Hi Ian,
I am looking forward to the responses of others on this issue,
because it's always a tough one. But I'll give you some quick thoughts
as I see them:
Essentially, there are no simple models for the ss values in
oxides. Einstein models don't work very well because there would
really have to be a separate Einstein temperature assigned for each
kind of bond, and even then you still don't have a formula to address
multiple-scattering. Debye models have similar problems.
X-ray crystallography values are giving the variance around a
lattice point; EXAFS gives the variance in the bond length. Thus I
think it is true that for distant (i.e. uncorrelated) scatterers, the
EXAFS value should be roughly twice the XRD value (somebody please
confirm my reasoning on this!). But for bonded pairs this is certainly
not true...acoustic modes generally dominate over optical modes under
these circumstances, and thus the EXAFS value for nearby pairs should
be lower than for distant pairs, all else being equal.
The temperature dependence of metals and oxides are not related
in any simple way of which I am aware. After all, that would imply
that things like specific heats of oxides should correlate to the
metals...think about water ("hydrogen oxide"), for
example.
Note that if you are expecting changes in CN, it is particularly
unlikely that a simple theoretical model will cover changes in ss2's,
since the former should have an actual physical effect on the latter
(as opposed to just a fitting correlation).
OK, so you're probably wondering what you can do. Although
there have been some attempts to theoretically model the Debye-Waller
factors of oxides that I'm sure people on this list could point you
toward, in most cases the more practical solution for your problem is
to fit standards, or to complement with other experimental techniques.
In other words, can you find a closely related material that is not
expected to show CN changes and measure its ss2's as a function of
temperature? Or can you get data on CN's at even a few of the
temperatures some other way?
--Scott Calvin
Sarah Lawrence College
There is little discussion over the significance of fitted
Debye-Waller factors (ss2) found for metal centers in metal oxides of
heterogeneous catalysts. I am searching for a better way of
determining how reasonable these values are in the fits I get.
1. Are phenomenological models like the correlated Debye model
and Einstein model appropriate? It seems that Debye temperatures are
hard to find for oxides.
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?
3. Is the temperature dependence reported for the ss2 for some metals
(like Cu and Al) similar to their respective oxides? 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).
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?