Phase Diagrams in Chemistry

Phase Diagrams

• A phase diagram is a graphical representation of the phases present and the ranges in composition, temperature, and pressure over which the phases are stable.
• It is a collection of curves showing solubility limits and is also called an equilibrium phase diagram because all reactions represented in the diagram are allowed to go to equilibrium.

Types of Phase Diagrams

• Unary phase diagram: one component
• Binary phase diagram: two components
• Ternary phase diagram: three components

Features in a Phase Diagram

• Axes:
  • y-axis: temperature (°C or °F)
  • x-axis: composition (wt% or atom%)
• Lower-case Greek letters (α, β, γ, etc.): solid solutions
• L or Lx: denotes a liquid phase
• Phase field/region: defined by the phase or phases that exist over a range of compositions and temperatures
• Phase boundary: lines that separate different phase fields
• Solidus: locus of temperature below which only solids are present
• Liquidus: locus of temperatures above which only liquids are present
• Solvus: boundary between a single solid phase field and a two solid phase field

Phase Diagram: Interpretation

• Phases present: locate the temperature-composition point on the diagram and note the phase(s) that are present
• Composition of phases: expressed in terms of the concentrations of the components
• Quantity of phases in equilibriated mixtures: can be determined using the Lever Rule

Lever Rule

• STEPS:

  1. Define alloy composition and temperature

  2. Set tie line and define compositions at the ends of the tie line

  3. To find the amount of one phase, use the equation:

     % amount of one phase = (difference in composition between the two ends of the tie line) / (difference in composition between the two phases)

Invariant Reactions

• Eutectic: L1 → S1 + S2
• Eutectoid: S1 → S2 + S3
• Peritectic: S 1 + L 1 → S2
• Peritectoid: S 1 + S 2 → S3
• Monotectic: L1 → S1 + L2
• Syntectic: L 1 + L 2 → S1

Fe-Fe3C Phase Diagram

• Phases:
  • 𝝰-Fe / alpha Ferrite: BCC crystal structure, stable form of iron at room temperature, maximum solubility of carbon is 0.022 wt% at 727 °C
  • 𝝲-Fe / Austenite: FCC crystal structure, maximum solubility of carbon is 2.14 wt% at 1147 °C
  • 𝜹-Fe / delta Ferrite: BCC crystal structure, stable only at high temperature
  • Fe3C / iron carbide / cementite: metastable intermetallic compound, remains as a compound indefinitely at room temperature, but decomposes (very slowly, within several years) into α-Fe and C (graphite) at 650-700 °C

Invariant Reactions in Fe-Fe3C Phase Diagram

• Peritectic, 1493 °C: L 0.53 wt% C + 𝜹 0.09 wt% C ⇌ 𝜸(0.41 wt% C)
• Eutectic, 1147 °C: L 4.30 wt% C ⇌ 𝜸 2.14 wt% C + Fe3C(6.70 wt% C)
• Eutectoid, 727 °C: 𝜸 0.76 wt% C ⇌ 𝜶 0.022 wt% C + Fe3C(6.70 wt% C)

Hypoeutectoid Composition

• Amount of phases can be determined using the Lever Rule
• Example: For a 99.65 wt% Fe–0.35 wt% C alloy at a temperature just below the eutectoid, determine the fractions of total ferrite and cementite phases, the fractions of the proeutectoid ferrite and pearlite, and the fraction of eutectoid ferrite.### Hypereutectoid Composition
• The fraction of eutectoid ferrite (α) can be calculated using the formula: 𝑊𝑒𝑢𝑡𝑒𝑐𝑡𝑜𝑖𝑑 𝛼 = 𝑊𝑡𝑜𝑡𝑎𝑙 𝛼 − 𝑊𝑝𝑟𝑜−𝛼
• For example, if the total amount of α is 0.95 and the amount of pro-eutectoid α is 0.56, then the fraction of eutectoid α is 0.39 (0.95 - 0.56)

Phase Amount

• The amount of pro-eutectoid cementite (𝑊𝑝𝑟𝑜−𝐹𝑒𝐶) can be calculated using the formula: 𝑊𝑝𝑟𝑜−𝐹𝑒𝐶 = (𝑪′𝟏 − 𝟎.𝟕𝟔) / (𝑽+𝑿)
• The amount of pearlite (𝑊𝑝𝑒𝑎𝑟𝑙𝑖𝑡𝑒) can be calculated using the formula: 𝑊𝑝𝑒𝑎𝑟𝑙𝑖𝑡𝑒 = (6.70 − 𝐶1′) / (𝑽+𝑿)

Hypereutectoid Composition: Phase Amount

• For a 98.90 wt% Fe–1.10 wt% C alloy at a temperature just below the eutectoid, the fractions of total ferrite and cementite phases can be calculated as follows:
  • The fraction of total ferrite (𝑊𝛼) is 0.839
  • The fraction of total cementite (𝑊𝐹𝑒3𝐶) is 0.161
• The fractions of the pro-eutectoid cementite and pearlite can be calculated as follows:
  • The fraction of pro-eutectoid cementite (𝑊𝑝𝑟𝑜−𝐹𝑒𝐶) is 0.057
  • The fraction of pearlite (𝑊𝑝𝑒𝑎𝑟𝑙𝑖𝑡𝑒) is 0.943
• The fraction of eutectoid cementite (𝑊𝑒𝑢𝑡𝑒𝑐𝑡𝑜𝑖𝑑 𝐹𝑒3 𝐶) is 0.104

Phase Transformation

• Equilibrium conditions occur when there is very slow cooling or heating, and the phase diagram is used to predict phase transformations
• Non-equilibrium conditions occur when there is rapid cooling or heating, and the TTT curve and/or CCT curve is used to predict phase transformations

Time-Temperature-Transformation Curve

• The TTT curve is used to predict the microstructure and corresponding amount after some period of constant temperature
• The TTT curve is also known as the Isothermal Transformation Curve (IT)

Continuous-Cooling Transformation Curve

• The CCT curve is used to predict the microstructure after continuous cooling treatments
• The CCT curve shows the effect of cooling rate on the microstructure

TTT vs CCT

• The TTT curve is used for isothermal treatments, while the CCT curve is used for continuous cooling treatments
• The TTT curve shows the effect of time on the microstructure, while the CCT curve shows the effect of cooling rate on the microstructure

Example Problems

• Example 1: Eutectoid Steel - Microstructures and/or phases present: Pearlite (50%), Bainite (50%)
• Example 2: AISI 1045 - Microstructures and/or phases present: Bainite (50%), Martensite (50%) with some retained austenite
• Example 3: AISI 1045 - Microstructures and/or phases present: Pro-Ferrite (42%), Pearlite (29%), Bainite (29%)
• Example 4: AISI 1045 - Microstructures and/or phases present: Pro-Ferrite, Pearlite, Bainite, Martensite
• Example 5: AISI 4340 - Microstructures and/or phases present: Bainite, Martensite at a cooling rate of 5°C/s
• Example 6: AISI 4340 - Microstructures and/or phases present: Pro-Ferrite, Pearlite, Bainite, Martensite at a cooling rate of 0.01°C/s

Phase and Phase Equilibrium

• A phase is a homogeneous portion of a system that has uniform physical and chemical characteristics.
• Phase equilibrium refers to systems where more than one phase may exist, with the system at equilibrium if its free energy is at a minimum under specific temperature, pressure, and composition combinations.

Phase Diagrams

• A phase diagram is a graphical representation of phases present and the ranges in composition, temperature, and pressure over which the phases are stable.
• Phase diagrams are used to predict phase transformations and their products, understand microstructure formation, predict existing phases for selected alloy compositions at desired temperatures, determine the chemical composition of each phase, and calculate the quantity of each phase present.

Types of Phase Diagrams

• There are three types of phase diagrams: unary, binary, and ternary.

Unary Phase Diagram

• A unary phase diagram shows the phases present in a one-component system.

Hypoeutectoid Composition: Phase Amount

• The fraction of proeutectoid ferrite can be calculated using the lever rule.
• The fraction of pearlite can be calculated by subtracting the fraction of proeutectoid ferrite from 1.
• The fraction of eutectoid ferrite can be calculated by subtracting the fraction of proeutectoid ferrite from the total ferrite composition.

Hypereutectoid Composition: Phase Amount

• The fraction of proeutectoid cementite can be calculated using the lever rule.
• The fraction of pearlite can be calculated by subtracting the fraction of proeutectoid cementite from 1.
• The fraction of eutectoid cementite can be calculated by subtracting the fraction of proeutectoid cementite from the total cementite composition.