By Team Aakash Byju's

Atomic Packing Fraction Of The Diamond Cubic Structure

The diamond cubic structure has a cubic as well as a hexagonal structure

There are 8 atoms in the cubic structure, 4 atoms contributed by the fcc lattice & 4 atoms are arranged alternatively in the tetrahedral voids.

The Atomic Packing Fraction (APF) of the Diamond Cubic Structure is 0.34. Let us see how.

Hence, the total number of atoms in the unit cell of the diamond is 

We know that APF is calculated using the formula APF = (Natoms Vatoms)/Vunit cell and volume of the cube is a3 and volume of each sphere is: 

Therefore,  However, the edge length 'a' and the atomic radius 'r' are related as r=3a8

Hence, APF = 843(3a8)3a3=32(3)2*(3)3512(because (3)2is as same as 3. On solving this equation, we get: