Investigation of Atomic and Electron Structureof Nanocarbon Materials

by Use of EXAFS and NEXAFS Spectroscopy Techniques

V.V. ShnitovIoffe Institute, 194021, St. Petersburg, Russia

e-mail: v.shnitov@mail.ioffe.ru

ACN’2011Conference/School of Young Scientists" Diagnostics of Carbon Nanostructures "

July 6, 2011, St. Petersburg, Russia

Contents

1. Introduction. Basic Concept and Definitions.

2. Theoretical Background and a Little of History .

3. Some Aspects of Modern XAFS Experiments and XAFS Data Processing Technique.

4. The information that can be obtained by NEXAS/EXAFS.Some Nanocarbons Related Examples.

5. Conclusions.

6. Main Sources.

I. Basic Concepts and Definitions

X-ray Absorption Spectroscopy (XAS): Basic Concepts …

( )o( ) ln I Iμ ω ∝

o( )I ω

x

source detector

sample

o( ) ( ) xI I e μω ω −=

x-ray absorption coefficient

XAS of a polyimide polymer

Figure reproduced from the site http://ssrl.slac.stanford.edu/stohr/nexafs.htm

presenting the book“J. Stöhr. NEXAFS spectroscopy. Springer, 1996”

…and Basic Definitions

250 300 350 400 450

EdEo

Δ(ћω) ∼ 50÷1000 eV

Δ(ћω) ∼ 30÷40 eV

Carbon K-edge

EXAFS

μ (ћ

ω)

ћω (eV)

NEXAFS (XANES)Near Edge X-ray Absorption Fine Structure

– NEXAFS

X-ray Absorption Near Edge Structure –XANES

Extended X-ray Absorption Fine Structure– EXAFS

Surface Extended X-ray Absorption Fine Structure – SEXAFS

X-ray Absorption Fine Structure – XAFS

o

o

d

d

E - ( C ) E 285 eVE

Carbon edge edge

Divide between a NEXAFS EXAFS E 320 eV

nd

K K−

−

-

∼

XAS of HOPG

EF

EV

VB

K

Continuum

photoelectrone−

core-hole

ħωo= Eo

Eo- energy of absorption K-edgeτh, τa, τf - total and partials

core-hole lifetimes

ω

X-ray Absorption

VB

auger electrone−

Auger Effect

VB

photon

ω′

ω′

X-ray Fluorescence

15 13 15if Z 8 then 10 s 10 s 1 1 1 1 10 sa a af h fτ τ τ τ τ τ− − −≤ ⇒ = + ≅∼ ∼ ∼

E

Important Details of X-ray Absorption Process

II. Theoretical Background and a Little of History

( )2 2

22

2 2 ( )( ) ( ) sin 2 ( )

j j

o j jj

k R kj j

j

N f k e ek S kR k

kR

σ λ

χ δ− −⋅ ⋅ ⋅

= ⋅ +∑

2

xFermi's Golden Rule ( ) ( ) ( ) f

ifif E Eσ ω δ ω∝ Ψ ⋅ Ψ ⋅ −⇒ −∑ r E

-12

-2 -1xnumber of absorbed photons [s ] [nm ]

photon flux [nm s ]σ =

⋅

( ) ( )x anμ ω σ ω= ⋅

32 [cmx-ray absorption cross-section , atomic density ] [atoms cm ]n ax − − σ −⋅

X-ray Absorption Cross-Section

initial wave function

localized state with radius

ZB

i

a

− Ψ

∼

final w ave funtion

delocalized state w ith w ave num ber

and w a2 2

ve length

o

f

k

k E

−

λπ πλ

ω= =

−

Ψ dipole transition operator

electric field vector

( )

- edges of C, for the only possible transition

O, N, F1 2

Ks p

⋅ −

−

→

r E

E

The Roots of Difference between NEXAFS and EXAFS

(0) (1)

( single weak scatt regimeering )

EXAFS

f ffΨ ≅ Ψ + Ψ

1 0

R

large small ( ) ( ) sin

( )

(2

)k f kk f k kRμ

→

⋅∼

reflection of interference patterntraced along photoelectron wave numbe

r EXAF

scS -

ale

(0) (1) (2) ( )

( multiple strong scattering )

... ,

regime

n 1

NEXAFS

nf f f ffΨ ≅ Ψ + Ψ + Ψ + + Ψ

small large ( ) ( , )

( )k f kE l Eμ ρ∝

→

- reflection of - projected density of unoccupied states NEXAFS

( , )l

l Eρ

elasticscatteringamp

( , )

litude

f k θ −

2( ) ( ) ifkμ ∝ Ψ ⋅ Ψr E

2

0n

3

1120

NEXAFS Dependence on X-Ray Polarization

E(1s)

E

σ∗

π∗EF

EVħω

- DOSp

(

( ) ( , )E Eμ μ θ

⋅

↓→

r E)

C -edge XAS of HOPGK

oθ 0=

oθ 0=1

oθ 20=

oθ 30=

oθ 40=

oθ 50=

oθ 0= 6

σ*

(eV)E

2 2( , ) ( ) sin ( ) cosE E Eπ σμ θ ρ θ ρ θ∼ ⋅ + ⋅

z

y

Eθ

22

in-plane *- orbitals

σ* s cos θ

σ

⋅r E ∼

22

out-of-plane *- orbitals

π* s sin θ

π

⋅r E ∼

zEθ

yπ*

( )Eμ

the figure reproduced from R.A. Rosenberg et al.. Phys. Rev. B 4034 (1986).33,

Main features of CK-edge NEXAFS

V

V

V V

F V

F

F

ex

*1. - resonances (exciton-like) :

for HO

E E E E E E E 4.7 eV

.

PG:

2 - core hole (Frenkel) excitons:

σE 1 eV E E e

π

3

*

ex

eπ

ϕ

∗

< <= +

= +

+ < < +

V EXAFS

EXAFS

FEXAFS

*

VE 291.65 eV

. σ E 3 eV E E

for HOPG:

3 - resonances : lower bounda E - EXAFS

ry of regi

me

f E E 30 eV or O

*

H PG:

ex

σ

=

+ < <

+

reflects: x-ray polarization dependent, core hole-perturbed partial density of unoccupiedstates localized within a few atomic sites from the excited at

NEXAFS

(p-DOS) (R 5 angstreom ms) ∼ [*].

[*] J. Schiessling et al.. J. Phys.: Condens. Matter , 6563 (2003). 15

C -edge XAS of HOPGK

285 290 295 300 305 310 315

C60

HOPG

EV

π*- resonances

σ*- resonances EF

μ (Ε

)Ε (eV)

ex* core hole excitonσ −

Isolation of the Fine-Structure Oscillations χ(k)

o2

( ) ( ) 2 ( ) ( ) ( )( ) ( )o oE E m E E k kE k kμ μ μ μχ χμ μ

− − −= = =

Δ Δ

XAFS μo(E) for FeO [*] Isolated XAFS χ(k) for FeO [*]

EXAFS

kmin

μo(E) - absorption in the absence of neighboring scatterers (atomic-like background ) km – lower EXAFS boundary

m in m in( ) ( )k k k kχ χ< >[* ] M . N e w v ille . F u n d am e n ta ls o f X A F S . U n iv e rs ity o f C h ic a g o , 2 0 0 4 .

kr (kr 2 ( ))

(0) (1)

(0) (1)

(0) (1)

outgoing wave backscatt

,

,

ered

( , )

( ,

wave

backscattering amplitud)

e

i i k

f f f

f f

f fe ef kr r

f k

δ

− −

π

π −

+

∝ ∝

Ψ = Ψ Ψ

Ψ Ψ

Ψ Ψ

+

( ) phase shif t kδ −

2Rj

(0)fΨ

(1)fΨ

(0)2 2

0 (k)(k)

( ) ( ) ( )fi ifk

μμ

χ ∝ Ψ ⋅ Ψ − Ψ ⋅ Ψr E r E

( )2

w here are coo rd ination num ber

( ) ( ) s in 2 ( )

an d avareg e d is tan ce to a to m s in sh al

N

l

R

j jj

j j

j j

j

N f kk kR k

kR

j

χ δ

⋅= ⋅ +

,

∑

o o-1

min lower boundary

if then

2 EXAFS

1.42 A 4.5 A d

kR

R k

π= −

= ≅

Single Scattering Model

EXAFS as a Quantum Interference Phenomenon

Taking into Account Many-body Effects

The figure reproduced from M. Newville. Fundamentals of XAFS. University of Chicago, 2004.

2

2

2

2 22

Intrinsic Losses

( and processes )amplitude reduction factor;

Structural and Te

shake-up

mperature

shake-

Disord

o

e

f

r

f

j

o

o

j k

S

S

e

eσ

σ

−

−

−

→

→2 2

2

2 ( )

Debye-Waller factormean square displasment of shall atoms

( )

Extrinsic Losses photoelectron mean free path determined

by l

ine a

k

j

jR k

k

j

e λ

−−

σ

λ

−→

−stic scatterings and finite core-hole lifetime

( )2 2

22

2 2 ( )( )( ) sin 2 ( )

j j

o j jj

k R kj j

j

N f k e ek S kR k

kR

σ λ

χ δ− −⋅ ⋅ ⋅

= ⋅ +∑

Extraction of Structural Parameters from χ(k) - function

The figures reproduced from P. Castrucci et al. Phys. Rev. B , 035420 (2007).75

maxminEXAFS

and are determined, respectively, by lower boundary andby acceptable sign

al/noivalue of rati se o

k k

1 1maxmin

for carbon materials: 4 and A 11 12 Ak k− −÷

max

min

Radial structure function can be obtained using Fourier transf

( )( ) [*] :

( ) ( ( )) sin(2 )

ormati

on of k

k

F Rk k

F R dk kχ k kR

χ

= ⋅∫

[*]- D . E. Sayers,, E . A. Stern, and F. W . Lytle, Phys. Rev. Lett. , 1204 (1971).27

FEFFx (FEFF6 FEFF8)→

The Key Points of NEXAFS/EXAFS History

Discovery of X-Rays - Röntgen (1895)

First measurements of absorption edge – Maurice de Brogelie (1913)

The first observation of the fine structure – Fricke (K-edges) (1920), Hertz (L-edges) (1920)

The first theory of NEXAFS (“Kossel structure”) and EXAFS (“Kronig Structure”) –

Kossel (1920), R. Kronig (1931)

Creation of valid shot-range-order theory of EXAFS – D. Sayers, E. Stern, F. Lytle (1968-1971)

Appearance of the name EXAFS - F. Lytle, J. Prins (1968)

The dawn of “Synchrotron Era” – (1970s)

Appearance of the names XANES/NEXAFS - A. Bianconi (1980)/J. Stöhr(1982)

Development of highly quantitative multiple-scattering theories of XAFS – (1980s - present time)

Improvement of theoretical models and experimental facilities (1930s – 1960s)

III. Some Aspects of Modern XAFS Experimentsand XAFS Data Processing Technique

Storage Ring as a X-ray Source

The figure taken from site:http://www.odec.ca/projects/2005/shar5a0/public_html/images /model_animated.gif

Storage Ring Scheme Synchrotron’s Characteristics:

Electron beam energy :Current:

Circu

[GeV] [mA]

mference:Pulse duration (

[m] (ps) FWHM):

Bending M ag [net Fie Td ]l :

e

e

E

B

i Lτ

C

C

17

2

Critical

[keV][photons/

Photon Energy : Total Ph s]oton Flux:

2

0.665

1.3 10

C

e e

e

EF

L R

E E B

F i E

π

ω

=

= = ⋅ ⋅

≅ ⋅ ⋅ ⋅

Main Characteristic of Synchroton Radiation

The figure taken from prof. D. Attwood lecture " Intro to Synchrotron Radiation" EE290F, 16 Jan 2007. Berkeley. USA.

Advanced Light Source (ALS).Berkeley. USA

2

1 mrade em c Eθ

θΔ =Δ ∼

Dipole Synchrotron Radiation (SR)

θΔ E

e− e−

- electric field vector E

bendingmagnet

10

1. linear polarization of (in the plane of e orbit)

2. extrimely high brightness ( 10 brighter than the most powerful laboratory source)

−E

∼

Monochromatization of Synchrotron Radiation

focusing mirror

bending magnet

focusing mirror

plane gratingmonochromator (PGM)

exit slit

e −

Storage Ring

1 10 100 1000 100001E10

1E11

1E12

1E13

BESSY II

Phot

on F

lux

( s-1

)

Photon Energy (eV)

Ee = 1.7 GeV

1 10 100 1000 100001E10

1E11

1E12

1E13

ΔE ∼ 0.05 eV

Phot

on F

lux

( s-1

)

Photon Energy (eV)

BESSY IIEe = 1.7 GeV

high vacuumanalytical chamber

sample410R E E= Δ ∼

Energy resolution is determined by design and exit

PGMslit

wi dth

R

Typical Parameters of Third Generation Synchrotrons

Facility ALS BESSY II ESRF SPring-8

Country USA Germany France Japan

Electron energy 1.90 GeV 1.70 GeV 6.04 GeV 8.00 GeVCurrent (mA) 400 200 300 100Circumference (m) 197 240 884 1440RF frequency (MHz) 500 500 352 509Pulse duration (FWHM) (ps) 35-70 20-50 70 120

Bending magnet field (T) 1.27 1.30 0.806 0.679Critical photon energy (keV) 3.05 2.50 19.6 28.9Bending magnet sources 24 32 32 23

The Table taken from prof. D. Attwood lecture " Intro to Synchrotron Radiation" EE290F, 16 Jan 2007. Berkeley. USA.

Recording of the XAS in the Reflection Mode

o

o o

esin 1 e abs

xI ID I I I I

μ

μ θ μ

−

⇒ − ∝ ⋅=

=

θ

e

electronescape

depth D photon penetration depth sinθ μ

o ( )I ωe−

pA

electron analyzer

ω′

photon detectorY ( )f ω

Y ( , )e eEω

totY ( )ω

( ) Y ( ) Y ( )

Y ( ) fluorecence yeild (FY) Y ( ) electron yeild (EY)

1 ( ) if Z 16 Y ( ) Y ( )

eabs f

f

e

e f

ef

I

D D

ω ω ω

ωω

μ ωω ω

∝ ∝

−−

′≤

∼

totY ( ) Y ( , 0 )e eE eω ω ω ϕ= ≤ ≤ −

TEY - Total YieldTFY - Total

ElectronFluorecence Yield

Peculiarities of Different Electron Yield Techniques

se

pe

ae

secondary, photo and auger electrons., ,se pe ae −

Y Y Y Y Y Ytot se ae pe ae pe= + + +

Choice of recording modede

XASits informatiter on mine ds epth

o

o o

o

o

o

o

1. TEY: ( ) Y ( ) D 50 A

2. PEY: ( ) Y ( ) 10 A D 50 A

3. AEY: ( ) Y ( ) D 10 A

tot

part

ae

e

e

e

I

I

I

μ ω ω

μ ω ω

μ ω ω

∝ →

∝ → ≤ ≤

∝ → ∼

e escape depth D XAS information depthe =−

TEY - Surface Bulk TFY - Bulk

+

Normalization and Background Correction of the XAS

Y ( , X)( ) const ( ,X) Y ( , Au)

eo

eI ωω μ ω

ω≠ =

0 400 800 1200 16000.00

0.04

0.08

0.12

Abs

orpt

ion

Coe

ffic

ient

(nm

)

Photon Energy (eV)

CK-edgeOK-edge TÅ

Y (

arb.

un)

Au

BESSY II, Russian-German Beam Line

( , Au) T( ) Y ( , Au)

( , Au) T( )Y ( , Au)

e

e

μ ω ω ω

μ ωωω

= ⋅

=

Measured electron yeild must be corrected for beam line transmission function

Y ( ) T( )

e ωω

for CK-edge NEXAFS ( , Au) constμ ω

Normalization and Background Correction of the XAS

pApA

o ( )I ω

clean reference grid mon

Auitor

clean reference sa

Au mple

refsampY ( )ωref

gridY ( )ω

refgridY ( ) accounts for photon flux instabilitiesω −

refsampY ( ) more simple and controllable ω −

BESSY II, Russian-German Beam Line (RGBL)

280 290 300 310 320

x3

Normalized C60 TEY

C60

TEY

(ar

b.un

.)Photon Energy (eV)

Au reference sample

60Normalization TEY of C film using clean Au reference sample

Normalization requires reference monitor

direct comparison with properly normalized

Simplified

reference sp

e

Way

ctra

decomposition into set of steps and peaks, theoretical modeling,

Complica

etc

t

.

ed

..

Way

[*]

Analysis and Interpretation of NEXAFS Spectra

The figure reproduced from J. Diaz, S. Anders,X. Zhou et al. Phys. Rev. B , 125204 (2001). 64

285 290 295 300 305 310

HOPG

SWNT SWNT+H2

C-H

*

CK-edge XASσ*π*

A

bsor

ptio

n co

effic

ient

(arb

.un.

)

E (eV)

( )( )

2* SWNT H0.72 0.07

* SWNTπ

π+

= ±

SWNT hydrogenation.

[* ] For details see references [1- 4] from Main Sources.

IV. The information that can be obtained byNEXAS/EXAFS Spectroscopy.

Some Nanocarbons Related Examples

NEXAFS of Fullerites and Fullerides

60 60XAS of C and C films [*] 3 60XAS of crystalline K C [**]

3 60

3 60

half-filled LUMO (a ) in K C . large general shift ( 0.35 eV)

of

1.

K C LU

2

.

MOs

′∼

60 70

narrow * and * resonaces show that solid

are the molecul C andar cry s

Ctals

π σ

[*] L.J. Termenello et al. Chem. Phys. Letters, , 491 (1991). 182 [**] T. Kaambre et al. Phys. Rev. B , e195432 (2007). 75

Experimental and Theoretical study NEXAFS of C60F36 [*]

[*] L.G. Bulusheva, A.V. Okotrub, V.V. Shnitov, V. V. Bryzgalov et al. J. Chem. Phys. , 014704 (2009). 130

60 36The structure of C F isomers

T -sym m etry (65% )

1C -symmetry (30%)

3C -symmetry (5%)

1 30.65T 0.3C 0.05C+ +

60 36C F isomers

bare carbon atoms

fluorenatedcarbon atoms

NEXAFS of fluorinated MWCNT [*]

[*] M. M. Brzhezinskaya et al. Phys. Rev. B 155439 (2009) . 79,

Fluorination dramaticallychanges MWNT CK-edge, but does not affect thei

r FK-edge

2 3

*- resonancesFluorination "kills" sp sp

π↓→

Study of metallicity-sorted SWCNT [*]

XAS of metallic (M) andsemiconducting (S) SWCNTs

High-resolution XAS C1s absorption edges togetherwith the results of a line shape analysis (thin lines) and TB DOS broadened by the experimental resolution.

[*] P. Ayala et al. Phys. Rev. B 205427 (2009).80,

Semiconducting SWNTsMetallic SWNTs

MS

CK-edge NEXAFS of Few Layer Graphene (FGL) [*]

makes possible to distinguish between graphenes with different number o

f la

NE

ye

XAFS

rs

[*] D. Pacile et al., Phys. Rev. Lett. 066806 (2008) . 101,

*π

*σ

*π

FLG

NEXAFS study of FLG Grown on 6H-SiC(0001) [*]

CK-edge NEXAFS spectra measured at different incident angles

[*]. Ki-jeong Kim. J. Phys.: Condens. Matter 20, 225017 (2008).

o1st annealing at T= 900 C (for substrate outgasing).

o 3rd annealing at T=1180 C (growth of single phase graphene layers )

o 2nd annealing at T=1080 C (formation of mixed phase (buffer) layer)

o 4th annealing at T=1400 C (formation of thick graphene layer )

EXAFS study of I-doped SWNTs [*]

[*] T. Michel et al. Phys. Rev. B 195419 (2006). 73,

EXAFS experiment at the ESRF (France)

o

Measurements made: in the transmission mode at the edge ( ) at low tem

iodine E =33.169 keVperature T=10( K)

K -

TABLE 1. Structural parameters deduced from the least square fit of the first shells of the I-doped SWNTs samples

FEFF calculation

V. CONCLUSIONS

1. Modern NEXAFS spectroscopy proved to be one of the most powerful experimental techniques widely used for investigation of nanocarbon materials. It makes possible to probe not only their local electronic structure, but also a chemical composition and even atomic structure.

2. Application of EXAFS spectroscopy in this area of research is much more restricted. As a rule, this technique is used for probing a local atomic structure of composite materials, which along with the carbon atoms contain also the atoms of higher Z elements (such Fe, Ru, I) characterizing by much higher values of absorption edge energy and backscattering amplitude.

VI. MAIN SOURCES:

1. J. Stöhr. NEXAFS spectroscopy. Springer, 1996.

2. M. Newville. Fundamentals of XAFS. University of Chicago, 2004.

3. J. J. Rehr, R. C. Albers. Theoretical approaches to x-ray absorption fine structure.Reviews of Modern Physics, 72, 621 (2000).

4. X-ray Absorption: Principles, Applications, Techniques of EXAFS,SEXAFS, and XANES, in Chemical Analysis, D. C. Koningsberger andR. Prins, ed., John. Wiley & Sons, 1988.

5. F.W. Lytle. The EXAFS family tree: a personal history of the developmentof extended X-ray absorption fine structure. J. Synchrotron Rad. 6, 123 (1999).

Interior view of Synchrotron BESSY II

Experimental Station of Russian-German Beam Line