Re: [sdpd] structure and structureless lattice determination

[Jacco van de Streek <streek...@ccdc.cam.ac.uk>]

Armel Le Bail wrote:
> 
> Hi,
> 
> >I'm interested in cell lattice determination using both Le Bail and
> >Rietveld analysis with structure refinement, using the same data.
> >Specifically, where the cell dimensions obtained are not the same.
> 
> Whole profile refinement with cell constraint but without the structure
> constraint, as practiced with the Pawley or Le Bail methods, is able
> to produce better fits than with structure constraint (Rietveld method).
> This is not surprising, but it is not necessary to publish any comparison
> for guessing that this better fit does not necessarily produce better
> cell parameters (removing constraints always produce better fits).

Yes, the visual fit will be better and all mathematical indicators will be
lower, but the cell parameters could still be worse.

> I think that, if not properly applied, or if overlapping is really large,
> the Pawley and Le Bail methods will produce worse cell parameters
> than by using the Rietveld method.

If not properly applied, the Rietveld method will produce worse cell parameters
then by using the Pawley and Le Bail methods.

> The structure constraint
> force the correct calculated peaks to match with the observed ones
> not only in position but also in intensity. I would never believe
> any paper concluding that the Pawley or Le Bail methods produce
> better cell parameters than the Rietveld ultimate fit. Pawley
> and Le Bail methods are the penultimate test, not the ultimate.

I would have expected that in practice the differences between the cell
parameters should always be well within experimental error. It would therefore
be interesting to know if there are (m)any examples where the structure-less fit
gave different results, and more specifically, what these differences were
caused by.

I don't know enough about LeBail fitting (which the original question was
about), but from what I know about Pawley fitting, I would expect the cell
parameters obtained from the Pawley refinement to be superieur to those obtained
from Rietveld refinement. The least-squares criterion used for both Pawley and
Rietveld fitting is based on the assumption that the model being fitted matches
the data exactly, and that any discrepancies are due to random errors with a
Gaussian distribution only. Pawley fitting has so many degrees of freedom, that
this can be expected to hold more so for Pawley than for Rietveld fitting.
Traces of disorder, preferred orientation and absorption will change the
intensities and invalidate the fundamentals of the Rietveld refinement, and the
least-squares procedure will start to distort the remaining parameters, the cell
parameters among them, in order to make up for these systematic errors in the
intensities. Pawley fitting should not suffer from these distortions, or at
least less so.

Since I expect the differences in the calculated intensities to be the main
reason for discrepancies between the Pawley fit and the Rietveld fit (in fact, I
can't see any other difference), I would expect the cell parameters from the
Pawley fit always to be superieur.

(A maximum-likelihood Rietveld refinement may well give cell parameters
superieur to those from a least-squares Pawley fit.)

Anyone from a more mathematical background that has an opinion?

> The advice is that you should not make the economy of the final
> Rietveld fit

Do you have a reference? As I never refine the cell parameters obtained by the
Pawley fit, this is not purely an academic point for me.

Best wishes,
-- 
Jacco van de Streek
Research Scientist
Cambridge Crystallographic Data Centre
Cambridge, United Kingdom

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