Phase diagrams and the iron-carbon diagram

Metallurgical and Materials Engineering (B.E./B.Tech) · Physical metallurgy · free study notes for exams, placements and interviews

In short

A phase diagram is a map of which phases are stable in an alloy at a given composition and temperature at equilibrium (usually 1 atm). The iron-iron carbide (Fe-Fe₃C) diagram is the single most important one in metallurgy because it explains why plain carbon steel exists in grades from mild steel to tool steel, and why cast irons behave differently. It is the backbone of heat-treatment practice at SAIL, Tata Steel, JSW, Jindal Stainless, foundries and forging shops, and is used daily by QA and process metallurgists. Phase diagrams carry heavy weight in GATE MT (lever rule, phase rule, invariant reactions, microstructure fractions) and in university Physical Metallurgy papers, and almost every campus technical round asks you to draw and label the Fe-Fe₃C diagram.

Explained

Basic definitions and the phase rule

Phase: a physically distinct, chemically homogeneous, mechanically separable portion of a system (e.g. ferrite, cementite, liquid). Component: the independent chemical species needed to describe the system (Fe and C, or Fe and Fe₃C).
System: the alloy under study; equilibrium means minimum Gibbs free energy — reached only with slow cooling. Real industrial cooling gives metastable structures (martensite, bainite), which is why the diagram alone cannot predict all microstructures.
Solid solution: solute atoms dissolved in a solvent lattice — substitutional (similar size, e.g. Ni in Cu; Hume-Rothery rules: size difference < ~15%, same crystal structure, similar valency and electronegativity) or interstitial (small atoms in holes, e.g. C, N, H in Fe).
Intermediate phase / intermetallic compound: a phase with its own structure and a narrow composition range, e.g. Fe₃C (cementite), orthorhombic, 6.67 wt% C.
Gibbs phase rule: P + F = C + 2 for a general system; at constant pressure, P + F = C + 1. P = phases, F = degrees of freedom, C = components.
For a binary alloy at fixed pressure: one phase → F = 2 (T and composition free); two phases → F = 1; three phases → F = 0, an invariant point (eutectic, eutectoid, peritectic, peritectoid, monotectic).
Degree of freedom = 0 explains why a eutectic or eutectoid reaction occurs at a single fixed temperature and composition.

Types of binary phase diagrams and invariant reactions

Isomorphous (complete solid solubility): Cu-Ni, Ag-Au, Ge-Si. Liquidus above, solidus below, a two-phase L+α lens in between. No invariant reaction.
Eutectic: L → α + β on cooling, at one temperature. Examples: Pb-Sn (61.9% Sn, 183 °C — the classic solder), Al-Si (12.6% Si, 577 °C — the basis of piston alloys), Ag-Cu.
Eutectoid: γ → α + β (solid → two solids). In Fe-Fe₃C: γ → α + Fe₃C at 727 °C, 0.76-0.8 wt% C.
Peritectic: L + β → α. In Fe-Fe₃C: L + δ → γ at 1495 °C, 0.17 wt% C.
Peritectoid: α + β → γ (all solid). Monotectic: L₁ → α + L₂.
Partial solubility with terminal solid solutions: Pb-Sn, Al-Cu (the Al-Cu diagram with decreasing solubility of Cu in Al is the basis of precipitation hardening of Duralumin).
Congruent transformation: liquid and solid of the same composition (pure metal melting, or a congruent melting intermetallic).
Liquidus: locus above which everything is liquid. Solidus: below which everything is solid. Solvus: solid-solubility limit line.
Cooling curves: a pure metal shows a horizontal arrest at its melting point; a solid solution shows two slope changes (liquidus and solidus); a eutectic composition shows a long horizontal arrest; an off-eutectic alloy shows a slope change plus an arrest. Thermal analysis of cooling curves is how diagrams are determined experimentally (along with metallography, dilatometry, XRD, DTA).

Reading a diagram: tie line and lever rule

At a point in a two-phase field, draw a tie line (horizontal isotherm) across the field. Its ends on the two boundaries give the compositions of the two phases.
The lever rule gives the amounts: the fraction of a phase is proportional to the length of the lever arm on the *opposite* side.
Phase composition and phase amount are different questions — exam marks are routinely lost by mixing them.
Coring / microsegregation: in real solidification the solid does not homogenise, so dendrite cores are solute-lean and boundaries solute-rich; cured by homogenising anneal. Non-equilibrium cooling can produce a eutectic in an alloy that should not contain one.

Allotropy of iron and the Fe-Fe₃C diagram

Pure iron: α (BCC, ferrite) up to 912 °C → γ (FCC, austenite) 912-1394 °C → δ (BCC) 1394-1538 °C → melts at 1538 °C. The Curie temperature 768-770 °C marks loss of ferromagnetism (a magnetic, not a crystallographic, change).
The practical diagram is Fe-Fe₃C, metastable, drawn 0 to 6.67 wt% C. True equilibrium would give graphite; cementite is retained because graphite nucleation is slow (Si and slow cooling promote graphite — that is how grey cast iron forms).
Phases: α-ferrite (BCC, max 0.022% C at 727 °C — soft, ductile, ferromagnetic); γ-austenite (FCC, max 2.11% C at 1148 °C — soft at temperature, non-magnetic, octahedral interstices are larger, hence higher C solubility); δ-ferrite (BCC, max 0.09% C at 1495 °C); Fe₃C (6.67% C, hard, brittle, ~800 HV); liquid.
Invariant reactions (learn all three):
1. Peritectic at 1495 °C: L(0.53% C) + δ(0.09% C) → γ(0.17% C).
2. Eutectic at 1148 °C: L(4.3% C) → γ(2.11% C) + Fe₃C → the structure ledeburite.
3. Eutectoid at 727 °C: γ(0.76% C) → α(0.022% C) + Fe₃C(6.67% C) → the structure pearlite (alternating lamellae of ferrite and cementite).
Critical lines (old but universally used labels): A₁ = 727 °C eutectoid line; A₃ = γ/(α+γ) boundary, falls from 912 °C to 727 °C; A_cm = γ/(γ+Fe₃C) boundary, rises from 727 °C to 1148 °C; A₂ = Curie line; A₄ = γ/δ change at 1394 °C. On heating they are written Ac₁, Ac₃ (chauffage), on cooling Ar₁, Ar₃ (refroidissement) — hysteresis makes Ac > Ar.
Classification by carbon content: steel < 2.11% C (industrially < ~2.0%); cast iron > 2.11% C (usually 2.5-4%). Hypoeutectoid steel < 0.76% C; eutectoid = 0.76% C; hypereutectoid 0.76-2.11% C. Hypoeutectic cast iron < 4.3% C; hypereutectic > 4.3% C.

Microstructures and how they develop

Hypoeutectoid steel (e.g. 0.4% C): on cooling from γ, proeutectoid ferrite nucleates at austenite grain boundaries along A₃; the remaining austenite reaches 0.76% C at 727 °C and transforms to pearlite. Structure = ferrite + pearlite; pearlite fraction rises linearly with carbon.
Eutectoid steel (0.76% C): fully pearlitic.
Hypereutectoid steel (e.g. 1.2% C): proeutectoid cementite forms as a network on austenite grain boundaries along A_cm; rest becomes pearlite. The brittle cementite network is why such steels are spheroidised before machining.
Pearlite: lamellar; interlamellar spacing decreases with faster cooling (coarse → fine pearlite), and strength follows a Hall-Petch-type relation with spacing. Pearlite from slow cooling ≈ 250 HB; fine pearlite ≈ 350 HB.
Cast iron structures: white cast iron = pearlite + cementite + ledeburite (hard, wear resistant, unmachinable); grey cast iron = graphite flakes in a ferrite/pearlite matrix (good damping, machinability, IS 210 grades FG 150-FG 400); ductile/SG iron = spheroidal graphite from Mg treatment (IS 1865); malleable iron from annealing white iron.
Property trends with carbon in steel: hardness, UTS and yield strength rise with carbon up to about 0.8%; ductility, toughness, weldability and formability fall. Above ~0.8% UTS falls again because of the brittle cementite network while hardness keeps rising.
Effect of alloying elements (shifts the diagram — commonly examined): Ni, Mn, Cu, N, C are austenite stabilisers (γ-looping expands, A₃ falls); Cr, Mo, Si, Ti, V, W, Al are ferrite stabilisers and most are strong carbide formers. Alloying elements lower the eutectoid carbon content and change the eutectoid temperature (Ni, Mn lower it; Cr, Mo, Si, Ti raise it). This is why 18-8 stainless is austenitic at room temperature.

Limits of the diagram and Indian practice

The diagram assumes equilibrium: it predicts phases, not rates. Rapid cooling gives martensite or bainite, which appear nowhere on it — those need TTT/CCT diagrams.
It is a binary diagram; real steels contain Mn, Si, S, P, N and alloy additions, so critical temperatures shift (empirical formulas for Ac₁/Ac₃ are used in plants).
It gives no information on grain size, inclusion content or residual stress, all of which control service behaviour.
Indian standards that encode these distinctions: IS 2062 for hot-rolled structural steel (E250 to E650 grades, low carbon for weldability); IS 1786 for high-strength deformed reinforcement bars (Fe 415/500/550/600 and D/S variants); IS 1875 and IS 1570 series for carbon and alloy steel chemical composition; IS 210 for grey iron castings; IS 1865 for SG iron; IS 11169 and allied standards cover heat-treatment practice. BIS quality control orders make conformity mandatory for several steel products; quote the current edition of a standard, as many older IS numbers have been revised or withdrawn.
Workplace note: metallography labs use etchants (2% nital, picral) under the occupational safety and working-conditions provisions of the Labour Codes in force from 21 November 2025, which replaced the Factories Act for safety, health and welfare duties.

Key points

Phase - homogeneous, physically distinct, mechanically separable part of a system.
Gibbs phase rule (condensed) - P + F = C + 1 at constant pressure; three phases in a binary system means zero degrees of freedom.
Tie line - horizontal line in a two-phase field; its ends give phase compositions.
Lever rule - fraction of a phase = opposite arm / total tie-line length.
Isomorphous - complete solid solubility in liquid and solid, e.g. Cu-Ni.
Eutectic - L → α + β at one temperature; Fe-Fe₃C: 4.3% C, 1148 °C, gives ledeburite.
Eutectoid - γ → α + Fe₃C at 727 °C, 0.76% C, gives pearlite.
Peritectic - L + δ → γ at 1495 °C, 0.17% C in the Fe-Fe₃C system.
Allotropy of iron - α BCC → γ FCC at 912 °C → δ BCC at 1394 °C → liquid at 1538 °C.
Maximum solubility of carbon - 0.022% in α at 727 °C; 2.11% in γ at 1148 °C; 0.09% in δ at 1495 °C.
Austenite dissolves more carbon than ferrite - FCC octahedral interstitial sites are larger despite FCC having higher packing density.
Steel vs cast iron - 2.11% C is the dividing line.
Proeutectoid phase - ferrite in hypoeutectoid steel, cementite in hypereutectoid steel, formed before the eutectoid reaction.
Pearlite - lamellar ferrite + cementite, about 88% ferrite and 12% cementite by mass.
Cementite - Fe₃C, 6.67% C, orthorhombic, hard and brittle, metastable with respect to graphite.
A₁, A₃, A_cm - eutectoid line, ferrite-austenite boundary, cementite solvus; Ac on heating, Ar on cooling.
Austenite vs ferrite stabilisers - Ni, Mn, C, N expand γ; Cr, Mo, Si, Ti, V, Al expand α.
Limitation - an equilibrium diagram cannot show martensite or bainite; use TTT/CCT for those.

Formulas and examples

Gibbs phase rule: P + F = C + 2 (pressure variable); P + F = C + 1 (constant pressure). P = number of phases, F = degrees of freedom, C = number of components.

Lever rule in a two-phase (α + β) field with overall composition C₀, phase compositions C_α and C_β (all wt%):
W_α = (C_β − C₀) / (C_β − C_α) ; W_β = (C₀ − C_α) / (C_β − C_α) ; W_α + W_β = 1 (mass fractions, dimensionless)

Volume fraction from mass fraction: V_α = (W_α/ρ_α) / (W_α/ρ_α + W_β/ρ_β), ρ in g/cm³ (ρ_ferrite ≈ 7.87, ρ_cementite ≈ 7.66)

Pearlite constituents at 727 °C: W_α = (6.67 − 0.76)/(6.67 − 0.022) = 0.889 ; W_Fe3C = (0.76 − 0.022)/(6.67 − 0.022) = 0.111

Hypoeutectoid steel just below 727 °C (overall C₀ < 0.76):
W_pearlite = (C₀ − 0.022)/(0.76 − 0.022) ; W_proeutectoid α = (0.76 − C₀)/(0.76 − 0.022)

Hypereutectoid steel just below 727 °C (0.76 < C₀ < 2.11):
W_pearlite = (6.67 − C₀)/(6.67 − 0.76) ; W_proeutectoid Fe3C = (C₀ − 0.76)/(6.67 − 0.76)

Example 1 — Pearlite constituents. Find the mass fractions of ferrite and cementite in fully pearlitic 0.76% C steel at 726 °C.

Tie line from C_α = 0.022 to C_Fe3C = 6.67; total length = 6.648.
W_α = (6.67 − 0.76)/6.648 = 5.91/6.648 = 0.889 (88.9%).
W_Fe3C = (0.76 − 0.022)/6.648 = 0.738/6.648 = 0.111 (11.1%).
Check: 0.889 + 0.111 = 1.000. So pearlite is roughly 8 parts ferrite to 1 part cementite — hence its mostly ductile behaviour.

Example 2 — 0.4% C steel (a typical IS C40 / forging steel), just below 727 °C.

Total ferrite and cementite (microconstituent-blind): W_α total = (6.67 − 0.40)/6.648 = 6.27/6.648 = 0.943; W_Fe3C = (0.40 − 0.022)/6.648 = 0.378/6.648 = 0.0569.
Now split by microconstituent using the 0.76 tie line: W_pearlite = (0.40 − 0.022)/(0.76 − 0.022) = 0.378/0.738 = 0.512 (51.2%); W_proeutectoid ferrite = (0.76 − 0.40)/0.738 = 0.36/0.738 = 0.488 (48.8%).
Check: 0.512 + 0.488 = 1.000. Micrograph prediction: about half the field is light proeutectoid ferrite, half is lamellar pearlite.

Example 3 — 1.2% C hypereutectoid steel at 726 °C.

W_pearlite = (6.67 − 1.20)/(6.67 − 0.76) = 5.47/5.91 = 0.9255 (92.6%).
W_proeutectoid Fe₃C = (1.20 − 0.76)/5.91 = 0.44/5.91 = 0.0745 (7.4%).
Total cementite = (1.20 − 0.022)/6.648 = 1.178/6.648 = 0.1772; eutectoid cementite in pearlite = 0.1772 − 0.0745 = 0.1027.
Volume fraction of total cementite ≈ (0.1772/7.66)/((0.1772/7.66) + (0.8228/7.87)) = 0.02313/(0.02313 + 0.10455) = 0.181 (18.1%) — slightly more than the mass fraction because cementite is less dense.

Example 4 — Austenite at 900 °C in 0.4% C steel, and phase rule.

At 900 °C and 0.4% C the alloy is single-phase γ: P = 1, C = 2 → F = C + 1 − P = 2 (temperature and composition can both be varied).
At 727 °C exactly, γ, α and Fe₃C coexist: P = 3 → F = 2 + 1 − 3 = 0, an invariant point. This is why the eutectoid holds at a fixed temperature and composition.
Cool the same steel to 800 °C: it lies in the α + γ field. If the tie line at 800 °C gives C_α = 0.015 and C_γ = 0.48, then W_γ = (0.40 − 0.015)/(0.48 − 0.015) = 0.385/0.465 = 0.828 and W_α = 0.172. (The boundary compositions must be read off the diagram supplied in the question.)

Example 5 — Pb-Sn solder, 40% Sn at 150 °C. Take C_α(Pb-rich) = 11% Sn and C_β(Sn-rich) = 98% Sn.

W_α = (98 − 40)/(98 − 11) = 58/87 = 0.667; W_β = (40 − 11)/87 = 29/87 = 0.333.
Just above 183 °C the alloy is α + L with C_α = 18.3, C_L = 61.9: W_L = (40 − 18.3)/(61.9 − 18.3) = 21.7/43.6 = 0.498, so about half the alloy is still liquid at the eutectic temperature — the pasty range that makes 60/40 solder workable.

Microconstituent	Phases present	Carbon, wt%	Typical hardness	Formed by
Ferrite (α)	BCC Fe	≤ 0.022	80-100 HB	Slow cooling, below A₃
Austenite (γ)	FCC Fe	≤ 2.11	soft at temperature	Above A₃/A_cm
Cementite	Fe₃C	6.67	~800 HV	Eutectoid / proeutectoid
Pearlite	α + Fe₃C lamellar	0.76	200-350 HB	Eutectoid reaction at 727 °C
Ledeburite	γ (→ pearlite) + Fe₃C	4.3	very hard	Eutectic reaction at 1148 °C

Reaction	Type	Temperature	Equation
Peritectic	L + S → S	1495 °C	L(0.53) + δ(0.09) → γ(0.17)
Eutectic	L → S + S	1148 °C	L(4.3) → γ(2.11) + Fe₃C
Eutectoid	S → S + S	727 °C	γ(0.76) → α(0.022) + Fe₃C

Where it is used

Integrated steel plants (Tata Steel Jamshedpur/Kalinganagar, JSW Vijayanagar, SAIL Bhilai/Rourkela/Bokaro, RINL Visakhapatnam): selecting carbon and alloy aim-chemistry, setting reheat and rolling temperatures above A₃, and controlled cooling of rails, plates and TMT bars.
Foundries (Kirloskar, Brakes India, SG-iron pipe makers): choosing carbon equivalent and composition relative to the 4.3% eutectic to get grey, white, malleable or SG iron per IS 210 and IS 1865.
Automotive and forging (Bharat Forge, Mahindra, Ashok Leyland, bearing and gear makers): medium-carbon and alloy steels specified by the proeutectoid-ferrite/pearlite balance; C40, C55, EN series equivalents.
Welding and fabrication (L&T, BHEL, pipeline contractors): HAZ microstructure and hydrogen cracking risk are read off carbon content and carbon equivalent; low-carbon IS 2062 grades are chosen for weldability.
QA / metallography labs and NABL-accredited test houses: microstructure identification, percentage pearlite, decarburisation depth and banding ratings are reported against the diagram.
Job roles: process metallurgist, heat-treatment engineer, failure-analysis engineer, materials QA engineer, R&D at DMRL/BARC/ISRO/NML; also the basis of questions in GATE MT, ESE, PSU (SAIL MT/OCT, NTPC, IOCL) and defence lab recruitment.

Interview questions

Q: Why does FCC austenite dissolve far more carbon than BCC ferrite, though FCC is more closely packed? A: FCC has larger octahedral interstitial sites (octahedral hole radius ~0.414r in FCC vs ~0.155r in BCC, where carbon sits), so carbon fits with less lattice strain — 2.11% versus 0.022%.
Q: Why is the Fe-Fe₃C diagram called metastable? A: Graphite, not cementite, is the true equilibrium carbon-rich phase; cementite forms because graphite nucleation is kinetically difficult, and it decomposes to Fe + graphite on very long high-temperature holds.
Q: State the eutectoid reaction with compositions and temperature. A: Austenite of 0.76 wt% C transforms at 727 °C into ferrite of 0.022 wt% C plus cementite of 6.67 wt% C, giving lamellar pearlite.
Q: Difference between eutectic and eutectoid? A: A eutectic is a liquid transforming into two solids; a eutectoid is one solid transforming into two solids — both are invariant (F = 0) in a binary system.
Q: What distinguishes steel from cast iron on the diagram? A: The 2.11% C solubility limit of austenite — below it the alloy can be made fully austenitic and hot-worked; above it a eutectic (ledeburite) forms and the alloy is cast rather than rolled.
Q: Give the lever rule and say what it computes. A: W_α = (C_β − C₀)/(C_β − C_α); it gives the *amount* of each phase, while the tie-line ends give their *compositions*.
Q: Why does the strength of plain carbon steel fall above about 0.8% C while hardness keeps rising? A: Proeutectoid cementite forms a brittle continuous network on prior austenite grain boundaries, so the steel fractures before reaching a higher strength.
Q: What is proeutectoid ferrite and where does it nucleate? A: Ferrite formed between A₃ and A₁ in a hypoeutectoid steel, nucleating on austenite grain boundaries, leaving the remaining austenite enriched to 0.76% C.
Q: Why is the austenitising temperature different for hypo- and hypereutectoid steels? A: Hypoeutectoid steels are heated above A₃ to dissolve all ferrite; hypereutectoid steels are heated only above A₁ (between A₁ and A_cm) because full solution above A_cm coarsens grains and risks quench cracking.
Q: Can the Fe-Fe₃C diagram tell you whether a part will be martensitic? A: No — it is an equilibrium diagram giving only phases and amounts at equilibrium; cooling-rate-dependent products like martensite and bainite require TTT or CCT diagrams.
Q: How do Ni and Cr change the diagram? A: Ni (like Mn, C, N) stabilises austenite, expands the γ field and lowers A₃ and the eutectoid temperature; Cr (like Mo, Si, Ti, V) stabilises ferrite, forms carbides and raises the eutectoid temperature; both lower the eutectoid carbon content.
Q: Why is 1148 °C and not 1130 °C quoted in some books for the eutectic? A: Accepted values of the Fe-Fe₃C invariant points have been revised as thermodynamic assessments improved; 1148 °C / 2.11% C and 727 °C / 0.76% C are the current CALPHAD-based figures, while 1130 °C / 2.0% / 0.8% appear in older texts — state the source you are using.

Common mistakes

Using the tie-line end compositions as phase *amounts*, or the overall composition as a phase composition.
Taking the tie line to the wrong boundary — for hypoeutectoid steel below 727 °C, the *microconstituent* split uses the 0.76 tie line, the *phase* split uses the 6.67 tie line; the two answers differ and both are valid for different questions.
Calling pearlite, ledeburite or martensite "phases" — pearlite and ledeburite are two-phase microconstituents, and martensite is not on the diagram at all.
Writing the eutectoid as austenite → pearlite + cementite, or forgetting that the eutectoid ferrite is 0.022% C and not pure iron.
Confusing eutectic with eutectoid, or quoting 0.8%/2.0%/1130 °C and 0.76%/2.11%/1148 °C interchangeably within one answer.
Forgetting the peritectic at 1495 °C and the δ-ferrite region, which is examined and matters in continuous-casting crack sensitivity around 0.17% C.
Converting mass fractions to volume fractions without using the densities, and ignoring that the diagram says nothing about grain size, inclusions or cooling rate.