The use of integrals of the Airy diffraction intensity profile in X-ray topography of `spike' diffuse reflexions

The average radius of platelet-like defects in crystals may be estimated by the non-destructive technique of X-ray topography of `spike' diffuse reflections, applicable to platelet radii several orders of magnitude smaller than the resolution limit of conventional X-ray topographic techniques. With the most favourable diffraction geometry, the diffuse topograph image may be regarded simply as the convolution of the platelet number density projected along the diffracted beam direction with the Airy diffraction intensity pattern appropriate to the radius of individual platelets. Different integrals of the Airy diffraction intensity profile are involved in photometric traverses of `spike' section topographs and of `spike' projection topographs. The required integrals are evaluated and discussed.