Caleulate the packing efficiency in a unit cell of Cubic Close Packing(CCP) structure. 

Explanation

The number of atoms per unit cell is foc, cep structures is four. Each atom is considered as one sphere.
let the edge length of the unit cell = a
Radius of the sphere = r.
Length of the face diagonal = b.

In ABC
`AC^(2)=BC^(2)+AB^(2)`
`b^(2)=a^(2)+a^(2)`
`b=sqrt2a`
But `b=4r`
`therefore sqrt2a=4r`
`a=(4r)/(sqrt2)=2sqrt2r`
`"Volume of one sphere "=(4)/(3)pir^(3)`
Since ccp, fcc lattice contains 4 atoms [sphere] per unit cell.
The volume ofthe 4 sheres in FCC is `4xx(4)/(3)pir^(2)=(16)/(3)pir^(2)`
Total volume of the unit cell
`rArr a^(3)=(2sqrt2r)^(3)`
`"Packing efficiency "=("Volume of four shepers in unit cell")/("Total volume of the unit cell")xx100%`
`"Packing efficiency "=((16)/(3)pir^(3))/((2sqrt2r)^(3))xx100=74%`