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

A straightforward method is presented for calculating the angle settings of a five-circle diffractometer used in surface diffraction experiments at synchrotron sources. Unlike the conventional four-circle unit, the five-circle diffractometer considered herb allows detector motion perpendicular to the vertical scattering plane. The calculation method described here differs from previous ones for other diffractometers by resolving both the vector G to be accessed in the sample's reciprocal space and the wavevector transfer Q into components parallel and perpendicular to a surface of interest. These vector components of G are a convenient means of describing the sample's initial orientation in the laboratory coordinate system. The corresponding components of Q allow two constraints on the diffraction condition to be simply expressed in the laboratory frame used throughout the calculations. One constraint is considered from each of the two sets: (1) fixing the incident or exit angle of the X-ray beam with respect to the surface of interest; and (2) fixing the angle that the exit beam makes with the vertical scattering plane or requiring either the diffraction rod of interest or the normal to the cut surface of the crystal to remain in the horizontal plane. This method of calculating the angle settings can also be applied to other five-circle diffractometers as well as to four-circle diffractometers.