Cation-anion bond valence

One reason for the failure of the radius ratio rules is that ions do not behave like hard spheres. Even those that are hard in the Pearson (1973) sense can still be compressed. This is clearly seen in the way the bond length varies with the bond valence. If cation anion bonds can be compressed, so can the distance between the 0 ions in the first coordination sphere. The stronger the cation anion bonds, therefore, the closer the anions in the first coordination sphere can be pulled together (Shannon el al. 1975). 

The valence and coordination symmetry of a transition metal ion in a crystal structure govern the relative energies and energy separations of its 3d orbitals and, hence, influence the positions of absorption bands in a crystal field spectrum. The intensities of the absorption bands depend on the valences and spin states of each cation, the centrosymmetric properties of the coordination sites, the covalency of cation-anion bonds, and next-nearest-neighbour interactions with adjacent cations. These factors may produce characteristic spectra for most transition metal ions, particularly when the cation occurs alone in a simple oxide structure. Conversely, it is sometimes possible to identify the valence of a transition metal ion and the symmetry of its coordination site from the absorption spectrum of a mineral. 

In a metallic compound the valence electrons form a collective belonging to the whole crystal. In a non-metallic compound, on the other hand, it is a useful approximation to consider the bonding valence electrons as localized between cation and anion in covalent crystals or on the anion in purely ionic crystals. Moreover, the electron balance is not influenced by the degree of covalency of the bonds, so that formally we can treat all cation-anion bonds as if they were ionic. For the valence electrons of a normal ionic compound Mm X the following relation holds ... 

Surprisingly many spinel-type chalcogenides form with copper as an A element. In a ternary representative Cu should be divalent in order to satisfy the valence rules. The spinel structure, however, shows no Jahn-Teller distortions contrary to the oxides. Assuming the cation-anion bonds to be saturated, the metallic properties must be due either to a metallic de band of Cu2+ or to the simultaneous presence of T4+ and T3+. 

In rickardite CtuTes additional cation valence electrons are available from the octahedrally-coordinated cations which will be divalent. In Cu3Te2 the cations would just furnish enough valence electrons to saturate the cation-anion bonds, assuming Cu+ on tetrahedral and Cu2+ on octahedral sites. However, the compound would be metallic because of a metallic dy band of Cu2+, since the structure is only weakly deformed (c/a = 1.09 for the f.c. tetragonal anion sublattice). Moreover, the exact 3 2 stoichiometry seems to lie beyond the homogeneity range (217). 

In 1929 Pauling proposed as the second of his Principles Determining the Structures of Complex Ionic Crystals [1], that a cation-anion bond could be characterized by the oxidation state (atomic valence) of its cation divided by its coordination number. He showed that the total amount of this quantity, usually now called the Pauling Bond Strength, received by the anion was approximately equal to the anion oxidation state. He called this the Electrostatic Valence Principle, but it is now commonly referred to as Pauling s Second Rule. 

Thus values of Rijcan be determined for pairs of atoms in a variety of coordinations in experimental crystal structures, and are generally found to be nearly constant for a given pair. Particularly in the case of oxides, for which a large data base exists, Rjj values are known rather accurately (Brown Altermatt, 1985). Bond valence parameters for a wide variety of cation - anion bonds were subsequently determined by Brese O Keeffe (1991) using an interpolation technique. Parameters for anion-anion bonds in solids have also been determined (O Keeffe Brese, 1992). 

The phenomenon of tautomerism comprises many different types of which the prototropic tautomerism that we consider here is only one. Prototropic tautomerism exists when the two tautomers differ only in the position of a proton (this is, of course, an approximation there are other differences between two tautomers, for example, in precise bond lengths). Other important types of tautomerism include the following (1) anioniotropy, where the two tautomers differ only in the position of an anion, which moves from one place to another in the molecule (2) cationiotropy, where the two tautomers differ in the position of a cation (other than a proton), which moves from one place to another in the molecule (3) ring-chain tautomerism and (4) bond-valence tautomerism. 

Here, N and B are constants for a given pair of atoms. A significant feature of bond valence in crystals is that the sum around a cation or an anion, i, to its coordinating ions of opposite charge, j, is a constant. 

Theoretical aspects of the bond valence model have been discussed by Jansen and Block (1991), Jansen et al. (1992), Burdett and Hawthorne (1993), and Urusov (1995). Recently Preiser et al. (1999) have shown that the rules of the bond valence model can be derived theoretically using the same assumptions as those made for the ionic model. The Coulomb field of an ionic crystal naturally partitions itself into localized chemical bonds whose valence is equal to the flux linking the cation to the anion (Chapter 2). The bond valence model is thus an alternative representation of the ionic model, one based on the electrostatic field rather than energy. The two descriptions are thus equivalent and complementary but, as shown in Section 2.3 and discussed further in Section 14.1.1, both apply equally well to all types of acid-base bonds, covalent as well as ionic. 

However, we do not need to abandon the bond valence model for those few inorganic compounds which contain homoionic bonds since there are a number of ways of adapting the model depending on the nature of the structure. If the two cations or two anions that form the bond are equivalent by symmetry, as the two Hg cations are, for example, in the tetragonal crystals of Hg2Cl2 (65441, Fig. 3.4), the normal rules still apply. In this compound the two Hg ... 

Rule 4.1 (An operational definition of a bond). A bond exists between a cation and an anion if its experimental bond valence is larger than 0.04 x the cation valence. 

One can calculate cation bonding strengths, s, in the same way as anion bonding strengths by dividing the valence (or formal ionic charge) of a cation by its ideal coordination number, (eqn (4.2)) ... 

Not all structures are based on close packed lattices. Ions that are large and soft often adopt structures based on a primitive or body centred cubic lattice as found in CsCl (22173) and a-AgI (200108). Others, such as perovskite, ABO3 (Fig. 10.4), are based on close packed lattices that comprise both anions and large cations. The larger and softer the ions, the more variations appear, but the lattice packing principle can still be used. Santoro et al. (1999,2000) have shown how close-packing considerations combined with the use of bond valences can give a quantitative prediction of the structure of BaRuOs (10253). 

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