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 <[email protected]> > 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 > > ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > Please do NOT attach files to the whole list <[email protected] > > > Send commands to <[email protected]> eg: HELP as the subject with no body > text > The Rietveld_L list archive is on > http://www.mail-archive.com/[email protected]/ > ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > > > -- 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 ,_. | \ | v- ,' \ | ( \__Montevideo, Uruguay
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Please do NOT attach files to the whole list <[email protected]> Send commands to <[email protected]> eg: HELP as the subject with no body text The Rietveld_L list archive is on http://www.mail-archive.com/[email protected]/ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
