Dear Radovan and Rietvelders, I apologize for such late response.
Here is a plot of FWHM vs 1/d. https://www.dropbox.com/s/ndn58ua1317bmhb/quat_Heusler_FWHM_1%3Ad_plot.pdf?dl=0 All-odd line is nicely shifted as Radovan suggested. According to microstructure analysis for CW method, the plot indicates that all peaks have a strain effect and all-odd peaks have stronger size effect than other peaks. But, is it allowed to apply the idea of FWHM vs.1/d plot both qualitatively and quantitatively to TOF data without any consideration? I am afraid that there would be pitfalls one should avoid. At least, I have noticed that I need to be careful about how to get peak width. In the plot above and the one I posted before, FWHMs are obtained by simple gaussian fitting of individual peak to check the broadening behavior qualitatively. If I want do quantitatively reliable microstructure analysis (I am not sure that there is an established method for TOF data yet), I should take into account rising and decay convolutions to get “real” peak width in addition to instrumental resolution. Then, if I converted TOF profiles into 1/d, I will be stuck because I cannot use a conventional analytical form of a convoluted peak shape function. Or just taking integral breadths is enough? I understand TOF is not suitable for microstructure analysis because peak shape is rather complicated than CW. This is also indicated by the fact that all of the explanations about microstructure analysis which I have read are based on CW and none of them mentioned about TOF. It was not a purpose of our measurement, but I just want to try to extract microstructure information from my TOF data. Best regards, Kotaro //================//================// Kotaro SAITO High Energy Accelerator Research Organization Institute of Materials Structure Science 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan //================//================// > 2015/08/10 16:37、Radovan Cerny <radovan.ce...@unige.ch> のメール： > > Dear Kotaro, > > I think that it is a good track to follow. Compared to Mg(BH4)2 you may have > also chemical order of your four elements ABCD on top of the coherent domains > ordering. Both are of course related. > The antiphase domain ordering is visible in line broadening as a size effect > which is constant in the scale 1/d. It means that it is not constant in the > scale d. Have you plotted your powder pattern in the scale 1/d? > > Best regards > > Radovan > > > Radovan Cerny > Laboratoire de Cristallographie, DQMP > Université de Genève > 24, quai Ernest-Ansermet > CH-1211 Geneva 4, Switzerland > Phone : [+[41] 22] 37 964 50, FAX : [+[41] 22] 37 961 08 > mailto : radovan.ce...@unige.ch > URL : http://www.unige.ch/sciences/crystal/cerny/rcerny.htm > > De : rietveld_l-requ...@ill.fr [mailto:rietveld_l-requ...@ill.fr] De la part > de Kotaro SAITO > Envoyé : vendredi 7 août 2015 09:49 > À : Alan Hewat; loba...@inorg348-1.chem.msu.ru; Rietveld_l@ill.fr; > l_solov...@yahoo.com > Objet : Re: Selective peak broadening - interpretation and handling in > FullProf > > > Alan and Maxim, > > Thanks for the comment and the article. > I relieved that I know the point. > > > Leonid, > Yes, the instrumental resolution itself increases with d (or TOF). > But it is still strange for me that only all-odd peaks show different > d-dependence from CeO2 and other all-even peaks in terms of slope in the > delta-d/d vs d plot. > > Now, I think a similar situation as high temperature phase of Mg(BH4)2 occurs > in my quaternary Heusler sample. > For all-odd hkl, structure factor is F_hkl=4(f_A-f_C)+/-4i(f_B-f_D). Here, > A-D denote four fcc sublattices in Heusler alloys, or 4a,4c,4b,4d sites in > F-43m. > If there exist ABCD and CDAB type domains, those domain have out-of-phase > scattering for all-odd reflections and same story as Mg(BH4)2 can be applied. > But still I don’t understand why peak widths show such strong dependence on d > (or TOF). > > Concerning attachment files. > This time I use Dropbox but I don’t guarantee it as an image archive because > the image might be removed by me a few years later when I clean up my folders. > > //================//================// > Kotaro SAITO > High Energy Accelerator Research Organization > Institute of Materials Structure Science > 1-1 Oho, Tsukuba, Ibaraki, 305-0801, Japan > //================//================// > > > 2015/08/04 19:34、Alan Hewat <alan.he...@neutronoptics.com> のメール： > > > > On 4 August 2015 at 11:54, Kotaro SAITO <kotaro.sa...@kek.jp> wrote: > > Or do I miss some basic points about diffraction? > > > > I won't try to address your specific material... and I'm being called to > > lunch :-) But for beginners who may be lost in these technical papers, I > > will attempt the following trivial explanation > > > > If you have a layered material where two layers A and B are slightly > > different you will have super-structure reflections. These will be as sharp > > as the main reflections (from the average structure) if the order of the > > layers is perfectly regular ABABABAB... > > > > But if the layers only have short-range order eg ABABBABAAB... then these > > superlattice reflections will be broadened, and even completely washed out > > if the order between layers is completely random. Otherwise the width > > delta-d of the superstructure reflections will give you the short range > > order length - the shorter the correlation length the broader the > > superlattice reflections. > > > > Obviously delta-d doesn't depend on the d-spacing between layers, only on > > the length of their order. So the broadening is constant in d-space as > > usually plotted for TOF neutron diffraction. > > > > For angular dispersion eg with a constant x-ray or neutron wavelength, > > Bragg's law 2d.sin(theta)=lambda comes in. If you differentiate Bragg's law > > you will find a simple relation between delta-d and delta-2theta, the line > > broadening for angular dispersion measurements. > > > > Alan. > > (Everything should be as simple as possible... but no simpler.) > > BTW, thanks for using dropbox instead of an attachment. That's the way to > > go... > > -- > > ______________________________________________ > > Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE > > <alan.he...@neutronoptics.com> +33.476.98.41.68 > > http://www.NeutronOptics.com/hewat > > ______________________________________________ > > ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > > Please do NOT attach files to the whole list <alan.he...@neutronoptics.com> > > Send commands to <lists...@ill.fr> eg: HELP as the subject with no body text > > The Rietveld_L list archive is on > > http://www.mail-archive.com/rietveld_l@ill.fr/ > > ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > > > > ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > Please do NOT attach files to the whole list <alan.he...@neutronoptics.com> > Send commands to <lists...@ill.fr> eg: HELP as the subject with no body text > The Rietveld_L list archive is on > http://www.mail-archive.com/rietveld_l@ill.fr/ > ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ >
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