Ionic coordination polyhedra

Lower Limiting Values of Radius Ratios for Stability of Ionic Coordination Polyhedra... 

A coordination polyhedron of anions is formed around every cation. The cation-anion distances are determined by the sum of the ionic radii, and the coordination number of the cation by the radius ratio. 

Hazen and Finger (1979) extended equation 1.110 to mean polyhedral compressibility (mean compressibility of a given coordination polyhedron within a crystal structure), suggesting that it is related to the charge of ions in the polyhedron through an ionicity factor, analogous to what we have already seen for thermal expansion—i.e.. 

The data of Table 10.8 show that Zr prefers 7- or 8-coordination by F , the shape of the coordination polyhedron adjusting to the nature of the cations, and F Zr ratios less than the coordination number requiring the sharing of vertices or edges of the coordination polyhedra. The inadvisability of trying to relate ionic sizes to coordination number and shape of coordination polyhedron is nicely illustrated by the structure of RbsZr4F2i. In this crystal there are four kinds of coordination of Zr ions ... 

On the kind of isomorphic substitutions significant influence has the arrangement of external electronic shell of lore It is linked with mixed kind of bonds, which never are pure ionic. Some share of covalent bond, which is always oriented in space, as the effect of Itybridized oibitals formation, significantly facilitates the coordination polyhedron formation, in accoidance with the directions of covalent bonds. The example can be the Si-0 bond (only about 60 % ionic), in which the hybridized orbitals participate. 

Despite its simplicity, the tolerance factor has reasonable predictive power, especially for oxides, where ionic radii are known with greatest precision. Ideally t should be equal to 1.0 and it has been found empirically that if t lies in the approximate range 0.9-1.0 a cubic perovskite structure is a reasonable possibility. If t>l, that is, large A and small B, a hexagonal packing of the AXj layers is preferred and hexagonal phases of the BaNiOj type form (Chapter 3). In cases where t of the order of 0.71-0.9, the structure, particularly the octahedral framework, distorts to close down the cuboctahedral coordination polyhedron, which results in a crystal structure of lower symmetry than cubic. For even lower values of t, the A and B cations are of similar size and are associated with the ilmenite, FeTiOj, structure or the C-type rare earth Ln Oj stmcture. 

The majority of inorganic substances contain bonded atoms of three or more different elements. Salts with mixed anions (LaOF, PbFCl, BiOX, etc) have been discussed in Sect. 5.2, those with mixed cations are discussed here, as well as complex compounds which are combinations of intrinsically stable molecules. In complex compounds the bonding is essentially covalent within the coordination polyhedron but essentially ionic outside it. Complex compounds where the central atom is metal (especially transition metal) are known as coordination compounds. Thus, KNO3 and BaSOa are complex compounds, but not coordination compounds. The amount of structural information on such compounds is immense, therefore we shall concentrate on a few problems. 

Another important factor that can affect the value of Ui is the structural type chosen by the crystal, which acts throngh its specific value of the Madelung constant, A (Table 3). Figure 8 illustrates the structural types adopted by some of the most common ionic componnds. It is worthwhile to remember that the choice of the struc-tnral type, coordination number (CN), and coordination polyhedron is essentially determined by the valne of the radius ratio (rcAi/rAN) according to the rules illustrated in Table 4. 

Apart firom the unphysical nature of ionic radii, they are subject to the further criticism that they do not lead to correct predictions in mixed anion compounds such as oxyfluorides [9]. Also they do not allow one to handle correctly compounds in which there is a range of bond lengths within a given coordination polyhedron. One example of the latter is afforded by the case of B2O3 which is discussed below. 

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