An Inverse Spinel - NiFe2O4
Spinel is the name given to the mineral MgAl2O4. It has a common structural arrangement shared by many oxides of the transition metals with formula AB2O4.
In the normal pattern the oxygens (red) form a cubic close packed (ABCABC or face centred) array and the Mg(II) (A(II)-green) and Al(III) (B(III)-silver) sit in tetrahedral (1/8 occupied) and octahedral (1/2 occupied) sites in the lattice, giving a Unit Cell with 8 Mg's, 16 Al's and 32 O's.
An inverse spinel is an alternative arrangement where the divalent ions swap with half of the trivalent ions so that the M(II) now occupy octahedral sites
i.e. B(AB)O4.
In this case Ni(II) is octahedral and half of the Fe(III) are tetrahedral.

Complexes that share this structure include..
a number of 1st row TM oxides and sulfides.
The display shows an idealised unit cell (Space group 216 F-43m). The cubic cell lengths used were a=b=c=8.0858A. These are not the usual values quoted and come from what seems to be an overlooked paper in Proc. Roy. Soc., 1983, 386, 333-245. Their crystallographic evidence suggests that a better fit of the data comes from F-43m, rather than the often quoted Fd3m centrosymmetric space group.
One method of predicting whether a structure will be normal or inverse is to calculate Octahedral Site Preference Energies for both the A(II) and B(III). The ion with the more stable energy is predicted to fit into the octahedral site.
However, see J. Am. Chem. Soc., 1982, 104, 92-95 for a different method that does NOT involve OSPE calculations.
For alternate views of spinels,
pictures of spinel layers

and check out the following sites; Wellesley College and the University of Le Mans.
Information is available to show how the individual structural pages were created.
Return to the structure of binary salts introductory page.
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Created and maintained by Prof. Robert J. Lancashire,
The Department of Chemistry, University of the West Indies,
Mona Campus, Kingston 7, Jamaica.
Created March 2000. Links checked and/or last modified 27th November 2014.
URL http://wwwchem.uwimona.edu.jm/courses/invspinel.html