Hii,

The diamond lattice is face-centered cubic.

The simplified packing fraction is 8 x (V atom) / V unit cell.

After making substitutions for known volume of spheres and cubes and simplifying, the equation becomes √3 x π/16 with a solution of 0.3401.

Or we can also define it as..

The atomic packing factor of the diamond cubic structure (the proportion of space that would be filled by spheres that are centered on the vertices of the structure and are as large as possible without overlapping) is π√316 ≈ 0.34

Hope this will help you,

All the very best!!