xas: x-ray absorption xafs: x-ray absorption fine structures xanes: x-ray absorption near edge...
TRANSCRIPT
XAS: X-ray Absorption
XAFS: X-ray Absorption Fine Structures
XANES: X-ray Absorption Near Edge Structures
NEXAFS: Near Edge X-ray Absorption Fine Structure
EXAFS: Extended X-ray Absorption Fine Structures
X-ray Absorption Spectroscopy:The extended region
X-ray absorption spectroscopy
Io I
t
I I e t I Iot
o ; ln ( / )
e
hvf
hvop
ion
Transmission:
Yield spectroscopy:
t Y hv
t f hv Y hv
( )
( ) ( )
Photon
Absorption across an edge
Eo element specific
bondingsymmetry
local structure
What does (hv) measure across an edge?
The modulation in above the edge is the XAFS, it contains information about the structure and bonding of the absorbing atom in a chemical environment
Edge jump: threshold of the core excitationNear edge region: core to bound and quasi bound state transition – multiple scattering effect dominatesExtended region above the threshold: core to continuum transition, single scattering dominates, interference of outgoing and backscattering waves
t EXAFS
Near edge
What is XAFS?
Si(CH3)4
Origin of XAFS
Free atom
hv (photon)
e- (photoelectron) wave
core hole (K, L1, L2, L3 etc)
previously unoccupied bound states
hv threshold energy of the core electron (binding energy)
Selection rule: electric dipole
decay
De-excitation/yield spectroscopy
e- with KE > 0 propagates as a wave with k ~ (KE)1/2. If it does not encounter another atom in the vicinity, the (hv) varies monotonically as a function of photon energy
edge
Origin of EXAFS
Rydberg
Outgoing wave (spherical wave)
Backscattering wave (dominant for fast electrons)
Diatomic molecule
If the outgoing and backscattered waves are in phase, the interference is constructive, if they are out of phase, the interference is destructive
Transition toLUMO, LUMO + XANES(X-ray AbsorptionNear Edge Structures)
hv (photon)hv > Eo (binding energy)
The forward and backscattered waves will interfere constructively and destructively at the absorbing atom, producing oscillations in (hv) EXAFS
destructive
constructive
Origin of EXAFS
EXAFS
XANES
LUMO
outgoing e- wave
absorbing atom
R
The interference modulates . Thus depends on of the outgoing wave, the electronic structure (amplitude of the scattering atom and the phase shift of both atoms) and the inter-atomic distance(R)
destructive interference yields a minimum
constructive interference yields a maximum
Kr Br2
( )k sam ple a tom
atom
EXAFS:
oscillations
Interference of outgoing and backscattered wave
Brian M. Kincaid, "Synchrotron Radiation Studies of K-Edge X-ray Photo-absorption Spectra: Theory and Experiment", Stanford University, 1975; Advisor: S. Doniach
EXAFS: the modern view
• EXAFS is the oscillations in beyond the XANES region• The oscillations arise from the interference of the outgoing and the backscattered electron wave which modulates the absorption coefficient (no neighboring atom, no EXAFS)• Single scattering pathway dominates at high k (energy)• The thermal motion modifies the amplitude of the EXAFS• It is a short range phenomenon (~ 4 Å) (IMFP of electrons)• It works for disorder systems (liquid, amorphous materials)• EXAFS is additive - all absorber-scattering atom pairs contribute to EXAFS additively• The phase and amplitude are transferable for chemically similar systems; they are also separable by Fourier Transform• Theoretical phases and amplitudes are often used in analysis; they can be generated in the FEFF code developed by J.J. Rehr of the University of Washington
EXAFS of medium and high Z atomsXANES
EXAFS
Conversion of kinetic energy E – Eo to wave vector k
k A m E E E eV
k E
o( ) ( / )( ) . ( )
.
0 122
2 0 2 6 3
0 5 1 3
Where Eo is the threshold energy (usually the point of inflection of the edge jump), E is the photon energy.Thus 50 eV above the threshold corresponds to a k value of 3.63 Å-1 k = 2 Å-1 corresponds to 15.2 eV above threshold
Photon Energy (eV)
11080 11100 11120 11140 11160
de
riva
tive
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
ab
sorp
tion
0.0
0.5
1.0
1.5 Ge K-edge
t
d(t)/dE
Eo
8200 8400 8600 8800 9000 9200 9400
0.2
0.4
0.6
0.8
1.0
1.2
1.4
abso
rptio
n =
ln (
I o/I)
Photon Energy (eV)8200 8400 8600 8800 9000 9200 9400
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Abs
orpt
ion
Photon Energy (eV)
2 4 6 8 10 12 14 16 180.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
Abs
orpt
ion
k (A-1)
2 4 6 8 10 12 14 16 18
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
X(k
)
k(A-1)
Ni K-edge
Normalizededge jump to 1
spline fit to atomic Backgroundo
Ni foil
( )k o
o
Extracting EXAFS data from absorption spectrum
converted to k space k ~0.513 (E)0.5
44.2 cm2/g 334.6 cm2/g = 1 (334.6-44.2 )8.9 = 2584.56cm-1
density of Ni
2 4 6 8 10 12 14 16 18
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
(k)
k(A-1)
( )( , )
s in [ ( )]
( ) ( )
/ ( )
kN S f k e e
kRkR k
A k k
jR k k
jjj
j e j
02 2 2
2
2 2
2
A(k)
The EXAFS formula
EXAFS formula and relevant parameters
The EXAFS equation
( )( , )
s in [ ( )]
( ) ( )
/ ( )
kN S f k e e
kRkR k
A k k
jR k k
jjj
j e j
02 2 2
2
2 2
2
Nj: coordination number of atom type j, e.g. TiCl4, NCl = 4So
2: amplitude reduction term (shake-up, shake-off loss)f(, k): atomic scattering amplitude, e.g. f(, k) for single scattering
e eR k kj e j 2 2 2 2/ ( ) , : amplitude damping terms due to electron
escape depth e and mean displacement due to thermal motion j,
Rj : interatomic distance, (k) = 2a(k)+ b(k) : phase function with contributions from the absorber a(k) and the backscatterer b(k)
amplitude
phase
Relationship between (E) and (k): A simplified EXAFS equation
We recall
i i
( ) 'E Hi f 2
f f
'H
Initial state wavefunction, describing the core electron
Interaction, H’ = ekr ~ 1 (dipole)
Final state wavefunction describing the photoelectron, sensitive to chemical environment
where all the actions are
Footnote : interaction of light with a bound electron in an atom
E field interacts with electron charge, B field interacts with magnetic dipole momentFor a plane wave B and E have equal strength in free spaceWhich interaction is more important?
E field interacts with electron charge
The interaction energy U e ·V = e E dr
Interaction energy ~
potential electric field
distance
eE a oIf we take the radius of the atom as ao = Bohr’s radius
B field interacts with magnetic dipole moment
The interaction energy U ~ (eћ/mc) ·B
gyromagnetic ratio: magnetic dipole moment /angular momentum
magnetic field
Footnote, cont’
Relative strength of magnetic/electric interaction
U
U
e
m cB
eE a
B
m cE am ag
elec t o o
Since ae
m co 2 2
2
1
e
c
2 1
1 3 7And fine structure constant
U
U
B
m cE
m c
em ag
elect
2
22 1
1 3 7
Electric interaction is more than two orders of magnitudestronger than the magnetic interaction
Footnote, cont’
Dipole approximation
The photon field in the electromagnetic wave is a plane wave
A A eoi k r t
rea l { }( )
If the wavelength is larger than the diameter of the atom, the eikr term can be replaced with 1 in the expansion (small atom approx.)
Footnote, cont’
e i k r ik r ik rikr 11
2
1
32 3( )
!( )
!( )
The term (k·r)n is called electric 2(n+1) pole and magnetic 2n -pole transition. E.g.: n = 0, electric dipole and magnetic monopole, n = 1, electric quadrupole and magnetic dipole etc.
Dipole approximation
The interaction Hamiltonian
He
m cA P
can be replaced with
He
m cA P to co s
vector potential · momentum
Same as ( ·r) discussed earlier
Time dependentperturbation
Footnote, cont’
f sca ttf f f 0
free atom neighboring atom
( ) ' 'E H i H f fi f sca tt 2
0
2
Expanding we get
( ) (
)'
' ' *
'E i H f
i H f f H i
i H fcom plex con juga tesca tt 0
2 0
0
21
This is the only term that is sensitive to the environment
( ) ( )[ ( )]E E E 0 1
( ) 'E i H f i fsca tt sca tt
Final state in EXAFS
( ) 'E i H f i fsca tt sca tt
EXAFS involves the change in the photoelectron wavefunction due to back scattering.
( ) ( ) ( ) ~ ( )E r r drsca tt sca tt 0
Thus EXAFS is the modulation of the photoelectron wavefunction at the absorbing atom resulting from its backscattering from neighboring atoms
initial
scattering
final at r~ 0
Vanishes if there isno neighboring atom
Since the initial state is localized spatially ( function), We have
EXAFS of a diatomic molecule
A e f
e
rrikx
ikr
( ) ( )
plane wave spherical wave
Scattering angle
De Broglie wave
e-
Out going photoelectronspherical wave
hvBackscattering photoelectronspherical wave carrying info.
of amplitude and phase of the scattering atom
f k ee
ri k
ikr
( , )( )( ) f
e
ro
ikr
Since ( ) ~ ( )E sca tt 0
We can build a simple model to account for EXAFS by considering the following events [ref. Newville, XAFS workshop http://cars9.uchicago.edu/xafs_school/]
• outgoing photoelectron (spherical wave)• scattering of the electron wave by the neighboring atom• returning of the backscattered wave to the absorbing atom
( ) ( , ) ( ) . .( )ke
kRk f k e
e
kRc c
ikRi k
ikR
2
amplitude phase-shift
For the spherical photoelectron wave, eikr/kr, with a neighboring atom at a distance R, we get
The EXAFS of an atom in a diatomic molecule is
2
))(2(),(Im)(
kR
ekfk
kkRi
)(2sin),(
)(2
kkRkR
kfk
R
absorbing atom
backscattering atom
amplitude for 180o backscattering
phase shift has both absorbing and back-scattering atom contributions
Since the molecule vibrates, leading to an instantaneous variation of the bond length, the effect is represented by the mean square displacement, 2 , an amplitude damping term, the Debye-Waller (DW) factor,
R
DW = 1 when = 0, when > 0, DW < 1, thusvibration contributes to the damping of the amplitude
DW term
the Debye-Waller (DW) factor
)(2sin),(
)(2
2 22
kkRkR
ekfk
k
222 ke
For a multi-atom system with coordination number Nj
We next consider the inelastic scattering of the photoelectron, the escape depth, (k) contributing to a amplitude loss, e
k = 0.513E
Free mean path term
jjj
j
kjj kkR
kR
ekfNk
j
)(2sin),(
)(2
2 22
jjj
j
kRkjj kkR
kR
eekfNk
jj
)(2sin),(
)(2
)(/22 22
)(/2 kR je
The last term to consider is the manybody effect term associated with shake-up and shake-off, contributing to amplitude loss. This is to be distinguished from the inelastic loss, which takes place after the electron has left the atom. This term is often denoted as “So
2”
S o fN
oN2 1 1
2
fully relaxed un-relaxed
So2 = 1 in the absence of manybody effect (single particle
approximation); in reality, it has a constant in k for modest k values, ranging from 0.7 ~ 0.9 (depending on the chemical environment)
For more detailed information visit the following site and down load course materials from the 2009 XAFS workshophttp://cars9.uchicago.edu/xafs_school/
Summary: The EXAFS formula
( )( , )
s in [ ( )]/ ( )
kN S f k e e
kRkR kj
R k k
jjj
j e j
02 2 2
2
2 2
2
Amplitude, A(k)Phase, (k)Coordination
no., Nj
Manybody, So
2
Atomic scattering Factor, f (k,)Free mean
path e –2Rj/(k)
DW exp[-2k22]
Interatomic distance, Rj
absorbing atom phase shift a (l)
backsacttering atom phase shift b
Interatomic distance, R
K-edge l =1, p wave
The behavior of EXAFS parameters in k space
( ) s in [ ( )]k kR kj 2 The phase
ab a bk k k p w ave d ipo le( ) ( ) ( ) , , ( , ) 1 1
For K, L1 edge
ab : Phase function of the absorber-backscatterera
l ; Phase shifty of the outgoing e- from the absorbing atomb : Phase shift of the neighboring atom
ab a bk k k d ipo le( ) ( ) ( ) , ( , ) 2 0 1
For L 3,2 edge
Note: the phase shift difference between K and L3-edge is
Eo
)()()( 1 kkk blaab
)()()( 0,2 kkk blaab
)()()( 1 kkk blaba
mMax Min, phase shifted by
K-edge
L1-edge
L2,3-edge
Hexamethyl disilane, Si K & L-edge
flip
Theoretical phase functions
Backscattering Atom phase shifts b
Absorbing atom phase-shifts al for the K-edge, l = 1, p - wave
For low and medium z elements, ab = + k is a good approximation
Si-C =Si(a)+C(b)
Pd-Ti =Pd(a)+Ti(b)
( ) s in [ ( )]k kR kj 2 0
The large the R, the shorter the period in k space
Sin(2kR)
R1
R2
2kR
( ) s in [ ( )]k kR kj 2 When (k) ~ + k is included, the separation between oscillation maximum increases in k
Solid curve: (k) = 0
Dashed curve (k) = + k
The behavior of EXAFS parameters in k space
Amplitude, A(k) =
Coordination no., Nj
Manybody, So
2
Atomic scattering Factor, f (k,)
Free mean path e –2r/(k)
DW exp[-2k22]
constant
~ constant, 0.7 – 0.9
modified by
Damps A(k) as k increase
Element specific
Atomic scattering factor, f (k,)
Backscattering ( = ) amplitudeWith max in the low k region
Backscattering ( = ) amplitudeWith max in the medium k region
f(k, )•sin[2kR +(k)]
f ’(k, )•sin[2kR +(k)]
ff ’
( ) ( , ) s in [ ( )]k f k kR kj 2
Theoretical backscattering amplitude, f(k, )B.K. Teo and P.A. Lee J. Amer. Chem. Soc. 101 2815(1979)
FEFF developed byJ.J. Rehr, (best calculation)
Teo and Lee (old data) produce qualitatively the same shape of A(k) but the max/min occurs at higher k
f k e kR kR kj
j e( , ) s in [ ( )]/ ( ) 2 2 f k e kR kkj( , ) s in [ ( )] 2 2 2
2
0 2000 4000 6000 8000 100000
50
100
150
200
250
Si
NaCl
SiO2
GaAs
Au
Electron Kinetic Energy (eV)
Inela
stic
Mean
Pat
h (
A)
Lab XPS
Damps the A(k) more significantly in low k Damps the A(k) more significantly in high k
larger
XAFS measurements
• Transmission• Total electron yield (vacuum)• Partial electron yield (vacuum)• Ion yield (vacuum) • Fluorescence yield• Photoluminescence yield• Photoconductivity (dielectric liquid)
Yield(soft x-ray)
Assumption: Yield t (not always the case)Y ield f hv I eo
t ( ) ( )1
For a thin sample:
Y ield f hv I t t to ( ) [ ( ( ) ]!1 1 12
2
Transmission
IoIt
Incident flux Transmitted flux
t
Beer-Lambert law
I I e
I I I I et o
t
a o t ot
( )1
TransmissionAbsorption
tI
Io
t
ln To be measured
Ionization chamber
An Ion chamber is filled with inert gas ( He, Ar, N2 etc. ). The absorption of x-rays produces ion pairs, typically, it requires ~30 eV (W value) to produce 1 ion pair at 1 atm pressure (e.g. 27 eV for Ar and 33 eV for N2). Thus for Ar, a 2700eV photon produces 100 ion pairs. The flux I emerging from an Ar ion chamber is
X-ray detectors300 to 500 V typical
tcurrent amplifier
voltage to frequency converter
IIinc
I pho tons s iw A re
eE hv e
A r t
A r t( / ) ( )
( )( )
( )
( )
1current photon energy
Electron yield detectors
ADC
bias V (50 V)e
The specimen current (total electron yield)
e
Channeltron (TEY)
hemispherical analyzer, energy selected
(Auger)
e
Analog (current) to digital (counts) converter
V to F
X-ray Fluorescence yield
• Scintillation counter• Ion chamber (Lytle detector) (with filters)
Nondispersive
Moderate energy resolution
High energy resolution
Solid state detectors (Ge, Si)
WDX detector (crystal monochromator)
S.Helad, APS workshop 2005
hv
Wavelebgth
2.1 2.2 2.3 2.4 2.5 2.6
Inte
nsit
y
0.000
0.002
0.004
0.006
Photon Energy (eV)
5710 5720 5730 5740 5750 5760 5770
FL
Y
0.000
0.002
0.004
0.006
0.008
0.010
0.012
Ce L3-edgeFluorescence X-rays
Ce L
Ce L
Green Titanite
Brown Titanite
Ce in Titanite
~10 eV
EXAFS AnalysisI. Data reduction: extract EXAFS from the absorption
8200 8400 8600 8800 9000 9200 9400
0.2
0.4
0.6
abso
rptio
n =
ln (
I o/I)
Photon Energy (eV)
pre-edge points are fitted to a victoreen C3+D4
a) Pre-edge background removal
8200 8400 8600 8800 9000 9200 9400
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Ab
sorp
tion
Photon Energy (eV)
EJ
Subtract pre-edge background, divided by EJ
Ni metal
8400 8600 8800 9000 9200
0.0
0.2
0.4
0.6
0.8
1.0
1.2A
bso
rptio
n
Photon Energy (eV)
b) Determine Eo and convert data to k space
k A k E( ) .0 1
0 5 1 3
8300 8320 8340 8360 8380 8400-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2Eo = 8333 eV
Photon Energy (eV)
0 200 400 600 800
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Abso
rption
Photon Energy (eV)
2 4 6 8 10 12 14 16 18
0.95
1.00
1.05
1.10
Ab
sorp
tion
k (A-1)
Spline fit, 3rd order polynomial, 3 sections
2 4 6 8 10 12 14 16 18
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
X(k
)
k(A-1)
Remove spline
( )k o
o
c) Get (k) by removing atomic contribution
E = E - Eo
II. Data Analysis:a) Separation of amplitude and phase
2 4 6 8 10 12 14 16 18
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
X(k
)
k(A-1)
2 4 6 8 10 12 14 16 18
10
20
30
40
50
60
70
80
Ph
ase
(k)
k (A-1)2 4 6 8 10 12 14 16 18
-0.07-0.06-0.05-0.04-0.03-0.02-0.010.000.010.020.030.040.050.06
Fir
st s
he
ll a
mp
litu
de
k (A-1)
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
2.5
Mag
nitu
de
R (A)
FTWindow filter
Back transform
A(k)(k)
Fourier Transform in EXAFS ( ) ( ) s in [( ( )]k A k kr kj
jj 2
F T k k e dk
A k kr k e dk
F T k
ikr
jj j j
ik r
jj
j
j
[ ( )] ( )
( ) s in [ ( )]
[ ( )]
2
22
Consider the Fourier transform of EXAFS
F T k F T A k kr kj j j j[ ( )] { ( ) sin [ ( )]} 2
Consider the FT of one single shell
amplitude phase
F T k F T kr kj j j[ ( )] { sin [ ( )]} , 2 ( )k k a b kj j 2
F T kr r b k k
r r bjj j
j j
[ ( )]s in ( )( )
( )m ax m in
2for r >0
<=>
FT
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
2.5
Ma
gnitu
de
k ( A-1)
2 4 6 8 10 12 14 16 18
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
x(k
)
k (A-1)
r = rj + bj
The r space peak position is shorter than the real rj (b ~ - 0.2 to -0.3 Å); this is often referred to as the phase-shift uncorrected value
In k space, A(k) is convoluted in the oscillatory behavior of the phase so that
kmax
kmin
For multi-shells
2 4 6 8 10 12 14 16 18
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
X(k
)
k(A-1)
0 2 4 6 8 10
0.0
0.5
1.0
1.5
2.0
2.5
Mag
nitu
de
R (A)
Ni
FCC BCC Diamond HCP
Shell Atom Distance Atom Distance Atom Distance Atom Distance
1st 12 1/2 8 3/2 4 3/4 6 1/3+b/4
2nd 6 1 6 1 12 2/2 6 1
3rd 24 6/2 12 2 12 11/4 6 4/3+b/4
4th 12 2 24 11/2 6 1 2 b
Distance in unit of a, b = (c/a)2
Ni fccF T k F T kjj[ ( )] ( )
a
k n weighting and filteringFT is a frequency filter for an infinite sine wave the FT is a function (localized)
EXAFS is not an infinite sine function but a sum of discrete sine waves, FT yields a broadened, sometimes distorted peak, k n weighting and filtering are often used to improve the quality of the analysis
k n weighting ( n = 0 – 3)
0 2 4 6 8 10 12 14 16 18
-30
-20
-10
0
10
20
30
x(k
)kn
k (A-1)
0 2 4 6 8 100
200
400
600
800
Mag
nitu
de k
n
R (A)
k1, k2, k3
k3, k2, k1
Filtering window
Discrete FT leads to leakage in R space (side lobes), proper window selection can suppress side lobes and distortion
We often use a filter window in the back transform
Windows often used are RectangleHammingHanning etc.
Methods in EXAFS analysisPhase difference and log ratio method: Effective when we are interested in the difference in bond length between two closely related systems such as bulk-nano structures, metal ions in solution and metal oxides with different oxidation states, Let
be the phase of the unknown and the phase of the model compound isAnd k’ is an adjustable parameter then
( ' ) ' ( ' )k k r k 2
( ) ( )k kr km m m 2
( ' ) ( ) ' ( ' ) ( )k k k r kr k km m m 2 2
Bt adjusting Eo of k’ until (k’) -m(k) = 0The bond length difference can be obtained from the slope of
( ) ( , ) ( , )
( ) s in ( )
s in [( ) ]
k A k r k r
k k
r k
2
k
kr
02
2 m ax ( )
difference between adjacent maximum
Find from model compound
Alternatively, we can consider the difference in adjacent maximum of the oscillations in k space
kmax
Amplitude log ratio
( )( , )
s in [ ( )]/ ( )
kN S f k e e
kRkR kj
R k k
jjj
j e j
02 2 2
2
2 2
2
For two closely related samples, we assume that in A(k) everything is the same except N, R and , then we have
ln( )
( )ln ( )
A k
A k
N R
N Rk1
2
1 22
2 12
222
122
k2
N R
N R1 2
2
2 12
ln( )
( )
A k
A k1
2
22
21
2 slope
intercept
Beating method
When atomic shells are close to each other, the beating of the two waves produces minima in the total amplitude A(k) and “kinks” in the the total phase. The position of the beat nodes satisfies
2 1 31 2k R n nn , , . . . .
Since the phase for different shells is the same we have
2 1 3k R n nn , , , . . . .
bcc Fe, the first and second shell is very close, R = 0.385Å
FT
filteredback FT
A(k) (k)
2k1R = ,
R = 0.385Å
2 1 3k R n nn , , , . . . .
2k3R = 3,
R = 0.381Å
Curve fitting
( )( , )
s in [ ( )]/ ( )
kN S f k e e
kRkR kj
R k k
jjj
j e j
02 2 2
2
2 2
2
Useful parameters can be obtained by fitting the data to the following equation
There are many codes to perform fitting analysis. Details will not be discussed in this course. Typically, theoretical amplitude and phase (FEFF) or experimental data of standards are used for the fitting. More details can be obtained from web site references.
Several useful sites can be linked from http://publish.uwo.ca/~tsham/Click on “link” then “spectroscopy”
Data analysis computer codes
Ban: Dos based, good for preliminary examination of data
Athena: Window based contemporary version (public domain, by Bruce Ravel of NIST) (recommended)
Winxas: Commercial soft ware
EXAFS: Other Examples
(CH3)4Si
Si-C bondsingle sinusoidalCurve in k space
Singlebondlength
FT
Identical backscattering atoms
Beating of two sine waves is apparent
FT shows two peaks associated Si-C andSi-Si bonds
Two types of backscattering atoms
Si-CSi-Si
Si C
Electron exchange reactions (nuclear tunneling) Fe*(H2O)6
3+ + Fe(H2O)62+=> Fe*(H2O)6
2+ + Fe(H2O)63+
Acc. Chem. Res. 19, 99(1986)
Fe3+
Fe2+
e
Fe2+
Fe3+
equal radius
stretching motion
The bigger the separationthe shorterthe bond
EXAFS of other electron exchange pairs
Qualitatively, wecan predict which complex has a longer bond from the progressive mismatching of the oscillation maximum
k
kr
02
2 m ax ( )
accurate R
kmax
k’max
max
max
22
2
2
kr
rk
'max
2'2
kr
max'max
112)()'(2
kkrr
max'max
11
kkr
From one max to the next, the phase changes by 2