. 4.

Representations of the fluorescence and Auger effects. When X-rays are absorbed through the photoelectric effect, the excited core-hole will relax back to a “ground state” of the atom. This will not affect the absorption process. A higher level core electron drops into the core hole, and a fluorescent X-ray (a, b) or an Auger electron (c) is emitted.

Fig. 6.

(a) k3χ(k) EXAFS signal for a glass at the Zr K edge. Weighting by k3 amplifies the oscillations at high k values. (b) Fourier transform of the k3chi;(k) EXAFS signal in a glass at the Zr K edge showing two distinct major contributions of neighbours around 1.7 Å and 3 Å without phase correction. (c) Back Fourier transform of the first peak of the FT in (b) of a glass at the Zr K edge and best fit for the first neighbours oxygen shell, (d) best fit for the second neighbours silicon shell.

Fig. 6.

(a) k3χ(k) EXAFS signal for a glass at the Zr K edge. Weighting by k3 amplifies the oscillations at high k values. (b) Fourier transform of the k3chi;(k) EXAFS signal in a glass at the Zr K edge showing two distinct major contributions of neighbours around 1.7 Å and 3 Å without phase correction. (c) Back Fourier transform of the first peak of the FT in (b) of a glass at the Zr K edge and best fit for the first neighbours oxygen shell, (d) best fit for the second neighbours silicon shell.

Fig. 16.

Pressure-composition domains: T domain with only tetrahedral Ge, T + Oc domain with both [4]Ge and [6]Ge and Oc domain with only octahedral Ge.

Fig. 16.

Pressure-composition domains: T domain with only tetrahedral Ge, T + Oc domain with both [4]Ge and [6]Ge and Oc domain with only octahedral Ge.

Contents

GeoRef

References

References

Allard
,
T.
Ildefonse
,
P.
Beaucaire
,
C.
Calas
,
G.
(
1999
):
Structural chemistry of uranium associated with Si, Al, Fe gels in a granitic uranium mine
.
Chem. Geol.
 ,
158
:
81
103
.
Allison
,
N.
Finch
,
A.
Sutton
,
S.V.
Newville
,
M.
(
2001
):
Sr-heterogeneity in coral aragonite
.
Geochim. Cosmochim. Acta
 ,
65
:
2669
2676
.
Altarelli
,
M.
Schlacter
,
F.
Cross
,
J.
(
1998
):
Making ultrabright X-rays
.
Sci. Am.
 ,
268
:
66
73
.
Ankudinov
,
A.L.
Rehr
,
J.J.
(
2003
):
Development of XAFS theory
.
J. Synchrotron Radiat.
 ,
10
:
366
368
.
Ankudinov
,
A.L.
Ravel
,
B.
Rehr
,
J.J.
Conradson
,
S.D.
(
1998
):
Real space multiple scattering calculation of XANES
.
Phys. Rev.
 ,
B58
:
7565
.
Ankudinov
,
A.L.
Rehr
,
J.J.
Bouldin
,
C.
Sims
,
J.
Hung
,
H.
(
2002
):
Parallel calculation of electron multiple scattering using Lanczos algorithms
.
Phys. Rev.
 ,
B65
:
104107
.
Asakura
,
K.
Ijima
,
K.
(
2001
):
Polarization-dependent EXAFS studies on the structures of Mo oxides dispersed on single crystals
.
J. Electron Spectrosc. Relat. Phenom.
 ,
119
:
185
192
.
Bassett
,
W.A.
Brown
,
G. E.
(
1990
):
Synchrotron radiation: applications in the Earth sciences
.
Annu. Rev. Earth Planet. Sci.
 ,
18
:
387
447
.
Binsted
,
N.
Campbell
,
J.W.
Gurman
,
S.J.
Stephenson
,
P.C.
(
1990
):
SERC Daresbury Laboratory EXCURV90 program.
 
Warrington
:
Daresbury Laboratory
.
Binsted
,
N.
Campbell
,
J.W.
Gurman
,
S.J.
Stephenson
,
P.C.
(
1991
):
SERC Daresbury Laboratory EXCURV92 program.
 
Washington
:
Daresbury Laboratory
.
Bish
,
D.L.
(
1981
):
Cation ordering in synthetic and natural Ni-Mg olivines
.
Am. Mineral.
 ,
66
:
770
776
.
Boström
,
D.
(
1987
):
Single crystal X-ray diffraction studies of synthetic Ni-Mg olivine solid solutions
.
Am. Mineral.
 ,
72
:
965
972
.
Brown
,
G.E.
Jr.
Calas
,
G.
Waychunas
,
G.A.
Petiau
,
J.
(
1988
):
X-ray absorption spectroscopy and its applications in mineralogy and geochemistry
.
In
Hawthorne
,
F.C.
(ed.):
Spectroscopic methods in mineralogy and geology /Rev. Mineral.
 ,
18/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
431
-
512
–.
Brown
,
G.E.
Jr.
Farges
,
F.
Calas
,
G.
(
1995
):
X-ray scattering and X-ray spectroscopy studies of silicate melts
.
In
Stebbins
,
J.F.
McMillan
,
P.F.
Dingwall
,
D.B.
(eds.):
Structure, dynamics and properties of silicate melts /Rev. Mineral.
 ,
32/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
317
410
.
Brown
,
G.E.
Jr.
Sturchio
,
N.C.
(
2002
):
An overview of synchrotron radiation applications to low temperature geochemistry and environmental science
.
In
Fenter
,
P.
Rivers
,
M.
Sturchio
,
N.
Sutton
,
S.
(eds.):
Applications of synchrotron radiation in low-temperature geochemistry and environmental science./Rev. Mineral. Geochem.
 ,
49/.
Washington (D.C.)
:
Mineral. Soc. Am.
,
1
115
.
Burns
,
R.G.
(
1993
):
Mineralogical applications of crystal field theory.
 
New York (N.Y.)
:
Cambridge Univ. Press
.
Calas
,
G.
Bassett
,
W. A.
Petiau
,
J.
Steinberg
,
D.
Tchoubar
,
D.
Zarka
,
A.
(
1984
):
Mineralogical applications of synchrotron radiation
.
Phys. Chem. Miner.
 ,
121
:
17
36
.
Calas
,
G.
Brown
,
G.E.
Jr.
Farges
,
F.
Galoisy
,
L.
Itié
,
J.P.
Polian
,
A.
(
1995
):
Cations in glasses under ambient and non-ambient conditions
.
Nucl. Instrum. Methods
 ,
B97
:
155
161
.
Calas
,
G.
Cormier
,
L.
Galoisy
,
L.
Jollivet
,
P.
(
2002
):
Structure properties relationships in multicomponent oxide glasses
.
C.R. Chimie
 ,
5
:
831
843
.
Charnock
,
J.M.
Moyes
,
L.N.
Pattrick
,
R.A.D.
Mosselmans
,
J.F.W.
Vaughan
,
D.J.
Livens
,
R.
(
2003
):
The structural evolution of mercury sulfide precipitate: an XAS and XRD study Am. Mineral.
 ,
88
:
1197
1203
.
Comez
,
L.
Cicco Di
,
A.
Itié
,
J.P.
Polian
,
A.
(
2002
):
High-pressure and high-temperature X-ray absorption study of liquid and solid gallium
.
Phys. Rev.
 ,
B65
:
14114
.
Cormier
,
L.
Creux
,
S.
Galoisy
,
L.
Calas
,
G.
Gaskell
,
P.
(
1996
):
Medium range order around cations in silicate glasses
.
Chem. Geol.
 ,
128
:
77
91
.
Cormier
,
L.
Galoisy
,
L.
Delaye
,
J.M.
Ghaleb
,
D.
Calas
,
G.
(
2001
):
Short- and medium – range structural order around cations in glasses: a multidisciplinary approach
.
C.R. Acad. Sci., Sér. IV
 ,
2:
249
262
.
Coulston
,
G.W.
Bare
,
S.R.
Kung
,
H.
Birkeland
,
K.
Bethke
,
G.K.
Harlow
,
R.
Herron
,
N.
Lee
,
P.L.
(
1997
):
The kinetic significance of V5+ in n-butane oxidation catalyzed by vanadium phosphates
.
Science
 ,
275
:
191
193
.
Dähn
,
R.
Scheidegger
,
A.M.
Manceau
,
A.
Curti
,
E.
Baeyens
,
B.
Bradbury
,
M.H.
Chateigner
,
D.
(
2003
):
Structural evidence for the sorption of Ni(II) atoms on the edges of montmorillonite clay minerals. A polarized X-ray absorption fine structure study
.
Geochim. Cosmochim. Acta
 ,
67
:
1
15
.
Dalba
,
G.
Fornasini
,
P.
Rocca
,
F.
(
1993
):
Cumulant analysis of the extended X-ray absorption fine structure of β-AgI
.
Phys. Rev.
 ,
B47
:
8502
8514
.
Davenport
,
A. J.
Ryan
,
M.P.
Simmonds
,
M.C.
Ernst
,
P.
Newman
,
R. C.
Sutton
,
S.R.
Colligon
,
J.S.
(
2001
):
In Situ Synchrotron X-ray Microprobe Studies of Passivation Thresholds in Fe-Cr alloys
.
J. Electrochem. Soc.
 ,
148
:
B217
B221
Derbyshire
,
G.
Cheung
,
K.-C.
Sangsingkeow
,
P.
Hasnain
,
S.S.
(
1999
):
A low-profile monolithic multi-element Ge detector for X-ray fluorescence applications
.
J. Synchrotron Radiat.
 ,
6
:
62
63
.
Di Cicco
,
A.
(
1995
):
EXAFS multiple-scattering data-analysis: GNXAS methodology and applications
.
Physica B
 ,
208
209
:
125
.
Di Cicco
,
A.
(
1997
):
Short-range structure in solid and liquid matter using multiple-edge EXAFS refinement
.
J. de Physique IV. Colloque C2
 ,
171
.
Duff
,
M.C.
Hunter
,
D.B.
Triay
,
I.R.
Bertsch
,
P.M.
Reed
,
D.T.
Sutton
,
S.R.
Shea-McCarthy
,
G.
Kitten
,
J.
Eng
,
P.
Chipera
,
S.J.
Vaniman
,
D.T.
(
1999
):
Mineral associations and average oxidation states of sorbed Pu on tuff
.
Environ. Sci. Technol.
 ,
33
:
2163
2169
.
Ellis
,
J.P.
(
1995
):
Structural studies of metalloproteins using X-ray absorption spectroscopy and X-ray diffraction.
Ph.D. Thesis
 ,
Univ. of Sydney
,
Australia
.
Eng
,
P.J.
Rivers
,
M.
Yang
,
B.X.
Schildkamp
,
W.
(
1995
):
Micro-focusing 4 keV to 65 keV X-rays with bent Kirkpatrick-Baez mirrors
.
In
Yun
,
W.
(ed.):
X-ray microbeam technology and applications /Proc. SPIE
 ,
2516/
,
Bellingham (Wash.)
:
SPIE
,
41
51
.
Farges
,
F.
Sharps
,
J.A.
Brown
,
G.E.
Jr.
(
1993
):
Local environment around gold(III) in aqueous chloride solutions: an EXAFS spectroscopy study
.
Geochim. Cosmochim. Acta
 ,
57
:
1243
1252
.
Farges
,
F.
Brown
,
G.E.
Jr.
Calas
,
G.
Galoisy
,
L.
Waychunas
,
G.A.
(
1994
):
Structural transformation in Ni-bearing Na2Si2O5 glass and melt
.
Geophys. Res. Lett.
 ,
21
:
1931
1934
.
Farges
,
F.
Fiquet
,
G.
Andrault
,
D.
Itié
,
J.-P.
(
1995
):
In situ high-temperature (?2100 K): XAFS and anharmonicity
.
Physica B
 ,
208
209
:
263–264
.
Farges
,
F.
Brown
,
G.E.
Jr.
Petit
,
P.E.
Munoz
,
M.
(
2001
):
Transition elements in water-bearing silicate glasses/melts. Part I. a high-resolution and anharmonic analysis of Ni coordination environments in crystals, glasses, and melts
.
Geochim. Cosmochim. Acta
 ,
65
:
1665
1678
.
Fernandez-Garcia
,
M.
Marquez-Alvarez
,
C.
Halle
,
G.L.
, (
1995
):
XANES-TPR study of Cu-Pd bimetallic catalysts: Application of factor analysis
.
J. Phys. Chem.
 ,
99
:
12565
12569
.
Filipponi
,
A.
Di Cicco
,
A.
(
1994
):
Development of an oven for X-ray absorption measurements under extremely high temperature conditions
.
Nucl. Instrum. Methods Phys. Res.
 ,
B93
:
302
310
.
Fornasini
,
P.
(
2001
):
Study of lattice dynamics via extended X-ray absorption-fine structure
.
J. Phys., Condens. Matter
 ,
13
:
7859
7872
.
Frenkel
,
A.I.
Kleifeld
,
O.
Wasserman
,
S.R.
Sagib
,
I.
(
2002
):
Phase speciation by extended X-ray absorption fine structure spectroscopy
.
J. Chem. Phys.
 ,
116
:
9449
9456
.
Fujino
,
K.
Sasaki
,
S.
Takeuchi
,
Y.
Sadanaga
,
R.
(
1981
):
X-ray determination of electron distributions in forsterite
.
Acta Crystallogr.
 ,
B37
:
513
518
.
Galoisy
,
L.
Calas
,
G.
(
1992
):
Network forming nickel in silicate glasses
.
Am. Mineral.
 ,
77
:
677
680
.
Galoisy
,
L.
Calas
,
G.
(
1993
a
):
Structural environment of nickel in silicate glass/melt systems. I. Spectroscopic determination of coordination states
.
Geochim. Cosmochim. Acta
 ,
57
:
3613
3626
.
Galoisy
,
L.
Calas
,
G.
(
1993
b
):
Structural environment of nickel in silicate glass/melt systems. II. Geochemical implications
.
Geochim. Cosmochim. Acta
 ,
57
:
3627
3633
.
Galoisy
,
L.
Calas
,
G.
Brown
,
G.B.
Jr.
(
1995
):
Intracrystalline distribution of Ni in San Carlos olivine: An EXAFS study
.
Am. Mineral.
 ,
80
:
1089
1092
.
Galoisy
,
L.
Cormier
,
L.
Rossano
,
S.
Ramos
,
A.
Le Grand
,
M.
Calas
,
G.
Gaskell
,
Ph.
(
2000
):
Cationic ordering in oxide glasses: the example of transition elements
.
Mineral. Mag.
 ,
64
:
207
222
.
Galoisy
,
L.
Calas
,
G.
Arrio
,
M.A.
(
2001
):
High-resolution XANES spectra of iron in minerals and glasses: structural information from the pre-edge region
.
Chem. Geol.
 ,
174
:
307
319
.
Galoisy
,
L.
Calas
,
G.
Cormier
,
L.
(
2003
):
Chemical stability of Ni-enriched nanodomains in alkali borate glasses
.
J. Non-Cryst. Solids
 ,
321
:
197
203
.
Greaves
,
G.N.
(
1985
):
EXAFS and the structure of glass
.
J. Non-Cryst. Solids
 ,
71
:
203
217
.
Greaves
,
G.N.
(
2000
):
Structure and ionic transport in disordered silicates
.
Mineral. Mag.
 ,
64
:
441
446
.
Greaves
,
G.N.
Ngai
,
K.L.
(
1995
):
Reconciling ionic transport properties with atomic structure in oxide glasses
.
Phys. Rev.
 ,
B52
:
6358
6380
.
Gurman
,
S.J.
(
1988
):
The small atom approximation theory
:
J. Phys. C: Solid State Phys.
 ,
21
:
3699
3717
.
Gurman
,
S.J.
Binsted
,
N.
Ross
,
I.
(
1984
):
A rapid, exact curved-wave theory for EXAFS calculations
.
J. Phys. C: Solid State Phys.
 ,
17
:
143
151
.
Gurman
,
S.
Binsted
,
N.
Ross
,
I.
(
1986
):
A rapid, exact, curved-wave theory for EXAFS calculations: II. The multiple-scattering contributions
.
J. Phys. C.
 ,
19
:
1845
1861
Hayes
,
T.M.
Boyce
,
J.B.
(
1982
):
Extended X-ray absorption fine structure spectroscopy
.
Solid State Phys.
 ,
37
:
173
365
.
Isaure
,
M-P.
Laboudigue
,
A.
Manceau
,
A.
Sarret
,
G.
Tiffreau
,
C.
Trocellier
,
P.
Lamble
,
G.
Hazemann
,
J.-L.
Chateignier
,
D.
(
2002
):
Quantitative Zn speciation in a contaminated dredged sediment by μ-PIXE, μ-SXRF, EXAFS spectroscopy and principal component analysis
.
Geochim. Cosmochim. Acta
 ,
66
:
1549
1567
.
Itié
,
J.P.
Polian
,
A.
Calas
,
G.
Petiau
,
J.
Fontaine
,
A.
Tolentino
,
H.
(
1989
):
Pressure-induced coordination changes in crystalline and vitreous GeO2
.
Phys. Rev. Lett.
 ,
63
:
398
401
.
Itié
,
J.P.
Polian
,
A.
Martinez-Garcia
,
D.
Briois
,
V.
Di Cicco
,
A.
Filipponi
,
A.
San Miguel
,
A.
(
1997
):
X-ray absorption spectroscopy under extreme conditions
.
J. Phys. IV
 ,
7
:C
2
31
.
Jalilehvand
,
F.
Spandberg
,
D.
Lindqvist-Reis
,
P.
Hermansson
,
K.
Persson
,
I.
Sandstrom
,
M.
(
2001
):
Hydration of the calcium ion. An EXAFS, large angle X-ray scattering and molecular dynamics simulation study
.
J. Am. Chem. Soc.
 ,
123
:
431
441
.
Juillot
,
F.
Morin
,
G.
Ildefonse
,
Ph.
Trainor
,
T.P.
Benedetti
,
M.
Galoisy
,
L.
Calas
,
G.
Brown
,
G.E.
Jr.
(
2003
):
Ocurrence of Zn/Al hydrotalcite in smelter-impacted soils from Northern France: Evidence from EXAFS spectroscopy and chemical extractions
.
Am. Mineral.
 ,
88
:
509
526
.
Koningsberger
,
D. C.
Prins
,
R.
(
1988
):
X-ray absorption: Principles, applications, techniques of EXAFS, SEXAFS, and XANES
 .
New York (N.Y.)
:
Wiley
.
Kuzmin
,
A.
Obst
,
S.
Purans
,
J.
(
1997
):
X-ray absorption spectroscopy and molecular dynamics studies of Zn2+ in aqueous solutions
.
J. Phys., Condens. Matter
 ,
9
:
10065
10078
.
Lee
,
P.A.
Citrin
,
P.H.
Eisenberger
,
P.
Kincaid
,
B.M.
(
1981
):
Extended X-ray absorption fine structure – its strengths and limitations as a structural tool
.
Rev. Mod. Phys.
 ,
53
:
769
806
Lytle
,
F.W.
(
1989
):
Applications of synchrotron radiation.
 
New York (N.Y.)
:
Gordon & Breach
.
Lytle
,
F.W.
(
1999
):
The EXAFS family tree: a personal history of the development of extended X-ray absorption fine structure
.
J. Synchrotron Radiat.
 ,
6
:
123
134
.
Majérus
,
O.
Cormier
,
L.
Itié
,
J.-P.
Galoisy
,
L.
Neuville
,
D.R.
Calas
,
G.
(
2004
):
Pressure-induced Ge coordination change and polyamorphism in SiO2–GeO2 glasses
.
J. Non-Cryst. Solids
 ,
in print
.
Manceau
,
A.
Bonnin
,
D.
Kaiser
,
P.
Frétigny
,
C.
(
1988
):
Polarized EXAFS of biotite and chlorite
.
Phys. Chem. Miner.
 ,
16
:
180
185
.
Manceau
,
A.
(
1990
):
Distribution of cations among the octahedra of phyllosilicates: insight from EXAFS
.
Can. Mineral.
 ,
28
:
321
328
.
Manceau
,
A.
Chateigner
,
D.
Gates
,
W.P.
(
1998
):
Polarized EXAFS, distance-valence least-squares modeling (DVLS), and quantitative texture analysis approaches to the structural refinement of Garfield nontronite
.
Phys. Chem. Miner.
 ,
25
:
347
365
.
Mayanovic
,
R.A.
Anderson
,
A.J.
Bajt
,
S.
(
1995
):
Development of micro-XAFS: applications to studies of single fluid inclusions
.
Physica
 ,
B208
209
:
239-240
.
McKale
,
A.G.
Knapp
,
G.S.
Chan
,
S.-K.
(
1986
):
Practical method for full curve wave theory analysis of experimental extended X-ray absorption fine structure
.
Phys. Rev.
 ,
B33
:
841
846
.
McKale
,
A.G.
Veal
,
V.W.
Paulikas
,
A.P.
Chan
,
S.K.
Knapp
,
G.S.
(
1988
):
Improved ab initio calculations of amplitude and phase functions for extended X-ray absorption fine structure spectroscopy
.
J. Amer. Chem. Soc.
 ,
110
:
1255
1265
.
Michalowicz
,
A.
(
1991
):
EXAFS pour le MAC. In Logiciels pour la Chimie
.
Paris: Soc. Fr. Chim.
 ,
102
103
.
Miyauchi
,
K.
Qiu
,
J.
Shojiya
,
M.
Kawamoto
,
Y.
Kitamura
,
N.
Fukumi
,
K.
Katayama
,
Y.
Nishihata
,
Y.
(
2002
):
In situ EXAFS study on GeS2 glass under high-pressure
.
Solid State Commun.
 ,
124
:
189
193
.
Morin
,
G.
Ostergren
,
J. D.
Juillot
,
F.
Ildefonse
,
Ph.
Calas
,
G.
Brown
,
G.E.
Jr.
(
1999
):
XAFS determination of the chemical form of lead in smelter-contaminated soils and mine tailings: Importance of adsorption processes
.
Am. Mineral.
 ,
84
:
420
434
Morin
,
G.
Juillot
,
F.
Ildefonse
,
Ph.
Samama
,
J. C.
Brown
,
G. E.
Jr.
Chevallier
,
P.
Calas
,
G.
(
2001
):
Mineralogy of lead in a Pb-mineralized sandstone (Ardèche, France)
.
Am. Mineral.
 ,
86
:
92
104
.
Morin
,
G.
Lecocq
,
D.
Juillot
,
F.
Ildefonse
,
Ph.
Calas
,
G.
Bellin
,
S.
Briois
,
V.
Dillmann
,
Ph.
Chevallier
,
P.
Gauthier
,
Ch.
Sole
,
A.
Petit
,
P-E.
Borensztajn
,
S.
(
2002
):
EXAFS evidence of sorbed arsenic (V) and pharmacosiderite in a soil overlying the Echassiere geochemical anomaly, Allier, France
.
Bull. Soc. Géol. Fr
 .,
173
:
281
291
.
Mosselmans
,
J.F.W
Schofield
,
P.F.
Charnock
,
J.M.
Garner
,
C.D.
Pattrick
,
R.A.D.
Vaughan
,
D.J.
(
1996
):
X-ray absorption studies of metal complexes in aqueous solution at elevated temperatures
.
Chem. Geol.
 ,
127
:
339
350
.
Mottana
,
A.
(
2004
):
X-ray absorption spectroscopy in mineralogy: Theory and experiment in the XANES region
. In
Beran
,
A.
Libowitzky
,
E.
(eds.):
Spectroscopic methods in mineralogy/EMU Notes Mineral.
 ,
6/.
Budapest: Eötvös Univ. Press
,
465
552
.
Munoz
,
M.
Argoul
,
P.
Farges
,
F.
(
2003
):
Continuous Cauchy wavelet transform analyses of EXAFS spectra: a qualitative approach
.
Am. Mineral.
 ,
88
:
694
700
.
Mustre de Leon
,
J.
Rehr
,
J.J.
Zabinsky
,
S.I.
Albers
,
R.C.
(
1991
):
Ab initio curved-wave X-ray-absorption fine structure
.
Phys. Rev.
 ,
B44
:4146.
Newville
,
M.
(
2002
):
XAFS: X-ray absorption fine structure.
 
http://cars.uchicago.edu/xafs/
.
Newville
,
M.
Ravel
,
B.
Haskel
,
D.
Stern
,
E.A.
(
1995
):
Analysis of multiple-scattering XAFS data using theoretical standards
.
Physica B., Condens. Matter
 ,
208–209
:
154
156
.
Ohtaka
,
O.
Yoshiasa
,
A.
Fukui
,
H.
Murai
,
K.
Okube
,
M.
Takebe
,
H.
Katayama
,
Y.
Utsumi
,
W.
(
2002
):
XAFS study of GeO2 glass under pressure
.
J. Phys., Condens. Matter
 ,
14
:
10521
10524
.
Rajamani
,
V.
Brown
,
G.E.
Jr.
Prewitt
,
C.T.
(
1975
):
Cation ordering in Ni-Mg olivine
.
Am. Mineral.
 ,
60
:
292
299
.
Reeder
,
R.J.
Lamble
,
G.M.
Northrup
,
P.A.
(
1999
):
XAFS study of the coordination and local relaxation around Co2+, Zn2+, Pb2+, and Ba2+ trace elements in calcite
.
Am. Mineral.
 ,
84:
1049
1060
.
Rehr
,
J.J.
Albers
,
R.C.
(
1990
):
Scattering-matrix formulation of curved-wave multiple-scattering theory: Application to X-ray-absorption fine structure
.
Phys. Rev.
 ,
B41
:
8139
49
.
Rehr
,
J.J.
Albers
,
R. C.
(
2000
):
Theoretical approaches to X-ray absorption fine structure
.
Rev. Mod. Phys.
 ,
72
:
621
654
.
Rehr
,
J.J.
Mustre de Leon
,
J.
Zabinsky
,
S.I.
Albers
,
R.C.
(
1991
):
Theoretical X-ray absorption fine structure standards
.
J. Am. Chem. Soc.
 ,
113:
5135
.
Rehr
,
J.J.
Zabinsky
,
Z.I.
Albers
,
R.C.
(
1992
):
High order multiple scattering calculations of X-ray K absorption fine structure
.
Phys. Rev. Lett.
 ,
69
:
3397
3400
.
Ressler
,
T.
(
1998
):
WinXAS: a program for X-ray absorption spectroscopy data analysis under MS-Windows
.
J. Synchrotron. Radiat.
 ,
5:
118
122
.
Richard-Plouet
,
M.
Guillot
,
M.
Chateigner
,
D.
Traverse
,
A.
Vilminot
,
S.
(
2003
):
Polarised EXAFS as a characterisation tool for new hybrid organic-inorganic nickel phyllosilicates
.
Nucl. Instrum. Methods Phys. Res.
 ,
B200
:
148
154
.
Robinson
,
A.L.
(
2001
):
History of synchrotron radiation
. In
Thompson
,
A.C.
Vaughan
,
D.
(eds.):
X-ray data booklet.
 2nd ed.
Berkeley (Cal.)
:
Lawrence Berkeley Nat. Lab., Univ. of California
,
2
17
.
Rossano
,
S.
Ramos
,
A.
Delaye
,
J.M.
Filipponi
,
A.
Creux
,
S.
Brouder
,
C.
Calas
,
G.
(
1999
):
Iron surrounding in CaO-FeO-2SiO2 glass: EXAFS and molecular dynamics simulation
.
J. Synchrotron Radiat.
 ,
6
:247.
Rossano
,
S.
Ramos
,
A.
Delaye
,
J.M.
Creux
,
S.
Filipponi
,
A.
Brouder
,
Ch.
Calas
,
G.
(
2000
):
EXAFS and molecular dynamics combined study of CaO-FeO-2SiO2 glass. New insight into site significance in silicate glasses
.
Europhys. Lett.
 ,
49
:597.
San Miguel
,
A.
Pellicer-Porres
,
J.
Itié
,
J.P.
Polian
,
A.
Gauthier
,
M.
(
2000
):
Single crystal EXAFS at high pressure
.
High Press. Res.
 ,
19
:
335
340
.
Sayers
,
D.E.
Bunker
,
B.A.
(
1987
):
Extended X-ray absorption fine structure.
 
New York (N.Y.)
:
Wiley
.
Schlegel
,
M.L.
Manceau
,
A.
Chateigner
,
D.
Charlet
,
L.
(
1999
):
Sorption of metal ions on clay minerals: I. Polarized EXAFS evidence for the adsorption of Co on the edges of Hectorite particles
,
J. Colloid Interface Sci.
 ,
215
:
140
158
.
Seifert
,
F.
Paris
,
E.
Dingwell
,
D.B.
Davoli
,
I.
Mottana
,
A.
(
1993
):
In situ X-ray absorption spectroscopy to 1500 °C: cell design, operation and first results
.
Terra Abstr.
 ,
1
:366.
Signorato
,
R.
Sole
,
V.A.
Gauthier
,
C.
(
1999
):
Performance of the ESRF ID26 beamline reflective optics
.
J. Synchrotron Radiat.
 ,
6
:
176
177
.
Stern
,
E.A.
Heald
,
S.M.
(
1979
):
X-ray filter assembly for fluorescence measurements of X-ray absorption fine structure
.
Rev. Sci. Instrum.
 ,
50
:
1579
1585
.
Stern
,
E.A.
Sayers
,
D.E.
Lytle
,
F.W.
(
1975
):
Extended X-ray fine structure technique. III. Determination of physical parameters
.
Phys. Rev.
 ,
B11
:
4836
4846
.
Teo
,
B.K.
(
1986
):
EXAFS: Basic principles and data analysis.
 
Berlin
:
Springer-Verlag
.
Teo
,
B.K.
Lee
,
P.A.
(
1979
):
Ab initio calculations of amplitude and phase functions for extended X-ray absorption fine structure spectroscopy
J. Am. Chem. Soc.
 ,
101
:
2815
2832
.
Trainor
,
T.P.
Fitts
,
J.P.
Templeton
,
A.S.
Grolimund
,
D.
Brown
,
G.E.
Jr.
(
2002
):
Grazing-incidence XAFS studies of aqueous Zn (II) sorption in α-Al2O3 single crystals
.
J. Colloid Interface Sci.
 ,
244
:
239
244
.
Von Barth
,
G.
Hedin
,
A.
(
1972
):
A local exchange-correlation potential for the spin polarized case: I
.
J. Phys. C. Solid State Phys.
 ,
5
:
1629
1642
Wasserman
,
S.R.
(
1997
):
The analysis of mixtures: Application of principal component analysis to XAS spectra
.
J. Phys. IV
 ,
7
:
C2–203
C2–205
.
Wasserman
,
S.R.
Winans
,
R.E.
McBeth
,
R.
(
1996
):
Iron species in Argonne Premium coal samples: An investigation using X-ray absorption spectroscopy
.
Energy Fuels
 ,
10
:
392
400
.
Wasserman
,
S.R.
Allen
,
P.G.
Shuh
,
D.K.
Bucher
,
J.J.
Edelstein
,
N.M.
(
1999
):
EXAFS and principal component analysis: a new shell game
J. Synchrotron Radiat.
 ,
6
:
284
286
.
Westre
,
T.E.
Di Cicco
,
A.
Filipponi
,
A.
Natoli
,
C.R.
Hedman
,
B.
Solomon
,
E.I.
Hodgson
,
K.O.
(
1994
):
Determination of the Fe-N-O angle in FeNO7 complexes using multiple scattering EXAFS analysis by GNXAS
.
J. Am. Chem. Soc.
 ,
116
:
6757
.
Winick
,
H.
(
1987
):
Synchrotron radiation
.
Sci. Am.
 ,
275:
88
99
.
Winterer
,
M.
(
1997
):
XAFS – A data analysis program for materials science
.
J. Phys IV.
 ,
7
:243.
Yamaguchi
,
K.
Ito
,
Y.
Mukoyama
,
T.
(
1999
):
The regularization of the basic X-ray absorption spectrum fine structure equation via the wavelet-Galerkin method
.
J. Phys. B, At. Mol. Opt. Phys.
 ,
32
:
1393
1408
.
Zabinsky
,
S.I.
Rehr
,
J.J.
Ankudinov
,
A.L.
Albers
,
R.C.
Eller
,
M. J.
(
1995
):
Multiple scattering calculations of X-ray absorption spectra
.
Phys. Rev.
 ,
B52
:
2995
3009
.

Related

Citing Books via

Close Modal
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close Modal
Close Modal