Question

Unit cells can be divided into two categories, primitive and centred unit cells. 

(a) Differentiate between Unit Cell and Crystal Lattice.

(b) Calculate the number of atoms per unit cell in the following:

(i) Body centred cubic unit cell (bcc)

(ii) Face centred cubic unit cell (fee)

Answer 1

(a) Unit Cell – It is the smallest portion of a crystal lattice which, when repeated in different directions, generates the entire lattice.

Crystal Lattice – It is the regularthree dimensional arrangement of points in space.

(b) 

(i) Body centred cubic unit cell (bcc) – It has atoms at each of its corners and one atom at its body centre.
8 corners x \(\frac{1}{8}\) per corner atom = 8 x \(\frac{1}{8}\) = 1 atom

1 body centre atom = 1 x 1 = 1 atom

∴ Total number of atoms per unit cell = 2 atoms

(ii) Face centred cubic unit cell (fee) – It contains atoms at all the corners and at the centre of all the faces of the cube.

8 corners x \(\frac{1}{8}\) per corner atom

=8× \(\frac{1}{8}\) =1 atom

6 face – centred atoms x \(\frac{1}{2} \) atom per unit cell =6 × \(\frac{1}{2}\)= 3 atoms

∴ Total number of atoms per unit cell = 4 atoms