Fe–C microstructure — composition of pearlite Pearlite (the eutectoid mixture in plain-carbon steel near 0.8% C) consists approximately of which constituents by weight?

Introduction / Context:
Pearlite is the lamellar mixture formed when austenite of eutectoid composition transforms at about 727°C in plain-carbon steel. Understanding its phase fractions is essential for interpreting microstructures, mechanical properties, and heat-treatment responses in steels.

Given Data / Assumptions:

• Pearlite is made of alternating layers of ferrite (α-iron) and cementite (Fe3C).
• Cementite contains 6.67% carbon by weight; ferrite contains very little carbon at room temperature.
• Weight fractions derive from the lever rule at the eutectoid composition.

Concept / Approach:
At the eutectoid composition (~0.76–0.8% C), the austenite transforms to pearlite. Applying the lever rule between ferrite (≈0.02% C at room temperature) and cementite (6.67% C) yields approximately 12–13% cementite and 87–88% ferrite by weight in pearlite. These fractions govern hardness and strength; more cementite increases hardness and brittleness, while ferrite provides ductility.

Step-by-Step Solution:
Identify phases: ferrite + cementite in lamellae.Use eutectoid composition and end-member carbon contents to estimate fractions.Lever rule leads to about 12.5–13% cementite and 87–87.5% ferrite by weight.Therefore, the best answer is 13% cementite and 87% ferrite.

Verification / Alternative check:
Metallography references often quote pearlite as roughly 1/8 cementite and 7/8 ferrite by weight—consistent with option (b).

Why Other Options Are Wrong:
(a) confuses carbon content with cementite fraction. (c) inverts the correct proportions. (d) states cementite’s stoichiometric carbon, not pearlite composition. (e) 50/50 by weight is not supported by the lever rule.

Common Pitfalls:
Mixing up weight and volume fractions; the lamellar spacing affects hardness but not the overall phase fractions at a given composition.

Final Answer:
13% cementite and 87% ferrite