[Ifeffit] Interest in more accurate theoretical standards

[Matt Newville]

Hi Sam,

On Tue, Mar 25, 2014 at 3:30 PM, Samuel T. Chill <samchill at utexas.edu> wrote:
> Dear List,
>
> I have noticed that EXAFS fits to Au foils at 298 K underestimate the known
> equilibrium bond length. According to the CRC Handbook the lattice constant
> at 298 K is 4.0782 +/- 0.0002 Å. This is a bond length of 2.884 Å. However,
> in published EXAFS work[1] as well as fits that I have performed the bond
> length is about 2.867 Å. The error is small -- about half a percent too
> short -- but I am interested in using EXAFS to study relatively small
> changes in bond length and I am curious about the resolution that can be
> achieved.

You didn't report an uncertainty for the distance refined from EXAFS.
 If you're interested in relatively small changes in bond length and
resolution, you'll probably want to consider that.

> I want to understand the source of this error. I think the two biggest
> sources of error would be correlation between variables in the fitting model
> and errors in the theoretical standard (FEFF6 in this case).

I would agree that errors from Feff (especially Feff6) could be a
substantial source of error here, and I don't think you'll get an
argument from anyone else.  I do not necessarily agree that
correlation between variables is a *source* of error -- it is an
important consideration, but I don't know why a correlation by itself
should skew results one way or the other.  The correlation will
increase the uncertainty (but this is, to first order, accounted for),
but shouldn't move the most likely value.

Depending on how you do the analysis, you may be missing other sources
of error.  First, you're expecting the interatomic distance from EXAFS
to match the distance between lattice points. Thermal vibrations make
average interatomic distance greater than the distance between lattice
points.   Yes, EXAFS distances *should* be longer than the distances
between lattice points, approximately by sigma2/(2*R) (See the work by
Fornasini for more details).

Second, you didn't clarify if you were including anharmonicity in the
analysis.  For Au at room temperature, this can be significant.
Ignoring anharmonicity in closed-packed systems tends to cause
distances to be underestimated.

There are other potential effects too, including the effect of sigma2
on the 1/R term in the EXAFS equation and the interaction between
sigma2 and the mean-free-path term.  These are sometimes mentioned in
the literature as necessary corrections, but if you're using
Artemis/Ifeffit,  these effects are already taken into account.

> The random experimental error for a foil should be negligible.

Random experimental errors wouldn't be correlated with distances even
if they were large (they're random). On the other hand. a systematic
error in the energy scale from the monochromator would be correlated
with distance.   The effect would typically be small, but if you're
interested in small absolute errors, you might need to consider this.

> I would like to know if it is possible to create a better theoretical standard using a more ab
> initio approach.

Yes, using Feff 8.5 and a multiple-pole self energy may help
significantly.  I think there may have been an improvement in the
relativistic potentials too, which would be important for Au.

> Is anyone aware of any other software for performing more accurate EXAFS
> calculations? It is okay if it is a very expensive calculation as I have
> plenty of computer time.

I'm not aware of any such software.

> I have seen that some DFT packages can perform XANES calculations, but I
> have seen no mention of EXAFS.

Yes, the "real-space" approach of propagate/scatter/propagate is
definitely preferred for EXAFS, and a k-space approach is known to be
prohibitive at high energies and heavy scatterers.  I don't you'll
find a DFT code that can do EXAFS.

Cheers,

--Matt