1.8
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
Answers
(i) Face-centred cubic
8 lattice points at corners and 6 lattice points at face centres are present in face-centred cubic.
A corner lattice point contributes one eight to the unit cell and a lattice point at face centre contributes one half to the unit cell.
Total number of lattice points per unit cell:
8× 1/8 + 6 × 1/2 = 1 + 3 = 4
(ii) Face-centred tetragonal
8 lattice points at corners and 6 lattice points at face centres.
A corner lattice point contributes one eight to the unit cell and a lattice point at face centre contributes one half to the unit cell.
Total number of lattice points per unit cell:
8× 1/8 + 6 × 1/2 = 1 + 3 = 4
(iii) Body-centred
8 lattice points at corners and 1 lattice point at body centre.
A corner lattice point contributes one eight to the unit cell and a lattice point at body centre contributes one to the unit cell.
Total number of lattice points per unit cell:
8× 1/8 + 1 × 1 = 1 + 1 = 2