Following is a reply from Bob von Dreele on
Spherical Harmonics. Forwarded with permission
to the list.
Lachlan.
======
Forwarded message:
>From [EMAIL PROTECTED] Thu Sep 16 16:47:26 1999
The spherical harmonics stuff was put into GSAS for two reasons. One was
that it provided a very nifty method for extracting texture information
that was mathematically rigorous (see stuff by Bunge & others on this).
Secondly it gives a correction to "regular" diffraction data that is almost
"fool proof". The down side is that it does generate a lot of parameters
for low symmetry cases and one can get into the "given enough
parameters..." situation pretty easily. One way I use to determine if I
have "over parameterized" the problem is to look at pole figures or axial
distributions computed from the harmonic coefficients (POLFPLOT in GSAS).
My impression of physically meaningful textures is that these should always
be positive and not too "wiggly". Positivity is obvious as these plots
represent probability distributions for grain orientations within the
sample. In fact GSAS has facilities for "restraining" the texture to be
always positive to help this situation. Look at the "Z" option in the
spherical harmonics editing menu. Wigglyness in the distributions comes
about because the suite of diffraction data sets (one for ordinary
experiments & dozens for our neutron TOF texture measurements) does not
provide enough information to determine the values of particular harmonic
terms. This problem becomes more apparent for higher order harmonics where
all the diffraction measurements can, by chance, fall at the nodes (i.e.
zeros) of a particular high order harmonic. Consequently the coefficient
for this harmonic term takes on an arbitrary value (usually large!) in the
refinement. We will then frequently see a "pie crust" effect or other
nonphysical wiggles in the pole figures. To suppress this, GSAS has a
facility for providing restraints that says that the value of a pole figure
should be one (with a large esd); look at the same "Z" option. This trick
has a very distinctly Baysian flavor to it, but seems to work quite well to
help extend the useful range in the maximum value for harmonic order.
One other point is that if the texture (preferred orientation) is very
strong or sharp then it will require a relatively high order to the
spherical harmonics to adequately fit it. So high order harmonics isn't a
bad thing; it might be necessary in some cases.
Bob Von Dreele
At 10:54 AM 9/15/99 -0400, you wrote:
>
>
>At the ILL Powder meeting earlier this year
>Juan Rodriguez-Carvajal was asked when/if Spherical
>Harmonics might be put into Fullprof.
>Juan's reply was more of the nature you should
>try and do the best sample preparation possible
>and get the best diffraction data possible rather
>than try and model/fudge corrections into the data.
>
>Seeing Spherical Harmonics in action in GSAS and Topas,
>it is easy to see why people using Spherical Harmonics
>must love this correction as it can make what looks
>like quite a bad fit become exceptionally good at the
>flick of a switch. Thus giving the impression that
>something this good must be evil!?
>
>Given Spherical Harmonics can have this affect at
>making the fit look very nice, are there recommendations
>on how to review results that have included
>Spherical Harmonics corrections for preferred
>orientation?
>
>i.e.,
>
>What is considered appropriate and worrying in terms
>of the "order" used and values of the GSAS Texture
>Index when using Spherical Harmonics?
>Should people be providing before Spherical Harmonics and
>after Spherical Harmonics goodness of fit plots for publication
>and review? (possible the same should go for any use of
>preferred orientation corrections?)
>
>Lachlan.
>
--
Lachlan M. D. Cranswick
Collaborative Computational Project No 14 (CCP14)
for Single Crystal and Powder Diffraction
Daresbury Laboratory, Warrington, WA4 4AD U.K
Tel: +44-1925-603703 Fax: +44-1925-603124
E-mail: [EMAIL PROTECTED] Ext: 3703 Room C14
http://www.ccp14.ac.uk
