$($a$)$ Explain what Nucleation and Growth in Phase transformation is$.(10$ Marks$)($b$)$ Explain the how temperature effect the nucleation and phase transformation rate $(10$ marks$)($c$)$ What is the key difference between equilibrium and non$-$equilibrium cooling$/$heating$?(10$ Marks$)($d$)$ Explain how the grain size can be changed by controlling the cooling rate $(10$ Marks$)($e$)$ An alloy, illustrated by the phase diagram below, is currently at the temperature indicated as $($Ts$).$ The $\backslash$alpha phase is highly electrically conductive, and the $\backslash$beta phase is low in electrical conductivity. Explain the required cooling process to obtain $($i$)$ a high $($ii$)$ an intermediate $($iii$)$ and a low electrically conductive material using the material at composition and Ts indicated in the diagram. $(30$ Marks$)$