Abstract
By integrating joint probability distributions of two related invariant phases with respect to one of the variables over the range 0 to π, enantiomorph-dependent phase indications may be obtained. In the present paper the full potential of such a strategy is described. For probability distributions correct up to and including terms of order N-1, all cases of interest appear to consist of combinations of two invariants with one or two structure factors in common. For each case the joint probability distribution of the phases of such a pair of invariants, given a number of suitable structure-factor amplitudes, is derived. Subsequently, all these distribution functions are integrated from 0 to π with respect to one or other variable, thus exploring the full range of enantiomorph-dependent distributions. The resulting expressions are grouped together according to whether the chosen enantiomorph definer is a triplet, quartet, quintet or higher-order invariant, thereby facilitating their future implementation in direct-methods procedures.
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