From: Frank Girgsdies <[EMAIL PROTECTED]>
Subject: Anisotropic peak broadening with TOPAS
To: Rietveld_l@ill.fr
Date: Wednesday, October 29, 2008, 11:04 AM
Dear Topas experts,
this is my first email to the list, so if you would like
to know something about my background, please refer to
the "about me" section at the end of this mail.
My question is concerning advanced modeling of anisotropic
peak broadening with Alan Coelhos program
"Topas".
I'm working on a transition metal mixed oxide phase of
orthorhombic symmetry. Composition, lattice parameters,
crystallite size etc. may vary from sample to sample.
I'm using Topas to fit the powder patterns with a
"structure phase". If the peaks exhibit more or
less
homogeneous peak widths, I refine the "Cry Size
L"
and/or "Cry Size G" parameters to model the peak
shapes. Thus, I can obtain the LVol-IB as a measure
for the average crystallite size.
In some cases, however, I observe strongly anisotropic
peak broadening, with the 00l series of reflections
being much sharper then the hk0 and hkl reflections.
This observation fits nicely with the electron
microscopy results, where the crystals are needles of
high aspect ratio, the long axis being the c-axis of
the crystal (thus, I assume that the peak broadening
is dominated by the crystallite size effect, so
let us ignore the possibility of strain etc.).
In such case, I leave the GUI and switch to launch mode,
where I can successfully model the anisotropic peak
broadening with a second order spherical harmonics
function, following section 7.6.2. of the Topas (v3.0)
Technical Reference. So far, so good.
However, since the peak width is now primarily a
function of hkl (i.e. the crystallographic direction)
instead of a function of 1/cos(theta), I lose the size
related information. Of course, I'm aware of the
fact that the LVol-IB parameter is based on the
1/cos(theta) dependence and thus cannot be calculated
for a spherical harmonics model.
But the peaks still have a width, so it should be
possible somehow to calculate hkl-dependent size
parameters. And this is the point where I'm hoping
for some input from more experienced Topas users.
I could imagine three directions of approach:
A) The refined spherical harmonics functions
yields a set of coefficients. I'm not a mathematician,
so how to make use of these coefficients for my
purpose is beyond my comprehension.
I imagine the refined spherical harmonics function
as a 3-dimensional correction or scaling function,
which yields different values (scaling factors)
for different crystallographic directions.
Thus, it should be possible to calculate the
values for certain directions, e.g. 001 and 100.
I would expect that the ratio of these two values
is somehow correlated with the physically observed
aspect ratio of the crystal needles, or at least a
measure to quantify the "degree of anisotropy".
Is there a recipe to re-calculate (or output) these
values for certain hkl values from the set of
sh coefficients?
B) As far as I understand the spherical harmonics
approach as given in the Topas manual, it REPLACES
the Cry Size approach. However, it might be possible
to COMBINE both functionalities instead. Within a
given series of reflections (e.g. 00l) the
1/cos(theta) dependence might still be valid.
I could imagine that the spherical harmonics model
might be used as a secondary correction function
on top of a 1/cos(theta) model.
I think such approach would be analogous to the use
of spherical harmonics in a PO model, where the
reflection intensities are first calculated from
the crystal structure model and then re-scaled
with a spherical harmonics function to account for
PO.
If such an approach would be feasible, it should
be possible to extract not only relative (e.g. aspect
ratio) information as in A), but direction dependent
analogues of LVol-IB, e.g. LVol-IB(a), LVol-IB(b)
and LVol-IB(c) for an orthorhombic case.
C) One could leave the spherical harmonics approach
and go to a user defined model, which refines different
Cry Size parameters for different crystal directions.
In my case, two parameters would probably be sufficient,
one for the c-direction, and a common one for the a- and
b-direction.
The Topas Technical Reference, section 7.6.3. gives a
similar example of a user defined peak broadening function,
depending on the value of l in hkl.
I could probably come up with an analogous solution
which has a 1/cos(theta) dependence and two parameters,
one for the 00l and one for the hk0 case.
My problem with this approach is how to treat the
mixed reflections hkl. I suppose they should be
scaled with a somehow weighted mix of the two
parameters, where the weighting depends on the
angle between the specific hkl and the c-axis.
However, I no idea how a physically reasonable
weighting scheme (and the corresponding Topas syntax)
should look like.
So, if anyone has a suggestion how to realize one
or another approach to model anisotropic peak
broadening AND extract size-related parameters
using Topas, I'd be very grateful.
Please mention the letter of the approach (A, B, C)
you are referring to in your reply.
Thanks!
And now, as this is my first mail to the list,
a brief introduction about myself:
I'm an inorganic chemist who became interested
in crystal structures and has picked up some
crystallography knowledge here and there.
I did my diploma in solid state chemistry,
using powder diffraction on perowskite-related
materials.
For my Ph.D. I turned to organometallic chemistry
to learn single crystal structure analysis on
molecular compounds, solving around 100 small
molecule crystal structures.
Now, I'm back to solid state chemistry and powder
diffraction in the context of heterogeneous
catalysis. Exploiting the structure solution
approach of the Topas software, I even managed to
solve two inorganic structures from powder data
(mainly by trial-and-error), thus bridging between
my current and former occupation.
I am a pragmatically oriented guy, i.e. I am a
"structure solver", not a real crystallographer,
because I lack the deep and thorough training
of a real crystallographer. My mathematical
and programming skills are just basic.
I tend to dive into such things just as deep as
necessary to achieve my goals.
I hope that you do not think by now that I am a
"I just push the button on that black box"
type of guy. I'm fully aware of the fact that
some insight into the things that go on inside
the "black box" is necessary to evaluate the
results for their physical relevance.
However, as my emphasis is on application of
XRD in chemistry and not on its fundamentals,
my insight naturally has its limitations.
Cheers,
Frank
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Frank Girgsdies
Department of Inorganic Chemistry
Fritz Haber Institute (Max Planck Society)
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