Leonid (and others) just my 2 cents to the whole story (as this is a long standing point of discussion: Davor correct me if I'm wrong, but this was also one of the key points in the latest size-strain meeting in Prague, right?)
> Your recipe for estimating size distribution from the parameters of a > Voight-fitted profile is clear and straightforward, but I wonder have > you, or someone else, tested it on, say, simulated data for the model > of spherical crystallites having lognormal size distribution with > various dispersions? done several times... if you start from a pattern synthesised from a lognormal and you analyse it using a post-mortem LPA method (i.e. extract a width and a shape parameter and play with them to get some microstructural information), you obtain a result which (in most cases) does not allow you to reconstruct the original data (the Fourier transform of a Voigt and that of the function describing a lognormal distribution of spherical domains are different). I would invite all people using ANY "traditional" line profile analysis method to do always this check. Davor already pointed out cases where it works and cases where it does not: according to my experience those belonging to the first category are just a few. With a whole pattern approach and working directly with the profile arising from a distribution of domains, in most cases you're able to recostruct the original distribution without making any assumption on its functional shape (after all, most of the information to do so is contained in the whole pattern, even if it is well hidden). Concerning the Beyesian/maxent method, well, it is always a great idea, but unfortunately right now it is not mature enough to cope with a simple problem of combined instrumental, size AND strain broadening (unless something has been done in the last year). So ok it gives you the best result compatible with your hypotheses, but beware that "absence of any other source of broadening" should be listed among them.. and I'm not sure this is always the case! To put some water on the fire (otherwise it will burn all of us), I think the level of detail one needs on the microstructure, conditions the methods one's going to use to extract a result. No need to use highly sophisticated methods to roughly estimate a domain size (with an error up to +/- 50%) or to establish a trend within a homogeneous set of data, or also to obtain a better fit in the Rietveld method. Conversely, if a very high level of detail is sought, then I'd forget about a "traditional Rietveld refinement" and start approaching the problem from the microstructure point of view (after all, if one is interested in winning a F1 GP, he'd certainly not go for a Ferrari powered by a John Deere tractor engine!). cheers Mat ------------------------- Matteo Leoni, PhD Department of Materials Engineering and Industrial Technologies University of Trento 38050 Mesiano (TN) ITALY
