Calculate the packing fraction and density of diamond if a=3.57 Å. Diamond crystallizes in fcc lattice with some more carbon atoms in alternate tetrahedral voids.

Calculate the packing fraction and density of diamond if a=3.57 Å. Di

1.	Calculate the packing fraction and density of diamond if a=3.57 Å. Diamond crystallizes in fcc lattice with some more carbon atoms in alternate tetrahedral voids.
Answer» Solution :c-atoms PER unit cell of fcc LATTICE =4 `therefore` No. of tetrahedral voids =8 As C-atoms are present in alternate tetrahedral voids, no. of C-atoms in tetrahedral voids=4 `therefore` Total no. of C-atoms in the unit cell of DIAMOND =4+4=8 i.e., Z=8 Packing fraction=`"Volume occupied by SPHERES"/"Volume of the unit cell"=(8xx4/3pir^3)/a^3=8xx4/3xx(pir^3)/a^3` As alternate tetrahedral voids are also occupied by C-atoms, it can be seen that `sqrt3` a =8r = a=`"8r"/sqrt3` `therefore` Packing efficiency =`(8xx4/3pir^3)/(("8r"/sqrt3)^3)=32/3xx22/7xx(3sqrt3)/(8xx8xx8)`=0.34 Density, `rho="ZM"/(a^3N_0)` =`(8xx12)/((3.57xx10^(-8))^3 (6.023xx10^23))=3.5 g//cm^3`