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