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Spinel Structure (MgAl2O4)

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Spinel (MgAl2O4)
A cubic structure with Mg2+ in tetrahedral sites and Al3+ in octahedral sites within a close-packed O2- framework.
The spinel structure features a cubic close-packed array of oxide ions with cations distributed in tetrahedral and octahedral interstitial sites. In normal spinel (like MgAl₂O₄), Mg2+ occupies 1/8 of tetrahedral holes and Al3+ occupies 1/2 of octahedral holes. The structure belongs to space group Fd3̄m with 8 formula units per unit cell. The general formula is AB₂O₄ where A is divalent and B is trivalent. Inverse spinels exist where half the trivalent cations occupy tetrahedral sites: B(AB)O₄. This versatile structure type accommodates many combinations of cations and is important in magnetic materials (magnetite Fe₃O₄) and gemstones.

Problem 1

Question: In normal spinel (MgAl₂O₄), which cations occupy tetrahedral holes and which occupy octahedral holes?

Solution

Answer:

Tetrahedral holes (A-sites): Mg²⁺ ions (1/8 of tetrahedral holes)

Octahedral holes (B-sites): Al³⁺ ions (1/2 of octahedral holes)

General formula: A[B₂]O₄, where A is in tetrahedral and B is in octahedral sites.

Problem 2

Question: In the spinel structure, O²⁻ ions form cubic close packing (CCP/FCC). How many O²⁻ ions are there per unit cell?

Solution

Calculation:

For FCC arrangement of O²⁻:

Corner atoms: 8 × (1/8) = 1

Face-centered atoms: 6 × (1/2) = 3

But spinel has 8 formula units, so: 8 × 4 = 32 O²⁻ ions per unit cell

Problem 3

Question: What is the difference between normal spinel and inverse spinel?

Solution

Answer:

Normal spinel (MgAl₂O₄): Mg²⁺ in tetrahedral holes, Al³⁺ in octahedral holes

Formula: Mg[Al₂]O₄

Inverse spinel (Fe₃O₄): Half of B³⁺ in tetrahedral holes, A²⁺ and other half of B³⁺ in octahedral holes

Formula: B[AB]O₄ or Fe³⁺[Fe²⁺Fe³⁺]O₄

The arrangement depends on crystal field stabilization energy.

Numerical Problem

Question: The spinel structure has the general formula AB₂O₄. In normal spinel MgAl₂O₄:

(a) How many Mg2+ ions are present per formula unit?

(b) How many Al3+ ions are present per formula unit?

(c) Calculate the total positive charge from all cations in one formula unit of MgAl₂O₄. Does it balance the negative charge from oxygen ions?

[Given: Charge on Mg2+ = +2, Charge on Al3+ = +3, Charge on O2- = -2]

Solution

(a) Number of Mg2+ ions per formula unit:

The formula is MgAl₂O₄

The subscript of Mg is 1 (understood when not written)

Number of Mg2+ ions = 1

(b) Number of Al3+ ions per formula unit:

The formula is MgAl₂O₄

The subscript of Al is 2

Number of Al3+ ions = 2

(c) Charge balance verification:

Total positive charge from cations:

• Charge from Mg2+ = 1 × (+2) = +2

• Charge from Al3+ = 2 × (+3) = +6

• Total positive charge = +2 + 6 = +8

Total negative charge from anions:

• Number of O2- ions = 4

• Charge from O2- = 4 × (-2) = -8

Charge balance:

Total positive charge = +8

Total negative charge = -8

Net charge = +8 + (-8) = 0

Yes, the charges are balanced! ✓

Note: In any ionic compound, the total positive and negative charges must balance to give a neutral compound. This is a fundamental principle of ionic structures.

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