Vacant space in body centered cubic (BCC) lat | vedclass

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(D) For a $BCC$ unit cell,the number of atoms per unit cell is $2$. The packing efficiency is calculated as: $	ext{Packing Efficiency} = \frac{Z 	im

Vedclass · Accepted Answer

$32$

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(D) For a $BCC$ unit cell,the number of atoms per unit cell is $2$. The packing efficiency is calculated as: $	ext{Packing Efficiency} = \frac{Z 	imes \frac{4}{3} \pi r^3}{a^3} 	imes 100$. For $BCC$,the relation between edge length $a$ and radius $r$ is $a = \frac{4r}{\sqrt{3}}$. Substituting this,$	ext{Packing Efficiency} = \frac{2 	imes \frac{4}{3} \pi r^3}{(\frac{4}{\sqrt{3}} r)^3} 	imes 100 = 68 \%$. Therefore,the vacant space (void space) is $100 \% - 68 \% = 32 \%$.

Vacant space in body centered cubic $(BCC)$ lattice unit cell is about (in $\%$)

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