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.

Calculate the packing efficiency of a fcc crystal in which all the tet

1.	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» SOLUTION :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`