GATE 2026 CY – Question 53

Correct answer: (B) BaTiO3 has a perovskite structure; (D) γ-Al2O3 is a defect spinel

Explanation

Check each statement about the structure of metal oxides.

• **A. Spinel has 8 tetrahedral sites and 4 octahedral sites per formula unit.** False. A spinel $AB_2O_4$ has 1 tetrahedral and 2 octahedral sites occupied per formula unit (in the unit cell of 8 formula units, 8 of the 64 tetrahedral holes and 16 of the 32 octahedral holes are filled). The counts given are wrong.
• **B. $\text{BaTiO}_3$ has the perovskite structure.** True. ✓
• **C. In $\text{Fe}_3\text{O}_4$, $\text{Fe}^{2+}$ occupies both tetrahedral and octahedral sites.** False. Magnetite is an inverse spinel: $\text{Fe}^{3+}$ fills the tetrahedral sites and half the octahedral sites, while $\text{Fe}^{2+}$ occupies only octahedral sites.
• **D. $\gamma$-$\text{Al}_2\text{O}_3$ is a defect spinel.** True. It has the spinel structure with vacancies on the cation sites. ✓

Answer **B and D**.