EXAFS

Santiago J. A. FigueroaResearcherBeamline coordinator XAFS2santiago.figueroa@lnls.br

Extended X-Ray Absorption Fine Structure

EXAFS

Campinas, 23 de Agosto de 2016

5th School on X-Ray Spectroscopy Methods

1.Interaction of X-rays with matter

2.Basics aspects about XAFS

3.Understanding the EXAFS equation

Overview

hTransmissionMATTER

h

Scattering

Compton

h h '

Thomson

Photoelectric absorption

Pair productionh > 1M eV

X-rays

Interaction of X-rays with matter

h

Decay processes

Fluorescence Auger electrons

h f

Primary competing processes and some radiative and non-radiative decay processes

Thomson Observed data

Pair production

Compton

Absorption

Photonuclear absorption

Cro

ss s

ecti

on

(b

arn

s/at

om

)

1

103

106

10 eV 1 KeV 1 GeV1 MeV

Cu Z=29

Energy

X-ray attenuation :

Photoelectric effect is thedominating process at the x-rayenergy range (200-100 keV)

Interaction of X-rays with matter

• What is XAFS?

– XAFS studies the details of the x-ray absorptioncoefficient around an absorption edge.

– It reveals a wealth of information regarding thegeometric and electronic structure of materials.

11.2 11.6 12.0 12.4-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

mt

Energia(keV)

Basics aspects about XAFS

Basics aspects about XAFS

103

104

10

102

103

104

K

LI

LII

Co

eficie

nte

de

ate

nu

açã

o (

cm

2/g

)

Energia (eV)

Ge (Z=32)

LIII

XAFS: Study the details of the variation on the absorption

coefficient (fine structure) after the edge.

K 1s p

L1 2s p

L2 2p1/2 s, d

L3 2p3/2 s, d

Absorption edges

11.2 11.6 12.0 12.4-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

mt

Energia(keV)

Basics aspects about XAFS

X-ray attenuationAbsorption coefficient:

tII dd m

Mass absorpion coefficient:

jj

jg

m

m

Mass fraction of el. j

Atomic absorption coefficient:

N

Aj

j

a

j

mm

units (cm2/g)

Units: 10-24cm2 (1 barn)

h h

amostra

I0I1

t

µ : linear absorptioncoefficient

t : thickness

µt: absorbance

)exp(01 tII mIncludes contributions from allscattering and absorption precesses

Basics aspects about XAFS

Basic XAFS experiment – sequential mode

Radiation source

monochromatorIo I

sample

detectors

1

0logI

Itm

Basics aspects about XAFS

X-ray energy

m

EXAFS spectrum

Fluorescence X-rays

TEY

SAMPLE

Incident X-rays Transmitted X-rays

Visible light

XEOL

h

h

e-

Basics aspects about EXAFS

Always transmission, if possible

Most accurate method, best overall S/N

counting statistics of about 10-4 from

beamlines with more than 108 photons/s)

Which method for which application?

The most important criterion:

The best signal to noise ratio for the

element of interest

hh fluor .

e-h lu min.

h

Ie-

Fluorescence for very diluted samples

A specific signal reduces the large

background (but maximum tolerable

detector count-rate can result in very long

measuring times).

Total electron yield (TEY)

for surface sensitivity and surface

XAFS (adsorbates on surfaces)

TEY for thick samples that cannot be

made uniform.

XEOL X-ray excited optical luminescence

VIS/UV detection from luminescent samples

Basics aspects about XAFS

XAFS = XANES + EXAFS

12.0 12.5 13.00.1

0.2

0.3

0.4

0.5

0.6

E0=11.867 keV

InAs - As K-Edge mt

Photon Energy (keV)

XANES EXAFS

X-ray Absorption NearEdge Strucuture

Extended X-ray AbsorptionFine Strucuture

Near Edge X-rayAbsorption Fine Strucuture

NEXAFS

high Z elements

low Z elements

XANES is the region ~50 eV around the edge

Basics aspects about XAFS

Information content

•Fermi energy•Projected density of unoccupied states•Oxidation states •Coordination symmetry

Information content

•interatomic distances•disorder•coordination numbes•Bond-angle distributions•Partial pair distribution•Vibrational properties.

XANES : transitions to unoccupied states (localized and continuum)

low energy photoelectron multiple scattering (MS)

EXAFS: high energy photoelectron single scattering + some important MS

Basics aspects about XAFS

K

L

M

Fermi Energy

Continuum

1s

2s, 2pfóton

Bin

din

g En

erg

y

N

3s, 3p, 3d

4s, 4p, 4d, 4f

0

Ocupped states

Unnocuped statesXANES

Basics aspects about XAFS

E

m

E

m

i >

E

f >

i >

E

Fermi Golden rule

i >

E

f >

f

Arctangent curve

Inflectionpoint

XANES: pre edge structure

E

ma

b

0

0

0

0

0

K

L

M

Fermi Energy

Continuum

1s

2s, 2pfóton

Bin

din

g En

erg

y

N

3s, 3p, 3d

4s, 4p, 4d, 4f

0

Ocupped states

Unnocuppied statesEXAFS

Information obtained:•Coordination number•Interactomic distances•Disorder

Basics aspects about XAFS

Basics aspects about XAFS

XAFS = XANES + EXAFS

12.0 12.5 13.00.1

0.2

0.3

0.4

0.5

0.6

E0=11.867 keV

InAs - As K-Edge mt

Photon Energy (keV)

EXAFS

Extended X-ray AbsorptionFine Strucuture

EXAFS is the region from 50 – 1200 eV after the edge

Fine Strucuture

Basics aspects about XAFS

R

•Interference in between propagating waves and retrodispersed ones. Thismoduls the absorption coefficient.

•Photon energy (E) > Binding Energy (El): Photoelectric effect.

•Kinetic energy of the photoelectron (Ec)= E - EL

•Wave-Particle duality: The photoelectron travel as a esferic wave: Ec = h

2

)(2

Le EEmk

•Wavevector of the photoelectron: K

•Phase difference of the incoming and outgoing waves: Δ

kR2

•Quantical state of the photoelectron: superposition of thepropagating wave with the retrodispersed waves on theneightbourgs

•Oscilation frequence: 2R•Oscilation amplitudes: number of neightbourgs and disorder

Understanding the XAFS equation

7000 7200 7400 7600 7800 8000 8200

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

mx

Energia(eV)

Here we add (superpose) oscilations ofdifferent frequencies (radial distances), one for each coordination shell

-2 0 2 4 6 8 10 12 14 16 18-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

(k

)

Vetor de onda do fotoelétron: k(Å-1)

•Coordination shell: Refers to the aggrupation's of atoms at the same distance to the absorber atom.

•Coordination Number: amount of atoms in a coordination shell

m

0mm

mm

0

Understanding the XAFS equation

)](2sin[ kkR ii

i

R

i

i

i

i

ik

eekFSkR

N

2

2

02

222

)()(k

iR

iN

i2

2

0S)(kF

)(k

Estructural parameters

ab initio

Atomic parameters: Absoption and dispersion of thePhotoelectron

Understanding the XAFS equation

Principal hypothesis:•Final states are plane waves•Gaussian disorder•Dipolares transitions•One active electron•Photoelectron dispersion is single

Sayers et al.,PRL 27, 1204 (1971)

)(ê)(2

f

EE

f

EirfEFf

m

max

min

2e)(2

1)(

k

k

Rki dkkRTF

Understanding the XAFS equation

max

min

2e)(2

1)(

k

k

Rki dkkRTF

Understanding the XAFS equation

max

min

2e)(2

1)(

k

k

Rki dkkRTF

-5 0 5 10 15 20 25 30 35

0

2

4

6

8

R=1

R=2

R=2.5

sin(2*R*k)

(k

)

k(Å-1)

R=3

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0

4

8

12

16

20

24

28

32

36

Módulo

da T

F

R(Å)

Understanding the XAFS equation

max

min

2e)(2

1)(

k

k

Rki dkkRTF

0 5 10 15 20 25 30

-1.0

-0.5

0.0

0.5

1.0

(k

)

k(Å-1)

i*sin(2*R

i*k)

1=6

2=4

3=5

4=12

0 1 2 3 4 50

2

4

6

8

10

12

Módulo

da T

F

R(Å)

)](2sin[ kkR ii

i

R

i

i

i

i

ik

eekFSkR

N

2

2

02

222

)()(k

Understanding the XAFS equation

0 5 10 15 20-8

-6

-4

-2

0

2

4

6

(k

) x k

2

k(Å-1)

0 1 2 3 4 5 60

2

4

6

8

10

Módulo

da T

F

R(Å)

Signal at Ge-K edge

1a shell: R =2.45 Å N=4

2a shell: R = 4.00 ÅN=12

3a shell: R = 4.69 Å N=12

4a shell: R = 5.66N=4

Fourier Transform (FT)

FT: is not a Radial Distribution function buthave some resemblance

)](2sin[ kkR ii

i

R

i

i

i

i

ik

eekFSkR

N

2

2

02

222

)()(k

oK

Understanding the XAFS equation

0 5 10 15 20

-3

-2

-1

0

1

2

3

x

k2

k(Å-1)

N=4

N=3

N=2

N=1

0 5 10 15 20

-3

-2

-1

0

1

2

3

x

k2

k(Å-1)

N=4

N=3

N=2

N=1

0 5 10 15 20

-3

-2

-1

0

1

2

3

x

k2

k(Å-1)

N=4

N=3

N=2

N=1

0 5 10 15 20

-3

-2

-1

0

1

2

3

x

k2

k(Å-1)

N=4

N=3

N=2

N=1

0 1 2 3 40

2

4

6

8

10

Módulo

da T

F

R(Å)

N=4

N=3

N=2

N=1

0 1 2 3 40

2

4

6

8

10

Módulo

da T

F

R(Å)

N=4

N=3

N=2

N=1

0 1 2 3 40

2

4

6

8

10

Módulo

da T

F

R(Å)

N=4

N=3

N=2

N=1

0 1 2 3 40

2

4

6

8

10

Módulo

da T

F

R(Å)

N=4

N=3

N=2

N=1

Changes on the EXAFS signal with variations on the Coordination number

Understanding the XAFS equation

Changes onthe EXAFS signal with a variation onthe0 5 10 15 20

-3

-2

-1

0

1

2

3

x k

2

k(Å-1)

R0

R0 + R

0 1 2 3 4 50

2

4

6

8

10

Módulo

da T

F

R(Å)

R0

R0 + R

0 5 10 15 20

-3

-2

-1

0

1

2

3

x k

2

k(Å-1)

R0

R0 - R

0 1 2 3 4 50

2

4

6

8

10

Módulo

da T

F

R(Å)

R0

R0 - R

Å1.0R

Understanding the XAFS equation

Changes on theEXAFS with a variation onthe structuraldisorder

0 1 2 3 4 50

2

4

6

8

10

Módulo

da T

F

R(Å)

Sem desordem

Com desordem

0 1 2 3 4 50

2

4

6

8

10

Módulo

da T

F

R(Å)

Sem desordem

Com desordem

0 5 10 15 20

-3

-2

-1

0

1

2

3

x k

2

k(Å-1)

Sem desordem

Com desordem

0 5 10 15 20

-3

-2

-1

0

1

2

3

x k

2

k(Å-1)

Sem desordem

Com desordem

Gaussian Disorder: σ = 0.03 Å

m

mm

0

m0m

12600 12800 13000 13200 13400 13600 13800

0.0

0.5

1.0

1.5

2.0

ab

so

rbâ

ncia

Energia(eV)

xm

bkg

Victoreen

CdSe - Borda K do Se

Data treatment1 – background extraction

12800 13000 13200 13400 13600 13800

-0.10

-0.05

0.00

0.05

0.10

(E

)

Energia (eV)

Understanding the XAFS equation

0 2 4 6 8 10 12 14 16 18

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

k(Å-1)

k)*

k2

-2 0 2 4 6 8 10 12 14 16 18

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

k

k(Å-1)

0 2 4 6 8 10 12 14 16 18

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

k(Å-1)

k)*

k2

Conversion Ek

2

)(2

Le EEmk

K-weigthing

Understanding the XAFS equation

0 2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

|FT

((k

))|

R(Å)

0 2 4 6 8 10

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

|FT

((k

))|

R(Å)

0 2 4 6 8 10 12 14 16 18

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

k(Å-1)

k)*

k2

0 2 4 6 8 10 12 14 16 18

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

k(Å-1)

k)*

k2

Structural parameters: Minimal Square fitting

Phases and amplitudes of the retrodispersion

Understanding the XAFS equation

)](2sin[ kkR ii

i

R

i

i

i

i

ik

eekFSkR

N

2

2

02

222

)()(k

iR

iN

i2

2

0S)(kF

)(k

Estructural parameters

ab initio

Atomic parameters: Absoption and dispersion of thePhotoelectron

Understanding the XAFS equation

Principal hypothesis:•Final states are plane waves•Gaussian disorder•Dipolares transitions•One active electron•Photoelectron dispersion is single

Sayers et al.,PRL 27, 1204 (1971)

)(ê)(2

f

EE

f

EirfEFf

m

But remeber....

Obrigado pela sua atenção!

Questions, please email me:santiago.figueroa@lnls.br

More info about XAFS:https://speakerdeck.com/bruceravel?page=2http://cars.uchicago.edu/ifeffit/Mailing_Listhttp://xafs.org/Tutorialshttp://www.ixasportal.net/ixas/http://cars.uchicago.edu/ifeffit/DocumentationAcknowlegments: To Gustavo Azevedo, Valmor Mastelaro, AnatolyFrenkel por some slides