Apparatus function of a five-crystal X-ray diffractometer with a four-reflection monochromator

An apparatus function is derived in order to separate the influences of the diffractometer from those of the investigated sample crystal. Then, rocking curves can be calculated by the convolution of the apparatus function with the reflection profile of the sample. The resolution of the diffractometer is achieved by examining the dependence of the apparatus function on the Bragg angle of the sample. The characteristics of the primary beam leaving the monochromator are described by the transmittance. This transmittance forms the basis for the graphical understanding of the resolution of the diffractometer. The mathematical treatment is sufficiently flexible to be adapted to other multiple-crystal arrangements and includes the two polarizations. Furthermore, the correlation between the resolutions of the diffractometer and the coherence of the primary beam is discussed. The formalism, utilizing the apparatus function, is applied to measured rocking curves of a silicon crystal and shows an almost perfect accordance between theory and experiment. All necessary reflection profiles are calculated according to the dynamical scattering theory of X-rays.