Acta Cryst. (2001). A57, 461-472 [doi:10.1107/S0108767301003762]
Abstract: In 1993, alternative normalized structure factors for incommensurately modulated structures were defined [Lam, Beurskens & van Smaalen (1993). Acta Cryst. A49, 709-721]. The probability distribution associated with the structure invariants E(-H)E(H')E(H - H') has approximately the same functional form as the Cochran distribution. It was shown, however, that triplet-phase relations are relatively less reliable when satellites are involved [de Gelder, Israël, Lam, Beurskens, van Smaalen, Fu & Fan (1996). Acta Cryst. A52, 947-954]. In the present paper, an alternative approach is presented: instead of studying the distribution of a three-phase invariant, the probability distribution of the phase sum of two first-order satellite reflections (h,k,l,1 and h',k',l',-1) has been derived under the assumption that the phase of the associated main reflection (h 
h',k k',l l',0) can be calculated from the known main (or averaged) structure. Intensive tests with randomly generated artificial structures and one real structure show a significant improvement of direct-methods phase-sum statistics. Functional similarities with conventional direct methods, employing normalized structure factors and the Cochran distribution, are discussed.
Online 21 June 2001
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