A TEST OF THE IMPORTANCE OF WEAK REFLECTIONS IN RESOLVING A SPACE-GROUP AMBIGUITY INVOLVING THE PRESENCE OR ABSENCE OF AN INVERSION CENTER

The structure of margarite, CaAl2[Al2Si2O10](OH)2, has been reported in space group C2/c, and in the corresponding non-centrosymmetric space group Cc. Previous refinements of margarite in space group Cc were marred by strong correlations affecting parameters that are inversion related in C2/c. Refinement of single-crystal X-ray diffraction data, collected with synchrotron radiation, converged without large correlations in Cc. The refinement was based on 4056 F(obs), without merging Friedel pairs, including all the weak reflections (R = 0.027). No atom in Cc is removed further than 0.08 angstrom from its corresponding position in C2/c. The R in space group C2/c, after merging of the Friedel mates, was 0.059 (2658 F(obs)). For the weak F(obs) the disagreement in space group C2/c is much worse than in Cc. This agrees with the waming that it is the weak F(obs) which are most sensitive to small non-centrosymmetric distortions [Schomaker & Marsh (1979). Acta Cryst. B35, 1933-1934]. Removing weak F(obs) from the data results in a data set resembling one that could have been collected using an X-ray tube (with omission of weak F(obs)). In the Cc model without weak F(obs) many of the correlation coefficients rose dramatically to values over 0.9, and consequently difficulties occurred in converging the refinement and the estimated standard deviations increased fourfold compared to the values obtained for refinement of the full data set. Therefore, if one wishes to resolve a space-group ambiguity: (1) one should collect precise data, and especially collect as many weak reflections as precisely as possible; (2) one should include all reflections in the refinement, even if this raises the R value - a more complete data set, with a higher R value may be more important in establishing the symmetry than a smaller data set with a lower R value; (3) when measuring at a synchrotron one should use a wavelength which emphasizes the anomalous-dispersion contribution in order to make the differences between the Friedel pairs more significant.