The Iron-Carbon Phase Diagram: A Complete Technical Guide

Introduction

The iron-carbon binary phase diagram is the single most important diagram in ferrous metallurgy. It encodes the thermodynamic equilibrium between phases in Fe-C alloys as a function of temperature and composition, providing the theoretical foundation for understanding every steel and cast iron microstructure. No metallurgist can design a heat treatment cycle, predict a microstructure, or troubleshoot a manufacturing problem without a thorough command of this diagram.

This guide explains every region, line, and reaction point of the Fe-C diagram, demonstrates application of the lever rule, and connects the diagram to practical heat treatment and manufacturing outcomes.

The Pure Iron Side: Allotropy of Iron

Pure iron (0% C) undergoes two solid-state allotropic transformations with temperature:

• α-iron (BCC): Stable from room temperature to 912°C. Ferromagnetic below 770°C (Curie temperature). Dissolves only 0.02% C at maximum (at 727°C).
• γ-iron (FCC): Stable from 912°C to 1,394°C. Paramagnetic. Dissolves up to 2.14% C — much higher due to the larger octahedral interstitial sites in the FCC lattice.
• δ-iron (BCC): Stable from 1,394°C to melting point (1,538°C). High-temperature BCC phase; dissolves up to 0.09% C.

The 912°C BCC-to-FCC transformation is the critical transition that makes steel heat treatment possible. Heating into the austenite field (γ-iron) dissolves carbon into homogeneous solid solution; controlled cooling then produces the desired microstructure.

Key Boundary Lines

The A1 (Eutectoid) Line — 727°C

The horizontal line at 727°C represents the eutectoid temperature — the temperature of the invariant eutectoid reaction. At this temperature and 0.77% C, austenite transforms simultaneously to ferrite + cementite (pearlite). This is the most important line in the diagram for steel heat treatment.

The A3 Line (Ac3)

The upper boundary of the α+γ two-phase field for hypoeutectoid steels. Above A3, steel is fully austenitic. A3 decreases from 912°C at 0% C to 727°C at 0.77% C.

The Acm Line

The upper boundary of the γ+Fe₃C two-phase field for hypereutectoid steels. Above Acm, the steel is fully austenitic (all cementite dissolved). Acm rises from 727°C at 0.77% C to 1,148°C at 2.14% C.

The Liquidus and Solidus

The liquidus (upper line) marks the temperature above which the alloy is completely liquid; the solidus (lower line) marks the temperature below which it is completely solid. Between these lines, a two-phase mixture of liquid and solid coexists. In continuous casting, the slab centre (mushy zone) between liquidus and solidus is the region of high porosity and segregation risk.

Invariant Reactions

The Eutectoid Reaction (0.77% C, 727°C)

γ (0.77% C) → α (0.02% C) + Fe₃C (6.67% C)
Cooling reaction: a single solid phase transforms simultaneously to two different solid phases.

This produces pearlite: alternating lamellae of ferrite (α) and cementite (Fe₃C). The spacing of the lamellae depends on undercooling below 727°C — greater undercooling produces finer lamellae. Pearlite hardness ranges from 160 HBN (coarse, formed at 650–700°C) to 400 HBN (very fine/sorbite, formed at 550–600°C).

The Eutectic Reaction (4.30% C, 1,148°C)

L (4.30% C) → γ (2.14% C) + Fe₃C (6.67% C)
Cooling reaction: liquid transforms simultaneously to two solid phases (ledeburite).

This produces ledeburite — the iron-iron carbide eutectic. All cast irons (>2.14% C) pass through this reaction on solidification. Below 727°C, the austenite in ledeburite further transforms to pearlite, producing transformed ledeburite (pearlite + cementite).

The Peritectic Reaction (0.17% C, 1,493°C)

L (0.53% C) + δ (0.09% C) → γ (0.17% C)
A liquid and a solid phase react to produce a new, single solid phase.

The peritectic reaction occurs in steels near 0.17% C and is important in continuous casting. The γ-phase that forms has lower density than δ-iron, causing a volume contraction that can produce surface cracks in the solidifying shell — a major cause of longitudinal surface cracking in peritectic-composition cast slabs.

Applying the Lever Rule

The lever rule calculates the weight fraction of each phase at a given temperature and composition within a two-phase field:

Fraction of phase B = (C₀ − C_A) / (C_B − C_A)
Fraction of phase A = (C_B − C₀) / (C_B − C_A)

where C₀ is overall composition, C_A is composition of phase A endpoint, and C_B is composition of phase B endpoint.

Worked Example: 0.4% C Steel at Room Temperature (Equilibrium)

At room temperature (well below 727°C), the two phases are ferrite (0.008% C) and cementite (6.67% C):

• Fraction cementite = (0.40 − 0.008) / (6.67 − 0.008) = 0.392 / 6.662 = 0.059 = 5.9%
• Fraction ferrite = 1 − 0.059 = 94.1%

At 750°C (just above Ac1, in the α+γ field), the two phases are ferrite (~0.02% C) and austenite (~0.60% C at 750°C for this composition):

• Fraction austenite = (0.40 − 0.02) / (0.60 − 0.02) = 0.38 / 0.58 = 0.655 = 65.5%
• Fraction ferrite = 34.5%

Steel Microstructures and the Phase Diagram

Hypoeutectoid Steels (0–0.77% C)

On slow cooling from fully austenitic conditions: proeutectoid ferrite nucleates at austenite grain boundaries (Widmanstätten ferrite or polygonal ferrite depending on cooling rate) as the composition moves along A3. Ferrite growth enriches remaining austenite in carbon. At 727°C, remaining austenite (now 0.77% C) transforms to pearlite. Final microstructure: ferrite + pearlite; proportion of pearlite increases linearly with carbon content — approximately 13% pearlite per 0.1% C above 0% C.

Eutectoid Steel (0.77% C)

No proeutectoid phase forms. The entire microstructure transforms to pearlite at 727°C (under equilibrium conditions). 100% pearlite is the expected microstructure.

Hypereutectoid Steels (0.77–2.14% C)

On slow cooling from fully austenitic conditions (above Acm): proeutectoid cementite precipitates at austenite grain boundaries as a continuous network. At 727°C, remaining austenite (0.77% C) transforms to pearlite. Final microstructure: pearlite + cementite network. The cementite network is detrimental to toughness — it is broken up by spheroidising annealing or by hot working.

Cast Irons and the Phase Diagram

Alloys with >2.14% C are cast irons. At and above the eutectic composition (4.3% C), solidification produces ledeburite. But whether this cementite remains as Fe₃C (white iron) or decomposes to graphite (grey iron) depends on the carbon equivalent (CE = C + Si/3) and cooling rate:

• High CE + slow cooling: Grey iron — graphite flakes form during solidification. Silicon promotes graphitisation by reducing the stability of Fe₃C.
• Low CE + fast cooling: White iron — cementite is retained. Hard, brittle, excellent wear resistance.
• Mg treatment + controlled CE: Ductile (SG) iron — graphite forms as nodules rather than flakes.

The Metastable vs Stable System

The Fe-C diagram discussed here is technically the metastable Fe-Fe₃C system. Iron carbide (Fe₃C, cementite) is metastable — it will decompose to iron and graphite given sufficient time and temperature. The stable Fe-C system shows graphite as the equilibrium carbon phase, not cementite. In practice, decomposition to graphite is negligible in steels under normal heat treatment conditions (thousands of years at ambient temperature), but is relevant for cast irons (graphitisation during annealing) and for grey iron solidification.

Effect of Alloying Elements on Phase Diagram

Every alloying element shifts the critical temperatures and the eutectoid composition:

• Austenite stabilisers (Ni, Mn, Cu, N): Lower Ac1, shift γ-field to lower temperatures and higher carbon contents. Sufficiently high Ni (>25%) suppresses the BCC transformation entirely at room temperature (austenitic stainless steel remains FCC to cryogenic temperatures).
• Ferrite stabilisers (Cr, Mo, W, V, Si, Al): Raise Ac1, shrink the γ-loop, and shift the eutectoid to lower carbon content. High Cr steels (ferritic stainless) have a dramatically reduced or absent γ-loop.
• Carbide formers (Cr, Mo, W, V, Nb, Ti): Partition carbon into alloy carbides, shifting the effective eutectoid composition to lower carbon levels.

Frequently Asked Questions

Q: Why is the eutectoid at 0.77% C and not at some other value?
A: The eutectoid composition is determined by the relative stability of ferrite and cementite as a function of carbon content — it is a thermodynamic consequence of the free energy curves for each phase. In alloyed steels, the eutectoid composition shifts as described above.

Q: Does the iron-carbon phase diagram apply to stainless steels?
A: Only qualitatively. Stainless steels contain >10.5% Cr, which dramatically alters the diagram — the γ-loop shrinks, the eutectoid shifts, and Cr carbides (Cr₂₃C₆, Cr₇C₃) replace cementite. Multi-component phase diagrams (calculated by CALPHAD software) are required for accurate phase prediction in stainless steels.

Q: Why does cast iron have better fluidity than steel?
A: Cast iron compositions near the eutectic (4.3% C) have the lowest liquidus temperature (~1,148°C) in the Fe-C system. This low melting point, combined with the eutectic solidification mode (formation of two phases simultaneously from liquid), produces good fluidity and mould-filling ability — superior to steel which solidifies over a wider temperature range.

Conclusion

The Fe-C phase diagram is the roadmap of ferrous metallurgy. Every heat treatment temperature, every microstructure, and every phase transformation in steel and cast iron is defined by this diagram. Mastering the diagram — understanding the eutectoid and eutectic reactions, applying the lever rule, and recognising how alloying elements shift the boundaries — is the essential foundation for practical metallurgy. See also: Crystal Structures and Metal Properties and Annealing Processes in Steel.

References

• Callister, W.D. and Rethwisch, D.G., Materials Science and Engineering: An Introduction. 10th ed. Wiley, 2018.
• Bhadeshia, H.K.D.H. and Honeycombe, R., Steels: Microstructure and Properties. 4th ed. Butterworth-Heinemann, 2017.
• ASM Handbook Vol. 3: Alloy Phase Diagrams. ASM International, 1992.