[Ifeffit] Debye-Waller factors for metal oxides ?

Matt Newville newville at cars.uchicago.edu
Mon Feb 7 16:25:31 CST 2005


Hi Ian, 

I think that Scott, John, and Shelly answered some of your 
questions about XAFS Debye-Waller factors, and gave many of
the standard answers about how to deal with these in the
analysis of real XAFS data.  
Here are some more thoughts on this:

> 1.  Are phenomenological models like the correlated Debye
> model and Einstein model appropriate?  It seems that Debye
> temperatures are hard to find for oxides.

The Einstein model asserts that there is a single, dominant (or
effective) vibrational mode between two atoms, with a
vibrational amplitude related to the Einstein temperature.  For
first shell EXAFS, this is almost always an appropriate model.  
But, if you don't know what that Einstein temperature is, you
have to treat it as an unknown.

Einstein / Debye temperatures are hard to find for metal oxides
because most bulk measurements of thermal properties don't fit
with these simple models.  That doesn't mean that the
metal-near-neighbor-oxygen bond doesn't have a single, dominant
(or effective)  vibration, just that the other vibrational modes 
of the solid are important in the total thermal behavior.
 
But a result of the Einstein model that may be important for
your application is that sigma2 is linear in T over most of the
temperature range.

> 2. Is there an equivalent value for ss2 in x-ray
> crystallography data that I can refer to for comparison in
> these materials?  What should I look for in reviewing
> published x-ray crystallographic data?

Crystallographic Debye-Waller Factors are generally unrelated to
XAFS Debye-Waller Factors.  Many people have tried to make this
relation.  In my maybe-not-so-humble-as-it-should-be opinion,
they're all doomed to fail.  They're very different views of
thermal and static disorder.  One is with respect to the
near-neighbors, the other with respect to "the fixed stars" of
the crystal.

On the other hand, molecular vibrational information from IR,
Raman, NMR, Mossbauer, etc, also estimate bond strengths and
disorder in bond length, and are more like the XAFS Debye-Waller
Factors in their 'localness'.  As others have said, XAFS cares
about the vibrational mode between the two atoms, and so is most
strongly related to the optical phonon modes.  In many of these
other vibrational spectra, these modes can be selected and their
amplitudes extracted.

I don't think much (or enough) effort has been put into relating
vibrational measurements to XAFS DWFs.  It seems like an
interesting and potentially useful approach.

It's been more common for people to try to fit the experiment
into the Einstein model by taking temperature dependent data
well below room temperature or by coming up with models to
relate crystallographic and XAFS DWFs.  I think these are not
appropriate for most systems, including yours.

> 3. Is the temperature dependence reported for the ss2 for some
> metals (like Cu and Al) similar to their respective oxides?  

No, not at all.  Metallic bonds are generally weak, and so tend 
to have larger sigma2 than metal-oxygen bonds.

> For example, in Debye-Waller factor calculations reported for
> Al metal by R.C.G Killean (in J.Phys.F: Metal Phys., v. 4, pg.
> 1908, 1974), the ss2 changes by a factor of three between 25C
> and 300C.  Would I expect a factor of three increase in
> crystalline zeolites (AlO4 structural units).

Nope. The Al-O bond strength is much higher than Al-Al (Al melts 
at 660C, Al2O3 at 2050C).

> 4.  Specific to my work:  I have studied Al containing oxides
> at temperatures between 25 and 300 C.  I would like to
> quantify coordination changes by doing EXAFS fitting of the Al
> K-edge data.  The EXAFS was taken at temperature and I observe
> no change in the broadening of the data.  Likewise, the
> fitting shows no sensitivity in the Debye-Waller factor.  It
> is nearly constant at 0.001 A over the temperatures of
> interest.  Since ss2 and the coordination number (CN) are
> correlated, I would like a way to bind the error on the fitted
> CN by modeling real physical changes in the Debye-Waller
> factors.  Do you have any suggestions?

As others mentioned, you could model the temperature dependence.  
You can probably model sigma2 as simply as:

   sigma2(T) = sigma2_off  + T * sigma2_slope

With T either in C or K.  That is, since you're probably well
below the Einstein temperature and bond-breaking temperature,
sigma2 is probably linear in T.  The offset term incorporates
the static disorder as well as the thermal disorder at your
lowest temperature.

Then the sigma2 values for all your temperature dependent data
get mapped to two variables (sigma2_off and sigma2_slope).  If
coordination number is assumed to be independent of temperature,
you'll have three parameters to fit the amplitudes of all your
temperature-dependent data.  It sounds like you might find an
appreciable static disorder and a very small slope.  That could
be right, but  would indicate a very strong bond.

Hope that helps,

--Matt






More information about the Ifeffit mailing list