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Structure of a mixed oxide is cubic close-packed (c.c.p). The cubic unit cell of mixed oxide is composed of oxide ions. One fourth of the tetrahedral voids are occupied by divalent metal A and the octahedral voids are occupied by monovalent metal B. The formula of the oxide is:

1. ABO₂
2. A₂B₄O₄
3. A₂B₃O₄
4. AB₂O₂

Correct answer: A₂B₃O₄

Solution

In a c.c.p. structure, the number of oxide ions (O²⁻) per unit cell is 4. The number of tetrahedral voids is twice the number of oxide ions, i.e., 8, and one-fourth of these are occupied by A²⁺, giving 2 A²⁺ ions. The number of octahedral voids equals the number of oxide ions, i.e., 4, and all are occupied by B⁺ ions. Thus, the formula is A₂B₄O₄, which simplifies to A₂B₃O₄.

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