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

L3

L2

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

Abs

orpt

ion

Coe

ffici

ent

　 P hoton E nergy

N E XA FS E XA FS

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

c

2224

i: wave function of the initial state1sf: wave function of the final state superposition of the ejected wave and back-scattered waves

0

0

k EXAFS function

222

2exp)2exp(),(

)(22sin)()(

krkr

kfNkA

kkrkAk

jj

jj

jjj

j

Point atom, plane wave, and single scattering approximations

iii

i kRkAk 2sin

EXAFS oscillation

02 EEmpk

Ri:bond distance

Phase shifti

Ｒ

Phase shift

iii

i kRkAk 2sin

-6.0

-2.0

2.0

6.0

10.0

14.0

4 6 8 10 12 14 16

Pb

Sn

Ge

SiC

Phase shift of the X-ray absorbing atom

k/A-1

i

ii

i

ii

RkkF

kR

NkA 2exp2exp

222

*

EXAFS　 amplitude

Effective Coordi-nation number

Back scatteringamplitude

Debye-Wallerfactor

Electron meanfree path

5 10 15k(A -1)

B ackscatte ring Am plitude F (k)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

F(k

)

CS i

Ge

Sn

Pb

i

ii

i

ii

RkkF

kR

NkA 2exp2exp

222

*

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

photoelectron

Auger electron

sample

X -ray

Ionization chamber

Filter and solar slit

Fluorescence

Absorption

Cu K-XAFS of CuSO4 10mMol aq. solution

Transmission Fluorescence

0.5 mmfilm

6m 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 +　

Fourier transform

Am

plit

ude

EX

AF

S f

unct

ion

Back Fourier Transformation

k

Amplitude Envelope

Kind of scattererCoordina-tion number

Polarization

Direction ofBond, Adsorp-Tion site

Temperature

Bond stiffness

EX

AF

S f

unct

ion

E

Polarization Dependent EXAFS K-absorption(1s p-like continuum)

Polarization Dependent EXAFS K-absorption(1s p-like continuum)

Temperature dependence

　 )(22sin)()( kkrkAk jjj

j

222

2exp)2exp(),(

krkr

kfNkA j

j

jj

22

122

1

2 2),(

),(ln TTk

TkA

TkA

22

122

1

2 2),(

),(ln TTk

TkA

TkA

c-As

Determination of 2(T)

What can we get from 2(T)

u0

u0 ui

Ri

R0 Ri

O

iiiiii

iii

RuRuRuRu

Ruu

0

2

0

2

2

02

2

0

0

RR

RRR

i

ii

kTT

Ei 2

coth2

2

12

2

2coth

2coth

2 kTkTEi

Einstein model

22EE cf

Einstein frequency

c-As 　As-As: 216 cm-1

a-As As-As: 234 cm-1

c-As2S3

As-S: 332 cm-1

g-As2S3

As-S: 330 cm-1

c-As4S4

As-As: 222 cm-1 As-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 (k)

Atomic distance(Å) EXAFS (k)

EX

AF

S k (w ave num ber)

EXAFS analysis-1

Am

plit

ude

D istance r= r +i i

iii

i krkAk 2sin

Phase shift

Atomic distance

amplitude

1st nearest

2nd nearest

3rd nearest

Fourier transformation

EX

AF

S k (w ave num ber)

EXAFS analysis-2

Effective CoordinationNumber

Debye-Wallerfactor

Backscatteringamplitude

Direction ofchemicalbond

PairPotentialFunction

Kind ofscatteringatom

Limitation and Improvement of XAFS

theory　• Multiple scattering effect

which 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

33

44

222

22

3

4),(2sin

3

22exp),(

!

)2(2exp),(Im)(

kCkRkkRkCkCkRkFkR

N

Cn

ikikRkRkf

kR

Nk

effeff

nn

n

eff

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 take　　 into 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), surf

ace/interface and biomaterials• Measurable under various conditions under high pressure, gaseous atmosphere, for real c

atalysis• Polarization dependence direction of the bond• Temperature dependence strength of any specific b

ond • Combined with microbeam local structure of a loc

al area• Pump-probe experiment dynamics of local structur

e