Spinel inverse spinels

These include mostly transition metal oxides and sulfides that can be classified in several ways, e.g., according to their red-ox potentials 2, 3, 4, 5 V vs. Li/Li ", or according to their structure, e.g., layered, spinel, inverse spinel, olivine. Typical 2-3 V materials are LixMoeOg chevrel phase (0 < x < 4), TiS2, M0S2. Typical 3-4V materials are Li Mn02 (0 < x < 1), Li VO , LixCo02,... 

The site preference of several transition-metal ions is discussed in References 4 and 24. The occupation of the sites is usually denoted by placing the cations on B-sites in stmcture formulas between brackets. There are three types of spinels normal spinels where the A-sites have all divalent cations and the B-sites all trivalent cations, eg, Zn-ferrite, [Fe ]04j inverse spinels where all the divalent cations are in B-sites and trivalent ions are distributed over A- and B-sites, eg, Ni-ferrite, Fe Fe ]04 and mixed spinels where both divalent and trivalent cations are distributed over both types of sites,... 

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. ... 

The sensitive dependence of the electrical and magnetic properties of spinel-type compounds on composition, temperature, and detailed cation arrangement has proved a powerful incentive for the extensive study of these compounds in connection with the solid-state electronics industry. Perhaps the best-known examples are the ferrites, including the extraordinary compound magnetite Fc304 (p. 1080) which has an inverse spinel structure (Fe )t[Fe Fe ]o04. 

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. 

It is worthwhile to point out that lithium extraction from inverse spinels V[LiM]04, such as V[LiNi]04 and V[LiCo]04 takes place at high voltage, typically between 4 and 5V [153]. Lithium is extracted from the octahedral 16d sites of these spinels with a concomitant oxidation of the divalent nickel or cobalt ions. From a structural point of view, this can be readily understood because lithium must be dislodged from the 16d octahedral sites, which are of low-energy, into neighboring energetically unfavorable 8b tetrahedra, which share all four faces with 16d sites that are occupied by nickel or cobalt and by lithium. Lithium extraction reactions... 

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... 

In the following, we start by assuming purely ionic structures. In spinel the oxide ions form a cubic closest-packing. Two-thirds of the metal ions occupy octahedral interstices, the rest tetrahedral ones. In a normal spinel the A ions are found in the tetrahedral interstices and the M ions in the octahedral interstices we express this by the subscripts T and O, for example Mgr[Al2](904. Since tetrahedral holes are smaller than octahedral holes, the A ions should be smaller than the M ions. Remarkably, this condition is not fulfilled in many spinels, and just as remarkable is the occurrence of inverse spinels which have half of the M ions occupying tetrahedral sites and the other half occupying octahedral sites while the A ions occupy the remaining octahedral sites. Table 17.3 summarizes these facts and also includes a classification according to the oxidation states of the metal ions. 

Arbitrary intermediate states also exist between normal and inverse spinels they can be characterized by the degree of inversion X ... 

X = 0 normal spinel X = 0.5 inverse spinel The distribution of the cations among the tetrahedral and octahedral sites is then expressed... 

Decide whether the following compounds should form normal or inverse spinels using the ligand field stabilization energy as the criterion ... 

Fe304, NiFe204 (inverse spinels) ttm Y3Fe5012 (garnet)... 

In NiFe204, an inverse spinel Fe +[Ni2+Fe3+]004, the spins of the octahedral sites are parallel with one another the same applies to the tetrahedral sites (Fig. 19.8). The interaction between the two kinds of sites is mediated by superexchange via the oxygen atoms. High-spin states being involved, Fe3+ (d5) has five unpaired electrons, and Ni2+ (ds) has two unpaired electrons. The coupled parallel spins at the octahedral sites add up to a spin of S = + =. It is opposed to the spin of S = of the Fe3+ particles at the tetrahedral sites. A total spin of S = 1 remains which is equivalent to two unpaired electrons per formula unit. 

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