Consider \(3.5 \mathrm{~kg}\) of austenite containing \(0.95 \mathrm{wt} \%\) C and cooled to below \(727^{\circ} \mathrm{C}\left(1341^{\circ} \mathrm{F}\right)\). (a) What is the proeutectoid phase? (b) How many kilograms each of total ferrite and cementite form? (c) How many kilograms each of pearlite and the proeutectoid phase form? (d) Schematically sketch and label the resulting microstructure.

Understanding the proeutectoid phase in the context of the iron-carbon phase diagram is essential for predicting the microstructure of steel. The term 'proeutectoid' refers to a phase that forms from the parent phase (austenite, in case of steel) before the eutectoid transformation takes place.

In the given exercise, we're dealing with an alloy that falls on the hypereutectoid side of the iron-carbon phase diagram, specifically an alloy containing 0.95 wt% C which is greater than the eutectoid composition of 0.76 wt% C. As the alloy is cooled below the eutectoid temperature of 727°C, the proeutectoid phase that forms is cementite (Fe3C).

This phase will form initially at grain boundaries of the austenite and gradually grow, affecting the overall properties of the steel. In hypereutectoid steels, the proeutectoid cementite forms a network that encloses regions that will eventually transform into pearlite, a mixture of ferrite and cementite.

The lever rule is a powerful tool used to determine the proportions of different phases in an alloy at equilibrium conditions. It is derived from the conservation of mass and allows us to make quantitative predictions based on the iron-carbon phase diagram.

The equation for the lever rule is:\(\text{Fraction of phase } i = \frac{C_{opposite \,side} - C_{overall}}{C_{opposite\,side} - C_{side\,of\,phase\,i}}\)
In the context of the exercise, the lever rule helps calculate the fraction of cementite and pearlite based on the overall composition of carbon in the alloy and the key compositions at phase boundaries. These calculations are essential to determine the mass of each phase present in 3.5 kg of the steel alloy.

Applying the lever rule allows students to bridge the gap between the theoretical phase diagrams and practical, real-world situations where precise quantities of different microconstituents are needed.

Pearlite is a common microstructure found in steel, which contains bands or layers of ferrite (α-Fe) and cementite (Fe3C) phased in an alternating pattern. It forms when austenite transforms at the eutectoid point, which for iron-carbon alloys occurs at around 0.76 wt% C and 727°C.

In exercise (c), this microstructural constituent is part of the calculation needed to determine how much pearlite forms when the hypereutectoid steel alloy is cooled below the eutectoid temperature. Pearlite's distinct layered structure is a result of the alternating ferrite (which is rich in iron) and cementite (which is rich in carbon) and under a microscope it presents a characteristic appearance due to these differing compositions.

It's important for students to recognize that pearlite is not a phase but a mixture of two phases, and its properties such as hardness and strength are intermediate between those of the softer ferrite and the harder cementite. As indicated in the exercise, pearlite comprises 87.5 wt% ferrite and 12.5 wt% cementite, and this proportionality plays a vital role in calculating the total masses of the microconstituents in the alloy.