[Ifeffit] Debye model and Debye Waller factor

[Matt Newville]

Dear Sebastiano,

I'll attempt to answer these questions.

On 10/19/07, Cammelli Sebastiano <Sebastiano.Cammelli at psi.ch> wrote:
> In your "Introduction to FEFFIT"
> (http://feff.phys.washington.edu/~ravel/) you suggest in
> the beginning to use the DW factor according to the Debye model [debye(temp,
> thetad)] for the simple Cu foil. Then you ask to try with the Einstein
> model. I gave a look at the theory but I did not understand how to apply it
> to the fit. Anyway performing some FEFF calculation of this Cu foil, it
> looks that the Debye model works quite well but I am a very beginner
> feffusers and I am not an expert about IFFEFIT too.

First, a fairly general answer:  The Debye and Einstein models both
map a characteristic temperature to the thermal vibrations in a solid,
and so to the sigma2 values for a scattering path.  For very simple
compounds  (mono-atomic metals and some diatomic solids), these
models work well for sigma2 for XAFS paths, and can be used to predict
both the temperature dependence of sigma2 for a particular scattering
path, and predict the values for sigma2 for different scattering paths at
the same temperature.  For more complex systems, the models are
pretty close to worthless.

For calculating thermodynamic properties, the differences between the
two models can be significant, but for XAFS they are not very different,
though the characteristic temperatures are different. The Einstein model
is simpler, and fine for single-scattering XAFS, while the Debye model does
a better job at modeling sigma2 for multiple-scattering paths (though, to be
honest, none of this is "proven" to be right).

To *use* these models in (I)Feffit, you simply define the sigma2 for a path
to be
      debye(t, theta)
or
      eins(t, theta)

where t = sample temperature, and theta = characteristic temperature,
which you can then either set to some value or potentially even allow to be
refined in the fit.

It is often easier to find tabulated Debye temperatures than Einstein
temperatures, but they are typically related by theta_D ~= 1.27 * theta_E
(I believe: Lottici, PRB 35, p 1236, 1987)

> Anyway the samples I have to analyze are metallic alloy mainly based on Fe
> with some diluted element such as (Cu, Ni, Mn each less than 1at%). Is the
> Debye model good approximation for transition metal alloy? Is it better just
> to leave all Debye Waller factors free?

Well, the Debye (or Einstein) models probably are good approximations for
the sigma2 values in these systems, but .... if you're looking at the dilute
species (say, Cu in Fe), knowing the appropriate characteristic temperature
will be challenging, as you really want the strength of the Cu-Fe bond, not
that of the Fe-Fe bond.   You can probably use temperature-dependent
XAFS to determine this.   That is, Mn-Fe and Cu-Fe bonds probably have
different Debye temperatures.

As for leaving sigma2 values free in a fit, well, that depends on what you're
trying to learn from your data.   If you have data at one temperature and are
interested in the impurity-Fe first neighbor distance, then there probably
isn't much advantage to using the Debye or Einstein model compared with
allowing sigma2 to vary freely.

> In FEFF calculation, does it have any meaning to use the NOHOLE card and
> the S02=0.9?

Yes, these have meaning -- but they are probably not what you want.  The
NOHOLE card is probably not appropriate for any XAFS analysis.  While you
can set S02 in Feff,  I recommend leaving it as 1.0, and then setting this
parameter in (I)Feffit, where you will have more control over it.

Hope that helps,

--Matt