Question

Discuss the characteristics of various types of unit cells.

Answer 1

Unit cells are the smallest repeating structural units of a crystal lattice that represent the entire crystal’s symmetry and structure. Based on the arrangement of particles (atoms, ions, or molecules).

1. Primitive (Simple) Unit Cell:
   1. Atoms are present only at the 8 corners of the cube.
   2. Each corner atom is shared by 8 adjacent unit cells.
   3. Effective number of atoms per unit cell = `8 xx 1/8` = 1
   4. Coordination number is 6.
   5. Packing efficiency is 52.4% (least efficient).
   6. Example: Polonium
2. Body-Centred Cubic (BCC) Unit Cell:
   1. Atoms are present at the 8 corners and 1 at the centre of the cube.
   2. Corner atoms are shared as above; the body-centre atom belongs entirely to that cell.
   3. Effective number of atoms = `(8 xx 1/8) + 1` = 2
   4. Coordination number is 8.
   5. Packing efficiency is 68%.
   6. Examples: Iron (α-Fe), Chromium, Potassium
3. Face-Centred Cubic (FCC) Unit Cell:
   1. Atoms are present at the 8 corners and centres of all 6 faces.
   2. Corner atoms contribute 1 atom; each face-centred atom is shared between 2 unit cells.
   3. Effective number of atoms = `(8 × 1/8) + (6 × 1/2)` = 4
   4. Coordination number is 12.
   5. Packing efficiency is 74% (most efficient packing).
   6. Examples: Copper, Aluminum, Silver, Gold