Sorry, this got bounced last night so I am resending. ---------- Forwarded message ---------- From: Simon Billinge <[EMAIL PROTECTED]> Date: Thu, Jun 12, 2008 at 9:30 PM Subject: Fwd: PDF refinement pros and cons To: rietveld_l@ill.fr
Hi Alan, greetings to the Antipodes. Fitting F(Q) and G(r) should give identical results if the model has the same degrees of freedom in both spaces and the data are fit over the same range, however: To get G(r) we typically Fourier transform data over a Q-range up to 25-50 A-1 and we take Bragg and Diffuse scattering weighted by inverse form-factor squared and by Q (the high-Q information is therefore heavily weighted. This means that to be fitting the equivalent function in Q-space the fit should be made over the same wide range of Q with the same Q-weighting. This is not typically (ever?) done. The Q-space model also has to fit the Bragg and diffuse scattering at the same time. This is possible in a kind of "big-box" scenario as used in RMC type modeling where you can have correlated regions of local order that extend only over a few angstroms or nm (and RMC fits sometimes do fit in Q-space) maybe superimposed on a crystalline background. By fitting in real-space it is possible to separate the local from the average structure by fitting G(r) over different ranges. r-dependent fits are now quick and becoming more common. This is a computationally efficient way of getting information on the local structure. Finally, G(r) is a very intuitive function and the physical meaning is often quite direct, so people like it. Structural parameters tend to be differently correlated, and as Alan points out the convergence may be different (though it is not clear that it is better in real-space), but these things argue for fits to be done in _both_ real and reciprocal space, if the above mentioned difficulties can be overcome. This is the approach of RMCProfile, for afficionados of big-box modeling. Pure real-space fitting with PDFgui or (TOPASpdf Alan?) allows small-box crystallographic type models to be applied to the study of local structure. Both approaches can lead to the physical insight we are after. Those are my thoughts, Simon ---------- Forwarded message ---------- From: AlanCoelho <[EMAIL PROTECTED]> Date: Thu, Jun 12, 2008 at 8:17 PM Subject: PDF refinement pros and cons To: rietveld_l@ill.fr HI all Looking at the Pair Distribution Function and refinement I come away with the following: Fitting in real space (directly to G(r)) should be equivalent to fitting to reciprocal space except for a difference in the cost function. Is this difference beneficial in any way. In other words does the radius of convergence increase or decrease. The computational effort required to generate G(r) is proportional to N^2 where N is the number of atoms within the unit cell. The computational effort for generating F^2 scales by N.Nhkl where Nhkl is the number of observed reflections. Is there a speed benefit in generating G(r) - my guess is that it's about the same. Note, generating G(r) by first calculating F and then performing a Fourier transform is not considered. In generating the observed PDF there's an attempt to remove instrumental and background effects. In reciprocal space these unwanted effects are implicitly considered. This seems a plus for the F^2 refinement. >From my simple understanding of the process, there seems to be good qualitative information in a G(r) pattern but can someone help in explaining the benefit of actually refining directly to G(r). Cheers Alan -- 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 Condensed Matter and Materials Science Brookhaven National Laboratory P.O. Box 5000 Upton, NY 11973-5000 email: sb2896 at columbia dot edu home: http://nirt.pa.msu.edu/ -- 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 Condensed Matter and Materials Science Brookhaven National Laboratory P.O. Box 5000 Upton, NY 11973-5000 email: sb2896 at columbia dot edu home: http://nirt.pa.msu.edu/
