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?