Direct methods for incommensurately modulated structures. On the applicability of normalized structure factors
De Gelder R, Israel R, Lam EJW, Beurskens PT, vanSmaalen S, Fu ZQ, Fan HF
ACTA CRYSTALLOGRAPHICA SECTION A 52: 947-954 Part 6 NOV 1 1996

Abstract:
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 invariants E(-H)E(H')E(H - H'), where a and H' are reciprocal vectors of main and/or satellite reflections, approximately has the same functional form as the Cochran distribution but triplet phase relations are relatively less reliable when satellites are involved. The use of the multidimensional Sayre equation for the determination of phases of satellite reflections [Hao, Liu & Fan (1987). Acta Cryst. A43, 820-824; Fu & Fan (1994). J. Appl. Cryst. 27, 124-127] is not improved by using normalized structure factors instead of ordinary structure factors.