Iron can exist in the FCC or BCC structure. For FCC iron, the crystal lattice parameter is a=0.3515nm and the atomic packing factor is 0.74. In an FCC structure, iron atoms have an atomic radius of 0.1263nm. Carbon steel is generated by adding carbon atoms (atomic radius of 0.079nm) into the intestinal sites( at rate of say 5 C atoms per 100 Fe atoms).
If the radius of the interstitial sites( i.e. the radius of SPACE available rather than the radius of the atom that is placed in that space) in an FCC structure are determined according to 2r_interstital + 2r_Fe= a, explain why the atomic packing factor of FCC steel is less than 0.74.