Consider \(1.5 \mathrm{~kg}\) of a \(99.7 \mathrm{wt} \% \mathrm{Fe}-0.3 \mathrm{wt} \%\) C alloy that is cooled to a temperature just below the eutectoid. (a) How many kilograms of proeutectoid ferrite form? (b) How many kilograms of eutectoid ferrite form? (c) How many kilograms of cementite form?

Proeutectoid ferrite is a key phase in steels and forms above the eutectoid temperature in hypoeutectoid alloys. In the context of the Fe-C phase diagram, it represents the part of the ferrite phase that crystallizes before the eutectoid reaction takes place. Understanding the formation of proeutectoid ferrite is crucial because it influences the mechanical properties of steel, such as hardness and strength.

During cooling, as the temperature drops just below the A3 line on the Fe-C phase diagram, carbon-rich austenite starts to reject iron atoms, leading to the formation of proeutectoid ferrite, which contains a lower concentration of carbon. This phase contains approximately 0.022 wt% carbon, as opposed to the 0.76 wt% carbon in the austenite. As the cooling process continues, the amount of austenite decreases while the amount of ferrite increases until the eutectoid temperature is reached, and eutectoid reaction commences.

After the proeutectoid ferrite forms, what remains is the eutectoid transformation at the eutectoid temperature, where austenite transforms into perlite, a lamellar structure composed of alternating layers of ferrite (eutectoid ferrite) and cementite. The eutectoid ferrite that forms at this stage has the same composition as the proeutectoid ferrite, about 0.022 wt% C, but differs in its formation — it occurs strictly at the eutectoid temperature of approximately 727°C.

The determination of the mass of eutectoid ferrite involves understanding the phase transformations and applying calculations like the lever rule. The lever rule, a graphical tool used to analyze phase diagrams and determine the composition of phases, reflects the way that the amount of each phase is influenced by the overall composition of the alloy and the relative distances on the phase diagram.

Cementite, or iron carbide (Fe3C), is a hard, brittle material and is a crucial phase in the Fe-C alloy system. It forms during the eutectoid reaction when austenite decomposes into ferrite and cementite at the eutectoid point. This process is essential for the development of mechanical properties in carbon steels.

In the solution of our exercise, the mass of cementite was determined after the calculation of eutectoid ferrite mass. Cementite plays a critical role in the strength and hardness of steels; more cementite means a harder and stronger material, although too much can lead to brittleness. Therefore, controlling the carbon content and the cooling rate after heat treatment is paramount to obtain the desired level of cementite in steel.

The lever rule is an indispensable tool for materials scientists and metallurgists working with phase diagrams. It enables the quantification of the phase fractions based on the overall composition of an alloy and the compositions of each phase present. It's analogous to a see-saw, where the mass fractions are proportional to the opposite

The Fe-C phase diagram is a roadmap for understanding how iron and carbon interact at various temperatures and compositions. It's a visual representation that shows the phases present in an iron-carbon alloy, depending on the temperature and carbon content. The diagram includes critical points such as the eutectoid point, where austenite transforms to perlite, and the solubility lines for different phases, like ferrite and cementite.

This diagram is essential for predicting the structure and properties of steel and cast iron during thermal processing. Comprehending the Fe-C phase diagram is pivotal, whether one is dealing with heat treatment procedures or analyzing the microstructure of a given alloy.