CopyrightThis document is copyright (c) 2012 by Paul Fons

An Introduction to Xray Absorption
Spectroscopy

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2

1

2

XAFS Characteristics

What is XAFS
(X-ray Absorption Fine-Structure)• elementally selective• local atomic coordination• chemical / oxidation state• applies to any element• works at low concentrations• small sample volumes (even monolayers)• XAFS (also XAS) refers to the modulation of the x-ray
absorption coefﬁcient near and above an absorptionedge.

• XAFS is elementally selective and can explore the local
atomic environment about the absorbing atom

3

4
3

4

XAFS Example

XAFS Example

Complex Scattering Factor of Fe

15

Complex Scattering Factor of Fe

15

10

10

f’’

f’’
5

5
Pre-Edge

00Pre-Edge

2000

4000

Energy (eV)

6000

0

8000

Modulation of the x-ray absorption above the edge
constitutes the XAFS signal

0

2000

4000

Energy (eV)

6000

8000

Modulation of the x-ray absorption above the edge
constitutes the XAFS signal
5

5
5

5

XANES vs. EXAFS

XAFS Example• XANES X-ray Absorption Near-Edge Spectroscopy (0-40 eV)• EXAFS Extended X-ray absorption Spectroscopy (40-1000 eV)
XANES and EXAFS are labels for two parts of the same spectra.
They are distinguished due to the approximations used in theanalysis of data
XANES region: The energy of the photoelectron (PE) is small,the mean free path long (nm) and PE interactions strong
requiring more time consuming cluster calculations

Pre-Edge

EXAFS region: The PE energy is higher and scattering can betreated as a ﬁnite series of interactions that can be wellapproximated by the the EXAFS equations we will encounter.

Modulation of the x-ray absorption above the edge
constitutes the XAFS signal
5

6
5

6

A visual interpretation of XAFS
Photon In
B

Photoelectric EffectPhotoelectron out
B

For a s-state core level, an
outgoing spherical wave
moves out from theabsorbing atom.

B

eA

A

B

B

• An x-ray is absorbed

Continuum

via the photoelectric effect inwhich Ephoton induces a transition
from a core-level to a continuum
state

The outgoing spherical wave is scattered by the (coloumb)potentials of neighbor atoms causing interference with itself.
The absorbing atom serves both as the source of thephotoelectron and the detector. In other words, the XAFS signal
reﬂects the local neighborhood about the absorbing atom.

• The atom is left in an excited statewith an empty level (core hole)• Excess energy becomes kinetic

energy of ejected photoelectron
EKinetic = hν - EEdge

V

Energy

IV

M III
II
I

III

L II
I

K

I

A K-shell excitation

7

8
7

8

Recombination Processes

Linear Absorption Coefﬁcient

When a core-hole is created, the absorbing atom is in an
excited state and can return to the ground state via Auger
electron emission (AES) or X-ray ﬂuorescence (XRF)

The intensity of an x-ray beam passing through matter can be
described byContinuumContinuum

M
L

M
L

K

K

K

Continuum

M
L
K

K

I = I0 e−μtwhere I0 is the initial intensity, t is the sample thickness, and µ
is the x-ray absorption coefﬁcient

XRF: photon out. Ephoton
is element speciﬁc andoffers a way to measure
XAFS signals selectively
and with great sensitivityµ depends on the x-ray
energy, the atomic number
Z of the absorber, thedensity ρ, and the atomic
mass A

AES: Unlike XRF which has an (energy
dependent escape depth typically intens of μm in the hard x-ray region,
AES is a surface sensitive detection
technique

ρZ 4
μ∝
AE 3
9

10
9

10

EXAFS

Absorption in a Compound

Extended X-ray Absorption Fine Structurez

The loss in a slice of thickness dz

We are interested in the interference function in the absorption
signal as it contains information about local structuredI = −I(z)μdz

χ(E) =The number of absorption events W is
thus

W = I(z) ρat σa dz = I(z)μ dz


ρm NA
σa
μ = ρσa =M
whereρat = atomic number density
σa= atomic cross sectiondz

μ(E) − μ0 (E)Δμ(E0 )

By subtracting away the smooth atomic “bare atom” backgroundand dividing by the edge step Δµ0 we can ﬁnd the oscillations χ
normalized to a single absorption eventµ for a compound canthus be calculated as

3

5
2

0

 j
μ(E) =
ρat σj

1

-5
0

j

-10
11100

11200

11300

11400
E(eV)

11500

11600

11700

µ(E) and smooth µ0 for GeTe
11

100

200

300

400

500

600

µ(E) and smooth µ0 for GeTewith E0=11103 eV

11

EXAFS Equation

12
12

XANES

increasing
valence

While the XANES region requires calculations, the EXAFS region
can be ﬁt using the EXAFS Equation
XANES region (absorption edge) can beused to determine chemical valence
Unlike EXAFS contains bond angle
information although not simply extracted

Here Fi(k) and δ(k) encompass the photoelectric scattering propertiesof the ith neighboring atom. If we know F and δ, we can ﬁt:Spectra can be added to match
experimental spectra revealing the local
chemical environment

R the distance to the neighboring atom i
N coordination number of the neighboring atom
σ2 mean squared disorder

XANES edge for S compounds in
different oxidation states

For light elements XANES spectra canreveal the conduction band DOS

Both Fi(k) and δ(k) depend on the atomic number Z so the type ofatom surrounding the absorbing atom
13
13

XANES spectra for Cr6+ and Cr3+

14
14

Measurement Techniques

Transmission
I0

I1

Gas Ion Chambers• We would like to measure a signal proportional to theμ(E)t = −ln(I/I0 )number of x-rays absorbed• Transmission (directly measure the transmitted beam)• Fluorescence (measure the outgoing photon when the• For concentrated samples, transmission is often best techniquefor XAFS, but proper sample preparation is required∋ 1 < Δμ < 3• Want• For Fe foil Δµ=1 requires 3.7 μm thick foil!

core hole recombines: see slide 8)• Electron Yield/Conversion Electron Yield (measure the
Photoelectron/Auger electron signal)

often solution is to make BN+sample powder pellet• samples must be uniform without pinholes• the grain size must be smaller than the absorption length
15

16

15

16

Fluorescence Measurements

Fluorescence Measurements

Fluorescence
Detector If• For a good ﬂuorescence experiment
Energy Discrimination: Eliminate unwanted energy photons by physical orelectronic ﬁlter
Solid Angle: As emitted XRF photons are isotropic, maximize solid angle

An example of physical ﬁltering is the use ofa so-called “Z-1” ﬁlter.

•

For example, the Fe Kα emission lines arelocated below the K-edge of the next “Z-1”element down, Mn.

can be measured

Background from other signals candominate leading to dead time poor S/N• Sample non-uniformity big problem (Icorrection can fail)0

X-ray Fluorescence Spectrum

Can be used with a detector with no energy
resolution or to reduce ﬂux to reduce deadtime for energy discriminating ﬂuorescence
detector

Z-1 Filter Plot
4

Mn filter
Fe K α1
Fe K α23

Fe K edge• Concentrations down to the ppm level

Filter and Lines

Ionization
Chamber I0

2
1
0

6000

7000

6500

7500

Energy (eV)Fe Kα emission lines and a“Z-1” Mn ﬁlter

17

18

17

18

An EXAFS Experiment

Experiment Design
Important considerations for designing an XAFS experiment include:• To collect EXAFS data, we need to scan a monochromatic x-ray

Monochromatic x-rays: Need x-rays with a small energy spread or bandwidth
ΔE ≈ 1 eV at 10keV. Second harmonics of the monochromator need to beeliminatedbeam through the edge. Typical ranges are below• In the EXAFS region, it is common to step in constant kLinear Detectors: The XAFS χ(k) ∼ 10−2 or smaller, so we need many photons anddetectors that are very linear in x-ray intensity (ion chambers). This usually means
using a synchrotron source.
Well-aligned Beam: The x-ray beam hitting the detectors has to be the same beamhitting the sample.

• If errors are the result of Poisson statistics to have a 1%

Homogeneous sample: For transmission measurements, we need a sample that is of
uniform and appropriate sample thickness of Δμ∼1 absorption lengths. It should befree from pinholes. Powders need to be very ﬁne-grained.

statistical error will require √N/N=0.01 㱺10,000 counts

Counting Statistics: μ(E) should have a noise level of about 10−3. That means we needto collect at least ∼ 106 photons. For very low concentration samples, this may require
hours of counting time.

Typical Ranges for
XANES and EXAFS
19

RegionPre-edge
XANES
EXAFS

Start E (eV)
-200
-20
30

End (eV)
-20
40
~800

Step (eV)5.00.25-0.50
0.05 Å-1

20

19

20

Free Atom Absorption

Backscattering

Upon absorption of an x-ray with energy E0 by a free atom, a corehole is created with K.E. (E-E0). The core hole is ﬁlled by anotherelectron (ﬂuorescence) or an Auger process occurs and another e- isejectedThe photoelectron propagates outward in the form of a sphericalwave (for k-shell holes) and parts of the wavefunction scatter off
surrounding atoms and return to the absorbing atom.
The backscattered photoelectron will then interfere with itself.

EnergyTransitions into the continuum lead tophotoelectron
large increases in absorption
V(x)µ increases sharply at E0 edge for a
free atom and monotonicallydecreases with increasing energy

x-ray
free atom

XAFS is thus caused by thephotoelectron interfering with itself
due to the presence of neighboring
atoms

absorption
probability

21

EnergyThere must be empty states at (E-E0)
at the absorbing atom μ to be nonzero.
The amplitude of the backscatteredwavefunction at the absorbing atom photoelectron
and its variation with energy give rise
to oscillations in μ that are XAFS. V(x)EnergyEnergyA transition can only occur if there isan empty state for the core electron
to move into.

x-ray
absorbingatom

scatteringatom

absorption
probability

22
21

22

EXAFS: Physics

EXAFS: Physics
Now let us ﬁnd a simple form for χ. First we note that the initial state is acore state and we wish to ﬁnd the effect of backscattering on the ﬁnal
state. If we recall the deﬁnition for μ(E)χ(k) =EXAFS is a “ﬁnal state effect”. As the initial state is deep and localized, itchanges little due to neighboring atoms. The ﬁnal state does howeverchange due to backscattering from a neighboring atom. If is the ﬁnal
state of an isolated atom, the ﬁnal state isexpanding in μ to
second order gives:

μ(E) − μ0 (E)Δμ(E0 )μ describes a transition between states and can be written in terms of
Fermi’s golden rule:

H is the interaction. In the dipole
approximation

EnergyEnergyas

Note that the initial state is a core state anda photon; this state is not changed by thepresence of a neighboring atom

whereimplies,

If we take the initial state as a delta function δ(0), Χ becomes

photoelectronV(x)is the ﬁnal state which consists of aphotoelectron, a core hole, and no photon. The
photoelectron is scattered by the neighboringatom.

Conclusion: is the part of the photoelectron wavefunction that isbackscattered to the origin by neighboring atoms

x-ray
absorbingatom

scatteringatom

absorption
probability

23

24

23

24

EXAFS: A simple picture
If, we can understandphotoelectron ψp’s path

EXAFS: A simple picture
Combining all terms, we get the expression for a single scattering atom

by following theBB• ψp leaves the absorbing atom
• part of ψp scatters off a nearby atom
• returns to the absorbing atom
outgoing ψABB

If N atoms are present with a thermal and static disorder of σ2 (whichgive the mean square displacement in R, we ﬁnd

backscatteringWith a spherical wave eikr/kr for the outgoing photoelectron and ascattering atom at distance r=R,
In a real structure, there are neighbors at different distances and a sum
must be taken
where scattering from the neighboring atom gives rise to the amplitude
f(k) and phase shift δ(k) to the photoelectron
25

26

25

26

EXAFS: A simple picture

Mean Free Path

To get the expression,
We used a spherical wave (eikr/kr) for the photoelectron, but we musttake into account inelastic scattering processes. To do this, we include a
damping function representing that limits how far a photoelectron can
travel and still return to interfere coherently
Here λ is the mean free path (andincludes core-hole lifetime effects)

The mean free path λ depends on k, but λ < 25 Å for the
EXAFS range. The λ term and R-2 lead to EXAFS being ashort range probe.

This leads to our ﬁrst version of the EXAFS equation

Note that λ and R-2 get large for low k (e.g. the XANES
region)
27

28

27

28

Amplitude Reduction Term

The EXAFS Equation
The EXAFS equation thus takes the form

The one remaining correction term in the EXAFS equation is the
Amplitude Reduction Factor or S02 . This term is due to therelaxation of the other electrons in the atom due to the presence of acore hole.

The sum is taken over all “shells” of atoms or “scattering paths” forthe photoelectron.
If we know the scattering properties of: fi(k) and δ(k) as well as
λ(k), we can determine:

Here theterm accounts for the relaxation of the N-1 electrons
left behind with the core hole relative to the same electrons in theunexcited atom
. In ﬁtting the EXAFS equation, S02 is often taken
2
as a constant 0 < S0 < 1.

N the coordination number about the absorbing atom
R the distance to the nearest atom
σ2 the mean-squared disorder of the corresponding neighbor distance

While great strides have been taken into calculations of λ and S02, typically
S02 is still taken as a constant for the absorbing atom in ﬁtting data.
This and other issues make the accuracy in determining
R (phases) better than N (amplitudes)

As the amplitude f(k) and phase-shift δ(k) depend on atomic
number, XAFS is also sensitive to the Z of the neighboring atom.

29

30

29

30

Scattering amplitude f(k) and phaseshift δ(k) examples

Using feff to calculate f(k) and δ(k)The scattering amplitude f(k) and phase-shift(k) depend on
atomic number and can be calculated.

• Feff is a real-space Greens function code that solves thescattering problem and computers the effective scattering
amplitude fi(k) and phase-shift δi(k) a given path i.

• Input to Feff (version 9 at the moment) consists of

The scattering amplitude f(k) peaks at
different k-values and goes to larger k-values
as Z increases. Note the structure in f(k) for
heavy elements like Pb.

specifying the location of atoms in space, their (Z) types,
and the absorbing atom. The resulting f(k),δ(k), and λ foreach path are saved in ﬁles feff0001.dat, feff0002.dat, etc.

• Recent ﬁtting programs use feff directly to model EXAFS
data.

The phase-shift δ(k) changes abruptly forlarge Z. The Z of a neighboring atom cantypically be determined ±3 using phase-shifts.
Accurate values for f(k) and δ(k) can be calculatedusing ﬁrst-principles code such as FEFF9.

• A structure close to unknown is sufﬁcient for feff input
and ﬁtting allows the reﬁnement of distances andcoordination numbers.

31

32

31

32

Multiple Scattering

Fitting Strategy• Convert measured intensities to μ(E)• Subtract a smooth pre-edge function to eliminate background

The path sum in the EXAFS equation can include manyshells (1st, 2nd, 3rd nearest-neighbors). For paths beyond
the nearest neighbor path, multiple-scattering paths canbecome important
singlescattering

triangular focused multiple
paths
scattering paths

from instruments or other edges• Normalize μ(E) to go from 0 to 1 so that it represents the

For multiple scattering paths, theamplitude depends on scattering angles.

absorption of one x-ray photon.

• Remove a smooth post-edge background function to

For triangular paths with 45 <θ< 135°
not strong, but may be many in number.

For nearest-neighbor analysis, multiple
scattering is rarely needed.

approximate μ0(E) to determine χ(k)For linear-paths, with angles θ~180°, arevery strong: the photoelectron can befocused from one atom to the next

• Convert E to k-space• Assign a k-weighting function to χ(k) and the Fourier Transformto real space

Multiple scattering strongest for θ>150°• Isolate the χ(k) for a particular “shell” by Fourier ﬁltering33
33

Next: Model f(k) and δ(k) to ﬁt χ(k)3434

Data Reduction:Transmission

Data Reduction: Athena
GeTe at 300 K @bl01b1

Converting raw measured intensities (in transmission) to μ(E)3μpre-edgepost-edge

I0

xμ(E)

2

I

50x10

1

3

Δµ0

2200

I1 (counts)

I0 (counts)

40

2100

Pre-Edge Subtraction
Pre-Edge subtraction removes
the effect of other edges/
background effects

0

30

-1
20

2000

11000

11200

11.0

11.5

3

12.0

11.0

12.5x10

11400

11600

Energy (eV)

10

1900

11.5

Energy (eV)

12.0

3

12.5x10

Normalization

Energy (eV)2normalized xμ(E)-ln(I/I0)
For XAFS in transmission-0.6

ln(I0/I1)-0.8

Post-edge subtraction
determines Δµ0 so the EXAFS
event is for a single x-ray
photon

1

-1.0

0

-1.2

11000

-1.4
11.0

11.5

12.0

11200

11400

11600

Energy (eV)312.5x10

Energy (eV)

35

36

35

36

Data Reduction: Athena
3

Data Reduction: Athena

μ0 spline

k-weighted χ(k): k2χ
χ(k) is composed of sine waves
from individual paths so we willtransform to R-space. Use aapodization window to avoid“ringing” effects

0.5

I1

xμ(E)

2

Post-Edge Backgroundμ0(E) is approximated by asmooth spline with no Fouriercomponents in the EXAFS
region

1

0

-1
11000

11200

11400

0

-0.5

0

11600

5

10

15

Energy (eV)k2 Weighted χ Function

0.5

0.6

After subtraction of spline
approximation to μ0(E), convert
to momentum units

0

0.3

0.2

-0.5

0
0

5

10

15

0

1

2

3

4

5

6

χ(R)
The Fourier Transform of k2χ
has two main peaks. The spectra
are shifted with respect to thetrue bond lengths due to thephase-shift δ(k). A shift of 0.5Åis typical

37

38

37

38

Data Reduction: Athena

The Information Content of EXAFSThe number of parameters obtainable from a single set of data is limited:

0.6

N∼

0.3

Here Δk and ΔR are the k- and R-ranges of the data used. For typicalranges of k=[3,12]Å-1 and R=1,3] Å, there are about 11.5 statisticaldegrees of freedom or parameters that can be ﬁt from EXAFS.

0.2

0

2ΔkΔR
π

0

1

2

3

4

5

The “Goodness of Fit” statistics and corresponding conﬁdence in themeasured parameters need to reﬂect this limitation.

6

It is often important to constrain parameters R, N, and σ2 for different
paths or even different data sets (different T, element edges etc.)

χ(R) is complex. Often only the magnitude is shown.
χ(R) is not a radial distribution function, but an interference function
In data ﬁtting, both the real and imaginary parts are used39

We can use chemical plausibility to weed out bad results orincorporate additional known data (coordination, Bond Valence Modeletc. ) to improve the quality of the ﬁt.

39

A Fitting Example

40
40

A Fitting Example

41

42

41

42

A Fitting Example

A Fitting Example

43

44

43

44

Experimental Considerations

BL01B1• In what follows a brief introduction to some of the• Si double monochromator (111), (311), or (733)• Focusing harmonic rejecting mirrors• automatic adjustment of beam location with energy• energy range 4.5-110 keVcomponents of a beamline will be shown

45

46

45

46

Bl01B1 Energy Dependence

Absorption Edges
K and L3 edges
105• K Edge Energies ∝ Z• Elements with Z>18 have either a2

predicted by the program SPECTRA (http://
radiant.harima.riken.go.jp/)

K-edges104

K or an L-edge accessible between
3 and 35 keV

Log Edge Energy eV• The energy dependence of x-rays from bl01b1 as

L3-edges

1000

100

10

•
• Edges with E<3 keV require special
Soft x-ray XAFS possible as well

0

20

40

60

80

Atomic Number

K and L3 edges
30 000Elements up to Z=53
K-edges

25 000Edge Energy eV

preparation (vacuum) while edges
over E>35 keV can suffer fromreduced cross section, Compton
scattering, and multielectron effects.
(3 keV<E<35 keV Hard X-ray
region easy to measure in)

Elements up to Z=93

1

20 000
15 000
10 000L3-edges
5000
0
0

10

47

20

30

40

Atomic Number

50

48

47

48

Measurement Techniques

Harmonic Rejection

x-raysI0

sample

I1• The intensity of the synchrotron varies with time. It

must be normalized. Typically this is done by using an ion
chamber which measures the current of ionized gas
between two capacitors.

• As the monochromator lets through x-rays that satisfy• To optimized statistics without too much signal

the Bragg condition (λ=2d sinθ) not only λ, but λ/2, λ/3(higher harmonics) are transmitted as well.

attenuation, the I0 chamber should operate at about
15% attenuation. I1 should be about 85%.

• At bl01b1, higher harmonics are rejected using a mirror,
for a ﬁxed wavenumber k, x-rays will not reﬂect forangles greater than the critical angle αc.
αc =fundamental λ is reﬂected but higher
harmonic λ/2 and above are not

√

2δ =

4πρr0
k

ρ number density of coating
r0 electron scattering length=2.82 x 105 Å
k = incident wavevector

Hephaestus can help.
At 12 keV, a 140 mm Ion Chamber
will absorb 15% of the incoming
signal if a N2/Ar mixture in a ratioof 85:15 is used.

49

50

49

50

Absorption Length• One can also calculate the absorption length using Hephaestus(part of the Horae suite).
http://cars9.uchicago.edu/ifefﬁt/Downloads

52
52

Absorption Lengths andParticle Size

X-ray Fluorescence• X-ray ﬂuorescence is highly sensitive• A good sample is:• dilute (to avoid self absorption)• homogeneous (I will not divide• It is important to keep particle size
below one absorption length0• This leads to sample areas that areout if sample is non-uniform)

opaque and gaps that distort the“white line” and affects σ2 as well

• If there is only one strong

Lytle-Heald Detector(not energy senstive)

EnergyDispersive
Analyzer(Ge SSD)

ﬂuorescence, a Lytle-Heald detector
can be used (ion-chamber)• Samples should be uniform on thelength scale of the absorption length(small particles must be used)• If several elements are present, anenergy dispersive (Ge SSD) can beused, but dead time can be a
problem.

MnO spectra as a function ofparticle size (10% leakage)
53

54

53

54

Disorder in EXAFS and diffraction
In diffraction, we deﬁne single center
displacement parameters u

−
→
u
1

Spatial Resolution (Beats)

−
→
u
2

The ability to resolve two distances “close” to each other.
R1

R1

−
−
→ −
→ −
→ 
→ 
u21 = (R1 − R1 )2 , u22 = (R2 − R2 )2

OR
R2

R2
R

In EXAFS, we deﬁne correlated displacement parameters also
known as Mean Squared Relative Displacement (MRSD)
2
σ12
=



−
→ −
→
−
→ −
→ 2
(R2 − R1 ) − (R2 − R1 )=Intuition: To resolve needs R to be a significant fraction of smallest p.e.
wavelength:




 −
→ −
−
→ −
→
→ 
(R2 − R2 ) − (R1 − R1 )

 

→·−
→
2
2
u
= u21 + u22 − 2 (−
1 u2 ) = u1 + u2 − 2u1 u2 uˆ1 · uˆ2 

If |u1 | = |u2 |      

 







 



 




σ 2 = 2u2 , if uˆ1 · uˆ2 = 0

De Broglie 

σ 2 = 0, if uˆ1 · uˆ2 = 1
σ 2 = 4u2 , if uˆ1 · uˆ2 = −1
55

56

55

56

Spatial Resolution (Beats)

Features of XANES• Pre-edge region• Features caused by dipole transitions to (empty)
bound states.

• Local geometry about absorbing atom
• Absorption Edge
• ionization threshold to continuum states• Larger oxidation state (chemical shift) moves edge up
in energy• XANES region is characterized by multiple scattering.

Includes information about bond angles and distances.
Need to use simulation (Feff9) to understand structure

57

58

57

58

Selection Rules

K-edge Pre-Edge Peaks

XANES probes unoccupied electron states•

Dipole selection rule

•

Edges

• In a metal, a K-edge transition implies a s © p liketransitionΔl (orbital angular momentum) = ±1, Δj (total angular momentum) = ±1

• For Octahedral coordination site iscentrosymmetric implying no p-d mixing (onlyweak quadrupole transitions)• K-edge and L Edges: s (l=0) © p (l=1)• L , L -Edges: p(l=1) © d(l=2) or s(l=0)• Note that states can mix hence by using the12• p-d mixing becomes possible with distortion
from octahedral point symmetry3• tetrahedral site symmetry, largest pre-edge

selection rules XANES can be used as a probe of
hybridization

peaks

note that quadrupole transitions are possible but typically have about 1/100 of the strength of
dipole transitions
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Using XANES with mixtures

XANES Summary• The coherence length (the distance over which the• The XANES signal is signiﬁcantly larger than EXAFS andmultiple scattering occurs) in XANES is on the order of
1 nm

exhibits little temperature dependence.

• If the sample is homogeneous over distances of 1 nm,• XANES spectra can be used as a ﬁngerprint and linear

Example of the decomposition of PtO1.6• The multiple scattering present in XANES spectra makecombination type analyses are easily carried out. Simple
selection rule considerations can give considerable
insight into the bonding in a sample.

then different regions of the sample will add
incoherently
XANES(mixture) = Σfi XANESi

it more difﬁcult to treat theoretically, but the real-space
multiple scattering code Feff (now at version 9) allows
calculation of theoretical spectra using only thecoordinates and types of atoms in a cluster.
http://leonardo.phys.washington.edu/feff/

Example: The decomposition of PtO1.6
All XANES spectra collected repeatedly during the thermal
decomposition process could be ﬁt by a weighted sum of Pt and thestarting compound PtOx demonstrating that no intermediate phases
were involved. The ﬁgure on the left shows the metal fraction allowing
the kinetics of the reaction to be explored

Kolobov et al., Appl. Phys. Lett. 86, 12 (2005), 121909.

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References

Quick Fit
• Books•

If time allows, we shall interactively do a quick ﬁt of GeTeat the Ge edge.

•

Introduction to XAFS: A Practical Guide to X-ray Absorption Fine Structure
Spectroscopy by Grant Bunker•

X-Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXAFS and
XANES (Chemical Analysis: A Series of Monographs on Analytical Chemistry and Its
Applications) by D. C. Koningsberger and R. Prins•

Elements of Modern X-ray Physics by Jens Als-Nielsen and Des McMorrow• Review Articles•

Theoretical approaches to x-ray absorption fine structure by J. J. Rehr and R. C. Albers,
Rev. Mod. Phys. 72 (3) 621-654 (2000)• Internet•

http://www.xafs.org International XAFS Organization
This site has links to tutorials by synchrotron organizations and other useful
information including an online magazine. Membership is free.

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