We've seen that asymmetric profile in our graphene simulations. .
How many 1000s of atoms can debussy/discus reasonably deal with? Matthew On Thu, 6 Jun. 2019, 19:39 Reinhard Neder, <reinhard.ne...@fau.de> wrote: > Dear Mr Girgsdies, > > Off hand I am not aware of any critical discussion. Let me add a few > thoughts though that may help to explain the issues at hand. > > A Rietveld program calculates the diffraction pattern as a sum of all > Bragg reflections. Initially these Bragg peaks are treated as > infinitesimally sharp points at a fixed 2Theta position. This hold in > particular for the calculation of the structure factor, which is calculated > at the corresponding point in reciprocal space for the integer values > triplet hkl. In a second step these sharp peaks are widened by a profile > function to describe the experimentally observed broad peaks. The > broadening of the profile function has components due to the instrumental > resolution and sample contributions (size and strain). > > The Rietveld treatment implicitly assumes perfect translational > periodicity, as all calculations in reciprocal space are limited to the > integer Bragg positions. The sample contribution to the broadening is thus > a bit of an artificial "trick" to get a good/reasonable agreement. > > In the actual diffraction experiment the diffraction pattern arises form > the sum of all secondary waves emitted by all atoms. This sum of all the > secondary waves is a continuous function in reciprocal space. Only in the > limit of a perfect infinite crystal will the sum reduce to the Bragg > positions, and be zero at all other points in reciprocal space. > > For a (very) small nanoparticle this sum of the secondary waves will > naturally "widen" the Bragg positions compared to those of a large crystal. > If one looks at a point slightly off the Bragg position, one has to keep in > mind that this diffraction angle differs from that of the integer Bragg > reflection. As a consequence, the individual atomic form factors and the > structure factor will differ from the values at the integer Bragg position. > This difference is not included in the Rietveld algorithm. This difference > can lead to an asymmetric profile function. This profile may be asymmetric > enough to have its maximum off the Bragg position and one must be super > careful not to mistake the location of the maximum intensity of such an > asymmetric profile with the actual Bragg position. This is described nicely > in Tchoubar & Drits X-ray Diffraction by disordered lamellar structures. > There are a bunch of "lovely" papers that do misinterpret this. > > The small nanoparticles below 3 nm diameter will add two more > complications to the situation. > > A) The (irregular) surface will likely truncate the average bulk unit cell > at different positions around the nanoparticle. Thus the Rietveld > assumption that the crystal consists of identical unit cells is no longer > absolutely correct. This may change the relative intensities. > > B) The surface is bound to be subject to > distortions/reconstructions/different surface chemistry compared to the > interior of the nanoparticle and will in many cases cause an appreciable > strain across the particle, which again is not part of the Rietveld > algorithm. > > All in all I would recommend to calculate the diffraction pattern of such > small nanoparticles by use of the Debye-Scattering-Equation. This algorithm > adds up the diffraction pattern from the contribution of all atom (pairs) > and gives a direct diffraction pattern without the need of a sample related > profile function. The Debussy program by Antonio Cervellino J.Appl.Cryst > 48, 2026 (2015) and my own DISCUS program JAC 32, 838 (1999) > "https://github.com/tproffen/DiffuseCode"; > <https://github.com/tproffen/DiffuseCode> are two examples of such > programs. > > The special issue of Acta Crystallographica A72 (2016) has several papers > related to the Deby-Scattering-Equation, Paolo Scardi and Matteo Leoni have > written several papers on the sample related profile function. > > Sincerely > > Reinhard Neder > Am 06.06.19 um 12:39 schrieb Frank Girgsdies: > > Dear fellow Rietvelders, > > Could anyone point me to some nice literature which critically discusses > the limitations of the Rietveld method when it comes to nano-crystalline > materials (specifically in the 1 to 3 nm range)? > As far as I'm aware, the core Rietveld literature seems to touch this > point only in the passing. > > Background: > To the best of my knowledge, Rietveld-derived parameters (like lattice > constants or domain sizes) should not be trusted as being "physically > meaningful" anymore when you fit the powder pattern of a material in the > few nm range with standard Rietveld tools. > My naive understanding of this problem is that the physical principles of > diffraction (or rather the best way to model it) gradually change when you > go from long-range ordered to medium-/short-range ordered materials. > Being a Rietveld practitioner rather than a theoretician, and having no > first-hand experience with WPPM and PDF methods, I am often confronted with > the problem to explain to my "customers" why I can't extract trustworthy > lattice constants or domain sizes from their nano-crystalline samples, > especially if it seems technically possible to fit the pattern with a > Rietveld program. > I think it would be nice if I could cite some critical discussion, or > overview article with further references, to put my finger on the problem. > Especially in the catalysis community literature, my impression is that > the applicability of the Rietveld method is sometimes overestimated, > leading to overinterpretation of the results. > > Any suggestions? > > Best wishes, > Frank Girgsdies > > > > > ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > Please do NOT attach files to the whole list <alan.he...@neutronoptics.com> > <alan.he...@neutronoptics.com> > Send commands to <lists...@ill.fr> <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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