DIRECT-METHODS FOR INCOMMENSURATELY MODULATED STRUCTURES - ON THE APPLICABILITY OF NORMALIZED STRUCTURE FACTORS

The recently defined normalized structure factors for incommensurately modulated structures [Lam, Beurskens & van Smaalen (1993). Acta Cryst . A49, 709-721] have been subjected to extensive tests regarding their applicability in direct methods for phase determination. It is shown that the probability distribution associated with the structure invari ants E(-H)E(H')E(H - H'), where a and H' are reciprocal vectors of mai n and/or satellite reflections, approximately has the same functional form as the Cochran distribution but triplet phase relations are relat ively less reliable when satellites are involved. The use of the multi dimensional Sayre equation for the determination of phases of satellit e reflections [Hao, Liu & Fan (1987). Acta Cryst. A43, 820-824; Fu & F an (1994). J. Appl. Cryst. 27, 124-127] is not improved by using norma lized structure factors instead of ordinary structure factors.