In this kind of job, you cannot rush without to think a bit. Applicability limits have been estimated. See if your problem dimensions are not quite out of these limits and make use of your common sense.

One can estimate limits by considering the recognized maximum number of parameters refinable by the Rietveld method which is the normal ultimate stage of the whole process. The values proposed here are personnal estimations which you may try to pass beyond. Corresponding to minimal FWHM (Full Width at Half Maximum) of the order of 0.12° 2-theta somewhere on the pattern (usually in the 20-40° range), 50 to 70 free atomic coordinates (x,y,z) are refinable reasonably (without taking account of fixed coordinates due to special positions nor of thermal parameters). This corresponds to 17 up to 23 independent atoms in general position (or more if some atoms accupy special positions).

Corresponding to these limits, cell volumes can be more or less estimated,
depending on the crystal system and on the Bravais lattice. For centrosymmetrical
space groups, these maximal volumes are the following :

Vmax(Å^{3}) Multiplicity of the Lattice System general position

500 2 Triclinic 1000 4 P Monoclinic 2000 8 C ,, 2000 8 P Orthorhombic 4000 16 A,B,C,I ,, 8000 32 F ,, etc for tetragonal, hexagonal and trigonal 12000 48 P Cubic 24000 96 I Cubic 48000 192 F Cubic

Translated in maximal number of reflections, any of these above maximal
possibilities corresponds to approximately 1000 to 1500 reflections for
a pattern extending from 5 to 150° 2-theta recorded with a ~1.5 Å
wavelength. One will have approximately 20 reflections per xyz refined
parameter. In a single crystal study, 10 reflections per parameter, including
the thermal ones, is something considered as normal. The fact that a larger
value is proposed for powder data is a consequence of reflection overlapping.
I hope that you will find these limits impressive after all. You shall
divide the above volumes by 2 if you are working with an acentric space
group. Divide them also by two if you wish accuracy otherwise you may have
to present dubious interatomic distances in your manuscript and the reviewers
will not be happy. At the beginning of the real expansion of this new sub-discipline
(1986-1987) I had to face a lot of incredulity. Some reviewers simply reply
to the editor that such a job was impossible...

Now if your minimal FWHMs decrease down to 0.06 or 0.02° 2-theta,
all you have to do is to multiply the maximum volumes listed at chapter
3.1.1 (given for minimal FWHM ~ 0.12° 2-theta)
by 2 or 6. This is much more comfortable than with conventional X-ray data.
It can be expected really to play with 150 independent atoms, corresponding
to 450 xyz refinable parameters. Up to 9000 or 10000 reflections could
be extracted from a synchrotron powder pattern. Triclinic centrosymmetrical
cells with up to 3000 Å^{3} volume or cubic cells with F
lattice as large as 300000 Å^{3} are the theoretical upper
limits which one could expect to attain by using high resolution synchrotron
data ! No study has approached such limits up to now. This is because no
try has been done. Very recently, FWHMs as low as 0.008° 2-theta were
obtained at the ESRF facility. These
synchrotron high performances may need a counting step as low as 0.002°
2-theta corresponding to 75000 points if the pattern was measured in the
5-155° 2-theta range. If compared to the 10000 expected reflections,
this gives one new reflection as a mean every 7 points. This appearss manageable,
however the range is generally limited to 2-80°, selecting a short
wavelength, because the sample fall down easily at larger angle if unpacked.
Actually, the largest problems solved (up to 60 independent atoms, 180
xyz parameters refined) are considerable. However they are far from the
limits suggested here. A list of complex experimental cases already published
may be found as a Top 50 inside the SDPD-Databank.
On another hand, the maximal limits suggested for conventional in-laboratory
diffractometers have been already reached without too much difficulties
for triclinic, monoclinic or orthorhombic cells. Consequently, one can
predict exceptional results in a very near future from synchrotron data.

Neutron conventional theta-2theta diffractometers present at best minimal
FWHMs ~ 0.12° or at worst ~ 0.25 to 0.30° 2-theta. As a consequence,
the maximal cell volumes of chapter 3.1.1 would be
respectively applicable or would need to be divided by 2 or 3. Nevertheless,
the maximum number of parameters that one could expect to refine by the
Rietveld method is not a sufficient criterion for an estimation of the
feasibility limits of an *ab initio* structure determination from
powder diffraction data. Indeed, winning the game depends on the successful
application of the Patterson or Direct methods. One has to obtain a starting
model sufficiently large for being able to start the refinement and then
complete the structure by difference Fourier syntheses. With the presence
of atoms distinctly heaviest than the others, in the sense of having distinctly
higher diffusion factors or Fermi lengths, it is generally sufficient to
locate them for the initial structure model building. Without these heavy
atoms, one has to locate almost the whole structure before to be able to
refine. Neutron data place you almost systematically in this later case.
Indeed, the Fermi lengths are of the same order for all atoms. Therefore,
a structure determination from exclusively neutron data is generally much
more difficult than from X-ray data, however organic compounds are difficult
whatever the data. It is advisable to make use of both X-ray and neutron
data, playing with their complementary advantages. A structure can be determined
partly from X-ray data by locating heavy atoms, and it can be completed
and/or the accuracy on the light atom positions can be improved from neutron
data. Finally, one can refine the structure simultaneously from both data,
a few softwares allow this. In the SDPD-Databank, the top
30 lists the most complex structures according to the criterion of
the largest number of atoms simultaneously located at the stage of applying
the Patterson or Direct methods. The upper limit is relatively low with
18 atoms from X-ray data (6 only from neutron data). This rather small
record should be broken soon by using synchrotron data with the highest
resolution. More people have to be convinced that structure determination
has become a quasi routine task by using powder diffraction data with some
expertize. The difference with solving a structure from single crystal
data is that much expertize is needed for powder data because several essential
steps in the whole process are not 'automatized' : the goal is to locate
goodies among garbages.

Copyright © 1997- Armel Le Bail