Question

In which pair most efficient packing is present?

• A. $hcp$ and $bcc$
• B. $hcp$ and $ccp$
• C. $bcc$ and simple cubic cell
• D. $bcc$ and $ccp$

Answer 1

The correct option is B $hcp$ and $ccp$

$\begin{array}{cccc}\text{Crystal lattice type}& \text{Number of atoms/unit cell}& \text{Coordination number}& \text{Packing efficiency}\\ \text{Simple cubic}& 1& 6& 52\%\\ \text{Body-centered cubic}& 2& 8& 68\%\\ \text{Hexogonal close packing}& 6& 12& 74\%\\ \text{Cubic close packing}& 4& 12& 74\%\end{array}$

$\text{Analyzing the options}$

Option (A):

Packing efficiency:

Hexagonal close packing $\left(hcp\right)=74\%$
Body centered cubic $\left(bcc\right)=68\%$

Option (B):

Packing efficiency:

Hexagonal close packing $\left(hcp\right)=74\%$
Cubic close packing $\left(ccp\right)=74\%$

Option (C):

Body centered cubic $\left(bcc\right)=68\%$
Cubic close packing $\left(ccp\right)=74\%$

Option (D):

Body centered cubic $\left(bcc\right)=68\%$
Simple cubic $\left(sc\right)=54\%$