Vacancy octahedral

Although the microdomain description is adequate for many compounds, for some phases a more accurate picture is obtained if they are described in terms of two (or more) mutually interacting subsystems. The distribution of atom/vacancies, octahedral tilt, distortion or similar features may not follow a strict crystallographic repeat distance but may be modulated into a wave-like repetition, the wavelength of which is a function of composition, preparation conditions and so on. As an example, suppose that the unit cell for a perovskite has instead of octahedra with alternate tilts +

[Pg.75]

The second type of covalent Ti(3rf)-Ti(3(i) bonds is formed between Tit" 3dy orbitals of Ti atoms surrounding a vacancy. Because the number of pd bonds in which Ti -3rf , 3dy orbitals are involved is reduced in the substoichiometric compounds, the Ti -34z and 3dy orbitals can form better overlapping (stronger) Ti -Ti " dda bonds. These bonds are oriented along the edges of the octahedra formed by the Ti atoms surrounding a vacancy ( octahedral bonds ). This type of bond... 

Crystal structure of solids. The a-crystal form of TiCla is an excellent catalyst and has been investigated extensively. In this particular crystal form of TiCla, the titanium ions are located in an octahedral environment of chloride ions. It is believed that the stereoactive titanium ions in this crystal are located at the edges of the crystal, where chloride ion vacancies in the coordination sphere allow coordination with the monomer molecules. 

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. 

This conceptual link extends to surfaces that are not so obviously similar in stmcture to molecular species. For example, the early Ziegler catalysts for polymerization of propylene were a-TiCl. Today, supported Ti complexes are used instead (26,57). These catalysts are selective for stereospecific polymerization, giving high yields of isotactic polypropylene from propylene. The catalytic sites are beheved to be located at the edges of TiCl crystals. The surface stmctures have been inferred to incorporate anion vacancies that is, sites where CL ions are not present and where TL" ions are exposed (66). These cations exist in octahedral surroundings, The polymerization has been explained by a mechanism whereby the growing polymer chain and an adsorbed propylene bonded cis to it on the surface undergo an insertion reaction (67). In this respect, there is no essential difference between the explanation of the surface catalyzed polymerization and that catalyzed in solution. 

The structural relationships in Bi203 are more complex. At room temperature the stable fonn is monoclinic o -Bi203 which has a polymeric layer structure featuring distorted, 5-coordinate Bi in pseudo-octahedral iBiOs units. Above 717°C this transforms to the cubic -form which has a defect fluorite structure (Cap2, p. 118) with randomly distributed oxygen vacancies, i.e. [Bi203D]. The )3-form and several oxygen-rich forms (in which some of the vacant sites are filled... 

Similarly to Mn,Ox and related compounds, the chalcophanite structure can be interpreted as a filled Cdl2-type structure. The space in the octahedral layer is filled by an additional layer of water molecules and some foreign cations. A comparable situation is found in several hy-droxozincates, e.g., Zn5(OH)8Cl2 H20 or Zn5(OH)6(CO)3. In these compounds the layers are formed by edge-sharing zinc hydroxide octahedra, Zn(OH)6, and the space between the layers is filled with chloride and carbonate anions and some Zn2+ cations, which are located above and below vacancies in the Zn - OH layers. 

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 ... 

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. 

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.

Figure 3 shows the calculated energy barrier for Mn and Co hopping directly through an octahedral edge (E) into a Li/vacancy layer octahedron. The barrier illustrated at the top of Figure 3 is the calculated result when the Li content is Xu = 0 (i.e., MO2, M = Mn or Co) the bottom plot corresponds to... 

Figure 3. Energy of Co/Mn ion along the Oh Oh transition path from an octahedral site in the TM layer, through a shared edge, to an octahedral site in the vacancy/ Li layer (top) delithiated Xu = 0 (M +), (bottom) half-lithiated Xu = 1/2 (average M +). (A (on j axis)) Layered structure with no transition metal in the empty/lithium layer (i.e., no defects). (B) A single TM atom located in the shared edge between neighboring octahedra (i.e., E in Figure 2). (C) A single TM atom defect in an empty/lithium layer octahedron.

---