Spinel structure inverse

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. 

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... 

The mineral magnetite is a naturally occurring form of Fe304 that has an inverse spinel structure as a result of both Fe2+ and Fe3+ being present. 

Complex lithium halide spinels (Kanno, Takeda and Yamamoto, 1982 Lutz, Schmidt and Haeuseler, 1981), based on Li2CdCl4 and Li2MgCl4 have remarkably high Li ion conductivity for close packed structures. Fig. 2.11. These are complicated materials however, they have essentially inverse spinel structures but may exist also in various distorted forms. Some of them undergo a phase transition to defect rock salt structures at high temperatures some are non-stoichiometric. 

Figure 8. Formation energy versus Li concentration for three structures of Mn oxide (top) and Co oxide (bottom) ( ) 5-LiJM204-labeled spinel, (0) 7-LiJMn02-labeled layered, and (+) partially inverse spinel structure with 1/4M tetrahedral (ps-(LiJM)tet(LijM3)oct08 0 < x< 1 and 0 < y < 2) labeled 1/4 Mn tet. As the Li content is increased, the Li is added to the tetrahedral site first of p5-(LiJM)ter (LijM3)octOs, and then to the octahedral sites. For Mn, there also is the energy of (a) a structure with one-sixth of the Mn in tetrahedral sites at Xu =1/3 labeled 1/6 Mn tet with a triangle data point and (x) a structure with one-eighth of the Mn in tetrahedral sites at Xu =1/4 labeled 1/8 Mn tet.

For example, the inverse spinel structure of magnetite (see Chap. 2) results from the fact that the CFSE of Fe is greater for octahedral than for tetrahedral coordination, so Fe preferentially occupies octahedral sites. For Fe the CFSE is zero for both octahedral and tetrahedral coordination, so that this ion has no preference for either type of coordination. 

Fig. 32. The inverse spinel structure of TeLi204 projected on (100) of the tetragonal unit cell (compare Fig. 29). Large circles are Li and medium circles are Te (filled and open at heights of a/4 and 3 a/4 respectively) small circles are O. Heights are in units of a/100...

Further adding to the complexity of the spinel structure are three possible arrangements of the metal ions in the cubic close-packed anions. The ordering of divalent metal ions (such as Mg2+) on the proper tetrahedral sites and all the trivalent ions (as Ai3+) in the correct octahedral sites, will give rise to the normal spinel structure. If the divalent ions occupy some of the octahedral sites and half of the trivalent ions move to the tetrahedral sites, the structure is then referred to as the inverse spinel structure. The last case exists when the tetrahedral sites and the octahedral sites are occupied by a mixture of di- and tri-valent ions. This type is known to generate the random spinel structure, and the exact composition and populations in the... 

Ferrite compounds with the inverse spinel structure are similar to magnetite, with different ions substituting for the iron atoms. As with FeO (cf. Figure 6.62), the oxygen ions have no permanent magnetic moment. Tetrahedral sites in the FCC oxygen array are occupied by half of the trivalent cations, and octahedral sites are occupied equally by divalent cations and the remaining trivalent cations. 

Person 1 Calculate the net magnetic moment per unit cell for copper ferrite. Remember that there is more than one formula unit (CuFe204) per unit cell in the inverse spinel structure. 

When compounds of general formula AB2O4 adopt the inverse-spinel structure, the formula is better written as B(AB)04, because this indicates that half of the B ions now occupy tetrahedral sites, and the remaining half, together with the A ions, occupy the... 

The name ferrite was originally given to a class of mixed oxides having an inverse spinel structure and the formula AFe204 where A is a divalent metal ion. The term has been extended to include other oxides, not necessarily containing iron, which have similar... 

In addition, there are 2N tetrahedral sites, and the divalent ions (Mg +) occupy one-eighth of these. In the inverse spinel structure, the oxide ions are also in a cubic close-packed arrangement, but the divalent metal ions occupy octahedral sites and the trivalent ions are equally divided amongst tetrahedral and octahedral sites. 

ZnPe204 has the inverse spinel structure at low temperatures. What type of magnetism would you expect it to exhibit ... 

FbjO has the inverse spinel structure, with all the Fe " ions and half of the Fe " ions located in octahedral sites (B sites) in the oxygen network and the remaining half of the Fe ions located on tetrahedral sites (A sites). It undergoes a ferrimagnetic-paramagnetic transition around 850 K and another transition around Ty = 123 K (Verwey transition). The material is a semiconductor both above and below the Verwey... 

A closely related group of AB2O4 oxides has the inverse spinel structure. Here, again, there is a ccp array of 02, but the B atoms are equally divided between T- and O-sites, and all of the A ions appear in O-, not T-, holes. Thus, we have B(AB)C>4 with B in one-eighth of the T-holes, A in one-quarter of the O-holes, and B in one-quarter of the O-holes. 

The inverse spinel structure differs in that one type of cation occupies the tetrahedral and half of the octahedral sites of the spinel lattice, and the other cations occupy the remaining octahedral sites. This is indicated by writing the formula of, for example, zinc titanium spinel as Zn(TiZn)04. Spinels containing di- and tetravalent cations are mostly of the inverse type. Normal and inverse spinels should be regarded as idealized limiting structures, intermediate forms are often observed in practice. A... 

Commonly, many compounds with the same formula type have the same type of structure. Usually the most common compound is chosen as representative, but it could be the first structure of the type studied. For example, hundreds of binary compounds of the MX type have the same crystal structure as NaCl. Other compounds can be described as having the NaCl (or halite, the name of the mineral) structure. If the structure being considered has slight differences, these differences can be described in terms of the reference structure. One often sees statements such as a compound has a disordered spinel (MgAl204) type structure or an inverse spinel structure. This requires knowledge of the spinel structure because "inverse" or "disordered" terms describe variations of occupancies of octahedral and tetrahedral sites. 

This compares well with the experimentally determined value (approximately 3 x 105Am 1). The discrepancy is probably due partly to the assumption that Ni0Fe203 has the ideal inverse spinel structure and partly to the incomplete quenching of the orbital moment. 

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