The minimum scan range and detector aperture as a function of specimen size in X-ray diffractometry

The theoretical functional relationship of scan range and detector aperture to (spherical) crystal size in respect of scattering angle θ in X-ray diffractometry for different scan modes is not clearly defined in the literature. It is shown that it is necessary to examine separately the factors determining the angular apertures of the beam incident on the crystal and of the beam diffracted from the crystal, and then the appropriate relationship is derived for a point source and a small spherical crystal for the ω-scan mode. The required aperture is shown to be 2a_ccos²θ, where a_c is the diameter of the crystal. Using (Δω, Δ2θ^(s)) component diagrams [Mathieson, (1983). Aust. J. Phys. 36, 79–83], the corresponding results are derived for the ω/θ- and ω/2θ-scan modes and the three results are shown to be consistent with the earlier deductions which yielded cos²θ for the ω-scan mode but not with those which yielded cos θ.