The role of the crystal rotation axis in experimental three- and four-beam phase determination

The geometry of four-beam diffraction and procedures for generating it systematically are described. These utilize relatively simple Renninger-type experimental arrangements. The four reciprocal-lattice points involved in each four-beam interaction are located at the comers of rectangles or symmetrical trapezoids in reciprocal space. One of the sides, or a diagonal, of each such quadrilateral serves as the axis of the azimuthal rotation of the crystal. Experiments designed to compare the relative merits of different types of rotation axes have been carried out. It is found that axes of twofold (or higher) symmetry provide advantages over alternate arrangements for experimental phase determination. Four-beam interactions are then generated systematically and in greater abundance than in all other n-beam interactions combined (n > 2). Such interactions usually provide stronger phase indications than comparable three-beam interactions. The experiments also showed that, although the phase of an 'invariant' quartet is clearly invariant to the choice of unit-cell origin, it is not necessarily invariant to a change of rotation axis from one two-fold axis to another.