Fe–C diagram — maximum solubility of carbon in austenite (gamma iron) Validate the statement: “The maximum solubility of carbon in austenite is 1.7% at 1130°C.” State whether it is correct or not for the iron–iron carbide system.

Introduction / Context:The iron–iron carbide (Fe–Fe3C) phase diagram is foundational in metallurgy. One key datum is the maximum solubility of carbon in austenite (gamma iron), which controls hardenability, carbon gradients during heat treatment, and the chemistry of cast irons.

Given Data / Assumptions:

• Equilibrium (slow) conditions in the Fe–Fe3C system.
• Temperatures expressed in degrees Celsius.
• Unalloyed iron (no strong austenite stabilizers like Ni or Mn).

Concept / Approach:In the Fe–Fe3C diagram, the maximum solubility of carbon in austenite occurs at the eutectic temperature around 1147°C, and the accepted value is approximately 2.11% C by mass (often rounded to 2.0–2.1%). The quoted 1.7% at 1130°C is too low and at a slightly lower temperature than the maximum-solubility point.

Step-by-Step Solution:

Verification / Alternative check:Standard diagrams and metallurgy texts consistently cite ~2.11% C at ~1147°C as the maximum solubility in austenite under equilibrium.

Why Other Options Are Wrong:

• “Yes” contradicts accepted data.
• Nickel or rapid cooling qualifiers do not define the equilibrium maximum in plain Fe–C.
• “True at 1000°C” is also incorrect; solubility decreases as temperature drops from the maximum.

Common Pitfalls:Confusing eutectoid (0.8% C at ~727°C) with maximum austenite solubility; misreading scales on phase diagrams.

Final Answer: