The packing density (PD) in SC :-
1 x (4/3) PI (R)3 / (a)3
i.e. 1/1 x 4/3 x PI/1 x [a /2]3 x 1/ (a)3
i.e. PI / 6
i.e. 0.52
The percentage of void space in SC :-
(1 - PD) x 100
i.e. (1 - 0.52) x 100 = 48%
The packing density in BCC :-
2 x (4/3) PI (R)3 / (a)3
i.e. 2/1 x 4/3 x PI/1 x [(square root of 3) x a /4]3 x 1/ (a)3
i.e. (square root of 3) x (PI / 8)
i.e. 0.68.
The percentage of void space in BCC :-
(1 - PD) x 100
i.e. (1 - 0.68) x 100 = 32%
The packing density in FCC :-
4 x (4/3) PI (R)3 / (a)3
i.e. 4/1 x 4/3 x PI/1 x [(square root of 2) x a /4]3 x 1/ (a)3
i.e. PI / (3 x square root of 2)
i.e. 0.74.
The percentage of void space in FCC :-
(1 - PD) x 100
i.e. (1 - 0.74) x 100 = 26%
Hence the FCC structure possesses maximum packing density and minimum percentage of void space among the three crystal structures SC, BCC and FCC.
Density = n M / N (a)3
So, for SC, where n = 1,
Density = M / N (a)3
So, for BCC, where n = 2,
Density = 2M / N (a)3
So, for FCC, where n = 4,
Density = 4M / N (a)3