[Ifeffit] EXAFS sample prep

[Kelly, Shelly D.]

Hi Ritika,

I hope you do not mind, I'm sending this to the Ifeffit mailing list
since others might be interested as well.  

This email message is about how to prepare an EXAFS sample.  We are
talking about measuring a Ti-edge from some sample in solution.  But any
edge and any sample in any matrix will also work just file.

You want to set-up your sample so that you have a lot of Ti atoms in the
path of the x-ray beam.  This is because the EXAFS signal comes from the
adsorption from the Ti atoms.  Hence more Ti atoms give more adsorption
events resulting in a smaller statistical error in the EXAFS spectra. 

BUT.....

In transmission mode the EXAFS signal comes measuring the number of
x-rays incident on the sample and transmitted through the sample.  If
all the x-rays are adsorbed by the Ti atoms in the sample then you do
not have any transmitted x-ray signal.  Hence you get really noise data
because you have no statistically significantly transmitted x-ray
signal.  So you need your sample to be thin so that a lot of the x-rays
pass through the sample such that you have something to measure.  

In fluorescence mode the EXAFS signal comes from the x-rays emitted by
the Ti atoms as the core hole is re-filled.  These emitted x-rays need
to escape the sample without being re-adsorbed by the sample.  Hence the
sample needs to be dilute for fluorescence mode measurements.  When you
make a measurement in fluorescence mode it is always best to collect the
transmitted x-ray signal as well.  Then you can make a comparison to see
if "self adsorption effects" are small.

Transmission measurements typically have better signal to noise ratio
than fluorescence measurements.  So if you can, make your measurements
in transmission mode.

You can use Tkatoms or Artemis to calculate the best sample thickness
and the best concentration to use for the measurements and which EXAFS
mode will work best for your samples.

>From the components of your sample you can calculate the thickness of
the sample that will give 2.5 adsorption lengths.  The transmitted x-ray
intensity is given by the incident x-ray intensity multiplied by the
exponential of the absorption coefficient times the sample thickness.
I = I0 * exp(-mu(E) * x)

Where I is the transmitted x-ray intensity
I0 is the initial x-ray intensity
Mu(E) is the absorption coefficient = weighted sum of absorption
coefficient from each atom in the beam.
X is the thickness of the sample.

IF mu(E) * x = 2.5 then the percent of transmitted x-rays is about 10%
of the incident x-ray intensity.  This is just enough at NSLS where the
incident x-ray intensity will be about 10^6 x-rays per second.  This
means that 10^4 x-rays per second will hit your transmitted Ion chamber.
You want to make the transmitted ion chamber adsorb all (99%) of theses
x-rays.  Then your statistical error in the measurement will be
1/sqrt(N) or 1/sqrt(10^4) or 1%.  You need to have at least this many
x-rays to measure.  At the beam line you measure the total absorption
edge.  The EXAFS signal, if you are lucky, makes up about 10% of the
absorption edge.  Hence you need to have a statistical error of no more
than 1% to make a measurement.  If you can make the sample thinner then
you do even better.

Now for the other problem:  You want to get as many Ti atoms into the
sample with a total sample thickness of 2.5 absorption lengths.  To do
this part you need to calculate the absorption of just the Ti atoms in
the sample.  I call this delta_mu(E).  If you can get the delta_mu(E) *
x to be between 0.1 and 1.0 with the total absorption of the sample
below 2.5 then you can make the measurement in transmission mode.  This
means that between 10% and 70% of the absorption in the sample will be
due to the Ti atoms.  This is enough to get a good transmission signal.

If you adsorption from the Ti atoms in the sample is between 1% and 10%
then you will hope to make the measurement in fluorescence mode.  


Now for the practical part:

Say you have a solution with 1% Ti-stuff in water by NUMBER of atoms.
If you usually work by weight then you need to convert to number for
this calculation. 

Take the feff.inp file for Ti-stuff.  Look at the top of the file.  You
should find total_mu(E) (absorption of the entire sample at the Ti
edge), and delta_mu(E) (absorption of Ti atoms at the Ti-edge).  

Then use Hephaestus to calculate the total_mu(E) for water at the Ti
edge energy.  

To get the total absorption you need to calculate the weighted average
for water and Ti-stuff.  See how thick you can make your sample and
satisfy the criteria for less than a total absorption length of 2.5. 

(99%_by_number_water_atoms * total_mu(E)_for_water +
1%_by_number_Ti-stuff * total_mu(E)_for_Ti-stuff ) * sample_thickness =
2.5

Once you have that thickness then you can see what the absorption for
just the Ti atoms is.  

1%_by_number_Ti-Stuff*delta_mu(E)_for_Ti * sample_thickness =
absorption_length_for_Ti

And then you can figure out if you have a fluorescence or transmission
experiment. Absorption_length = 0.1 to 1.0 you have transmission.
Absorption_length=0.01 to 0.1 you have fluorescence.

Usually you have to go around and around with this sort of calculation
to optimize the conditions for the measurements.

Hope that Helps
Shelly