Dear Christina,
Chi2 may be small because of a high noise, so it indicates that the
model is over-refined with respect to the quality of the data (quick
collection using analyzer crystal). This is a trivial case and you
can't help it.
The other (more likely) option is that you have low-noise data from an
area detector, but the data file includes only 2theta - intensity values,
and no sigmas. In this case, Rietveld programs estimate sigmas as a
square root of the intensity, which is a huge underestimation of the
collected statistics, since they ignore the fact that the average
was taken over the integrated rings. The highly overestimated sigmas
screw up then the weighting scheme and give wrong chi2. You can help
it by adding a third column to your data file, taking into account the
geometry of the detector (pixel size, sample-detector distance). Below
is a little script in Basic for the MAR345 data integrated by Fit2D.
It should work for other detectors, change the pixel size in mm from
0.150 to your value, and the sample-to-detector distance D, in mm.
You can read more about this in Vogel S., Ehm L., Knorr K., Braun G.
AdV. X-Ray Anal. 2002, 45, 31–33. Keep in mind: after adding sigmas,
the chi2 will be very large, since it is practically impossible to
account for all differences using very low noise data. But the
weighting scheme will be proper and thus the results more accurate.
OPEN "RT_002.chi" FOR INPUT AS #1
OPEN "RT_002s.dat" FOR OUTPUT AS #2
line input #1, line$
line input #1, line$
line input #1, line$
line input #1, line$
D=250
[loop]
if eof(#1) <> 0 then [quit]
line input #1, line$
TT$ = mid$(line$, 1, 15)
TT = val(TT$)
I$ = mid$(line$, 16, 15)
I = val(I$)
if I > 0 then
N = 2*3.14159*D*tan(3.14159*TT/180)/0.150
sigma = SQR(I/N)
line$ = line$; " "; str$(sigma)
print #2, line$
end if
goto [loop]
[quit]
[exit]
CLOSE #1
CLOSE #2
END
Best regards,
Yaroslav
===8<==============Original message text===============
Dear all,
I am working on a refinement of synchrotron-X-ray powder data; the fit
is ok (though certainly not perfect) but I ended up with a confusingly
small reduced chi^2:
Rp = 23.4%
wRp = 16.9%
F^2 = 18.6%
chi^2 = 0.755
(1733 observations, 15 variables).
I would be very grateful for any suggestions on how to solve this problem.
Regards,
Christina
--
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.
===8<===========End of original message text===========
