MMSC418 MATERIALS SCIENCE
Unit 9
Phase Diagrams
Lecturer: Mrs Annalene Olwagen
Email: aolwagen@cut.ac.za
Office: ETB009D
Textbooks
Prescribed textbook:
– Materials Science and Engineering: An Introduction. Seventh Ed. By
William D. Callister, Jr
Course Outline
Learning area (LA) activity
Unit 1: Classification of materials
Unit 2: Atomic structures
Unit 3: Lattice structures – arrangement of atoms in lattices
Unit 4: Lattice structures – defects and dislocations in lattices
Unit 5: Extraction technology and refinement of metals
Unit 5: Dislocations and strengthening mechanisms
Unit 6: Phase equilibrium diagrams and microstructures of metal alloys
Unit 7: Heat treatment of metal alloys
Unit 8: Polymers, ceramics and composites
Phase Diagrams
Plain carbon steel with 0.44
wt% C.
Proeutectoid ferrite.
Pearlite
Phase Diagrams
• Learning Objectives
1. (a) Schematically sketch simple isomorphous and eutectic phase diagrams.
(b) On these diagrams label the various phase regions.
(c) Label liquidus, solidus, and solvus lines.
2. Given a binary phase diagram, the composition of an alloy, its temperature,
and assuming that the alloy is at equilibrium, determine:
(a) what phase(s) is (are) present,
(b) the composition(s) of the phase(s), and
(c) the mass fraction(s) of the phase(s).
3. For some given binary phase diagram, do the following:
(a) locate the temperatures and compositions of all eutectic,
eutectoid,peritectic, and congruent phase transformations;
and
(b) write reactions for all these transformations for either heating or
cooling
Phase Diagrams
• Learning Objectives
4. Given the composition of an iron–carbon alloy containing between 0.022
wt% C and 2.14 wt% C, be able to
(a) specify whether the alloy is hypoeutectoid or hypereutectoid,
(b) name the proeutectoid phase,
(c) compute the mass fractions of proeutectoid phase and pearlite, and
(d) make a schematic diagram of the microstructure at a temperature just
below the
eutectoid.
Phase Diagrams
Importance of Phase
Diagrams in Alloy Systems
• Strong correlation between microstructure and
mechanical properties.
• Microstructure development is influenced by the alloy's
phase diagram.
• Phase diagrams provide insights into:
- Melting behavior
- Casting processes
- Crystallization
- Other phase-related phenomena
Phase Diagrams
Topics Covered in This
Chapter
• Terminology
Definitions related to phase diagrams and phase transformations.
• P–T Diagrams for Pure Materials
Understanding phase behaviour under varying pressures and
temperatures.
• Phase Diagram Interpretation
How to read and analyse phase diagrams.
• Binary Phase Diagrams
Focus on common and simple systems, including the iron–carbon
diagram.
• Equilibrium Microstructure Development
How microstructures evolve during cooling under equilibrium
conditions.
Definitions and Basic
Concepts
• Components: Defined as pure metals and/or compounds in an alloy.
Example:Copper–zinc brass → Components: Cu and Zn
• Solvent: The element or compound that is present in the greatest
amount; also called host atoms.
• Solute: is used to denote an element or compound present in a minor
concentration.
• System:
- A specific material body (e.g., a ladle of molten steel).
- A range of possible alloys with the same components
(e.g., iron–carbon system).
• Solid Solution: Composed of two or more atom types.
Solute atoms occupy substitutional or interstitial positions.
The crystal structure of the solvent is preserved.
Solubility limit
• Maximum concentration of solute atoms that can dissolve in a solvent to
form a solid solution at a given temperature.
• Adding solute beyond this limit results in the formation of a second phase
(new solid solution or compound)
• Example: Sugar–Water System
- Sugar dissolves in water to form a syrup.
- As more sugar is added:
– The solution becomes more concentrated.
– Eventually reaches the solubility limit (saturation point).
• Beyond this point:
– Excess sugar remains undissolved and forms a separate solid phase.
– System consists of two phases: syrup + solid sugar.
• This solubility limit of sugar in water depends on the temperature of the
water and may be represented in graphical form
Solubility limit
Solubility limit
• Temperature–Composition Diagram:
• Y-axis: Temperature
• X-axis: Composition (wt% sugar, increasing left to right)
• Solubility limit shown as a nearly vertical line.
• Left of line: Single-phase syrup solution.
• Right of line: Syrup + solid sugar coexist
• Solubility limit increases with temperature.
• Example: At a certain temperature, maximum solubility =
65 wt% sugar.
Phases
• Phase: Defined as a homogeneous portion of a system that has uniform
physical and chemical characteristics.
• Pure substances and solutions (solid, liquid, or gas) are each considered
single phases
• Example:
- Sugar–water syrup: One liquid solution phase.
- Solid sugar: A separate solid phase.
These phases differ in:
• Physical state (liquid vs solid)
• Chemical composition (solution vs pure substance)
• When two phases are present:
• They are separated by a distinct boundary.
• There is an abrupt change in physical and/or chemical properties
across this boundary.
• Only one type of difference (physical or chemical) is required for
phases to be distinct.
Phases
Examples of Coexisting Phases
• Ice and water:
• Same chemical composition (H₂O)
• Different physical states → Two phases
• Polymorphs (e.g., FCC vs BCC forms of a metal):
• Same composition
• Different crystal structures and properties → Distinct phases
• Single-phase system = Homogeneous
• Multi-phase system = Heterogeneous
• Most metallic alloys, ceramics, polymers, and composites are
heterogeneous.
• Multiphase systems often offer superior property combinations compared
to individual phases
Microstructure
• Mechanical behavior often depends on a material’s microstructure.
• Microstructure is observable via:
• Optical microscopes
• Electron microscopes
(see Sections 4.9 and 4.10)
• Microstructure in Metal Alloys
• Defined by:
• Number of phases present
• Proportions of each phase
• Distribution and arrangement of phases
• Influenced by:
• Alloying elements and their concentrations
• Heat treatment:
• Heating temperature
• Time at temperature
• Cooling rate
Microstructure
Specimen Preparation for Microscopy
• Involves polishing and etching.
• Different phases are distinguishable by contrast:
• E.g., light and dark regions in a two-phase alloy
• Single-phase alloys appear uniform, with grain boundaries
sometimes visible
Phase Equilibria
• Equilibrium: Occurs when a system’s free energy is at a
minimum under given conditions (T, P, composition).
• Free energy (G) is influenced by:
- Internal energy of the system
- Atomic or molecular disorder (entropy)
System at Equilibrium
- Stable: Characteristics (phases, compositions) do not change
over time.
- A disturbance (change in T, P, or composition) increases free
energy.
- The system may spontaneously shift to a new state of lower
free energy
Phase Equilibria
Phase Equilibrium
• Describes equilibrium in systems with multiple phases.
• Phase characteristics (type, composition, amount) remain constant over time.
• Example: Sugar–Water System
- At equilibrium and 20 °C → 65 wt% sugar syrup + solid sugar.
- Raise T to 100 °C → solubility increases → more sugar dissolves until new
equilibrium is reached at 80 wt%
Phase Equilibrium in Solids
• Important in metallurgy: involves solid phases only.
• Microstructure at equilibrium includes:
• Phases present
• Their compositions
• Relative amounts and distribution
Phase Equilibria
Metastable (Nonequilibrium) States
• Equilibrium not always reached, especially in solids — may be too slow.
• A metastable state persists for a long time with minimal change.
• Practical importance: Many alloy strengths depend on metastable
microstructures.
• E.g., certain steels and aluminum alloys (see Sections 10.5 & 11.9)
Takeaway
Understanding both:
- Equilibrium structures, and
- Rate of transformation to equilibrium (covered in Ch. 10 and 11.9)
is crucial for materials design and heat treatment strategies.
One-component (or unary)
phase diagrams
Phase Diagrams: Purpose & Parameters
• Phase diagrams (aka equilibrium diagrams) show phase
stability as functions of:
• Temperature
• Pressure
• Composition
• Most basic: One-component (unary) phase diagram
• Constant composition (pure substance)
• Variables: Temperature vs. Pressure
One-component (or unary)
phase diagrams
Unary Phase Diagram – Example: Water (H₂O)
• Axes:
• Vertical: Pressure (logarithmic scale)
• Horizontal: Temperature (°C)
• Three major phase regions:
• Solid (ice)
• Liquid (water)
• Vapor (steam)
One-component (or unary)
phase diagrams
One-component (or unary)
phase diagrams
Phase Boundaries & Transitions
• Phase boundaries: Lines separating two-phase equilibria:
• a–O: Solid ↔ Vapor (Sublimation / Deposition)
• b–O: Solid ↔ Liquid (Melting / Freezing)
• c–O: Liquid ↔ Vapor (Boiling / Condensation)
• Crossing a boundary = phase transformation
Important Points
• Point 2 (on b–O curve at 1 atm):
• Melting point of ice: 0 °C
• Point 3 (on c–O curve at 1 atm):
• Boiling point of water: 100 °C
One-component (or unary)
phase diagrams
Triple Point
• Point O:
• All three phases coexist in equilibrium
• For water:
• T = 273.16 K (0.01 °C)
• P = 0.00603 atm
• Also called an invariant point (fixed T and P)
Additional Notes
• Other unary systems may have:
• Multiple solid phases (allotropes)
→ e.g., graphite ↔ diamond in carbon
• Additional triple points for solid-solid equilibria
Binary Phase Diagrams
• Binary system: Two-component alloy system
• Common phase diagram type:
- Temperature vs. Composition
- Pressure held constant (usually 1 atm)
Why Binary?
• Simplifies analysis
• Even though most alloys have >2 components,
- Binary diagrams illustrate key phase transformation principles
- Serve as a foundation for understanding more complex systems
Binary Phase Diagrams
What They Show
• Relationships between:
• Temperature
• Composition
• Equilibrium phases present
• Predict:
• Which phases form
• When they form
• How much of each phase exists
Importance of Binary Diagrams
• Essential for understanding:
• Phase transformations (e.g., liquid → solid + solid)
• Microstructure evolution during cooling or heating
• Aid in designing alloys with:
• Desired mechanical properties
• Targeted phase compositions
Binary Phase Diagrams
• Phase changes during cooling → influence microstructure
• Microstructures may be:
- Equilibrium (slow cooling)
- Nonequilibrium (rapid cooling or special treatments)
Binary isomorphous systems
• What is an Isomorphous System?
• A binary alloy system with complete solubility in:
– The liquid state
– The solid state (single-phase solid solution)
• Cu–Ni is a classic example
- X-axis: Composition (0–100 wt% Ni)
- Y-axis: Temperature (°C)
- Three phase regions:
• Liquid (L): Fully molten solution
• Solid (α): Substitutional solid solution (FCC)
• L + α: Two-phase region (liquid + solid in equilibrium)
Binary isomorphous systems
Binary isomorphous systems
Key Lines
• Liquidus line: Above = all liquid
• Solidus line: Below = all solid
• Between = both phases coexist
Why Cu–Ni Is Isomorphous
• Same crystal structure (FCC)
• Similar atomic radii
• Close electronegativities
• Similar valences
• Complete liquid and solid solubility
Example: 50 wt% Ni – 50 wt% Cu
• Melting starts ≈ 1320°C
• Melting ends ≈ 1380°C
• Between these: L + α region (partial melt)
Interpretation of phase
diagrams
• Given a composition & temperature at equilibrium, you can
determine:
1. Phases present
2. Phase compositions
3. Phase fractions (amounts)
Determining Phases Present
• Locate point on the phase diagram (composition vs.
temperature)
• Check the phase region it falls into:
• One-phase region: e.g., α (solid) or L (liquid)
• Two-phase region: α + L
Interpretation of phase
diagrams
Determining Phase Compositions
• Use a tie line (horizontal line at the given temperature):
• Left intersection = composition of solid (α) phase
• Right intersection = composition of liquid (L) phase
• Example (Point B, 35 wt% Ni at 1250°C):
• Cₐ (solid) = 42.5 wt% Ni
• CL (liquid) = 31.5 wt% Ni
Interpretation of phase
diagrams
Determining Phase Amounts: The Lever Rule
• Use lever rule only in two-phase regions!
Lever Rule Formulas:
• Liquid fraction:
• Solid (α) fraction:
Property
Single-Phase
Two-Phase
Phases
Read directly
Read from region
Composition
Same as alloy
Use tie line ends
Amounts
100% one phase
Use lever rule
• https://youtu.be/_UGVDKlquxo