EXAFS

3

The 2nd AOFSRR Summer School- Cheiron School 2008 –SPring-8
Sept. 30th, 2008

Extended X-ray Absorption Fine Structure
2Iwao Watanabe
Ritsumeikan University

16800

7000

7200

7400

7600

7800

EXAFS
TheoryQuantum Mechanics
ModelsApproximations
ExperimentLight Source
Monochromator
Higher Harmonics Rejection
Sample Preparation
Detection Methods
Polarization XAFSData Analysis
Limited Usable Range in Experimental
Data
Estimation of Background Curves
Fourier Transform
Multi-Scattering
Curve Fitting Procedure
Phase Problems
Debye-Waller-Like Parameter
Anharmonicity in Potential

X-ray absorption measurement by transmission method
The most reliable and basic method+1000V
double-crystal
monochromatorsynchrotron

white X-ray

monochromatic
X-rayslits

sampleIo

Bragg diffraction

PC and interfaces
Io current

calculation ofabsorbanceA = - log(I )Io+1000V

I currentGas
ionizationchamber（He, N2, Ar, Kr, etc）

IXAS of Fe(III) aqueous solution

I0

µxI0
lnI

1

intensity

3I

0.5

21
6800

7000

7200

7400

7600

X-ray photon energy / eV

7800

0

H2O

Fe(III)Fe(III)ion in water

3Fer(Fe-O)=2.01Å

21E006800

7000

7200

7400

X-ray photon energy / eV
0200
400
photoelectron kinetic energy / eV
Focusing on K shell(1s electron)
2 1.3 1excitation
photoelectron wave length / Å7600

7800
600

Backgrounddue
0.8 0.7
0.6 absorption0.5
to other atoms and othershell electrons

XAFS: X-ray Absorption Fine Structure
Fe ions in aqueous solutions

XANES

Fe(III)Fe(II)µ2

EXAFS

106800

7000

7200

7400

X-ray energy / eV

7600

7800

XANES: X-ray Absorption Near Edge Structure
Fe ions in aqueous solutions
2µFe(III)
Fe(II)
1071007120

71407160
X-ray energy / eV

7180

7200

EXAFS: Extended X-ray Absorption Fine Structure
Fe ions in aqueous solutions

XANES

µt

2

µ0106800

Fe(III)Fe(II)

7000

EXAFS

7200

7400

7600

7800

X-ray energy / eV

µ (k ) − µ 0 (k )
χ (k ) =µ0 (k )k=2me ( E − E0 )h2

EXAFS: χ(k) spectra

Fe(III)Fe(II)

Fe(III)
longer → shorter distance012345678910111213k / Å-110 k2040 60
100 140: wavenumber,wave 200
vector 300k=2πλ2me ( E − E0 )k=h2400500600( E − E0 )kinetic energy ofphotoelectronSimplest model to explain how theEXAFS oscillation occurs

H2OFe(III)Fe(III)ion in water

3Fer(Fe-O)=2.01Å

21E006800

7000

7200

X-ray photon energy / eV

7400

0200

photoelectron kinetic energy / eV

2 1.3

1

photoelectron wave length / Å

0.8 0.7

7600

7800

4006000.60.5

X-ray photon

kinetic energy of the photoelectron
photoelectron

7213eVeV010FeN
M4s, 4p, 4d3s, 3p, 3d(700〜800eV)

an electron with Ek=100eV behaves
as a wave with λ=1.2Å
h: de Broglie
λ=pThis wave length is just the order ofnormal atom-atom bond distance !!!

2s, 2pLenergy of
the photonabsorbed
by Fe atom

The cause for EXAFS appearance !!!

KE0
7113eV (1.743Å)

1sphotoelectron (wave)
going out

X-ray absorption
at atom

A＝black wave:
directly emitted
from theabsorbing atomneighbor atom
scattering thephotoelectron
wave back to theabsorbing atom+

red broken wave:
doubly scattered
at B and A

BBASIC EXAFS equationNiχ (k ) = −∑ 2 fi (k )exp(−2σ i2 k 2 − 2ri /λ )S02 (k )sin(2kri + φi (k ))i k riH2OFe(III)Fe(III)ion in water

3Fer(Fe-O)=2.01Å

21E006800

7000

7200

X-ray photon energy / eV

7400

0200

photoelectron kinetic energy / eV

2 1.3

1

photoelectron wave length / Å

0.8 0.77600

7800

400

600

0.60.5

BASIC EXAFS equationNi
2 22f(k)exp(−2σk−2r/λ)S(k )sin(2kri + φi (k ))ii0i2i k ri

χ (k ) = −∑oscillation part

amplitude part×kkk

photoelectron wave number (vector)

k=Fe(III)
Fe(II)2πλχ(k)Fe(III)
longer → shorter distance012345678910300

400

111213k / Å-1

10 20

40 60

100 140200

kinetic energy of the photoelectron / eV

500

600

BASIC EXAFS equationNiχ (k ) = −∑ 2 fi (k )exp(−2σ i2 k 2 − 2ri /λ )S02 (k )sin(2kri + φi (k ))i k rik photoelectron wave number

λ photoelectron mean path length

N number of coordinating atoms

S02 reduction factor

r distance between atoms A and B

φ phase shiftf scattering amplitude

σ 2 mean squared displacement in r
(Debye-Waller factor)

Fourier Transform:
Simplest way to analyze theEXAFS oscillation

photoelectron wave number (vector)

k=Fe(III)
Fe(II)

2πλχ(k) k3

Fe(III)
longer → shorter distance

01

234

5678

910300400

111213k / Å-1

10 2040 60

100 140200

kinetic energy of the photoelectron / eV

500600

The simplest way of knowing the wave
number (corresponding to the distance) is
Fourier Transformation of wave on k
0.5Fe(III)
Fe(II)

｜FT ｜

0.4
0.3
0.2
0.1
002Fe(III) shoter FeOFe(II) longer FeO4r/Å

68

24-Fe(CN)6N

03k χ(k)CFeEx2ctartk)(χonitillacos-2
05k /Å-1

10

Fourier Transform

μx1

｜FT｜

0.816800

7000

7200

7400

E / eV

7600

7800

0.6
0.4
0.2
00123r/Å456

Fourier Transform (Frequency Filter)
will let you know the frequenciesof the waves
k/Å-1r/Å

31201-1010sin(kr )

20

00

12

34562r1=2.01r2=2.50-1-20310or20

r1=2.0+2
101r2=2.5

234mixture

Fourier Transform for two-shell model
221

100-1-1-2
031020-2021020

2
1
10
12

340
1234

Fourier Transform fora three-shell model
1

0.5
1000-1010k /Å-1

20

12r /Å

34

This must be a BACKGROUND
structure, not corresponding toa real atom-atom distance.

k/Å

-1r/Å

3

1201-1011020003123456123456123456201-101020

1003201-10102000k / Å-1r/Å

3

120
1-10
1102000312345612345612345620
1-101020

100
320
1-1
0

1020

00

Fourier Transform for
フーリエ変換の範囲を変えたもの

1different k ranges

0-1
0

310-1

k/Å

202

1If you haveFT1_20.TXT
a small
FT3.15_15.75.TXT
FT5.05_12.55.TXT
number of cycles
in k,
FT7.55_10.05.TXT

orPme
bl!00123r /Å

456BASIC EXAFS equationNi
2 22f(k)exp(−2σk−2r/λ)S(k )sin(2kri + φi (k ))ii0i
2i k riχ (k ) = −∑amplitude part

oscillation part

By comparing the theoretical EXAFS χ(k)and experimental χ(k), you can determine;
N coordination number
r bond length
atomic type of coordination

You may get in trouble with thedata quality taken by transmission
methodTransmission method
Sample: Ge-Si powderorP
original powder

further ground to finer
powderBy Masaharu Nomura,
Photon Factory, KEKme
bl!

Fe(III)(III)

χ(k) k3

1or
P0me
bl!

-1
0

5

Fe(III) ions in aqueous
solution
possibly,
inhomogeneous
sample thickness-1 1015k/Å
2Fe(III)
(III)

10
7100

7120

7140

7160

7180

7200

X-ray beam frommonochromator

X-ray flux is nothomogeneous and thedensity pattern moves andchanges along with themonochromator angle
scan

Inhomogeneous
samplesolid powder

Leads to weaker EXAFS oscillation
amplitude and noisy spectrum

liquid or film

Yield methods:
Fluorescence yieldandTotal-conversion-electron-yieldX-ray absorption measurement by yield methods

double-crystal
monochromatorsynchrotron

white X-ray

monochromatic
X-raysample
slit

Io

Bragg diffraction

PC and interfaces
Io current

calculation ofabsorbanceA = - log(I )Io

I current

fluorescence X-ray,electron,luminescence,
heat, etc;
anything proportional to
the X-ray absorption

Lytle detector

Sample: 0.01 mol dm-3 Cu(II) solution
transmittance

By Masaharu Nomura,
Photon Factory, KEKfluorescencetransmittance
fluorescence
Cu 0.5 mm
Cu foil 6 µmor
Pmebl

fluorescence
fluorescence
Cu foil 6 µm

By Masaharu Nomura,Photon Factory, KEK

Cu foil 2 µm

Self-absorption effect → incorrect N!

Total-Conversion-Electron-Yield methodcounter electrodesampleX-ray
window
X-ray−1000Vto current
amplifierHe gasX-ray

1.5mm
glass

transmittancetransmission

Auger electrons(He gasionization)

This method can be applied to thicksamples owing to the short escapedepth of Auger electron.

total-conversionelectron-yield2μx

1µ m
Fe3O4

1〇7100070007150

7500
8000
E / eV8500

Can we distinguish oxygen from
nitrogen by EXAFS?

Almost
impossible !

Scattering amplitude

Scattering phase shiftNiχ (k ) = −∑ 2 fi (k )exp(−2σ i2 k 2 − 2ri /λ )S02 (k )sin(2kri + φi (k ))i k ri

Ni
2 22f(k)exp(−2σk−2r/λ)S
ii0 (k )sin(2kri + φi (k ))2 ii k ri

χ (k ) = −∑amplitude partf scattering amplitude

oscillation partφ phase shift

Can we distinguish oxygen atoms
15% distant from others byEXAFS?

Yes, but at incorrect
position by using FT
method !

James E. Penner-Hahn J. Am. Chem. Soc. 1998,120,8401

Can we distinguish sulfur fromnitrogen (or oxygen) by EXAFS?

Almost
impossible !

Can we detect the end-end atomic
interaction in I-I-I molecule (I3-) byEXAFS?

I K-edge EXAFS FT for I3−I −I −I３Å
３Å

Dissolved in organic solvents(n-C3H7)4N I3 powder

H. Sakane, T. Mitsui, H. Tanida, I. Watanabe. J. Synchrotron Rad. 8, 674 (2001).

I-I bond is very soft and vibrating: large
Debye-Waller like parameter

Almostimpossible !

Iodine K-edge EXAFS Fourier transform for the compound spectrum made up
from 12 independent spectra for organic solvent solutions.
H. Sakane, T. Mitsui, H. Tanida, I. Watanabe. J. Synchrotron Rad. 8, 674 (2001).

Large symmetrical cluster ofmolybdenum oxide complex

Mo K-edge XAFS

Mo6O192‐Mo

0.5

μxO

0-0.5
20000

21000
E / eV

Almost undetectable next
2neighbor oxygens!

1|FT|

Mo-Mo

0-1010-1k/Å

20100123r/Å

456

FEFF Mo-O.SMP

Mo-O 1.6A
Mo-O 1.8A
Mo-O 2.0A
Mo-O 2.2A
Mo-O 2.4A
Mo-O 2.6A

10-1246-1k/Å

810EXAFSThe 2nd AOFSRR Summer School- Cheiron School 2008 –SPring-8
Sept. 30th, 2008

Extended X-ray Absorption Fine Structure
Theory; very difficult.
Experiment; looks easy.
Data analysis; looks straight forward.
Thanks to the advanced data
analysis software.

EXAFSThe 2nd AOFSRR Summer School- Cheiron School 2008 –SPring-8
Sept. 30th, 2008In reality,
Theory; becomes even more and more complex anddifficult to understand.
Experiment; to obtain CORRECT spectral data is
NOT an easy task.
Data analysis; no one except for the GOD knows
whether the conclusion from the EXAFS
analysis is CORRECT.

EXAFS is a tricky technique.

The 2nd AOFSRR Summer School- Cheiron School 2008 –SPring-8Sept. 30th, 2008

Then, what do we have to do ?
Use
★ other analytical methods,★ knowledge of chemistry and physics,
and★ good sense as a scientistand combine them together withthe EXAFS analysis.

erawtfoseerf

http://cars9.uchicago.edu/~ravel/software/

XAS Analysis Software Using IFEFFIT

Current release: 0.8.056
Release date: 26 July, 2008
ATHENA is an interactive graphical utility forprocessing EXAFS data. It handles most of the common
data handling chores of interest, including deglitching,aligning, merging, background removal, Fouriertransforms, and much more.

Current release: 0.8.012
Release date: 26 July, 2008
ARTEMIS is an interactive graphical utility forfitting EXAFS data using theoretical standards
from FEFF and sophisticated data modellingalong with flexible data visualization andstatistical analysis. ARTEMIS includes
interfaces to ATOMS and FEFF.