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, Russia
http://sites.google.com/site/solovyovleonid
*******************************************************
________________________________
From: Matthew Rowles <rowle...@gmail.com>
To: "Sitepu, Husinsyah" <husinsyah.sit...@aramco.com>
Cc: "daniel.chateig...@ensicaen.fr" <daniel.chateig...@ensicaen.fr>;
"rietveld_l@ill.fr" <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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