What is the percentage of unoccupied volume in BCC structure?
What is the percentage of unoccupied volume in BCC structure?
$32 \%$
$74 \%$
$26 \%$
$68 \%$
Solution
Packing efficiency
$\begin{aligned}
& \text { P.E. }=\frac{z \times \frac{4}{3} \pi \mathrm{r}^3}{V}=\frac{2 \times \frac{4}{3} \times \pi\left(\frac{\sqrt{3} a}{4}\right)^3}{a^3}=\frac{\sqrt{3} \pi}{8}=0.68 \\
& {\left[\because z=2, r=\frac{\sqrt{3} a}{4}, V=a^3\right]}
\end{aligned}$
In B.C.C., $68 \%$ of total volume is occupied by atoms or ions.
And $100-68=32 \%$ of total volume is unoccupied.