Question

A CCP of n spheres of radius r, n spheres of radius 0.414 r and 2n spheres of radius 0.225 r are introduced in the octahedral and tetrahedral void respectively. Therefore packing fraction of the lattice.

• A. 0.74
• B. 0.81
• C. 0.68
• D. 0.79

Answer 1

Answer: (B)

0.81

Answer 2

P.F =

$\frac{4 \times \frac{4}{3}\pi r^{3} + 4 \times \frac{4}{3}\pi \times (0.414r)^{3} + 8 \times \frac{4}{3}\pi \times (0.225r)^{3}}{(2\sqrt{2}r)^{3}}$

P.F = $\frac{4 \times \frac{4}{3}\pi r^{3}\lbrack 1 + (0.414)^{3} + 2 \times (0.225)^{3}\rbrack}{16\sqrt{2}r^{3}}$

P.F = $\frac{\pi}{3\sqrt{2}}\lbrack 1 + (0.414)^{3} + 2 \times (0.225)^{3}$

= $\frac{\pi}{3\sqrt{2}}$ (1 + 0.070958 + 0.022781)

or P.F = 0.8096 ~ 0.81