Dear Kamil,

Since you have an initial model that is presumably close to what you expect
to find in your sample, then Rietveld refinement is the right choice. In
cases where no initial model is available, other types of refinement are
suitable, such as Pawley or Le Bail, which refine lattice and peak shape
parameters only.

Regarding the order in which parameters are introduced to a fit, a good
starting point would be:
- lattice parameters and zero shift
- peak shape parameters and scale factor
- background terms
- atomic positions
Depending on the quality of your data and the nature of your sample, more
parameters could be refined (i.e. atomic displacement parameters, preferred
orientation, absorption etc.).

My suggestion would be to get a better understanding of the effect of each
parameter to the fit, in order to troubleshoot your refinement more
effectively. For example, peak positions depend on lattice parameters (and
space group setting), therefore refining e.g. the scale factor would not
help much if expected peak positions are in the wrong place. The following
article might be helpful to you.
McCusker, L.B., Von Dreele, R.B., Cox, D.E., Louër, D., Scardi, P., 1999.
Rietveld refinement guidelines. Journal of Applied Crystallography 32,
36–50. https://dx.doi.org/10.1107/S0021889898009856

As for the single peak not being explained by the fit, it could be due to
deviations in lattice parameters, but in that case more than one peak would
not match. If every other peak fits nicely and only one does not, I would
think that it is due to coexistance of a second, trace, crystalline phase
in the sample. In most refinement software you have the option of excluding
a peak from refinement. Refining atomic positions would not help, as these
change the relative peak intensities, not peak positions. However, if you
could share a few images of the fit, it would really help to better
understand what's going on.

Finally, with regards to software, you could also try GSAS
<https://subversion.xray.aps.anl.gov/trac/pyGSAS>. It is one of the most
widely used software for powder diffraction and it is free. There is
also a mailing
list <https://mailman.aps.anl.gov/mailman/listinfo/gsas-ii>, consisting
mainly of powder diffractionists, and a handful collection of tutorials
<https://subversion.xray.aps.anl.gov/pyGSAS/trunk/help/Tutorials.html>.

Best wishes,
Dimitris


On Thu, Nov 12, 2020 at 12:18 AM Kamil Krawczyk <
kamil.krawczyk7...@gmail.com> wrote:

> Hello!
>
> First, apologies if the scope of the question is beyond that of the
> listserv - I was recommended this discussion page through a colleague.
>
> I am incredibly new to refinement, and have been trying to employ the use
> of Rietveld refinement to better determine the crystal structure of my lead
> sulfide (PbS) quantum dots. Data was acquired as images on a home-built
> tabletop time-resolved electron diffraction setup, and converted to
> diffractogram through a combination of center finding and background
> subtraction. However, since these are small (~ 5 nm), and we are certainly
> sampling the ensemble average (as our focused beam is about 120 um in
> diameter), our pattern is that of a polycrystalline sample.
>
> From what I've encountered in my research, Rietveld is best suited for
> this case. I have taken an initial structure as inferred from
> literature/the bulk and refined that (relatively successfully to a Rwp
> value of ~2 - 6%). I do have a few questions regarding this process as I
> believe I am not being as rigorous as possible:
>
> - is there a 'best practices' order of refinement operations? e.g. refine
> the lattice parameters first, then peak profiles, etc.
> - there is a single peak that is not matching (likely due to a slight
> deviation in atomic positions from the expected simple cubic structure) -
> is refinement capable of moving individual atoms or clusters of atoms to
> better match a small, unaccounted for reflection?
>
> For what it's worth, I have been using Reflex in Materials Studio; if
> there is a more appropriate software for this application, I would be happy
> to hear!
>
> If any additional clarification is need, I'll fill it in!
>
> Best,
> Kamil
>
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