AOFSRR Cheiron School 2010, SPring-8

EXAFS

Oct. 14th, 2010

Extended X-ray Absorption Fine Structure
Iwao Watanabe
Ritsumeikan University

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

I current+1000V

Gasionizationchamber（He, N2, Ar, Kr, etc）

I

XAS of Fe(III) aqueous solution

I0lnII

X-ray photon energy / eV

intensity

μxI0

H2O

Fe(III)Fe(III)ion in water

3Fer(Fe-O)=2.01Å

21
E0

06800

7000

7200

7400

X-ray photon energy / eV0200400
photoelectron kinetic energy / eV

Focusing on K shell (1selectron) excitation

2 1.3

1photoelectron wave length / Å7600

7800
600

Background
0.8 0.7
0.6 absorption due
0.5 toother atoms and other shellelectrons

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

X-ray energy / eVXANES: X-ray Absorption Near Edge Structure

μFe ions in aqueous solutions

X-ray energy / eVWong et al. Phys.Rev.B 30(1984) 5596

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

XANESμt

2μ0106800

Fe(III)Fe(II)

7000

EXAFS7200

7400

7600

7800

X-ray energy / eV

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

EXAFS: χ(k) spectra
Fe(III)k / Å -1

k : wave number, wave vector
k=2πλ

k=

2me ( E − E0 )h2( E − E0 )kinetic energy ofphotoelectronSimplest model to explain how theEXAFS oscillation occurs

H2O

Fe(III)Fe(III)ion in water

3Fer(Fe-O)=2.01Å

21E006800

7000

7200

X-ray photon energy / eV7400

0200

photoelectron kinetic energy / eV2 1.3

1photoelectron wave length / Å

0.8 0.7

7600

7800

4006000.60.5

X-ray photon

kinetic energy of the photoelectron
photoelectron

FeN
M

4s, 4p, 4d3s, 3p, 3d(700～800eV)

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

2s, 2pLenergy of thephoton
absorbed by
Fe atom

The cause for EXAFS appearance !!!

KE07113eV (1.743Å)

1sphotoelectron
going out(wave)

B
X-ray absorptionat atomA＝

black wave:
directly emitted
from the absorbing
atomneighbor atom
scattering thephotoelectron wave
back to theabsorbing atom+

red broken wave:
doubly scattered atB and Aphotoelectron
going out(wave)＝

black wave:
directly emitted
from the absorbing
atom+

red broken wave:
doubly scattered at B
and A

If they are in phase , (2r)k=2nπ (k=2π/λ) or 2r=nλ,→ larger photoelectron wave
→ larger probability of finding photoelectrons(amplitude squared).

B
X-ray absorption
at atomA

If they are out of phase , (2r)k=(2n+1) π , and equal
amplitudes,→ photoelectron waves disappear→ no photoelectrons found outside.

The law of conservation of energy tells thatwhen no photoelectrons are emitted, no photons should be absorbed !!!
if the X-ray photons are absorbed, the photoelectrons must be emitted !!!
Larger probability of finding photoelectrons → STRONG X-ray absorption
Smaller probability of finding photoelectrons → WEAK X-ray absorption

H2O

Fe(III)Fe(III)ion in water

3Fer(Fe-O)=2.01Å

21E006800

70007200

X-ray photon energy / eV

7400

0200

photoelectron kinetic energy / eV

2 1.3

10.8 0.7

7600

7800

400

600

0.60.5photoelectron wave length / ÅBASIC EXAFS equationNiχ ( k ) = − ∑ 2 f i ( k )exp( − 2σ i2 k 2 − 2 ri /λ )S02 ( k ) sin(2 kri + φ i ( k ))i k riBASIC EXAFS equationNiχ ( k ) = − ∑ 2 f i ( k )exp( − 2σ i2 k 2 − 2 ri /λ )S02 ( k ) sin(2 kri + φi ( k ))i k rioscillation part

amplitude part×kkkχ(k) k 3Fe(III)k / Å -1

kinetic energy of the photoelectron / eVphotoelectron wave number (vector)
2π
k =λFourier Transform:
Simplest way to analyze the EXAFSoscillation

｜FT ｜The simplest way of knowing the wave
number (corresponding to the distance) is
Fourier Transformation of wave on kFe(III) shoter

FeFe(II) longerFeO
Or/Å4-Fe(CN)6CFeNμx

Fourier TransformE / eVFourier Transform (Frequency Filter)
will let you know the frequenciesof the wavessin(kr )r1=2.0r2=2.5

orr1=2.0+r2=2.5

mixtureFourier Transform for two-shell model

Fourier Transform for athree-shell modelThis must be a BACKGROUND
structure, not corresponding to areal atom-atom distance.

Fourier Transform fordifferent k ranges

If you have a small
number of cycles in k,

BASIC EXAFS equationNiχ ( k ) = − ∑ 2 f i ( k )exp( − 2σ i2 k 2 − 2 ri /λ )S02 ( k ) sin(2 kri + φi ( k ))i k riamplitude part

oscillation part

By comparing the theoretical EXAFS χ(k) andexperimental χ(k), you can determine;
N coordination numberr bond lengthf(k) and φ(k) are element specificatomic type of coordination

You may get in trouble with the data
quality taken by transmission method

Transmission method
Sample: Ge-Si powder
original powder

further ground to finer
powderBy Masaharu Nomura,
Photon Factory, KEKχ(k) k3

-1

Fe(III) ions in aqueous
solution
possibly, inhomogeneous
sample thicknessk/ÅX-ray beam frommonochromator

X-ray flux is nothomogeneous and thedensity pattern moves andchanges along with themonochromator angle scanInhomogeneoussample
solid powderLeads to weaker EXAFS oscillation
amplitude and noisy spectrum

liquid or film

Si(311) double-crystal monochromator
Output pattern

before improvements on the crystal
holding method

after improvements

1mm x 1mm slit

Io

0.6mm x 0.6mm holeIYield methods:
Fluorescence yield
andTotal-conversion-electron-yieldX-ray absorption measurement by yield methods

double-crystal
monochromatorsynchrotron

white X-ray

monochromatic
X-raysampleslit

Io

Bragg diffraction

PC and interfaces
Io current

calculation ofabsorbanceA = - log(I)IoI 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, KEK

fluorescencetransmittance
fluorescence
Cu 0.5 mm
Cu foil 6 μm

fluorescence
Cu foil 6 μm

By Masaharu Nomura,
Photon Factory, KEK

fluorescence

Cu foil 2 μm

Self-absorption effect → incorrect N

Total-Conversion-Electron-Yield methodcounter electrodesample

X-raywindow
X-ray－1000V

to current
amplifierHe gasX-ray

1.5mmglasstransmission

Auger electrons

μx

1μ m
Fe3O4(He gasionization)

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

E / eVCan we distinguish oxygen from
nitrogen by EXAFS?

Almost
impossible !

Scattering amplitude

Scattering phase shiftNiχ ( k ) = − ∑ 2 f i ( k )exp( − 2σ i2 k 2 − 2 ri /λ )S02 ( k ) sin(2 kri + φi ( k ))i k riNi2 22f(k)exp(−2σk−2r/λ)S
ii0 ( k ) sin(2 kri + φ i ( k ))2 ii k ri

χ (k ) = − ∑amplitude partf scattering amplitude

oscillation partφ phase shift

Can we distinguish oxygen atoms 15%
distant from others by EXAFS?

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

Can we distinguish sulfur from
nitrogen (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

Dissolved in organic solvents－I －I －I３Å
３Å

(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‐Mo0.5μxO0-0.52000021000
E / eV

Almost undetectable next
neighbor oxygens !
Mo-Mo-1k/Å

r/Å

-1k/Å

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

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

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

XAS Analysis Software Using IFEFFIT
Current release: 0.8.059
Release date: 1 July, 2009ATHENA is an interactive graphical utility for processing EXAFS data. It handles
most of the common data handling chores of interest, including deglitching,aligning, merging, background removal, Fourier transforms, and much more.

Current release: 0.8.013
Release date: 15 December, 2008
ARTEMIS is an interactive graphical utility for fitting EXAFS data using
theoretical standards from FEFF and sophisticated data modelling along withflexible data visualization and statistical analysis. ARTEMIS includes
interfaces to ATOMS and FEFF.