$ZrC$ has a rock salt structure $(NaCl)$ which may be considered as two interpenetrating f$.$c$.$c$.$ lattices of two types of atoms. Corners and faces of the unit cell are located by $C$ ions, and $Zr$ ions locate at the edges and inside of the unit cell. $($radius of $Zr$ is $0\mathrm{.}23nm$ and radius of $C$ is $0\mathrm{.}17nm)$

a$)$ Draw $ZrC$ unit cell showing the $Zr$ and $C$ ions and determine number of atoms.

b$)$ The atomic weight of $Zr$ is $91\mathrm{.}2\frac{g}{?}$ mole and that of $C$ is $12\frac{g}{?}$ mole. Calculate the theorical density of $ZrC$ in grams $\frac{?}{c{m}^3}.$

c$)$ Calculate the ionic packing factor of $ZrC$

$"$In BCC metals, critical resolved shear stress which is necessary for deformation, is hundred times higher than FCC$".$ Please explain this expression drawing required figures.

Please calculate the change in the activation energy when temperature increases twice. Use the relationship between temperature and diffusion coefficient. Explain by using drawing.

a$)$ Please classify the ionic structures. What is the main criterion for this classification?

b$)$ Draw a diamond cubic unit cell. Which elements have a diamond cubic structure?

a$)$ Please write the strengthening mechanisms of metals and alloys, which are used to control "structure and properties", and classify them briefly.

b$)$ Which strengthening mechanisms can be applied for the A$-6$B alloy?