Question

Calculate the packing efficiency for a ccp unit cell, take 2(2)1/2 r as a cube edge length, where r is the radius of sphere. Assume that all the atoms are identical!

Answer 1

packing efficiency = {(total volume occupied by atom)/(total volume available)}*100
as every atom is made up of sphere
volume occupied by each atom = (4/3)*3.14*r^3
there are 6 atom one at each face centr
and each atom is shared by two unitcell
6*(1/2) = 3
so, effectevely there are 3 atom on face centr
also, at each corner 1 atom is present and each is shared by 8 unitcell
8*(1/8) = 1
so, effectevely 1 atom is present on corner
so,total
there are 4 atom in ccp unit cell
total volume occupied by atom = 4*(4/3)*3.14*r^3

total volume available = (edge length)^3
edge length = 2*2^1/2*r
total volume available = (2*2^1/2*r)^3
= 16*2^1/2*r^3

packing efficiency = {(4*(4/3)*3.14*r^3)/(16*2^1/2*r^3)}*100
= 74.2 %

Answer : 74.2 %