1- F. d’Acapito - HERCULES X

Introduction to the X-rayAbsorption Spectroscopy

(XAS)

Dr. Francesco d’Acapito

INFM-OGG c/o GILDA CRG -ESRFBP-220 F-38043 Grenoble (France)

(dacapito@esrf.fr)

2- F. d’Acapito - HERCULES X

Synchrotron Radiation Sources

Location of the different sources in the tunnel

Emission from a bending magnet

Emission from an insertion device

Comparison between the brlliance of undulators and wigglers.

3- F. d’Acapito - HERCULES X

The GILDA Beamlinehttp://www.esrf.fr/exp_facilities/BM8/handbook/handbook.htm

BM8 at ESRF

Energy range5-70 KeVFlux on the sample108 - 1010 ph/s

Beam size on the sample2 mmEnergy Resolution∆E/E ≈ 10-4

CrystalsSi (311), Si(511)

Energy range

22.9

m

24.2

m

25.2

m

26.2

m

27.9

m

28.5

m

29.1

m

5 cm31

.0 m

33.0

m

32.0

m

35.3

75 m

WALL

SIDE VIEW

2nd MIRROR CHAMBER

FLOOR

COOLED

SLITS

FILTER

HOLDERWHITE BEAM

POSITION MONITOR BERYLLIUM

WINDOWBEAM POSITION

MONITORBERYLLIUM

WINDOW1° EXPERIMENTAL HUTCH

MONOCHROMATOR

COOLED

BERYLLIUM

WINDOW

SECONDARY

BEAM STOPPERMONOCHROMATIC

BEAM POSITION

MONITOR

COOLED

BERYLLIUM

WINDOW

1st MIRROR CHAMBER

14501400

γ φ

θ2 (α)

second crystal

first crystal

sample

θ1

ESRF

2 α = 3.6 mrad (Mot + piézo)

(Moteur)

4- F. d’Acapito - HERCULES X

EXAFS HUTCH

Helium Cryostat

0

Ion Chamber2nd Ion

Chamber

EXAFS REFLEXAFS

2nd Slit + Norm. diode Refl. diode

Hp- Ge fluo detector

1st slit

Collection modes• Transmission(Concentrated samples)

• Fluorescence(Diluted samples)

• Total & Partial electron Yield• Total reflection

• Optical luminescenceDetectors• Ion Chambers

• 13 element High purity Ge• Electron multiplier

• Si PIN diodesAncillary equipment• Criostat/oven (77<T<500 K)

• Liquid He criostat (4<T<300 K)• 1T Magnet

5- F. d’Acapito - HERCULES X

Sam

ple1 st Ionization cham

ber2nd Ionization C

hamber

X-ray B

eam

I1 = I0 * exp (-µ x)

µ = -ln (I1/I0)

I0I1

Measuring the X

-ray absorption coefficient

6- F. d’Acapito - HERCULES X

Ionized state

Continuum

X-ray

fluorescence

Auger

electron Y

ield

Fluorescence

Experim

ental apparatus

Sam

ple

Ion Cham

ber

X-ray or E

lectron D

etector

X-ray

Beam

= electron

= H

ole

Indirect methods

7- F. d’Acapito - HERCULES X

Extended X-ray Absorption Fine Structure

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

40200404004060040800410004120041400

Sa

mp

le A

bso

rptio

n (A

rb.U

n.)

Energy (eV)

Absorption spectrum of Crystalline CeO2Absorption Spectrum of gaseous Kr

General Features:I) Chemical Selective

II) Information about the local structure

Information provided(for the first coordination shells)

I) Nearest neighbor nature and number ( ±0.5)II) Interatomic distances ( ± 0.02 Å)Debye-Waller Factors σ2 (± 10%)

8- F. d’Acapito - HERCULES X

EXAFS Theory

Absorption Coefficient µ from the Fermi Golden Rule

µ = < i | p ⋅A | f >2

<i| = <1s|, <2s|, <2p1/2|, <2p3/2|< f | isolated atom = e-i k r

k r Yl, m

< fatom in a cluster | = ?

= Absorbing Atom

= Backscattering Atom

R

Definition of the oscillatory function χ

χ = µ - µatomic

µatomic

EXAFS formula

χ = 3 S02Nj

k Rj2 Ak,Rj sin 2kRj + ϕk,Rj + 2δck ∑j

e-2k2σ2 e-2Rj / λ e⋅Rj

2

9- F. d’Acapito - HERCULES X

Amplitude of the backscattered electron wave

r

Ri

= Absorber

= Backscatterer

ê

Theta

ei∂ eikr

kr cos θ

Ri

ei∂ eikRi

kRi cos θ

r'

Ri

ei∂ eikRi

kRi cos θ T(k) eiβ eikr

kr

Ri

ei 2kRi + 2∂ + β

kRi2 cos θ T(k)

10- F. d’Acapito - HERCULES X

General formulation

Green function formalism

σ = σat Im1sin

2δL0

0 12 L0 + 1

T I-GT-1

L0,L0

0,0∑m0

≈ σat Im1sin

2δL0

0 12 L0 + 1

T GTn

L0,L0

0,0∑m0 ∑n

T= Atomic Scattering MatrixG= Propagator matrix

T =

t000t1

00

00tn

G =

0G0,1G1,00

G0,N-1G1,N-1

GN-1,0GN-1,10

TL, L'i, j

= δi, j δL, L' expi∂il sin∂i

l

GL, L'i, j

= δij 4π 2l+1 2l'+1 ×

× 2l''+1 l l' l''0 0 0 l l' l''

m -m' m'-m -1m'

il'+1

hl''+ kRij Yl'', m'-mRij ∑L''

The scattering cross section σ can be approximated by the so-called Multiple Scattering serie

made up of terms like:

Single Scattering (SS)

0

i

T0G0, iTiGi, 0T0

Multiple Scattering (MS)

(double scattering)

0

i

jT0G0, iTiGi, jTjGj, 0T0

Full Multiple Scattering

(FMS)

All possible pathsTI - GTL0, L0

0, 0

11- F. d’Acapito - HERCULES X

A FMS-MS-SS investigation: the structure of theCu+(CO)3 complex

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

8800890090009100920093009400

Ab

sorp

tion

coe

fficien

t µ (Arb

. Un

its)

Energy (eV)

FMS

MS and SS

O

CuC

Cu+(CO)3 complex

-0.1

0

0.1

0.2

0.3

0.4

0.5

2345678910

Cu - CCu - OCu - C - O

Simexpres

EX

AF

S sp

ectra

χ(k)

Electron wavenumber k (Å-1

)

-1.5

-1.0

-0.5

-101234

Experimental3042547090

En (Ry)

Ab

sorp

tion

Co

efficie

nt (A

rb.U

nits)

Contribution to the total EXAFS signal:

Cu-C SS; Cu-O SS; Cu-C-O MS.

Quantitative analysis

NCu-CO = 3 ± 0.3

RCu-C = 1.93 ± 0.02 Å

RC-O = 1.12 ± 0.03 Å

ΘCu-CO = 180 ±5 deg

FMS simulation of the XANES region for

different alpha angle values

30<alpha<90 deg

z

x,y plane

12- F. d’Acapito - HERCULES X

Example of a quantitative EXAFS analysis.

Determination of the Cu-Cu distance in the Cu 2O compound

Recall of the EXAFS formula in the single scattering framework

χ = 3 S02Nj

k Rj2 Ak,Rj sin 2kRj + ϕk,Rj + 2δck ∑j

e-2k2σ2 e-2Rj / λ e⋅Rj

2

The analysis method:

1) Evaluation of the amplitude Ã(k, Rj)S02A(k, Rj) exp(-2Rj/λ)

and phase P(k, Rj)[φ(k, Rj) + 2δc(k)]

terms from a compound with known structural parameters

2) Use of the cited terms in the determination of N j, σj and Rj of the

unknown compound.

13- F. d’Acapito - HERCULES X

Extraction of the EXAFS signal

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

108001100011200114001160011800120001220012400

Ab

sorp

tion

Co

efficie

nt (A

rb.U

nits)

Energy (eV)

Jp

Step 1 Background subtraction &normalization

0.00

1.00

2.00

3.00

4.00

5.00

01234567

MO

du

lus o

f the

Fo

urie

r Tra

nsfo

rm (A

rb. U

nits)

r (Å)

Transformation Window

Step 3 Isolation of the interestingpeak by back-transform

-0.10

-0.05

0.00

0.05

0.10

05101520

χ (k)

k (Å-1

)

Transformation Window

Step 2 Fourier Filtering of thespectrum

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

05101520

Filte

red

χ(k

)

k (Å-1

)

Step 4 fit to a model

14- F. d’Acapito - HERCULES X

Sample description

The model compound

Metallic Cu foil

Structurefcc1st shell nearest neighbours N:12 Cu

1st shell Cu- Cu distance R:2.5561 Å1st shell Debye-Waller factor σ

(77K)0.057 Å

The 'unknown' compound

Crystalline Cu2O powder

1st shell nearest neighbours:2 O1st shell Cu - O distance:1.85 Å

2nd shell nearest neighbours:12 Cu2nd shell Cu - Cu distance:3.019 Å

we will use the backscattering parameters of the Cu foil to extract the Cu-Cu distance in the oxide.

15- F. d’Acapito - HERCULES X

Experimental setup

Sample Ic 0 Ic 1

Sample

Ic 0

X-ray or Electron Detector

a) Transmission Modeb) Fluorescence (or Electron detection) Mode

Ic0 filled with 1000 mbar N2 Absorption =8%Ic1 filled with 300 mbar Ar Absorption = 80%

Samples at Liquid Nitrogen Temperature

Energy scan details

fixed energy step scan0.025 Å-1≤ ∆k ≤ 0.05 Å-1

Pre-edgeEdge -200 eV

Edge1st zoneEdge +100 eV

2 zoneEdge +400 eV

3 zonekmax=15Å-1

8800 eV8970 eV9010 eV9079 eV9379 eV9840 eV10 eV0.5 eV1 eV2 eV4 eV17 pts80 pts69 pts150 pts115 pts

3 s3 s3 s3 s3 s

16- F. d’Acapito - HERCULES X

Sample preparation

General rules:µtot < 2.5∆µCu≈1

Fundamental steps1) Find the weight fraction of the components:Cu2O: Mw= 2* 63.54 + 16 = 143.08 g/MolWt%Cu = 2*63.54/143.08 = 88.81 %Wt%O = 16/143.08 = 11.18 %

2) Read the absortion cross sections on tablesσ8978Cu = 36.1 cm2/gσ8980Cu = 287.2 cm2/g

σ8980O = 7.5 cm2/g

3) Calculate the sample weight for ∆µ=1 (typical S=1cm2 pellet)∆µCu = ∆σCu [cm2/g] * δCu [g/cm2]δCu = ∆µCu /∆σCu = 1/ (287.2 - 36.1) = 3.98 mgCu/cm2

Powder weight PP= δCu * S / Wt%Cu = 3.98e-3 * 1 / 0.8881 = 4.48 mgCu2O

δO = P * Wt%O / S= 0.5 mgO/cm2

4) Check if the total µ<2.5µ = σ8980Cu * δCu + σ8980O * δO = 1.143 + 0.0037 = 1.147

Your 4.5 mg/cm2 pellet is O.K.

17- F. d’Acapito - HERCULES X

The absorption spectra:

8731.42 8988.23 9245.03 9501.84 9758.6510015.45

-1.20000

-.900000

-.600000

-.300000

.000000

.300000

.600000

Metallic CuE (ev)

µ(E)

8918.06 9089.57 9261.07 9432.57 9604.07 9775.57 9947.07

-1.20000

-.800000

-.400000

.000000

.400000

Crystalline Cu2OE (ev)

µ(E)

18- F. d’Acapito - HERCULES X

Edge analysis

• The edge shape depends on the details of the local geometry around theabsorbing atom.• The edge energy (first inflection point of µ) is related with the valencestate of the absorber.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

89708980899090009010

Cu MetCu2OCuO

No

rma

lized

Ab

sorp

tion

µ (Arb

.Un

.)

Energy (eV)

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

89708980899090009010

Cu2OCu MetCuO

δ µ / δ E

(Arb

.Un

.)

Energy (eV)

8979 eV

8981 eV

8984 eV

19- F. d’Acapito - HERCULES X

EXAFS signal extraction

8700.00 8800.00 8900.00 9000.00 9100.00 9200.00 9300.00 9400.00 9500.00 9600.00 9700.00 9800.00 9900.00 10000.0 10100.0 10200.0 10300.0 10400.0rame_met1.absE (ev)

µ(E)

Pre-edge subtraction

9000.00 9100.00 9200.00 9300.00 9400.00 9500.00 9600.00 9700.00 9800.00 9900.00 10000.0 10100.0 10200.0 10300.0 10400.0

Atomic backgroundsubtraction

20- F. d’Acapito - HERCULES X

EXAFS spectra

4.00000 8.00000 12.0000 16.0000

-.900000

-.600000

-.300000

.000000

.300000

.600000

Metallic Cuk (Å-1)

k*khi(k)

4.00000 6.00000 8.00000 10.0000 12.0000 14.0000 16.0000 -.400000

-.200000

.000000

.200000

Crystalline Cu2Ok (Å-1)

k*khi(k)

21- F. d’Acapito - HERCULES X

Fourier Transforms

.000000 2.00000 4.00000 6.00000 8.00000 10.0000

10.0000

20.0000

30.0000

40.0000

50.0000

60.0000

Metallic CuR (Å)

F(R)

.000000 2.00000 4.00000 6.00000 8.00000 10.0000

3.00000

6.00000

9.00000

12.0000

15.0000

Crystalline Cu2OR (Å)

F(R)

Cu - O

Cu - Cu

22- F. d’Acapito - HERCULES X

Calculation of the backscattering parameters

4.00000 8.00000 12.0000 16.0000

-.400000

-.200000

.000000

.200000

.400000

Metallic Cu - 1st shellk (Å-1)

k*khi(k)

23- F. d’Acapito - HERCULES X

4.00000 8.00000 12.0000 16.0000Amplitude of rame_meta.fouk (Å-1)

A(k)

AmplitudeN = 12R = 2.5561 Åsigma = 0.057 Å

4.00000 8.00000 12.0000 16.0000Phase of rame_meta.fouk (Å-1)

phi(k)

PhaseR = 2.5561 Å

24- F. d’Acapito - HERCULES X

Back-Fourier transforms of the 'unknown' compound

4.00000 6.00000 8.00000 10.0000 12.0000 14.0000 16.0000 -.200000

-.100000

.000000

.100000

Cu2O Cu-O shellk (Å-1)

k*khi(k)

First (Cu-O) shell

4.00000 6.00000 8.00000 10.0000 12.0000 14.0000 16.0000

-.300000

-.200000

-.100000

.000000

.100000

.200000

.300000

Cu2O Cu-Cu shellk (Å-1)

k*khi(k)

Second (Cu-Cu) shell

25- F. d’Acapito - HERCULES X

The simulation

6.00000 8.00000 10.0000 12.0000

-.20

-.10

.00

.10

.20

Cu2O Simulation of the Cu-Cu shellk (Å-1)

k*khi(k)Fit : 1.252773E-02

Results of the simulation

ParameterValueN12.2 ± 0.5

R (Å)3.03 ± 0.03σ (* 10-2 Å)9.3 ± 2

The results are in agreement with the crystallographic data !

26- F. d’Acapito - HERCULES X

Suggestions for further reading

General papers

P.A.Lee, P.H.Citrin, P.Eisenberger, B.M.Kincaid Rev.Mod. Phys. 53(1981), 769

D.C.Köningsberger “X-ray Absorption”, Edited by D.C.Koningsbergerand R.Prins, John Wiley ans Sons New York 1988

Useful links(analysis programs and recent literature)

FEFF project ($)http://leonardo.phys.washington.edu/

GNXAS Project (no $)http://gnxas.unicam.it/

EXAFS analysis programs ($ and no $)http://www.esrf.fr/computing/scientific/exafs/