Incommensurate 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. 

Barandiaran et al. (1987) reported studies of the magnetic properties of RNi2Si2 compounds where R = Pr, Nd, Gd, Tb, Dy, Ho, Er and Tm. The results of resistivity, neutron diffraction, susceptibility and magnetization experiments are summarized in table 19. For all compounds the antiferromagnetic ordering of the incommensurate structure is observed. The magnetic moment of the Ian-... 

In concluding this section in which some properties of modulated structures and of quasicrystals have been considered, we underline that the characteristics of these two types of structures do not coincide. Incommensurately modulated structures show main and satellite diffractions, an average structure and crystallographic point symmetry. The quasicrystals have no average structure, non-crystallographic point symmetry, and give one kind of diffraction only. 

General speaking, a crystal defect is a type of microstructure in which the parent crystal structure is locally disturbed. Such a microstructure carmot be described by a superstructure, even by an incommensurate superstructure. Since the defect areas are usually very small, they may not be detected by XRD and neutron diffraction methods. HRTEM is the most powerful technique to detect them and to investigate their relation with the parent crystals. The defects can greatly change the properties of an oxide. Some examples of the common defects in oxides are given in the following sub-sections. 

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