buna Nicolae, > Not only arithmetic, I think is clear that both <R> and c were refined in a > whole pattern least square fitting. A private program, not a popular > Rietveld program because no one has inplemented the size profile caused by > the lognormal distribution.
not sure no one did.. we're working with that kind of profiles at least since 2000 (published in 2001 Acta Cryst A57, 204), without the need for any approximation going through Voigts or Pseudo Voigts. Using FFT and some math tricks you can compute the "true" profile for a distribution of crystallites almost in the same time you calculate a Voigt curve, so why the need to use any approximate function? I think this agrees with what Alan just pointed out (well 5000 profiles per second if you do not include any hkl dependent broadening that has to be calculated for each of them (and perhaps for each subcomponent)... otherwise the speed reduces.. but yes few ms for each profile is the current speed for my WPPM code, implementing all this stuff within the WPPM frame). > > But the most important disadvantage is the necessity to choose the > > exact type of size distribution. For Sample 1 (which, obviously, have > > certain distribution with certain <R> and c) you got quite different > > values of <R> and c for lognorm and gamma models, but the values of Dv > > and Da were nearly the same. Don't you feel that Dv and Da values > > "contain" more reliable information about <R> and c than those > > elaborate approximations described in chapter 6? > > Well, this is the general feature of the least square method. In the least > square you must firstly to choose a parametrised model for something that > you wish to fit. Do you know another posibility with the least square than > to priory choose the model? Without model is only the deconvolution, and > even there, if you wish a "stable" solution you must use a deconvolution > method that requres a "prior, starting model" (I presume you followed the > disertation of Nick Armstrong on this theme). also in this case it has ben shown possible to obtain a distribution without any prior information on its functional shape (J.Appl.Cryst (2004), 37, 629) and without taking the maxent treatment into account. I'm currently using without much problems for the analysis of nanostructured materials... advantages with respect to maxent are the speed and the fact that it can coexist with other broadening models (still not possible with maxent and still have to see a specimen where strain broadening is absent) and it's able to recover also a polydisperse distribution if it's present.... Just need to test it against maxent (if data would be kindly provided to do so). For the purists, just redo the calculation starting from different points and you can evaluate the error in the distribution using a MonteCarlo-like approach... As for the TCH-pV, well, it is no more than a pV with the Scherrer trend (1/cos) and the differential of Bragg's law (tan term) plugged in. This means it is ok as long as you consider a Williamson-Hall plot a good quantitative estimator for size and strain (IMHO). Mat PS I fully agree with Alan on the continuous request for Journals, but I bet the other Alan (the deus ex machina of the mailing list) should warn the members somehow... ---------------------------------------------- Matteo Leoni Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) ITALY
