xafs: study of the local structure around an x-ray absorbing atom (1) principle of xafs (2)...
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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
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
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
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
-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
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
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
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
Temperature dependence
)(22sin)()( kkrkAk jjj
j
222
2exp)2exp(),(
krkr
kfNkA j
j
jj
22
122
1
2 2),(
),(ln TTk
TkA
TkA
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
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
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