Phase Diagrams: Iron-Carbon and Copper-Nickel Systems Analysis

Iron-Carbon System Fundamentals

The iron-carbon system is one of the most important phase diagrams in engineering. It helps us understand how iron and carbon combine to form different structures, which influence the properties of steels and cast irons.

Iron-Carbon Phase Diagram Structures

• Pure iron changes its crystal structure as it is heated:
  • Ferrite (α iron) → BCC (Body-Centered Cubic) structure, stable at room temperature.
  • Austenite (γ iron) → FCC (Face-Centered Cubic) structure, stable between 912°C and 1394°C.
  • Delta Ferrite (δ iron) → BCC again, stable at high temperatures before melting at 1538°C.

These changes occur because different structures can hold carbon differently, affecting strength and hardness.

Cementite (Fe₃C) and Carbon Solubility

• Cementite (Fe₃C) is an iron-carbide compound that forms when carbon content is high.
• The solubility of carbon in iron depends on its structure:
  • Ferrite (α iron) can only dissolve 0.022% carbon (very low).
  • Austenite (γ iron) can dissolve up to 2.14% carbon at 1147°C (much higher).

Cementite is hard and brittle, making steel strong but less ductile.

Different Phases in the Iron-Carbon System

1. Ferrite (α iron) – Soft, magnetic, low carbon solubility, stable at room temperature.
2. Austenite (γ iron) – Non-magnetic, holds more carbon, important for heat treatment.
3. Delta Ferrite (δ iron) – Similar to ferrite, but exists only at high temperatures (not useful in practice).
4. Cementite (Fe₃C) – Extremely hard, increases steel strength but reduces flexibility.

Importance of Phase Control

• Heat treatment of steel relies on phase changes of iron-carbon alloys.
• Stronger steels are made by controlling how cementite and ferrite form.
• Cast iron (which has more carbon) is harder but more brittle than steel.
• Cementite is metastable, meaning that over many years at high temperatures, it can break down into iron and graphite (pure carbon).

This knowledge helps engineers and manufacturers control steel properties for different applications, like construction, automotive, and tools.

Gibbs Phase Rule Application

The Gibbs Phase Rule is a formula that helps us determine how many independent variables (like temperature, pressure, or composition) we can change in a system without altering the number of phases present.

The formula is:

F = 2 + C - P

Where:

• F = Degrees of freedom (how many variables we can control independently).
• C = Number of components in the system (different elements or compounds present).
• P = Number of phases present (solid, liquid, or gas).

Understanding with a Pure Substance (C = 1)

Let’s apply the rule to a single pure substance, meaning we have only one component (C = 1), such as water.

Case 1: Single Phase (P = 1)

• Example: Only liquid water, only ice, or only steam.
• Apply Gibbs Rule: F = 2 + 1 - 1 = 2
• This means we can change two variables independently (e.g., temperature and pressure).
• This is why we can heat or cool water freely and it remains a liquid (as long as we don’t hit the boiling or freezing points).

Case 2: Two Phases (P = 2)

• Example: Water coexisting with steam (boiling water) or ice coexisting with liquid water (melting ice).
• Apply Gibbs Rule: F = 2 + 1 - 2 = 1
• Now, only one variable can be changed independently.
• If we fix the pressure (e.g., normal atmospheric pressure), the temperature becomes fixed at the boiling or melting point.

Case 3: Three Phases (P = 3) – The Triple Point

• Example: Solid ice, liquid water, and water vapor all coexisting (occurs at a specific temperature and pressure).
• Apply Gibbs Rule: F = 2 + 1 - 3 = 0
• No freedom to change temperature or pressure–the system is fixed at a single unique point (called the triple point of water, which is 0.01°C and 0.006 atm).
• If we change either temperature or pressure, one of the phases disappears.

Gibbs Rule Summary

• F = 2 → One phase → We can control both temperature and pressure freely.
• F = 1 → Two phases → Only one variable (temperature or pressure) can be changed independently.
• F = 0 → Three phases → Temperature and pressure are fixed (only occurs at a single point).

This rule is important in metallurgy, chemistry, and engineering to predict phase changes in different materials.

Copper-Nickel Binary Phase Diagram Analysis

A binary phase diagram is like a map that tells us what happens to two mixed metals (alloys) at different temperatures. The copper-nickel system is one such example.

Key Features of the Copper-Nickel Phase Diagram

1. Axes of the Diagram:

   • The vertical axis (y-axis) represents temperature in degrees Celsius.
   • The horizontal axis (x-axis) represents the composition of the alloy (how much copper vs. nickel is present).

2. Composition of the Alloy:

   • On the left side (0% Ni, 100% Cu) → Pure Copper
   • On the right side (100% Ni, 0% Cu) → Pure Nickel
   • In between → Different mixtures of Cu and Ni

3. Phases in the Diagram:
   The diagram is divided into three regions:

   • Liquid (L): The alloy is completely melted.
   • Solid (α): The alloy is fully solidified, forming a single phase.
   • Two-phase region (α + L): The alloy has both liquid and solid at the same time.

Important Lines in the Diagram

• Liquidus Line:

  • This line separates the fully liquid phase from the mixed (solid + liquid) phase.
  • Above this line, the alloy is fully melted.

• Solidus Line:

  • This line separates the fully solid phase from the mixed (solid + liquid) phase.
  • Below this line, the alloy is fully solid.

• Between the Liquidus and Solidus Lines:

  • The material is partially solid and partially liquid (like slush).

Phase Diagram Applications

1. Complete Solubility:

   • Copper and nickel can mix completely in both liquid and solid states.
   • This means they form a single-phase solid solution (α phase) when cooled.

2. Melting and Solidification:

   • When heated, an alloy follows the solidus and liquidus lines to transition between solid and liquid.
   • If a 60% Ni – 40% Cu alloy is heated to 1100°C, it will be completely solid (α phase).
   • If a 35% Ni – 65% Cu alloy is at 1250°C, it will be in the mixed phase (solid + liquid).

Determining Phase Compositions (Tie Line Method)

When an alloy's composition and temperature fall in a two-phase region (α + L), we use a method called the tie line method to find the exact composition of the two phases (solid and liquid).

Steps to Find Phase Compositions

1. Draw a tie line (isotherm) at the given temperature. This is a horizontal line in the phase diagram.
2. Find where the tie line meets the phase boundaries (solidus and liquidus lines).
3. Drop vertical lines from these intersection points to the composition axis.
4. Read the compositions where these lines meet the axis.

Example Calculation

• Given alloy: 35 wt% Ni – 65 wt% Cu at 1250°C (this falls in the α + L region).
• From the phase diagram:
  • The liquid phase composition is 31.5 wt% Ni – 68.5 wt% Cu.
  • The solid (α) phase composition is 42.5 wt% Ni – 57.5 wt% Cu.

This means at 1250°C, the liquid has less nickel than the solid, and as the alloy cools, the solid phase forms with more nickel content.

Determining Phase Amounts (Lever Rule)

When an alloy is in the two-phase region (α + L), we calculate how much of each phase (solid and liquid) is present using the lever rule.

Steps to Use the Lever Rule

1. Draw a tie line at the given temperature across the two-phase region.
2. Find the alloy composition on the tie line.
3. Measure the distance from the alloy composition to the opposite phase boundary.
4. Divide this by the total tie line length to get the fraction of each phase.
5. Multiply by 100 to get percentage values.