Phase Diagrams

1. Introduction

A phase diagram (also called an equilibrium diagram) is a graphical representation showing the relationship between temperature, composition, and phases present in a material system at equilibrium.

A phase is a homogeneous, physically and chemically uniform part of a system (e.g., solid, liquid, gas).

2. Importance of Phase Diagrams

Phase diagrams help engineers to:

• Understand phase transformations
• Predict microstructure of alloys
• Select proper heat treatment processes
• Control mechanical properties
• Design new materials

3. Basic Terms in Phase Diagrams

1. Components

• Chemically distinct substances in a system
• Example: In Cu–Ni system → Copper and Nickel

2. Phases

• Solid, liquid, or gas regions
• Example: Solid solution, liquid alloy

3. Solubility Limit

• Maximum amount of solute that can dissolve in solvent

4. Liquidus Line

• Above this line → material is completely liquid

5. Solidus Line

• Below this line → material is completely solid

6. Solvus Line

• Separates different solid phases

4. Types of Phase Diagrams

A. Unary Phase Diagram (One Component System)

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• Contains only one component
• Example: Water (H₂O)

Key Features:

• Triple Point → Three phases coexist
• Critical Point → Beyond which liquid and gas become indistinguishable

B. Binary Phase Diagram (Two Component System)

1. Isomorphous System (Complete Solubility)

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• Complete solubility in liquid and solid state
• Example: Copper–Nickel system

Regions:

• Liquid (L)
• Solid (α)
• Liquid + Solid

2. Eutectic System

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• Limited solid solubility
• At eutectic point:

Reaction:$$L \rightarrow \alpha + \beta$$L→α+β

Example: Lead–Tin (Pb–Sn)

3. Peritectic System

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Reaction:$$L + \alpha \rightarrow \beta$$L+α→β

• Occurs at a specific temperature and composition

5. Lever Rule

Used to calculate the fraction of phases in a two-phase region.

$W_\alpha = \frac{C_L – C_0}{C_L – C_\alpha}, \quad W_L = \frac{C_0 – C_\alpha}{C_L – C_\alpha}$Wα​=CL​−Cα​CL​−C0​​,WL​=CL​−Cα​C0​−Cα​​

Where:

• $W_\alpha$Wα​, $W_L$WL​ → Weight fractions
• $C_0$C0​ → Overall composition
• $C_L$CL​, $C_\alpha$Cα​ → Phase compositions

6. Iron–Carbon Phase Diagram

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This is the most important phase diagram in engineering.

Key Phases:

• Ferrite (α) → Soft, ductile
• Austenite (γ) → FCC structure
• Cementite (Fe₃C) → Hard and brittle

Important Reactions:

1. Eutectoid Reaction:

$$\gamma \rightarrow \alpha + Fe_3C$$γ→α+Fe3​C

2. Eutectic Reaction:

$$L \rightarrow \gamma + Fe_3C$$

3. Peritectic Reaction:

$$L + \delta \rightarrow \gamma$$

7. Applications of Phase Diagrams

• Designing alloys
• Heat treatment (annealing, quenching)
• Predicting microstructures
• Controlling properties like hardness and strength

8. Advantages

• Easy visualization of phase changes
• Helps in industrial processing
• Guides material selection

9. Limitations

• Applicable only under equilibrium conditions
• Does not consider cooling rate effects
• Real systems may deviate

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