Consider isothermal transformation from austenite to ferrite in $Fe-0\mathrm{.}2wt\%C$ after

rapid quenching from $1000C$ to $750C.$ What is the ferrite fraction after a holding

time of $2$ minutes? Assume nucleation site saturation and the formation of a ferrite

film at prior austenite grain boundaries. The austenite grain size is $50m.$ A cubic

grain shape and a linearized $Fe-C$ phase diagram can be adopted for simplicity.

Construct the phase diagram using the following values: Austenite$-$ferrite

transformation temperature in pure $Fe$ is $912C,$ the eutectoid temperature is $723C,$

the eutectoid composition is $0\mathrm{.}76wt\%C$ and the carbon concentration in ferrite at the

eutectoid temperature is $0\mathrm{.}022wt\%.$ The diffusion coefficient of $C$ can be described

with a pre$-$exponential term of $0\mathrm{.}0076c\frac{m^2}{s}$ and an activation energy of $134k\frac{J}{m}ol.$