Question

In which of the following pair, most efficient packing is present?

• A. hcp and bcc
• B. hcp and ccp
• C. bcc and ccp
• D. bcc and simple cubic cell

Answer 1

The correct option is B

hcp and ccp

Explanation for correct option:

Bcc:

1. It is known as the body-centered cubic cell.
2. Every vertex of the cube represents an atom.
3. The coordination no. (number of atoms each atom touches) of bcc is 8.
4. Bcc has 2 atoms per unit cell.

Hcp:

1. Hcp is known as a hexagonal closed-packed cell.
2. It has an atom on each vertex and 3 atoms in the center.
3. It has 6 atoms per unit cell.
4. The coordination no. of hcp is 12.

Ccp:

1. Ccp is known as the cubic close-packed cell.
2. It comprises of four layers of atoms in a cubic close-packed (ccp) arrangement of atoms.
3. It has 4 atoms per unit cell.
4. Its coordination number is 12.

Scp:

1. Scp is known as a simple cubic unit cell.
2. It has the coordination no. of 6.
3. Scp has one atom per unit cell.
4. The atoms are present on the vertex of the cube.

Packing efficiency:

It is known as the amount of space held by the atoms/particles of the unit cell.

Packing efficiency = $\frac{\mathrm{Volume}\mathrm{occupied}\mathrm{by}\mathrm{atoms}}{\mathrm{Volume}\mathrm{of}\mathrm{unit}\mathrm{cells}}\times 100$

1. hcp = 74%
2. ccp = 74% bcc = 68%
3. Simple cubic = 54%

Hence, The most efficient packing is present in hcp and ccp.