[Ifeffit] Debye-Waller factors for metal oxides ?

Kelly, Shelly D. SKelly at anl.gov
Mon Feb 7 10:43:26 CST 2005


I agree with John Rehr.  With a temperature dependent data set, the best
model that I have found is to allow each atom pair to have a thermal and
static disorder component.  Sigma2 = debye(Temp,Td_O1) + stat_O1
(This example is for the first oxygen (O1) shell of the metal oxide)
The static disorder component should be the same for all data sets from
the same sample at the different temperatures.  The thermal component
should increase as the temperature increases.  If you are lucky a Debye
or Einstein model will work well enough.  You will have to test both.
In addition, the thermal change in sigma2 should be about the same for
different samples that are closely related.  (We could argue about this
last point.  The best thing to do is to test this constraint by first
not imposing it and determine within the uncertainties in the
measurement, if it is true.  I have found that it usually is an okay
constraint.)

In the end, you simultaneously model the temperature dependence and the
sample dependence spectra all together.  You constrain the static
disorder term to be independent of temperature, and you constrain the
debye temperature to be independent of sample change.  This should
impose enough constraints on sigma2 values to accurately look at changes
in coordination number.  Of course the coordination numbers do not
change as a function of temperature but only as a function of sample
changes.

HTH
Shelly

Shelly Kelly ---------------------------- skelly at anl.gov

Bldg 203, RM E113                           phone: (1) 630-252-7376
Argonne National Laboratory              fax:     (1) 630-252-9793
Argonne, IL 60439                             www.mesg.anl.gov 
              


> -----Original Message-----
> From: ifeffit-bounces at millenia.cars.aps.anl.gov [mailto:ifeffit-
> bounces at millenia.cars.aps.anl.gov] On Behalf Of John J. Rehr
> Sent: Monday, February 07, 2005 10:07 AM
> To: XAFS Analysis using Ifeffit
> Cc: John J. Rehr
> Subject: Re: [Ifeffit] Debye-Waller factors for metal oxides ?
> 
> 
> 
>    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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> >
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