Electronic Structures of the Spinels

Crystal structure of the spinels.—(1) The most probable arrangement of valence electrons is that in which there is a pair on or near each centerline between adjacent atoms. The valence shell of each oxygen and divalent metal atom is a tetrahedron of electronpairs; that of each trivalent metal atom is an octahedron of pairs. (2) The distances between adjacent atomic centers are calculated (from the densities) and the positions of the oxygen centers determined in crystals of Zn${\mathrm{Al}}_2$ ${\mathrm{O}}_4$, Zn${\mathrm{Cr}}_2$ ${\mathrm{O}}_4$, Zn${\mathrm{Fe}}_2$ ${\mathrm{O}}_4$, Mg${\mathrm{Al}}_2$ ${\mathrm{O}}_4$, Mg${\mathrm{Cr}}_2$ ${\mathrm{O}}_4$, Mn${\mathrm{Al}}_2$ ${\mathrm{O}}_4$, Mn${\mathrm{Cr}}_2$ ${\mathrm{O}}_4$, Cd${\mathrm{Cr}}_2$ ${\mathrm{O}}_4$, and Fe${\mathrm{Fe}}_2$ ${\mathrm{O}}_4$ by means of the assumptions that the Zn-O distance in the first three equals that in ZnO and that corresponding interatomic distances in different spinels are equal. (3) Densities of Mg${\mathrm{Fe}}_2$ $O_4$ and Mn${\mathrm{Fe}}_2$ $O_4$ are computed to be 4.47 and 4.90 gm/${\mathrm{cm}}^3$, respectively, on the basis of these same assumption. (4) Chemical formulœ. There is no physical basis in the arrangement of atoms and electrons for the formulæ R"O·${\mathrm{R}}_2$"'${\mathrm{O}}_3$ or R"${(\mathrm{R}"\text{'}{\mathrm{O}}_2)}_2$.