# [Ifeffit] Linear combination analysis

Bruce Ravel bravel at bnl.gov
Thu Jun 5 09:39:10 CDT 2008

```Hi Sebastiano,

> I study a binary alloy (Fe98.7Cu1.3) where a phase change from bcc to fcc
> is evident (at the Cu K edge of course) and it depends on the annealing
> time. I have 4 samples A,B,C,D,  where the A shows a perfect bcc structure,
> while the D a clear fcc structure. B and C have structure that is a mix
> between the fcc and bcc. I found very interesting to perform some linear
> fit simulations using the A and D of the XANES and EXAFS of the samples B
> and C. so  for instance it is possible to get the xanes of the B sample as
> linear combinations of A and D according to
>
> BXANES = x*AXANES+(1-x)*DXANES  and for the EXAFS
>
> BEXAFS = y*AEXAFS+(1-y)*DEXAFS
>
> The simulations work perfectly but:
>
> 1-       Of course I expect that x=y (am I wrong?). but this is not true
> according to the values that the linear fit provide me. There is a small
> but significant difference as x=48±2% and y=44±2%. Does this difference
> have any physical meaning? Is the error a bit too small (so should I
> increase it?)

I don't think you are either wrong or right -- it depends upon the
details of the system.  Were your system a mixture of two powders in
the ratios you observe in sample B and C, then you would indeed expect
x=y.

If I understand your situation correctly, you have an alloy that
displays a local structure (FCC-like around the Cu atom) that is
different from the bulk structure (presumably BCC since this is mostly
Fe).  That means that, on some length scale, the correlations in the
material change from FCC-like to BCC-like.

Suppose that length scale at which the correlations change is 10s of
Angstroms.  That is too far for the EXAFS-with-an-E to see, but near
the edge the mean free path of the photoelectron might be long enough
to start seeing that effect.  Thus the structure probed by the XANES
portion of the spectrum might not, in that sense, be identical to the
structure probed by the EXAFS.  In that case, you might not expect
x=y.  The extent of their difference is an indication that the XANES
is probing the system on a longer length scale than the EXAFS.

I admit that what I just wrote is a bit half-baked -- it's just my

> 2-       For the sample C, I got an amazing simulation adding some noise
> (0.001), but when I try to export the data (operation: "Write a report") I
> cannot get the data corrected with the noise (I can get only 6 columns: k,
> data, fit, residual, sample D, sample A). Is there any way to get the data
> from the data+noise curve?

Hmmm... I need to look into the soruce code, but I would guess that I
just forgot to apply the noise when writing out the LCF fit results.
I doubt that it will be a difficult fix and I will let the list know
when I have checked the fix into the SVN repository.  It is unlikely
that I'll have a chance to make a new Windows executable before
August, however.

As a work-around, you could generate a noise spectrum yourself and add
it to the data outside of Athena.  It won't be the same noise spectrum
that was used in the fit, but I suspect it'll be hard to tell the
difference when you make a plot.  As I say in the document "The noise
is randomly generated using an epsilon that is chosen as a fraction of
the size of the edge step."

B

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

National Institute of Standards and Technology
Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
Building 535A
Upton NY, 11973

My homepage:    http://xafs.org/BruceRavel
EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/

```