## Density and Packing Efficiency of Unit Cell (Contd.)

### Packing Efficiency of Face Centred Cubic Crystal Lattice (FCC):

• In a face centred cubic lattice the eight atoms are located on the eight corners of the cube and one at the centre of the cube.
• Let the edge length or side of the cube ‘a’, and the radius of each particle be r. The particles along face diagonal touch each other.

∴  AB = r + 2r + r = 4r  ……. (1)

• Thus radius of an atom is 1 / 8   times the side of the face centred cubic unit cell.
• The volume of the cubic unit cell

• Since a face centred cubic unit cell contains 4 atoms, the volume of the occupied space

• Now, packing efficiency

• The packing efficiency of face centred cubic cell is 74 %. Thus 26 % volume is empty space(void space).

### Summary of the Three Types of Cubic Structures (Density and Packing Efficiency of Unit Cell)

• No. of Atoms in unit cell and Co-ordination Number of cubic unit cells:

• Relation Between radius of constituent particles (r) and side (a) of cubic unit cell
• Packing Efficiency of cubic unit cell

### Note:

• From the unit cell dimensions, it is possible to calculate the volume of the unit cell. Knowing the density of the metal, we can calculate the mass of the atoms in the unit cell. The determination of the mass of a single atom gives an accurate method of determination of Avogadro constant.