Question

The correct statement(s) about the structure of metal oxides is(are)

• A. Spinel has 8 tetrahedral sites and 4 octahedral sites per formula unit
• B. \(\mathrm{BaTiO_3}\) has a perovskite structure
• C. In \(\mathrm{Fe_3O_4}\), \(\mathrm{Fe^{2+}}\) occupies both tetrahedral and octahedral sites in the unit cell
• D. \(\gamma\text{-}\mathrm{Al_2O_3}\) is a defect spinel

Hint:

Recall the ratio of tetrahedral to octahedral holes in a close packed oxide lattice, the classic \(\mathrm{ABO_3}\) perovskite structure, and which cation sits where in inverse-spinel magnetite.

Answer 1

The Correct Option is A, B, D

This question checks four separate facts about oxide structures: the site count in a spinel lattice, the structure type of $\mathrm{BaTiO_3}$, the cation distribution in magnetite, and the nature of $\gamma$-alumina.

1. Spinel has 8 tetrahedral sites and 4 octahedral sites per formula unit: Correct. A spinel unit cell holds 32 oxide ions in a cubic close packed lattice, which always generates twice as many tetrahedral holes as octahedral holes, giving 64 tetrahedral and 32 octahedral holes in total. Divided across the 8 $\mathrm{AB_2O_4}$ formula units in that cell, that works out to 8 tetrahedral and 4 octahedral sites per formula unit, matching the statement.
2. $\mathrm{BaTiO_3}$ has a perovskite structure: Correct. This is one of the defining perovskite oxides, with the large $\mathrm{Ba^{2+}}$ ion at the cube corners, the small $\mathrm{Ti^{4+}}$ ion at the body centre in an octahedral oxide hole, and the oxide ions at the face centres.
3. In $\mathrm{Fe_3O_4}$, $\mathrm{Fe^{2+}}$ occupies both tetrahedral and octahedral sites: Wrong. Magnetite is an inverse spinel, $\mathrm{Fe^{3+}(Fe^{2+}Fe^{3+})O_4}$, so the tetrahedral holes are filled only by $\mathrm{Fe^{3+}}$, while the octahedral holes carry the remaining $\mathrm{Fe^{3+}}$ together with all of the $\mathrm{Fe^{2+}}$. $\mathrm{Fe^{2+}}$ never sits in a tetrahedral hole here.
4. $\gamma$-$\mathrm{Al_2O_3}$ is a defect spinel: Correct. Its oxide ions pack the same way as in a spinel, but since the $\mathrm{Al^{3+}}$ to $\mathrm{O^{2-}}$ ratio of $\mathrm{Al_2O_3}$ does not match a normal $\mathrm{AB_2O_4}$ spinel, some cation sites stay empty. A vacancy-containing spinel lattice like this is what is meant by a defect spinel.

So the true statements describe the spinel site count, the perovskite structure of $\mathrm{BaTiO_3}$, and the defect spinel nature of $\gamma$-$\mathrm{Al_2O_3}$; the statement about $\mathrm{Fe^{2+}}$ in magnetite is false.

Let's summarize:

• A spinel cell has 8 tetrahedral and 4 octahedral sites per formula unit, from its close packed oxide ions.
• $\mathrm{BaTiO_3}$ is a classic $\mathrm{ABO_3}$ perovskite.
• Magnetite is an inverse spinel where $\mathrm{Fe^{2+}}$ sits only on octahedral sites.
• $\gamma$-$\mathrm{Al_2O_3}$ is a cation-deficient (defect) spinel.

The correct options are (A), (B), and (D).