Dear Leo and the rest
Thank you for the rapid answer. The statistical analysis of diffraction
data is indeed to my experience not much used - one usually performs one
measurement and obtains a perfect result, every time!
I should maybe clarify the Si correction procedure right away: we made a
refinement of the two-component powder sample letting all parameters go
free. Then we compared the observed Si lines with calculated ones, made
a second-decree correction function, and manually modified the 2-theta
of the data file so that the Si positions would hit the expected values.
Then we made a new refinement, once again with all parameters free, and
confirmed that the Si unit cell is indeed within 0.01 Å of the expected
value. If not, we would make another correction. So all unit cell
parameters are let free in the refinements.
Indeed the Si uncertainty is three orders of magnitude lower than that
of the sample and not contributing much to anything, but I am concerned
that any reviewer would give me a hard time if I simply ignored it in
the statistical analysis.
Best regards,
Arto
On 2013-09-13 17:18, Leopoldo Suescun wrote:
Dear Arto and rietvelders,
This probably should not taken as a definitive answer to the question
because I may have skipped something from my statistics clases, but
I'd be tankful if someone comments if the procedure I suggest below is
not a good option and why. I have found myself in situations like this
when s.u. determination is important but hard to perform within
statistically accepted procedures.
If you have some 5- to 10 independent determination of your cell
parameters at each temperature you can use the values as statistically
independent observations and estimate the s.u. using conventional
statistical analysis (average, variance and standard deviation using
statistical tables to asses the confidence range for your number of
observations). This will give you a valid s.u. value that will
estimate the aleatory variation of your cell parameters within your
procedure.
Now, you know there is a sistematic component of uncertainty that is
caused by correction of sample height with Si cell parameters and
other systematic efects intrinsic to the Rietveld method, such as
selection of profile function, etc.. Lets assume that FULLPROF
estimates your cell parameters uncertainty in such a way that it takes
into account all the s.u. of the parameters you use for the refinement
(including Si cell parameter that I guess you fixed in the refinement
to allow sample height to refine, but you included a s.u. for this
fixed parameter).Then the s.u. that FULLPROF gives you could be 100%
attributed to the procedure so you can combine your statistical s.u.
obtained above with the uncertainty from FULLPROF, using also
conventional combined uncertainty.
It is very important that the s.u. of Si cell parameter, that is your
callibration for temperature, includes a possible variation of cell
parameter with temperature. For instance, if your temperature
precision is 1 K, and Si cell parameter uncertainty is less than the
linear thermal expansion of Si, then you have an uncertainty that is
not considering that the temperature may be off by 1 K.
One way to assess if the FULLPROF uncertainty is atributable to a
systematic cause is to compare values from independent determinations.
I mean if you have very different s.u. extracted from FULLPROF for the
5-10 determinations, then this uncertainty may be influenced by other
factors that change within your independent determinations and make
them not comparable so you don't really have such well defined
procedure that determines the systematic uncertainty.
Finally, to make sure the aleatory component of uncertainty is
meaningful you have to make sure there is not a systematic evolution
of the cell parameters within the 5-10 determinations (such as
increase or decrease with time) that may imply that you have some
systematic problem with your data collection, such as temperature
variation in the surface of the sample, or sample
reaction/decomposition/interaction with atmosphere or Si, or other
kind of instability that will make all the procedure much harder to
assess and meaningful uncertainty to be determined.
In any case, if one of the two such uncertainties is much larger than
the other one it will not make a big effect on the total uncertainty.
I hope this helps or at least generates a useful discusion and
correction to my proposition if wrong.
Best regards,
Leo
2013/9/13 arto ojuva <arto.oj...@mmk.su.se <mailto:arto.oj...@mmk.su.se>>
Dear all
I would appreciate some statistical advice. We are measuring cell
parameters variations in-situ of some structures using in-house
diffractometers. Because the in-situ variations also causes sample
displacement, we have been using an added internal standard (Si)
and corrected the 2-theta axis so that the silicon lines are in
correct positions. Because we wanted to be sure that our method is
reproducible, we have repeated our experiments 5-10 times, and
that has given us a standard deviation for the unit cell parameters.
The standard deviation for the Si cell parameters is of course
very small, in the order of 10^-5 Å, whereas for the samples it is
in the order of 10^-2 Å. That is also the accuracy we can
reasonably report our data at.
I would like to know how to report a single statistical variation
from our values. We have the deviation of the IS, deviation of the
samples, and then the error of the refinement itself (multiplied
by a number given in the output files). How to put it all
together? Our software is FullProf 2k.
Thank you in advance,
Arto Ojuva
Stockholm University
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Dr. Leopoldo Suescun
Prof. Agr (Assoc. Prof.) de Física Tel: (+598) 29290648/29249859
Cryssmat-Lab./DETEMA Fax: (+598) 29241906
Facultad de Quimica, Universidad de la Republica
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