Diamond has an fcc Bravais lattice. The primitive lattice vectors are,
$\vec{a}_1=\frac{a}{2}\hat{x}+\frac{a}{2}\hat{y}$, $\vec{a}_2=\frac{a}{2}\hat{x}+\frac{a}{2}\hat{z}$, $\vec{a}_3=\frac{a}{2}\hat{y}+\frac{a}{2}\hat{z}$.
There are two atoms in the basis. The positions of the two carbon atoms given in terms of the fractional coordinates of the conventional unit are,
$\vec{B}_1=(0,0,0)$, $\vec{B}_2=(0.25,0.25,0.25)$.
(a) Draw the arrangement of the carbon atoms in the (110) plane using the Miller indices of the conventional unit cell. Label the directions in your drawing with Miller indices. Indicate the distance between the atoms in the two perpendicular directions.
(b) What is the volume of the primitive unit cell of diamond?
Solution