Analysis of Metal Oxide Structures

The question asks to identify the correct statements regarding the structures of various metal oxides.

Statement 1: Spinel Site Availability

The spinel structure formula is $AB_2O_4$. In a unit cell containing 8 formula units, there are typically 64 tetrahedral (T) and 32 octahedral (O) sites available for cations. Per formula unit:

• Available Tetrahedral sites = $\frac{64}{8}$ = 8
• Available Octahedral sites = $\frac{32}{8}$ = 4

Therefore, the statement "Spinel has 8 tetrahedral sites and 4 octahedral sites per formula unit" is correct.

Statement 2: Perovskite Structure

Barium titanate, represented as $BaTiO_3$, is a well-known example exhibiting the characteristic $ABO_3$ perovskite crystal structure. Thus, this statement is correct.

Statement 3: $Fe_3O_4$ Site Occupancy

Iron(II,III) oxide, $Fe_3O_4$ (magnetite), adopts an inverse spinel structure. In this structure:

• $Fe^{2+}$ ions exclusively occupy the tetrahedral sites.
• $Fe^{3+}$ ions are distributed between octahedral sites and tetrahedral sites.

The statement "$Fe_3O_4$, $Fe^{2+}$ occupies both tetrahedral and octahedral sites" is incorrect as $Fe^{2+}$ resides only in tetrahedral sites.

Statement 4: Defect Spinel Structure

Gamma alumina, $\gamma$-$Al_2O_3$, possesses a structure derived from the spinel framework but is classified as a "defect spinel". This is due to vacancies present within the normally occupied cation sites (T and O sites) in the oxygen lattice.

Therefore, the statement "$\gamma$-$Al_2O_3$ is a defect spinel" is correct.

Conclusion

Based on the analysis, the correct statements are:

• Statement 1: Spinel has 8 tetrahedral sites and 4 octahedral sites per formula unit.
• Statement 2: $BaTiO_3$ has a perovskite structure.
• Statement 4: $\gamma$-$Al_2O_3$ is a defect spinel.

The correct options are A, B, and D.