Oh good ! We are going to have one of those philosophical debates about
the fundamentals of Rietveld related refinement, where we can all safely
defend different opinions based on our limited personal experience.
PDF refinement is great, but is not new. It was known as the "Patterson
function" in crystallography well before any of us were born (even me) and
van Hove extended it to space-time correlations in ~1956 and produced a
classic Physics textbook.
PDF has been essential for diffraction from liquids and amorphous
materials (because you can't do any better :-) and for inelastic
scattering, but it is not much used today in its original form for
crystallography with single crystals. This even though PDF is in principle
more powerful when used with single crystals than with powders.
The reason is that PDF as its name implies only gives a list of
interatomic distances and scattering strengths, without even directions
for powders. And you don't want to throw away the information that you do
have about the atoms that are ordered, if only the "heavy" atoms. So
Patterson methods for single crystals have been superseded by difference
Fourier techniques. Still, if you can apply "heavy atom" or other
resonance scattering methods to help sort out the pairs, PDF like other
Fourier techniques remains important.
Potential disadvantages of PDF/Fourier techniques, such as calculation
efficiency, truncation errors etc are not really relevant with today's
powerful computers, hard X-rays, maximum entropy and other fancy tricks.
The problem with Rietveld refinement :-) is that you only get out a
refinement of the model you put in. If your model can't actually describe
the data, even the calculated errors will be wrong. But you may still
obtain useful information about where the model is wrong eg from
unreasonable anisotropic temperature factors that may indicate disorder or
lower symmetry.
A simple PDF function, unlike Rietveld refinement, does not assume
anything about the structure. Of course it may not help much either, since
in any but very simple structures there are a lot of different
inter-atomic pairs, and with a powder they are all collapsed to 1D, just
like the powder pattern itself. So you end up having to input a model
after all.
The advantage of Rietveld refinement :-) is that you only get out a
refinement of what you put in. You only refine a few physical parameters
such as lattice constants, atom positions etc, and so you reduce
correlations between these parameters, which is a major problem with peak
fitting methods due mainly to peak overlap, even for Pawley (or le Bail)
peak fitting.
OK, so you can also input a physically reasonable model for PDF
refinement, but then I suspect that the potential advantages become less
obvious. It does perhaps come down to a choice between fitting the actual
data or its PDF function. In the case of Rietveld refinement, you might
use a split-atom model guided by Fourier difference maps, so is there
really some model that can only be applied with PDF refinement and not
with Rietveld refinement ? Perhaps a "big box" model hasn't yet been tried
for refinement in real space?
Otherwise the methods must give much the same result, and it may become a
matter of personal choice. For my part, given a choice, I would prefer to
use the original data (with short wavelengths, combined neutron/xray data,
resonance scattering or whatever else is available and not specific to
PDF).
Alan.
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Dr Alan Hewat, NeutronOptics, Grenoble, FRANCE
<[EMAIL PROTECTED]> +33.476.98.41.68
http://www.NeutronOptics.com/hewat
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