The application of the principles of physical optics to crystal-structure determination

Abstract

The analogy between the diffraction of light by a set of holes, and the diffraction of X-rays by a set of atoms can be exploited in solving many different types of X-ray diffraction problem. A special instrument has been built to obtain diffraction patterns rapidly, making possible several different approaches to the determination of crystal structures. Of particular importance is that involving the 'optical transform' of a molecular representation. Consideration of the optical transform, which is closely related to the Fourier transform, can, for simple space groups, lead directly to the crystal structure. For more complicated space groups, optical transforms of molecules in different orientations have to be combined, and some rules governing their combination are given. The discussion includes several examples of structures which have been determined by optical-transform methods. These methods require the presentation of the X-ray data in the form of a weighted reciprocal lattice, from which information can often be obtained directly. For several new structures such information as the separation of two similarly oriented molecules, or the orientation of hexagonal arrangements of atoms, has been deduced by considering the weighted reciprocal lattice alone. In some cases this led to the complete structure; in others it was a valuable supplement to the optical transform method. Despite the lack of quantitative accuracy, optical methods can be of use in refining approximate structures by ordinary Fourier methods. Examples are given of the determination of the relative phase angles of the reflexions of both centrosymmetric and non-centrosymmetric structures. The relationships between optical methods and more conventional methods of structure determination are discussed.