## Materials Science and Engineering: An Introduction

$APF={\text{volume of atomic unit cell}}/{\text{total unit cell volume}}$ $V_{s}=\frac{4}{3}\pi r^3$ As we know BCC has a total of 2 atoms: $V_{s}=2\times\frac{4}{3}\pi r^3=\frac{8}{3}\pi r^3$ Thus: $V_{c}=a^3={\frac{4}{\sqrt{3}}r}^3$ $V_{c}=\frac{64}{3\sqrt{3}}r^3$ APF =$\frac{\frac{8}{3}\pi r^3}{\frac{64}{3\sqrt{3}}r^3}=0.68$