There are three cubic unit cells A, B and C. A is FCC and all of its tetrahedral voids are also occupied. B is also FCC and all of its octahedral voids are also occupied. C is simple cubic and all of

Question

There are three cubic unit cells A, B and C. A is FCC and all of its tetrahedral voids are also occupied. B is also FCC and all of its octahedral voids are also occupied. C is simple cubic and all of its cubic voids are also occupied. If voids in all unit cells are occupied by the spheres exactly at their limiting radius, then the order of packing efficiency would be

Prashant Kotian · Accepted Answer

Correct answer: B. In FCC, packing efficiency is 74%. In simple cubic, it is 52.4%. For A (FCC + tetrahedral): V_atoms = 4 × (4/3πR³) + 8 × (4/3π(0.225R)³) => efficiency ≈ 75.7%. For B (FCC + octahedral): V_atoms = 4 × (4/3πR³) + 4 × (4/3π(0.414R)³) => efficiency ≈ 79.2%. For C (Simple Cubic + cubic): V_atoms = 1 × (4/3πR³) + 1 × (4/3π(0.732R)³) => efficiency ≈ 72.9%. The order is C < A < B.

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