Unit Cell

The smallest repeating unit of the crystal lattice is the unit cell, the building block of a crystal.

• Parameters of unit cell

Edge length a,b, and c

The angles among these edges ∝, 𝛽 𝑎𝑛𝑑 𝛾

Seven types of crystal system

There are about 230 crystal forms, which have been grouped into 14 types of space lattices, called Bravais Lattices, on the basis of their symmetry and seven different crystal systems on the basis of interfacial angles and axes

Types Of Unit Cell

1. 1. Primitive Cubic Unit Cell
   2. Body-centered Cubic Unit Cell
   3. Face centered cubic unit cell

Number of Atoms in a Unit Cell

(i) Simple or primitive Unit cell

In which the particles are present at the corners only.

Thus in SCC cell we have :

• 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom

Therefore, the total number of atoms in a unit cell = 1 atom.

(ii) Face centred unit cell

In which the particles are present at the corners as well as at the centre of each of six faces

Thus in FCC cell we have :

• 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
• 6 face-centered atoms × 1/2 atom per unit cell = 3 atoms Therefore, the total number of atoms in a unit cell = 4 atoms. (iii) Body centred unit cell

In which the particles are present at the corners as well as at the centre of the unit cell.

Thus, in a BCC cell, we have:

• 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
• 1 body center atom = 1 × 1 = 1 atom

Therefore, the total number of atoms present per unit cell = 2 atoms

(iv) End centred unit cell

In which the particles are present at the corners and at the centre of two opposite faces.

Thus in ECC cell we have :

• 8 corners × 1/8 per corner atom = 8 × 1/8 = 1 atom
• 2 face-centered atoms × 1/2 atom per unit cell = 1 atom Therefore, the total number of atoms in a unit cell = 2 atoms