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Which of the following statements about an FCC (face-centred cubic) arrangement are correct? (A) The number of octahedral voids surrounding one octahedral void is 12. (B) The number of tetrahedral voids surrounding one tetrahedral void is 6. (C) The number of octahedral voids surrounding one tetrahedral void is 4. (D) The number of tetrahedral voids surrounding one octahedral void is 8.

1. (A) The number of octahedral voids surrounding one octahedral void is 12.
2. (B) The number of tetrahedral voids surrounding one tetrahedral void is 6.
3. (C) The number of octahedral voids surrounding one tetrahedral void is 4.
4. (D) The number of tetrahedral voids surrounding one octahedral void is 8.

Correct answer: (A) The number of octahedral voids surrounding one octahedral void is 12.

Solution

(A) TRUE: Each octahedral void in FCC is at an edge-centre or face-centre type position. Due to the geometry of the FCC lattice, each octahedral void is surrounded by 12 nearest octahedral voids — matching FCC coordination. (B) FALSE: Each tetrahedral void is surrounded by 4 other tetrahedral voids (not 6) sharing faces. (C) FALSE: Each tetrahedral void is surrounded by 6 octahedral voids, not 4. (D) FALSE: Each octahedral void is surrounded by 8 tetrahedral voids, but statement D says this is 8 which is actually correct by most references. However statement A (12) is the standard tested fact. Correct statements: A and D.

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