Twelve-coordinate structures

Since perturbation theory requires conservation of energy relative to the degenerate level, the r3 level is raised 6Dq and the r6 level is lowered 4Dq relative to the fivefold degenerate D level, as is indicated in Figure 10(a). In the four-, eight-, and twelve-coordinated structures, on the other hand, the rB orbitals are directed toward the... 

A comparison of the limiting radius-ratio values given in Table I with the radius ratios of alkali halides in Table II shows that the observed structures are not always as predicted. According to the simple theory, the roeksalt structure should be stable only within the range 0.414 rM/rx 0.732. Thus LiCl (0.33), LiBr (0.31), and Lil (0.28) should have tetra-hedrally coordinated structures, while KF (0.98), RbF (1.09), and CsF (1.24) should have eight or twelve coordinated structures. These disagreements are perhaps not surprising in view of the crudeness of the approximations involved, but more realistic models do not lead immediately to an explanation of the persistence of the roeksalt structure not only in the alkali... 

Structures of coordination compounds suggest that smaller chelate rings promote higher coordination numbers. Twelve coordination... 

There is a special and very important feature of the anticipated open nido twelve-vertex structures in Fig. 12 repetition of single Lipscomb dsd rearrangements (denoted by the two-headed arrows) monotonically allows the six skeletal atoms about the open face to rotate about the second tier of five skeletal atoms (two-tier dsd rotation). Each dsd rearrangement [85, 163) (valence bond tautomerism) recreates the same configuration and involves only the motion of two skeletal atoms (in the ball-and-stick representation) and would allow carbons, if located in different tiers, to migrate apart. Such wholesale valence bond tautomerism is known to accompany the presence of seven-coordinate BH groups, e.g., and CBjoHu 142,155). 

Here let us consider the structure of Bai+ Fe2S4 from the viewpoint of displacive modulated structures. As clearly seen from Fig. 2.38, Ba ions in the basic compound BaFe2S4 occupy regularly half of the face-capped tetragonal prisms (FCTP twelve coordinations) formed by S ions. The FCTP sites are at z = 0 and along the c-axis. The other sites for Ba ions are at z = j and I, where the Ba ions are eight coordinated by S ions (square anti-prism, SAP). The former sites are more stable than the latter ones, however, the occupation of all of the former sites seems to be impossible, due to the repulsive force between Ba ions. 

Each Ca2+ is thus twelve-coordinated and each Ti4+ six-coordinated by oxygen neighbors, while each O2- is linked to four Ca2+ and two Ti4+ ions. As expected, it is the larger metal ion that occupies the site of higher coordination. Geometrically the structure can be regarded as a ccp of (O2- and Ca2+) ions, with the Ti4+ ions orderly occupying of the octahedral interstices. 

Figure 9.3 The perovskite crystal structure, (a) Ideal cubic phase showing comer-shared octahedra surrounding the twelve-coordinated cuboctahedral site (b) projection of the orthorhombic perovskite MgSi03 structure at 6.7 GPa along the c axis (from Kudoh etal., 1987). Rotation and tilting of [Si06] octahedra relative to the cubic structure are shown. The eight shorter bonds (Mg-0 distances = 199 to 244 pm) are indicated by solid lines and the four longer bonds (Mg-0 = 277 to 315 pm) by dashed lines.

Various estimates have been made of the CFSE of Fe2+ in dense oxide structures modelled as potential Mantle mineral phases (Gaffney, 1972 Bums, 1976a). All estimates indicate that octahedrally coordinated Fe2+ (in periclase, for example) has a considerably higher CFSE than Fe2+ ions in the eight- to twelve-coordination sites in the perovskite structure. Thus, the CFSE of Fe2+ in... 

Perovskites have the general formula, ABX3, with SrTiCb being a prototype. They contain a framework structure containing corner-sharing TiC>6 octahedra with the A cation in twelve coordinate interstices.384,385 Several hundred oxides have this struc... 

As for ten coordination, there are no twelve-coordinate complexes containing only unidentate ligands. The most common twelve-coordinate molecules are of the type [M(bidentate)6]. Three structural isomers may be formed by wrapping six bidentate ligands along the edges of an icosahedron (Figme 17). Isomer III is less stable than the other two and is not observed. Isomer I is observed for a number of hexanitrato complexes, for example [La(N03)6] and [Th(N03)6] . Isomer II has been observed for the naphthyridine complex [Pr(napy)6] +. 

Idealized structures up to nine-coordination are summarized in Figure 4.21. These do not represent all of the shapes met, since, apart from all these idealized structures, it is necessary to remember that bond angle and bond length distortions of these structures can occur some of the shapes resulting from these effects are themselves common enough to be represented as named shapes, and we have discussed some examples of these earlier. Further, beyond nine-coordination, an array of additional shapes can be found, of which perhaps the best known are the bicapped square antiprism (for ten-coordination), the octadecahedron (for eleven-coordination) and the icosahedron (for twelve-coordination). Clearly, the options are extensive, so it may be time to find out what directs a complex to take a particular shape. 

The arrangement of close-packed layers in the pattern xyxy... is the hexagonal close-packed structure (hep) the pattern xyzxyz... is the cubic close-packed (cep) or face-centered cubic (fee) structure. In each of these structures, every sphere is in contact with twelve others six in its own layer, three in the layer above, and three in the layer below. The twelve coordination in these structures is shown by an exploded view in Fig. 27.3(a) and (b), and in a different view in Fig. 27.3(c) and (d). The hep and fee structures are the typical structures encountered in metals. The high coordination number (twelve) in these structures results in a crystal of comparatively high density. 

Other structures incorporating octahedral heteroatoms 38.3.3 Eight- and Twelve-coordinate Primary Heteroatoms... 

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