The determination of a crystal structure normally proceeds in three distinct stages. The first is the measurement of the intensities of the Bragg reflexions and the calculation from them of amplitudes, reduced to a common scale and corrected for various geometrical and physical factors. These amplitudes are known as ‘observed structure amplitudes’ or ‘observed structure factors’. The second stage is the solution of the phase problem: the phases of the reflexions cannot be measured directly, and yet they must be derived in some way before the structure can be solved by Fourier methods. Because of uncertainties in the amplitudes and phases, this first structure is only approximately correct. The third stage in the structure determination consists of refining the approximate atomic positions so as to obtain the best possible agreement between the observed structure factors and the ‘calculated structure factors’, that is, those calculated from the approximate atomic positions of the successive stages of refinement.

This book describes counter methods of obtaining the set of observed structure factors of a single crystal, and so is concerned with the first stage only. The rapidly developing interest in automatic methods of collecting structure–factor data, and in measuring intensities to a high level of accuracy, have stimulated the development of counter methods. Photographic methods are still widely used in X–ray crystallography, but in neutron diffraction the single crystal diffractometer has remained the basic instrument for measuring neutron structure amplitudes since systematic studies began in the early 1950's.