Q3(a). NiCr₂O₄ and NiCo₂O₄: normal or inverse spinel

1. Normal spinel A[B₂]O₄: A²⁺ in tetrahedral holes (1/8), B³⁺ in octahedral holes (1/2) of a ccp oxide lattice. MgAl₂O₄: Mg²⁺ (Td), Al³⁺ (Oh), no CFSE preference, so it is normal.
2. Deciding factor: the octahedral site preference energy (OSPE = CFSE(Oh) - CFSE(Td)). itemize
3. Ni²⁺ d⁸: -1.2Δₒ in Oh against -0.36Δₒ in Td: OSPE about 86 kJ mol⁻¹.
4. Cr³⁺ d³: -1.2Δₒ in Oh against -0.27Δₒ in Td: OSPE about 158 kJ mol⁻¹ (the highest of all ions).
5. Co³⁺, high spin d⁶ in an oxide lattice: -0.4Δₒ in Oh against -0.27Δₒ in Td: OSPE only 0.13Δₒ (small). itemize
6. NiCr₂O₄: Cr³⁺ (158) is far more octahedral-loving than Ni²⁺ (86): Cr³⁺ takes Oh sites, Ni²⁺ is left in Td: normal, like MgAl₂O₄. (Ni²⁺ Td adds a Jahn–Teller-type distortion; the compound is a distorted tetragonal normal spinel at room temperature.)
7. NiCo₂O₄: Ni²⁺ (86 kJ mol⁻¹) ≫ Co³⁺ (small): Ni²⁺ goes to Oh, and the Co³⁺ divides between Td and Oh: inverse spinel, structurally different from MgAl₂O₄.

inverse spinels (Fe₃O₄, NiFe₂O₄) are ferrimagnetic: unequal opposed moments on Td and Oh sublattices; NiCo₂O₄ is a good oxygen-evolution catalyst.