Korrelationsfunktionen in Flüssigkeiten oder Gasen · Korrelationsfunktionen in Flüssigkeiten...

Korrelationsfunktionen in Flüssigkeiten oder GasenKorrelationsfunktionen in Flüssigkeiten oder Gasen

L. Van Hove, Phys. Rev. 95, 249 (1954)

mittlere Dichte

Relaxationszeit T0

Inelastische und quasielastische StreuungInelastische und quasielastische Streuung

M. Bée, Chem. Phys. 292, 121 (2003)

Energie- und Impulsüberträge von Neutronenspektrometern

Energie- und Impulsüberträge von Neutronenspektrometern

M. Bée, Chem. Phys. 292, 121 (2003)

Flugzeitspektroskopie(time-of-flight)

Rückstreu-spektrometer(backscattering)

Neutronen-Spin-Echo-Spektrometer

Struktur von KaliumamidStruktur von Kaliumamid

monoklinkubisch

M. Müller, Dissertation (Kiel 1996)

M. Müller, Dissertation (Kiel 1996)

Quasielastische Streuung: KaliumamidQuasielastische Streuung: Kaliumamid

monoklin

M. Müller, Dissertation (Kiel 1996)

Quasielastische Streuung: KaliumamidQuasielastische Streuung: Kaliumamid

monoklin

kubisch

Neutronen-FlugzeitspektrometerNeutronen-Flugzeitspektrometer

IN6 (ILL)

X-ray absorption spectroscopyin materials science

X-ray absorption spectroscopyin materials science

Martin MüllerInstitut für Experimentelle und Angewandte Physik

der Christian-Albrechts-Universität zu Kiel

• Photoelectric absorption

• XANES

• EXAFS

• Instrumentation

• Examples

Uses of X-ray spectroscopyUses of X-ray spectroscopy

• element-specific• diluted or concentrated systems can be studied• study of disordered systems possible• wide temperature and pressure range

XAFS: X-ray absorption fine structure

local technique:

Photoelectricabsorption

Photoelectricabsorption

(a) ionisation energy of inner shell smaller than

X-ray energy⇓

photoemissionof core electron

(b,c) two possiblesecondary processes

to fill the hole

zeIIT μ−==0

aAm

AN σρμ ⎟

⎠⎞

⎜⎝⎛=

Transmission and absorption cross sectionTransmission and absorption cross section

transmitted intensity decays exponentially with thickness:

absorptioncoefficient

absorptioncross-section

Avogadro‘s numberatomic mass number

mass density

3−∝ Eaσ

4Za ∝σ

Absorption edgesAbsorption edgesgeneral behaviourof cross-section:

sudden increase in absorbance at ionisation energyof core electron= absorption edge

Absorption edgesAbsorption edges

electronstates

nomenclatureof edges

Fine structure of absorption edgesFine structure of absorption edges

example: krypton

K edge

2D crystalgas

X-ray Absorption Near-Edge Structure

Extended X-ray Absorption Fine Structure

≈ 40 eV

XAFS

**

*

RgDsMtHsBhSgDbRfLrRaFr

RnAtPoBiPbTlHgAuPtIrOsReWTaHfLuBaCs

XeITeSbSnInCdAgPdRhRuTcMoNbZrYSrRb

KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK

ArClSPSiAlMgNa

NeFONCBBeLi

HeH

**

*

NoMdFmEsCfBkCmAmPuNpUPaThAc

YbTmErHoDyTbGdEuSmPmNdPrCeLa

XANES only

EXAFS difficult

K-edge EXAFS

L3/K-edge EXAFS

L3-edge EXAFS

XAFS accessible elementsXAFS accessible elements

X-ray absorption spectroscopyin materials science

X-ray absorption spectroscopyin materials science

• Photoelectric absorption

• XANES

• EXAFS

• Instrumentation

• Examples

Mn compound: shift of edge position

Energy shift of edge positionEnergy shift of edge position

energy to eject core electron depends on charge it experiences:edge energy depends on oxidation state

electron might also beexcited into

bound states

Pre-edge peaksPre-edge peaks

Pre-edge peaksPre-edge peaks

9.03 8.95

← Energy (keV)

K Edge ~1.38Å1s→4p

Abso

rptio

n

1s→4s

1s→3d

CuCl2 . 2H2O

CuCl

E (eV)

depend on geometry:• oxidation state• site symmetry• surrounding ligands• nature of bonding

XANES white linesXANES white lines

E (eV)

in transition metals:area of white lineindicates number of empty d-states

XANES fingerprintingXANES fingerprinting

XANES characteristic of chemical environment and valence state:• fingerprinting• phase analysis by linear combination of known species

unknownS spectrum

known references(oxidation numbers

0, 2, 4, 6)

high sensitivityto electronic states!

X-ray absorption spectroscopyin materials science

X-ray absorption spectroscopyin materials science

• Photoelectric absorption

• XANES

• EXAFS

• Instrumentation

• Examples

Principle of EXAFS oscillations

Principle of EXAFS oscillations

AnimationAnimation

Interference of wavefunctionsof photoelectron and of backscattered electrons(from neighbouring atoms)

Parameters accessible with EXAFSParameters accessible with EXAFS

• type of atoms surrounding central absorber (Z ± 3)• number of atoms surrounding absorber (± 20%)• distances absorber – scatterer (accuracy 0.1 Å)

EXAFS data analysisEXAFS data analysis

)()()(

))((0

0

EEE

Eqμ

μμχ χ −

=

KEmq ωhh

−=2

22

EXAFS signal: isolated atom

in material of interest

electron wave vector

Fourier transform:radial distribution function

one shell

CdTe nanocrystals

The EXAFS formula …The EXAFS formula …

many shells

CdTe bulk

• sum over j neighbouring shells• goal: extract radii Rj and

occupation numbers Nj• damping due to loss (mean free

path Λ) and disorder (Debye-Wallerfactor)

• phase shifts• backscattering amplitude

difficult…

X-ray absorption spectroscopyin materials science

X-ray absorption spectroscopyin materials science

• Photoelectric absorption

• XANES

• EXAFS

• Instrumentation

• Examples

Absorption spectrometerAbsorption spectrometer

IC: ionisation chamber

fixed-exit double crystal monochromator

(fast scanning withpiezos: QEXAFS)

θ

θ

scanning

EXAFS / XANES in one shot: DEXAFSEXAFS / XANES in one shot: DEXAFS

polychromator:bent Si(111) crystal

energy dispersiontranslated into positiondependence on detector

„white“synchrotronradiation

energy-dispersive

Bent crystal polychromator @ ID24 (ESRF)Bent crystal polychromator @ ID24 (ESRF)

Alternatives to transmission

measurements

Alternatives to transmission

measurements

fluorescence(high sensitivity)

Auger yield(if fluorescence

yield low)

X-ray absorption spectroscopyin materials science

X-ray absorption spectroscopyin materials science

• Photoelectric absorption

• XANES

• EXAFS

• Instrumentation

• Examples

Homogeneous catalytic reaction mechanismsHomogeneous catalytic reaction mechanisms

ESRF Highlights 2004

Cu(II) catalyst (arylation)

• XANES time resolution: 10-200 ms• combination with UV-vis spectroscopy

XANES

UV-vis

Adsorbate-induced phase change in Rh catalystsAdsorbate-induced phase change in Rh catalysts

ESRF Highlights 2002

car exhaust catalytic converters:NO converted to N2

Rh nanoparticles rapidlychange upon exposure to NO

Rh metal

Rh2O3 oxide

time-resolved EXAFS study

Synchronizing IR spectroscopy and XAFS Synchronizing IR spectroscopy and XAFS

ESRF Highlights 2006

sub-second EXAFS and IR time resolution

again de-NOx Rh catalyst: many different components

IR EXAFS

Rh(NO)2

NO- (bent)

NO on metal

NO+ (linear)

Rh metal

Rh2O3oxide