Question

Calculate the packing efficiency of a fcc crystal in which all the tetrahedral and octahedral voids are occupied by the largest spheres without disturbing the lattice.

Answer 1

fcc has 4 atoms per unit cell
No. of tetrahedral voids=8
No.of octahedral voids=4
If R is the radius of the atoms in the packing.
Radius of tetrahedral void =0.225 R
Radius of octahedral void =0.414 R
For Fcc, `a=2sqrt2r =2sqrt2R` (`because` Here, r=R)
Packing efficiency =`"Volume occupied by spheres"/"Volume of the unit cell"`
`=(4xx4/3piR^3+8xx4/3pi(0.225R)^3+4xx4/3pi(0.414R)^3)/((2sqrt2R)^3)=0.81`