Q 8 How many lattice points are there in one unit cell of each of the following lattice? (i) Face–centred cubic (ii) Face–centred tetragonal (iii) Body–centred

Q 8 How many lattice points are there in one unit cell of each of the following lattice?

(i) Face–centred cubic

(ii) Face–centred tetragonal

(iii) Body–centred

Solution: :–

(i) Face–centred cubic

(i) A face–centred cubic (fcc) unit cell contains atoms at all the corners and at the centre of all the faces of the cube.

So lattice point at the corner               = 8

Lattice point at the center of all faces  = 6

Total number of lattice point                = 14

(ii) Face–centred tetragonal

lattice point at the corner                    = 8

Lattice point at the center of all faces  = 6

Total number of lattice point                     = 14

(iii) Body–centred

In Body centered cubic there are 8 lattice point at the corner and 1 is at the center so total 8+1 =9 lattice point