The Spinels

The successful rationalization of these transition-metal inverse spinel structures in terms of the relative LFSE s of tetrahedral and octahedral sites is another attractive vindication of ligand-field theory as applied to structure and thermodynamic properties. Once again, however, we must be very careful not to extrapolate this success. Thus, we have a clear prediction that LSFE contributions favour tetrahedral over octahedral coordination, except for d with n = 0, 5 or 10. We do not expect to rationalize the relative paucity of tetrahedral nickel(ii) species relative to octahedral ones on this basis, however. Many factors contribute to this, the most obvious and important one being the greater stabilization engendered by the formation of six bonds in octahedral species relative to only four bonds in tetrahedral ones. Compared with that, the differences in LSFE s is small beer. Why , one asks, was our rationalization of spinel structures so successful when we neglected to include consideration of the bond count The answer is that cancellations within the extended lattice of the spinels tend to diminish the importance of this term. 

Recall that the unit cell in the spinels comprises AgBi6032. In the normal structure, there are 16 B ions in octahedral sites and 8 A ions in tetrahedral ones. That corresponds to 96 octahedral B-0 bonds and 32 tetrahedral A-0 bonds or 128 bonds in all. In the inverse structure, we have 8 B ions in tetrahedral sites, 8 B ions in octahedral ones, and 8 A ions in octahedral sites. This corresponds to 48 octahedral B-O bonds, 32 tetrahedral B-O bonds and 48 octahedral A-O bonds or once again, 128 bonds in all. So the total number of M-O bonds, different types to be sure, is the same in both normal and inverse spinel structures. We could spend quite some time estimating the different bond energies of A-0 and B-O or of octahedral versus tetrahedral, but that would undoubtedly involve a lot of guesswork. We can at least observe that the bond count factor difference between the spinel 

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Manganates III), again mixed-metal oxides present in the spinel Mn304, Mn Mn 204. 

Titanium IV) oxide, T1O2. See titanium dioxide. Dissolves in concentrated alkali hydroxides to give titanates. Mixed metal oxides, many of commercial importance, are formed by TiOj. CaTiOj is perovskite. BaTiOa, per-ovskite related structure, is piezoelectric and is used in transducers in ultrasonic apparatus and gramophone pickups and also as a polishing compound. Other mixed oxides have the il-menite structure (e.g. FeTiOj) and the spinel structure (e.g. MgjTiO ). 

The structure of these solid compounds is not known with certainty but an approximate formula might be NaAlOj.xHjO. Many aluminates occur in minerals, for example the spinels of general formula M (A102)2 where M may be Mg, Zn or Fe these have a mixed oxide structure, i.e. consist essentially of M AF and O ions. 

An example is a LEIS study on a specific spinel, namely ZnAl204, for which cations (Zn) in tetrahedral sites are expected [3.145] to be less stable and therefore move to sites below the surface where they are better shielded, yielding a lower LEIS signal. This has been confirmed by Brongersma et al. [3.146] (Fig. 3.59). This figure shows that LEIS is very sensitive to Zn, as shown by LEIS from ZnO, but for the spinel no Zn is visible in the surface. 

Figure 7.7. The spinel strueture. The unit eell can be divided into octants - tetrahedrally coordinated cations A. octahedrally coordinated eations B, and oxygen atoms (large cireles) are shown in two oetants only (adapted from Smit and Wijn 1959).

Many of the spinel-type compounds mentioned above do not have the normal structure in which A are in tetrahedral sites (t) and B are in octahedral sites (o) instead they adopt the inverse spinel structure in which half the B cations occupy the tetrahedral sites whilst the other half of the B cations and all the A cations are distributed on the octahedral sites, i.e. (B)t[AB]o04. The occupancy of the octahedral sites may be random or ordered. Several factors influence whether a given spinel will adopt the normal or inverse structure, including (a) the relative sizes of A and B, (b) the Madelung constants for the normal and inverse structures, (c) ligand-field stabilization energies (p. 1131) of cations on tetrahedral and octahedral sites, and (d) polarization or covalency effects. ... 

M2Ti04 (M = Mg, Zn, Mn, Fe, Co) have the spinel stmcture (MgAl204, p. 248) which is the third important stmcture type adopted by many mixed metal oxides in this the cations occupy both octahedral and tetrahedral sites in a cep array of oxide ions. Ba2Ti04, although having the same stoichiometry, is unique amongst titanates in that... 

Zirconates and hafnates can be prepared by firing appropriate mixtures of oxides, carbonates or nitrates. None of them are known to contain discrete [M04]" or [MOs] ions. Compounds M ZrOs usually have the perovskite structure whereas M2Zr04 frequently adopt the spinel structure. 

Although Fc304 is an inverse spinel it will be recalled that Mn304 (pp. 1048-9) is normal. This contrast can be explained on the basis of crystal field stabilization. Manganese(II) and Fe" are both d ions and, when high-spin, have zero CFSE whether octahedral or tetrahedral. On the other hand, Mn" is a d and Fe" a d ion, both of which have greater CFSEs in the octahedral rather than the tetrahedral case. The preference of Mn" for the octahedral sites therefore favours the spinel structure, whereas the preference of Fe" for these octahedral sites favours the inverse structure. 

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