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) ------------------------------------------
