‘Normal’ spinel and ‘inverse’ spinel lattices

    A large group of minerals called spinels have the general formula AB₂X₄ in which X is most commonly oxygen and the oxidation states of metals A and B are +‏2 and ‏+3 respectively; examples include MgAl₂O₄ (spinel, after which this structural group is named), FeCr₂O₄ (chromite) and Fe₃O₄ (magnetite, a mixed Fe(II), Fe(III) oxide). The spinel family also includes sulfides, selenides and tellurides, and may contain metal ions in the ‏+4 and +‏2 oxidation states, e.g. TiMg₂O₄, usually written as Mg₂TiO₄. Our discussion below focuses on spinel-type compounds containing A²⁺‏ and B³⁺‏ ions.

   The spinel lattice is not geometrically simple but can be considered in terms of a cubic close-packed array of O^2- ions with one-eighth of the tetrahedral holes occupied by A^2+‏ ions and half of the octahedral holes occupied by B^3+‏ ions.

     The unit cell contains eight formula units, i.e. [AB₂X₄]₈. Some mixed metal oxides AB₂X₄ in which at least one of the metals is a d-block element (e.g. CoFe₂O₄) possess an inverse spinel structure which is derived from the spinel lattice by exchanging the sites of the A^2+‏ ions with half of the B^3+‏ ions. The occupation of octahedral sites may be ordered or random, and structure types cannot be simply partitioned into ‘normal’ or ‘inverse’. A parameter λ is used to provide information about the distribution of cations in the interstitial sites of the close-packed array of X^2- ions; λ indicates the proportion of B³⁺‏ ions occupying tetrahedral holes. For a normal spinel, λ = 0; for an inverse spinel, λ = 0:5. Thus, for MgAl₂O₄, λ = 0, and for CoFe₂O₄, λ  = 0:5. Other spineltype compounds have values of λ between 0 and 0.5; for example, for MgFe₂O₄, λ  = 0:45 and for NiAl₂O₄, λ = 0:38.

   The inverse spinel structure of Fe₃O₄ showing the unit cell and the tetrahedral and octahedral environments of the Fe centres. The vertex of each tetrahedron and octahedron is occupied by an O atom.