RE: UVW - how to avoid negative widths?
matthew.row...@csiro.au said: From what I've read of Cagliotti's paper, the V term should always be negative; or am I reading it wrong? That's right. If FWHM^2 = U.tan^2(T) + V.tan(T) + W then the W term is just the Full Width at Half-Maximum (FWHM) squared at zero scattering angle (2T). FWHM^2 is then assumed to decrease linearly with tan(T) so V is necessarily negative, but at higher angles a quadratic term (+ve W) produces a rapid increase with tan^2(T). Cagliotti's formula assumes a minimum in FWHM^2, but if that minimum is not well defined, U,V,W will be highly correlated and refinement may even give negative FWHM. In that case you can reasonably constrain V by assuming the minimum is at a certain angle 2Tm, which may be close to the monochromator angle for some geometries. So setting the differential of Cagliotti's equation with respect to tan(T) to zero at that minimum gives: 2U.tan(T) + V =0 at T=Tm or V = -2U.tan(Tm) this approximate constraint removes the correlation and allows refinement. Cagliotti's formula simply describes the purely geometrical divergence of a collimated white neutron beam hitting a monochromator, passing through a second collimator, then scattered by a powder sample into a collimated detector. It takes no account of other geometrical effects (eg vertical divergence) or sample line broadening etc. This geometry is appropriate for classical neutron powder diffractometers, but not really for X-ray and other geometries. Still, such a quadratic expression with a well defined minimum in FWHM, may be a good first approximation in many other cases, requiring only a few parameters, hence its success. There are many more ambitious descriptions of FWHM for various scattering geometries and sample line broadening, usually allowing more parameters to be refined to produce lower R-factors :-) Alan __ Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE alan.he...@neutronoptics.com +33.476.98.41.68 http://www.NeutronOptics.com/hewat __
Re: K6H2Nb6O19.8H2O
I didn´t find the crystalline phase K_6 H_2 Nb_6 O_19 .8H_2 O in ICSD database There are very many phases containing niobium oxide blocks, with various other cations and hydration states, so you may not find an exact match. You can still use ICSD to help understand the structure if you relax the search criteria. If you search eg for elements K Nb6 H O you get only 10 results, including eg K7(H Nb6O19).(H2O)10 which is already pretty close, with one more K, one less H, plus some extra water. You should of course remain sceptical about the precise formula that people report, especially if they report X-ray structures of hydrogenous heavy metal oxides :-) If you can index the pattern determine the unit cell, you can narrow the possibilities greatly, but again watch out for weak peaks due perhaps to superstructure, especially for heavy metal oxides. Alan. __ Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE alan.he...@neutronoptics.com +33.476.98.41.68 http://www.NeutronOptics.com/hewat __
Re: K6H2Nb6O19.8H2O
I didn´t find the crystalline phase K_6 H_2 Nb_6 O_19 .8H_2 O in ICSD database K7(H Nb6O19).(H2O)10 which is already pretty close, I should have given the reference for this and other similar Nb6O19 cluster compounds as: Solid-state structures and solution behavior of alkali salts of the (Nb6 O19)(8-) Lindqvist ion. Nyman, M.;Alam, T.M.;Bonhomme, F.;Rodriguez, M.A.;Frazer, C.S.;Welk, M.E. Journal of Cluster Science (2006) 17, 197-219 If you use Jmol in ICSD to draw these structures you find that they consist of clusters of 6 Nb-oxide octahedra (Nb6O19) held together with water hydrogen bonds and K+ or other cations for charge balance. Alan __ Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE alan.he...@neutronoptics.com +33.476.98.41.68 http://www.NeutronOptics.com/hewat __
Cagliotti and Other Issues
Back to basics and First Principles As Alan says, the [use of the Cagliotti function is appropriate for the neutron case], but not really for X-ray and other geometries. My recollection is the Cagliotti function was adapted to the x-ray case when we had low resolution x-ray instruments and slow (or no) computers. Now that we have high resolution instruments and fast computers, why does this inappropriate function continue to be used? On another note, the world is venturing into the infinitely small realm of nano-particles. The classical rules for crystallography work very well for ordered structures in the macro-world (particles of the order of micron-sizes). However, as the particles become smaller, does one not need to address the contribution of the surface of the particles? The volume of the surface becomes much greater relative to the volume of the bulk of the crystal. Models today account for stress and strain in the macro-world. As the relative fraction of the bulk becomes smaller, both the physical structure as well as the mathematics used to describe the bulk suffer from termination-of-series effect, do they not? Does any of this make sense? Any thoughts? Frank May St. Louis, Missouri U.S.A. From: Alan Hewat [mailto:he...@ill.fr] Sent: Fri 3/20/2009 2:13 AM To: rietveld_l@ill.fr Subject: RE: UVW - how to avoid negative widths? matthew.row...@csiro.au said: From what I've read of Cagliotti's paper, the V term should always be negative; or am I reading it wrong? That's right. If FWHM^2 = U.tan^2(T) + V.tan(T) + W then the W term is just the Full Width at Half-Maximum (FWHM) squared at zero scattering angle (2T). FWHM^2 is then assumed to decrease linearly with tan(T) so V is necessarily negative, but at higher angles a quadratic term (+ve W) produces a rapid increase with tan^2(T). Cagliotti's formula assumes a minimum in FWHM^2, but if that minimum is not well defined, U,V,W will be highly correlated and refinement may even give negative FWHM. In that case you can reasonably constrain V by assuming the minimum is at a certain angle 2Tm, which may be close to the monochromator angle for some geometries. So setting the differential of Cagliotti's equation with respect to tan(T) to zero at that minimum gives: 2U.tan(T) + V =0 at T=Tm or V = -2U.tan(Tm) this approximate constraint removes the correlation and allows refinement. Cagliotti's formula simply describes the purely geometrical divergence of a collimated white neutron beam hitting a monochromator, passing through a second collimator, then scattered by a powder sample into a collimated detector. It takes no account of other geometrical effects (eg vertical divergence) or sample line broadening etc. This geometry is appropriate for classical neutron powder diffractometers, but not really for X-ray and other geometries. Still, such a quadratic expression with a well defined minimum in FWHM, may be a good first approximation in many other cases, requiring only a few parameters, hence its success. There are many more ambitious descriptions of FWHM for various scattering geometries and sample line broadening, usually allowing more parameters to be refined to produce lower R-factors :-) Alan __ Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE alan.he...@neutronoptics.com +33.476.98.41.68 http://www.NeutronOptics.com/hewat __
RE: UVW - how to avoid negative widths?
As I have said before countless time, one should not lose sight of the objective of Rietveld refinement, that it is to refine a sensible crystallographic structure. One can reduce R factors in all sorts of ways by playing with the peak shape functions (even by using lower symmetry and increasing the number of refinable parameters!) but in the end what matters is: does the structure make sense? My own experience is that by judicious use of methods like bond valence calculations, studies of the bond lengths etc one can rule out unlikely refinements better than by concentrating on R factors. Many times one can reduce R factors by playing with the diffraction geometry terms, but with little obvious improvement of the structural results. -Original Message- From: Alan Hewat [mailto:he...@ill.fr] Sent: 20 March 2009 07:13 To: rietveld_l@ill.fr Subject: RE: UVW - how to avoid negative widths? matthew.row...@csiro.au said: From what I've read of Cagliotti's paper, the V term should always be negative; or am I reading it wrong? That's right. If FWHM^2 = U.tan^2(T) + V.tan(T) + W then the W term is just the Full Width at Half-Maximum (FWHM) squared at zero scattering angle (2T). FWHM^2 is then assumed to decrease linearly with tan(T) so V is necessarily negative, but at higher angles a quadratic term (+ve W) produces a rapid increase with tan^2(T). Cagliotti's formula assumes a minimum in FWHM^2, but if that minimum is not well defined, U,V,W will be highly correlated and refinement may even give negative FWHM. In that case you can reasonably constrain V by assuming the minimum is at a certain angle 2Tm, which may be close to the monochromator angle for some geometries. So setting the differential of Cagliotti's equation with respect to tan(T) to zero at that minimum gives: 2U.tan(T) + V =0 at T=Tm or V = -2U.tan(Tm) this approximate constraint removes the correlation and allows refinement. Cagliotti's formula simply describes the purely geometrical divergence of a collimated white neutron beam hitting a monochromator, passing through a second collimator, then scattered by a powder sample into a collimated detector. It takes no account of other geometrical effects (eg vertical divergence) or sample line broadening etc. This geometry is appropriate for classical neutron powder diffractometers, but not really for X-ray and other geometries. Still, such a quadratic expression with a well defined minimum in FWHM, may be a good first approximation in many other cases, requiring only a few parameters, hence its success. There are many more ambitious descriptions of FWHM for various scattering geometries and sample line broadening, usually allowing more parameters to be refined to produce lower R-factors :-) Alan __ Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE alan.he...@neutronoptics.com +33.476.98.41.68 http://www.NeutronOptics.com/hewat __
RE: UVW - how to avoid negative widths?
Hi to all!, in fact, the Cagliti's expression is just a way to show the angular variation of fwhm, as was mentioned was usef for neutron diffraction and adopted in XRD, we can also build another dependence such as FWMH vs 2theta directly and it is useful to evaluate size and strain, the problem is that many refinement codes have the FWMH angular dependence in terms of Caglioti's equation. By the way, how can I get the paper of Young and Desai?,because I have tried a search in the web,but i did'nt find the article- best regards. Miguel Hesiquio Miguel Hesiquio-Garduño Profesor Titular A Departamento de Ciencia de Materiales Academia de Ciencias de la Ingeniería ESFM-IPN. tel 57 29 60 00 ext. 55003, ext. 55011 On Thu, March 19, 2009 5:22 pm, matthew.row...@csiro.au wrote: From what I've read of Cagliotti's paper, the V term should always be negative; or am I reading it wrong? Additionally, there is some good work on the use of the Cagliotti (and TCHZ) functions in the paper by Young and Desai; it also goes over how to incorporate sample dependent terms into the expression. Young, R. A. Desai, P. 1989, 'Crystallite Size and Microstrain Indicators in Rietveld Refinement', Archiwum Nauki o Materialach, vol. 10, no. 1-2, pp. 71-90. Alan Hewat wrote: if you have access to the refinement code. This is why I love Topas. All of the the code used in the refinements is there for you to see! :) 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: matthew.row...@csiro.au
LANSCE Neutron School at the Lujan Neutron Scattering Center - July 7-17, 2009
LANSCE will host its 6th annual Neutron School at the Lujan Neutron Scattering Center, this year focused on Application of Neutron Scattering to Study Phase Transformations, on July 7-17, 2009. The school will include lectures from some of the preeminent scientists in the field and hands on experiments on the HIPPO, SMARTS, NPDF, FDS, and LQD instruments at the Lujan Center. The school is focused of graduate students beginning there thesis research and post doctoral researchers. Industrial applicants will also be considered. There is no tuition and travel expenses are covered. As an added bonus, we will take Sunday off for a day of hiking, sightseeing, etc. For more information and application instructions please visit the Neutron School website (http://lansce.lanl.gov/neutronschool). Applications are due April 13, 2009. On the website is also a link to the poster announcing the school, we kindly ask you to print and post it appropriately at your institution. Please send questions to Sven Vogel (s...@lanl.gov). Sven Vogel Chair of the 2009 LANSCE Neutron School We wish to acknowledge the support of the Department of Energy, National Science Foundation, and New Mexico State University