Calculate the efficiency of the packaing in case of face - centered cubic crystal .

Explanation

Packing efficiency of face centered cubic crystal :
In fcc lattice assume that atoms are touching each other . Here unit cell edge length a = 2 `sqrt2 r`
Each unit cell as effectively four spheres .
Total volume of four spheres = `4 xx ((4)/(3)) pi r^(3)`
Volume of cube = `a^(3) = (2sqrt2 r)^(3)`
Packing efficiency = `("Volume occupied by four spheres of unit cell")/("Total volume of unit cell") xx 100`
`= (4 ((4)/(3)) pi r^(3) xx 100)/((2sqrt2 r)^(3))`
`= (((16)/(3))pi r^(3) xx 100)/(16 sqrt2 pi ^(3)) = 74 %` .