Dear Frantisek,
your question refers to the application of spherical harmonic models for
PO description/correction in Rietveld QPA of minerals in multiphases
samples. My five cents:
The spherical harmonic models do not have any direct physical meaning.
They just fulfill the symmetry of the Laue class, and they can only be
applied if the geometry of you diffraction experiment is rotational
symmetric (e.g. in Bragg-Brentano geometry with flat (rotating) sample
and point detector). The models can work successfully in QPA only if
the normalization of the scale factors works correctly. Improved Rwp is
not a criterion for good/bad model decision.
From practical point of view, the models can be applied only if there
is enough information in the powder pattern (measured peak intensities
in different hkl directions), in relation of the degrees of freedom
(number of refineable parameters what are introduced by the the models).
The effective number of parameters of the several orders of these
functions and related to the Laue classes is discussed, for example, in
S. Matthies and K. Helming. General Consideration of the loss of
information on . . . . phys. stat. sol. (b), 113:569–582, 1982, or
table 1 in J. Bergmann, T. Monecke, and R. Kleeberg. Alternative
algorithm for the correction of preferred orientation in rietveld
analysis. J. Appl. Cryst., 34:16–19, 2001., cited from Bunge, H. J.
(1993). Texture Analysis in Material Science: Mathematical Methods. GoÈ
ttingen: Cuvillier.
Accordingly, you need higher orders of SH's for higher symmetric
materials. My personal rule of thumb for minerals is order 2 for
triclinic and monoclinic, 4 for orthorhombic/hexagonal/tetragonal, and 6
for cubic phases. Doing so, you introduce maximum of 6 effective
correction parameters but still have a correction effect. (For
comparison, for triclinic structure a 6. order would introduce 28 (!)
effective parameters, "with enough parameters you can fit...".)
To reduce the danger of over-parametrization by such models, the BGMN
software automatically deactivates SH models when not enough peaks or
not enough intensity is in the patterns as found in the first refinement
cycles. The fit becomes worse of course, but totally nonsense QPA
results are avoided.
However, even by this strategy correction models may fail in QPA, when
extreme correction factors are calculated maybe by correlation problems
etc.. Thus, one should have a look on the hkl specific correction
factors (m.r.d.'s). Of course, negative intensities should not appear
at all, if the software uses a quadratic or exponential form, like BGMN.
But extremely sharp PO may still be a significant problem for SH models.
Personally, I don't trust my QPA results when correction factors of <
0.4 or > 3 appear in a QPA refinement. In such cases we try to prepare
a better (more randomly oriented) powder sample and repeat the analysis.
Best regards
Reinhard
Am 17/01/2017 um 16:33 schrieb Laufek František:
Here it is:
J. Appl. Cryst. (2005), 38, 158-167.
Powder Diffraction (2009), 24(4), 315-326.
Frantisek
*From:*rietveld_l-requ...@ill.fr [mailto:rietveld_l-requ...@ill.fr]
*On Behalf Of *Cline, James Dr. (Fed)
*Sent:* Tuesday, January 17, 2017 2:54 PM
*To:* Laufek František
*Cc:* rietveld_l@ill.fr
*Subject:* RE: order of Spherical Harmonics for correction of PO
OK, can you list the citations for the papers in question?
Jim
James P. Cline
Materials Measurement Science Division
National Institute of Standards and Technology
100 Bureau Dr. stop 8520 [ B113 / Bldg 217 ]
Gaithersburg, MD 20899-8523 USA
jcl...@nist.gov <mailto:jcl...@nist.gov>
(301) 975 5793
FAX (301) 975 5334
*From:*rietveld_l-requ...@ill.fr <mailto:rietveld_l-requ...@ill.fr>
[mailto:rietveld_l-requ...@ill.fr] *On Behalf Of *Laufek František
*Sent:* Tuesday, January 17, 2017 8:30 AM
*To:* 'Sitepu, Husinsyah' <husinsyah.sit...@aramco.com
<mailto:husinsyah.sit...@aramco.com>>
*Cc:* rietveld_l@ill.fr <mailto:rietveld_l@ill.fr>
*Subject:* RE: order of Spherical Harmonics for correction of PO
Dear Husin,
Thank you very much for the papers!
Best Regards,
Frantisek
*From:*Sitepu, Husinsyah [mailto:husinsyah.sit...@aramco.com]
*Sent:* Tuesday, January 17, 2017 6:37 AM
*To:* František Laufek
*Subject:* RE: order of Spherical Harmonics for correction of PO
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*Dear Dr Laufek,*
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*The enclosed articles are probably useful information to answer your
question.*
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*All the best for the New Year.*
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*Husin*
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*From:*rietveld_l-requ...@ill.fr <mailto:rietveld_l-requ...@ill.fr>
[mailto:rietveld_l-requ...@ill.fr] *On Behalf Of *František Laufek
*Sent:* Monday, January 16, 2017 12:11 AM
*To:* rietveld_l@ill.fr <mailto:rietveld_l@ill.fr>
*Subject:* order of Spherical Harmonics for correction of PO
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Dear colleagues,
I use Rietveld method for quantitative phase analysis. I use Topas 5
and now I have started using
Spherical Harmonics for correction of preferred orientation (instead
of March-Dollas correction).
I mainly collect data in Bragg-Brentano geometry; samples are usually
prepared by front or side-loading.
My question is: Which order of Spherical Harmonics do you recommend to
use for the purpose of QPA? i.e. for mineral phases like calcite,
mica, feldspars, plagioclase, kaolinite?
(Most atomic position are usually fixed, refined are only scale
factors, unit-cell parameters, size, Debye-Waller parameters…).
I know that using high order Spherical Harmonic may lead to nice fits,
however with meaningless results and therefore the high orders should
be used with cautions.
I observe the drop of Rwp when introducing the Spherical Harmonics
correction and when it becomes insignificant, than I reduce the order.
E.g. for calcite, it is order of 2, for kaolinite order of 4 (i.e.
using higher order lead only to insignificant drop of Rwp).
Your suggestions, experiences and comments are welcome.
Frantisek Laufek
Czech Geological Survey,
Prague
Czech Republic
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