XAFS:Study of the local structure

around an X-ray absorbing atom

(1) Principle of XAFS(2) Instrumentation(3) XAFS spectral analysis(4) XAFS applications(5) New directions of XAFS

T.Ohta, Univ.Tokyo, Japan

(1) Principle of XAFS

X-ray

Diffracted X-rays

Photoelectrons

Transmitted X-rays

Diffracted X-rays

Scattered X-rays

Fluorescent X-rays

Desorbed ions

Phenomena caused by X-ray irradiation

1.4 1.0 0.6 0.2波長

L3L2

L1

K

X-ray absorption spectrum from Pt foil

wavelength

XAFSX-ray Absorption Fine Structure :Local electronic and geometric structures around

the x-ray absorbing atom

Abso

rptio

n C

oeffi

cien

t

　Photon Energy

NEXAFS EXAFS

Threshold

30-50 eV 50 - 1000 eV

XAFS spectrum from an atom

XAFS spectrum from a diatomic molecule

X-ray absorption： Fermi’s Golden Rule

( )fae EirefN

cρ

ωπµ

2224⋅=

i: wave function of the initial state 1sf: wave function of the final state

superposition of the ejected wave and back-scattered waves

( )0

0

µµµ

χ−

=k EXAFS function

[ ]

( ) ( )222 2exp)2exp(

),(

)(22sin)()(

krkr

kfNkA

kkrkAk

jj

jj

jjj

j

σλπ

δχ

−−=

+= ∑Point atom, plane wave, and single scattering approximations

( ) ( ) ( )iii

i kRkAk φχ += ∑ 2sin

EXAFS oscillation

( )hh

02 EEmpk−

==

Ri:bond distance

Phase shiftφi

Ｒ

Phase shift

( ) ( ) ( )iii

i kRkAk φχ += ∑ 2sin

-6.0

-2.0

2.0

6.0

10.0

14.0

4 6 8 10 12 14 16

Pb

SnGe

SiC

Phase shift of the X-ray absorbing atom

k/A-1

( ) ( ) ( )

−−=

λσ i

iii

ii

RkkF

kRN

kA 2exp2exp22

2

*

EXAFS amplitudeEffective Coordi-nation number

Back scatteringamplitude

Debye-Wallerfactor

Electron meanfree path

5 10 15k(A-1)

Backscattering Amplitude F(k)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

F(k)

CSi

Ge

Sn

Pb

( ) ( ) ( )

−−=

λσ i

iii

ii

RkkF

kRN

kA 2exp2exp22

2

*

EXAFS amplitude

Effective Coordi-nation number

Back scatteringamplitude

Debye-Wallerfactor

Electron meanfree path

High coordination numberLow temperature

High Z scatterer Short distance

Au K-EXAFS of Au foil

278K

77K

EXAFS oscillation of Au K-edge

77K

278K

Photon Energy

If the coordination number decreases,

Photon Energy

If the bond distance increases,

(2) Instrumentation

monochromatorIo I

sample

Data processing

X-rays

Ion chamber

《transmission method》

Experimental method of XAFS

X-ray escape depth>1000A

Electron escapedepth ＜50 A

FluorescentX-rays

Secondary electron

photoelectronAuger electron

sampleX -ray

Ionization chamber

Filter and solar slit

Fluorescence

Absorption

Cu K-XAFS of CuSO4 10mMol aq. solution

Transmission Fluorescence

0.5 mmfilm

6µm film

Partial electron yield x-ray absorption of surface atoms

Total electron yield

Photon energy

Sample leak current

Partial electron yield

(3) XAF S spectral analysis

R+ φ

Fourier transform

Am

plitu

deEX

AFS

func

tion

Back Fourier Transformation

k

Amplitude Envelope

Kind of scattererCoordina-tion number

Polarization

Direction ofBond, Adsorp-Tion site

Temperature

Bond stiffness

EXA

FS fu

nctio

n

E

Polarization Dependent EXAFSK-absorption(1s p-like continuum)

Polarization Dependent EXAFSK-absorption(1s p-like continuum)

Temperature dependence

[ ])(22sin)()( kkrkAk jjj

j δχ += ∑

( ) ( )222 2exp)2exp(

),(kr

krkfN

kA jj

jj σλ

π−−=

( ) ( )[ ]22

122

1

2 2),(),(

ln TTkTkATkA

σσ −≅

( ) ( )[ ]22

122

1

2 2),(),(ln TTk

TkATkA

σσ −≅

c-As

Determination of σ2(T)

What can we get from σ2(T)

u0

u0 ui

Ri

R0 Ri

O

( )[ ]( ) ( ) ( ) ( )iiiiii

iii

RuRuRuRu

Ruurvrr

r

⋅⋅⋅+⋅+⋅=

⋅−=

02

02

20

2

2

σ

0

0

RRRRR

i

ii −

−=

r

( )

=

kTT

Ei 2

coth2

2 ωµω

σ hh

−

=

12

2

2coth

2coth

2 kTkTEi

ωωµω

σ hhh

Einstein model

22EE cf µω=

Einstein frequency

c-AsAs-As: 216 cm-1

a-AsAs-As: 234 cm-1

c-As2S3As-S: 332 cm-1

g-As2S3As-S: 330 cm-1

c-As4S4As-As: 222 cm-1As-S : 342 cm-1

Data acquisition

Determine E0 , Convert from eV to k

Background subtraction and normalization

Multiply kn

Fourier transformation

Fourier filtering

Back Fourier transformationCurve fitting in real space

Model structure

X-ray energy(eV) EXAFS χ(k)

Atomic distance(Å) EXAFS χ(k)

EXAF

S χ k (wave number)

EXAFS analysis-1

Ampl

itude

Distance r=r+i iφ

( ) ( ) ( )iii

i krkAk φχ += ∑ 2sin

Phase shift

Atomic distance

amplitude

1st nearest

2nd nearest

3rd nearest

Fourier transformation

EXAF

S χ k (wave number)

EXAFS analysis-2

Effective CoordinationNumber

Debye-Wallerfactor

Backscatteringamplitude

Direction ofchemicalbond

PairPotentialFunction

Kind ofscatteringatom

Limitation and Improvement of XAFS theory

• Multiple scattering effectwhich is enhanced at XANES region and also at longer distance above 3 A.

FEFF program developed by J.Rehr can be used for spectral simulation.

Shadowing effectnegligible

Non-negligible

+−+

−+−=

+= ∑

∞

=

LL 33

44

222

22

34),(2sin

322exp),(

!)2(2exp),(Im)(

kCkRkkRkCkCkRkFkRN

CnikikRkRkf

kRNk

effeff

nn

n

eff

φ

χ

>=< rR

>−=< 22 )( RrC >−=< 3

3 )( RrC22

44 3)( CRrC −>−=<

Limitation and Improvement of XAFS theory•Vibrational anharmonicity

The formula assumes a Gussian distribution.Cumulant expansion method has been developed to takeinto the anharmonicity,

which gives the information of real bond distance, thermal expansion coefficients, radial distribution curve.

where

(4) XAFS applications• Catalysis• Amorphous systems• Material physics(High Tc, CMR,….)• Magnetic materials XMCD• Thin films and Surface science • Environmental science • Biological materials

(5) Challenge of XAFS

• Time-resolved XAFS spectroscopy

• Micro XAFS or Nano XAFS

Summary--Features of XAFS• Applicable to any phase (amorphous, liquid, gas),

surface/interface and biomaterials• Measurable under various conditions

under high pressure, gaseous atmosphere, for real catalysis

• Polarization dependence direction of the bond• Temperature dependence strength of any

specific bond • Combined with microbeam local structure of a

local area• Pump-probe experiment dynamics of local

structure