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

FeatureDescription
LiquidusLine above which everything is liquid
SolidusLine below which everything is solid
SolvusSolid solubility limit boundary
Eutectic pointLowest melting point composition

Lever Rule (for two-phase regions)

To find the fraction of each phase at a given temperature and composition:

Wα=CβC0CβCαWβ=C0CαCβCαW_\alpha = \frac{C_\beta - C_0}{C_\beta - C_\alpha} \qquad W_\beta = \frac{C_0 - C_\alpha}{C_\beta - C_\alpha}

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

ReactionDescriptionExample
EutecticL → α + β (liquid to two solids)Pb-Sn solder at 183°C
Eutectoidγ → α + β (one solid to two solids)Fe-C at 727°C
PeritecticL + 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

PhaseSymbolStructureCarbon ContentProperties
FerriteαBCC≤ 0.022% CSoft, ductile, magnetic
AusteniteγFCC≤ 2.14% CSoft, ductile, non-magnetic
CementiteFe₃COrthorhombic6.67% CVery hard, brittle
PearliteLayered α + Fe₃C0.76% CModerate strength/ductility
MartensiteBCTSame as parent γVery hard, brittle (quenched)

Key Points on the Fe-C Diagram

PointTemperatureCompositionSignificance
Eutectoid727°C0.76% Cγ → α + Fe₃C (pearlite)
Eutectic1,147°C4.30% CL → γ + Fe₃C
Max C in austenite1,147°C2.14% CSteel vs cast iron boundary

Steel Classification by Carbon Content

TypeCarbon %Properties
Low carbon (mild)< 0.25%Ductile, weldable, low strength
Medium carbon0.25-0.60%Balance of strength and ductility
High carbon0.60-2.14%Hard, strong, less ductile

Heat Treatment

TreatmentProcessResult
AnnealingHeat above critical T, slow cool (furnace)Soft, ductile, stress-relieved
NormalizingHeat above critical T, air coolRefined grain, moderate properties
QuenchingHeat above critical T, rapid cool (water/oil)Hard, brittle martensite
TemperingReheat quenched steel below critical TReduces brittleness, restores toughness
Case hardeningHarden 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