X-ray intensity statistics of a pair of related crystals

Abstract

We have been investigating the problem of the probability distributions connected with the X-ray intensities of two crystals. Two ideal situations may be considered: (a) when the two crystals are fully related, that is, when the atoms in one form a part of the atoms in the other; (b) when they are unrelated, that is, when the atoms in the two structures are in entirely different positions. It is of course assumed that the two unit cells are exactly the same or very nearly so. When a protein crystal and its heavy atom derivative form an isomorphous pair, they are related in the foregoing sense, and the present investigation has resulted in the formulæ which could be used to test the isomorphism of such a pair of crystals. The term 'relatedness' is used in preference to 'isomorphism' for the more general concept, following the suggestion of some senior crystallographers.