What is the packing efficiency in BCC unit cell ?

Step-by-step solution

In a body-centered cubic (BCC) unit cell, the atoms touch each other along the body diagonal. Let the edge length of the unit cell be a and the radius of the atom be r . The length of the body diagonal is 3 a . Since the atoms touch along the body diagonal, we have: 3 a = 4r a = 4r 3 The number of atoms per unit cell in a BCC structure is Z = 2 . Volume of the unit cell is V = a^3 = ( 4r 3 )^3 = 64r^3 3 3 Volume occupied by the atoms is v = 2 4 3 r^3 = 8 3 r^3 Packing efficiency is given by: Packing efficiency = v