[Ifeffit] Debye-Waller factors for metal oxides ?

[Scott Calvin]

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?
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