What is the main difference between hot and cold deformation? Why annealing is applied to cold worked metals? Please explain the annealing steps.

The hypothetical binary phase diagram is given below. According to this diagram, determine the which material or materials with given compositions are age$-$hardenable and explain your answer in detail. Also, write why age hardening cannot be applied in other compositions.

Please explain the "strain hardening" mechanism by using stress$-$strain diagram. Do you think this mechanism could be used at high temperatures or not?

a$)$ What is the difference between homogeneous and heterogeneous nucleation?

b$)$ How does cooling rate affect the microstructure? Explain.

$A{l}_2{O}_3$ and $C{r}_2{O}_3$ display unlimited $($complete$)$ solid solubility.

a$)$ Draw a hypothetical binary phase diagram for $A{l}_2{O}_3-C{r}_2{O}_3$ system, and label the curves, regions, etc. $($Melting temperatures of $A{l}_2{O}_3$ and $C{r}_2{O}_3$ are $2045C$ and $2275C,$ respectively$).$

b$)$ Which requirements should be satisfied to obtain a complete solid solubility?