Dear Frank,
I don’t have an exact recipe for Topas, but a general consideration of the
problem you face with may be found in J. Appl. Cryst. (2008) 615–627. If you
read the paper don’t miss the last sentence of the Conclusions :)
Regards,
Leonid
*******************************************************
Leonid A. Solovyov
Institute of Chemistry and Chemical Technology
K. Marx av., 42
660049, Krasnoyarsk Russia
Phone: +7 3912 495663
Fax: +7 3912 238658
www.icct.ru/eng/content/persons/Sol_LA
*******************************************************
--- On Wed, 10/29/08, Frank Girgsdies <[EMAIL PROTECTED]> wrote:
> 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
>
> ------------------------------------------
> Frank Girgsdies
> Department of Inorganic Chemistry
> Fritz Haber Institute (Max Planck Society)
> ------------------------------------------
