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Information content EXAFS, SEXAFS Bond
lengths. Especially useful because these
technique probe the local order. While
diffraction methods require crystallinity,
EXAFS/SEXAFS can be applied to amorphous
materials. EXAFS typically measures the
absorption of X-rays or possibly X-ray
fluorescence. SEXAFS uses the Auger electrons
emitted, and therefore is surface-sensitive
because of the short escape depth. A second
useful features of EXAFS/SEXAFS is that one can
tune to a specific absorption edge of a material
of interest. So, for studying various dopants
(for example) that might be present in fairly low
concentrations, it is still possible to study
them by tuning to an absorption edge of the atom
of interest. NEXAFS (XANES) focuses on the
near-edge structure, which is very sensitive to
the valence-band hybridization. It is difficult
to interpret quantitatively, but is good for
looking at the local bonding around atoms,
especially for non-crystalline materials.
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NEXAFS
XANES Spectra are very sensitive to oxidation
state (like XPS) and also to local coordination
environment Interpretation of XANES spectra is
quite difficult due to breakdown of EXAFS
equation at small k and the increase in electron
mean-free path at low energy
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Why are X-ray absorption peaks asymmetric ??
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Free electron
Density of states This is the number of allowed
k states per unit interval of energy
X-ray absorption peaks are asymmetric because the
final state electron can have a large number of
different kinetic energies. There are many final
states that have kinetic energy near zero, but
only a few states at high energy.
E here refers to the kinetic energy of the
electron so the absorption coefficient has a
dependence like (1/sqrt(E-E0)) where E0 is the
absorption edge.
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XANES NEXAFS Looks at oscillations within
300 eV of edge
EXAFS Looks at oscillations more than 300 eV
of edge
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Incident wave
Incident wave
1
2
2
a
Scattered wave
Scattered by atom 1 and atom 2
Phase shift kad1
Phase shift 2ka2d1d2
Phase shift due to scattering at atom 1,
reflection back from atom 2, and then back
to atom 1 is 2ka2d1d2
Sum of incident planewave scattered wave
1expi(2ka2d1d2)
Total absorption intensity EE
1sin(2ka2d1d2)
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EXAFS Equation
Scattering intensity of the jth atom
disorder term (decreases intensity of
oscillations)
Electron scattering (linelastic mean free path)
Number of atoms j
Interference factor
Sum over atoms
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Scattering probability and phase shift depend on k
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This is just a re-plotting of the graph we looked
at earlier for the inelastic mean free path vs.
energy, now plotted as mean-free path vs.
wavevector !
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Pre-edge subtraction and normalization
Post-edge subtraction and normalization mo(E)
convert from X(E) to X(k), weight by k2
Fourier Transform of X(k) gives The radial
distribution function essentially a probability
map for various bond lengths. Here, we see that
the atom of interest has nearest neighbors at
distancesof !1.5 and 2.7 Angstroms weaker peaks
a longer distances are other atoms farther away
Real
Imaginary
EXAFS gives bond distances even for
non-crystalline /amorphous materials
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XANES Look very close to the absorption edge.
Here, bonding and hybridization strongly affect
the detailed shape. Difficult to analyze
quantiatively, but can get some very useful
information. Often necessary to run reference
compounds for comparison
K-edge XANES
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NEXAFS
XANES Spectra are very sensitive to oxidation
state (like XPS) and also to local coordination
environment Interpretation of XANES spectra is
quite difficult due to breakdown of EXAFS
equation at small k and the increase in electron
mean-free path at low energy
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Information content EXAFS, SEXAFS Bond
lengths. Especially useful because these
technique probe the local order. While
diffraction methods require crystallinity,
EXAFS/SEXAFS can be applied to amorphous
materials. EXAFS typically measures the
absorption of X-rays or possibly X-ray
fluorescence. SEXAFS uses the Auger electrons
emitted, and therefore is surface-sensitive
because of the short escape depth. A second
useful features of EXAFS/SEXAFS is that one can
tune to a specific absorption edge of a material
of interest. So, for studying various dopants
(for example) that might be present in fairly low
concentrations, it is still possible to study
them by tuning to an absorption edge of the atom
of interest. NEXAFS (XANES) focuses on the
near-edge structure, which is very sensitive to
the valence-band hybridization. It is difficult
to interpret quantitatively, but is good for
looking at the local bonding around atoms,
especially for non-crystalline materials.
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COORDINATION CHEMISTRY Regular, distorted
octahedral, tetrahedral coordination MOLECULAR
ORBITALS p-d orbital hybridization crystal field
theoryBAND STRUCTURE The density of available
electronic statesMULTIPLE SCATTERING Multiple
bounces of the photoelectron
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Books and Review Articles X-ray Absorption
Principles, Applications, Techniques of EXAFS,
SEXAFS, and XANES in Chemical Analysis vol. 92
edited by D.C. Koningsberger and R.Prins, John
Wiley Sons, 1988 Basic Principles and
Applications of EXAFS, Chapter 10 of Handbook of
Synchrotron Radiation, pp 995--1014. E. A. Stern
and S. M. Heald, edited by E. E. Koch,
North-Holland, 1983. Elements of Modern X-ray
Analysis, Jens Als-Nielsen, Des McMorrow. John
Wiley Sons, 2001. This is an excellent book
covers many aspects of x-ray and synchrotron
science, includ ing a brief section on x-ray
absorption, EXAFS, and dichroism. Theoretical
approaches ot x-ray absorption fine structure, J.
J. Rehr and R. C. Albers, Reviews of Modern
Physics Vol 72, pp. 621-892 (2000). Analysis of
Soils and Minerals Using X-ray Absorption
Spectroscopy Kelly, S.D., Hesterberg, D., and
Ravel, B., in Methods of Soil Analysis, Part 5
-Mineralogical Methods, (A.L. Ulery and L.R.
Drees, Eds.) p. 367. Soil Science Society of
America, Madison, WI, USA, 2008.
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