Xray absorption structure XAS:

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X-ray absorption structure (XAS) Theory and
applications
K. Rickers-Appel
HASYLAB _at_ DESY, Notkestrasse 85, 22603 Hamburg,
Germany karen.rickers_at_desy.de
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Outline
Introduction basic principle of XAFS and
XANES and a glimpse on data evaluation Experimen
tal set-up and sample preparation Monochromator
Experiment Transmission XAFS experiment
Special XAFS experiments fluorescence
XAFS quick-XAFS Applications in Earth
Sciences minerals melts fluids Outlook
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XAFS Basics
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What do we measure in XAFS Spectroscopy?
In principle the measured quantity is the
absorption coefficient µ cm-1 The intensity I1
of a beam with an initial intensity I0 after
passing through a sample with thickness d is I1
(E) I0 (E) e-µ(E)d (Beer-Lambert law)
d
gt µ(e)d -ln(I1 (E) /I0 (E))
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Origin of the attenuation of the beam in a sample
Interactions of X-rays with matter

• Scattering elastic and inelastic (Rayleigh,
  Compton, Thompson)
• Absorption / photoelectric effect

What is absorption?
A photon is absorbed when its energy is consumed
by an excitation of an electron. For that, its
energy must be greater than the binding energy of
the electron.
X-rays needed for K-shell excitation
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Transitions responsible for the attenuation of
X-rays
from Adler (1967)
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energy dependence of photoelectric mass
attenuation coefficients
µ for a given element depends strongly on X-ray
photon energy and shows additional sharp
absorption edges
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XAFS XANES EXAFS
EXAFS
XANES
XANES X-Ray absorption Near Edge Structure, ends
50-100 eV above the edge EXAFS Extended X-Ray
Absorption Fine Structure, starts 50 - 100 eV
above the edge
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The origin of the oscillatory part - Fermis
golden rule
- A transition of an electron between the ground
state and an excited state can only happen if an
exited state is available - Within the dipole
approximation the transition probability (W) can
be described by Fermis golden rule, it describes
W as a function of the initial and the final state
with ?final final state ?initial initial
state H Hamilton operator
Courtsey E. Welter
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The origin of the modulations of the excited state
Interference shown for two distances D1 and D2
with D1 lt D2
Courtsey E. Welter
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XANES / EXAFS - differences
EXAFS is caused by single scattering (that is
only half the truth!) XANES is caused by
electronic transitions and multiple
scattering Note the different concepts
Scattering paths versus co-ordination spheres
Courtsey E. Welter
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XAFS Data Evaluation
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Data evaluation Background subtraction of
measured x?(E)
Raw data
Removal of pre-edge and post-edge background
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Data evaluation edge normalisation
µ (E)
Dµ0
Normalised XAFS spectrum of pressed powder tablet
of anatas
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Data evaluation extraction of the EXAFS
modulation c(E) transformation to k-space Å-1
with me mass of electronE and E0 in J
k² weighed c(k) of an pressed tablet of anatas
powder
Photo Electron Wavenumber Å-1
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Data evaluation Fourier transformation of ?(k)
first shell second shell third shell
Radial distribution function
Single shell filtering with inverse Fourier
Transformation
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Create an EXAFS theory
Important factors Distance r (influences
frequency) Nature of neighbour (scattering
amplitude, phase shift) Number of neighbours
(influences amplitude)
Interference shown for two distances r1 and r2
with r1 lt r2
Courtsey E. Welter
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Data evaluation Fourier transformation gives
EXAFS contribution from selected region e.g.
single shell
EXAFS amplitude to coordination number
EXAFS means square displacement
dampens oscillations exponentially
Longer bond distances result in a shorter
periodicity of their EXAFS oscillations
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Final result of XAFS data evaluation
Anatas TiO2
3.03
3.03
1.96
1.93
1.93
1.93
1.93
1.96
3.03
3.03
3.785
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Experimental Set-up
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• The standard XAFS transmission experiment
• - Monochromatic X-rays (DE / E 10-4)
• The X-ray photon energy must be changeable over
  1000 - 2000 eV
• Position of incident beam on sample should be
  unchanged during energy scans
• - Detectors with a large linear working range
• - Large number of photons (EXAFS oscillations are
  small, 10-3 - 10-2 effect) gt 106 photons/sec
  for statistical noise lt 10-3
• gt Synchrotron radiation necessary
• Bending magnet delivers 108 photons/(sec x mm² x
  10-4 BW)
• gt flux from bending magnets is sufficient for
  normal transmission XAFS
• - Homogenous samples, concentrations of more than
  1 wt for element of interest

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Working principle of a Monochromator
Bragg equation nl2d sinq with ? wavelength,
d lattice spacing? angle between beam an
crystal plane
lattice planes
white beam
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monochromator concept
movements of crystals during energy changes
Fixed exit design

5 tilt
55.4 tilt

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Example of fixed-exit double crystal monochromator

• Parameters
• Si(111) and Si(311) crystal sets,
• interchangeable by every user by
• translation of vacuum chamber
• - common central rotation
• - ex-vacuo goniometer (Huber 420)
• first crystal translates vertically
• second crystal translates tangentially
• Bragg angle 5 to 55.5
• - energy range 2.4 - 22.6 keV, Si(111)
• 4.6 - 43.4 keV, Si(311)
• angle encoding by incremental optical
• encoder in-vacuo (Renishaw)
• - vacuum lt 10-7 mbar

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Monochromator
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Integration of monochromator into beamline
optics hutch
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XAFS experimental hutch
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Standard XAFS set-up
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An XAFS measurement
Count time 1 - 10 sec / point gt Some minutes to
hours per spectrum
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A transmission measurement at HASYLAB beamline C
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XAFS Sample preparation
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sample preparation transmission samples thickness
I1 I0 e-?µx (Beer-Lambert law)

• ?m mass absorption coefficient
• ? absorption
• density
• x sample thickness

I0
( )
??? ??mx ln
I1
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sample preparation transmission samples
homogeneity
pinholes
Most serious for thick samples (? gt 3-4)
The signal is transported with low
intensity Pinholes add a lot of intensity without
signal
Inhomogeneity in particle size
Some parts off the beam cant pass (thick spots),
some parts see a thin sample and some a thick and
even worth when there are additionally pinholes.
Achieved is only an overall absorption coefficent
but the EXAFS signal is strongly damped!
Homogeneity and ideal thickness are crucial to
achieve good data quality!