The spinel structure is a type of arrangement of ions within a compound where the anions (usually oxide ions,
02− ) form a close-packed cubic (ccp) framework. In this ccp arrangement, there are interstitial sites where cations can reside: tetrahedral and octahedral holes.
In a normal spinel structure, specifically, the divalent cation (here
Zn2+ ) occupies one-eighth of the tetrahedral holes. Since there are 8 tetrahedral holes in a ccp structure for every formula unit, only one of these is taken by a
Zn2+ ion
(×8=1).
Regarding the octahedral holes, half of them are filled with trivalent cations (here
Fe3+ ions). Since there are typically 4 octahedral holes in a ccp structure per formula unit, half of these holes being filled means exactly two
Fe3+ ions occupy these sites
(×4=2. ).
The formula of the compound comprises the cations and the anions in a ratio that balances the overall charge. Since the ccp structure comprises 4 oxide ions (
O2− ) for charge neutrality, the whole compound must be electrically neutral. The formula can be inferred by balancing the positive and negative charges from the cations and anions.
With one
Zn2+ and two
Fe3+ for every four
O2−, the resulting compound formula is
ZnFe2O4, where the charges of the cations and anions balance out to give a net neutral compound.