Commensurate structures diffraction properties

In terms of diffraction properties and structural properties, a commensurate inclusion compound behaves as a conventional crystal. The periodicities of the host and guest molecules within the inclusion compound are described by a common three-dimensional (3D) periodic lattice, and the symmetry of the structure is described by a conventional 3D space group. Correspondingly, all diffractionmdLXima. in the diffraction pattern are described by a single 3D periodic reciprocal lattice. As discussed in more detail below, the inability to rationalize all diffraction maxima in the diffraction pattern of an inclusion compound by a single 3D periodic reciprocal lattice often provides the first indication that the structure may be incommensurate. 

The very existence of the powder diffraction pattern, which is an experimentally measurable function of the crystal structure and other parameters of the specimen convoluted with various instrumental functions, has been made possible by the commensurability of properties of x-rays and neutrons with properties and structure of solids. As in any experiment, the quality of structural information, which may be obtained via different pathways (two possibilities are illustrated in Figure 2.62 as two series of required steps), is directly proportional to the quality of experimental data. The latter is usually achieved in a thoroughly planned and well executed experiment as will be detailed in Chapter 3. Similarly, each of the data processing steps, which were described in this chapter and are summarized in Figure 2.62, requires knowledge, experience and careful execution, and we will describe them in practical terms in Chapters 4 through 7. 

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