Angular distribution of reflections in Laue diffraction

An analysis is presented of the angular distribution of reflections in Laue diffraction, with particular application to the spatial overlap problem in synchrotron macromolecular crystallography. Spatial overlaps of spots on the detector occur when the angular separations of adjacent diffracted beams are very small. The maximum density of spots occurs at θ_c = sin⁻¹ (λ_minD*/2) and the majority of spots in this region of θ have short wavelengths. At higher θ the mean wavelength increases steadily. On a flat detector the spots of a Laue pattern lie on intersecting conics. Each conic corresponds to a zone plane of reciprocal-lattice points (RLPs), whose zone axis is represented by a point uvw in the direct lattice. If P[uvw] is the distance of uvw from the origin and ψ is the angle between the zone axis and the incident beam, then the average spacing between spots on a conic is proportional to P sin ψ and the width of the clear gap bordering a conic is proportional to 1/P. This explains why the densest conic arcs are flanked by the larger clear spaces and shows that local spatial overlap problems are inherently one dimensional in character. The vast majority of small angular separations are associated with pairs of adjacent single-order reflections. Multiples have larger separations from their nearest neighbours, which are always singles. The detailed analysis shows the factors that govern the spatial overlap of spots and indicates tactics for experimental design. The analysis is also relevant to polychromatic neutron diffraction.