  A thorough consideration of the relation between the lattice parameters of
185 binary and ternary spinel compounds, on one side, and ionic radii and
electronegativities of the constituting ions, on the other side, allowed for
establishing a simple empirical model and finding its linear equation, which
links together the above-mentioned quantities. The derived equation gives good
agreement between the experimental and modeled values of the lattice parameters
in the considered group of spinels, with an average relative error of about 1%
only. The proposed model was improved further by separate consideration of
several groups of spinels, depending on the nature of the anion (oxygen,
sulfur, selenium/tellurium, nitrogen). The developed approach can be
efficiently used for prediction of lattice constants for new isostructural
materials. In particular, the lattice constants of new hypothetic spinels
ZnRE2O4, CdRE2S4, CdRE2Se4 (RE=rare earth elements) are predicted in the
present paper. In addition, the upper and lower limits for the variation of the
ionic radii, electronegativities and certain their combinations were
established, which can be considered as stability criteria for the spinel
compounds. The findings of the present paper offer a systematic overview of the
structural properties of spinels and can serve as helpful guides for synthesis
of new spinel compounds.
