Question

Choose the correct statement(s) regarding voids in hcp arrangemnt.

• A. It has 12 tetrahedral voids per unit cell
• B. Number of tetrahedral voids is same as octahedral voids.
• C. It has 8 octahedral voids per unit cell
• D. Number of particles per unit cell is 6

Answer 1

Answer: (A), (D)

Number of particles per unit cell is 6

In hcp unit cell , 8 tetrahedral voids are present completely inside the unit cell and 12 voids are present at edge centre.
Contribution of voids present inside the unit cell is 1
Contribution of each edge centre void is $\frac{1}{3}$.
So, the total number of tetrahedral voids in hcp lattice are :
$(8\times 1)+(12\times \frac{1}{3})=12$

Also, there are six octahedral voids .All of them are present completely inside the unit cell.
We know, for a hcp lattice, the number of particles per unit cell are 6.
$\therefore$
$\text{Number of atoms per unit cell of hcp}=N$
$\text{Number of octahedral voids per unit cell}=N$
$\text{Number of tetrahedral voids per unit cell}=2N$

Thus, statements (a) and (d) are correct.