Dear Rietvelders.... What is the most complete and authoritative source for issues such as profile function definitions, what is their scientific basis, and when are they appropriate to use, etc.? I am guessing there is not one-stop-shop solution (Young's book? GSAS manual? Rietveld list archive?) but advice on this would be helpful.
I wonder if we should, as a community, put some of this stuff on wikipedia, or another such place. In other words, distill the community's collective knowledge in a single place that can be updated in the future, and also curated for correctness also by the community. What are people's thoughts on this? Rietveldipedia? S 2009/3/20 May, Frank <frank.l....@umsl.edu>: > 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 > ______________________________________________ > > > > > -- Prof. Simon Billinge Applied Physics & Applied Mathematics Columbia University 500 West 120th Street Room 200 Mudd, MC 4701 New York, NY 10027 Tel: (212)-854-2918 (o) 851-7428 (lab) Condensed Matter and Materials Science Brookhaven National Laboratory P.O. Box 5000 Upton, NY 11973-5000 (631)-344-5387 email: sb2896 at columbia dot edu home: http://nirt.pa.msu.edu/
