The crystalline structure of a solid is CCP for 'X' atoms. If 'Y' atoms occupy all the octahedral voids and 'Z' atoms occupy all the tetrahedral voids, without any distortion in the CCP arrangement of

Question

The crystalline structure of a solid is CCP for 'X' atoms. If 'Y' atoms occupy all the octahedral voids and 'Z' atoms occupy all the tetrahedral voids, without any distortion in the CCP arrangement of 'X' atoms, then the fraction of body diagonal of body diagonal not covered by the atoms is

Prashant Kotian · Accepted Answer

Correct answer: B. In FCC, body diagonal D = a × √3 = 2√2 Rx × √3 = 2√6 Rx ≈ 4.899 Rx. Covered length along body diagonal = 2 × Rx (corners) + 2 × Ry (octahedral at body center) + 4 × Rz (two tetrahedral voids along the diagonal). Since voids are occupied at limiting radius: Ry = 0.414 Rx, Rz = 0.225 Rx. Covered length = 2Rx + 2(0.414Rx) + 4(0.225Rx) = 3.728 Rx. Fraction covered = 3.728 Rx / 4.899 Rx ≈ 0.761. Uncovered fraction = 1 - 0.761 = 0.239 ≈ 0.24.

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