Octahedral versus tetrahedral coordination spinels

The distribution of metal ions between tetrahedral and octahedral sites in a spinel (see Box 13.6) can be rationalized in terms of LFSEs. In a normal spinel A B 04 the tetrahedral sites are occupied by the A ions and the octahedral sites by ions (A ) (B )2° 04. In an inverse spinel, the distribution is (B ) (A B )° 04. For spinel itself, A = Mg, B = Al. If at least one of the cations is from the t/-block, the inverse structure is frequently 

Consider compounds with normal spinel structures in Zn Fe 04 (r/ and d ), LFSE = 0 for each ion in Fe Cr 04 (J and r/ ), Cr + has a much greater LFSE in an octahedral site than does high-spin Fe in Mn Mn 04 (r/ and d ), only Mn has any LFSE and this is greater in an octahedral than a tetrahedral site. Now consider some inverse spinels in Ni°Ga 04, only Ni d ) has any LFSE and this is greater in an octahedral site in each of Co°Fe 04 d and d ) and Fe°Fe 04 d and fi ), LFSE = 0 for Fe and so the preference is for Co and Fe respectively to occupy octahedral sites. While this argument is impressive, we must note that observed structures do not always agree with LFSE expectations, e.g. Fe°Al 04 is a normal spinel. 

In aqueous solution, water is replaced by other ligands (equation 21.27, and see Table 7.7) and the position of equilibrium will be related to the difference between two LFSEs, since Ao t is ligand-dependent. 

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Many spinel compounds adopt an alternative structure where half the B cations occupy the tetrahedral sites while the remaining B cations and A cations occupy the octahedral sites. These are known as inverse spinels. The occupancy of the latter sites may be random or ordered. The adoption of an inverse spinel versus a spinel structure depends on a variety of factors the relative size of the A and B cations, the relative lattice energies, ligand-field stabilization, energies of octahedral versus tetrahedral coordination, and polarization or covalency effects. For example, in MgABOq one might expect the small... 

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