We have referred already (see p. 7) to the two principal methods of measuring a set of Bragg reflexions. The first is the inclination method, which is related to the photographic Weissenberg technique. The second, the normal–beam equatorial method, has no counterpart in photographic work. In this chapter we shall describe the diffraction geometry associated with these two methods and derive formulae for the setting angles of the crystal and detector, both in a general form and in various simplified forms for special settings and particular crystal symmetries. We shall then compare the two geometries and show how the special settings which are used in either method are related to one another. Finally, we shall discuss the problem of measuring several reflexions at the same time with a diffractometer.

It is necessary to describe first the geometrical requirements for setting the crystal and detector and for measuring the reflexion. Bragg's law imposes certain geometrical conditions on the positions of the crystal and the detector, and these conditions must be satisfied before the measurement begins. Once the crystal and detector are correctly set, the reflexion is measured by counting the number of diffracted X–ray quanta or slow neutrons received by the detector as the crystal rotates uniformly through the Bragg reflecting region. These geometrical considerations are best described in terms of the reciprocal lattice and the Ewald sphere of reflexion.