The influence of ionic radii of cations and covalent forces on the unit cell dimensions of spinels

Fe-, Cr- and Al-spinels were synthesized and their unit cell sizes determined by means of X-rays. Differential thermal curves show that the magnetic inversion of Fe₂O₃ at 680° C accelerates the formation of the ferrites when the constituent oxides are heated together.A correlation can be made between ionic radii of cations and unit cell dimensions provided the effect of covalent forces in the lattice is taken into account. The values for ionic radii of cations as given byAhrens (1952) permit a better correlation than those ofGoldschmidt.A shrinkage of 0.01 Å in the unit cell size per 0.01 Å decrease in the ionic radius of the divalent cations was determined when spinels with the same cation arrangement in the same group were compared. A shrinkage of 0.027 Å in the unit cell size per 0.01 Å decrease in the ionic radius of the trivalent cations was determined in spinels having the same divalent cation and cation arrangement when the trivalent cations form the same type of bonds.The half-occupation of the 3d orbits in Mn²⁺ and Fe³⁺ causes abnormally high unit cell dimensions in spinels where these ions are incorporated in octahedral sites. This is attributed to the formation of electrovalent bonds by these ions. Variable forces of contraction in the lattice are revealed when the unit cell dimensions are correlated with the ionic radii of cations. The force of contraction can be satisfactorily explained as being due to covalent forces in the spinel structure. The magnitude of this force or the degree of covalence in the bonds increases in the following order of cations where these are situated in tetrahedral sites:The divalent transition element ions, Fe²⁺, Co²⁺ and Ni²⁺; the B-Sub-group element ions Cd²⁺ and Zn²⁺; Fe³⁺ in tetrahedral co-ordination.