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Absorption Techniques in X-ray Spectrometry
Jun Kawai
in
Encyclopedia of Analytical Chemistry
R.A. Meyers (Ed.)
pp. 13288–13315
 John Wiley & Sons Ltd, Chichester, 2000
1
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
Absorption Techniques in
X-ray Spectrometry
Jun Kawai
Kyoto University, Kyoto, Japan
1 Introduction
2 Acronyms and a Brief History
3 X-ray Absorption Near-edge Structure
3.1 Chemical Shift and Line Shape
3.2 Calculation Method for X-ray
Absorption Near-edge Structure
Spectra
4 Theory of Extended X-ray Absorption
Fine Structure
4.1 Single Scattering Theory
4.2 Relation to Other Techniques
(X-ray Photoelectron Diffraction,
Low-energy Electron Diffraction,
X-ray Fluorescence Holography)
5 Data Analysis and Software Packages
for X-ray Absorption Fine Structure
6 Instrumentation
6.1 Laboratory Extended X-ray Absorption Fine Structure
6.2 Synchrotron Radiation Extended
X-ray Absorption Fine Structure
6.3 Secondary Yield Techniques and
Applications
7 Sources and Databases
8 Alternative Methods
8.1 Electron Energy Loss Spectroscopy
8.2 Self-absorption
8.3 Extended X-ray Emission Fine
Structure
8.4 X-ray Raman Scattering
8.5 Diffraction Anomalous Fine
Structure
8.6 b-Environment Fine Structure
8.7 Inverse Photoemission Spectroscopy
9 Conclusion
Abbreviations and Acronyms
Related Articles
References
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8
of analyte. X-ray absorption spectrometry is a technique
for analyzing the chemical environment of an element in
an unknown material. This method is closely related to
photoelectron spectroscopy, Auger electron spectroscopy,
and X-ray fluorescence spectroscopy.
Chemical information in the chemical shift and line
shape of XANES (X-ray absorption near-edge structure)
spectra is described. The history and theory of EXAFS
(extended X-ray absorption fine structure) are discussed
in relation to other experimental techniques. Data analysis
methods, databases, software packages, instrumentation,
and synchrotron radiation facilities for X-ray absorption
analysis are overviewed. Alternative methods such as
electron energy loss spectroscopy (EELS), self-absorption
effect, extended X-ray emission fine structure (EXEFS), Xray Raman scattering, diffraction anomalous fine structure
(DAFS), b-environment fine structure (BEFS), and inverse
photoemission spectroscopy (IPES) are also described.
8
8
1 INTRODUCTION
10
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15
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X-ray absorbance depends on the wavelength of the X-rays,
atomic number, chemical environment, and concentration
Encyclopedia of Analytical Chemistry
R.A. Meyers (Ed.) Copyright  John Wiley & Sons Ltd
X-rays are absorbed in matter and the energy of
the X-rays is converted into the kinetic energy of
photoelectrons, Auger electrons, secondary electrons,
or fluorescent X-rays. The incident X-ray energy finally
becomes the thermal energy of the absorber.
The amount of energy absorbed by a matter is usually
estimated by a transmission method, but can also be
estimated by measuring these secondary phenomena,
such as photoelectrons, Auger electrons, secondary
electrons, fluorescent X-rays, thermal radiation, and drain
electric currents. The X-ray intensity of wavelength l
before (I0 ) and after (I) the transmission of a thin film of
thickness d is expressed by I.l/ D I0 .l/ exp[ µi .l/ri d],
where µi .l/ and ri are the mass absorption coefficient
and mass density, respectively, of the ith element in the
thin film and their dimensions are [cm2 g 1 ] and [g cm 3 ],
respectively..1 – 7/ The mass absorption coefficient µ of
a specimen which contains n kinds of elements is
expressed by µ D µ1 .l/W1 C µ2 .l/W2 C Ð Ð Ð C µn .l/Wn ,
where W1 , W2 , . . . , Wn are the weight fractions of element
1, 2, . . . , n in the specimen. The wavelength dependence
of the absorption coefficient µ.l/ is clarified when log µ.l/
is plotted against log l as shown in Figure 1; µ.l/ values
are taken from Henke et al..8/ in this plot. Henke et al..8/
tabulated µ.l/ from Z D 1 to 92 at energy from 50 eV to
30 keV.
The plot of the mass absorption coefficients of matter
against the incident X-ray energy or wavelength is called
an X-ray absorption spectrum (XAS), where we find some
jumps at particular X-ray energy, corresponding to K, LI ,
LII , LIII , . . . electron shell binding energies as shown in
2
X-RAY SPECTROMETRY
Table 1 Relation between the hole
state and the electron configuration
106
105
Zn Fe V
µ (cm2 g–1)
104
103
L edge
102
Hole state
Electron configuration
K
L1
L2
L3
M1
M2
M3
M4
M5
[1s]
[2s]
[2p1/2 ]
[2p3/2 ]
[3s]
[3p1/2 ]
[3p3/2 ]
[3d3/2 ]
[3d5/2 ]
Zn Fe V
101
K edge
100
0.1
1.0
10.0
Wavelength (nm)
Figure 1 Mass absorption coefficients of V, Fe, and Zn plotted
against wavelength. Both axes are on a logarithmic scale.
1
p D K.Z
l
Absorbance
L edge
L1
L2
L3
K edge
0
1.4
1.2
1.0
state has a total angular momentum 12 , and the subscript 12
is usually omitted. The multiplicity of the state, which is
crudely proportional to the spectral intensity, is 2j C 1.
The jump is called the absorption edge, and the
wavelength is highly correlated with the atomic number
similarly to Moseley’s law.1/ in X-ray emission spectra.
Moseley’s law in emission spectra is expressed as
Equation (1):
0.8
0.6
0.4
0.2
Wavelength (Å)
Figure 2 Platinum powder XAS. (Reproduced by permission
from Udagawa..9/ )
Figure 2..9/ K, LI , LII , and LIII denote electron deficiency
states from 1s, 2s, 2p1/2 , and 2p3/2 orbitals, respectively.
Arabic numerals 1, 2, 3, . . . have more recently been used
in the subscript rather than Roman numerals I, II, III, . . .
The electron configuration of one electron deficiency
from the 2p orbital is expressed as 1s2 2s2 2p5 3s2 3p6 for an
Ar atom. This state has two energy levels corresponding to
j D 12 and 32 states, where j is the eigenvalue of vector sum
s C l, where s and l are called spin and angular momentum
vectors, respectively, and the vector j is called the total
angular momentum. These two states are written as 2p1/21
and 2p3/21 , or [2p1/2 ] and [2p3/2 ].
The relation between the electron deficient state and
the electron configuration is listed in Table 1. The s 1 hole
s/
.1/
where l is the X-ray wavelength, Z is the atomic number,
and K and s are constants for a spectral series. The
absorption coefficient is crudely proportional to Z4 l3
except for the edge jumps. The energy at which the jump is
observed is called the threshold energy, but the definition
of the threshold is not exact, because it corresponds to the
transition from a core orbital to the lowest unoccupied
orbital. The ionization limit is a few or a few tens of
electron-volts higher than the edge energy.
The mass per unit area is given by rd, where r is
the mass density. The linear absorption coefficient µl is
defined by µl D µr, and its dimension is [cm 1 ]. The Xray attenuation length 1/µl is the length at which the
X-ray intensity becomes 1/e after traveling in matter. The
attenuation length of Cu Ka1 X-rays (8047.8 eV) is 79 µm
in aluminum, 4.2 µm in iron, 24 µm in copper, and 3.9 µm in
lead. The attenuation length of Al Ka X-rays (1486.7 eV)
is 9.2 µm in aluminum and 0.4 µm in iron. The intensity of
X-rays emitted by a copper target X-ray tube is, however,
attenuated by only half after transmission through 2-mmthick aluminum, but depends on the applied power
on the X-ray tube, because the X-rays emitted from
an X-ray tube are not monochromatic. Thus it should
be noted that the X-ray shielding thickness for safety
cannot be determined only from the monochromatic Xray attenuation length.
The linear absorption coefficient can otherwise be
expressed as µ1 D 4pb/l, where l is the X-ray wavelength
and b the imaginary part of the complex refractive index
3
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
Nr0 l2 f1
2p
Nr0 l2 f2
bD
2p
dD
.2/
.3/
where N is the number of atoms in unit volume and
r0 D e2 /.mc2 / D 2.818 ð 10 13 cm is the classical electron
radius (e the electron charge, m the mass, and c the speed
of light). The real part f1 is the Fourier transform of
the electron density distribution in an atom. The relation
between the absorption coefficient and atomic form factor
is used in DAFS described below.
The mass absorption coefficient is the sum of two
effects: photoelectric absorption and scattering of Xrays. The photoelectric absorption is the ionization of an
inner-shell electron. Therefore, the absorption coefficient
due to the photoelectric part can be calculated by the
photoionization cross-section..8/ The scattering part is
due to the Rayleigh (coherent) and Compton (inelastic)
scattering of X-rays, but X-ray absorption spectra are
often taken as if they represent only the photoelectric
absorption effect, although the experimental spectra
contain both effects.
The mass absorption coefficients or physically equivalent parameters.8,9 – 13/ and the absorption edge energy or
wavelength.14,15/ can be found in the literature. The value
of the absorption edge energy is close to the electron binding energy, which is used in electron spectroscopy, ESCA
(electron spectroscopy for chemical analysis) or XPS (Xray photoelectron (photoemission) spectroscopy)..16,17/
The absorption edge jump is not exactly the same as
the electron binding energy, because the absorption edge
energy corresponds to the excitation of core electrons
into the lowest unoccupied molecular orbital (LUMO)
in the molecular orbital picture, or Rydberg state in the
atomic orbital picture. The Rydberg state and continuum state threshold are clearly seen in rare gas X-ray
absorption spectra but are not clear for condensed matter. The difference between the vacuum level and Fermi
energy, which defines the highest energy of electrons in
a conduction band, is called the work function, . This
is another source of the difference between the electron binding energy observed in XPS and the absorption
edge. The photoionization cross-sections.18,19/ and the
electron binding energies.20,21/ can be found in the literature. The relation between the electron photoionization
cross-section (barns) and mass absorption coefficient is
simple when the angular dependence is averaged..11/
Absorption techniques in X-ray spectrometry are
used to measure the X-ray absorption spectra using
various methods described below, and to analyze the
obtained spectral line shapes to obtain information on the
element, oxidation state, concentration, atomic distance,
coordination number, surface geometry, and reaction on
solid surfaces, catalysts, or electrodes.
2 ACRONYMS AND A BRIEF HISTORY
The mass absorption coefficient plotted against the Xray energy is called the XAS. The X-ray absorption
spectra of condensed matter near the threshold energy
have fine structures as shown in Figure 2. Fine structures are sometimes observable at energies less than
the threshold energy, and are called the pre-edge structure (Figure 3)..22/ These fine structures are called the
XANES, usually pronounced as ‘‘zaenz’’. The absorption fine structure will extend up to 1000 eV above the
threshold energy, and thus it is called the EXAFS,.23 – 26/
pronounced ‘‘eksafs’’. XANES is restricted from the
threshold to ca. 50 eV above (this energy approximately
corresponds to kR D 2p, where k is the ejected photoelectron momentum and R the nearest-neighbor atomic
MnO
X-ray absorption intensity
(n D 1 d ib)..7/ The atomic form factor, f D f1 C if2 ,
which is used in the analysis of X-ray diffraction, is related
to the refractive index (Equations 2 and 3):
KMnO4
0
10
20
30
40
50
Energy (eV)
Figure 3 Mn K edge XANES spectra of MnO (octahedral, Oh ,
symmetry) and KMnO4 (tetrahedral, Td , symmetry). Pre-edge
peak is found in the KMnO4 spectrum. Chemical shift of the
edge is found; the edge of KMnO4 is higher than that of MnO.
(Reproduced by permission from Pandya et al..22/ )
4
X-RAY SPECTROMETRY
Photoelectron wave
Scattered electron wave
EXAFS
k > k crt
XANES
k crt = 2π /R
k < k crt
Shape resonance
Figure 5 Schematic illustration of electron wave propagating
and scattering in a solid. (Reproduced by permission from
Udagawa..9/ )
R
X-ray
absorbing
atom
Electron
scattering
atom
Figure 4 Illustration of electron standing wave between the
X-ray absorption atom and its neighboring atom. (Reproduced
by permission from Udagawa.9/ and Ishii..26/ )
distance as shown in Figure 4.9,26/ ). The momentum of the
photoelectron is k D [2m.E E0 /]1/2 /h̄, where E is the
photoelectron kinetic energy, E0 the threshold energy, m
the electron mass, and h̄ Planck’s constant. The photoelectron matter wave in a condensed system propagates
as a spherical wave and forms a standing wave as shown
in Figure 5..9/ Recently, XANES has come to be called
near-edge X-ray absorption fine structure (NEXAFS),.27/
pronounced ‘‘neksafs’’. All the fine structures including
NEXAFS and EXAFS are grouped into the term X-ray
absorption fine structure (XAFS), pronounced ‘‘zafs’’.
The history of the development of the understanding and application of XAFS has an interesting feature, as stated by Lytle et al.,.28/ Shiraiwa,.29/ Stern,.30/
and Lytle..31/ Barkla (after Stern.30/ ) or de Broglie
(after Lytle.31/ ) firstly found the X-ray absorption edge.
Although XANES was found for both solids and gases,
EXAFS was found only for condensed matter such as
molecules, solids and liquids. EXAFS was first reported
by Fricke in 1920.32/ and was theoretically interpreted
by Kossel..33/ He explained that the fine structure was
due to the excitation of inner-shell electrons to an
unoccupied level. This theory was valid for XANES,
and thus XANES was called the Kossel structure. The
Kossel theory was called short-range order (SRO) theory, because the electronic structures of unoccupied levels
are mostly determined by orbital hybridization between
the center atom and the nearest-neighbor atoms. On
the other hand, Kronig.34/ explained that fine structure
was the result of the diffraction of photoelectrons as a
matter wave when moving in a conduction band of a
solid. The electron matter wave travels in a solid when
the wavelength of an electron le does not satisfy the
Bragg condition, 2d sin q D nle . When the Bragg condition is satisfied, then the electrons are scattered and leave
the solid. His theory explained EXAFS and thus EXAFS
was called the Kronig structure. His theory was called
the long-range order (LRO) theory because the band
structure is determined by the long-range periodic boundary conditions. Hayasi.35/ considered that the electron
waves that satisfied the Bragg condition form a standing
wave in a solid, and thus the electron transition from an
inner orbital to a standing wave state yields a maximum
of X-ray absorption. Shiraiwa et al..36/ and Kozlenkov.37/
improved the SRO theory to explain the EXAFS, but
their method needed to solve a Schrödinger equation to
obtain the EXAFS. Sayers et al..38/ proposed a Fourier
transform method to obtain local structural information
on condensed systems. Owing to their Fourier analysis,
we do not need to solve the Schrödinger equation directly
to obtain the local structure of matter. EXAFS had at that
time great potential to be developed as a powerful method
of analyzing the local structure of matter. The inelastic
mean free path (IMFP) of a photoelectron is usually
2 nm. When the photoelectron is scattered inelastically,
the coherence is forgotten. The coherent length, i.e. the
length within which the electron matter waves emitted
from a single source can interfere with each other, is
an important length to apply in the EXAFS method to
analyze a condensed system. When the IMFP is included
in the LRO theory, it is equivalent to the SRO theory.
5
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
EXAFS
XANES
S6+
Valence
band
εp
1s
S2–
ε
0
Figure 6 Schematic illustration of X-ray absorption and photoelectron excitation from the 1s to the unoccupied p state.
The XAFS represents the unoccupied electron density
of states for atoms, molecules, solids, or liquids. One of
the inner shell electrons, say a 1s electron, is excited into a
discrete or continuum unoccupied state by the incident Xray photon. The transition probability from the 1s to the
unoccupied state equals the X-ray absorption intensity
(only the photoelectric part is considered here), and
thus the plot of the intensity against the incident X-ray
energy is the XAS of a specimen. XANES is chiefly due
to the transition from the inner shell to the unoccupied
discrete level (Figure 6), and EXAFS is to the unoccupied
continuum level.
Total electron yield (arbitrary units)
Unoccupied p
state density
Energy
O
S2O32– S S O
O
2–
S4+
SO32–
2–
S
OOO
S6+
SO42–
O
S
OOO
2–
3 X-RAY ABSORPTION NEAR-EDGE
STRUCTURE
3.1 Chemical Shift and Line Shape
The XANES spectra show both the line shape modification and chemical shift.39/ of the absorption edge or
peak. Figure 7.40/ shows typical examples for the S K
edge for Na2 SO4 , Na2 SO3 , and Na2 S2 O3 . The sharp and
prominent absorption peak shown in Figure 7.40/ is called
the ‘‘white line’’. This is because in the early days of X-ray
experiments a white line developed on the X-ray film was
observed. The white line for insulators is usually sharper
than that for metals, because it corresponds to a 1s ! pŁ
electron transition, where the asterisk denotes an unoccupied antibonding orbital. The pŁ state is usually a sharply
localized state. The metal has a broad conduction band,
and thus the absorption spectra show an edge jump but
not a white line.
The white line energy plotted against the oxidation
number of sulfur is shown in Figure 8..41/ The source of
the chemical shift is both the unoccupied level shift and
core level shift. The range of the unoccupied level shift
ranges from the Fermi level (D0 eV) to the band gap
energy (Da few electron-volts). The core level shift is due
to the screening of core electrons by valence electrons;
2460
2470
2480
2490
2500
2510
Energy (eV)
Figure 7 Sulfur K edge absorption spectra of Na2 SO4 , Na2 SO3 ,
and Na2 S2 O3 . (Reproduced by permission from Sekiyama
et al..40/ )
if the atom is negatively charged then the core level is
shifted to a shallower binding energy, and if an atom is
positively charged then it is shifted to a deeper energy.
The source of the core level shift is the same as that of an
ESCA chemical shift.
In Figure 9.42/ is shown another example of a chemical
shift of the absorption edge for Al compounds: Al metal,
AlN, and four- and six-fold coordinated oxides. The
Al O distance of four-fold coordinated aluminum oxide
(0.17 nm) is shorter than that of six-fold coordinated
oxide (0.19 nm), because the oxygen ions interfere with
each other and cannot be close to the Al atom for six-fold
coordinated oxide. Thus the orbital hybridization of fourfold coordinated oxide is stronger than that of six-fold
coordinated oxide, and consequently the six-fold form is
6
X-RAY SPECTROMETRY
X-ray absorption
peak energy (eV)
2485
2480
S
OOO
2475
S
2–
2–
OOO
2470
O
S S O
O
–2
0
2465
2–
2
4
6
Nominal oxidation number
Figure 8 Relation between X-ray absorption peak and nominal
sulfur oxidation number. (Reproduced by permission from
Kawai et al..41/ )
Normalized absorbance
3
AIO6 in
kyanite
AIO4 in
sodalite
2
AIN4 in AIN
1
AI metal
0
–10
0
10
20
30
40
well of neighboring atomic potentials, is called the shape
resonance (Figure 4).
While the 1s ! pŁ transition is a sharp white line, the
1s ! sŁ transition usually results in a broad and weak
hump at higher energy,.44/ which is called the shape
resonance. The term shape resonance is used in the field
of atomic spectra. The excited state or ionized state is
bound in a potential wall, because of the centrifugal
force potential of a high angular momentum orbital such
as an f orbital, or surrounding potential such as F in
SF6 . However, as shown schematically in Figure 4, such a
surrounding potential does not have sufficient height to
enclose the electron, but a weak resonance is observable.
This is the origin of the term shape resonance.
The pre-edge structure shown in Figure 3 above is
observed for the K edge of transition metal compounds
whose local symmetry around the X-ray absorbing atom
is Td (tetrahedral). On the other hand, it is not observable
for locally Oh (octahedral) symmetry solids. This pre-edge
is sometimes said to be an electric quadrupole transition
from 1s to 3d, whereas ordinary optical absorption is the
electric dipole transition (1s ! 2p or 2p ! 3s, 3d). The
quadrupole transition probability is, however, very weak,
as shown in Table 2, where the probability is calculated by
the Dirac – Fock method..45/ The origin of such a strong
absorption as shown in Figure 3 is due to the electric
dipole transition. The unoccupied p orbitals strongly
hybridize with the d band for tetrahedral symmetry
compounds based on the group theory as shown in
Table 3,.46/ where both p and d orbitals belong to the
t2 orbital. Thus the electric dipole transition is strongly
observed at the energy of an empty d band. On the other
Energy – E0 (eV)
Table 2 Calculated transition
Figure 9 Al K edge XANES spectra of Al metal, AlN, sodalite,
probability for Cu
and kyanite. AlXn denotes the first shell coordination of
Al in each material. (Reproduced from J. Wong et al., ‘New
Opportunities in XAFS Investigation in the 1 – 2 keV Region’,
Solid State Commun., 92, 559 – 562,  1994, with permission
from Elsevier Science.)
ionic and the four-fold form is covalent. The effective
positive charge of six-fold coordinated Al3C is larger than
that of four-fold coordinated oxide. The chemical shift
of six-fold coordinated oxide is larger than that of fourfold coordinated oxide. The shift is strongly correlated
to Pauling’s electronegativity.43/ of the neighboring atom,
because the electronegativity determines the effective
charge of the ion.
The unoccupied discrete level is composed of Rydberg
states in the atomic picture, pŁ and sŁ orbitals in
the molecular-orbital picture (the asterisk denotes an
antibonding molecular orbital), or conduction bands in
crystals. The sŁ transition, which is formed in a potential
K – L1
K – L2
K – L3
K – M1
K – M2
K – M3
K – M4
K – M5
0.00000038
0.19
0.37
0.000000072
0.022
0.043
0.000025
0.000036
Table 3 Part of the character table of Td
Td
a1
a2
e
t1
t2
p
d
x2 C y2 C z2
(2z2
(x, y, z)
x2
y2 , x2
(xy, xz, yz)
y2 )
7
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
Table 4 Part of the character table of Oh
Oh
a1g
a2g
eg
t1g
t2g
a1u
a2u
eu
t1u
t2u
p
d
x2 C y2 C z2
(2z2
x2
y2 , x2
y2 )
(xy, xz, yz)
(x, y, z)
C
D
Absorption (arbitrary units)
E
[Co(NH3)6]l3
A
B
[Co(NH3)6]Br3
The chemical shifts of reference samples are measured
and plotted against the electronegativity, and then the
neighboring atom type is estimated for an unknown
material from the chemical shift of the absorption edge.
After the discovery of high-temperature superconductors,.49/ the understanding of the electron correlation
effect of transition metal compounds.50/ and rare earth
compounds has been greatly improved by the study of
XPS. Consequently, the understanding of the correlation effect, i.e. how the hole left in the final state of
photoionization interacts with d holes in transition metal
compounds, has developed substantially. Many reports
have been published concerning the electron correlation effect on the XANES line shape of complicated
materials..51/
Mixed-valence rare earth compounds are clearly
observed by the measurement of XANES, as shown in
Figure 11,.52/ but the intensity ratio sometimes does not
directly represent the mixed-valence components because
of a dynamic electron transfer, i.e. correlation effect, due
to the core hole screening..53/ The peak decomposition
of XANES spectra into Eu2C and Eu3C , as shown in
Figure 11, yields a rough estimate of the mixed-valence
state. However, the core hole created by the X-ray
absorption rearranges the valence electrons and thus
the peak intensity does not always represent the exact
[Co(NH3)6]Cl3
273 K
7700
7750
Energy (eV)
Figure 10 Co K edge spectra of [Co(NH3 )6 ]X3 (X D Cl,
Br, and I). The vertical bars show calculated spectra for
[Co(NH3 )6 ]3C . Peak A is due to the electric quadrupole
transition but still mixed with the p orbital owing to the
skewing of the molecular structure from exact octahedral
symmetry. (Reproduced by permission from Sano..47/  1988
The American Chemical Society.)
hand, p and d orbitals never mix with each other for Oh
symmetry, as shown in Table 4,.46/ where the p orbital
belongs to t2u and d belongs to eg and t2g . Therefore, the
p transition emerges at a different energy from the empty
d band for octahedral symmetry compounds. The true
electric quadrupole transition is very weak, as shown in
Figure 10..47/ However, even in this case, the observable
strength is due to the hybridization of the p character
into the empty d band. The intensity and energy shift of
the pre-edge peak are good indices for fingerprinting the
chemical environment in the compounds, especially for
biological samples..48/
Absorption (arbitrary units)
1.5
1.0
0.5
0.0
19 K
1.5
1.0
0.5
0.0
6.94
6.96
6.98
7.00
Energy (keV)
Figure 11 XANES spectra of EuNi2 Si0.5 Ge1.5 at 19 and 273 K.
The dashed-dotted and the dashed spectra indicate the Eu2C
and Eu3C final state components, respectively. (Reproduced
by permission from Wortmann et al..52/  1991 The American
Physical Society.)
8
X-RAY SPECTROMETRY
3.2 Calculation Method for X-ray Absorption
Near-edge Structure Spectra
The electronic states of photoelectrons whose kinetic
energy is from a few electron-volts to a few tens of
electron-volts are treated as conduction electrons in a
conduction band. Thus a multiple scattering (MS) method
or Green’s function method, which has been used to
calculate the electronic structure of conduction electrons
near the Fermi energy in metals, is applicable to calculate
the XANES of materials. The line shape of a XANES
spectrum represents the partial and local electron density
of states of the X-ray absorbing atom..54/ Hence any
kinds of electronic structure calculations other than the
MS theory, such as the LCAO-MO (molecular orbital
derived from a linear combination of atomic orbitals)
method or the APW (augmented plane wave) method, are
also applicable to interpret the near-edge fine structure.
One of the most popular methods for calculating XANES
spectra is the MS theory.
In the MS theory, a sphere of radius ri centered at the ith
atom is considered, and the solid is divided by spheres. A
spherically symmetric atomic potential V.r/ is put inside
each sphere and the potential equals zero or constant
outside the spheres. This is called the muffin-tin (MT)
potential. The wave function in the solid is expressed as
the overlap of spherical Bessel functions (radial part of
the wave function) multiplied by the spherical harmonic
functions (angular part of the wave function).
The wave function y.r/ of a photoionized electron is
scattered by an atomic potential V.r/ near the ionized
atom, and finally it becomes itself after being scattered
many times (Equation 4)
Z
1
exp.ikjr r0 j/
y.r/ D
V.r0 /y.r0 / dr0
.4/
4p
jr r0 j
where k2 D e is the kinetic energy of a photoelectron and k is real for e > 0 (photoionized electron),
exp.ikjr r0 j//.jr r0 j/ represents a spherically expanding wave, and V.r/ is the MT potential. This method
is called the MS method, Green’s function method, or
Korringa – Kohn – Rostker (KKR) method..55/ The KKR
method is only exact for solids that have translational
symmetry, or periodic boundary conditions. Small clusters, molecules, amorphous or surface adsorbates have a
lower symmetry, and it is difficult to apply directly the
KKR method. Thus the cluster calculation method was
proposed by Johnson.56/ and was called the multiple scattering Xa (MS-Xa) method, because Slater’s Xa exchange
potential.57/ is used in place of the Hartree – Fock (HF)
exchange integral. The Xa method is also called the
Intensity
portion of the Eu2C and Eu3C states before the X-ray is
absorbed.
E
T
640
650
Energy (eV)
Figure 12 Mn L2,3 XAS (E) of MnF2 compared with atomic
3d5 multiplet calculation including the crystal field splitting (T).
(Reproduced by permission from de Groot et al..60/  1990 The
American Physical Society.)
Hartree – Fock – Slater (HFS) method, and recently it has
been developed as a local density approximation (LDA)
theory. The calculation method for XANES spectra is
a modified MS-Xa method..58/ In another way, the MS
method is the expansion of the wave function of positive
energy by an infinite sum of the spherically outgoing and
incoming scattering waves. The electrons excited into the
continuum level have a wave function of a standing wave
formed by the infinite number of incoming and outgoing spherically traveling waves. That is to say, a wave
whose intensity is V.r0 /y.r0 / coming from every point r0
in space is synthesized and forms a wave y.r/ at point
r. This method produces a wave function similar to the
APW method, which is an appropriate method to calculate a metallic band structure, but APW requires a
greater number of basis functions than the MS method.
The wave function at point r is the sum of all the scattered
waves multiplied by the phase factor. The LCAO-MO
method is another choice for calculating the electronic
structures of solid or molecules, and is thus applicable to
the calculation of XANES spectra..59/
An atomic calculation yields a satisfactory agreement
between experiment and theory, as shown in Figure 12,.60/
after the inclusion of the perturbation of crystal field
splittings. Bragg reflection of electrons in a crystal
reproduces a rough XANES spectrum..61/
4 THEORY OF EXTENDED X-RAY
ABSORPTION FINE STRUCTURE
4.1 Single Scattering Theory
Whereas MS of photoelectrons in a solid is a good
approximation to treat XANES, because the electron
kinetic energy of the EXAFS region is very high, single
scattering is a good approximation to EXAFS except for
9
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
fk .r/
! exp.ikz/ C
f .#/
exp.ikr/
r
.5/
where f .#/ is the scattering amplitude and # is the
scattering angle (# D 0° for forward scattering and
# D 180° for backscattering). The scattering amplitude
of an electron of velocity v scattered by an atom of atomic
number Z is expressed by the first Born approximation
(Equation 6):
2
f .#/ D
e
[Z
2mv2
A.#/]
1
2
sin .#/2/
.6/
where e and m are the charge and the mass of an electron,
respectively, and A.#/ is the atomic structure factor for
X-rays, given by Equation (7):
Z 1
sin kr
r.r/r2 dr
.7/
A.#/ D 4p
kr
0
where k D .4pmv/h/ sin.#/2/ is the change in electron
momentum before and after the scattering and r.r/ is the
charge distribution in an atom. The forward scattering
amplitude crudely depends on the atomic number in a
way such that (Equation 8)
Z
1 1
1
4pr.r/r4 dr D Zhr2 i
.8/
f .0° / D
3 0
3
in atomic units, because (Equation 9).62/
Z 1
ZD
4pr2 r.r/ dr
.9/
0
where h i denotes an average. The calculated scattering
amplitude is shown in Figure 13..63/
The EXAFS is expressed by Equation (10):.64/
c.k/ D
X Nj
jf .k, p/j exp. 2s2j k2 / sin[2kRj C fj .k/]
2 j
kR
j
j
.10/
p
where k D 2m.hn E0 //h̄ is the photoelectron wave
vector, Nj is the number of nearest neighbors, jf .k, p/j
is the backscattering amplitude, and Rj is the distance
from the center atom. The exponential term contains
the Debye – Waller-like vibrational effect and dumping.
The dumping due to the finite coherent length of
the photoelectron, exp[ 2Rj /l.k/], is multiplied for
a more exact expression. The Debye – Waller factor
contains both effects of thermal vibration and geometric
randomness. The oscillating part of the EXAFS equation,
sin 2kR/.kR/2 , if plotted as a function of kR, is the
EXAFS oscillation.
1.0
f (θNi)(arbitrary units)
special cases. The wave function fk .r/ of a photoelectron
scattered by a single atom is asymptotically expressed by
Equation (5):
50 eV
50 eV
100
100
140
200
285
140
200
285
505
505
1320
0
0°
Forward
1320
45°
90°
135°
180°
Back
Scattering angle (θNi)
Figure 13 Calculated plane-wave scattering factor amplitude
jf j of nickel as a function of both the scattering angle qNi
and the photoelectron kinetic energy. (Reproduced from
M. Sagurton et al., ‘Derivation of Surface Structures from
Fourier Transforms of Photoelectron Diffraction Data’, Phys.
Rev. B, 30, 7332 – 7335,  1984, with permission from Elsevier
Science.)
The EXAFS oscillation amplitude is larger when the
atomic number of neighboring elements is higher. For
example, the Si K edge EXAFS oscillation amplitude
of Si is stronger than that of SiO2 , because the atomic
number of Si is higher than that of O. The white line
of SiO2 is sharper and stronger than that of Si. Hence
the EXAFS oscillation and the white line intensity do
not directly indicate the concentration of the atom in the
analyte. However, the edge jump is a good measure of
concentration, and the measurement of edge jump could
determine the concentration without a working curve, as
shown in Table 5..65/
The effect of thermal vibration on the line shape
of X-ray absorption spectra is shown schematically in
Figure 14..44/ This is the line in the XANES region.
Similarily, the EXAFS oscillation becomes unclear owing
to thermal vibration. As the atomic number becomes
Table 5 Results of copper – zinc
solution to test the trace element
analysis
Zn (µg mg 1
Cu solution)
Edge jump
0.092
0.049
0.020
0.000
0.0059
0.0035
0.0021
0.0010
Reproduced by permission from
Nomura..65/  1992 The American
Chemical Society.
10
X-RAY SPECTROMETRY
and it probes the local structure within the IMFP.
Thus 1 – 2 nm regularity, usually up to the next-nearest
neighbors, in the structure is sufficient for the EXAFS
oscillation to emerge.
Intensity (arbitrary units)
Asymmetric lineshape
4.2 Relation to Other Techniques (X-ray Photoelectron
Diffraction, Low-energy Electron Diffraction, X-ray
Fluorescence Holography)
Photon energy (arbitrary units)
Figure 14 Asymmetric line shape of X-ray absorption spectra
caused by the vibration of a diatomic molecule. (Reproduced by
permission from D.A. Outka, J. Stöhr, ‘Curve Fitting Analysis
of Near-edge Core Excitation Spectra of Free, Adsorbed and
Polymeric Molecules’, J. Chem. Phys., 88, 3539 – 3554 (1988). 
1998 American Institute of Physics.)
higher, the core hole lifetime becomes shorter. A
shorter lifetime of the inner shell level indicates that
the energy of the inner shell becomes vague because
of Heisenberg’s uncertainty principle. Consequently, the
EXAFS oscillation of the K spectrum for higher atomic
number elements is not clear compared with that of the
L edge spectrum of the same element.
The IMFP of photoelectrons is a function of kinetic
energy for a particular material, as shown in Figure 15..66/
It is 1 – 2 nm for the usual EXAFS experiments. Hence the
photoelectron is only coherent within a few nanometers,
Mean free path (nm)
5
4
3
X-ray photoelectron diffraction (XPD).62/ is used to study
the local structure of surfaces. The photoelectron intensity
as a function of detected polar and azimuthal angles is
measured in this technique. The photoelectron intensity
is anisotropic in its detection angle. This effect is due to
photoelectron diffraction, but roughly speaking it is due
to the photoelectron’s forward scattering by the nearestneighbor atoms around the photoelectron-emitting atom.
XPD uses forward scattering of photoelectrons; EXAFS
uses backscattering of photoelectrons.
Recently XPD has been treated as photoelectron
holography (PEH)..67/ The intensity distribution of the
photoelectrons of a single crystal is measured and Fourier
transformed, and then a local atomic structure of the
single crystal near the photoelectron-emitting atom can be
constructed. The phase shift of electron waves scattered
by a neighboring atom makes the analysis of the Fourier
transform for PEH complicated. The angular distribution
of the X-ray fluorescence intensity is measured and the
Fourier transform of the angular distribution reconstructs
the crystal image. This is called X-ray fluorescence
holography (XFH)..67/ XFH is free from the phase shift
problem, but this method is bulk sensitive, whereas XPD
and PEH are surface sensitive.
Low-energy electron diffraction (LEED).68/ is a surface
crystallography experimental method where electrons
of a few hundred electron-volts impinge on a single
crystal and a diffracted electron pattern is observed.
The penetration depth of these energy electrons is a
few nanometers, hence this method is surface sensitive.
Electron diffraction requires a periodic structure of at
least 10 nm on the surface, hence the LEED method
cannot probe the structure clusters of a few nanometers
on a surface.
2
5 DATA ANALYSIS AND SOFTWARE
PACKAGES FOR X-RAY ABSORPTION
FINE STRUCTURE
1
0
1
10
100
1000
10 000
Electron energy (eV)
Figure 15 Calculated IMFP of photoelectrons in gold. (Reproduced by permission from Kuzmin..66/ )
The measured (Figure 16a) X-ray absorption spectral
energy is converted into photoelectron momentum. The
smooth background µ0 .E/, which means an isolated atom
absorption coefficient, is subtracted from the observed
11
E
FY
TEY
0.7
,
,
,,,,,,,,,
,,,,,,,,
,
,,
,
,
,
,
,
,,,,,,,,,
,,,,,,,
,,
0.8
0.6
R1
0.5
0.4
0.3
0.2
0.1
0.0
1800
1900
2000
2100
2200
2300
2400
2500
Photon energy (eV)
(a)
2.5
Calc. EXAFS intensity
Absorption (arbitrary units)
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
E
4.0
1.3 Å
3.0
O
2.0
1.0
0.0
FY
TEY
500
800
900
1000
8
10
12
–1
Wavenumber, k (Å )
(b)
3.5
FY
TEY
3.0
R2
Calc. EXAFS intensity
6
,
,
,,,,,,,,,
,,,,,,,,
,
,
,
,
,
,,,,,,,,,,,,
,,,,,,,
,,
k 2 χ( k )
4
2.5
F (R )
700
E
0.0
–2.5
2.0
1.5
2.0
1.5
1.0
O
(b)
0.5
Cu
2.0 Å
0.5
0.0
500
1.0
(c)
600
Photon energy (eV)
(a)
0.0
C
600
700
800
900
1000
Photon energy (eV)
Figure 17 Schematic illustration of diatomic molecule (full
0
1
2
3
4
5
6
Distance, R (Å)
Figure 16 (a) Si K edge EXAFS spectra of an Si(001) wafer
measured using the X-ray fluorescence yield (XFY) method
and total electron yield (TEY) method. (b) Oscillation function
of (a). (c) Fourier transforms of (b). (Reproduced by permission
from Y. Kitajima, ‘Fluorescence Yield X-ray Absorption Fine
Structure Measurements in the Soft X-ray Region’, Rev. Sci.
Instrum., 66, 1413 – 1415 (1995).  1995 American Institute of
Physics.)
value µ.E/ and normalized according to Equation (11):
µ.E/ µ0 .E/
c.k/ D
µ0 .E/
.11/
and open circles) adsorbed on a four-fold coordinated site
of metal substrate (hatched circles). When the incident X-ray
beam electric vector is parallel to the diatomic molecular axis,
the absorption spectrum of the molecule is obtained (a strong
white line due to an insulating compound is observed). When
the incident X-ray beam electric vector is perpendicular to
the molecular axis, information on the metallic bond between
the adsorbed atom and the substrate metal is obtained.
(Reproduced by permission from J. Stöhr, ‘Geometry and Bond
Lengths of Chemisorbed Atoms and Molecules: NEXAFS and
SEXAFS’, Z. Phys. B: Condens. Matter, 61, 439 – 445 (1985). 
1985 Springer-Verlag.)
This is the EXAFS oscillation. If we want to enlarge the
oscillation for a larger k region, we sometimes plot k3 c.k/
or k2 c.k/ in place of c.k/ as shown in Figure 16(b)..69/
12
Then this is Fourier transformed as shown in Figure 16(c),
and a radial distribution function is obtained. To
obtain the coordination geometry, measurement of the
polarization-dependent EXAFS oscillation is important,
as shown in Figure 17(a) and (b)..70/ An example of S K
edge spectra of CS2 on a Cu(111) surface is shown in
Figure 18..71/
A spline function or higher order polynomial determines the smooth background. Theoretically, the smooth
background has a shape of tan 1 q at the threshold,
because the discrete absorption line shape is a Lorentzian
function and its sum in a Rydberg series becomes tan 1 q
as shown in Figure 18.
An incident X-ray beam forms a standing wave in
a large-sized single crystal. In this case, additional fine
structure, the 1985-eV structure in Figure 19,.72/ for
example, depending on the incident angle of X-rays,
is observable. The standing wave profile is sensitive to
the location of impurity atoms in a crystal, i.e. which site
in the lattice. The use of standing waves is one of the
92 K 30 L
σ∗
92 K 0.02 L
2460
1840 1860 1880 1900 1920 1940 1960 1980 2000
Photon energy (eV)
Figure 19 TEY spectrum of partially oxidized Si(111) wafer.
Additional structure at 1985 eV is due to the incident X-ray
Bragg diffraction (standing wave). (Reproduced from T. Ohta
et al., ‘A Possible Use of the Soft X-ray Standing Wave Method
for Surface and Interface Structure Analysis’, Nucl. Instrum.
Methods Phys. Res. A, 246, 760 – 762,  1986, with permission
from Elsevier Science.)
surface analysis methods, but sometimes interferes with
obtaining c.k/, as shown in Figure 19.
Another effect interfering with the observation of c.k/
is the multiple ionization effect. The effect of an additional
one or two electrons ionized from outer shell(s) is not
negligibly small..73/ The double ionization probability is
sometimes more than 30% of single K shell ionization.
This is a source of error in EXAFS analysis.
EXAFS Fourier analysis is sometimes not easy when
additional peaks such as multiple ionization, standing
wave structure, and impurity peaks originating from the
analyte, X-ray source, or X-ray optics emerge.
Data analysis methods have been developed and
several standard computer programs are now available.
CS2 /Cu(111)
θ = 55°
Exp.
Calc.
θ = 15°
θ = 55°
Fluorescence yield
Total electron yield
π∗
Total electron yield
(arbitrary units)
X-RAY SPECTROMETRY
Table 6 XAFS analysis computer programs
θ = 90°
2470
2480
2490
2500
2510
Photon energy (eV)
Figure 18 Experimentally obtained S K-edge XANES spectra
(dots) of a CS2 multilayer (30 L) at an X-ray incident angle
of 55° , and submonolayer (0.02 L) at 15° , 55° , and 90° .
(Reproduced from S. Yagi et al., ‘Structural and Electronic
Properties of Molecularly Adsorbed CS2 on Cu(III) Studied by
X-ray Absorption and Photoelectron Spectroscopies’, Surf. Sci.,
311, 172 – 180,  1994, with permission from Elsevier Science.)
ATOMS
AUTOBK
AUTOFIT
BAN
CDXAS
CERIUS2
EDA
EX.TR.As
EXAFIT
EXAFS and FITEX
EXAFS (for Mac)
EXAFSPAK
EXBACK
EXBROOK
EXCALIB
EXCURVE98
FEFF
FEFFIT
FUSE
G4XANES
GNXAS
LASE
MacXAFS
MURATA
REDUCE
REX
REX2
SEDEM
TT-MULTIPLETS
UWXAFS
WinXAS
XAFS
XAID
XANADU
XDAP
XFIT
13
FEFF is the most popular program that is used by EXAFS
users. The EXAFS analysis program is not difficult to
code, and a laboratory that studies EXAFS may have
its own program, but not always published. Some of the
programs listed in Table 6 can be down-loaded from Web
sites.
Posit
ion-s
dete ensitive
ctor
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
X-ray source
Sample
tor
a
rom
och
Mon
6 INSTRUMENTATION
6.1 Laboratory Extended X-ray Absorption Fine
Structure
To measure the X-ray absorption spectra, a strong X-ray
source of continuous energy is required, such as white
radiation from an X-ray tube or synchrotron radiation
(SR). A metallic wheel is rotated in vacuum and a
high electric potential is applied between the wheel
and a filament. Thermal electrons are emitted from the
filament and bombard the wheel target. Water flows
inside the wheel to cool it against heating by the electron
bombardment. To eliminate the heating, the wheel is
rotated. Therefore, this type of rotating anode X-ray tube
produces one order of magnitude stronger X-rays than the
ordinary sealed X-ray tubes. The electron deceleration at
the metal target converts the electron kinetic energy into
X-ray energy. The X-rays thus produced are continuum
X-rays in addition to characteristic X-rays and the
maximum energy is the acceleration electric potential
applied. The X-rays from the X-ray tube are then
monochromated by a crystal monochromator using the
Bragg diffraction condition. Then the monochromatic
X-rays are incident on the specimen as shown in
Figure 20..74/ Sometimes, to compensate for the weak
source intensity, a position-sensitive proportional counter
is used as shown in Figure 21..75/ However, the very simple
experimental set-up shown in Figure 22.76/ is sometimes
used.
Bent crystal
X-ray source
Fluorescent
X-ray detector
I0
Sample
I
Rowland circle
Figure 20 Example of EXAFS spectrometer using a rotating
anode X-ray tube. (Reproduced by permission from Rigaku..74/ )
Figure 21 Example of EXAFS spectrometer using a position-sensitive proportional counter. (Reproduced by permission
from Maeda et al..75/ )
iza
Ion
tion
m
cha
ber
Monochromator
I0
I
X-r
ay
tu
be
Sample
Figure 22 Laboratory EXAFS using a q – 2q goniometer.
(Reproduced by permission from K. Sakurai, ‘High-intensity
X-ray Line Focal Spot for Laboratory Extended X-ray Absorption Fine-structure Experiments’, Rev. Sci. Instrum., 64, 267 – 268
(1993).  1993 American Institute of Physics.)
6.2 Synchrotron Radiation Extended X-ray Absorption
Fine Structure
Recently, SR has frequently been used as an X-ray source.
Synchrotron is the name of an electron (or positron)
accelerator made of an ultrahigh vacuum (UHV) ring
and electrons rotating inside the ring. High voltage is
applied to the rotating electrons using variable-frequency
radio waves and the frequency is synchronized with the
electron rotation during the acceleration of the electrons
in the ring. When the electron speed reaches close to the
speed of light, a very sharp X-ray beam is emitted in a
tangential direction because of the relativistic effect. This
X-ray beam is called the SR. Usually SR from a storage
ring is used. A ring in which electrons (or positrons) are
rotated at a certain constant speed is called the storage
ring. Usually electrons accelerated to a sufficient speed by
a synchrotron or a linear accelerator are injected into the
storage ring, and the tangential radiation when a magnet
bends the electron beam is used as an X-ray source..77/ The
SR thus produced from a bending magnet is continuous
over a wide range (more than 1000 eV) of X-ray energy
and a few orders of magnitude stronger than the rotating
14
X-RAY SPECTROMETRY
,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,
,,,,,,,,,,,,
,,,,,,,,,,,,
,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,
,
,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,, , , ,
,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,
,,,,,,,,,,,,,,
,,,,,,,,,,,,,,
,,,,,,,,,,,,,,
,,,,,,,,,,,,,,
,,,,,,,
,,,,,,,,,,,,,,,,,,,,
,,,,,
,,,,,
,,
27-pole wiggler
e+
2.5-GeV storage ring
Directly
water-cooled
first crystal
Sagittally bent
second crystal
Vertical
focusing mirror
,,,
Slits
i0
monitor
Sample
7-element Si(Li)
detector
φ
ω
α
Figure 23 Schematic view of X-ray wiggler beam line. (Reproduced by permission from Oyanagi et al..78/ )
anode X-ray tube. The smaller emittance indicates the
electron orbit stored in a storage ring being sharpened,
but practically it indicates a smaller X-ray beam size
and higher photon density. The emittance is measured in
meter Ð radians (m Ð rad). The emittance is a measure of
beam quality. The smaller the emittance, the more the
beam becomes parallel. The SR is monochromated by a
single crystal.
Continuous X-rays from a bending magnet are most
convenient for X-ray absorption spectroscopic experiments. The rotating axis of monochromator crystals is
parallel to the electric vector of the SR X-rays to make
good use of the X-rays. To obtain stronger X-rays, SR
from an undulator or wiggler beam line is used. The
undulator and wiggler are insertion devices in the storage
ring, and made of many strong permanent magnets. The
electron beam in the storage ring is undulating when
it goes through an undulator, and a coherent quasimonochromatic X-ray beam is produced. It consists of
many harmonics and each harmonic has a narrow (say
100 eV) bandwidth. By changing the magnet gap width,
the peak energy of the X-rays from the undulator is
controlled; the wider the gap, the lower is the energy.
Thus, to scan the energy over 1000 eV continuously using
an undulator, both the undulator gap and monochromator crystal rotation should be controlled simultaneously.
This is a difficult task but now routinely done in some
SR undulator beam lines. An undulator can produce a
few orders of magnitude stronger X-rays than a bending
magnet beam line. If the X-rays produced by undulating by magnets are not coherently interfered, such an
insertion device is called a wiggler. X-rays from a wiggler
are not strong compared with those from an undulator
but are continuous in energy, and thus much easier to
use in X-ray absorption experiments than those from an
undulator. An example of the experimental set-up of a
wiggler is shown in Figure 23..78/
SR facilities are classified into first-, second-, and thirdgeneration sources. The first-generation synchrotrons
were particle accelerators, and spectroscopists parasitically used the SR. Such SR was unstable. The secondgeneration synchrotrons use a storage ring to obtain SR
but the emittance is still not small enough, i.e. 10 7 mrad.
The emittance of the third-generation synchrotrons have
emittance as small as 10 9 m Ð rad. Such a small-emittance
storage ring requires a large-radius electron orbit because
a large number of magnets are required to keep the electron beam cross-section small. The fourth generation of
synchrotron has not yet been constructed and not defined,
but may be a free electron laser facility using an electron
accelerator. The third-generation SR facilities are tabulated in Table 7, and the second-generation SR facilities
can be reached via the links of the Web pages listed.
The first crystal in the monochromator used in an SR
beam line experiences a high heat load, and the lattice
constant is slightly different from the second crystal.
The crystal optics should be cooled by flowing water.
To adjust the difference in the lattice constant between
the first and the second crystals, usually one of the two
crystals is independently finely moved by a piezoelectric
Table 7 Third-generation SR facilities and Web
sites
ALS
APS
ESRF
SPring-8
http://www-als.lbl.gov/als/
http://epics.aps.anl.gov/welcome.html
http://www.esrf.fr/
http://www.spring8.or.jp/
15
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
mechanism. The adjustment of the two crystals should
always be monitored for the measurement of EXAFS for
the 1000-eV range. The monitoring of the adjustment is
done by measuring the incident X-ray intensity, which is
maximized at every energy point scanned.
Sample
I0
(a)
El
de ectro
tec n
tor
6.3 Secondary Yield Techniques and Applications
The intensity of the monochromated X-rays is monitored by an ionization chamber. X-rays pass through
the ionization chamber (I0 ) and are then incident on a
specimen, and the transmitted X-ray intensity is measured by another ionization chamber. The XAS is
the plot of log.I/I0 / against the X-ray energy. The
absorption spectra are usually measured by this transmission method as shown in Figure 24(a)..79/ When the
X-rays are absorbed strongly by the sample, the secondary responses such as photoelectron intensity, sample
electric current intensity, secondary electron intensity
(electrons whose kinetic energy < 50 eV is mostly the
secondary electrons), Auger electron intensity, and X-ray
fluorescence intensity become strong. Therefore, equivalent spectra to the absorption spectra are measurable
by these secondary phenomena such as photoelectron
intensity, secondary electron intensity, Auger electron
intensity (Figure 24b), sample drain current (Figure 24c
and d), X-ray fluorescence intensity (Figure 24e), ion
intensity due to photostimulated desorption, and other
secondary techniques.
The photoelectron intensity for a single crystal has
an anisotropy with respect to the observed direction
because of the photoelectron diffraction. The angular
average of the photoelectron intensity measured as
the change in incident X-ray energy is the XAS. This
method is called the photoelectron yield method. If
Auger electrons are detected, this is the Auger electron
yield method. The intensity of Auger electrons from
a single crystal also has an angular anisotropy. The
detection angle is therefore important for interpreting
the observed data for these electron yield methods.
Many kinds of electrons are detected, such as secondary
electrons, core photoelectrons, valence photoelectrons,
and Auger electrons, as shown in Figure 25(a – c)..80/
The different kinetic energy electrons correspond to the
different probing depths. Thus the electron yield spectra
are a mixture of various depth spectra as well as a mixture
of various processes of electron production. The relation
between the X-ray absorption process and the electron
emission process is neither direct nor clear.
The electric drain current is of the order of 10 9 A
when using a bending magnet SR beam line. The electric
drain current is a measure of X-ray absorption, and this
method is called the TEY method. This is because the
drain current represents the sum of all the electrons
I
X-ray
(b)
e
X-ray
A
Grid
(c)
e
X-ray
A
X-ray
(d)
X-ray
detector
(e)
Flu
X-r ores
ay cen
t
X-ray
Figure 24 Various methods of measuring X-ray absorption
spectra. (a) Transmission method; (b) partial electron yield
method; (c, d) TEY method; and (e) XFY method. (Reproduced from J. Kawai et al., ‘Depth Selective X-ray Absorption
Fine Structure Spectroscopy’, Spectrochim. Acta Part B, 49,
739 – 743,  1994, with permission from Elsevier Science.)
emitted from the sample. The electrons produced in a
solid are scattered in the solid as shown in Figure 26,.81/
and only electrons produced near the surface contribute to
the electric drain current. When we detect ions desorbed
from the surface due to X-ray absorption, the ion intensity
represents the surface top layer.
These methods of detecting electrons (or electric
current) or ions are surface sensitive and therefore are
called surface extended X-ray absorption fine structure
(SEXAFS). If the sample current is measured in an
air or helium atmosphere, then the ejected electrons are
converted into O2 or other ions and a positive or negative
current is observable depending on the sample electric
potential with respect to the ground. This method is called
the conversion electron yield (CEY) method.
The XFY method is not surface sensitive, because
the fluorescent X-rays originate from as deep a location
as the X-ray attenuation length. However, if XFY is
combined with the grazing-incidence X-ray technique
(Figure 27),.82/ where the total reflection X-ray technique
is combined with the TEY and CEY methods, it becomes
more surface sensitive than normal-incidence TEY or
16
X-RAY SPECTROMETRY
φ
EF
Binding energy (eV)
EV
O
hν 1
(a)
Photoemission
B
hν 2
VB
,
,
,
,
,
,
,,,,, , ,,,,,,
,
,, ,, ,,,, ,, ,,,,
,
,
,
,
,
,
,
,
,
,
,
,
,
,,,,, ,,,, ,, ,,,,,
,
,
,
,
,
,
,
,
,
,
,
,
,,,, ,,,,,, ,, ,,,,,
,,
,
,,,
A
Kinetic energy (eV)
Auger
(b)
hν 3
B
A
Auger
VB
Yield window settings
Secondary
Elastic Auger
Partial Auger
Total
(c)
ES
EP
EA
Figure 25 Schematic photoelectron spectra for (a) the excitation energy below the excitation threshold of core level A, (b) just
above the absorption threshold but below the photoionization threshold, and (c) far above the threshold. The contributions to the
photoelectron intensity from different level photoelectrons and Auger electrons are indicated. At the bottom the window settings
for various electron yield X-ray absorption techniques are shown. (Reproduced by permission from Stöhr et al..80/  1984 The
American Physical Society.)
CEY. The X-rays are totally reflected on the surface
and the evanescent X-ray wave penetrates only a few
nanometers from the surface. X-ray reflectivity is also a
measure of XAFS.
The grazing exit angle method is also possible, as shown
in Figure 28,.83/ because of the reciprocal theorem of
optical beams. The XFY method has atomic selectivity
because an X-ray detector usually has energy resolution,
hence the signal-to-noise ratio is better than in the
TEY method, and minor elements adsorbed on the
surface can be detected by the XFY method. Xray absorption spectra of very dilute analytes can be
detected using the XFY method; the detection limit is
<1012 atoms cm 2 .
The X-rays emitted from a deep location in a specimen
suffer from the self-absorption effect and the spectral
shape is different from that of an absorption-free
spectrum..84/ The XFY method combined with the grazing
incidence method does not suffer heavily from the selfabsorption effect compared with the normal-incidence
method.
Some materials emit luminescence in the visible
wavelength range when irradiated with X-rays. This
optical luminescence signal intensity corresponds to the
17
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
hν
hν
Proportional
counter
e−
,
,,
,,
,,
,,
,,
,,
,
Vacuum
Adsorbate
atoms
A
Electron
escape
depth
L ~ 50 Å
θE
E
TEY
hν
Substrate
atoms
B
A
Sample
e−
Photon
mean free
path
1/µ> 1000 Å
Figure 28 Schematic experimental set-up of grazing exit angle
experiment for XFY and TEY. (Reproduced by permission
from Kitajima..83/ )
Figure 26 Photoabsorption and electron production in a solid
consisting of substrate atoms B and an adsorbed layer A. Only
electrons originating within a depth L from the surface will
contribute to the TEY signal. (Reproduced from J. Stöhr et al.,
‘Surface Crystallography by Means of Electron and Ion Yield
SEXAFS’, Surf. Sci., 117, 503 – 524,  1982, with permission
from Elsevier Science.)
amount of X-rays absorbed by the specimen. Various
processes of optical luminescence de-excitation are shown
in Figure 29..85/ Optical luminescence is usually strong
for rare earth compounds, but some crystals which
have defects in their crystal structure emit stronger
luminescence, although a perfect single crystal of the
same material does not emit optical luminescence.
The photoacoustic (PA) effect produces sound on
irradiating a sample surface by a chopped photon beam.
This effect was discovered by Alexander Graham Bell.
Heat is produced while the sample is irradiated by an
optical beam and it diffuses during the beam chopping.
The chopping frequency usually ranges from a few to
a few hundred hertz. The sound wave is detected by a
microphone or a piezoelectric device. When the chopping
frequency is low, the heat diffuses into deeper location in
the sample compared with when it is high. Thus the
probing depth is variable by changing the chopping
frequency. All the incident photon energy is finally
converted into thermal energy through nonradiative
transition processes in the solid. The PA process in the
visible wavelength range is used for the very sensitive
absorption spectrometry of thick bulk samples, which are
not transparent to an optical beam. This method has been
applied to the measurement of the X-ray absorption,.86/
where the incident X-ray beam should be chopped to
produce acoustic waves in the sample. This method is a
thermal yield method.
Bias
voltage
Sample chamber
Be
window
Si(111) mono.
Be
window Ionization
chamber
Slit
Cu mesh
Ionization
chamber
SR
XY
slit
Image
intensifier
Sample
Current
amp.
Current
amp.
Beam
stop
Current
amp.
V/F conv.
V/F conv.
Figure 27 Schematic experimental set-up for TEY and CEY at grazing angles. (Reproduced by permission from Zheng and
Gohshi..82/ )
18
,
,
,
,
,,,,
,
,,,,,
,,,,,
,,,,,,,,
,,,,,, ,
,,,,,
X-RAY SPECTROMETRY
,,,,,,,,,,
, ,
,,,,,,,,,,,
,
,,,,,,, ,
,,,,,,,,,,,,,,,,
,
,
,
,,,,,,,,,,,,, ,,,,,,
3
,,
,,,
,,,
,,,
,
,,,
,,,
,,,,
,,,,,
µ
η2 η1
η3
X-rays
2s
X-rays
X-rays
µ2
µ1
1s
Figure 29 Schematic diagram of X-ray absorption and optical
luminescence processes. Three different excitation processes,
from the 1s orbital to a continuum state (absorption coefficient µ1 ) and to a bound state (µ2 ), and from the 2s orbital
to a continuum state (µ3 ), give rise to a single luminescence
with luminescence yields h1 , h2 , and h3 , respectively. X-ray fluorescence, KLL Auger, electron multiscattering, nonradiative
decay, and radiative decay processes are schematically shown.
(Reproduced by permission from Emura et al..85/  1993 The
American Physical Society.)
the photoconductive spectra; electrical conductivity is
induced by the incident X-rays. Spectra thus measured
are sometimes the inverse of the transmission spectra and
sometimes similar to the transmission spectra, depending
on the concentration..88/ Electrode surface reaction
processes can be measured using X-ray absorption in
combination with the total reflection X-ray technique.
X-ray submicrometer beams are now available in major
SR facilities, and using these beam lines micro- or
nanobeam techniques are now applicable, as shown in
Figure 31,.89/ where the XFY is measured by a solid-state
detector (SSD). The energy resolution of an SSD is of the
order of 100 eV, while the energy shift of an absorption
edge is a few electron-volts. If the incident X-ray energy is
between the edge energies of two chemical states (say FeO
and Fe2 O3 ), then only one kind of chemical state (FeO)
can emit the X-ray fluorescence. Using this technique,
chemical state mapping is possible.
Using a bent crystal monochromator as shown in
Figure 32,.90/ multiple-energy X-rays can be focused
on a sample and the transmitted X-rays are detected
by a position-sensitive detector, which is made of a
photodiode array (PDA). Using such a kind of energydispersive optics, one spectrum can be measured within
a few milliseconds..91/ This method is called quick X-ray
absorption fine structure (Q-XAFS).
Circularly polarized X-rays can be produced by
linearly polarized X-rays transmitted through a diamond
single crystal at a special angle depending on its
wavelength, which is called the phase retarder, as shown in
Figure 33..92/ The vertical and horizontal components, the
ratio of which is called helicity, of the X-ray electric vector
can be controlled by the small rotation and tilting of the
diamond crystal. Absorption spectra of a magnetic sample
are measurable. This is X-ray magnetic circular dichroism
(XMCD) X-ray absorption. The magnetic S and N poles
applying the magnetic field to the sample are inverted
Leads
L
electrodes
,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,, , ,,l , , ,, , ,,
Microscope
with CCD
w
Mylar
window
Leads
Figure 30 Schematic illustration of a liquid cell. (Reproduced
by permission from T.K. Sham, R.A. Holroyd, ‘Photoconductivity Measurements of X-ray Absorption of Liquids: Fe K-edge
Spectrum of Ferrocene in 2,2,4-Trimethylpentane’, J. Chem.
Phys., 80, 1026 – 1029 (1983).  1983 American Institute of
Physics.)
Liquid samples are inserted into a cell shown in
Figure 30,.87/ and an electrode is used to measure
TV monitor
Ionization
chamber
SR
Si(111)
monochromator
,
,,,,,,
,, ,,,
,, , ,,,,,
,, ,,,
,,,,,,,,,,,,
,, ,
hν
,,,,,,,,,,,,,,,,,,,, Quartz tube
,
,,, ,,,, ,,,,,, ,,,, ,
,, ,
, , Ni
Pinhole
Sample
stage
y
Focusing mirror
x
Si(Li) SSD
Data
processor
Electronics
Figure 31 Schematic illustration of an X-ray fluorescence
microprobe at the Photon Factory. (Reproduced from Nakai
et al.,.89/ courtesy of Marcel Dekker, Inc.)
19
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
Monochromator
Magnetic field
Energy
SR
Fermi energy
Sample
L3
L2
Position-sensitive
detector
Figure 34 One-electron model used to explain the X-ray
Figure 32 Energy-dispersive system at a synchrotron facility.
(Reproduced by permission from Derbyshire et al..90/ )
or the circularly rotating direction of the X-ray electric
field is inverted and the difference in the absorbance
is measured. The former is usually used to measure
the dichroism. Magnetic thin multilayers have recently
become important for information mass storage devices,
and these materials are characterized with microbeam
XMCD X-rays. The difference in the absorption coefficients for the left and right circularly polarized X-rays
is illustrated schematically in Figure 34..93/ The details of
MCD are described in several books..94 – 97/
High-resolution X-ray fluorescence spectra of transition
metal compounds show multiplet splitting due to the
exchange interaction between the unoccupied 3d level
and the core X-ray hole. Thus the XFY absorption
spectrum of each multiplet line provides spin-selective
Si(111) double-crystal
monochromator
Diamond
phase retarder
absorption dichroism process and intensities. The d band is split
into spin-up and spin-down bands. The absorption of circularly
polarized X-ray photons by the spin – orbit split 2p shell creates
a spin-polarized core hole. (Reproduced by permission from
Duda et al..93/  1994 The American Physical Society.)
absorption spectra, as shown in Figure 35..98/ This method
can measure spin-selective X-ray absorption spectra
without applying a magnetic field to the sample. This
method is useful for characterizing mixed-valence protein
compounds.
The phase transition due to the temperature change is
observable, as shown in Figure 36..99/ The phase transition
is a small change in bond distance and bond angle,
and consequently the electronic structure of the sample
changes. Thus both XANES and EXAFS region spectra
change their line shapes.
The surface of water, where a liquid monolayer is
present, could be analyzed by grazing incidence X-ray
reflection XAFS..100/ When the monolayer absorbs metal
Ionization
chamber (I 0)
Electromagnet
Ionization
chamber (I )
X-ray from
undulator
Piezo translator
From piezo driver
Sample
To current amplifier
To current amplifier
Figure 33 Experimental set-up for XMCD measurements with the helicity-modulation technique. (Reproduced by permission
from Suzuki et al..92/ )
20
X-RAY SPECTROMETRY
n
de
ci
In
tX
ys
-ra
3d
3d
3p
3p
7
P
K β 1,3 X-rays
1s
1s
Photoionization X-ray fluorescence
of 1s electron by
X-ray absorption
Figure 35 Schematic illustration of absorption and emission
(Kb1,3 lines) of X-rays due to 1s down-electron photoionization
of Mn2C ion; 1s up-electron photoionization produces the Kb0
X-ray emission spectral line. (Reproduced by permission from
Grush et al..98/ )
Normalized intensity
σ*
π*
d
RT
120 °C
530
535
Photon energy (eV)
Figure 36 O 1s absorption spectra of VO2 measured at room
temperature and at 120 ° C. (Reproduced by permission from
Abbate et al..99/  1991 The American Physical Society.)
ions from the water solution, the concentration of the
metal ion on the surface is slightly higher than that in the
water. The coordination structure around the metal ion
is analyzed by the EXAFS method.
When a powder is measured by the XFY and TEY
methods on a substrate, then the depth-selective chemical
state analysis of a fine particle can be performed. Fly ash
is a powder of micrometer-sized particles, which are a
source of acid rain when they are dispersed in the air. The
particles are put on an aluminum foil and irradiated
by monochromated X-rays, and XANES spectra are
measured by TEY and XFY methods..101/ The TEY
method is sensitive to the surface chemical state of the
powder particle, and XFY is sensitive to deep parts of the
particle (micrometers). The chemical shift of the white
line in the absorption spectra is a measure of the oxidation
state of an element in the particle.
The surface catalyst process could be elucidated by the
analysis of EXAFS spectra. The incident X-ray polarization dependence is an important parameter for the determination of the geometry of a reactant and the surface..102/
X-ray detectors in the XFY method have been
developed for X-ray absorption experiments, such as
a 19-element Ge detector array; a schematic illustration
of a seven-element detector is shown in Figure 23; a 100element detector array can be used for more efficient
detection of X-rays.
Transition metals are usually a target of XAFS analysis,
the energy range of which is from 5 to 20 keV. The
beamline for X-rays of this energy range uses Be and
polymer films as windows to separate the vacuum system
from the atmosphere. Both lower and higher energy
XAFS experiments require different techniques.
Soft X-ray XAFS experiments, ranging from 0.1 to
5 keV, require UHV techniques. This is because any
windows between the SR storage ring and the sample
heavily absorb X-rays, hence a windowless beamline is
required. Consequently, the sample chamber is made
of UHV components and must be baked out up to
200 ° C. The contaminants in X-ray windows and other
X-ray optics are carbon and oxygen, which are in the
soft X-ray region (250 – 600 eV). Hence a windowless
system is appropriate for the analysis of these elements.
The shortcoming of the soft X-ray region experiment
is the UHV system, because samples requiring X-ray
absorption analysis could not always be inserted into
the UHV system because they would emit gas into the
clean system. A vacuum of 10 2 Pa is sufficient to avoid
the absorption of X-rays in the X-ray path. The XAFS
spectra of this soft X-ray region are surface sensitive and
the profile changes of the spectra due to chemical state
are very large. The spectra measured can be used for the
same purpose (chemical state analysis) as XPS or ESCA.
The detection limit of XAFS is usually lower than that of
ESCA, hence XAFS has an advantage over ESCA if SR
is available.
XAFS experiments higher than 20 keV require different experimental techniques. The number of application
examples is not large, mainly because high-energy X-ray
sources are limited without using third-generation SR
facilities. In place of measuring this energy range K-edge
XAFS, the L-edge XAFS, the energy of which usually
falls in the range 5 – 20 keV, is measured. The L XAFS
spectra are composed of L1 , L2 and L3 edge jumps, which
interfere with each other. To avoid this, the K edge is
useful for the analysis. The lifetime of the K hole state
of high-energy K-edge XAFS of higher atomic number
elements is, however, shorter than the long-wavelength
region. Because of the Heisenberg uncertainty principle,
21
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
the line widths of the absorption spectral components
are as large as 100 eV. Both the EXAFS oscillation and
XANES lose fine structure owing to this lifetime broadening. High-energy XAFS has recently been measured
with the development of third-generation SR facilities,
because the numerical analysis overcomes the short lifetime effect.
7 SOURCES AND DATABASES
Academic societies and E-mail lists discuss the standardization of X-ray absorption spectrometry. As XAFS is
used in many areas of research, standardization has been
required. To achieve standardization, the International
XAFS Society (IXS) was established in the 1990s. The
purpose of the IXS is stated as follows:
The International XAFS Society represents all those
working on the fine structure associated with inner-shell
excitation (near-edge and extended) by various probes
(e.g. X-rays and electrons), and related techniques for
which the data are interpreted on the same physical basis.
The purpose of the IXS is to oversee activities which
benefit the community as a whole, to establish operational
committees, to provide for education in the field, to
disseminate relevant information, to work with other
related regional, national and professional organizations
in promoting and developing XAS and related disciplines,
and to act as representative for the community to other
professional organizations.
This society has a close relation to the International Union
of Crystallography (IUCr). The WWW home page of the
IXS is at Illinois Institute of Technology, http://ixs.iit.edu/,
where a large number of XAFS databases are presented.
This WWW page links to other related WWW home
pages. National society and working groups are active
in many countries. All the information concerning these
activities is obtainable at the international conferences on
XAFS. The first XAFS international conference was held
at Daresbury, UK, in 1981, and subsequent conferences
are listed in Table 8.
Many kinds of activity reports published by SR facilities
are useful sources of experimental methods and standard
spectra. Journal sources are listed in Table 9. Fundamental reviews in Analytical Chemistry published in even
years relate to X-ray absorption spectrometry..113 – 120/
In a book by Meisel et al.,.121/ references are classified
by atomic number and spectral series. Recently several
books which treat newer X-ray techniques.122 – 126/ and
concerning X-ray absorption.127,128/ have been published.
The Materials Research Society has held symposia on
applications of SR in materials science..129 – 131/
The Denver X-ray analysis conference and international conferences on electron spectroscopy, on X-ray
Table 8 List of international XAFS conferences and
proceedings
Conf. no.
1st
2nd
3rd
4th
5th
6th
7th
8th
9th
10th
11th
Date
Location
Ref.
March 1981
September 1982
July 1984
July 1986
August 1988
August 1990
August 1992
August 1994
August 1996
August 1998
August 2000
Daresbury
Frascati
Stanford
Fontevraud
Seattle
York
Kobe
Berlin
Grenoble
Chicago
Ako
103
104
105
106
107
108
109
110
111
112
–
Table 9 Source of information (journals)
Advances in X-ray Analysis
Analytical Chemistry, Fundamental Review, even years.113 – 120/
Journal of X-ray Science and Technology
Journal of Electron Spectroscopy and Related Phenomena
Journal of Synchrotron Radiation
Physical Review B
Surface Science
Synchrotron Radiation News
X-ray Spectrometry
and inner-shell processes and on vacuum ultraviolet
physics are sources of X-ray absorption spectroscopy
and spectrometry.
8 ALTERNATIVE METHODS
8.1 Electron Energy Loss Spectroscopy
An electron beam, with an energy from a few hundred electron-volts to a few hundred kiloelectron-volts,
impinges on a sample and loses its kinetic energy. When
the sample is a bulk material, reflected electron energy is
measured. Usually the loss of transmitted electron energy
is measured for thin-film samples less than a few micrometers or a few tens of nanometers thick. This is called
EELS..132/ EELS is usually combined with transmission
electron microscopy (TEM). The electron energy loss
structure is similar to the XAFS. The EXAFS region in
EELS is called the extended electron energy loss fine
structure (EXELFS). Forward-scattered (0° ) electron
energy loss spectra, formed when electrons are transmitted in a thin film, are approximately equivalent to the
optical spectra; the selection rule is the electric dipole.
Energy loss spectra of electrons scattered at a large angle
are not treated by the electric dipole transition, and
sometimes include optically forbidden transitions. The
transmission method used in TEM has a very high spatial
22
Although the characteristic X-ray wavelength of an
element is usually separated from the absorption edge
wavelength of the same element for hard X-rays, they
are very close to each other for the soft X-ray region.
These close lines are, for example, transition metal La,b
X-ray emission lines and L2,3 absorption edges. The La
and Lb X-ray emission lines emitted in a deep location
in a solid are absorbed during the travel in the solid.
Hence the X-ray emission spectra have dips due to the
X-ray absorption spectra. The profiles of the La,b X-ray
emission lines of transition metals excited by different
electron energies (3 and 16 keV) change because of the
self-absorption effect..135/ If the electron energy is high
(16 keV), then the penetration depth of the electron
is deeper. Hence the X-ray emission spectrum suffers
heavily from the self-absorption effect. In contrast, if the
electron energy is low (3 keV), then the penetration depth
is shallow, and the X-ray emission spectrum is free from
the self-absorption effect. The comparison of these two
spectra yields an X-ray absorption. Similarly, one set of
X-ray emission spectra is obtainable by tilting the sample
to the X-ray detector or to the incident electron beam,
when the electron energy is fixed.
2000
1500
A
1000
500
0
1200
B
1180
1160
1140
1120
1100
Energy (eV)
Figure 37 (A) Low-energy satellites (the radiative Auger
satellites) of the Ka X-ray fluorescence spectrum of MgO
compared with (B) XANES measured at an SR facility.
(Reproduced by permission from Kawai and Takahashi..136/ )
Rayleigh
θ = 60°
Intensity
8.2 Self-absorption
2500
Intensity (counts per 4 s)
resolution, hence chemical state imaging by the chemical shift of the absorption edge is possible..133,134/ High
energy resolution and high spatial resolution are not
always achieved by a single instrument. The EELS spectra are sensitive for low atomic number elements such as
boron and carbon. It is not easy to measure the XAFS
spectra of these long wavelengths using an SR facility.
X-RAY SPECTROMETRY
Raman
×10
Compton
8.3 Extended X-ray Emission Fine Structure
The radiative Auger effect (RAE) is always associated
with the X-ray characteristic lines and this effect is an
energy loss structure in characteristic X-ray emission, as
shown in Figure 37..136/ The second electron shaken up
into an unoccupied orbital has similar information to the
XAFS. This is called EXEFS..137/ This method is used to
measure low atomic number elements such as Na, Mg, Al,
and Si, because the RAE satellite intensity is strong for
these elements. If wavelength-dispersive electron probe
microanalysis (EPMA) is available, XAFS spectra of 1 µm
diameter area are measurable using this method.
8.4 X-ray Raman Scattering
X-ray Raman scattering is the effect of energy loss
on X-ray scattering. Raman scattering is a similar
physical process to Compton scattering. The difference
is that Raman scattering involves scattering by core
electrons whereas Compton scattering involves scattering
0
500
8265
7765
Energy (eV)
Figure 38 Rayleigh, Compton, and Raman scattering spectra
of 8265-eV incident X-rays by graphite observed at q D 60° .
(Reproduced by permission from Tohji and Udagawa..138/ 
1987 The American Physical Society.)
by conduction band electrons. X-ray Raman scattering is
a method for measuring soft X-ray absorption spectra
(say of carbon) with a hard X-ray spectrometer (a few
kiloelectron-volts). Hard X-rays can be measured in
air; soft X-ray absorption spectroscopy, which usually
requires UHV, is possible in air by this method. Hard Xrays (8265 eV) impinge on a carbon-containing sample,
and the X-rays lose energy by the carbon K edge due to the
Raman scattering (ca. 300 eV), as shown in Figure 38..138/
23
ABSORPTION TECHNIQUES IN X-RAY SPECTROMETRY
The X-ray that should be detected is at ca. 8 keV, which
still falls in the hard X-ray region. The XAFS study of
catalysts during reaction with gases is possible using the
Raman effect.
also powerful for analyzing mixed chemical states in
industrial, environmental, and biological analytes. The
development of SR facilities will make it possible to
measure nanometer-sized samples in less than a few
milliseconds.
8.5 Diffraction Anomalous Fine Structure
DAFS was proposed by Stragier et al..139/ XAFS usually
measures the wavelength dependence of f2 , the imaginary
part of the atomic structure factor; DAFS measures f1 .
The wavelength dependence of f1 and f2 has a close
relation through the Kramers – Kronig transformation.
In the DAFS experiment, the intensity of a diffraction
peak of a specimen is measured by the change in the
incident X-ray energy. The sample and detector angles
(q 2q) are measured by the change in the incident
X-ray energy, or powder X-ray diffraction patterns are
measured by the change in incident X-ray energy. This
method can measure site-selective XAFS of the same
element, because the diffraction peak corresponds to a
different site in the crystal. If the diffraction peaks which
originate from the surface and bulk phases are separated,
space-selective EXAFS-like spectra are obtainable by
this method.
8.6 b-Environment Fine Structure
The b-electron emission process in a nuclear conversion
process suffers interference by the crystal structure for
the same reason as EXAFS. This method is called
BEFS..140/
8.7 Inverse Photoemission Spectroscopy
IPES is an alternative method to measure the unoccupied electronic structure by irradiating electrons and
detecting photons..141/ This method is otherwise called
bremsstrahlung isochromat spectroscopy (BIS). The
extended structure like EXAFS is also observable in BIS
and this is called the extended X-ray bremsstrahlung
isochromat fine structure (EXBIFS)..142/ The BIS is
usually combined with an ESCA instrument, and thus
occupied and unoccupied electronic structures (similar to
XANES) are measurable..143/
ABBREVIATIONS AND ACRONYMS
APW
BEFS
BIS
CEY
DAFS
EELS
EPMA
ESCA
EXAFS
EXBIFS
EXEFS
EXELFS
HF
HFS
IMFP
IPES
IUCr
IXS
KKR
LCAO-MO
LDA
LEED
LRO
LUMO
MS
MS-Xa
MT
NEXAFS
9 CONCLUSION
X-ray absorption spectroscopy is chiefly used in the area
of electronic structure study and structural analysis for
the study of new materials, surfaces, and catalysts. The
spectra measured are surface sensitive or bulk sensitive
depending on the detection method. Chemical shift and
profile changes are observable. Thus the spectral analysis
is useful for materials characterization. This method is
PA
PDA
PEH
Q-XAFS
RAE
SEXAFS
SR
Augmented Plane Wave
b-Environment Fine Structure
Bremsstrahlung Isochromat
Spectroscopy
Conversion Electron Yield
Diffraction Anomalous Fine Structure
Electron Energy Loss Spectroscopy
Electron Probe Microanalysis
Electron Spectroscopy for
Chemical Analysis
Extended X-ray Absorption Fine
Structure
Extended X-ray Bremsstrahlung
Isochromat Fine Structure
Extended X-ray Emission Fine
Structure
Extended Electron Energy Loss
Fine Structure
Hartree – Fock
Hartree – Fock – Slater
Inelastic Mean Free Path
Inverse Photoemission Spectroscopy
International Union of
Crystallography
International XAFS Society
Korringa – Kohn – Rostker
Linear Combination of Atomic
Orbitals-Molecular Orbital
Local Density Approximation
Low-energy Electron Diffraction
Long-range Order
Lowest Unoccupied Molecular Orbital
Multiple Scattering
Multiple Scattering Xa
Muffin-tin
Near-edge X-ray Absorption Fine
Structure
Photoacoustic
Photodiode Array
Photoelectron Holography
Quick X-ray Absorption Fine Structure
Radiative Auger Effect
Surface Extended X-ray Absorption
Fine Structure
Synchrotron Radiation
24
X-RAY SPECTROMETRY
SRO
SSD
TEM
TEY
UHV
XAFS
XANES
XAS
XFH
XFY
XMCD
XPD
XPS
Short-range Order
Solid-state Detector
Transmission Electron Microscopy
Total Electron Yield
Ultrahigh Vacuum
X-ray Absorption Fine Structure
X-ray Absorption Near-edge Structure
X-ray Absorption Spectrum
X-ray Fluorescence Holography
X-ray Fluorescence Yield
X-ray Magnetic Circular Dichroism
X-ray Photoelectron Diffraction
X-ray Photoelectron Spectroscopy
RELATED ARTICLES
Environment: Water and Waste (Volume 4)
X-ray Fluorescence Spectroscopic Analysis of Liquid
Environmental Samples
Surfaces (Volume 10)
Auger Electron Spectroscopy in Analysis of Surfaces ž
Soft X-ray Photoelectron Spectroscopy in Analysis of
Surfaces ž X-ray Photoelectron Spectroscopy in Analysis
of Surfaces
4.
5.
6.
7.
8.
9.
10.
11.
12.
Electroanalytical Methods (Volume 11)
X-ray Methods for the Study of Electrode Interaction
X-ray Photoelectron Spectroscopy and Auger Electron
Spectroscopy (Volume 15)
X-ray Photoelectron and Auger Electron Spectroscopy ž
X-ray Photoelectron Spectroscopy and Auger Electron
Spectroscopy: Introduction
X-ray Spectrometry (Volume 15)
Energy Dispersive, X-ray Fluorescence Analysis ž Structure Determination, X-ray Diffraction for ž Total
Reflection X-ray Fluorescence ž Wavelength-dispersive
X-ray Fluorescence Analysis ž X-ray Techniques:
Overview
13.
14.
15.
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