Calculate the void space in fcc packing of n spheres of radius 1 nm, n spheres of radius 0.414 nm, and 2n spheres of radius 0.225 nm in appropriate voids.

Options

A. 0.19
B. 0.26
C. 0.17
D. 0.12

Answer

A

Explanation

Consider unit cell of fcc, volume occupied by spheres
`=(4xx(4)/(3)pixx1^(3))+4xx(4)/(3)pi(0.414)^(3)+8xx(4)/(3)pi(0.225)^(3)=18.32cm^(3)`
Edge length `a=(4r)/(sqrt2)=(4)/(sqrt2)`
Volume of cube`=((4)/(sqrt2))^(3)=22.627`
Packing fraction`=(18.32)/(22.627)=0.8096=80.96%`
It is clear from the figure that the arrangement is sc, with coordination number (CN) of each point=6.
(The arrangement shown in figure consists of 4 unit cells. taking a view of one unit cell, the atoms are occupied at corners and face centres of each unit cell).