On Mon, 19 Jan 1998 12:08:23 -0600, Matthew Henrichsen wrote:
>I've heard from others at Northwestern University using Reitveld that
>thermal parameters cannot be reliably refined from x-ray powder
>diffraction data (XRPD). There are several published reports containing
>thermal parameters obtained using single crystal x-ray diffraction,
>diffuse x-ray scattering, and neutron powder diffraction on the material
>I'm working with (Beta" alumina).
>
>Why does x-ray powder diffraction fail? Why do the others work?
At my opinion, the errorneous Debye-Waller-Factors of X-ray Rietveld
results from systematic errors, especially of the profile shapes.
Fundamental parameters profile shapes should give good Debye-Waller-Factors.
I cite from an e-mail from Jul 17 1996:
---------citation-----------------------------------------------------------
2nd example: Comparison of Debye-Waller-Factors
***********************************************
(round robin PbSO4)
(I heared the measuring data are from CSIRO)
Measuring conditions and results of other authors are cited in
J. Appl. Cryst. (1992) 25, 589-610.
I will compare results of other authors vs. my own computations.
2a) Isotropic Debye-Waller factors
**********************************
Values of B are in Angstroem**2.
Atomic own Result range of other single crystal
position results results
------------------------------------------------------------
Pb 1.502+- 0.9...2.39 1.48
0.014
S 0.920+- 0.29...1.37 0.74
0.064
O1 1.39+- 0.50...4.2 1.87
0.19
O2 1.44+- 0.1...5.8 1.76
0.17
O3 1.04+- 0.8...4.6 1.34
0.11
Please note: I only have cited the X-ray results.
Errors are given as 1 sigma (standard deviation).
As you can see, my results fit into the 3-sigma-range of the
single crystal results. They are much better than others.
2b) anisotropic Debye-Waller factors
************************************
This beta values are dimensionless.
Atomic own Result range of other single crystal
position results results
------------------------------------------------------------
Pb
beta11 0.00374 0.0027-0.0200 0.0039
beta22 0.01732 0.0124-0.0140 0.0166
beta33 0.00724 0.0075-0.0090 0.0072
beta13 0.00026 -0.0004-+0.0004 0.0004
S
beta11 0.00281 -0.0014-+0.0036 0.0025
beta22 0.00692 0.0010-0.0030 0.0070
beta33 0.00506 0.0060-0.0140 0.0035
beta13 0.00051 0.0005-0.0020 -0.0003
O1
beta11 0.00408 --- 0.0040
beta22 0.02212 --- 0.0250
beta33 0.00587 --- 0.0080
beta13 -0.00487 --- 0.0030
O2
beta11 0.00345 --- 0.0040
beta22 0.01214 --- 0.0270
beta33 0.01491 --- 0.0050
beta13 0.00709 --- -0.0020
O3
beta11 0.00373 --- 0.0060
beta22 0.01011 --- 0.0080
beta33 0.00379 --- 0.0070
beta12 -0.00059 --- -0.0010
beta13 0.00108 --- -0.0010
beta23 -0.00298 --- -0.0010
Note: no other author gave anisotropic values for oxygen atoms.
Please note, my private re-evaluation reaches an Rwp=7.33%,
which is much better than the best value of the article cited above.
-------------end of citation------------------------------------------
Due to correlations of peak intensities, the errors of Rietveld Debye Waller
factors are some times larger than those obtained from single crystal
measurements.
Sincerely Yours
J. Bergmann
