$1$a$)$ i$)$ Using phase transformation theory, explain in detail the two stages of formation of

particles of a new phase. Explain the role of undercooling $T$ in formation of eutectoid

microstructures in engineering alloys and Avrami's equation for the kinetics of transformation

product.

$1$a ii$)$ Rank the following iron$-$carbon alloys and associated microstructures from the highest to

the lowest ductility and justify the ranking for each.

$50\%$ martensite and $50\%$ bainite

$100\%$ coarse pearlite

$100\%$ spheroidite

$50\%$ fine pearlite and $50\%$ martensite

$100\%$ bainite

$1$a iii$)$ Consider casting a cube and a sphere of the same volume from the same polymer or

metal or ceramic material. Which one would solidify faster? Why?

$1$a iv$)$ For the Transformation from Austenite to Pearlite for a eutectoid alloy $(0\mathrm{.}76wt\%C)$ the

isothermal fraction reacted versus the logarithm of time at the $3$ temperatures is shown below.

Calculate the Nucleation times and the rate of transformation at the temperatures $600C,650$

$C,675C.$