Strategy

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Strategy

Structure solution from powder diffraction data is a technique that has seen rapid development during the decade of the 1990's. It has come about for several reasons:

Firstly, the pattern decomposition methods described in the next few pages have allowed the intensities of a large numbers of reflections to be obtained automatically without recourse to individual peak-fitting procedures.

Secondly, the resolution and performance of powder diffractometers at X-ray synchrotron sources now allows exceptionally high-quality powder data to be obtained routinely. There have been relatively few examples of so-called ab-initio structure solution from powder neutron data because of the much lower resolution of most neutron powder diffractometers and the fact many of the materials investigated have been organic (i.e. contain many H atoms), a direct result of the strong interest in knowing the crystal structures of materials of pharmaceutical relevance.

It should be obvious that the above procedure is not totally automatic and does require some significant intelligent input from the crystallographer. Even the first step is non-trivial in that all too often powder diffraction data is collected for one purpose, and then attempts are made to use it for another. In this instance, it may make more sense to collect more than one data set: for example, indexing requires accurate and precise peaks positions, especially for the large d spacings, while structure solution requires reliable intensities, and structure refinement requires high-quality small d spacing (i.e. high angle for angle-dispersive) data.

For success in SDPD, this first step is crucial. The strategy of data collection for SDPD is quite different from that, say, for qualitative analysis. In particular, for structure solution it is important that all peaks in the powder pattern are collected with similar statistics. Whether the X-ray data is collected in the laboratory or at a synchrotron source, variable count-time data is the optimum strategy for SDPD. Variable count-time acquisitions have been discussed already.

In addition, high-resolution data is required, i.e. narrow 2θ peak widths. Clearly, synchrotron data will normally be better here, though many structures have been determined from high-quality laboratory data. Although it may be stating the obvious, high sample purity is required in order to have a probability of success in SDPD.

One potential adverse effect of using very high-resolution powder diffractometers is that any impurity peaks from the sample are more easily seen. This can have the knock-on effect concerning pattern indexing since success or failure in indexing is seriously effected by the absence or presence of spurious 2θ values from extraneous material in the sample. For a 100% pure sample, indexing is best effected by including all weak low-angle peaks. However, if the pattern fails to index, then sometimes it is these same peaks that should be omitted in case they are due a contaminating impurity phase in the sample (as discussed previously in pitfalls in indexing).

The one step in the whole procedure that is difficult to automate reliably is the choice of space group. In a single-crystal experiment there is far less ambiguity in the choice of space group, partly because the Laue class can be measured directly. This is not the case for powders. Indexing can (in most cases) distinguish the crystal system as one of triclinic, monoclinic, orthorhombic, tetragonal, cubic, rhombohedral, or trigonal/hexagonal. In addition, lattice centrings such as A, B, C, I, F, or R can usually be determined reliably since they have a big effect on the density of observed reflections (as discussed earlier in space-group determination).

What may not be so clear is the presence of glide planes since apart from the very-lowest angle reflections, the few hk0 (or h0l, 0kl, etc.) reflections may overlap with other hkl reflections. There is even more difficulty in ascertaining the presence or absence of screw axes since the average powder pattern is likely to contain only a few reflections of the type h00 (or 0k0, etc.). The paucity of data therefore results in real ambiguities in the choice of space group.

To some extent, ambiguity can be avoided by practical considerations:

Firstly, if there is a choice between a commonly-observed space group and a rare one as based on occurrence in, say, the Cambridge Crystallographic Database (e.g. Cmca versus Cmcm), then the best approach will be to attempt to solve the crystal structure using the more common space group first.

Secondly, there may be molecular packing considerations to take into account. For molecular systems (i.e. most organic and organometallic compounds), the number of molecules, Z, per unit cell can usually be estimated from the unit cell volume. A very rough estimate is given formulae such as Z = V / (18 * N), where the units of V are ų and N is the number of non-hydrogen atoms in the molecule. The value of 18 used in this formula is an empirical observation that works better with some substances than with others: it does not work well for: compounds with an abnormal number of hydrogen atoms, such as methane (CH₄), some organometallic compounds with large metal clusters, or framework structures, such as diamond.

Cimetidine, as discussed in more detail on the CCP14 web site (see external links), is a suitable example. This drug molecule has the chemical formula C₁₀H₁₆N₆S and a monoclinic form with unit cell parameters a = 6.823 Å, b = 18.815 Å, c = 10.392 Å, β = 106.44°, V = 1279.5 Å³, space group P2₁/c (see external links). From the formula, N = 17, so an estimated value of Z is 1279.5 / (18 * 17) = 4.18 ≈ 4. Given that the number of symmetry equivalent positions in this space group is 4, then this would suggest that the number of molecules in the asymmetry unit, Z′, is equal 1, which is the most commonly observed value.

As an example of ambiguity, consider the case of a molecular structure for which Z = 8 and the reflection conditions are ambiguous and indicate either Pnma or Pbca. (This situation can easily happen due to overlap of key reflections in the powder diffraction data.) Both space groups are observed to occur frequently for molecular compounds so both may seem equally likely. However, for space group Pbca, one molecule in the asymmetric unit is implied whereas for Pnma the presence of the mirror plane would suggest either two molecules related by mirror symmetry (an unlikely event given packing considerations) or two molecules per asymmetric unit with the mirror plane passing through both molecules (which is equally unlikely). Thus, the first choice of space group is Pbca in this instance. Conversely, if the estimated value of Z were equal to 4, and the molecular symmetry included a mirror plane, Pnma would be the most likely space group in this example.

However, there is another solution to the problem of space-group determination, and this involves whole pattern fitting in which the diffraction profile is fitted in the absence of a structural model, but in the presence of the reflection conditions of the various space groups under consideration. Whole pattern fitting is also used to routinely extract the intensity of individual reflections and to test for consistency with the assigned space-group symmetry: this forms the subject of the next few pages, as does structure solution.

Finally, once a structural model has been established, the crystal structure can be refined by the Rietveld method, which has been the subject of a previous section of the course, and if successful publication (and fame) may follow.

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