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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
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(1) Principle of XAFS
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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
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1.4 1.0 0.6 0.2波長
L3L2
L1
K
X-ray absorption spectrum from Pt foil
wavelength
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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
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XAFS spectrum from an atom
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XAFS spectrum from a diatomic molecule
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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
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( ) ( ) ( )iii
i kRkAk φχ += ∑ 2sin
EXAFS oscillation
( )hh
02 EEmpk−
==
Ri:bond distance
Phase shiftφi
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R
Phase shift
( ) ( ) ( )iii
i kRkAk φχ += ∑ 2sin
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-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
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( ) ( ) ( )
−−=
λσ i
iii
ii
RkkF
kRN
kA 2exp2exp22
2
*
EXAFS amplitudeEffective Coordi-nation number
Back scatteringamplitude
Debye-Wallerfactor
Electron meanfree path
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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
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( ) ( ) ( )
−−=
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
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Au K-EXAFS of Au foil
278K
77K
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EXAFS oscillation of Au K-edge
77K
278K
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Photon Energy
If the coordination number decreases,
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Photon Energy
If the bond distance increases,
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(2) Instrumentation
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monochromatorIo I
sample
Data processing
X-rays
Ion chamber
《transmission method》
Experimental method of XAFS
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X-ray escape depth>1000A
Electron escapedepth <50 A
FluorescentX-rays
Secondary electron
photoelectronAuger electron
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sampleX -ray
Ionization chamber
Filter and solar slit
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Fluorescence
Absorption
Cu K-XAFS of CuSO4 10mMol aq. solution
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Transmission Fluorescence
0.5 mmfilm
6µm film
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Partial electron yield x-ray absorption of surface atoms
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Total electron yield
Photon energy
Sample leak current
Partial electron yield
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(3) XAF S spectral analysis
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R+ φ
Fourier transform
Am
plitu
deEX
AFS
func
tion
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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
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E
Polarization Dependent EXAFSK-absorption(1s p-like continuum)
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Polarization Dependent EXAFSK-absorption(1s p-like continuum)
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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 −≅
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( ) ( )[ ]22
122
1
2 2),(),(ln TTk
TkATkA
σσ −≅
c-As
Determination of σ2(T)
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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
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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
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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
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X-ray energy(eV) EXAFS χ(k)
Atomic distance(Å) EXAFS χ(k)
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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
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EXAF
S χ k (wave number)
EXAFS analysis-2
Effective CoordinationNumber
Debye-Wallerfactor
Backscatteringamplitude
Direction ofchemicalbond
PairPotentialFunction
Kind ofscatteringatom
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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
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+−+
−+−=
+= ∑
∞
=
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
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(4) XAFS applications• Catalysis• Amorphous systems• Material physics(High Tc, CMR,….)• Magnetic materials XMCD• Thin films and Surface science • Environmental science • Biological materials
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(5) Challenge of XAFS
• Time-resolved XAFS spectroscopy
• Micro XAFS or Nano XAFS
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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