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In a cubic close-packed (ABC-type) arrangement, let X be the distance between two nearest successive tetrahedral voids and Y be the distance between two nearest successive octahedral voids within a unit cell of lattice parameter a. Find the value of Y*sqrt(2) / X.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

In FCC (CCP), tetrahedral voids at body-diagonal quarter-points give nearest separation X = a/2. Octahedral voids at edge-midpoints give nearest separation Y = a/sqrt(2). So Y*sqrt(2)/X = (a/sqrt(2))*sqrt(2)/(a/2) = a/(a/2) = 2.

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