Simple cubic, face centered and body centered

Calculation of Number of Particles per Unit Cell of a Cubic Crystal System.

Keeping the following points in mind we can calculate the number of atoms in a unit cell.

• An atom at the corner is shared by eight unit cells. Hence an atom at the corner contributes 1/8 to the unit cell

• An atom at the face is a shared by two unit cells

Contribution of each atom on the face is 1/2 to the unit cell.

• An atom within the body of the unit cell is shared by no other unit cell

Contribution of each atom within the body is 1 to the unit cell.

• An atom present on the edge is shared by four unit cells

Contribution of each atom on the edge is 1/4 to the unit cell.

By applying these rules, we can calculate the number of atoms in the different cubic unit cells of monoatomic substances.

fig 2.4

Simple cubic:

In this type of unit cell, there are eight atoms at the corners and each such atom makes�

contribution to the unit cell.

Body centered cubic:

This type of unit cell has eight atoms at corners and one at the body center. Each corner atom makes contribution and the atom at the body center belongs only to the particular unit cell.

Hence, a body centered cubic unit cell has,

Face centered cubic:

A face centered cubic unit cell has one atom at each corner and one atom at each face center, being shared by two unit cells and making a

Hence, a face centered cubic unit cell has,