Question $6$

Figure $9\mathrm{.}24$ The iron$-$iron carbide phase diagram.

$[$Adapted from Binary Alloy Phase Diagrams, Vol. $1,2$nd edition, T$.$ B$.$ Massalski $($Editor$-$in$-$Chief$),1990.$ Reprinted by permission of ASM International, Materials Park, OH$.]$

$($From Callister & Rethwisch$)$

The technologically important part of the iron$-$carbon phase diagram is shown above. Using this diagram, answer the following questions:

$($a$)$ For a $1\mathrm{.}10wt\%$ plain carbon steel that has been austenitized at $1100C$ and then cooled under equilibrium conditions to room temperature, what is the proeutectoid $($or primary$)$ phase that forms? Also, for this steel, determine: $($i$)$ the wt$\%$ of pearlite and the $wt\%$ of the proeutectoid phase in the microstructure at room temperature, and $($ii$)$ the total amount $(wt\%)$ of ferrite in the microstructure at room temperature.

$($b$)$ For an $Fe-3wt\%C$ alloy in equilibrium at $1000C,$ what are the equilibrium phases. Also, for this alloy at $1000C,$ determine $($i$)$ the composition of the equilibrium phases, and $($ii$)$ the wt$\%$ of each phase.

$($c$)$ Explain why steel microstructures such as bainite and martensite are not shown on the diagram.