RE: Anisotropic peak broadening with TOPAS
Hi Frank I'm not 100% sure what you have been doing but I think the copying and pasting to get LVol values for particular sets of hkls can be maybe done in a more simple manner as shown below. If it's not clear then contact me off the list. prm lor_h00 300 min .3 prm lor_0k0 300 min .3 prm lor_00l 300 min .3 prm lor_hkl 300 min .3 prm gauss_h00 300 min .3 prm gauss_0k0 300 min .3 prm gauss_00l 300 min .3 prm gauss_hkl 300 min .3 prm = 1 / IB_from_CS(gauss_h00, lor_h00); : 0 ' This is LVol prm = 0.89 / Voigt_FWHM_from_CS(gauss_h00, lor_h00); : 0 ' This is LVol_FWHM lor_fwhm = (0.1 Rad Lam / Cos(Th)) / IF And(K == 0, L == 0) THEN lor_h00 ELSE IF And(H == 0, L == 0) THEN lor_0k0 ELSE IF And(H == 0, K == 0) THEN lor_00L ELSE lor_hkl ENDIF ENDIF ENDIF ; gauss_fwhm = (0.1 Rad Lam / Cos(Th)) / IF And(K == 0, L == 0) THEN gauss_h00 ELSE IF And(H == 0, L == 0) THEN gauss_0k0 ELSE IF And(H == 0, K == 0) THEN gauss_00L ELSE gauss_hkl ENDIF ENDIF ENDIF ; Cheers Alan -Original Message- From: Frank Girgsdies [mailto:[EMAIL PROTECTED] Sent: Friday, 31 October 2008 11:29 PM To: Frank Girgsdies; Rietveld_l@ill.fr Subject: Re: Anisotropic peak broadening with TOPAS Dear Topas users, thanks to your helpful input, I've now come up with a (probably clumsy) solution to achieve my goal (see my original post far down below). For those who are interested, I'll explain it in relatively high detail, but before I do so, I want to make some statements to prevent unnecessary discussions. The reasoning behind my doing is the following: Investigating a large series of similar but somehow variable samples, my goal is to derive numerical parameters for each sample from its powder XRD. Using these parameters, I can compare and group samples, e.g. by making statements like "sample A and B are similar (or dissimilar) with respect to this parameter". Thus, the primary task is to "parametrize" the XRD results. Ideally, such parameters would have some physical meaning, like lattice parameters, crystallite size etc. However, this does not necessarily mean that I would interpret or trust parameters like e.g. LVol-IB on an absolute scale!!! After all, it is mainly relative trends I'm interested in. LVol-IB is is one of the parameters I get and tabulate if the peak broadening can be successfully described as isotropic size broadening. [For details on LVol-IB, see Topas (v3) Users Manual, sections 3.4.1 and 3.4.2)] If, however, the peak broadening is clearly anisotropic, applying the isotropic model gives inferior fit results. LVol-IB is still calculated, but more or less meaningless. Thus, I wanted an anisotropic fit model that BOTH (a) yields a satisfactory fit AND (b) still delivers parameters with a similar meaning as the isotropic LVol-IB. Applying a spherical harmonics function satisfied condition (a), but not (b) (maybe just due to my lack in mathematical insight). Applying Peter Stephens' code (but modified for size broadening) met condition (a) and brought me halfway to reach condition (b). As I did not find a way of "teaching" (coding) Topas to do all calculations I wanted in the launch mode, I developed a workaround to reach (b). Now in detail: The modified Stephens code I use looks like this: prm s400 29.52196`_2.88202 min 0 prm s040 40.52357`_4.10160 min 0 prm s004 6631.09739`_227.63909 min 0 prm s220 54.23582`_13.82762 prm s202 1454.83518`_489.04664 prm s022 5423.10499`_765.48349 prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 + H^2 K^2 s220 + H^2 L^2 s202 + K^2 L^2 s022; lor_fwhm = (D_spacing^2 * Sqrt(Max(0,mhkl)) / 1) / Cos(Th); Compared to Peters original code, I have changed the strain dependence "* Tan(Th)" into the size dependence "/ Cos(Th)" and re-arranged the remaining terms in that line of code. [Peter has mentioned that from the fundamental theoretical point of view, spherical harmonics might be better justified then his formula for the case of SIZE broadening. Anyway, it works for me from the practical point of view, thus I'll use it.] This rearrangement emphasizes the analogy between the isotropic case "c / Cos(Th)" (where c is valid for ALL peaks) and the anisotropic one, where c is replaced by the hkl dependent term (D_spacing^2 * Sqrt(Max(0,mhkl)) / 1). Thus, I freely interpret this term as some sort of c(hkl), which I will use for some specific values of hkl to derive hkl dependent analogues of LVol-IB. The first step of this calculation I managed to code for Topas based on P
Re: Anisotropic peak broadening with TOPAS
Dear Topas users, thanks to your helpful input, I've now come up with a (probably clumsy) solution to achieve my goal (see my original post far down below). For those who are interested, I'll explain it in relatively high detail, but before I do so, I want to make some statements to prevent unnecessary discussions. The reasoning behind my doing is the following: Investigating a large series of similar but somehow variable samples, my goal is to derive numerical parameters for each sample from its powder XRD. Using these parameters, I can compare and group samples, e.g. by making statements like "sample A and B are similar (or dissimilar) with respect to this parameter". Thus, the primary task is to "parametrize" the XRD results. Ideally, such parameters would have some physical meaning, like lattice parameters, crystallite size etc. However, this does not necessarily mean that I would interpret or trust parameters like e.g. LVol-IB on an absolute scale!!! After all, it is mainly relative trends I'm interested in. LVol-IB is is one of the parameters I get and tabulate if the peak broadening can be successfully described as isotropic size broadening. [For details on LVol-IB, see Topas (v3) Users Manual, sections 3.4.1 and 3.4.2)] If, however, the peak broadening is clearly anisotropic, applying the isotropic model gives inferior fit results. LVol-IB is still calculated, but more or less meaningless. Thus, I wanted an anisotropic fit model that BOTH (a) yields a satisfactory fit AND (b) still delivers parameters with a similar meaning as the isotropic LVol-IB. Applying a spherical harmonics function satisfied condition (a), but not (b) (maybe just due to my lack in mathematical insight). Applying Peter Stephens' code (but modified for size broadening) met condition (a) and brought me halfway to reach condition (b). As I did not find a way of "teaching" (coding) Topas to do all calculations I wanted in the launch mode, I developed a workaround to reach (b). Now in detail: The modified Stephens code I use looks like this: prm s400 29.52196`_2.88202 min 0 prm s040 40.52357`_4.10160 min 0 prm s004 6631.09739`_227.63909 min 0 prm s220 54.23582`_13.82762 prm s202 1454.83518`_489.04664 prm s022 5423.10499`_765.48349 prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 + H^2 K^2 s220 + H^2 L^2 s202 + K^2 L^2 s022; lor_fwhm = (D_spacing^2 * Sqrt(Max(0,mhkl)) / 1) / Cos(Th); Compared to Peters original code, I have changed the strain dependence "* Tan(Th)" into the size dependence "/ Cos(Th)" and re-arranged the remaining terms in that line of code. [Peter has mentioned that from the fundamental theoretical point of view, spherical harmonics might be better justified then his formula for the case of SIZE broadening. Anyway, it works for me from the practical point of view, thus I'll use it.] This rearrangement emphasizes the analogy between the isotropic case "c / Cos(Th)" (where c is valid for ALL peaks) and the anisotropic one, where c is replaced by the hkl dependent term (D_spacing^2 * Sqrt(Max(0,mhkl)) / 1). Thus, I freely interpret this term as some sort of c(hkl), which I will use for some specific values of hkl to derive hkl dependent analogues of LVol-IB. The first step of this calculation I managed to code for Topas based on Peters equations, but for specifc hkl values: prm ch00 = (Lpa^2 * Sqrt(s400) / 1); : 0.24382`_0.01190 prm c0k0 = (Lpb^2 * Sqrt(s040) / 1); : 0.45185`_0.02287 prm c00l = (Lpc^2 * Sqrt(s004) / 1); : 0.13114`_0.00225 As you can see, the "c(hkl)" term becomes very simple for the cases hkl = 100, 010 and 001. For these reflections, the "D_spacing" can be replaced with the corresponding reserved variables for the lattice parameters. Now, I want to calculate something like "LVol-IB(hkl)" from these "c(hkl)" values. I still don't know how to code this in launch mode, so I developed a workaround and switch back to GUI mode. In the GUI, I do the following: 1) I fix the lattice parameters to the values obtained after running the anisotropic fit in launch mode. 2) I deactivate the "Cry Size L" parameter on the "Structure" tab and add a Lorentzian type 1/Cos(Th) convolution on the "Additional Convolutions" tab instead. Both do the same thing, but only the latter has the input format I need. 3) I paste one of the "c(hkl)" values from the *.out file of the anisotropic refinement, e.g. the value calculated for ch00, into the "Value" box of that convolution and keep it fixed. Then I start the refinement. Since lattice parameters and peak shape are fixed, there is not much to be refined. Not surprisingly, I obtain an ugly looking fit in which only few reflections are adequately described (e.g. the h00 series in this case). 4) I use the "Capture" option to grab the calculated pattern which is then inserted as a ne
[Re: Anisotropic peak broadening with TOPAS]
Original Message Subject: Re: Fw: Anisotropic peak broadening with TOPAS Date: Thu, 30 Oct 2008 08:43:07 +0100 From: Frank Girgsdies <[EMAIL PROTECTED]> To: [EMAIL PROTECTED] References: <[EMAIL PROTECTED]> Thanks a lot Peter for this piece of code. It was really helpful. First I tried it "as is", but the fit was only partially successful. Then I thought about the meaning of the Tan(Th) term, and that you mentioned it would fit strain broadening. Thus, I changed "* Tan(Th)" into "/ Cos(Th)" and: bingo!, the fit worked perfectly well. In fact, the calculated pattern looks almost exactly like the one I had obtained before using spherical harmonics. However, in contrast to the (at least to me) abstract spherical harmonics function, the Miller indices are now explicitly included, plus that I have basically a modified 1/cos(theta) function. Instead of lor_fwhm = c / Cos(Th) (as applied by the CS_L macro), I have now lor_fwhm = (D_spacing^2 * Sqrt(Max(0,mhkl)) / 1) / Cos(Th), effectively replacing the overall parameter c with an hkl-dependent term. I'm currently trying to make Topas calculate equivalents of LVol-IB for me. As this calculation seems to need the convolution features of Topas (because it involves "translation" of lor_fwhm into Voight Intergal Breadth), I think I can't do it by hand. My main problem now is how to make Topas' macros address one particular hkl peak instead of all peaks, and then output the result. Thanks again to Peter and all other contributors! Cheers, Frank [EMAIL PROTECTED] wrote: In response to the question posted this morning by Frank Girgsdies: Here is a little snatch of topas code for anisotropic broadening in orthorhombic system. (The fitted parameters come from a particular refinement I took this from; the factor of 10^4 is empirically chosen to get parameter values that are generally between unity and several thousand.) The "theory" behind this is given in PWS, Journal of Applied Crystallog. vol. 32, pp 281-289 (1999) and references therein. Generalization to other crystal systems is given in that paper as well. prm s400 0.0`_LIMIT_MIN_0 min 0 prm s004 1287.33878` min 0 prm s040 1.56981`_LIMIT_MIN_0 min 0 prm s220 32.53311` prm s202 5410.01715` prm s022 792.15586` prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 + H^2 K^2 s220 + H^2 L^2 s202 + K^2 L^2 s022; lor_fwhm = D_spacing^2 * Tan(Th) * Sqrt(Max(0,mhkl)) / 1; Application of this expansion to Lorentzian broadening is not mathematically rigorous, but seems to work OK within the framework of crystallographic refinements (i.e., if you don't try to interpret the fitted broadening parameters in some fundamental way). My experience is based on refinements from synchrotron data, which have mostly Lorentzian shape - you might play with using a Gaussian width as well. Note that the lor_fwhm command increases the width by that amount, so other terms in the lineshape, such as possibly a Lorentzian term in crystallite size (e.g., CS_L(@, 1000) ) are included as well. This formalism handles all of the strain broadening - even an isotropic component. At the risk of triggering a lengthy discussion, I would point out that this 4-th order polynomial expansion in Miller indices actually has some basis in elasticity theory (e.g., discussion at the end of the JAC paper cited above and subsequent work, for example by T. Ungar et al.), whereas spherical harmonic expansions really do not. Good luck with it, Peter ^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens Professor, Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800 fax 631-632-8176
Re: Anisotropic peak broadening with TOPAS
Dear Leonid, thanks for the literature hint. I had found that paper in "Web of Knowledge" before, but as our institute has no subscription for JAC only up to 2001 on, I was not sure whether I should order it (but now I did). Cheers, Frank Leonid Solovyov wrote: 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 d
Re: Anisotropic peak broadening with TOPAS
Dear Matthew, thanks for your reply. I hope to look a bit deeper into it (and try the code) a little later today. At the first glance, however, I'm not sure whether treating hk0 and hkl the same way would be appropriate from the theoretical point of view. But as I'm a practical guy, I will just give it a try. Thanks again! Frank [EMAIL PROTECTED] wrote: Sorry, pressed the wrong button... If you just want to try fitting the peaks, you could try something like this: str phase_name "Metal_oxide" local broad 100 'crys size for hk0 and hkl local sharp 2000 'crys size for 00l local csL = IF (And(H == 0, K == 0, L > 0)) THEN sharp ELSE broad ENDIF; CS_L(csL) 'insert remainder of structure... I don't know much about Lvol, but isn't an "average" crystallite size for a highly asymmetric crystal not all that meaningful? I am willing to be educated here, as I haven't had much need to get accurate crystallite size from diffraction data before Cheers Matthew Matthew Rowles CSIRO Minerals Box 312 Clayton South, Victoria AUSTRALIA 3169 Ph: +61 3 9545 8892 Fax: +61 3 9562 8919 (site) Email: [EMAIL PROTECTED] -Original Message- From: Frank Girgsdies [mailto:[EMAIL PROTECTED] Sent: Wednesday, 29 October 2008 22:05 To: Rietveld_l@ill.fr Subject: Anisotropic peak broadening with TOPAS Dear Topas experts, 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. -- Frank Girgsdies Department of Inorganic Chemistry Fritz Haber Institute (Max Planck Society) --
RE: Anisotropic peak broadening with TOPAS
Sorry, pressed the wrong button... If you just want to try fitting the peaks, you could try something like this: str phase_name "Metal_oxide" local broad 100 'crys size for hk0 and hkl local sharp 2000 'crys size for 00l local csL = IF (And(H == 0, K == 0, L > 0)) THEN sharp ELSE broad ENDIF; CS_L(csL) 'insert remainder of structure... I don't know much about Lvol, but isn't an "average" crystallite size for a highly asymmetric crystal not all that meaningful? I am willing to be educated here, as I haven't had much need to get accurate crystallite size from diffraction data before Cheers Matthew Matthew Rowles CSIRO Minerals Box 312 Clayton South, Victoria AUSTRALIA 3169 Ph: +61 3 9545 8892 Fax: +61 3 9562 8919 (site) Email: [EMAIL PROTECTED] -Original Message- From: Frank Girgsdies [mailto:[EMAIL PROTECTED] Sent: Wednesday, 29 October 2008 22:05 To: Rietveld_l@ill.fr Subject: Anisotropic peak broadening with TOPAS Dear Topas experts, 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. -- Frank Girgsdies Department of Inorganic Chemistry Fritz Haber Institute (Max Planck Society) --
Fw: Anisotropic peak broadening with TOPAS
In response to the question posted this morning by Frank Girgsdies: Here is a little snatch of topas code for anisotropic broadening in orthorhombic system. (The fitted parameters come from a particular refinement I took this from; the factor of 10^4 is empirically chosen to get parameter values that are generally between unity and several thousand.) The "theory" behind this is given in PWS, Journal of Applied Crystallog. vol. 32, pp 281-289 (1999) and references therein. Generalization to other crystal systems is given in that paper as well. prm s400 0.0`_LIMIT_MIN_0 min 0 prm s004 1287.33878` min 0 prm s040 1.56981`_LIMIT_MIN_0 min 0 prm s220 32.53311` prm s202 5410.01715` prm s022 792.15586` prm mhkl = H^4 s400 + K^4 s040 + L^4 s004 + H^2 K^2 s220 + H^2 L^2 s202 + K^2 L^2 s022; lor_fwhm = D_spacing^2 * Tan(Th) * Sqrt(Max(0,mhkl)) / 1; Application of this expansion to Lorentzian broadening is not mathematically rigorous, but seems to work OK within the framework of crystallographic refinements (i.e., if you don't try to interpret the fitted broadening parameters in some fundamental way). My experience is based on refinements from synchrotron data, which have mostly Lorentzian shape - you might play with using a Gaussian width as well. Note that the lor_fwhm command increases the width by that amount, so other terms in the lineshape, such as possibly a Lorentzian term in crystallite size (e.g., CS_L(@, 1000) ) are included as well. This formalism handles all of the strain broadening - even an isotropic component. At the risk of triggering a lengthy discussion, I would point out that this 4-th order polynomial expansion in Miller indices actually has some basis in elasticity theory (e.g., discussion at the end of the JAC paper cited above and subsequent work, for example by T. Ungar et al.), whereas spherical harmonic expansions really do not. Good luck with it, Peter ^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~^~ Peter W. Stephens Professor, Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800 fax 631-632-8176
RE: Anisotropic peak broadening with TOPAS
If you just want to try fitting the peaks, you could try something like this: str phase_name "Metal_oxide" local broad 100 'crys size for hk0 and hkl local sharp 2000 'crys size for 00l local cs = IF (And(H == 0, K == 0, L > 0)) THEN sharp ELSE broad ENDIF; CS_L(cs) 'insert remainder of structure... Cheers Matthew Matthew Rowles CSIRO Minerals Box 312 Clayton South, Victoria AUSTRALIA 3169 Ph: +61 3 9545 8892 Fax: +61 3 9562 8919 (site) Email: [EMAIL PROTECTED] -Original Message- From: Frank Girgsdies [mailto:[EMAIL PROTECTED] Sent: Wednesday, 29 October 2008 22:05 To: Rietveld_l@ill.fr Subject: Anisotropic peak broadening with TOPAS Dear Topas experts, 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.
Re: Anisotropic peak broadening with TOPAS
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 depe
Anisotropic peak broadening with TOPAS
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
