Packing Efficiency of Body Centred Cubic Crystal Lattice (BCC):
In a body-centred cubic lattice, the eight atoms are located on the eight corners of the cube and one at the centre of the cube. Let the edge length or side of the cube ‘a’, and the radius of each particle be r. The particles along the body diagonal touch each other.
∴ AD = r + 2r + r = 4r ……. (1)
Thus the radius of an atom is √3/4 times the side of the body-centred cubic unit cell.
The volume of the cubic unit cell
Since a body-centred cubic unit cell contains 2 atoms
The packing efficiency of the body-centred cubic cell is 68 %. Thus 32 % volume is empty space (void space).
Packing Efficiency of Face Centred Cubic Crystal Lattice (FCC):
In a face-centred cubic lattice, the eight atoms are located on the eight corners of the cube and one at the centre of the cube. Let the edge length or side of the cube ‘a’, and the radius of each particle be r. The particles along face diagonal touch each other.
∴ AB = r + 2r + r = 4r ……. (1)
Thus the radius of an atom is 1 / √8 times the side of the face centred cubic unit cell.
The volume of the cubic unit cell
Since a face centred cubic unit cell contains 4 atoms,
The packing efficiency of the face centred cubic cell is 74 %. Thus 26 % volume is empty space (void space).
