How many lattice points are there in one unit cell of each of the following lattice?
a. Face-centred cubic
b. Face-centred tetragonal
c. Body-centred

Explanation

(a) In face centred cubic arrangement, number of lattice points are:
8(at corners) + 6 (at face centres)
Lattice points per unit cell = `8 xx 1/8 + 6 xx 1/2 = 4`
(b) In face centred tetragonal , number of lattice points are :
= 8 (at corners) + 6(at face centres)
Lattice points per unit cell = `8 xx 1/8 + 6 xx 1/2 = 4`
(c ) In body centred cubic arrangement number of lattice points are :
= 8 (at corners) + 1 (at body centre)
Lattice points per unit cell = `8 xx 1/8 + 1 = 2`