Find Spinel or Inverse Spinel Structure

For the compounds (I-III), determine whether they have Spinel or inverse Spinel structure?
(I) Mn₃O₄ (II) NiFe₂O₄ (III) Fe₃O₄

(A) Spinel : Compound (II) and (III) and Inverse Spinel : Compound (I)
(B) Spinel : Compound (I) and (II) and Inverse Spinel : Compound (III)
(C) Spinel : Compound (I) and Inverse Spinel : Compound (II) and (III)
(D) Spinel : Compound (I) and (III) and Inverse Spinel : Compound (II)

Correct Answer: (C) Spinel : Compound (I) and Inverse Spinel : Compound (II) and (III)

Spinel structure refers to the general AB₂O₄ framework with face-centered cubic oxide ions. It is classified as:

• Normal (or direct) spinel: Divalent cation (A²⁺) in tetrahedral sites, trivalent cations (B³⁺) in octahedral sites.
  Formula: (A²⁺)_tet[B³⁺₂]_octO₄.
• Inverse spinel: Trivalent cation in tetrahedral sites, mixture of divalent and trivalent in octahedral sites.
  Formula: (B³⁺)_tet[A²⁺ B³⁺]_octO₄.

Compound (I) Mn₃O₄: Normal spinel. Mn²⁺ occupies tetrahedral sites, two Mn³⁺ occupy octahedral sites (tetragonally distorted due to Jahn-Teller effect, but cation distribution is normal).

Compound (II) NiFe₂O₄: Inverse spinel. Fe³⁺ in tetrahedral sites, Ni²⁺ and Fe³⁺ in octahedral sites.

Compound (III) Fe₃O₄ (magnetite): Classic inverse spinel. Fe³⁺ in tetrahedral sites, Fe²⁺ and Fe³⁺ in octahedral sites.

This classification is based on crystal field stabilization energy (CFSE) preferences and experimental structural determinations.