Calculate the packing fractionand density of diamond if a = 3.57Å . Diamondcrystallizes in fcc lattice with some more carbon atoms in alternate tetrahedral voids.

Calculate the packing fractionand density of diamond if a = 3.57Å . D

1.	Calculate the packing fractionand density of diamond if a = 3.57Å . Diamondcrystallizes in fcc lattice with some more carbon atoms in alternate tetrahedral voids.
Answer» Solution :C-atoms per cell of fcc lattice =4 No .of tetrahedal voids = 4 As C -atoms are present in ALTERNATE TETRAHEDRAL voids. no. of C-atoms in tetrahedrl voids = 4 Total no. of C -atoms in the unit cell of diamed= 4+ 4=8 ,i.e.,Z=8 packing fraction =` ("Volume occupied by spheres")/("Volume of the unit cell") = (8 xx 4/3 pi r^(3))/a^(3)= 8 xx 4/3xx (pir^(3))/a^(3)` As alternate tetrahedralvoids are also occupied by C-atoms , it canby seen that ` sqrt3 a = 8r or a = (8r)/sqrt3` packing effeiciency = `(8 xx 4/3 pi r^(3))/ ((8r)/sqrt3)^(3) = 32/3 xx 22/7 xx (3SQRT3)/( 8 xx8xx8) = 0.43` density` p = (ZM)/(a^(3)N_(0)) = ( 8 xx 12)/((3.57xx10^(-8))^(3) (6.023 xx 10^(23)) = 3.5"g/cm"^(3)`