Choice of scans in X-ray diffraction

In a recent paper (Werner, S. A. Acta Cryst. (1971). A27, 665) it was pointed out that the choice of scans in a neutron diffraction experiment should be based on the criterion that the diffracted beam enters the detector on its centerline for each angular setting of the crystal. The same criterion should be applied in X-ray diffraction. Since the spectral distribution of a source of X-rays and neutrons is quite different, conclusions regarding the optimum coupling between the detector and crystal motions are different in these two cases. In this paper, formulas are derived (within the framework of certain gaussian approximations) for the optimum scanning ratio g in equatorial plane X-ray diffraction experiments on single crystals. For the case when a monochromator is not used, g is independent of scattering angle 2θ_B for a large range of instrumental parameters and Bragg angles θ_B. It is found that a θ–2θ scan is essentially never advisable. An expression for g is derived for the case when a planar monochromator is used in symmetric Bragg reflection. The optimum scan is found to depend on the scattering angle, but not in such a marked way as in the neutron case. Coupling the detector and crystal motions in the manner suggested allows one to decrease the acceptance aperture to its minimum width, thus keeping the background due to thermal diffuse scattering (TDS) and incoherent scattering as low as possible.