Martin gives a good example for which interesting new information was
obtained from the PDF function - the fact that the Si-O bond lengths do
not change during a structural transition in quartz.
But quartz is a rather special case. First of all quartz is simple enough
that the Si-O distances might actually be measured directly from the PDF -
this cannot often be the case.
Second quartz is a material that exhibits strong librational motion of
small rigid units (associated with the transition) and unless such
libration is correctly modelled (using spherical harmonics in a periodic
structural model) this is a textbook example of Rietveld refinement
under-estimating bond lengths by trying to fit a banana-shaped
distribution with an ellipsoid. With a correct model for libration you
would also obtain correct bond lengths by refinement from the Bragg peaks
alone. As Martin says, "the Bragg peaks describe the average periodic
structure", which in this case consists of banana-shaped O-distributions
at constant distance from Si.
Let's not quibble over whether the PDF and Patterson functions are the
same or not; in 1935 Patterson didn't have a computer and could only
measure Bragg peaks. What he described is the instantaneous electron
density folded with itself, which is precisely the definition of the PDF
today. If you obtain this as he did by Fourier transforming the Bragg
intensities (F**2) you do ignore correlations that are non-periodic with
the lattice, but he had no choice.
Much is made of "total scattering" implying that modulations in the
background bring essential new information to PDF not available to
Rietveld. "Total scattering" was in fact advocated for Rietveld refinement
by Sabine 20+ years ago - see Young's book on the Rietveld method. (Sabine
wrote the first neutron paper with Rietveld (Nature 1961) and coined the
term Rietveld Refinement). A better example of the interest of background
scattering might be anti-ferroelectric perovskite transitions (Mike:-),
where atom displacements doubling the cell manifest as diffuse scattering
between peaks.
Of course if we *define* Rietveld refinement as Bragg peak refinement, we
restrict its power. I would define Rietveld refinement as direct
refinement of the structural parameters (atom positions etc) to fit the
observed data (without first extracting structure factors or performing
other intermediate operations, which was usual before Rietveld).
I still think that Fourier transforming the total scattering, and then
refining against that, cannot do more than refining against the total
scattering directly. Martin almost says as much when he talks about RMC.
The original question I think, was whether there is any computational
advantage in Fourier transforming the data before refining. Probably not.
Alan.
______________________________________________
Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE
<[EMAIL PROTECTED]> +33.476.98.41.68
http://www.NeutronOptics.com/hewat
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