X-ray Absorption Spectroscopyphome.postech.ac.kr/user/atl/note/Chapter5-3.pdf · X-ray & AT...

X-ray Absorption Spectroscopy

Yang Mo KooProfessor of GIFT

POSTECH

2007, Fall semester

• Overview of XAFS Spectroscopy• X-ray Absorption Process• XAFS Experiment • Analysis of EXAFS Data• Special Techniques of EXAFS Experiment• Theory of XANES• Examples of XANES Experiment

X-ray & AT Laboratory, GIFT, POSTECH

• X-ray absorption fine structure includes extended x-ray absorption fine structure (EXAFS) and x-ray absorption near edge structure (XANES).

• EXAFS spectroscopy uses the x-ray photoelectric effect and wave nature of the electron determine local structures around selected atomic species in materials: Unlike x-ray diffraction, it does not require long range transitional order. It works equally well in amorphous materials, liquids, crystalline solids, and molecular gases.

• XANES can provide information about site symmetry, bond lengths, and orbital occupancy.

Overview of XAFS Spectroscopy


( )xEII )(exp0

μ−=

The x-ray absorption coefficient is the central quantity of interest.Example: Iodine



XAFS spectroscopy is element selective experiment by choosing the energy of excitation, you can “tune into” different elements in a complex sample:K-edge; Ca (4.0keV), Fe (7.1keV), Zn (9.7keV), Mo (20keV) etc.



• Precise local structural information (distances, numbers of atoms, types, disorder) in crystalline or noncrystalline systems e.g. metalloprotein active sites, liquids, amorphous materials

• All atoms of selected type are visible-ther are no spectroscopically silent atoms for XAFS

• Information on charge state, orbital occupancy may be available by studying XANES depending on system edge

• in situ experiments, under conditions similar to natural state, as well as crystals.

• XFAS probes effects of arbitrary experimental conditions on sample (high pressure, low temperature, pH, redox state, pump-probe, T-jump, p-jump…)

• Oriented samples provide more angular information

XAFS Spectroscopy Provides



X-ray Absorption Process

( )2

*

2*

))i(

∫

∫⋅⋅+⋅≈

⋅∝ ⋅

rr(krεrε

rrε rk

d

de

if

ii

f

ψψ

ψψμ

))

) Dipole and quadrupole terms

Fermi’s “Golden Rule” (Dirac)

Matrix element projects out the part of the final state that is of right symmetry (e.g. p-symmetry for K-edge & dipole selection rules)

• K-edge: 1s initial state (n=1, l=0, m=0)• L1-edge: 2s initial state (n=2, l=0, m=0)• L2-edge: 2p (j=1/2) initial state (n=2, l=1)• L3-edge: 2p (j=3/2) initial state (n=2, l=1)• dipole selection rules project out specific symmetry components of final state wave

function- K, L1 edges probe p part of final states- L2,3 edges probe d (&s) part of final states


Spectral Lines: Selection Rules, Intensities, Transition Probabilities, Values, and Line Strengths



Following the excitation of a core level electron several ways of relaxation are possible (a). Thereby secondary electrons are generated which undergo multiple scattering processes before they leave the crystal structure as low-energy photo-electrons (b).


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Electron wave emitted by central atom is scattered by neighboring atoms. The out going and scattered parts of the final state wave function interfere where the initial state is localized. Interference is constructive or destructive depending on the distances and electron wave length. This information is encoded in the χ function:

( )

)E()E()E()E(

)E()E()E(

0

0

0 1

μμμχ

χμμ

−=

+=

and



• Isolated atom has no final state wave function interferences; Absorption coefficient varies smoothly with electron wavelength

• Scattering from neighboring atoms modifies wave function near center of absorber

XAFS determines the statistical properties of the distribution of atoms relative to the central absorbers. For analysis of χ function, in the case of single scattering the pair correlation function is probed and multiple scattering gives information on the higher order correlations.



EXAFS equation (χ- function )

EXAFS is basically a sum of damped sine waves → Fourier Transform, beat analysis





XAFS Experiment

• Double monochromator: monochromatic (~ 1eV band width), scannable beam, energy suitable for elements of interest.

• Detection: Transmission mode, Fluorescence mode, or Electron yield• Geometry: Total external reflection, Grazing incidence, or magic angle spinning




Which mode to use?• concentrated, not thick: use transmission• concentrated, thick: use electron yield, total external reflection

fluorescence, or apply fluorescence corrections numerically• dilute samples: use fluorescence detection• microbeams can used to measure small grains which may be

concentrated even if sample is dilute on average

In order to get good data:• Get rid of harmonics from x-ray source. • Alignment of x-ray beam path• Linearity of detector• Adjust the offset of detector

XAFS Experiment


Modern codes for calculating theoretical XAFS spectra are accurate enough to use to fi experimental data directly. “FEFF” is a leading program for calculating spectra.

FEFF does not analyze the data for you however. Add on the programs of various kinds use FEFF-calculated spectra to fit the data by perturbing from a guess structure.

Calculation of vibrations and some multi-electron excitations is an active research area recently.

Analysis of EXAFS Data


Apply instrumental corrections (e.g. detector dead time)Normalize data to unit edge step (compensates for sample concentration/thickness)Convert from E→k space (makes oscillations more uniform spatialfrequency for Fourier transform)Substrct background with cubic splines or other methodsWeight data with , (compensates for amplitude decay)Fourier transform to distinguish shells at different distancesFourier Filter to isolate shells (optional)Fit data in k-space or r-space using single or multiple scattering theory and theoretical calculations (e.g. feff8)Good open-source software is available e.g. feff6 (Rehr), ifeffit (Newville), Artemis/Athena (Ravel/Newville), SixPack (Webb),

EXAFSPAK (George), GNXAS (Di Cicco), etc.

3n1 , <<nk

Conventional Data Analysis



Raw XAFS data

→ normalize, convert to k space, subtract spline background



3k weight EXAFS



Fourier Transform



Fourier Filtered First Shell

Determine single shell’s amplitude and phase from real imaginary part of inverse Fourier Transforms



Single Scattering (SS) Fitting• If single scattering is good approximation, and shells are well isolated, you can fit shell by shell

• Complications still occur because of large disorder, accidental cancellations, and high fitting parameter correlations

Multiple Scattering (MS) Fitting• MS cannot be neglected (e.g. focusing effect)• MS fitting introduces a host of complications but also potential advantages

- SS contains no information about bond angles- MS does contain bond angle information (3-body and high

correlations)



Polarized EXAFS

( )2

∫ ⋅⋅+⋅≈ rr(krεrε d)) i*f ψψμ )) i(

{ }∑

+= −−

j j

jj)k(/rkj

*j kr

)k(krsinee)k(F)k(SN)k( jjj

20222 222 φ

χ λσ

ε̂

Directional structure can be obtained for which the polarized XAFS technique isapplied. Absorption coefficient is determined by final state of wave function whichIs also affected the polarization direction of the electric field .

Then the EXAFS function becomes

α2cosN N j*j = where the number of effective neighboring atoms, α is the angle

between the electric vector and the direction of the neighboring atoms from absorber atom.

Special Techniques of EXAFS Experiment


Polarized EXAFS

Co/Pd Multi-layer (111)

Co Kedge absorber

[ ][ ] [ ]inPdCoCoCo

outPdCoCoCo

parallelCo

outPdCoCoCo

perpenCo

)k()k()k()k()k(

)k()k()k(

−−−−

−−

+++=

+=

χχχχχ

χχχ



Polarized EXAFS



Theory of XANES

It has long been known that x-ray edge spectra are related to the structure around the absorbing atom. XAS was actively studied for more than four decades with some clarity and some confusion, Around 1970 Sayers, Stern, and Lytle put together the key elements that explained EXAFS as a short range order theory and how it could be used for structure determination.In the 70’s near edge structure (XANES) was still a puzzle. Over the next few decades it became clear that the basic phenomena in EXAFS and XANES are the same, but some complication in the theory such as a large multiple scattering tend to be less propound in EXAFS than in XANES.Consolidation: XANES+EXAFS=XAFS


Key factors influencing XANES

Selection rules for discrete transitionsThe final state wave function:

- Molecular orbital- Scattering- Band structure

Core hole life time

Theory of XANES


Energy Levels v.s. bond length (R)

Theory of XANES


Polarization effect

Theory of XANES


Pre-edge Transitions

Theory of XANES


Interpretation of XANES can be very informative. Empirical correlations between structure and spectra often can be readily observed.Simple relationships exist between symmetry, bond length, edge position, and intensities, but qualitative analyses should be backed up by theoretical understanding. Care must be taken to avoid thickness and particle size effects or spectra will be distorted and conclusions will be wrongModern theoretical tools can be a treat resource for deciphering XANES spectra.

What can we know with XANES Experiment?

Theory of XANES


Examples of XANES Experiment

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