We know that there are three different types of cubic unit cell. Crystals of elements consist of atoms. These atoms are arranged in different ways to give different types of unit cells. Face centred cubic different types of unit cells consist of different number of atoms. In order to calculate the number of atoms in a cubic unit cell, we should note that,
- 1} A Corner atom is shared equally by unit cells. Thus, each corner atom contributes 1/8 atom to a particular cubic unit cell.
- 2} A Face Centered atom is shared equally by two unit cells having common face. Therefore, an atom present at the center of the face of a unit cell contributes ½ atom to each unit cell.
- 3} A Body Centered atom belongs only to a particular unit cell. So, the atom at the body center of the unit cell contributes one atom per unit cell.
Corner atom is shared by eight unit cells and the face centered atom is equally shared by two unit cells. Let us now calculate the number of atoms of an element in different cubic unit cells.
Calculation of Number of Atoms of an Element in Cubic Unit Cells:
The number of particles in a unit cell of a cubic system can be calculated as follows:
1} Simple Cubic Unit Cell: In this type of unit cell, there is one atom at each corner of the cube. Since, each corner atom is shared equally by eight unit cells (cubes), hence each corner atom contributes 1/8 atom to each unit cell. There are 8 corners in a cube. Therefore,
No. of atoms in one simple cubic unit cell = 8 × 1/8 atom = 1 atom.
2} Body Centered Cubic Unit Cell: In a body centered cubic unit cell, there are 8 atoms at 8 corners of the cube, and 1 atom at the center. Therefore,
No. of atoms in body centered unit cell = ( 8 × 1/8 ) + 1 atoms = 1+1 = 2 atoms
3}Face Centered Cubic Unit Cell: In a face centered cubic unit cell there are 8 atoms, one at each of the 8 corners of the cube, and 6 atoms one in each face. Therefore,
Number of atoms per unit cell = (8 × 1/8) + (6 × ½) atoms = 4 atoms.