Question

When heated above ${916}^{\circ }C$, iron changes its crystal structure from body-centered cubic to cubic closed packed structure. Assuming that the metallic radius of the atom does not change, calculate the ratio of the density of the bcc crystal to that of the ccp crystal.

Answer 1

In body-centred packing, the efficiency of packing is $67.92$%. In the cubic closed packing, the packing efficiency is $74.02$%.
Let ${\rho }_1$ be the density when packing efficiency is $74.02$% and ${\rho }_2$ is the density when packing efficiency is $67.92$%.
$\frac{{\rho }_2}{{\rho }_1}=\frac{67.92}{74.02}=0.918$.