Question

If N is the number of tetrehedral voids in a close-packed structure, then the number of octahedral voids is:

• A. $\frac{N}{4}$
• B. $4N$
• C. $2N$
• D. $\frac{N}{2}$

Answer 1

The correct option is D $\frac{N}{2}$

Tetrahedral voids are formed when triangular voids of one close-packed layer do not overlap while octahedral ones when they overlap. The above relation is valid for both ABAB type(HCP) and ABCABC type(FCC) packing.
Number of tetrahedral void is double of octahedral void.
If there is N tetrahedral void in a closed pack structure then there will be $N/2$ octahedral void. for example ccp structure has 4 octahedral and 8 tetrahedral void. thus option d is correct.