Bergaya F. Handbook of Clay Science

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and larger distances are probed. Because an XAFS spectrum is taken over a range

of increasing X-ray energies, single- and multiple-scattering events dominate in

different portio ns of the spectrum. The higher energy portions of EXAFS spectra are

dominated by single-scattering events within only some tenth of nanometer

(500–600 pm) from the ab sorber, and contain information speciﬁc to the local struc-

ture surrounding the absorber. On the other hand, XANES or NEXAFS spectra,

being centred close to the absorption jump, are dominated by multiple-scattering

events extending a few nm from the absorber.

Comparisons of experimental Fe K EXAFS spectra with those calculated for

nontronites (derived from FEFF code (Rehr et al., 1991, 1992; Rehr, 2003)), indicate

that multiple-scattering events can be important at R*>450 pm (Manceau et al.,

1998), while co-linear multiple scattering events involving three or more high Z

atoms can be considerable at shorte r distances (Manceau et al., 2000a). Vantelon

et al. (2003) observed important amplitude differences in calculated Fe K EXAFS

spectra, incorporating multiple scattering, as compared with those that consider only

single-scattering events, especially in the 300–500 pm range. In modelling Al K

XANES spectra, Cabaret et al. (1996a) and Bugaev et al. (1998, 2000) found that

single-scattering events were unimportant.

B. XAFS Data Analysis

The procedures for XAS data processing (especially EXAFS) are standardised

(Stern and Heald, 1983; Rehr et al., 1991) and there are simpliﬁed, user-friendly

computer programs, such as IFEFFIT (Newville, 2003). Brown et al. (1988) and

Fendorf (1999) described XAFS data analysis methods suitable for use in c lay

and soil sciences, while detailed information on more diverse techniques was given

by Schulze et al. (1999), de Groot (2001), Bertsch and Hunter (2001) and Fenter

et al. (2002).

Spectral processing requires background and levelling corrections and energy

calibration. The amplitude of each spectrum must be normalised so that baseline

values of the amplitude function (m(E)) below the edge are near zero, and the

averaged value s of m(E) in the EXAFS portion are o1. Typically, a spline function

is applied to accomplish these steps (Fig. 12.3.1A). Energy and amplitude calibra-

tions must be performed because of ‘drift’ that occurs during data collection due to

differential heating of monochomators, beam instability and decay of the ring

current. The importance of these standardised ‘pre-conditioning’ treatments, and

their systematic and consistent application, cannot be stressed enough.

Analysis of XAFS spectra requires the extraction of data from the absorption

experiment. Owing to scattering interference and the limited mean free path of

the photoelectron, the magnitudes of X-ray scattering events typically decay rapidly

with increasing energy above the absorption edge (Fig. 12.3.1A). Therefore the

ﬁne structure amplitude function, w(E), of an EXAFS spectrum is isolated from

Chapter 12.3: X-ray Absorption Spectroscopy796

post-edge background, m

(E), using the relation (Teo, 1986)

wðEÞ¼

mðEÞm

ðEÞ

ð5Þ

where m(E) is the experimental absorbance as described above, m

(E) the atomic

contribution to the absorbance coefﬁcient (X-ray absorption without the EXAFS

oscillations), Dm

(E) the measured absorption jump and E the kinetic energy of the

photoelectron (the difference in the energies of the X-ray and that needed to eject the

photoelectron into the continuum). Eq. (5) provides a means of normalising and

correcting background for all portions of the XAFS spectra, whether one’s interest is

in the pre-edge, the XANES or the EXAFS regions (Fig. 12.3.1A).

Pre-edge and XANES spectral analyses often involve the de composition and as-

signment of spectral features (Figs. 12.3.1B, C) and/or comparison with known

reference spectra (Ildefonse et al., 1994, 1998). During decomposition of spectra,

derivative curves can be used to locate abscissa where peaks occur. In common with

other quantitative spectral analyses, decomposition generally incorporates Gaussian

(normal) or Lorentzian (bell shaped) line shape functions, or Voigt (mixtures of

Gaussian an d Lorentzian).

For EXAFS (and NEXAFS) spectral analysis, the contributions of single- and

multiple-scattering events need to be quantiﬁed since these events give rise to am-

plitude modulations in the spectra. The oscillations in the EXAFS spectra can be

described quantitatively by

wðkÞ¼

ðkÞe

sin 2kR

þ d

ðkÞ



ð6Þ

Here N

is the number of atoms making up the jth shell, f

(k) the backscattering

amplitude function corresponding to each atom within shell j, d

(k) the total phase

shift function associated with the backscattering atom, s

the EXAFS Debye–

Waller factor for thermal and static disorder, indicating the variance about the

interatomic distances (R

) between the absorbing and backscattering atoms of the jth

shell. The wavenumber of the wavevector, k, is given by

k ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

2mðE  E



ð7Þ

where E

is now deﬁned as the edge energy absorption threshold, usually located on

the edge at one-half Dm

(E)(Fig. 12.3.1A), m the electron mass and _ ¼ h=2p (h is

Planck’s constant). The backscattering amplitude function is speciﬁc to the atoms

involved in the backscattering process. The electronic terms, f

(k) and d

(k), in Eq. (6)

relate to the type of atom, while the terms N

, R

and s

are assocated with the

local arrangement of other atoms surroun ding the absorber. The EXAFS spectrum

therefore contains information on the number, identity and distance (72 pm) of

12.3.1. Synchrotron-Based Techniques 797

surrounding atoms as well as on the oxidation state and coordination number of the

absorbing atom. The task is to quantitatively extract N, R an d s from what is known

about the scattering amplitude f(k) and phase-shift d(k) of a given absorber and its

local chemical and structural environment.

The Fourier transform (FT) of Eq. (6) into ‘R’ space is deﬁned as

ðwRÞ¼

1

dk sinð2kRÞk

wðkÞOðkÞð8Þ

where O(k) is a window function and w a k weighting factor. The w(k) wavevector

spectrum is multiplied by the weighting factors, k

, where w ¼ 1, 2, 3, y , to enhance

regions of high k (Fig. 12.3.1D ). Sometimes the same data are analysed using

different w weight factors (e.g., w ¼ 1 and 3; Manceau et al., 2000a). Window

functions, such as the ‘Hannel’ or ‘Kaiser-Bessel’ windows are applied to a selected k

range to truncate the ends of the spectrum, thereby minimising ‘termination ripples’

in the FT (Waychunas et al., 1986). These mathematical functions inﬂuence the

form of the EXAFS and ultimately the amplitude, phase and position of peaks in

the resulting FT (Fig. 12.3.1E)(Teo, 1986). Their systematic application is thus

important.

Peaks in the FT represent atomic shells, and are often complex combinations of

several different atomic shells. Polarised EXAFS (Section 12.3.1F) can help differ-

entiate between sub-shells making up particular peaks in the FT of layered materials,

such as smectites. In powder EXAFS (Section 12.3.1E), however, entire peaks are

used to determine the contributions of sub-shells to structural information. The

papers by Teo (1986), Brown et al. (1988), Fendorf (1999) and Newville (2003)

should be consulted for more detailed information on XAFS data processing.

The FT of an EXAFS spectrum (Fig. 12.3.1E) provides infor mation on the

distribution of atomic shells as a function of distance from the target absorber. By

isolating shells of interest and bac k transforming the selected k region into ‘q space’,

one creates a partial EXAFS spectrum that can then be compared to calculated

scattering (f ) and phase (d) functions in order to determine N, R and s associated

with that particular shell. The FT is sometimes referred to as radial distribution

(RDF) or radial structure (RSF) functions. Whatever the designation, they

rep resent sums of all possible pair correlations involving the absorbing atom

(Waychunas et al., 19 86). Since phase corrections are usually not included in the

FT, represented distances (R*) are generally 20–30 pm less than real interatomic

distances (R).

Care should be taken to ensure consistency during sample preparation because

differences in sample thickness and density can have a profound impact on the

XAFS amplitude, Dm

(E)(Stern and Kim, 1981; Waychunas et al., 1983; Lu and

Stern, 1993 ; Manceau and Gates, 1997). Disagreements over the interpretation of

various XAFS spectra were documented, such as the structures of Co

-sepiolite

(Fukushima and Okomoto, 1987; Fukushima, 1988; Manceau and Decarreau, 1988),

Chapter 12.3: X-ray Absorption Spectroscopy798

tetrahedral Fe in ferrihydrite (Eggleton and Fitzpatrick, 1988; Combes et al., 1989a;

Manceau et al., 1990b; Drits et al., 1993; Manceau and Drits, 1993; Zhao et al., 1993,

1994; Manceau and Gates, 1997) and sorption complexes in oxides. These disagree-

ments may partly arise from differences in sample preparation and presentation. In

general, however, they can be attributed to variations in sample thickness and den-

sity, pre-analysis normalisation, data quality and the models used to interpret and

quantify the spectra. Although interpretational disagreements are an important and

necessary part of scientiﬁc research, they may cause considerable confusion for

novice XAS experimentalis ts and those who are not well acquainted with the lit-

erature. The potential for further confusion still exists.

C. Pre-Edge XAFS Spectroscopy

Features near the absorption edge are related to electronic transitions from core

states to empty bonding states. Oxygen 1s (K) XANES experiments and calculations

on transition metal dioxide (tetrahedr al) structures showed that ﬁlling of empty 3d

states in TiO

,VO

, CrO

and MnO

, are in agreem ent with experimental spectra

(de Groot, 2001) and correspond to increased 3d t

state occupancies: 0 for Ti(IV), 1

for VO

, 2 for CrO

and 3 for Mn(IV). Pre-edge features are often observed in the

XAFS spectra of transition metal absorbers (Figs. 12.3.1A, B). Sometimes these

features represent intense dipole-allowed transitions, such as the 1s-3d transition of

tetrahedral Cr(VI) in CrO

2

(Sutton et al., 1993 ; Bertsch and Hu nter, 2001)orof

tetrahedral Fe (Waychunas et al., 1983), due to symmetry allowed p-3d state mix-

ing (de Groot, 2001). For octahedra l symmetry, dipole (e.g., 1s-3d) transitions are

forbidden (Calas and Petiau, 1983) although pre-edge features can be observed be -

cause the octahedral sites in most minerals are distorted, allowing some p-3d state

mixing. Waychunas (1987) showed that the amount of distortion-induce d p-d

mixing inﬂuences the amplitude and shape of the transition metal pre-edge features

for many minerals. Manceau and Gates (1997) observed this also in the Fe K pre-

edge spectr a of nanocrystalline ferrihydrite.

Fig. 12.3.3A shows the effect of site distortions for the Fe K pre-edge XAFS

spectra of goethite, hydrous ferric oxide and nontronite. Being a centrosymmetric,

trans-vacant, dioctahedral smectite, nontronite has a relatively weak pre-edge struc-

ture, depending on tetrahedral Fe content. Furthermore, the octahedral sites in

nontronite are only moderately distorted (Manceau et al., 1998) with a ﬂattening

angle, b

FeyO

, of about 571. On the other hand, goethite (a-FeOOH) and hydrous

ferric oxide (HFO) can have appreciable octahedr al distortion due to hydroxylation

and hydration (Manceau and Gates, 1997; Ford and Bertsch, 1999). The increased

distortion of Fe octahedra in these two hydrous oxides results in 30–40% amplitude

enhancement compared with nontronite. Isomorphous substitutions of Al, Cr, Zn or

Cu for Fe in the structure of (hydr)oxides can result in considerable enhancement of

pre-edge amplitudes (Waychunas et al., 1986).

12.3.1. Synchrotron-Based Techniques 799

Energy (eV)

7090

7094 7098

Nontronite

αFeOOH

Normalized Absorbance

HFO

~30%

~nil

Ener

(eV)

7090

7094 7098

Garfield

NG-1

G500

Normalized Absorbance

~30

~15%

NAu-1

~nil

NAu-2

Spokane

~10%

~8%

SWa-1

Fig. 12.3.3. Examples of Fe K pre-edge XAFS spectra showing differences in the 1s-3d

transition (t

and e

) amplitudes and shape as a function of coordination environment and

site distortions. (A) Amplitude enhancement due to presence of tetrahedral coordination

(Fe

and FePO

), broadening due to multiple sites (Fe

) and amplitude enhancement due

to dispersion of FeyO distances and site distortion (FeOOH, HFO). (B) Amplitude en-

hancement due to incorporation of four-fold (NG-1) and ﬁve-fold (G500) Fe in the nontronite

structure. Also depicted is broadening due to distortions in the local Fe environment (G500).

G500 ¼ Garﬁeld nontronite heated to 500 1C for 3 h. HFO ¼ hydrous ferric oxide, NG-1

Spokane, Nau-1 and Nau-2 are nontronite specimens with varying tetrahedral Fe content.

Modiﬁed after Manceau and Gates (1997) and Gates et al. (2002).

Chapter 12.3: X-ray Absorption Spectroscopy800

D. X-ray Near-Edge Spectroscopy (XANES or NEXAFS)

The processes responsible for near-edge absorption structure are related to ejection

of core electrons into ‘continuum states’, and involve single- and multiple-scattering

events off the ﬁrst atomic shell surrounding the absorber, as well as multiple-

scattering events from more distant atomic shells (Fig. 12.3.1C). Edge features (po-

sition and shape) reﬂect oxidation states and coordination environments in the

vicinity of the absorber (Waychunas et al., 1983; Waychunas, 1987; Cressey et al.,

1993; Bajt et al., 1994, 1995; Ildefonse et al., 1994; Li et al., 1995; Delaney et al.,

1996a, 1996b; Wu et al., 1996; Gates et al., 1997; Manceau and Gates, 1997; Delaney

et al., 1998). This technique is now routinely applied to discern coordination and

oxidation states of metals in minerals at ng g

1

concentrations (e.g., Bertsch and

Hunter, 2001; Manceau et al., 2002a).

XANES spectra were traditionally interpreted by comparison with the spectra of

reference materials ( Waychunas et al., 1983; Waychunas, 1987; Bianconi, 1988;

McKeown et al., 1989; Ildefonse et al., 1994; Ildefonse et al., 1998). Decomposition

of the spectral components can indicate electron ‘density of states’ for the transition

metals (de Groot, 2001) as well as differentiate between different site symmetries

(Ildefonse et al., 1994, 1998; Bugaev et al., 1998, 2000) and assist in quantifying

oxidation states in various mineral species (Fig. 12.3.4)(Waychunas, 1987; Bajt

et al., 1995; Li et al., 1995; Delaney et al., 1996a, 1996b, 1998; Berry and O’Neill,

2004). Recent advances in multiple-scattering formalism, showed that XA NES

(NEXAFS) spectra can be treated like EXAFS spectra to gain element-speciﬁc

information on bonding environment, such as coordination number and inter-

atomic distances. Programs such as FEFF (Ankudinov et al., 1998; Rehr, 2003)or

SELCOMP (Bugaev et al., 1998, 2000), using self-consistent full-potential multiple-

scattering calculations, were instrumental in such advances. Simulations of multiple-

scattering events reveal that XANES spectra are generally well characterised by

nearest neighbour (single- and multiple-scatter ing events), next-nearest-neighbour

(multiple-scattering events) and next-next-nearest-neighbour (multiple-scatteri ng

events) intervals from the absorber.

Calculations by Cabaret et al. (1996a) indica ted that clusters with radii as large as

3 nm (30 A

or 3000 pm) are necessary to effectively model Al K-XANES spectra.

Thus, even XANES spectra can provide short- to medium-range structural infor-

mation. Although this ﬁnding has yet to be fully exploited in clay mineral studies,

Bugaev et al. (2002) reported that Fourier ﬁltering of XANES spectra can provide

quantitative information of coordination number and bond distances for both crys-

talline and short-range order compounds. Thus, detailed study of NEXAFS spectra

has the potential for more precise quantiﬁcation than can be obtained from spectral

comparison of targe t atoms for which the absorption edges of other elements overlap

within the EXAFS region of the spectrum. Such situations disallow the collection of

sufﬁcient data in k space (e.g., K edges of many 1st row transition metals overlap

with L edges of lanthanides) for satisfactory analysis to be carried out.

12.3.1. Synchrotron-Based Techniques 801

E. Powder EXAFS Spectroscopy

As already mentioned, the oscillations of an EXAFS spectrum result from inter-

ference between the outgoing ejected photoelectron wavefront and the scattered

wavefronts returning from near-neighbour environments. In clay structures, de-

structive interference occurs be tween waves backscattered from octahedral Fe and

octahedral Al (Fig. 12.3.5), because a near p -difference in phase shift exists between

3d (e.g., Fe, Mn, Ni) and 3p (e.g., Si, Mg, Al) elements (Waychunas et al., 1986;

Calas et al., 1990; Manceau, 1990). Similarly, a near p-difference in pha se shift

Energy (eV)

1570 15801560 1590 1600

Muscovite

Pyrophyllite

Kaolinite

Prassa Smectite

Oligocene Smectite

Illite

Fig. 12.3.4. Examples of Al K XANES (or NEXAFS) spectra of selected layer silicates.

Decomposition of the ﬁrst three peaks at 1564, 1566–1567 and 1569–1570 eV allows quan-

titative estimation of tetrahedral Al content. Adapted and redrawn from Ildefonse et al.

(1994).

Chapter 12.3: X-ray Absorption Spectroscopy802

Fe-Al d = 303 pm

Fe-Si d = 328 pm

Fe-Fe d = 303 pm

Fe-Si d = 328 pm

Fe-Fe d = 303 pm

Fe-Al d = 303 pm

2 4 6 8 10 14 16

Wavevector k(Å

-1

)

Arbitrary k

χ(q)

Fe-Fe d = 303 pm

Fe-O d = 201 pm

Fe-O d = 378 pm

Fig. 12.3.5. Comparison of the calculated amplitudes and phases of nearest ligand (FeyO)

and cation (FeyFe, FeySi, FeyAl) atomic shell contributions to Fe K EXAFS spectra of a

typical smectite structure. Top panel: octahedral Al shell at d ¼ 303 pm and tetrahedral

Si shell at d ¼ 328 pm. Upper middle panel: octahedral Fe shell at d ¼ 303 pm and octahedral

Al shell at d ¼ 303 pm. Lower middle panel: octahedral Fe shell at d ¼ 303 pm and tetrahedral

Si shell at d ¼ 328 pm. Bottom panel: octahedral Fe shell at d ¼ 303 and O shells at

d ¼ 201 pm and d ¼ 378 pm. All waveform amplitudes were adjusted to differing degrees

relative to the FeyFe signal.

12.3.1. Synchrotron-Based Techniques 803

occurs between waves that are backscattered from tetrahedral a nd octahedral cations

of the same species, at least for the phyllosilicates (Manceau et al., 1998; Gates et al.,

2002). These phenomena were exploited to study octahedral cation occupancies in

-smectite, Ni

-sepiolite, montmorillonites, ferruginous smectites and non-

tronites and can be applied to kaolinite, pyrophyllite, allophane, imogolite and other

important minerals.

Powder EXAFS spectroscopy of clays and clay minerals does suffer from rather

severe limitations, however. One limitation is the difﬁculty in discriminating between

atoms of similar atomic number (Z), due to the similarity of their backscattering

wave functions (Fig. 12.3.5). While improvements were made in modelling these

contributions, it is still not possible to unequivocal ly differentiate between Al, Si and

Mg, or between Ni, Mn and Fe, as second cation-shell neighbours in a smectite

structure. Another limitation is the existence and complexity of multiple sites oc-

cupied by a given absorbing species (Table 12.3.1). For example, in magnetite with

an inverse spinel structure, Fe occupies both octahedral and tetrahed ral sites, and

has two different oxidation states. Strong overlap of the backscattering amplitudes

of tetrahedral and octahedral cations (Fig. 12.3.5) adversely affects quantitative

resolution between these two sites. Further, suitable reference materials with varied

coordination sites are lacking. For example, the ﬁve-fold coordinated Fe(III), Fe(II)

or Al in dehydroxylated structures of smectites is highly distorted (Rossman and

Tarlan, 2001; see Fig. 12.3.3 for Fe(III)). Vacancies (e.g., goethite), defects (e.g.,

ferrihydrite) and poor order (e.g., octahedral sheet of dioctahedral smectites) in

Table 12.3.1. Scattering paths used in ﬁt of powder (ﬁlm at a ¼ 351) Fe K EXAFS of SWa-1

displayed in Fig. 12.3.6. Single-scattering paths alone were found to enable a satisfactory ﬁt



to determine N and R

eff

in IFEFFIT (Newville, 2003). Chemistry

and symmetry

were input

into TKATOMS (Ravel, 1999) to enable FEFF (Rehr, 2003) to determine scattering paths

Shell Scattering atom Path NR

eff

(pm)

FeyO

OFe-O-Fe 2 201

OFe-O-Fe 4 203

FeyM

Oct Al Fe-Al-Fe 0.7 301

Oct Fe Fe-Fe-Fe 2.3 307

Tet Si Fe-Si-Fe 4 337

FeyO

OFe-O-Fe 2 342

FeyO

OFe-O-Fe 2 371

OFe-O-Fe 4 388

FeyM

Tet Si Fe-Si-Fe 4 445

FeyInt Interlayer Na Fe-Na-Fe 2 510

FeyM

Oct Fe Fe-Fe-Fe 3 523



Fitting results: So

¼ 0:658; DE ¼ 25:58 eV; w

¼ 21. s was held constant at 0.07.

Chemistry from Gates (2004) or Gates et al. (2002).

c2/m.

Chapter 12.3: X-ray Absorption Spectroscopy804

mineral struc tures make unambiguous spectral interpretations the exception. In

layered structures, any preferential orientation will also affect the resulting EXAFS

amplitude, leading to misinterpretation. As already discussed, sample preparation,

presentation and spectral processing issues can also impact on the quality of the

XAFS spectrum and its interpretation.

EXAFS spectra can be quantiﬁed using IFEFFIT and associated program code

(Ravel, 1999, 2003a, 2003b; Newville, 2003), while scattering paths can be calculated

using TKATOMS (Ravel, 1999) and FEFF (Rehr, 2003). These programs incor-

porate the effects of curve waveforms and single- and multiple-scattering paths,

providing improved data analysis. The contributions of each scattering path within a

given distance from the absorber are calculated, and the resulting theoretical EXAFS

spectrum represents a sum of all these contributions. A scattering path deﬁnes the

atoms from which the photoelectron can scatter before returning to the absorber. As

described in Section 12.3.1A, single- and multiple-scattering paths occur, and based

on the crystallography of the mineral, calculated paths are used to deduce the atomic

shells surrounding the absorber. These are then compared to the experimentally

derived partial spectrum by applying least-squares analysis, which was back-

transformed from a peak isolated in the FT. The IFEFFIT code was recently

modiﬁed, allowing larger regions of the FT to be ﬁt simultaneously. For such

methodology to be used effectively in the analysis of disorde red clay minerals, the

user must have as much detailed knowledge as possible of the crystal chemistry of the

specimen being studied, or be able to extract this information from known reference

materials. Thus, EXAFS is rarely a suitable stand-alone technique for unknown

samples. Most studies use a variety of other more conventional measurements into

which EXAFS is incorporated as a secondary or supplementary technique.

The powder EXAFS spectrum of the ferruginous smectite, SWa-1 (Fig. 12.3. 6 )

illustrates some of the pros and cons of ﬁtting a large region (rather than isolated

peaks) of the EXAFS spectrum using IFFEFIT. Some different ﬁts are shown, while

the results of one ﬁt are displayed in Table 12.3.1. When the FeyM

shell was

isolated from the FT (Fig. 12.3.6, lower middle panel) ﬁtting of the partial EXAFS

spectrum resulted in two octahedral components consisting of 2.1Fe at d ¼ 305 pm,

0.9Al at d ¼ 303 pm, and one tetrahedral component of 4Si at d ¼ 337 pm. A ﬁt

of the entire FT from R* ¼ 0–600 pm results in 2.3Fe at d ¼ 307 pm, 0.7Al at

d ¼ 301 pm and 4Si at d ¼ 337 pm. Contrast these results with those of Manceau

et al. (2000a) and Vantelon et al. (2003) who studied the same mineral. The best ﬁt of

the FeyM

shell in the latter study was 2.2Fe at d ¼ 309 pm and 0.8Al at

d ¼ 302 pm, not too dissi milar from the results in Table 12.3.1 (Fig. 12.3.6, bottom

panel). The best ﬁt of the octahedral contributions to the Fe yM

shell by Manceau

et al. (2000a) was 2Fe at d ¼ 305 pm and 1Al at d ¼ 303 pm, similar to those dis-

played in Fig. 12.3.6 (lower middle panel). Since the octahedral contributions were

isolated using polarised EXAFS (P-EXAFS), the ﬁts of Manceau et al. (2000a)

should be considered superior. This example also illustrates the importance of col-

lecting high k data for good accuracy on R

eff

. While the N

eff

determined by both

12.3.1. Synchrotron-Based Techniques 805