Towards General Diffractometry. I. Normal-Beam Equatorial Geometry

Eulerian and κ goniometers, as well as real diffractometers with unavoidable misalignments of their shafts, are described as special cases of a general four-circle normal-beam equatorial diffractometer. The performance of these instruments can be improved by defining rotations about their real axes. Methods for transformation of the setting angles between the geometries based on different goniometer axes and procedures for positioning reflections are described. Analytical solutions for the transformations between Eulerian and the general version of the normal-beam equatorial diffractometer are presented.