This paper reviews the crystal structure of compounds with the general formula AB 2 X 4 , which crystallize with the same atomic structure as the mineral spinel, MgAl 2 O 4 . Three degrees of freedom associated with the detailed atomic arrangements of spinels are considered here: (i) the lattice parameter, a; (ii) the anion parameter, u; and (iii) the cation inversion parameter, i. Oxide spinels are used as examples to explore the interrelationships between these parameters.

In a previous paper it was shown that in-crystal ion polarizabilities derived from low-frequency precision measurements of the dielectric constants of single-crystal oxides can be given a quantitative interpretation using a quantum mechanically based result for a single, completely filled, electron subshell. In this paper, by exploiting the fact that the radii of related subshells differ only slightly, we propose an equation amended to include the possibility of contributions from incomplete or several subshells. Using the new result, effective electron numbers are derived for all the ions for which experimental polarizabilities have recently been published. It is shown that there is generally a good correspondence between these numbers and the known electronic configurations of the ions concerned. The new calculations show that the concept of a polarizability determined by the contribution of a single electron subshell is certainly valid with ions corresponding to elements of low atomic number, but that in the case of transition and rare earth ions there is probably more than one contributing electron subshell.

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