ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0108767301003762
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