Re: [sdpd] Problems with Chi2 and WRp

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

Chi^2 less than unity almost certainly means that the esd's of the input 
data are not correct.  Chi^2 = 1 means that the difference between data 
and model is entirely due to statistical fluctuations of the model.  Since 
x-ray (or neutron) counts are random events, you can't do better than 
that. 

Most Rietveld programs take the esd to be the square root of the number of 
counts, which is correct if the data have not been normalized (and if the 
number of counts per channel is sufficient that the Gaussian approximation 
to a Poisson distribution is accurate, say at least 10 counts per channel 
in the histogram).  If they have been normalized (e.g., synchrotron or 
pulsed neutron sources), it is necessary to propagate the statistical 
factors along with the normalization.

Another possible issue that could cause this symptom in GSAS, is that if 
you put in a manual background with esd's, the program reduces the pattern 
chi^2 in a way that I find a bit mysterious.  If you have esd's in a 
manual background, try taking them out and seeing if you get more 
reasonable answers.

All of this is complementary to Lubo's advice, with which I agree 
completely: the difference between correct and rubbish refinements cannot 
be found in specific numerical R-factors or chi^s.

^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~
Peter W. Stephens
Professor, Department of Physics and Astronomy
Stony Brook University
Stony Brook, NY 11794-3800
fax 631-632-8176


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