Equilibrium Diagrams

Equilibrium Diagrams

Phase Equilibrium Diagrams

  • Represent the stability limits of phases in alloy systems graphically based on temperature and composition.
  • For binary alloys AB:
    • Liquidus curve: Above this, only liquids are present.
    • Solidus curve: Below this, only solids are present.

Binary Equilibrium Diagram

  • Used to determine alloy composition in weight percentages at specific points.
  • Example:
    • Point A: 60% Ni, 40% Cu
    • Point B: 35% Ni, 65% Cu
  • Lever rule: Used to determine the percentage of each phase (liquid and solid) at a given point.
    • WL = \frac{C\alpha - C0}{C\alpha - C_L}
    • W\alpha = \frac{C0 - CL}{C\alpha - C_L}
    • Example at point B:
      • W_L = \frac{42.5 - 35}{42.5 - 31.5} = 0.68 (68% liquid phase)
      • W_\alpha = \frac{35 - 31.5}{42.5 - 31.5} = 0.32 (32% solid phase)

Eutectic Diagram

  • Eutectic: Liquid transforms into two solid phases (α + β).
  • Example: Cu-Ag system.
    • Eutectic temperature: 779 °C
    • Eutectic composition: 71.9 wt.% Ag, 28.1 wt.% Cu
  • Lever rule is applied to determine the composition of the two phases in the α+β region.

Iron-Carbon Equilibrium Diagram

  • Phases in Fe-C alloys:
    • Ferrite: Solid solution of C in Feα (BCC).
      • Maximum C solubility: 0.022 wt.% at 727 °C.
      • Magnetic below 770 °C.
    • Austenite: Solid solution of C in Feγ (FCC).
      • Maximum C solubility: 2.14 wt.%.
      • Not magnetic.
    • Cementite: Iron carbide (Fe3C).
      • Composition: 6.70 wt.% C, 93.30 wt.% Fe.
      • Hard (900 HB) but brittle.
  • Commercial iron: <0.008 wt.% C, mostly α-ferrite.
  • Steels: 0.008 - 2.14 wt.% C, α-ferrite and cementite phases.
  • Cast irons: 2.14 - 6.70 wt.% C.
  • Eutectic: Liquid → Austenite + Cementite (4.30 wt.% C at 1147 °C).
  • Eutectoid: Austenite → Ferrite + Cementite (0.76 wt.% C at 727 °C).

Eutectoid Steel

  • Composition: 0.76 wt.% C.
  • Upon cooling, austenite transforms into pearlite.
  • Pearlite: Alternating layers of ferrite and cementite.
  • Properties are intermediate between soft ferrite and hard cementite.

Microstructure Control in Steels

  • Cooling austenite results in different microstructures such as:
    • Pearlite
    • Bainite
    • Martensite

Transformations

  • Pearlite: Controlled by diffusion.
  • Martensite: Not controlled by diffusion.
  • Diffusion: Movement of atoms within a crystal structure.

Time-Temperature-Transformation (TTT) Diagrams

  • Show the transformation of austenite over time at different temperatures.
  • Used to determine the final structure of an alloy after cooling.

Heat Treatments

  • Annealing: Heating followed by slow cooling to reduce hardness and increase ductility.
  • Quenching: Rapid cooling to increase hardness (e.g., forming martensite in steels).
  • Tempering: Reheating quenched alloy to improve ductility.
  • Aging: Strengthening by precipitate formation.

Alloying Elements

  • Cr, Si stabilize ferrite (α phase).
  • Ni, Mn stabilize austenite (γ phase).

Stainless Steels

  • Contain ≥ 10.5% Cr for corrosion resistance.
  • Forms a passive Cr2O3 layer.

Types of Stainless Steels

  • Ferritic
  • Martensitic
  • Austenitic