Octahedral versus tetrahedral coordination: spinels

  Figure 20.26 indicates that, if all other factors are equal, d⁰, high-spin d⁵ and d¹⁰ ions should have no preference between tetrahedral and octahedral coordination, and that the strongest preference for octahedral coordination should be found for d³ and d⁸ ions. In practice, other factors do operate. For example, the smaller size of tetrahedral complexes results in higher lattice and solvation energies; thus, although Ni^2+‏ (d⁸) does not form tetrahedral complexes in aqueous solution, it does so in melts and non-aqueous media.

   The distribution of metal ions between tetrahedral and octahedral sites in a spinel can be rationalized in terms of LFSEs. In a normal spinel A^IIB^III₂O₄ the tetrahedral sites are occupied by the A²⁺‏ ions and the octahedral sites by B^3‏+ ions: (A^II)_tet(B^III(^oct₂O₄. In an inverse spinel, the distribution is )B^III)^tet(A^IIB^III)^octO₄. For spinel itself, A = Mg, B = Al. If at least one of the cations is from the d-block, the inverse structure is frequently (though by no means always) observed: Zn^IIFe^III₂O₄, Fe^IICr^III₂O₄ and Mn^IIMn^III₂O₄ are normal spinels while Ni^IIGa^III₂O₄, Co^IIFe^III₂O₄ and Fe^IIFe^III₂O₄ are inverse spinels. To account for these observations we first note the following:

• the Madelung constants for the spinel and inverse spinel lattices are usually nearly equal;
• the charges on the metal ions are independent of environment (an assumption);
• Δoct values for complexes of M³⁺‏ ions are significantly greater than for corresponding complexes of M²⁺‏ ions.

Consider compounds with normal spinel structures: in Zn^IIFe^III₂O₄ (d¹⁰ and d⁵), LFSE = 0 for each ion; in FeIICrIII₂O₄ (d⁶ and d³), Cr³⁺‏ has a much greater LFSE in an octahedral site than does high-spin Fe²⁺‏; in Mn^IIMn^III₂O₄ (d⁵ and d⁴), only Mn^3‏+ has any LFSE and this is greater in an octahedral than a tetrahedral site.    Now consider some inverse spinels: in Ni^IIGa^III₂O₄, only Ni^2‏+ (d⁸) has any LFSE and this is greater in an octahedral site; in each of Co^IIFe^III₂O₄ (d⁷ and d⁵) and Fe^IIFe^III₂O₄ (d⁶ and d⁵), LFSE = 0 for Fe³⁺‏ and so the preference is for Co^2+‏ and Fe^2+‏ 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^IIAl^III₂O₄ is a normal spinel.