Crystal structure inverse spinel

The ferrites generally have one of three crystal structures inverse spinel, gameL and hexagonal. The spinel structures (cf. 

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. 

Only few structure types have been observed for compounds of this composition. The spinel structure type of the compound Li2NiF4 (a = 8.313 A) 267) is unique. It crystallizes in the inverse spinel arrangement containing all the Ni and half of the Li cations in octahedral sites. 

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. 

Crystal chemistry of spinels. A classic example showing that transition metal ions display distinct site preferences in oxides stems from studies of spinel crystal chemistry. The spinel structure contains tetrahedral and octahedral sites normal and inverse forms exist in which divalent and trivalent ions, respectively, fill the tetrahedral sites. The type of spinel formed by a cation is related to its octahedral site preference energy (OSPE), or difference between crystal field stabilization energies in octahedral and tetrahedral coordinations in an oxide structure. Trivalent and divalent cations with large site preference energies (e.g., Cr3 and Ni2+) tend to form normal and inverse spinels, respectively. The type of spinel adopted by cations with zero CFSE (e.g., Fe3+ and Mn2+) is controlled by the preferences of the second cation in the structure. 

Magnetite (FC3O4) is a component of the water-gas shift reaction that crystallizes to the inverse spinel structure. The general formula of the oxides known as spinel is AB204. In the normal spinel-type structure, A is an A2+ metal, and B is a B3+ metal. O2- forms a CCP anionic framework, where the A atoms occupy 1/8 of the tetrahedral sites and the B atoms occupy 1/2 of the octahedral sites (see Figures 1.6 and 1.7). An example of a normal spinel is Mg A1204. 

Using crystal field model, explained why Fe304 has an inverse spinel structure while Mn304 has a normal spinal structure ... 

Finally, there is Fe304, a mixed Fc,l-Fe"1 oxide which occurs in Nature in the form of black, octahedral crystals of the mineral magnetite. It can be made by ignition of Fe203 above 1400°. It has the inverse spinel structure... 

The first two energies are usually sufficient to determine the total lattice energy in ionic, non-transition-metal oxides. Elastic energy refers to the degree of distortion of the crystal structure due to the difference in ionic radii assuming that ions adopt a spherical shape. Smaller cations, with ionic radii of 0.225-0.4 A, should occupy tetrahedral sites, while cations of radii 0.4-0.73 A should enter octahedral ones. This distribution leads to a minimum in lattice strain. Since trivalent cations are usually smaller than divalent ones, a tendency toward the inverse arrangement would be expected in 2, 3 spinels. 

The other important factor in ferrimagnetic compounds is the crystal stmcture of the compound. This can also be illustrated by the oxide Fe304, which adopts the inverse spinel structure (see Section 5.3.10). In this stmcture the cations are... 

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