[Ifeffit] Debye-Waller factors for metal oxides ?

[John J. Rehr]

   The lack of accurate Debye-Waller factors in complex materials, like
metal oxides, can be a real problem. In my view, simple phenomenological
methods like correlated Debye and Einstein models can't always be trusted.

   There is an alternative approach to fitting DW factors in such systems
which might be useful. The idea is to fit a few spring constants k_ij between
the atoms, rather than the DW factors themselves, e.g., for the most important
sites. This is efficient since the spring constants are temperture
independent.  This has been tested by Rossner et al. using their Bayesian
approach [Rossner, H. H.  and Krappe, H. J., (2004).  Phys. Rev. B 70, 104102]
The fitting is does via an analytical formula for the Debye-Waller factors
based on a fast recursion method [Poiarkova, A. V. &  Rehr, J. J. (1998).
Phys. Rev. B 59, 948].

  Of course, such an approach still misses contributions to the DW factors
due to structural disorder, which are addititive.

   J. Rehr



On Sun, 6 Feb 2005, Ian James Drake wrote:

> Hi,
>
> 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?
>
> Looking forward to your thoughts.
>
> Ian Drake
> Graduate Student
> UC Berkeley
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