Multiphase Structure

Phase

Definition: A phase is a region of a material that is chemically uniform, physically distinct, and mechanically separable. Phases may differ by crystal structure (allotropy), composition (solid solution vs. intermetallic), or state (solid, liquid, gas).

Characteristics

• Homogeneity: Uniform composition and structure within the phase.
• Interfaces: Phases meet at boundaries whose energy affects nucleation and microstructural evolution.
• Stability: At given temperature, pressure, and composition, the stable phases minimize the system’s Gibbs free energy.

Examples

• α-ferrite (BCC Fe) and γ-austenite (FCC Fe) in steels.
• α (HCP) and β (BCC) phases in titanium alloys.
• Matrix + precipitate phases (e.g., Al–Cu: θ′/θ in Al matrix).

Solid Solution

Solid solutions are single solid phases containing more than one chemical species. They provide a route to tune properties through composition while retaining a single-phase microstructure.

Types

• Substitutional: Solute atoms replace solvent atoms on lattice sites (e.g., Cu–Ni). Solubility enhanced when atomic size, valence, electronegativity, and crystal structure are similar (Hume–Rothery rules).
• Interstitial: Small solute atoms occupy interstitial sites (e.g., C in BCC Fe). Strong lattice distortion yields solid-solution strengthening.

Effects on properties

• Strengthening: Lattice strain fields around solute impede dislocation motion.
• Diffusion and phase stability: Composition shifts phase boundaries; alters transformation temperatures and kinetics.
• Electrical/thermal: Solute scattering reduces conductivity; useful in thermoelectrics.

Solvus and miscibility

• Solvus line: Boundary separating single-phase solid solution from two-phase region; solubility typically increases with temperature.
• Limited miscibility: If size/chemical mismatch is large, phase separation or intermetallic formation occurs.

Gibbs Free Energy

Gibbs free energy (G) determines phase stability at constant temperature and pressure. The stable state minimizes total G. Composition-dependent curves (G–x) and temperature dependence (G–T) rationalize solution behavior, phase separation, and invariant reactions.

Key relations

• Definition: G = H − T·S (enthalpy–entropy balance). Phases compete via enthalpy (bonding) and entropy (mixing, disorder).
• Chemical potential: μ_i = ∂G/∂n_i at constant T, P, n_j≠i; equality of μ across phases determines equilibrium tie lines.
• Common tangent: In binary G–x plots, coexisting phases lie at compositions where a common tangent touches both free-energy curves.

Driving forces

• Nucleation: ΔG_v (volume free-energy change) competes with interfacial energy γ; critical radius r* balances these terms.
• Growth and coarsening: Lowering total interfacial area (Ostwald ripening) reduces G over time in multiphase systems.

Phase Diagrams

Phase diagrams map the equilibrium phases as functions of temperature, pressure, and composition. They are essential for predicting microstructures and designing heat treatments and alloy compositions.

Binary isomorphous system (complete solid solubility)

• Features: Single liquidus/solidus separating liquid (L), solid solution (α), and two-phase (α + L) fields.
• Solidification path: As temperature falls, L → (α + L) → α.

Binary eutectic system (limited solid solubility)

• Features: Two solid solutions (α, β) and a eutectic reaction L → α + β at eutectic temperature and composition.
• Solvus lines: Boundaries for α and β solubility limits.

Reading phase diagrams

• Tie lines: At fixed T, a horizontal line intersects phase fields; compositions of coexisting phases are read at intersections.
• Lever rule: Phase fractions from segment lengths on the tie line: f_α = (x_β − x₀)/(x_β − x_α) and f_β = (x₀ − x_α)/(x_β − x_α).
• Continuous cooling: Actual process paths may deviate from equilibrium; CCT diagrams complement equilibrium maps.

Engineering use

• Alloy design (selecting compositions to enable precipitation hardening or avoid brittle phases).
• Heat treatment schedules (solutionizing, aging, normalization).
• Welding and casting (avoiding hot cracking, controlling segregation).

Eutectic Microstructure

A eutectic is an invariant reaction in which one liquid transforms into two solid phases simultaneously at a specific composition and temperature, producing a fine-scale, cooperative microstructure.

Reaction

• Generic form: L → α + β at T_eut, x_eut.
• Microconstituent: Lamellar or rod-like α/β arrangement; spacing depends on growth rate and undercooling.

Formation and scale

• Coupled growth: α and β grow side-by-side from liquid, sharing a common front to maintain local equilibrium.
• Spacing (λ): Finer spacing at higher undercooling or faster solidification; impacts strength, toughness, and thermal properties.

Examples

• Al–Si casting alloys (soft Al matrix with hard Si particles for wear resistance).
• Pb–Sn solder (low melting eutectic for electronics).
• Fe–C ledeburite (in cast irons, with subsequent transformations on cooling).

Invariant Reactions

Invariant reactions occur at a fixed temperature and composition where the number of phases and thermodynamic degrees of freedom satisfy the phase rule (F = 0 at constant pressure). In binary systems at 1 atm, typical invariant reactions include:

Common types

• Eutectic: L → α + β (on cooling).
• Peritectic: L + α → β (a liquid reacts with a solid to form a different solid).
• Monotectic: L₁ → L₂ + α (liquid phase separation plus solid formation).
• Eutectoid: α → β + γ (all solid, e.g., austenite → ferrite + cementite).
• Peritectoid: α + β → γ (two solids react to form a third solid).

Thermodynamic view

• G–x construction: Coexistence set by a common tangent touching free-energy curves of all participating phases simultaneously at the invariant point.
• Kinetics: Diffusion and interfacial energies govern lamellar spacing, colony size, and final morphology.

Processing implications

• Sharp transformation temperatures enable precise microstructural control if cooling rates are managed.
• Risk of segregation or coarse morphologies if solidification is slow or thermal gradients are large.

Engineering of Multiphase Structures

Property optimization often relies on tailoring phase fractions, distributions, and length scales.

Strategies

• Solid-solution strengthening: Choose solutes that maximize lattice distortion without forming brittle phases.
• Precipitation hardening: Solutionize, quench, and age to form fine, coherent precipitates that impede dislocations.
• Controlled solidification: Manage cooling to refine eutectic spacing, suppress segregation, and reduce porosity.
• Thermomechanical processing: Combine deformation and heat treatment to refine grains and precipitate distributions.

Trade-offs

• Strength vs. toughness: Finer second phases increase strength but may reduce fracture toughness if interfacial debonding occurs.
• High-temperature stability: Coarsening of precipitates reduces strength; select low-coarsening-rate chemistries.

Examples and Case Studies

• Al–Cu (2xxx series): θ″/θ′ precipitates in Al matrix; aging sequence tailors yield strength.
• Ni-based superalloys: γ (FCC matrix) + γ′ (L1₂ precipitates) for high-temperature creep resistance.
• Steels: Ferrite–pearlite balance set by composition and cooling; bainite/martensite via TTT/CCT control.
• Cast irons: Eutectic solidification to ledeburite; graphite morphology (flake, nodular) controlled by inoculation and chemistry.

Glossary

• Phase: Homogeneous portion of a system with uniform structure and composition.
• Solid solution: Single-phase solid containing multiple species (substitutional or interstitial).
• Gibbs free energy (G): Thermodynamic potential minimized at equilibrium (G = H − T·S).
• Solvus: Boundary in a phase diagram separating single-phase solid solution from two-phase region.
• Tie line: Isothermal line in two-phase region used to determine coexisting phase compositions.
• Lever rule: Graphical method to compute phase fractions in two-phase fields.
• Eutectic: Invariant reaction where liquid transforms to two solids at a fixed composition and temperature.
• Peritectic: Invariant reaction where liquid and one solid form a different solid.
• Eutectoid: Solid-state invariant reaction producing two solids from one solid.