3.4- Strategy for structure completion
Retaining an atom site as proposed by direct or Patterson methods is a question of common sense according to the knowledge of your compound already at your disposal. You may not have the exact formulation but you should know the composition of the magic pot at the synthesis stage. It is the examination of the interatomic distances which allows you to accept the model or not depending of the atom-types which are probably inside your compound. It may be useful to transfer the atomic coordinates of your model in a program more specialized in interatomic distance calculation than SHELXS86, and eventually in a structure drawing program.
When you believe having obtained a starting model, you have to test the hypothesis by using a single crystal refinement program applied to your "|Fobs|" : the scenario suggests SHELX76 or SHELXL93 and now the SHELX97 package, other are possible. The best appraoch is to try the proposition on a reduced dataset (apply the OVERLAP software with X = 0.02 or more, depending on your data resolution and on your problem size). A model which corresponds to a reliability R less than 40-35% begin to interest me, a fortiori if peaks extracted from the Fourier difference synthesis make sense. If the peaks pass the test of interatomic distances credibility, they are added to the model as atoms and a new refinement and Fourier synthesis are done (don't be too sure of your sample composition, times to times errors are produced or new reactions take place : Cl atoms enter sometimes in fluorides by the chloride flux method for instance, although this rarely occurs). Once it has become impossible to extract more informations from the "|Fobs|" set (reduced) as resulting from the Le Bail method application, and if the model seems coherent, it is time to apply the Rietveld method. The crystal structure will not be always complete at this first Rietveld method application so that the extraction of new "|Fobs|" at the last Rietveld refinement cycle and their new injection into SHELX76/SHELXL93/SHELX97 (or any single crystal refinement program you may select) will allow to go further if a new Fourier synthesis reveals new sites. The process has to be repeated up to complete satisfaction. Results which should be submitted for publication are those of the last refinement by the Rietveld method. Never consider the SHELX result as the final one, the Rietveld method is the only recognized method for powder data refinement ! We will continue with the scenario examples :
Na2C2O4
It is time to examine the 3 propositions from SHELXS86
gathered in naoxa10.html. In the first proposal
corresponding to the complete dataset, the atom noted 1 presents a peak
height (474) quite distinct from the others. It could be a sodium atom,
if yes, the atom number 4 at 1.25 Å from the peak one would be an
artifact. Atoms 3 and 2 (with peak height 184 and 251) would be respectively
a carbon and an oxygen atoms or vice versa. The latter option is more convincing
because we expect the carbon atom to be at larger distance from the sodium
atom (distance 2-1 = 3.06 Å) than the oxygen atom would be (distance
3-1 = 2.26 Å). Something is disturbing in this first proposition
which is the absence of a clear separation between the peak intensities
of what would be atoms and what would be artifacts (peak number 4). In
the second proposition starting from the dataset reduced to 286 hkl, the
peak number 1 would be a C atom, the second peak a Na atom and peaks 3
and 4 would be oxygen atoms. The third proposition starting from the 242
hkl reduced dataset is evenmore convincing with peak 1 as a Na atom, peaks
2 and 4 would be oxygens and peak 3 would be a C atom, then the intensity
decreases abruptly for the fifth peak. Note that proposals 1 and 3 are
similar for the three first peaks if peaks 2 and 3 are exchanged. Entering
the four suggested first atoms of proposal 3 into a structure drawing program
like STRUVIR, which also lists interatomic
distances, then a confirmation of the model credibility is obtained (see
naoxa11.html). In fact, STRUVIR already recognizes
the presence of NaO6 octahedra (you can visualize the structure
as a 3D model if you have a VRML
viewer plugged into you browser).
With this model, the refinement program SHELX76 is applied (figure 26) on the 242 hkl (the most reduced dataset) and the R factor fall down to 25% after 4 refinement cycles. Looking at the Fourier difference synthesis, nothing more is found (naoxa12.html). The ultimate confirmation has to be obtained from the Rietveld method. After refinement of a scale factor only, by using the FULLPROF program, keeping fixed the profile parameters as obtained after the Le Bail method application and keeping fixed the structure parameters as refined by SHELX76, one minute later (PC Pentium 90MHz art least) , the model is definetely confirmed by rather low reliability factors (figure 27). Ultimately, all the refinable parameters are allowed to move by the Rietveld method. The thermal parameters are first refined as isotropic (RP = 11, RWP = 13, RB = 8%), then they are made anisotropic (RP = 7.6, RWP = 8.8, RB = 5.0%, this is possible because all atoms are "light" atoms). Finally a preferred orientation is believed to exist in spite of the use of a vertically loaded sample holder (direction [001], March-Dollase parameter of 1.09 indicating in principle needles along the c axis, so that all the other orientations are preferred) and the result is in naoxa13.html. The figure 28 allows to judge of the final refinement quality (RP = 5.7, RWP = 7.2, RB = 2.6%).
[Pd(NH3)4]Cr2O7
With all the heavy atoms located (Pd and Cr) together
with some N and O atoms, a refinement by the Rietveld method is
the best thing to do. Reliabilities decrease quickly to RP =
24.6, RB = 20.3, RF = 11.2 % after the FULLPROF
application. In order to complete the structure, the "|Fobs|"
estimated at the end of the Rietveld method application will be
used by SHELX76. We should not forget that in this case we are outside
from the theoretical limits (see chapter 3.1)
so that it could be necessary to use OVERLAP for keeping the less dubious
reflections only. In fact, SHELX76 as applied to the 1528 reflections (up
to 120° 2-theta) entering the 7 independent atoms yet located allows
to get R = 0.109 (corresponding to the RF from FULLPROF). The
Fourier difference synthesis is in this case
not very well exploited by SHELX76 which does not propose many interatomic
distances. It is time to view the structure by STRUVIR
and to examine if the new atom sites as proposed by SHELX76 are convincing.
The file is quickly prepared, STRUVIR recognizes a complete CrO4
tetrahedron and square planes PdN4 for the two palladium sites
(figpd7.gif and figpd8.gif).
The interatomic distances show that peaks Q1,
Q5 and Q7 from the Fourier difference synthesis will constitute acceptable
N atoms whereas peaks Q3, Q9, Q11 and Q12 will reasonably correspond to
oxygen atoms. One oxygen atom will be lacking at this stage. It will be
located after a new FULLPROF-SHELX76 cycle. Its position could have been
guessed by the completion of the second CrO4 tetrahedron. Do
not expect to locate hydrogen atoms from these data, in presence of the
heavy Pd atoms. Nevertheless, not having located them led to a negative
thermal parameter for the N atoms in the final refinement (Powder Diffraction,
10, 1995, 159-164).
t-AlF3
The refinement of the positions of the 11 independent
atoms as provided by the direct methods leads to the definitive result
with Rp = 9.44 % (background subtracted), RB = 4.06
%, RF =3.60 % (provided a preferred orientation is refined in
the [001] direction : talf34.html). Further improvement
could be obtained when refining anisotropic thermal parameters for all
atoms (justified because all atoms are light in this compound).
beta-BaAlF5
The refinement of the positions of the 13 independent
atoms by the Rietveld method leads to RP = 14.3, RB
= 11.1 and RF = 5.5 % (see baalf55.html).
A Fourier difference synthesis made by the SHELX76 program allows the location
of the lacking Al atom (see baalf56.html) well
positioned in an AlF6 octahedron. The structure appears now
complete as revealed by a STRUVIR plot, the Q2 and Q5 sites being attributed
to Ba atoms. This structure determination from the low resolution neutron
data may looks like a miracle. Use preferably X-ray data for determining
a structure containing heavy atoms.
Cimetidine C10H16N6S
Introducing the 17 atoms as refined by SHELXL-97 into a Rietveld
refinement by FULLPROF led to RP =
12.4 %, RB = 7.73 %, RF = 7.55 %. The C10N6S
part of the structure is complete. Comparing with the previously published
single crystal data shows that the origin was displaced by 1/2, 1/2, 1/2.
Most of the hydrogen atoms are then located by a Fourier difference synthesis
realized by SHELXL-97 on the new "|Fobs|" generated by FULLPROF
(cim6a.html). The best would be to add them in
the Rietveld refinement with constraints on C-H and N-H interatomic distances.
This synchrotron example does not present FWHMs as low as could be expected
from the latest experiments (0.008° 2-theta). The U, V, W profile
width values are 0.01176, -0.000481 and 0.00223 corresponding to FWHMs
as 0.043° 2-theta (at 10° 2-theta), 0.042° (22°), 0.048°
(46°), 0.069° (70°). This is not much better than the highest
performances attained by the
current in-laboratory diffractometers equipped with variable entrance
slits. No special difficulty was encountered so that there is no reason
for not attempting to solve much more complex structures from synchrotron
powder data if really the FWHMs decrease to 0.01° 2-theta. Moreover,
there is no reason for not attempting to solve structures as difficult
as the cimetidine one from good quality in-laboratory conventional powder
diffraction data.
