--- title: "Iron-iron carbide phase diagram" subject: "Material Science" chapter: 6 key: "semester_3/material_science:iron-iron-carbide-phase-diagram" source: https://www.bctengineer.com/q/semester_3/material_science/iron-iron-carbide-phase-diagram site: BCT Engineering --- # Iron-iron carbide phase diagram Material Science · Chapter 6: Iron – Iron Carbide diagram and Heat Treatment of Steels - Asked in: year not given, 10 marks - Video: [Muddiest Point- Phase Diagrams III: Fe-Fe3C Phase Diagram Introduction](https://www.youtube.com/watch?v=IUMcbctDNtM) — MaterialsConcepts - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/material_science/iron-iron-carbide-phase-diagram - Whole chapter: https://www.bctengineer.com/md/semester_3/material_science/chapter-6 ## Question Draw the iron-iron carbide equilibrium diagram, label the phases, temperatures and compositions, and explain the invariant reactions. State the applications and limitations of the diagram. ## Short answer The Fe–Fe3C diagram shows ferrite (α BCC), austenite (γ FCC), cementite (Fe3C), pearlite and ledeburite. Invariant reactions: peritectic 1495°C L+δ→γ, eutectic 1147°C L→γ+Fe3C, eutectoid 727°C γ→α+Fe3C. It guides heat treatment temperatures and phase fractions. Limitations: equilibrium only, excludes martensite/bainite, ignores alloy effects and kinetics. ## Answer The Fe-Fe$_3$C diagram shows the phases of plain carbon steels and cast irons against carbon content (0 to 6.67 wt% C, where Fe$_3$C cementite forms) and temperature, under slow cooling. ```text T(C) (schematic) 1538 + Liquid (L) 1495 +-- delta / peritectic (0.17%C) 1147 +--- L + g ---- eutectic (4.3%C) -- L+Fe3C | Austenite (g) g+Fe3C Ledeburite 912 +-- a+g 727 +--- eutectoid (0.76%C) ------------------ | Ferrite+pearlite | Pearlite+Fe3C | Cast +-----|-------|---------|-------|-----> %C 0.022 0.76 2.14 4.3 6.67 ``` #### Phases - **Ferrite ($\alpha$)**: interstitial solid solution of C in BCC iron, max 0.022% C at 727 °C. Soft, ductile. - **Austenite ($\gamma$)**: C in FCC iron, max 2.14% C at 1147 °C. Non-magnetic, ductile, stable above 727 °C. - **$\delta$-ferrite**: C in BCC iron, up to 0.09% C at 1495 °C. - **Cementite (Fe$_3$C)**: hard, brittle compound with 6.67% C. - **Liquid (L)**. #### Invariant reactions | Reaction | Temp. | C content | Equation | |---|---|---|---| | Peritectic | 1495 °C | 0.17% | $L + \delta \rightleftharpoons \gamma$ | | Eutectic | 1147 °C | 4.3% | $L \rightleftharpoons \gamma + \text{Fe}_3\text{C}$ (ledeburite) | | Eutectoid | 727 °C | 0.76% | $\gamma \rightleftharpoons \alpha + \text{Fe}_3\text{C}$ (pearlite) | Critical lines: A$_1$ (727 °C), A$_3$ (GOS line, ferrite starts to form), A$_{cm}$ (SE line, cementite starts to form from austenite). #### Classification by carbon - Steel: up to 2.14% C (hypoeutectoid below 0.76, hypereutectoid 0.76-2.14). - Cast iron: 2.14-6.67% C (hypoeutectic below 4.3, hypereutectic above). #### Applications - Selecting austenitising temperatures for annealing, normalising, hardening. - Predicting microstructure and phase fractions with the lever rule. - Understanding properties of steels and cast irons, and welding behaviour. #### Limitations - It is an equilibrium diagram (very slow cooling); real heat treatment produces non-equilibrium phases such as martensite and bainite, which do not appear on it. - Alloying elements (Cr, Ni, Mn) shift transformation temperatures and the eutectoid composition; the diagram is valid only for plain carbon steel. - It gives no information about the rate of transformation (TTT/CCT diagrams are needed). - Cementite is actually metastable; graphite is the stable phase (Fe-C diagram). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What happens at the eutectoid point (727 °C, 0.76% C) on the Fe-Fe3C diagram? A. Liquid changes to austenite plus cementite B. Austenite changes to ferrite plus cementite (pearlite) C. Liquid plus delta-ferrite changes to austenite D. Ferrite changes to austenite plus cementite Answer: B. The eutectoid reaction is a solid-state change: gamma becomes alpha + Fe3C, giving the lamellar mixture called pearlite. (Key point: Eutectoid reaction) 2. Which invariant reaction occurs at 1147 °C and 4.3% C, and what does it produce? A. Peritectic, producing austenite B. Eutectoid, producing pearlite C. Eutectic, L to austenite + cementite, giving ledeburite D. Eutectic, L to ferrite + cementite, giving pearlite Answer: C. At 1147 °C and 4.3% C the liquid solidifies into austenite and cementite together, the mixture being ledeburite. (Key point: Eutectic reaction) 3. According to the diagram, how are steel and cast iron separated? A. Steel is up to 2.14% C; cast iron is 2.14-6.67% C B. Steel is up to 0.76% C; cast iron is above 0.76% C C. Steel is up to 0.022% C; cast iron is above 0.022% C D. Steel is up to 4.3% C; cast iron is 4.3-6.67% C Answer: A. 2.14% C is the maximum solubility of carbon in austenite and is the boundary between steel and cast iron. (Key point: Classification by carbon) 4. Why can martensite and bainite not be read from the Fe-Fe3C diagram? A. They contain no carbon B. They form only above 1147 °C C. They are forms of cementite D. It is an equilibrium diagram, and they form by non-equilibrium (fast) cooling Answer: D. The diagram applies to very slow cooling; rapid cooling gives non-equilibrium phases and the diagram also says nothing about transformation rate. 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