Section 2.2.1.4. Angular distribution of reflections in Laue diffraction

There is an interesting variation in the angular separations of Laue reflections that shows up in the spatial distributions of spots on a detector plane (Cruickshank, Helliwell & Moffat, 1991). There are two main aspects to this distribution, which are general and local. The general aspects refer to the diffraction pattern as a whole and the local aspects to reflections in a particular zone of diffraction spots.

The general features include the following. The spatial density of spots is everywhere proportional to 1/D², where D is the crystal-to-detector distance, and to 1/V*, where V* is the reciprocal-cell volume. There is also though a substantial variation in spatial density with diffraction angle ; a prominent maximum occurs at

Local aspects of these patterns particularly include the prominent conics on which Laue reflections lie. That is, the local spatial distribution is inherently one-dimensional in character. Between multiple reflections (nodals), there is always at least one single and therefore nodals have a larger angular separation from their nearest neighbours. The blank area around a nodal in a Laue pattern (Fig. 2.2.1.2) has been noted by Jeffery (1958). The smallest angular separations, and therefore spatially overlapped cases, are associated with single Laue reflections. Thus, the reflections involved in energy overlaps – the multiples – form a set largely distinct, except at short crystal-to-detector distances, from those involved in spatial overlaps, which are mostly singles (Helliwell, 1985).

From a knowledge of the form of the angular distribution, it is possible, e.g. from the gaps bordering conics, to estimate and λ_min. However, a development of this involving gnomonic projections can be even more effective (Cruickshank, Carr & Harding, 1992).