The normal and inverse spinel structures

The spinel structure is illustrated in Fig. 7.4(a). It is most easily visualized as an octahedral framework of composition AX2 (atacamite) which is derived from the NaCl structure by removing alternate rows of metal ions (Fig. 4.22(b), p. 143). Additional metal ions may then be added in positions of tetrahedral coordination (Fig. 7.4(3l), facing p. 268). In the resulting structure each 0 ion also has tetrahedral coordination, its nearest neighbours being three metal atoms of the octahedral framework and one tetrahedrally coordinated metal atom. 

The crystallographic unit cell of the spinel structure contains thirty-two approximately cubic close-packed oxygen atoms, and there are equivalent positions in this cell for eight atoms surrounded tetrahedrally by four 0 atoms and for sixteen atoms surrounded octahedrally by six 0 atoms. (These are not, of course, the total numbers of tetrahedral and octahedral holes, which are respectively 64 and 32 (see p. 127).) Since there are eight A atoms and sixteen B atoms to place in 

The nature of a spinel is described by a parameter X, the fraction of B atoms in tetrahedral holes some authors refer to the degree of inversion y (= 2X). For a normal spinel X = 0, and for an inverse spinel X =. Intermediate values are found (e.g. in a random spinel), and X is not necessarily constant for a given spinel but can in some cases be altered by appropriate heat treatment. For NiMn204 X varies from 0 37 (quenched) to 0-47 (slow-cooled). Values of X have been determined by X-ray and neutron diffraction, by measurements of saturation magnetization, and also by i.r. measurements. In favourable cases l.r. bands due to tetrahedral AO4 groups can be identified showing, for example, that in Li(CrGe)04 Li occupies tetrahedral positions.  

The spinels of composition between MgFe204 and MgAl204, which have been studied magnetically and also by neutron diffraction, are of interest in this connection. MgFc204 has an essentially inverse structure (X 0-45), that is, nine-tenths of the Mg ions are in octahedral (B) sites. As Fe is replaced by Al the latter goes into B sites and forces Mg into tetrahedral (A) sites, so that there is a continuous transformation from the inverse structure of MgFc204 to the normal structure of MgAl204. 

The structures of the spinels present two interesting problems. First, why do some compounds adopt the normal and others the inverse spinel structure Second, there are some spinels which show distortions from cubic symmetry. This is part of the more general problem of minor distortions from more symmetrical structures which was mentioned in connection with ligand field theory in Chapter 7. We deal with these points in turn. 

---