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) > ------------------------------------------