X-ray diffraction, optical transforms and fibre structures

Abstract

The classical approach to the interpretation of X-ray diffraction patterns of single crystals is through Bragg's law and it leads, all too easily, to the notion that each “reflection” is a separate entity in a list of data. The adoption of the Fourier transform approach—which incidentally also derives from Bragg's ideas—leads to a much more physical view of the diffraction process. X-ray diffraction is then seen as a branch of microscopy. Studies of the Fraunhofer diffraction patterns in visible light (optical transforms) of masks of holes representing the unit-cell contents of a crystal provide a visual means of testing the validity of trial structures. Also—because they are visual—they facilitate the rapid acquisition of experience of relationships between objects and their diffraction patterns. The technique extends quite naturally to imperfectly crystallized material. Its particular value in fibre studies is that masks can be made to represent extremely complex atomic arrangements and, once made, their patterns can be observed instantaneously. It thus becomes reasonable to test even wildly improbable ideas without wasting much time. It also seems practicable to use the optical approach to studies of fibre photographs by posing the question “What kind of diffracting object produced this X-ray pattern?” rather than the more specific question usually asked “Is this X-ray photograph consistent with the particular model being proposed?”.