Unit Cell:
For every crystal lattice it is possible to select a group of lattice points which is repeated again and again. This part of the space lattice is called unit cell. Therefore,
“A unit cell is the smallest repeating unit in space lattice which repeated over and over again produces the complete space lattice”.
Type of unit cell:
The unit cells can be broadly classified as into two categories-
1) Simple or basic unit cell
2) Face centred unit cell
3) Body centred unit cell
Simple or basic unit cell: A unit cell having lattice points only at the corners is called simple or basic unit cell.
Face centred unit cell: A unit cell having lattice points at the centre of each face, in addition to the lattice points at the corners, is called face centred unit cell.
Body centred unit cell: A unit cell having lattice points at the centre of the body, in addition to the lattice points at the corners, is called body centred unit cell.
Determination of number of particles in a unit cell:
In order to calculate the number of particles (atoms) in a unit cell the following rules must be obeyed.
(1) Each particle at the corner of a unit cell is shared by eight unit cells in the lattice and hence contributed by ⅛ to a particular unit cell.
(2) A particle at the edge centre is shared is shared by four unit cells in the lattice and hence contributes ¼ to a particular unit cell.
(3) A particle at the centre of the face of a unit cell is shared by two unit cells in the lattice and hence contributes ½ to a particular unit cell.
(4) A particle at the body centre of a unit cell is belongs to the particular unit cell.
By applying these rules, we can calculate the number of atoms in different unit cell.
For a simple unit cell,
The number of atoms present =⅛ (at each corner) x 8 = 1
For a body centred unit cell,
The number of atoms present =⅛ (at each corner) x 8 + 1 = 2
For a face centred unit cell,
The number of atoms present =⅛ (at each corner) x 8 + ½ (at each face) x 6 = 4