Calculate the number(n) of atoms contained within (i) a primitive cubic unit cell (ii) a body –centred cubic unit cell and (iii) a face-centred cubic (f.c.c) unit cell

Explanation

: (i) The primitive unit cell consists of one atom at each of the 8 corners, each atom is thus shared by 8 unit cells. Hence n = `8 xx (1//8) = 1`
(ii) The b.c.c unit cell consists of 8 atoms at the 8 corners and one atom at the centre. At each corner only `1//8^(th)` of the atom is within the unit cell. Thus the contribution of the 8 corners is `8 xx (1//8) = 1` while that of the body-centred atom is 1. Hence, n = 1+1 =2
(iii) The 8 atoms at the corners contribute 8 x (1/8) = 1 atom. There is one atom each of the 6 faces, which is shared by 2 unit cells each. Therefore, the contribution face-centred atoms = 6x (1/2) = 3 Hence, n = 1+3 = 4.