Vacancy tetrahedral

The occurrence of vacancies requires the adoption of two definitions of the degree of inversion, depending on the hypothesis made about the vacancies. Tetrahedral hypothesis . ft measures the concentration of indium in tetrahedral positions with respect to the maximum possible concentration. Octahedral hypothesis /3 measures the concentration of magnesium in octahedral positions with respect to the maximum possible concentration. 

The extent of substitution of magnesium and siUcon by other cations in the chrysotile stmcture is limited by the stmctural strain that would result from replacement with ions having inappropriate radii. In the octahedral layer (bmcite), magnesium can be substituted by several divalent ions, Fe ", Mn, or Ni ". In the tetrahedral layer, siUcon may be replaced by Fe " or Al ", leaving an anionic vacancy. Most of the other elements which are found in vein fiber samples, or in industrial asbestos fibers, are associated with interstitial mineral phases. Typical compositions of bulk chrysotile fibers from different locations are given in Table 3. 

Tetrahedral and octahedral interstitial holes are formed by the vacancies left when anions pack in a ccp array, (a) Which hole can accommodate the larger ions (b) What is the size ratio of the largest metal cation that can occupy an octahedral hole to the largest that can occupy a tetrahedral hole while maintaining the close-packed nature of the anion lattice (c) If half the tetrahedral holes are occupied, what will be the empirical formula of the compound MVAV, where M represents the cations and A the anions ... 

Recently lithium insertion in quaternary thiospinels like (Cug.giGeDg.ggjga [Fe4Sni2]i6dS32 and (Cu4.xGen3o+x)8a[Co4Sni2]i6dS32 have been reported [15, 16]. It is believed that the vacancies in the tetrahedral 8 a sites result from a topotac-tic substitution of four Cu ions by one Ge ion. 

The most stable cluster consists of an aggregation of four cation vacancies in a tetrahedral geometry surrounding an Fe3+ ion, called a 4 1 cluster. Cations in the sodium chloride structure normally occupy octahedral sites in which each metal is coordinated to six nonmetal atoms. The central Fe3+ ion in the 4 1 cluster is displaced into a normally unoccupied tetrahedral site in which the cation is coordinated to four oxygen ions. Because tetrahedral sites in the sodium chloride structure are normally empty, the Fe3+ is in an interstitial site. Equation (4.1) can now be written correctly as... 

Sodium chloride structure crystals have all octahedral sites filled, and so cation diffusion will be dependent upon vacancies on octahedral sites. In the zinc blende (sphalerite) structure, adopted by ZnS, for example, half of the tetrahedral sites are empty, as are all of the octahedral sites, so that self-diffusion can take place without the intervention of a population of defects. 

In terms of formal point defect terminology, it is possible to think of each silver or copper ion creating an instantaneous interstitial defect and a vacancy, Ag and VAg, or Cu and Vcu as it jumps between two tetrahedral sites. This is equivalent to a high and dynamic concentration of cation Frenkel defects that continuously form and are eliminated. For this to occur, the formation energy of these notional defects must be close to zero. 

Interstitial sites are defined as those that would usually be empty in an ideal structure. Occasionally in real structures, ions may be displaced from their lattice sites into interstitial sites Frenkel defect formation). Once this happens, the ions in interstitial sites can often hop into adjacent interstitial sites. These hops may be one stage in a long range conduction process. A schematic example is shown in Fig. 2.1(h) a small number of Na ions are displaced into the tetrahedral interstitial sites and can subsequently hop into adjacent tetrahedral sites. It should be noted, however, that while a small number of Frenkel defects may form in NaCl, conduction is primarily by means of vacancies whereas in some other structures, e.g. AgCl, Frenkel defects do predominate. 

A similar situation is illustrated by Bi203. The high-temperature 5-Bi203 phase has a face-centred-cubic Bi-atom array with O atoms occupying in a disordered manner three-quarters of the tetrahedral interstices. At lower temperatures, the anion vacancies become ordered on these sites, and the energy splitting AH of the vacant and occupied sites varies with the degree of order as described by equation (3.23). 

Figure 1. 7-LiJV[02 (layered) and 5-LiM204 (spinel) structures (M = 3d transition metal). M occupy octahedral sites in both structures. In 7-LiJV[02, M and Li (and/or vacancies) alternately occupy (111) planes of the ccp oxygen sublattice. The (111) plane parallel to the M layers is indicated by the black line between the layered and spinel structures. The [111] direction is shown as well. In s-Lii/2Mn02, (111) planes with three-fourths of the Mn alternate with (111) planes with one-fourth of the Mn. Li ions occupy tetrahedral sites in the planes with one-fourth of the Mn. The planes with three-fourths of the Mn are free of Li. In fully lithiated spinel-like 5-Li2Mn204, the Li move into octahedral sites. Three-fourths of the Li are in the (111) plane with one-fourth of the Mn, and one-fourth of the Li are in the plane with three-fourths of the Mn.

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