Iron-Carbon Phase Diagram — Complete Guide with All Zones, Lines, Points, and Lever Rule Calculator
The iron-carbon phase diagram — formally the Fe–Fe3C metastable diagram — is the single most important equilibrium diagram in all of ferrous metallurgy. It maps every phase that exists at thermodynamic equilibrium in a carbon steel or cast iron across any combination of temperature (up to the melting point) and carbon content (0 to 6.67 wt%), and it provides the thermodynamic framework within which every steel heat treatment, microstructure prediction, and failure analysis is anchored. No other diagram in engineering materials science is referenced as often or carries as much practical consequence. This article provides a graduate-engineer-level treatment of every phase, every invariant reaction, all critical temperature lines, the Gibbs phase rule, the lever rule with a built-in calculator, steel and cast iron classification, and the positioning of all standard heat treatments relative to the diagram boundaries.
Key Takeaways
- The Fe–Fe3C diagram is metastable: cementite (Fe3C) is not the true equilibrium carbon phase — graphite is — but it is the phase that forms under all practical steel cooling rates.
- Three invariant reactions occur: peritectic at 1493 °C / 0.17%C, eutectic at 1147 °C / 4.3%C, and eutectoid at 727 °C / 0.77%C. At each, the Gibbs phase rule gives zero degrees of freedom (temperature and all phase compositions are fixed).
- Ferrite (α-Fe, BCC) dissolves only 0.022%C at 727 °C; austenite (γ-Fe, FCC) dissolves up to 2.14%C at 1147 °C — the BCC tetrahedral void (r ≈ 0.036 nm) is far smaller than the FCC octahedral void (r ≈ 0.053 nm).
- The A1 line (727 °C) is the most important single line in steel metallurgy: no austenite exists below it at equilibrium; all steel heat treatments are referenced to A1, A3, and Acm.
- The lever rule gives phase fractions at any point in a two-phase field: fβ = (C0−Cα)/(Cβ−Cα) and fα = (Cβ−C0)/(Cβ−Cα).
- The steel/cast iron boundary at 2.14%C is set by the maximum carbon solubility in austenite: above this, the eutectic reaction produces ledeburite, a brittle cementite network that prevents hot working.
- Heating transforms Ac1/Ac3 are always above equilibrium A1/A3; cooling Ar1/Ar3 are always below — always use Ac values in heat treatment specifications.
Lever Rule & Phase Fraction Calculator
Fe–Fe3C diagram phase fractions at equilibrium | Proeutectoid / eutectoid fractions | Two-phase field
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fraction
Phase α fraction
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fraction
Phase β fraction
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(must = 1.000)
Sum check
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wt fraction
Pearlite
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wt fraction
Proeutectoid phase
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wt fraction
Total cementite
Applicable to hypoeutectoid steels (C₀ < 0.77%C) in the α + γ two-phase field. Uses the approximate linear A3 relationship and the Hultgren extrapolation for ferrite solvus.
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wt fraction
Austenite (γ)
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wt fraction
Ferrite (α)
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wt% C
C in austenite
The Five Phases of the Fe–Fe3C System
The iron-carbon system contains five thermodynamically distinct phases or phase mixtures. Mastering the identity, crystal structure, carbon solubility, and mechanical properties of each is the prerequisite for interpreting any steel microstructure or designing any heat treatment.
| Phase | Crystal structure | Max C solubility | Stability range | Hardness | Magnetic? |
|---|---|---|---|---|---|
| δ-Ferrite | BCC; a = 0.293 nm at 1400 °C | 0.09%C at 1493 °C | 1394–1538 °C (pure Fe) | Similar to α | Yes (T < Curie pt.) |
| α-Ferrite | BCC; a = 0.2866 nm at 25 °C | 0.022%C at 727 °C; ≈0.001%C at RT | Below A3/A1 | 70–100 HV | Yes (T < 770 °C Curie) |
| γ-Austenite | FCC; a = 0.356 nm at 900 °C | 2.14%C at 1147 °C; 0.77%C at 727 °C | Above A1/A3/Acm (within stability field) | ~170–220 HV | No (paramagnetic) |
| Fe3C (Cementite) | Orthorhombic; 12 Fe + 4 C per unit cell | Fixed composition 6.67%C (line compound) | Metastable at all T (graphite more stable) | 800–1100 HV | Weakly ferromagnetic (T < 210 °C) |
| Ledeburite | Eutectic mixture: γ + Fe3C | 4.3%C (eutectic composition) | Below 1147 °C; only in cast irons (>2.14%C) | ~700 HV (composite) | Partially (cementite component) |
Why BCC Ferrite Dissolves Far Less Carbon Than FCC Austenite
The enormous difference in carbon solubility between ferrite (0.022%C maximum) and austenite (2.14%C maximum) is the single most consequential fact in all of steel metallurgy. Its origin lies in the geometry of interstitial voids in the two crystal structures. In BCC α-ferrite, the largest interstitial void is the tetrahedral site with a void radius of approximately 0.036 nm. In FCC γ-austenite, the largest void is the octahedral site with a void radius of approximately 0.053 nm. The carbon atom has a radius of approximately 0.077 nm — larger than either void, so any dissolved carbon atom distorts the surrounding lattice. The distortion energy is far greater in the smaller BCC tetrahedral site than in the larger FCC octahedral site, which is why thermodynamics strongly limits carbon solubility in BCC ferrite and is far more accommodating in FCC austenite.
Interstitial void radii comparison:
BCC α-ferrite: tetrahedral void r_void ≈ 0.036 nm (= 0.291·a, a = 0.2866 nm)
octahedral void r_void ≈ 0.019 nm (= 0.067·a — even smaller!)
FCC γ-austenite: octahedral void r_void ≈ 0.053 nm (= 0.414·(a/√2))
Carbon atom radius: r_C ≈ 0.077 nm
Misfit ratio:
BCC tetrahedral: r_C / r_void = 0.077/0.036 = 2.14 (severe distortion)
FCC octahedral: r_C / r_void = 0.077/0.053 = 1.45 (less distortion)
Thermodynamic consequence:
Max C in α-ferrite (BCC): 0.022 wt% at 727°C ←→ 0.0218 atoms% C
Max C in γ-austenite (FCC): 2.14 wt% at 1147°C ←→ 9.1 atoms% C
Ratio of solubilities: ×98 in favour of FCC
This is why steels can be hardened:
Cool austenite (2.14% C max) rapidly → carbon cannot diffuse out → trapped in BCC lattice
→ BCC lattice severely distorted → martensite (BCT structure) → very hard (~800+ HV)
The Three Invariant Reactions
Three invariant reactions occur in the Fe–Fe3C system. Each is invariant in the sense that the Gibbs phase rule gives zero degrees of freedom at constant pressure: temperature and the compositions of all phases participating in the reaction are completely fixed by the diagram.
Gibbs Phase Rule (condensed system, pressure fixed): F = C − P + 1 C = number of components = 2 (Fe and C) P = number of phases present Single-phase field (P = 1): F = 2 − 1 + 1 = 2 → T and composition both variable Two-phase field (P = 2): F = 2 − 2 + 1 = 1 → fix T, compositions both fixed (tie-line) Invariant reaction (P = 3): F = 2 − 3 + 1 = 0 → T, all compositions completely fixed
1. Peritectic Reaction at 1493 °C, 0.17%C (Point H)
The peritectic reaction involves two phases forming from a third on cooling — specifically a solid and a liquid reacting to form a new solid:
Peritectic reaction:
L (0.53% C) + δ-Fe (0.09% C) → γ-Fe (0.17% C) at 1493°C
Reaction is peritectic: one solid (δ) + one liquid (L) → one new solid (γ)
Temperature is fixed at 1493°C; compositions are fixed at the three values above.
Engineering significance:
· In low-carbon steels (0.09–0.53%C range), this reaction occurs during solidification
· Associated with carbon-content-dependent contraction on cooling through this temperature
· In continuously cast slabs, peritectic steels (0.10–0.18%C) have highest tendency
for surface cracking because the δ→γ transformation involves a volume change of ~0.5%
that generates tensile stress at the solidifying shell surface — relevant to
mould oscillation control in continuous casting of peritectic steel grades
2. Eutectic Reaction at 1147 °C, 4.3%C (Point C)
The eutectic reaction transforms a single liquid phase simultaneously into two solid phases:
Eutectic reaction:
L (4.3% C) → γ-Fe (2.14% C) + Fe₃C (6.67% C) at 1147°C
Reaction produces ledeburite — intimate mixture of austenite + cementite.
All alloys with C > 2.14% pass through this reaction on solidification.
At compositions below 4.3%C (hypoeutectic CI): primary austenite solidifies first,
then eutectic reaction produces remaining ledeburite.
At 4.3%C: entirely eutectic; no primary phase.
Above 4.3%C (hypereutectic CI): primary cementite plates (kish cementite) solidify first,
then eutectic.
Eutectic temperature for Fe-graphite (stable equilibrium): ~1152°C, slightly higher.
The 5°C difference is the thermodynamic driving force for graphite vs cementite formation:
silicon additions (> ~1.5 wt% Si) provide sufficient additional driving force for graphite,
producing grey cast iron (graphite) rather than white cast iron (cementite/ledeburite).
3. Eutectoid Reaction at 727 °C, 0.77%C (Point S)
The eutectoid reaction is the most important reaction in all of steel metallurgy. It involves a single solid phase transforming simultaneously into two new solid phases on cooling:
Eutectoid reaction:
γ-Fe (0.77% C) → α-Fe (0.022% C) + Fe₃C (6.67% C) at 727°C
Product: pearlite — alternating lamellae of ferrite and cementite.
Lamellar spacing (S₀) determined by undercooling below 727°C:
S₀ = K / ΔT (ΔT = undercooling below A1)
Slow cooling (furnace anneal, ΔT ~ 5°C): S₀ ≈ 0.5–1.0 µm → coarse pearlite (~200 HV)
Normalising (air cool, ΔT ~ 20–30°C): S₀ ≈ 0.2–0.4 µm → fine pearlite (~280 HV)
Isothermal at 650°C (ΔT ~ 77°C): S₀ ≈ 0.1–0.2 µm → very fine pearlite (~320 HV)
Isothermal at 550°C (ΔT ~ 177°C): S₀ ≈ 0.05–0.1 µm → ultra-fine / upper bainite
Pearlite colony: region of aligned ferrite + cementite lamellae with same crystallographic
orientation — typically 10–100 µm diameter; nucleates at former austenite grain boundaries.
Cementite volume fraction in pearlite (lever rule at A1):
f_Fe3C = (0.77 − 0.022) / (6.67 − 0.022) = 0.748 / 6.648 = 11.25%
f_α = (6.67 − 0.77) / (6.67 − 0.022) = 5.9 / 6.648 = 88.75%
→ Pearlite is ~89% ferrite and ~11% cementite by weight — explains its intermediate hardness.
Critical Temperature Lines in Detail
The Fe–Fe3C diagram contains six named critical temperature lines, each of which marks a phase boundary with direct engineering significance:
| Line | Temperature / range | Phase boundary type | Engineering significance |
|---|---|---|---|
| A1 (eutectoid) | 727 °C (constant for all %C) | Eutectoid horizontal; lower limit of austenite stability | Most important line: no austenite below A1 at equilibrium. All hardening treatments require heating above A1. Ac1 (on heating) always > 727 °C; Ar1 (on cooling) always < 727 °C. |
| A3 | 727 °C (at 0.77%C) to 912 °C (at 0%C) | Ferrite/austenite boundary; decreases with increasing C | Upper boundary of two-phase α + γ field for hypoeutectoid steels. Above A3 = fully austenitic. Hardening of hypoeutectoid steels requires heating above A3. |
| Acm | 727 °C (at 0.77%C) to 1147 °C (at 2.14%C) | Cementite solvus; austenite/austenite+cementite boundary | Boundary for hypereutectoid steels. Above Acm = fully austenitic; below Acm = austenite + proeutectoid cementite. Hardening of hypereutectoid steels requires heating just above A1 (not above Acm) to retain some carbides. |
| Liquidus | 1538 °C (0%C) to 1147 °C (4.3%C) left side; 1147–1227 °C right side | Solidification onset boundary | Above liquidus = fully liquid. Sets casting temperature requirements for steels and cast irons. Peritectic and eutectic reactions occur on liquidus/solidus intersection. |
| Solidus | Varies; complex shape involving peritectic reaction | End of solidification boundary | Below solidus = fully solid. Homogenisation annealing for castings must be below the solidus to avoid incipient melting. |
| A4 | 1394 °C (pure Fe); decreases slightly with C | γ/δ boundary | Upper limit of austenite stability; δ-ferrite stable above. Relevant to solidification metallurgy and stainless steel welding (delta ferrite control); rarely encountered in conventional heat treatment. |
Ac and Ar Notation — Hysteresis in Practice
Never use equilibrium A1 and A3 directly in heat treatment specifications. The equilibrium temperatures assume infinitely slow heating and cooling. In practice, the actual transformation temperatures on heating (Ac1, Ac3) are always above equilibrium due to the kinetic requirement for nucleation. On cooling (Ar1, Ar3), the actual temperatures are always below equilibrium due to undercooling. The Ac/Ar gap widens with increasing heating or cooling rate and can be 50–100 °C for induction hardening applications. Empirical correlations are available for estimating Ac1 and Ac3 from chemical composition (e.g., the Grange equation):
Ac1 (°C) = 723 − 10.7·Mn − 16.9·Ni + 29.1·Si + 16.9·Cr + 290·As + 6.38·W
Ac3 (°C) = 910 − 203·√C − 15.2·Ni + 44.7·Si + 104·V + 31.5·Mo − 30·Mn
The Lever Rule — Derivation and Worked Examples
The lever rule is a mass-balance relationship that quantifies the proportion of each phase present at equilibrium in any two-phase field of any binary phase diagram. It is one of the most-used tools in practical metallurgy, allowing the prediction of microstructure fractions from composition and temperature alone.
Derivation from Mass Balance
Lever rule derivation:
Consider alloy of composition C₀ (wt% C) in a two-phase field:
Phase α with composition Cα (wt% C) — fraction fα
Phase β with composition Cβ (wt% C) — fraction fβ
Mass balance (conservation of carbon):
Total carbon = carbon in α + carbon in β
C₀ × 1 = fα × Cα + fβ × Cβ
Also: fα + fβ = 1 → fα = 1 − fβ
Substituting:
C₀ = (1 − fβ) × Cα + fβ × Cβ
C₀ − Cα = fβ × (Cβ − Cα)
Therefore:
fβ = (C₀ − Cα) / (Cβ − Cα) ← "opposite arm" of lever
fα = (Cβ − C₀) / (Cβ − Cα) ← "opposite arm" of lever
Mechanical analogy:
Imagine a lever with fulcrum at C₀:
Left arm length = C₀ − Cα (distance from α boundary to alloy)
Right arm length = Cβ − C₀ (distance from alloy to β boundary)
Phase fraction ∝ opposite arm length (like a see-saw balance)
Worked Example 1 — Hypoeutectoid Steel at 780 °C
Example: 0.40%C plain carbon steel at T = 780°C (between A1 and A3)
Field: α + γ two-phase field
Cα (carbon in ferrite at 780°C) ≈ 0.016% (small; from extrapolated ferrite solvus)
Cγ (carbon in austenite at 780°C) ≈ 0.57% (from A3/A1 interpolation)
Fraction austenite (γ):
fγ = (C₀ − Cα) / (Cγ − Cα) = (0.40 − 0.016) / (0.57 − 0.016)
= 0.384 / 0.554 = 0.693 → 69.3% austenite
Fraction ferrite (α):
fα = (Cγ − C₀) / (Cγ − Cα) = (0.57 − 0.40) / (0.57 − 0.016)
= 0.170 / 0.554 = 0.307 → 30.7% ferrite
Check: 0.693 + 0.307 = 1.000 ✓
Practical meaning: if this steel is partially austenitised at 780°C and quenched,
69.3% of the microstructure will be martensite (from the austenite),
and 30.7% will remain as ferrite → dual-phase steel microstructure!
Worked Example 2 — Phase Fractions Just Below A1 (Room Temperature Prediction)
Example: 0.40%C steel just below A1 (at 727°C, infinitesimally cooled)
Field: α + Fe₃C two-phase field (from A1 down to room temperature)
Cα (carbon in ferrite) = 0.022%C (maximum ferrite solubility at A1)
CFe3C = 6.67%C (fixed composition of cementite)
Fraction cementite:
fFe3C = (C₀ − Cα) / (CFe3C − Cα) = (0.40 − 0.022) / (6.67 − 0.022)
= 0.378 / 6.648 = 0.0569 → 5.69% cementite
Fraction ferrite:
fα = 1 − 0.0569 = 0.9431 → 94.31% ferrite
Pearlite fraction (fraction of austenite that was eutectoid):
Amount of pearlite formed = fraction of austenite present at A1 (from first lever rule):
fγ at A1 from hypoeutectoid: fγ = C₀/0.77 = 0.40/0.77 = 0.519 → 51.9% pearlite
Proeutectoid ferrite: 1 − 0.519 = 0.481 → 48.1% proeutectoid ferrite
Summary:
Proeutectoid ferrite: 48.1% (formed between A3 and A1 on cooling)
Pearlite colonies: 51.9% (formed at A1 by eutectoid reaction)
Total ferrite: 94.31% (= proeutectoid + ferrite within pearlite)
Total cementite: 5.69% (= cementite within pearlite only; no proeutectoid cementite
since C₀ < 0.77%C)
Steel Classification by Carbon Content
| Classification | Carbon range | Slow-cool microstructure | Proeutectoid phase | Typical applications |
|---|---|---|---|---|
| Low-carbon (mild) | 0–0.30%C | Predominantly ferrite; small pearlite islands (0–39% pearlite) | Ferrite (dominant) | Structural sections (S235, A36), sheet metal, cold-drawn wire, nails, pipe |
| Medium-carbon | 0.30–0.60%C | Ferrite + increasing pearlite fraction (39–78%) | Ferrite | Shafts, gears, connecting rods, railway axles, springs, bolts (Grade 8.8) |
| Eutectoid | 0.77%C (exactly) | 100% pearlite (no proeutectoid phase) | None | Piano wire, high-tensile bridge wire (>2000 MPa), rail head, saw blades |
| Hypereutectoid | 0.77–2.14%C | Pearlite + proeutectoid cementite network at prior γ grain boundaries | Cementite (network) | Tool steels (O1, W1), bearing steels (52100/100Cr6), files, dies |
| Hypoeutectic cast iron | 2.14–4.3%C | Primary austenite/pearlite + ledeburite | Pearlite + ledeburite | Pipes, engine blocks, machine tool beds (when grey CI with Si > 1.5%) |
| Eutectic cast iron | 4.3%C | Ledeburite = pearlite + cementite | Pure ledeburite | White cast iron wear parts; chilled iron rolls |
| Hypereutectic cast iron | 4.3–6.67%C | Primary cementite + ledeburite | Primary cementite plates | Wear-resistant white iron surfaces; carbide-rich cutting tools |
How Heat Treatments Use the Phase Diagram
Every standard steel heat treatment is a deliberate traversal of the Fe–Fe3C diagram — entering or exiting phase fields at controlled rates to produce a specific microstructure and property profile. The following treatment guide is organised by the phase field regions traversed.
Treatments That Require Entering the Austenite Field
Austenitisation (heating into single-phase γ field) is the prerequisite for hardening, normalising, and full annealing. The austenitising temperature depends on steel class:
- Hypoeutectoid steels (0–0.77%C): heat to A3 + 30–50 °C (above A3 to ensure complete dissolution of proeutectoid ferrite into austenite). Example: 0.4%C steel, A3 ≈ 780 °C → austenitise at 820–830 °C.
- Hypereutectoid steels (0.77–2.14%C): heat to A1 + 30–50 °C only — deliberately below Acm. This leaves a fraction of proeutectoid carbides undissolved in the austenite. On quenching, these residual carbides provide wear resistance; if heated above Acm, all carbon dissolves into austenite, giving high-carbon martensite that is excessively brittle and prone to quench cracking.
Cooling Rate Determines the Product Phase
After austenitisation, the cooling rate determines the transformation product. The Fe–Fe3C diagram only shows equilibrium products; the TTT (time-temperature-transformation) diagram and CCT diagram must be consulted for non-equilibrium cooling:
| Heat treatment | Austenitising T | Cooling method | Product microstructure | Typical hardness |
|---|---|---|---|---|
| Full annealing | A3 + 30–50 °C | Furnace cool (~10–30 °C/hr) | Coarse pearlite + proeutectoid ferrite | 150–200 HV |
| Normalising | A3 + 50–80 °C | Still air cool | Fine pearlite + proeutectoid ferrite | 180–280 HV |
| Spheroidise annealing | 680–720 °C (below A1) | Very slow cool or cycle above/below A1 | Spheroidised cementite in ferrite matrix | 140–180 HV; max machinability |
| Hardening (quench) | A3 + 30–50 °C | Rapid quench (water/oil/polymer) | Martensite (± retained austenite) | 500–900 HV (function of %C) |
| Austempering | A3 + 30–50 °C | Quench to 250–400 °C salt; hold | Bainite (upper or lower) | 350–550 HV |
| Marquenching | A3 + 30–50 °C | Quench to just above Ms; hold; air cool | Martensite (less distortion) | Similar to direct quench |
| Intercritical anneal | A1–A3 range | Water quench | Ferrite + martensite (dual-phase DP steel) | 250–400 HV composite |
| Stress relief | 500–650 °C (below A1) | Slow cool | No phase change; only stress reduction | Unchanged |
| Tempering (after hardening) | 150–650 °C (below A1) | Air cool after hold | Tempered martensite; carbide precipitation | Decreases with T: 700→350 HV |
The Fe-Graphite Equilibrium Diagram vs. Fe-Fe3C
The standard Fe–Fe3C diagram is metastable because Fe3C (cementite) is not the most thermodynamically stable carbon-rich phase — graphite is. The true equilibrium diagram uses graphite as the carbon-rich end member and is plotted slightly to the left and higher in temperature than the Fe–Fe3C diagram:
Fe-Graphite (stable) vs Fe-Fe₃C (metastable) comparison:
Fe-Fe₃C (metastable) Fe-Graphite (stable)
Eutectoid temperature: 727°C 738°C (+11°C)
Eutectoid composition: 0.77%C 0.68%C (shifted left)
Eutectic temperature: 1147°C 1154°C (+7°C)
Eutectic composition: 4.3%C 4.26%C (marginally less C)
Why Fe₃C forms instead of graphite in steels:
· Graphite nucleation requires a very high activation energy (highly ordered hexagonal
layer structure; very different from FCC austenite)
· Cementite nucleates much more easily from austenite (smaller structural difference)
· Under practical cooling rates, kinetics strongly favour cementite
· Only in the presence of silicon (≥ ~1.5 wt% Si in cast irons) does graphite form,
because Si strongly destabilises Fe₃C and lowers the energy barrier for graphite nucleation:
Si lowers cementite stability → graphite becomes kinetically competitive → grey cast iron
Practical consequence:
· All steel heat treatment uses the Fe-Fe₃C diagram — steel always forms cementite.
· Grey cast iron production exploits the Fe-Graphite diagram by using high Si.
· White cast iron (no Si) uses the Fe-Fe₃C diagram — cementite ledeburite forms.
Carbon's Effect on Mechanical Properties Through the Diagram
Because the Fe–Fe3C diagram determines the equilibrium microstructure at any carbon content and temperature, it also predicts the trend in mechanical properties of slowly cooled (normalised or annealed) steels. The property trends are dominated by the pearlite fraction, which increases linearly with carbon content up to 0.77%C:
Pearlite fraction for hypoeutectoid steel (slow cooled to room temperature): f_pearlite = C₀ / 0.77 (approximate; ignores ferrite carbon solubility) 0.10%C steel: f_pearlite = 13% → σ_y ≈ 220 MPa, UTS ≈ 350 MPa, elongation ≈ 35% 0.20%C steel: f_pearlite = 26% → σ_y ≈ 260 MPa, UTS ≈ 420 MPa, elongation ≈ 30% 0.40%C steel: f_pearlite = 52% → σ_y ≈ 340 MPa, UTS ≈ 560 MPa, elongation ≈ 22% 0.60%C steel: f_pearlite = 78% → σ_y ≈ 410 MPa, UTS ≈ 680 MPa, elongation ≈ 16% 0.77%C steel: f_pearlite = 100% → σ_y ≈ 450 MPa, UTS ≈ 750 MPa, elongation ≈ 12% Above 0.77%C: proeutectoid cementite network reduces ductility and toughness rapidly. 0.90%C (ball bearing / hypereutectoid): cementite film at grain boundaries → brittle 1.40%C (high-speed tool): must spheroidise to improve machinability; only useful hardened Martensite hardness at room temperature (after full quench): HV_martensite ≈ 250 + 950 · (%C)^0.6 (empirical, Krauss) 0.2%C martensite: ~550 HV 0.4%C martensite: ~700 HV 0.6%C martensite: ~800 HV 1.0%C martensite: ~900+ HV (with retained austenite complications)
Frequently Asked Questions
What is the Fe–Fe3C phase diagram and why is it called metastable?
The Fe–Fe3C diagram maps the equilibrium phases in iron-carbon alloys using iron carbide (cementite, Fe3C) as the carbon-rich end member rather than pure graphite. It is called metastable because Fe3C is not the true thermodynamic equilibrium phase — graphite is more stable at all temperatures. However, under practical cooling rates in steels, cementite always forms in preference to graphite because the kinetic barrier to graphite nucleation is very high. The true equilibrium Fe–graphite diagram has its eutectoid at a slightly higher temperature (~738 °C) and slightly lower carbon content (~0.68%C) than the metastable Fe–Fe3C eutectoid (727 °C, 0.77%C). All steel heat treatment practice is based on the metastable Fe–Fe3C diagram.
What are the three invariant reactions on the Fe–Fe3C diagram?
The three invariant reactions are: (1) Peritectic at 1493 °C, 0.17%C — liquid + δ-ferrite → austenite; (2) Eutectic at 1147 °C, 4.3%C — liquid → austenite + cementite (ledeburite); (3) Eutectoid at 727 °C, 0.77%C — austenite → ferrite + cementite (pearlite). Each reaction is invariant because the Gibbs phase rule gives F = C − P + 1 = 2 − 3 + 1 = 0 degrees of freedom at constant pressure; temperature and compositions of all three phases are fixed.
Why does ferrite dissolve only 0.022%C while austenite dissolves 2.14%C?
The difference arises from the size of interstitial voids in the two crystal structures. BCC α-ferrite has a tetrahedral interstitial void radius of approximately 0.036 nm; FCC γ-austenite has an octahedral interstitial void radius of approximately 0.053 nm. The carbon atom radius is approximately 0.077 nm — too large for either void, causing lattice distortion in both, but the distortion energy is far greater in the smaller BCC void. This greater lattice strain in BCC severely limits solubility: 0.022%C in BCC ferrite versus 2.14%C in FCC austenite at equivalent temperature — a factor of 98 difference.
What is the lever rule and how is it derived?
The lever rule gives the fraction of each phase in a two-phase field from a simple carbon mass balance. For alloy composition C0 in a two-phase field bounded by Cα and Cβ: fβ = (C0 − Cα)/(Cβ − Cα) and fα = (Cβ − C0)/(Cβ − Cα). The derivation uses conservation of mass: total carbon = carbon in α + carbon in β, combined with fα + fβ = 1. The mechanical analogy is a lever with the fulcrum at C0: each phase fraction equals the length of the opposite lever arm divided by total lever length.
What is the Gibbs phase rule and how does it apply to the Fe–Fe3C diagram?
The Gibbs phase rule states F = C − P + 2. At constant pressure (condensed system): F = C − P + 1 = 3 − P. In a single-phase field (P = 1): F = 2 — temperature and composition can both vary freely. In a two-phase field (P = 2): F = 1 — fixing temperature fixes all phase compositions (tie-line). At an invariant reaction (P = 3): F = 0 — temperature and all phase compositions are completely fixed. This is why the A1 eutectoid, 1147 °C eutectic, and 1493 °C peritectic are all horizontal lines at fixed temperatures with fixed participating phase compositions.
Why is 2.14%C the boundary between steel and cast iron?
2.14%C is the maximum carbon solubility in austenite at the eutectic temperature (1147 °C). Below this carbon content, the alloy passes through a fully austenitic single-phase field during heating or processing, allowing homogenisation, hot working (rolling, forging), and complete solution of carbon for subsequent heat treatment. Above 2.14%C, the alloy never enters a fully austenitic state; instead it passes through the eutectic reaction at 1147 °C where liquid transforms simultaneously to austenite and cementite, forming the brittle ledeburite network that prevents hot working. This fundamental difference in processability — hot workable below, brittle above — is the engineering basis for the steel/cast iron boundary.
What is proeutectoid ferrite and how does it differ from eutectoid ferrite?
Proeutectoid ferrite precipitates from austenite above the eutectoid temperature (727 °C) as a hypoeutectoid steel cools through the two-phase austenite + ferrite field between A3 and A1. It nucleates at prior austenite grain boundaries and grows as polygonal grains (slow cooling) or Widmanstätten plates (faster cooling). Eutectoid ferrite forms as part of the pearlite colony during the eutectoid reaction at 727 °C — simultaneously with cementite in alternating lamellae. Both appear white with nital etching in optical metallography and are crystallographically identical, but eutectoid ferrite is surrounded by cementite lamellae within pearlite colonies, while proeutectoid ferrite forms large polygonal grains at grain boundary positions.
What is ledeburite and where does it appear in the Fe–Fe3C diagram?
Ledeburite is the eutectic microstructure formed at 4.3%C and 1147 °C: L → γ + Fe3C. At high temperature it consists of austenite in a cementite matrix. Below 727 °C, the austenite within ledeburite itself transforms to pearlite by the eutectoid reaction, so room-temperature ledeburite consists of pearlite + cementite. Ledeburite appears in all iron-carbon alloys with C > 2.14%C (cast irons), and its presence as a continuous brittle cementite network is the primary reason cast irons cannot be hot worked — the cementite skeleton prevents plastic deformation.
How does the Ac1 temperature differ from the A1 temperature, and why does this matter for heat treatment?
A1 (727 °C) is the equilibrium eutectoid temperature from the phase diagram, valid only for infinitely slow heating. Ac1 (c from French chauffage = heating) is the actual temperature at which austenite begins to form during heating in practice, always above A1 due to nucleation kinetics requiring a thermodynamic driving force. Similarly, Ar1 (cooling) is always below A1. The Ac1/A1 difference is typically 10–30 °C at slow heating rates and 50–80 °C at rapid induction heating rates. Heat treatment specifications always use Ac1 and Ac3 to ensure complete austenitisation, because the furnace must exceed the actual transformation temperature, not the equilibrium value.
Recommended References
Steels: Microstructure and Properties — Bhadeshia & Honeycombe (4th Ed.)
The graduate-level reference for steel microstructure, phase transformations, and the Fe-C system; essential for all steel metallurgists.
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Steels: Processing, Structure & Performance — Krauss (2nd Ed., ASM)
Comprehensive ASM reference covering the Fe-C diagram, all heat treatment processes, hardenability, and microstructure-property relationships.
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Materials Science and Engineering: An Introduction — Callister (10th Ed.)
The standard undergraduate reference with clear coverage of the Fe-Fe₃C phase diagram, lever rule, and steel classifications.
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ASM Handbook Vol. 9: Metallography and Microstructures
The definitive atlas for identifying ferrite, pearlite, cementite, bainite, and martensite microstructures in etched steel specimens.
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Further Reading
ER
Eutectoid Reaction in Steel
Deep dive into pearlite formation, lamellar spacing kinetics, and colony growth at the 0.77%C eutectoid.
TT
TTT Diagram Explained
Time-temperature-transformation diagrams: how to read them, C-curve construction, and use in heat treatment design.
MT
Martensite — Lath vs. Plate
BCC/BCT martensite crystal structure, Ms temperature, lath vs. plate morphology, and carbon content effects.
BA
Bainite Microstructure Guide
Upper bainite, lower bainite, and granular bainite: formation, substructure, and mechanical properties.
PC
Pearlite Colony Growth
Ledge mechanism of pearlite growth, interlamellar spacing, and the relationship between spacing and strength.
FE
Ferrite in Steel — α-Iron
BCC structure, carbon solubility, ferrite morphologies, Hall-Petch, and alloying effects in α-iron.
GB
Grain Boundaries
Types, energy, segregation, and the role of grain boundaries as nucleation sites for eutectoid and proeutectoid phases.
AN
Annealing and Normalising
Full annealing, normalising, and spheroidise annealing: microstructures, temperatures, and property outcomes.
