Question

calculate the packing efficiency and free space of body centered cubic cell​

Answer 1

The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

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Answer 2

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The packing efficiency of both types of close packed structure is 74%, i.e. 74% of the space in hcp and ccp is filled. The hcp and ccp structure are equally efficient; in terms of packing. The packing efficiency of simple cubic lattice is 52.4%. And the packing efficiency of body centered cubic lattice (bcc) is 68%.

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✒ We know that

Packing fraction =

$\rightarrow \frac{Volume \: occupied \: by \: atoms \: in \: a \: unit \: cell}{Volume \: of \: the \: unit \: cell}$

For bcc,

Now, substituting the values,

Packing fraction =

$\boxed{ \rightarrow\frac{2 \times \frac{4}{3}\pi {r}^{3} }{ {( \frac{4r}{ \sqrt{3} } }^{3} ) } }$

$\boxed{ \rightarrow{ \frac{ \sqrt{3\pi} }{8} = 0.68}}$

Volume occupied = 68%

Volume vacant = 100 − 68 = 32%

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