Angle calculations for a five-circle diffractometer used for surface X-ray diffraction

The basic equations are derived for the calculation of the angle settings of a five-circle diffractometer used for surface X-ray diffraction. This is done for a specified angle of incidence. An additional constraint that may be imposed is the horizontal alignment of the diffraction rods to match the divergence of the synchrotron X-ray source or the horizontal setting of the physical surface normal. Alignment procedures and the derivation of the orientation matrix are discussed.