EXERCISE$-1$: Define the following terms for a crystal:

a$)$ Primitive cell

b$)$ Lattice constant

c$)$ Miller indices

d$)$ Diamond structure

EXERCISE$-2$: The unit cell of the silicon crystal has a diamond structure.

Plot the unit cell of the silicon and indicate the following planes and crystal directions:

a$)$ Planes: $(100),(111),(110),(010)$

b$)$ Directions: $<mn>1</mn><mn>0</mn><mn>0</mn>$:

EXERCISE$-3$: Calculate the volume density of Si atoms $($number of atoms$/$cm$3),$ given that the lattice constant of Si is $5\mathrm{.}43.$

EXERCISE$-4$: Calculate the areal density of atoms $($number $\frac{?}{c{m}^2})$ on the $(100)$ plane in Silicon.

EXERCISE$-5$: Find the Miller indices of the following crystal planse?