Phase Diagrams and Alloy Systems
Key Takeaways
- A phase diagram maps which phases are stable at each temperature and composition; liquidus, solidus, and solvus are the key boundaries.
- The lever rule gives phase fractions in a two-phase region: Wα = (Cβ − C₀)/(Cβ − Cα), using compositions at the ends of the tie line.
- Invariant reactions: eutectic (L → α + β), eutectoid (γ → α + β), and peritectic (L + α → β).
- The Fe–C diagram is central: steel is < 2.14% C, cast iron > 2.14% C; the eutectoid at 727 °C and 0.76% C forms pearlite.
- Key Fe–C phases: ferrite (α, BCC, soft), austenite (γ, FCC), cementite (Fe₃C, 6.67% C, hard/brittle), martensite (BCT, from quenching).
- Heat treatment tunes properties: annealing (soft), normalizing (refined grain), quenching (hard martensite), tempering (restores toughness).
Reading a Phase Diagram
A phase is a region of uniform composition and structure. A binary phase diagram plots temperature (y) versus composition (x) and shows which phase(s) are stable at any point.
| Boundary/feature | Meaning |
|---|---|
| Liquidus | Above it, everything is liquid |
| Solidus | Below it, everything is solid |
| Solvus | Solid-solubility limit between two solid phases |
| Single-phase region | One phase stable (α, β, L, γ) |
| Two-phase region | Two phases coexist along a horizontal tie line |
| Invariant point | Fixed T and composition where 3 phases coexist |
Inside a two-phase region, the tie line's endpoints give the compositions of the two coexisting phases, and the lever rule gives their amounts.
The Lever Rule
For an overall composition C₀ inside a two-phase (α + β) field with tie-line ends at Cα and Cβ:
The fraction of a phase is proportional to the length of the tie line on the opposite side of C₀ (the "lever" balances about C₀).
Worked example: An alloy with overall composition C₀ = 40% B sits in a two-phase region with α at Cα = 20% B and β at Cβ = 60% B. Then Wβ = (40 − 20)/(60 − 20) = 20/40 = 0.50, and Wα = (60 − 40)/(60 − 20) = 0.50. The alloy is half α, half β. (Always subtract along the tie line — using temperatures instead of compositions is a classic mistake.)
Invariant Reactions
| Reaction | Transformation on cooling | Example |
|---|---|---|
| Eutectic | L → α + β | Pb–Sn solder, 183 °C |
| Eutectoid | γ → α + β | Fe–C, 727 °C |
| Peritectic | L + α → β | Fe–C, 1,495 °C |
The Gibbs Phase Rule
The Gibbs phase rule tells you how many variables you can change independently: P + F = C + 2 (or at constant pressure, P + F = C + 1), where P = number of phases, F = degrees of freedom, and C = number of components. In a binary (C = 2) diagram at fixed pressure, a single-phase region has F = 2 (temperature and composition both free), a two-phase region has F = 1, and an invariant point (three phases, like the eutectic) has F = 0 — temperature and all compositions are fixed, which is exactly why those reactions occur at a single sharp temperature.
The Iron–Carbon Diagram
The Fe–C (Fe–Fe₃C) diagram is the most important system in engineering practice.
| Phase | Structure | Carbon | Character |
|---|---|---|---|
| Ferrite (α) | BCC | ≤ 0.022% | Soft, ductile, magnetic |
| Austenite (γ) | FCC | ≤ 2.14% | Soft, ductile, non-magnetic |
| Cementite (Fe₃C) | Orthorhombic | 6.67% | Very hard, brittle |
| Pearlite | Lamellar α + Fe₃C | 0.76% | Moderate strength + ductility |
| Martensite | BCT | = parent γ | Very hard, brittle (quenched) |
Key points:
| Point | T | C | Reaction |
|---|---|---|---|
| Eutectoid | 727 °C | 0.76% | γ → α + Fe₃C (pearlite) |
| Eutectic | 1,147 °C | 4.30% | L → γ + Fe₃C |
| Max C in austenite | 1,147 °C | 2.14% | Steel/cast-iron boundary |
The 2.14% C line divides steels (workable, weldable) from cast irons (castable, brittle). Steels are graded by carbon: low-carbon/mild (< 0.25% C, ductile, weldable), medium-carbon (0.25–0.60% C, balanced), and high-carbon (0.60–2.14% C, hard, strong, less ductile). Alloys at exactly 0.76% C are eutectoid (fully pearlite); below that are hypoeutectoid (proeutectoid ferrite + pearlite); above are hypereutectoid (proeutectoid cementite + pearlite).
Heat Treatment
Heat treatment manipulates the microstructure predicted by the Fe–C diagram to set hardness, strength, and toughness.
| Treatment | Process | Result |
|---|---|---|
| Annealing | Heat above critical T, slow furnace cool | Soft, ductile, stress-relieved, coarse pearlite |
| Normalizing | Heat above critical T, air cool | Refined grain, finer pearlite, moderate strength |
| Quenching | Heat to austenite, rapid water/oil cool | Hard, brittle martensite |
| Tempering | Reheat quenched steel below critical T | Trades some hardness for restored toughness |
| Case hardening | Carburize/nitride the surface only | Hard wear-resistant case, tough ductile core |
Why quenching hardens: rapid cooling gives carbon atoms no time to diffuse out of the FCC austenite, trapping them in a strained body-centered tetragonal (BCT) martensite. The lattice distortion blocks dislocation motion, producing extreme hardness but brittleness — which is why quenched parts are almost always tempered afterward to recover toughness.
The quench → temper sequence is the cornerstone of producing tough, high-strength steel components (gears, shafts, tools). Annealing and normalizing, by contrast, are used when softness, machinability, or a uniform refined grain is the goal.
Hardenability — how deeply martensite forms on quenching — depends on alloying elements (Cr, Mo, Ni) and is measured by the Jominy end-quench test; it differs from hardness, which is just the surface indentation value of the final part.
In the Fe–C phase diagram, the eutectoid transformation occurs at:
An alloy lies in a two-phase region with overall composition 35% B; the tie-line ends are α at 15% B and β at 55% B. What fraction is the α phase?
Which heat treatment produces hard, brittle martensite in steel?
A plain-carbon alloy contains 1.2% carbon. How is it classified relative to the eutectoid composition?