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

Explanation

a. Face-centred cubic: There are 8 lattic points on the corners and 6 lattice points at the body centre = 14.
However, atom per unit cell `= 8 xx (1)/(8) + xx (1)/(2) = 4`.
b. Face-centred tetragonal = 8 corners + 6 at face centres `(a = b != c, alpha = gamma = 90^(@)) = 14 implies 4//"unit cell"`.
c. Body-centred cubic : There are 8 lattice points on the corners and one lattic point at the body centre = 9. However, atom per unit cell `= 8 xx (1)/(2) + 1 = 2//"unit cell"`.