Question $4(5$ pts$)$:

Compare the planar density for a $(110)$ plane in BCC versus a $(100)$ plane for FCC$.$ Express this as a

ratio of planar density of BCC$/$FCC$.$

Solution

BCC $(110)$ plane: $\frac{0\mathrm{.}5R^2}{\frac{1}{2}\sqrt[\phantom{2}]{2}a\sqrt[\phantom{2}]{\frac{3}{2}}a}=\frac{}{16}3\sqrt[\phantom{2}]{2}$

FCC $(001)$ plane: $\frac{2R^2}{a^2}=\frac{}{4}$

$BC\frac{C}{F}CC=\frac{3\sqrt[\phantom{2}]{2}}{4}$