NCERT Section

1.4.1 Primitive and Centred Unit Cells

 

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

(a) Primitive Unit Cells

When constituent particles are present only on the corner positions of a unit cell, it is called as primitive unit cell.

(b) Centred Unit Cells

When a unit cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called a centred unit cell. Centred unit cells are of three types:

(i) Body-Centred Unit Cells: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre besides the ones that are at its corners.

(ii) Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face, besides the ones that are at its corners.

(iii) End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces besides the ones present at its corners.

 

Inspection of a wide variety of crystals leads to the conclusion that all can be regarded as conforming to one of the seven regular figures. These basic regular figures are called seven crystal systems. To which system a given crystal belongs to is determined by measuring the angles between its faces and deciding how many axis are needed to define the principal features of its shape. Fig. 1.11 shows seven crystal systems.
1.7_(New)
Fig. 1.11: Seven crystal systems
 
A French mathematician, Bravais, showed that there are only 14 possible three-dimensional lattices. These are called Bravais lattices. Unit cells of these lattices are shown in the following box. The characteristics of their primitive unit cells along with the centred unit cells that they can form have been listed in Table 1.3.

 

Table 1.3: Seven Primitive Unit Cells and their Possible Variations as Centred Unit Cells

1i1j

Unit Cells of 14 Types of Bravais Lattices

1k

1l