More about C1 and C2

The manuscript on the beta-Ba3AlF9 structure was first submitted to Nature, and found to be controversial. I was suggested to resubmit to Nature an article for their Scientific Correspondence with the controversial part and to submit to a more specialized journal the details of the structure determination. So I did. The experimental part was accepted by J. Solid State Chem. a week after the submission. The controversial part was finally rejected again by Nature. However I can't resist to report the original text here, dated February 1993. Was the "peer review" of this paper biased ? Mmmm, maybe, it was rejected by Nature on the suggestion by A.K. Cheetham that the conclusions were not serious. Was it serious to ask to A.K. Cheetham to make comments on a paper suggesting that his own results obtained from an elephant (a synchrotron) could have been obtained from a mouse (a conventional in-laboratory powder diffractometer) ? I don't think so.

Synchrotron is good for powders, conventional X-rays too !

SIR _ The structure of Ga2(HPO3)3.4H2O, determined by the complementary use of synchrotron X-ray and neutron-diffraction powder methods1, was presented as "considerably more complex than any other unknown structure solved using these techniques" (29 atoms in general position in the unit cell, 86 atomic coordinates to be refined). Structures of this complexity can be solved without resorting to synchrotron sources. This is demonstrated by the structure determination of gamma-Ba3AlF9 from conventional X-ray powder data2 (29 independent atoms, 74 coordinates refined).

Ab initio structure determination from powder data is a very young specialty. As no more than 50 non-trivial structures have been determined since 1977, the complexity record may be broken weekly. What is a complex structure? A definition may be: one we could not determine. Unless all atoms have similar scattering factors, structure determination feasibility is not conditioned by the whole structure complexity but by the possibility of access to a minimal fragment allowing the start of atomic coordinates refinement. The structure is completed then by Fourier syntheses. A complexity criterium could be based on the full number of independent atoms (C1). Obviously, another should be based on the starting structure-fragment size (C2). Following C1, gamma-Ba3AlF9 and the phosphite are bracketed equal. In the C2 sense, the fluoride, having 7 Ba atoms simultaneously located by the direct methods, is the winner (2 Ga atoms for the phosphite).

    Consider now (NH4)4[(MoO2)4O3](C4H3O5)2, the first non-trivial structure determined from Guinier-Hägg data3. The minimal fragment corresponded to 2 Mo atoms (Patterson). The final refinement included 16 atoms against 17 located from the synchrotron data in ref. 1. If hydrogen atoms were located from neutron data, the C1 score could be 31 (at least). So this case is virtually more complex than the phosphite one according to C1, both are of equal merit according to C2. The most complex structures top list, following C2, determined either from conventional (CX) or synchrotron X-rays (SX), is short. The starting structure-fragment corresponded to 9 independent atoms for NiV2O6 (CX4) and clathrasil Sigma-2 (SX5, cited in ref. 1 as the most complex before the phosphite), 11 for t-AlF3 (corresponding to the whole structure, CX6), 12 for Cr8O21 (CX7) and 14 for beta-VO(HPO4).2H2O (CX8). Some of these cases are also among the best according to C1 with a total of, respectively 14, 17, 11, 15 and 18 independent atoms. One must not forget (AlPO4)3.(CH3)4NOH (CX9) which obtained a score of 26 (C1) and 6 (C2). Conventional sources dominate the market, neutron powder diffraction is out of the competition.

    I estimate the upper limits of feasibility to be 1.5 to 2 times more complex than the present winners, according both criteria, for in-laboratory apparatus and six times more for synchrotron sources (500 coordinates refinable; 5000 reflections extractable). These limits are established by simple extrapolation from the gamma-Ba3AlF9 structure determined from a powder pattern having reflections with a minimal full width at half maximum near 0.12°(2). FWHM of 0.08° or even 0.06° are attainable with CX (but difficulties to model profile shapes are the price to pay), and 0.02° or even lower with SX. Of course, such limits, although respectable, are considerably lower than those admitted for single crystal diffraction studies. Also accuracy from powder data (unidimensional information) is far behind that expected from modern single crystal data (tridimensional), although it has reached the level which was obtained from single crystal film data in the sixties. Inaccuracy in bond lengths may be considered as tolerable if the crystal chemistry rules are respected, and particularly if there is no other way to obtain the structure.

   Synchrotron sources are unrivalled either for accuracy level in refinement or ease in structure determination, this cannot be questioned. Nevertheless, conventional sources will continue to dominate the market (in quantity, if not in complexity) for a simple reason: researchers who have not a synchrotron in their lab are numerous. With the opening of the ESRF just a few months away, future users of Big Science must know that any experience proposal of the kind discussed here will be rejected by the advisory board if a serious preliminary study has not been performed by using conventional X-rays. Clearly, most problems will be solved 'at home', reserving the rather expansive synchrotron experiments to highly 'complex' cases or to accuracy improvement.

Armel Le Bail

Laboratoire des Fluorures, CNRS-URA 449,
Université du Maine,
72017 Le Mans, France

 1. Morris, R.E., Harrison, W.T.A., Nicol, J.M., Wilkinson, A.P. & Cheetham, A.K. Nature      359, 519-522 (1992).
 2. Le Bail, A. J. Solid State Chem., in press.
 3. Berg, J.-E. & Werner, P.-E. Zeits. krist. 145, 310-320 (1977).
4. Le Bail, A. & Lafontaine M.-A. Eur. J. Solid State Inorg. Chem. 27, 671-680 (1990).
5. McCusker, L.B. J. Appl. Cryst. 21, 305-310 (1988).
6. Le Bail, A., Fourquet, J.L. & Bentrup, U. J. Solid State Chem. 100, 151-159 (1992).
7. Norby, P., Christensen, A.N., Fjellvag, H. & Nielsen, M. J. Solid State Chem. 94, 281-293      (1991).
8. Le Bail, A., Ferey, G., Amoros, P., Beltran-Porter, D. & Villeneuve, G. J. Solid State      Chem. 79, 169-176 (1989).
9. Rudolf, P.R., Saldarriaga-Molina, C. & Clearfield, A. J. Phys. Chem. 90, 6122-6125      (1986).

Submitted to Nature as an article for their Scientific Correspondence, February, 1993, and rejected.