Q.A compound is formed by two elements M and N. The element N forms ccp and atoms of M occupy 1/3rd of tetrahedral voids. What is the formula of the compound?

Take the ccp of N as $1$ atom; then there are $2$ tetrahedral voids. M occupies $\tfrac13$ of these: …

Step 1 – Fix a basis from the ccp of N.

Let there be 1 atom of N forming the ccp lattice.

Step 2 – Tetrahedral voids available.

In a close-packed arrangement the number of tetrahedral voids is twice the number of packing atoms:

Step 3 – Atoms of M.

M occupies $\tfrac13$ of the tetrahedral voids: …

Set N (the ccp lattice) as 1; tetrahedral voids $=2$; M $=\tfrac13\times$ voids. Simplify the M …

• Using 1 (octahedral) instead of 2 (tetrahedral) voids per atom.
• Forgetting to clear the fraction $\tfrac23:1$ to $2:3$, giving a non- …