Calculate packing efficiency in ccp structure.

For cubic close packed :

a = 2R√(2)

Since the radius of a sphere is given by 4πR³/3, the total volume of all the atoms in the unit cell is simply

4*[ 4πR³/3 ] = 16πR³/3
volume of the cube in terms of R is (2R√(2))³ = 16R³√(2).

Therefore, the efficiency of the ccp crystal structure is given by
(16πR³/3) / (16R³√(2)) = 0.74078... ≈0.74
volume of all spheres = 2*(4πR³/3) = 8πR³/3

The length of the edge of one of the cubes is related to R by
a = 4R/√(3)
So the volume of the cube in terms of R is

(4R/√(3))³ = 64R³/(3*√(3))

So the efficiency is
(8πR³/3) / [ 64R³/(3*√(3))] = 0.68017... ≈0.68