(Solved): 5. Fe-C Phase Diagram (15 points) The FeC phase diagram is shown below. a) Excluding pure iron a ...

5. Fe-C Phase Diagram (15 points) The $\mathrm{Fe}-\mathrm{C}$ phase diagram is shown below. a) Excluding pure iron and ${\mathrm{Fe}}_3\mathrm{C}$, how many invariant points exist within the phase diagram? Where are the positions? b) Sketch the microstructure when a proeutectic austenite with the composition of $0.5\mathrm{wt}\%$ $\mathrm{C}$ is slowly cooled from $1000^{\circ }\mathrm{C}$ to $726^{\circ }\mathrm{C}$. c) At $726^{\circ }\mathrm{C}$, Calculate the weight portion of $\alpha$-phase lamellar structure, excluding proeutectoid $\alpha$-phase.