ON INTEGRATING DIRECT-METHODS AND ISOMORPHOUS REPLACEMENT TECHNIQUES .1. A DISTRIBUTION FUNCTION FOR QUARTET INVARIANTS

For two isomorphous structures, the joint probability distribution fun ction of seven pairs of structure factors has been derived. The vector ial indices of the reflexions are the basis and the cross vectors of a quarter invariant. The atomic positions are assumed to be the primiti ve random variables. The characteristic function of the distribution i s expanded in a Gram-Charlier series: the distribution of the structur e factors is first obtained by a Fourier transform operation and then modified into the exponential form.