A (2+3)-type surface diffractometer: Mergence of the z-axis and (2+2)-type geometries

It is shown that the addition of an azimuthal detector rotation to a (2+2)-type diffractometer makes it fully equivalent to a z-axis type. Using this equivalence, the geometric correction factors for this (2+ 3)-type diffractometer, which are needed to obtain structure factors from measured integrated intensities, are derived. The (2+3)-circle diffractometer combines the ideal resolution behaviour of a z-axis diffractometer with the mechanical simplicity and range of a (2+2)-circle diffractometer. For sample alignment, two additional degrees of freedom are needed, leading to a total of seven circles.