Question

A crystal arrangement is formed such that it consists of Aatoms forming cubic close packing and B occupy all the octahedral voids. Assuming no distortion, calculate packing efficiency of the crystal. Express answer in nearest integer percentage:
[Use :$[1+(0.414{)}^3]=1.07,\frac{\pi }{3\sqrt{2}}=0.74]$

• A. 79.0
• B. 79

Answer 1

Answer: (A), (B)

Packing efficiency (in %)

$=\frac{4\times \frac{4}{3}+4\times \frac{4}{3}\pi (0.414r{)}^3}{a^3}\times 100;$

$=\frac{4\times \frac{4}{3}\pi r^3+[1+(0.414r{)}^3]}{(2\sqrt{2}{)}^3{r}^3}\times 100$

$=\frac{\pi }{3\sqrt{2}}\times 1.07\times 100$

$=0.74\times 1.07\times 100$

$=79\%$