Ta a lot for that Reinhard.
I'll have a read of the paper and see what I can do. I need to read more on
spherical harmonics as well, as they seem a little like magic to me at the
moment.
I agree that the best way is to avoid PO in the first place, but (at least
in this instance) it wasn't in my control.
Thanks
Matthew
On Wednesday, 26 March 2014, Reinhard Kleeberg <
kleeb...@mineral.tu-freiberg.de> wrote:
> Dear Matthew,
> in my knowledge, for calcite the {104} in the usual cell choice for
> hexagonal axes is equivalent to {10-11} in rhombohedral axes setting.
> Morphologically, this shape is called by mineralogists the "main
> rhombohedra" and the six faces belonging to {104} are indeed the directions
> of the perfect cleavage. Thus, the shape of calcite particles
> crushed/milled from bigger crystals are nearly perfect rhombohedra (btw a
> typical exercise used in undergraduate mineralogy classes for demonstrating
> "cleavage").
> In common powder sample preparation, you can expect preferred orientation
> of these planes parallel to the sample surface. For Bragg-Brentano geometry
> (rotational symmetric, observation direction perpendicular to the sample
> surface), you need any function fulfilling the symmetry of the Laue class
> for the description of the relative polar-axis density of the hkl oriented
> parallel to the sample surface. This is realized by symmetrized spherical
> harmonics as introduced by Järvinen et al. (1970), Popa (1992), Järvinen
> (1993, 1998). This and similar approaches are included in many Rietveld
> programs, e.g. GSAS, TOPAS, BGMN, MAUD, DDM (?)...
>
> Back to calcite: You can see an example of a practically working
> correction function in fig. 1c of
>
> Bergmann, J., Monecke, T., Kleeberg, R. (2001) Alternative algorithm for
> the correction of preferred orientation in Rietveld analysis. J. Appl.
> Cryst. 34, 16-19.
> This function has maxima in the direction of the {104} normal vectors. As
> Leonid wrote, the description of such a rhombohedral symmetry is not
> possible by any uniaxial function like March-Dollase related to one special
> hkl. So there is no way around to choose a more complicated model than the
> March-Dollase.
>
> However, keep in mind that all these models like spherical harmonics have
> no real physical meaning and are limited in their application. They can
> effectively describe the PO only for rotational symmetry of your
> diffraction experiment, only up to a certain (weak) degree of PO, and only
> if there is a homogeneous PO in your powder sample. So the application of
> any PO correction models in Rietveld analysis is a potential source of
> errors and just the second-best solution. The best is always an optimized
> preparation for a randomly oriented powder mount.
>
> Reinhard
>
> Am 26/03/2014 05:46, schrieb Leonid Solovyov:
>
> Dear Mathew,
>
> The 104 plane in calcite corresponds to the most intense reflection that is
> related, in turn, to the best "spacing" or "separation" between atomic
> "layers" along which the cleavage may occur. This is not a strict rule, of
> course, as real cleavage planes may be different depending on specific
> interatomic interactions in the crystal and other aspects, but it works in
> many cases.
> Note also, that the 104 plane in the hexagonal setting has several
> symmetry-equivalents, while most Rietveld programs normally generate only one
> equivalent hkl for each diffraction peak, which makes the uniaxial
> March-Dollase PO correction invalid for such peculiar directions. This
> problem is resolved in DDM, where I included a special expanded-hkl option to
> generate all equivalent hkl's for every peak. About other programs I'm not
> sure.
>
> Best regards,
> Leonid
> *******************************************************
> Leonid A. Solovyov
> Institute of Chemistry and Chemical Technology
> 660036, Akademgorodok 50/24, Krasnoyarsk, Russiasolovyovleonid
> <http://sites.google.com/site/solovyovleonid>
> *******************************************************
>
>
> ________________________________
> From: Matthew Rowles <rowle...@gmail.com>
> <javascript:_e(%7B%7D,'cvml','rowle...@gmail.com');>
> To: "Sitepu, Husinsyah" <husinsyah.sit...@aramco.com>
> <javascript:_e(%7B%7D,'cvml','husinsyah.sit...@aramco.com');>
> Cc: "daniel.chateig...@ensicaen.fr"
> <javascript:_e(%7B%7D,'cvml','daniel.chateig...@ensicaen.fr');>
> <daniel.chateig...@ensicaen.fr>
> <javascript:_e(%7B%7D,'cvml','daniel.chateig...@ensicaen.fr');>;
> "rietveld_l@ill.fr" <javascript:_e(%7B%7D,'cvml','rietveld_l@ill.fr');>
> <rietveld_l@ill.fr> <javascript:_e(%7B%7D,'cvml','rietveld_l@ill.fr');>
> Sent: Wednesday, March 26, 2014 8:16 AM
> Subject: Re: PO corrections in trigonal space groups?
>
>
>
> Thanks for your replies.
>
> Husin, is there any justification for the use of the 104 direction in
> calcite, other than this is the direction that works? I'm all for doing it if
> it works, but I'd like a little theoretical backup.
>
> Thanks Daniel. I'll put something together for a look-see. What corrections
> are being used in Maud? Are there any papers on them?
>
> THanks
>
> Matthew
>
>
>
> --
> TU Bergakademie Freiberg
> Dr. R. Kleeberg
> Mineralogisches Labor
> Brennhausgasse 14
> D-09596 Freiberg
>
> Tel. ++49 (0) 3731-39-3244
> Fax. ++49 (0) 3731-39-3129
>
>
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