Transcript No Slide Title

XAFS: X-ray Absorption Fine-Structure
Matt Newville
Consortium for Advanced Radiation Sources
University of Chicago / Advanced Photon Source
Overview of XAFS and XANES
XAFS experiment design: transmission and fluorescence
Fe foil, FeO, Fe2O3, Fe in cytochrome-c
Data Analysis overview
Today:
Lecture (1 hour)
XAFS measurements at 20-BM in groups of 5
(~1 hour/group).
Data Analysis on example and measured data.
Tomorrow: XAFS measurements (if needed)
Data Analysis on example and measured data.
2001-Aug-15
X-ray Absorption Spectroscopy
X-ray Absorption Spectroscopy: Measure energy-dependence
of the x-ray absorption coefficient m [either log(I0 /I) or (If / I0 )]
for an atomic core-level electron of a selected element.
Transmission Measurements:
Measured x-ray beam intensities for I0 (left) and I (right)
2001-Aug-15
X-ray Absorption Fine Structure (XAFS)
We’re interested in the oscillations
in m(E):
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X-ray Absorption: Atomic View
An atom absorbs and x-ray of energy E, destroying a core electron with energy E0
and creating a photo-electron with energy (E-E0). The core level is refilled and a
fluorescence x-ray or an Auger electron is ejected from the atom.
absorption
requires
an available electronic
state for the photoelectron.
No available state:
No absorption by
that core level
For an isolated atom, m(E) is a smooth function of energy.
2001-Aug-15
X-ray Absorption Fine-Structure Spectroscopy
With another atom nearby, the photo-electron can scatter from the neighbor atom.
The interference of the outgoing and scattered waves alters the photo-electron
wave-function at the absorbing atom, modulating m(E).
The absorption probability
m(E) depends on the spatial
overlap of the core-level
and photo-electron wavefunctions. The core-level is
localized, so the overlap is
determined by the photoelectron wave-function at
the absorbing atom.
The
interference
of
outgoing and scattered
photo-electron gives the
oscillations in m(E)
2001-Aug-15
X-ray Absorption Spectroscopy: Why Bother?
X-ray Absorption Spectroscopy: Measure
energy-dependence of the x-ray absorption
coefficient m(E) [either log(I0 /I) or (If / I0 )]
of a core-level of a selected element
Element Specific: Elements with Z>20
can have EXAFS measured at the APS.
Valence Probe: XANES gives chemical
state and formal valence of selected
element.
Local Structure Probe: EXAFS gives
atomic species, distance, and number of
near-neighbor atoms around a selected
element..
Low Concentration: concentrations down
to 10 ppm for XANES, 100 ppm for EXAFS.
Natural Samples: samples can be in
solution, liquids, amorphous solids, soils,
aggregrates, plant roots, surfaces, etc.
Samples do not need to be crystalline.
XANES = X-ray Absorption Near-Edge Spectroscopy
EXAFS = Extended X-ray Absorption Fine-Structure
2001-Aug-15
The EXAFS Equation
EXAFS: the fine-structure oscillations in m(E)
where k is the photo-electron wavenumber:
The EXAFS results from an outgoing
photo-electron scattering from a neighbor
atom, and returning to the core atom to
interfere with the core level:
Outgoing photo-electron
Scattering from neighbor atom
(amplitude and phase depend on
Z of neighbor atom)
Returning photo-electron
2001-Aug-15
The EXAFS Equation
Photo-electron scattering
The EXAFS Equation for 1
atomic site (no disorder)
Averaging over all atoms in the sample, which has a distribution of distances
(including structural and thermal disorder) the EXAFS Equation becomes:
s2 = mean-square
disorder in R
This fairly simple equation allows us to model near-neighbor species - through
f(k) and d(k) – and distance R, and coordination number N .
2001-Aug-15
X-ray Absorption Measurements: Experimental Design
Important points to consider for measuring XAFS are:
Monochromatic x-rays: Need x-rays with a small energy
spread or bandwidth. ~1eV at 10keV
Linear Detectors: The XAFS c(k) is ~10-2 or smaller, so
we need a lot of photons (ie, a synchrotron) and detectors
that are very linear in x-ray intensity (ion chambers).
Well aligned Beam: The x-ray beam hitting the detectors
has to be the same hitting the sample.
Homogeneous sample: No pinholes, and having a uniform
and appropriate sample thickness (for transmission) of ~2
absorption lengths.
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X-ray Absorption Measurements: The Experiment
Energy Scanning: The beamline needs to deliver monochromatic x-rays that
are tunable so that we can scan energy across the absorption edge.
We’ll scan from ~200eV below to ~800eV above the Fe K-edge, like this:
Pre-edge ( -200 to –20eV ): 5.0eV steps.
Edge
( -20 to + 20eV ): 0.5eV steps
EXAFS
( +20 to ~800eV): 0.05 A-1 (photo-electron wavenumber)
Counting statistics for Good Data: The EXAFS is fairly small, so
m(E) should have a noise level of about 10-3. That means we need to
collect ~ 106 photons.
Transmission mode:
no problem ( ~108 photons/sec)
Fluorescence mode:
may be a concern.
2001-Aug-15
X-ray Absorption Measurements: Transmission
For a concentrated sample (ie, most absorption is from the element of
interest), XAFS is best measured in transmission.
We need to get enough transmission through the sample to get a decent
signal in the ion chamber. With,
We adjust the sample thickness x so that
above the absorption edge.
For Fe foil:
But: the sample must be uniform, and free of pinholes.
If a transmission experiment can be done, this is an easy measurement
and gives very good data.
2001-Aug-15
X-ray Absorption Measurements: Fluorescence
For dilute atoms (say, in solution, or at low concentration) , the matrix may
absorb most of the x-rays, and we don’t get much change in transmission
for the element we care about.
XAFS can also be measured by monitoring the characteristic fluorescence
from the excited atom.
The measurement is different, but we
analyze the resulting m(E) in exactly
way the same as for transmission.
For Fe K-edge, we’ll measure the
Ka fluorescence line at 6.40keV.
But: There will also be elastic and
inelastic scatter that we don’t want:
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X-ray Fluorescence
X-ray Absorption
Incident x-ray is destroyed.
Core-level electron destroyed.
Photo-electron ejected from atom.
X-ray Fluorescence
Higher energy core electron fills
empty electron level, and ejects an
x-ray of fixed energy.
Ka : L electron fills K hole
Kb : M electron fills K hole
2001-Aug-15
X-ray Absorption Measurements: Fluorescence
To separate the Ka fluorescence line at 6.40keV
from the elastic scatter at ~7.10keV, we’ll use a filter
of Mn: with an absorption edge at 6.5keV, it will
absorb the scatter much more than the Fe Ka line.
To prevent too much Mn Ka
from getting in the detector,
we’ll use a set of slits.
Another common approach
is to use a detector with
energy
discrimination
to
select the fluorescence line
of interest.
2001-Aug-15
XAFS Analysis I: Data Reduction
No matter how we measure m(E), we’ll want to reduce this data to
c(k), where k is the photo-electron wave number (momentum):
1: convert measured intensities to m(E).
2: subtract a pre-edge background and scale m(E) to go from 0 to 1.
3: remove a post-edge smooth background function m0(E) to isolate
the XAFS:
4: weight XAFS and Fourier transform from k to R space.
5: Model f(k) and d(k) and analyze c(k) to get distances R, and
coordination number N .
2001-Aug-15
XAFS Data Reduction
1: convert measured intensities to m(E).
I0
I
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XAFS Data Reduction
2: subtract a pre-edge background and scale m(E) to go from 0 to 1.
Fit a line in the pre-edge region and
Fit a polynomial in the post-edge,
and determine the edge jump.
2001-Aug-15
XAFS Data Reduction
3: remove a post-edge smooth background function m0(E) to isolate
the XAFS:
Fit a smooth polynomial spline
to the XAFS to remove the
slowly varying (low-frequency)
components of m(E)
Edge Step
2001-Aug-15
XAFS Data Reduction
4: weight XAFS and Fourier transform from k to R space.
The XAFS is multiplied by k2 and
then multiplied by a smoothing
window function to eliminate ripple
from truncation of c(k).
Because of the d(k) term, the peaks
in |c(R)| are not at the interatomic
distances, but are shifted down by
~0.5A or so.
2001-Aug-15
XANES: oxidation state identification
X-ray Absorption Near-Edge Spectroscopy (XANES) is one of the only
techniques that gives a direct measurement of chemical state (valence state)
of an element. In many chemical and environmentally relevant systems, the
valence state is as important as the total concentration of an element.
XANES Analysis is somewhat more qualitative than EXAFS Analysis.
There is a shift of the
absorption edge by ~3eV per
formal oxidation state for Fe,
and qualitative differences in
line shape.
2001-Aug-15
XAFS Analysis II: Modelling c(k)
The XAFS for a coordination shell is modelled using
Where
and
are the photo-electron scattering factors.
These are non-trivial functions, and we’ve calculated them using an
Ab initio program called FEFF.
Once we have these, we can get
and
We’ll also adjust these parameters in the analysis:
Mean-square disorder in R
Amplitude reduction factor
Energy origin to define where
2001-Aug-15
XAFS Analysis II: Modelling c(k) Sum over Paths
The XAFS for a coordination shell is modelled using
And we now Sum over Scattering Paths to get the full XAFS, with
Contributions from all neighboring atom types and distances:
Now
and
coordination shell.
are calculated for each scattering path or
The Parameters N, R, s2 are now extended for each Path.
We’ll use 2 to 4 paths for most of the analysis here.
2001-Aug-15
XAFS Analysis With G.I.Feffit
To Start the XAFS Analysis Program, click on the G.I.Feffit icon:
The example data and analysis scripts are in C:\IFEFFIT\NXS\
G.I.Feffit will start in that directory,
At the command line, type ‘cd Fe’ to move to the
Fe subdirectory.
From the menus, pick File->Read Command File and Choose Analyze.iff.
Single Step through this script to see the steps involved in reducing raw data
All the way to
The command file Fit.iff will define the FEFF paths and fit the first shell of
Fe metal.
2001-Aug-15