It seems that we disagree on the meaning of some english words. English is not my mother language, so I may be wrong.
The naive character doesn't come from the approximation of the crystallite shape by an ellipsoid, but from the approximation of the size effect in powder diffraction by ellipsoid. In powder diffraction it is seen not one, but a (big) number of crystallites more or less randomly oriented. The crystallites in reflection "show" different diameters, not only one.
I was able to put one word on that definition (thanks for it) in my previous email : distribution (a size distribution).
In these earlier works (maybe you define any earlier work as being "naive" ?) it is not at all the crystallite shape which is approximated by an ellipsoid. The ellipsoid is there for modelling the variation of the average size M(hkl) (which is the mean of the size distribution).
Certainly, always one can use ellipsoids as a first approximation for any kind of anisotropy, with the condition to not violate some elementary principles, in particular, here, the invariance to symmetry.
So, thanks, I used ellipsoids in 1983-87 for describing some simple size and strain anisotropy effects in the Rietveld method. I think that no elementary principle was violated, though certainly the word "violation" can be used as a definition for an "extreme approximation". But calling it "first approach twenty years ago" is less violent, even if you think that it is particularly stupid. The ellipsoid method was applied to the recent Size-Strain Round Robin CeO2 sample, giving results not completely fool (in the sense that not a lot of anisotropy was found for that cubic sample showing almost size-effect only, and quasi-isotropy).
Not surprisingly, people are mainly interested to obtain a good structure refinement and ignore by-products like strain an size. Doesn't mean that strain and size can not be estimated better.
I have gathered some interesting examples of anisotropic effects (at large) in a database of powder patterns. There is a famous cubic case showing strong stacking fault effects for HNbO3 (cubic symmetry). A neutron pattern is available. I would be interested in a better estimation of the size and strain effects on that sample (not only a phenomenological fit). Can you provide that better estimation ? It was a D1A (ILL) pattern and you could use the CeO2 well-crystallized sample powder pattern made on the D1A instrument for the Size-Strain Round Robin. Type the keyword HNbO3 in the search system of PowBase and you will have a hyperlink toward a .zip file containing the data : http://sdpd.univ-lemans.fr/powbase/ See a part of the neutron powder pattern at : http://sdpd.univ-lemans.fr/powbase/31.gif The ellipsoid approach is of course unable to provide anything correct with that case... Can your approach tell something ? This would interest a lot of people.
The thermodynamics is phenomenological science, have we to consider it a naive or a less naive science?
You use the word "naive", not me, I only cited it under quotes. I would never use it concerning any science. I just tried to show that even the application of ellipsoids in order to model size and strain anisotropy was not "naive". It was old Science (in the sense "accepted for publication twenty years ago" ;-).
Best wishes with HNbO3,
Armel Le Bail
