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 cubic
A face-centred cubic (fcc) unit cell contains atoms at all the corners and at the centre of all the faces of the cube.each atom located at the face-centre is shared between two adjacent unit cells and only 1/2 of each atom belongs to a unit cell
Thus, in a face-centred cubic
(fcc) unit cell:
(i) 8 corners atoms × 1/8 atom per unit cell = 8×1/8 = 1 atom
(ii) 6 face-centred atoms ×1/2 atom per unit cell = 6 ×1/2 = 3 atoms
∴ Total number of atoms per unit cell = 4 atoms
body centre wholly belongs to the unit cell in which it is present. Thus
in a body-centered cubic (bcc) unit cell:
(i) 8 corners × 1/8 per corner atom= 8×1/8 = 1 atom
(ii) 1 body centre atom = 1 × 1 = 1 atom
∴ Total number of atoms per unit cell =1+1 = 2
(c) z = 2.