Re: [sdpd] Synchrotron powder diffraction

[pstephens...@notes.cc.sunysb.edu]

In reply to Armel Le Bail's discussion on the comparison between
synchrotron powder diffraction stations:

I think that most people active in this field understand that chi squared
is a measure of the statistical quality of a fit to data, and as such, it
cannot be much less than unity.  If a computer code gives you a value of
chi squared of 0.518  for a profile refinement, it must mean that there is
something wrong with the way that the program was used.  And I would not
think that any experienced user of powder diffraction software would accept
chi squared of 0.518 at face value.

One fact that may not be widely known about synchrotron sources is that
they are not constant, and so in step-scanning, it is necessary to keep a
monitor channel and normalize the intensity at each 2theta to a given
incident x-ray dose.  Then if statistics are to mean anything, the
estimated standard deviation (esd) of each data point must be normalized
the same way.  I forwarded the data I collected for the Size/Strain Round
Robin as {2theta, normalized counts, esd}, and I'm sure that Olivier Masson
and Andy Fitch did the same for the ESRF data.  Unfortunately, the esd's
were not posted on the Size/Strain Round Robin web page. I have placed the
original data on my web page, http://powder.physics.sunysb.edu; follow the
link to "Software and data."

In fact, in my data for the annealed CeO2 sample, the first point was 20
counts in approx. 400K monitor.  I conventionally scale data to 1M monitor,
so the data files report 50 counts.  My 20 counts have a fractional esd of
1/sqrt(20) = 22%, so the esd of the 50 counts should be 11.2.  Le Bail
reports a refinement without the esd's I provided, (for which the first
reported channel of 50 counts would have an esd of 7.1)
Using the correct statistical normalization with the Fullprof program, I
get a Le Bail refinement as follows:
 ==> RELIABILITY FACTORS WITH ALL NON-EXCLUDED POINTS:
 => R-Factors:  10.9     15.3     Chi2:   5.05     DW-Stat.:   0.5397
 => Expected :           6.82                                  1.9518
  => Conventional Rietveld Rp,Rwp,Re and Chi2:  12.3     16.4     7.28
5.050
  => N-sigma of the GoF:  362.086

Chi squared of 5.05 is a lot better than the 17.1 that Armel quoted for the
data from NSLS.  To people not used to synchrotron data, it may seem
awfully high, but it is compatible with what we usually observe due to the
very sharp peaks and low backgrounds.

This comparison will be a bit more sensible once the other data set is
analyzed with its proper statistical weights.

~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~
Peter W. Stephens
Professor and Director of the Graduate Program
Department of Physics & Astronomy
State University of New York
Stony Brook, NY 11794-3800


------------------------ Yahoo! Groups Sponsor ---------------------~-->
FREE COLLEGE MONEY
CLICK HERE to search
600,000 scholarships!
http://us.click.yahoo.com/47cccB/4m7CAA/ySSFAA/UIYolB/TM
---------------------------------------------------------------------~->

 

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/