INTENSITY STATISTICS AND DIRECT METHODS FOR INCOMMENSURATELY MODULATED CRYSTALS. Erwin J. W. Lam (Crystallography Laboratory, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands)

The application of direct-methods procedures for structure analysis to incommensurately modulated crystals is by no means trivial because, due to atomic modulations, the X-ray diffraction intensities of these crystals show different statistical behavior when compared to nonmodulated crystals. This is especially true for the satellite reflections. Although a study by Hao et al. (1987) showed that the Sayre equation can be applied successfully to X-ray diffraction data of incommensurately modulated crystals, this procedure employed structure factors (F) instead of normalized structure factors (E) because a definition of the latter was not at hand at the time.

It was shown by Lam et al. (1992, 1994) that average X-ray diffraction intensities for modulated crystals can be estimated from a Wilson-like plot in which the atomic modulations are taken into account by introducing overall modulation amplitudes. E values calculated from these average intensities were shown to be applicable in direct-methods procedures using the triplet-phase relation or the Hughes-Sayre equation (de Gelder et al., 1996).

Gelder, R. de, Lam, E. J. W., Israël, R., Beurskens, P. T., Smaalen, S. van, Fu, Z.-Q. & Fan, H.-F. (1996). Acta Cryst. A52. In press.

Hao, Q., Liu, Y.-W. & Fan, H.-F. (1987). Acta Cryst. A43, 820-824.

Lam, E. J. W., Beurskens, P. T. & Smaalen, S. van (1992). Solid State Commun. 82, 345-349.

Lam, E. J. W., Beurskens, P. T. & Smaalen, S. van (1994). Acta Cryst. A50, 690-703.