Phase Diagrams and Alloy Systems
Key Takeaways
- Phase diagrams show which phases are stable at given temperatures and compositions.
- The iron-carbon (Fe-C) phase diagram is the most important for engineers — steel (< 2.14% C) and cast iron (> 2.14% C).
- The lever rule calculates the fraction of each phase in a two-phase region.
- Eutectic, eutectoid, and peritectic are key invariant reactions in phase diagrams.
- For Fe-C: the eutectoid reaction at 727°C produces pearlite (alternating ferrite and cementite lamellae).
- Heat treatment (annealing, quenching, tempering) modifies microstructure and properties.
Last updated: March 2026
Phase Diagrams and Alloy Systems
Phase Diagram Basics
A phase is a homogeneous portion of a system with uniform physical and chemical properties.
Components of a phase diagram:
- Single-phase regions: Only one phase is stable
- Two-phase regions: Two phases coexist
- Phase boundaries (lines): Where phase changes occur
- Invariant points: Where multiple phases coexist at a fixed temperature
Binary Phase Diagrams
Key Features
| Feature | Description |
|---|---|
| Liquidus | Line above which everything is liquid |
| Solidus | Line below which everything is solid |
| Solvus | Solid solubility limit boundary |
| Eutectic point | Lowest melting point composition |
Lever Rule (for two-phase regions)
To find the fraction of each phase at a given temperature and composition:
where:
- C₀ = overall composition
- Cα = composition of phase α (left end of tie line)
- Cβ = composition of phase β (right end of tie line)
Invariant Reactions
| Reaction | Description | Example |
|---|---|---|
| Eutectic | L → α + β (liquid to two solids) | Pb-Sn solder at 183°C |
| Eutectoid | γ → α + β (one solid to two solids) | Fe-C at 727°C |
| Peritectic | L + α → β (liquid + solid to different solid) | Fe-C at 1,495°C |
The Iron-Carbon (Fe-C) Phase Diagram
This is the most important phase diagram for engineers:
Key Phases
| Phase | Symbol | Structure | Carbon Content | Properties |
|---|---|---|---|---|
| Ferrite | α | BCC | ≤ 0.022% C | Soft, ductile, magnetic |
| Austenite | γ | FCC | ≤ 2.14% C | Soft, ductile, non-magnetic |
| Cementite | Fe₃C | Orthorhombic | 6.67% C | Very hard, brittle |
| Pearlite | — | Layered α + Fe₃C | 0.76% C | Moderate strength/ductility |
| Martensite | — | BCT | Same as parent γ | Very hard, brittle (quenched) |
Key Points on the Fe-C Diagram
| Point | Temperature | Composition | Significance |
|---|---|---|---|
| Eutectoid | 727°C | 0.76% C | γ → α + Fe₃C (pearlite) |
| Eutectic | 1,147°C | 4.30% C | L → γ + Fe₃C |
| Max C in austenite | 1,147°C | 2.14% C | Steel vs cast iron boundary |
Steel Classification by Carbon Content
| Type | Carbon % | Properties |
|---|---|---|
| Low carbon (mild) | < 0.25% | Ductile, weldable, low strength |
| Medium carbon | 0.25-0.60% | Balance of strength and ductility |
| High carbon | 0.60-2.14% | Hard, strong, less ductile |
Heat Treatment
| Treatment | Process | Result |
|---|---|---|
| Annealing | Heat above critical T, slow cool (furnace) | Soft, ductile, stress-relieved |
| Normalizing | Heat above critical T, air cool | Refined grain, moderate properties |
| Quenching | Heat above critical T, rapid cool (water/oil) | Hard, brittle martensite |
| Tempering | Reheat quenched steel below critical T | Reduces brittleness, restores toughness |
| Case hardening | Harden surface only (carburizing, nitriding) | Hard surface, tough core |
Test Your Knowledge
In the Fe-C phase diagram, the eutectoid transformation occurs at:
A
B
C
D
Test Your Knowledge
An alloy at a given temperature is in a two-phase region. The overall composition is 40% B, and the phase boundaries are at 20% B (α phase) and 60% B (β phase). What fraction is the β phase?
A
B
C
D
Test Your Knowledge
What heat treatment produces martensite in steel?
A
B
C
D