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.
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
Why are X-ray absorption peaks asymmetric ??
 2k 2
E
2m
Free electron
dE  2 k

dk
m
dk
1
m

 2
dE
dE
k
dk
Density of states: This is the number of
allowed “k” states per unit interval of
energy
dk
1
m


dE dE
2m E
dk
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.
XANES = NEXAFS: Looks at oscillations within ~300 eV of edge
EXAFS: Looks at oscillations more than ~300 eV of edge
Incident wave
1
Incident wave
2
2
a
Scattered wave
Scattered by
Phase shift = ka+d1
atom 1 and atom 2
Phase shift = 2ka+2d1+d2
Phase shift due to scattering at atom 1, reflection back from atom 2, and then back to
atom 1 is 2ka+2d1+d2
Sum of incident planewave + scattered wave = 1+expi(2ka+2d1+d2)
Total absorption intensity ~ E*E ~ 1+sin(2ka+2d1+d2)
“EXAFS Equation”
Scattering intensity
of the jth atom
Number of
atoms j
 (k )  
“disorder” term
(decreases intensity of
oscillations)
2 k 2 2
N j f j (k ) exp
Sum over atoms
kR j
2
Electron scattering
=inelastic mean free path)
2 R j /  ( k )
exp
sin 2kR j + d j (k ) 
Interference factor
Scattering probability and phase shift depend on k
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 !
Pre-edge subtraction
and normalization
Post-edge subtraction
and normalization mo(E)
Real
Imaginary
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
EXAFS gives bond distances even for non-crystalline /amorphous materials
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
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
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.
COORDINATION CHEMISTRY:
Regular, distorted octahedral,
tetrahedral coordination
MOLECULAR ORBITALS: p-d
orbital hybridization crystal field
theory
BAND STRUCTURE; The density
of available electronic states
MULTIPLE SCATTERING: Multiple
bounces of the photoelectron
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.