# [Ifeffit] "Simple" question/s about fuzzy degeneracy

Bruce Ravel bravel at bnl.gov
Fri Jun 19 12:44:45 CDT 2015

```On 06/19/2015 12:08 PM, Juan Manuel Conde Garrido wrote:
> I'm somewhat new to EXAFS and this is my first question for the Ifeffit
> mailing list (which is a great source of information by the way).
> I was reading the excellent paper: "Path degeneracy and EXAFS analysis
> of disordered materials" and I have a "simple" question to ask:
> How do I get from table 1 to table 2?

Hi Juan,

The easiest way to understand that is probably to run Atoms a few
times.  Use this CIF file

https://raw.githubusercontent.com/bruceravel/demeter/master/examples/recipes/FuzzyOverSites/Zirconolite/zirconolite.cif

and look at the clusters that come from each of the three Ti sites.
You will find the nearest neighbor distances and degeneracies reported
in Table 1.

As I explain in the text near table one, the three Ti sites are not
equally represented in the unit cell.  1/2 of the Ti atoms in the unit
cell are Ti1.  Ti2 and Ti3 each represent 1/4 of the Ti population.

The first column in Table 2 condenses the 12 near-neighbor distances
given in Table 1 by taking into account the representation of each Ti
site in the unit cell and by grouping paths with similar lengths into
bins of a certain width.  The distances shown in the first column of
table 2 are the weighted average of the paths that have been binned
together.  The degeneracies reflect the proportional representation of
each Ti site in the unit cell.

The math for the paths at 2.050 and 2.498 is trivial.  The Ti2 site is
the only one that contributes scatterers at those long distances.  The
Ti2 site has two scatterers at, say, 2.050, but the Ti2 site only
accounts for 1/4 of all the Ti scatterers.  2*1/4 = 1/2 --> row 3 of
column 1 of Table 2.  The math for the two shorter distances is hardly
more complicated.  I am sure you can work it out for yourself.

I did not tablate the equivalent of Table 1 for the other kinds of
scatterers, but if you let Artemis expand the zirconolite CIF file
into feff.inp files for each of the three Ti sites, you can easily
make the equivalent of Table 1 for each of the other scatterers.

> Specifically, I think I know how to use fuzzy degeneracy in Artemis for
> the paths in one FEFF calculation, but in this case there are 3 sites
> for Ti, and that means 3 FEFF calculations (rigth?).

Sort of.  The magic cooked into Artemis manages the Feff calculations
in a way that may be a bit surprising to you.  Artemis has Feff
compute the scattering potentials for each of the equivalent sites.
It then checks the muffin tin radii of the absorber from each Feff
calculation and chooses the one whose absorber muffin tin radius is
the median of all the calculations.  Artemis saves the file with those
scsattering phase shifts and discards the others.

Artemis then runs its own implementation of the pathfinder on each of
the unique sites.  In the case of zirconolite, the pathfinder is run
on each of the three Ti sites.  The paths found are all tossed onto a
single heap (in the sense of http://dx.doi.org/10.1103/PhysRevB.52.2995)
with degeneracies that are weighted by the population of the cite in
the unit cell.  The degeneracy checker then runs, but with fuzzy
degeneracy.  That is, paths with similar length are grouped together
into bins of some width and presented to the user at their average
distance.

When one of these "fuzzy over sites" paths is used in a fitting model,
Artemis uses the scattering functions from the Feff calculation it
saved and the geometry of the fuzzily degenerate path to generate the
feffNNNN.dat file.

The idea of all of this machinery is to simplify the interaction with
a structure having the sort of local disorder that we see in
zirconolite.  My assertion is that the EXAFS data cannot possibly
resolve all the details of the Ti-O partial pair distribution
function.  This "fuzzy degeneracy over site" machinery provides a
simplified way of approximating the contribution from a complex,
highly non-Gaussian partial pair distribution.

> So how do I use fuzzy degeneracy for paths from different FEFF calculations?
> And by the way, is it right if I imagine the material as having only 1
> "fuzzy"/average site for Ti?

I don't think I quite understand this question, but I'll give it a
shot.

My intent is that you use fuzzy degeneracy over sites in the exact
same way you usually use Feff in Artemis.  Artemis has compressed the
three Feff calculations you would normally have to do into a single
fuzzily degenerate path list.

To say that another way, without "fuzzy degeneracy over sites", you
would have to run (in the case of zirconolite) three Feff calculations
then somehow figure out how to include all the possible Ti-O
scatterers into your fitting model.  Any sensible approach would likely
select one or a few representative O scatterers.  The parameters of
the EXAFS equation would  then be parameterized to attempt to capture
the full complexity of the Ti-O partial pair distribution.  "Fuzzy
degeneracy over sites" is a tool that attempts to automate that
tedious chore.

HTH,
B

--
Bruce Ravel  ------------------------------------ bravel at bnl.gov

National Institute of Standards and Technology
Synchrotron Science Group at NSLS-II
Building 535A
Upton NY, 11973

Homepage:    http://bruceravel.github.io/home/
Software:    https://github.com/bruceravel
Demeter:     http://bruceravel.github.io/demeter/

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