$(20$ pts total$)$ From the Fe$^(-)$Fe$\_(3)$C phase diagram below, answer the following questions.

$($a$)(6$ pts$)$ Name three transformation reactions in this phase diagram and write down the

corresponding reaction for each.

$($b$)(4$ pts$)$ According to the above phase diagram, what is the possible range for carbon

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composition that can make i$)$ steels and ii$)$ cast irons.

$($c$)(4$ pts$)$ At $1200^($@$)$C and $0\mathrm{.}76$wt$.\%$C$,$ specify the number of degrees of freedom $($i$.$e$.,$

number of external variables$)?$ What does this number mean?

$($d$)(6$ pts $)$ Consider a $1090$ steel, solution treated at $1100^($@$)$C and cooled to room

temperature. What are the phases present in this alloy, and relative amount of each

phase present in terms of mass fraction? Schematically sketch and label the resulting

microstructure of this alloy at room temperature.

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