Phase Diagrams & Phase Rule

Phase Diagrams

• Phase diagrams are useful for understanding the relationships between phases in a material system.

Phase Rule

• The phase rule defines the number of degrees of freedom (F) in a system.
• Degrees of freedom refer to the number of independent variables needed to define the system's state.
• The formula for calculating the number of degrees of freedom is F = C - P + 2.
  • C represents the number of components.
  • P represents the number of phases.

Cooling Curves

Pure Metal

• The melting point is indicated by point a on the diagram.
• The metal solidifies at a constant temperature between points b and c.
• The metal cools as a solid between points c and d.

Solid Solution Alloy

• Solid solution alloys freeze over a range of temperatures between points b and c.
• These alloys lack a sharp melting point.

Example 1: The Cu-Ni System

• This system has two components (C = 2): Copper (Cu) and Nickel (Ni).
• This system has two phases (P = 2): Liquid and Solid.
• Therefore, F = 2 - 2 + 2 = 2.
• Defining this system requires specifying two intensive variables, such as temperature and composition.
• If only one variable, such as composition, is defined, then F = 2 - 2 + 1 = 1.
• Specifying the temperature can then define the system.
• Liquidus line: the line above which only liquid exists.
• Solidus line: the line below which only solid exists.

Lever Rule

• The lever rule determines the composition of liquid and solid phases at a given temperature.
• The percentage of solid is calculated as: % solid = ((c-b)/(a-b)) * 100.
• The percentage of liquid is calculated as: % liquid = ((a-c)/(a-b)) * 100.
  • 'a' represents the overall composition of the alloy.
  • 'b' represents the composition of the solid phase.
  • 'c' represents the composition of the liquid phase.

Example 2: The Iron-Carbon System

• This system is relevant to steel production.
• This system consists of two components (C = 2): Fe and $Fe_3C$.
• This system consists of two phases (P = 2): Liquid and Solid.
• Therefore, F = 2 - 2 + 2 = 2.
• Defining the system requires specifying two intensive variables, such as temperature and composition.

Key points

• Austenite (γ-Fe): A solid solution of carbon in γ-Fe with an FCC structure, existing between 912 and 1394°C.
  • The maximum solubility of carbon in austenite is 2.14 wt% at 1147°C.
• $Fe_3C$ (Cementite): An intermetallic compound with a fixed composition of 6.7 wt% C, known for its hardness and brittleness.
• α-Ferrite: A solid solution of carbon in α-Fe with a BCC structure, existing below 912°C.
  • The maximum solubility of carbon in α-ferrite is 0.022 wt% at 727°C.
• δ-Ferrite: A solid solution of carbon in δ-Fe with a BCC structure, existing above 1394°C.
  • The maximum solubility of carbon in δ-ferrite is 0.09 wt% at 1493°C.

Reactions

• Eutectic: L ⟶ γ + $Fe_3C$ upon cooling, occurring at 1147°C and 4.30 wt% C.
• Eutectoid: γ ⟶ α + $Fe_3C$ upon cooling, occurring at 727°C and 0.76 wt% C.
• Peritectic: δ + L ⟶ γ upon cooling, occurring at 1493°C and 0.16 wt% C.

Microstructures

• Pearlite: A eutectoid mixture of α-ferrite and cementite with a lamellar structure.
• Hypoeutectoid steel: Steel with less than 0.76 wt% carbon, consisting of primary α-ferrite and pearlite.
• Hypereutectoid steel: Steel with more than 0.76 wt% carbon, consisting of primary cementite and pearlite.

Isothermal Transformation Diagrams

• These diagrams predict the microstructure of steel after heat treatment.
• They plot the time for phase transformation to begin and end at a constant temperature.

Example

• For eutectoid steel, the diagram shows austenite transforming to pearlite at a given temperature, with the nose of the curve around 550°C.
• Rapid cooling (quenching) results in hard, brittle martensite.
• Slow cooling results in soft, ductile coarse pearlite.