Phase Diagrams | Engineering Materials - Mechanical Engineering PDF Download

Phase

• Phase - a physically distinct, chemically homogeneous and mechanically separable region in a system at equilibrium.
• When more than one phase is present in a system, each phase has its own distinct properties and a definite boundary separating it from the others.

Gibbs' phase rule

F + P = C + 2

• F = number of degrees of freedom (intensive variables that can be changed independently, e.g., temperature, pressure, composition).
• P = number of phases present.
• C = number of components.

Note: The degree of freedom is zero at an invariant point such as a triple point.

Phase equilibrium

• Phase equilibrium is indicated when the physical and chemical properties of each phase remain constant with time under the given conditions.
• Phase equilibrium does not specify how long it takes to reach equilibrium; it only describes the condition when equilibrium has been attained.

Phase diagram (Equilibrium or Constitutional diagram)

• A phase diagram is a plot on a temperature-composition (and sometimes pressure) scale showing the stability regions of different phases of an alloy system under equilibrium conditions.
• Phase diagrams show relationships between temperature, composition and the amounts of phases present in an alloy under equilibrium.
• As temperature changes, various microstructures develop and transitions from one phase to another occur; these transitions can be predicted using phase diagrams.

Types of phase diagrams

1. Unary phase diagram (single component)

   Used for pure substances such as water, carbon (graphite, diamond) and pure metals. These are usually plotted on temperature-pressure axes and have limited practical application for alloy systems.

   Example: water, graphite, diamond, metallic carbon.

2. Binary phase diagram (two components)

   Binary diagrams are plotted on a temperature vs composition (percent of one component) scale and are the most useful for alloy systems.

   Type I: Binary systems with complete solubility in liquid and solid states (substitutional solid solutions)

   Such systems occur when the two components have similar crystal structures and their atomic radii differ by less than ≈8%. Most metals with similar structures form this type of diagram and give continuous solid solubility.

   Example: Cu-Ni system.

   

   Key features of a simple binary solid-solution diagram:

   • The locus where solidification starts on cooling is the liquidus (upper curved line).
   • The locus where solidification ends is the solidus (lower curved line).
   • Above the liquidus the alloy is single-phase liquid; below the solidus it is single-phase solid. Between liquidus and solidus a two-phase (mushy) region exists containing both liquid and solid.

Rules to determine phase compositions and amounts from binary diagrams

Rule 1: Chemical composition of phases (using a tie line)

At equilibrium, draw a horizontal isotherm (tie line) at the temperature of interest across the two-phase field. The intersection points of the tie line with the phase boundaries give the compositions of the two coexisting phases. A vertical line at the overall alloy composition locates the alloy on the diagram; projections to the phase-boundary compositions give the actual phase compositions.

Rule 2: Relative amount of each phase (Lever rule)

Using the same tie line, the relative amounts of the two phases are proportional to the lengths of the segments of the tie line measured from the overall composition point to the phase boundary on the opposite side. The fraction of a phase equals the length of the segment opposite to that phase divided by the total tie-line length.

Note: If only one intensive parameter (temperature) is changed for a binary system, the Gibbs phase rule reduces by 1 (because pressure is usually held constant), and the form used becomes F + P = C + 1 for constant pressure conditions.

Type II: Systems with complete solubility in liquid but partial solid solubility (Eutectic systems)

Partial solid solubility means one component dissolves in the other only up to a certain maximum concentration in the solid state. A binary eutectic system has three phases commonly encountered:

• α (solid solution richer in component A)
• β (solid solution richer in component B)
• L (liquid solution)

A eutectic point is an invariant point where the degree of freedom is zero; at this composition and temperature the liquid transforms isothermally into two solid phases.

1. α phase: Example description - rich in copper with silver as solute (FCC structure).
2. β phase: Rich in silver with copper as solute (also FCC in the example).
3. (α + β) mixture: Constitutes of lamellar or granular mixtures of the two solid solutions; solvus lines in the diagram demarcate the limits of solid solubility and the regions of single-phase α, single-phase β and the α+β two-phase field. For a Cu-Ag system, maximum solubility of Ag in Cu at about 779°C is ≈8%.

Different types of phase reactions in binary systems

1. Eutectoid reaction

   A solid phase (α) transforms isothermally into two other solid phases (β + γ). This is invariant (degree of freedom zero) at the eutectoid temperature and composition. Eutectoid reactions are analogous to eutectic reactions but occur entirely in the solid state.

   
2. Peritectic reaction

   On cooling, a solid and a liquid combine isothermally to form a new solid phase: solid1 + liquid ↔ solid2. Peritectic reactions commonly produce an intermediate solid phase and occur in systems with large melting-point differences.

   
3. Peritectoid reaction

   Two solid phases react isothermally to form a different solid phase: solid1 + solid2 ↔ solid3. This is the solid-solid analogue of the peritectic reaction.

   
4. Monotectic reaction

   A liquid transforms to a liquid of different composition plus a solid on cooling: liquid1 ↔ liquid2 + solid. Monotectic behaviour appears in some alloy systems.

   

Note: The eutectic temperature corresponds to the lowest melting point in the binary system for which a liquid coexists with two solids at that temperature.

Iron-Carbon (Fe-Fe₃C) phase diagram

1. The Fe-Fe₃C system is commonly used to describe steels and cast irons and is defined by five phases and four invariant reactions.

   Five phases:

   • α (ferrite): a BCC iron-based solid solution with small amounts of carbon in interstitial sites.
   • γ (austenite): an FCC iron-based solid solution (greater carbon solubility than α).
   • δ (delta ferrite): a high-temperature BCC iron solid solution.
   • Fe₃C (cementite): an iron carbide intermetallic compound.
   • Liquid: molten iron-carbon solution.
2. Four invariant reactions occur in the Fe-Fe₃C system: eutectic, eutectoid, monotectic and peritectic (locations and temperatures given below).
3. Pure iron shows two allotropic transformations with temperature (α ↔ γ ↔ δ); these are changes in crystal structure with heating.

4. Carbon is present in iron as an interstitial impurity and forms solid solutions with the iron phases. Carbon solubility is smallest in α-ferrite (≈0.02 wt% at 723°C).

Fe-Fe₃C invariant reactions (important points):

• Peritectic at ≈1495°C and 0.16 wt% C: δ-ferrite + L ↔ γ (austenite).
• Monotectic at ≈1495°C and 0.51 wt% C: L ↔ L + γ (austenite).
• Eutectic at ≈1147°C and 4.3 wt% C: L ↔ γ + Fe₃C (cementite). The γ + Fe₃C mixture at this composition is called ledeburite.
• Eutectoid at ≈723°C and 0.8 wt% C: γ ↔ α + Fe₃C (this microstructure of alternating α and Fe₃C is known as pearlite).

Microstructures of various phase of steel.

Time-temperature-transformation (TTT) diagrams

1. A TTT diagram (isothermal transformation diagram) shows how the phases in a steel change with time when the alloy is rapidly cooled to and held at a constant temperature. Temperature is plotted along the vertical linear axis and time on the horizontal logarithmic axis.
2. TTT diagrams give the times for the start and completion of transformations at a given constant temperature. These curves are useful to determine heat-treatment schedules such as quenching, annealing and isothermal transformation treatments.
Temperature-Time diagram
3. The characteristic S-shaped curves are sometimes called the C-curve or S-curve; the outer curve marks the start of transformation and the inner curve marks completion. The point where the start-time is minimum is called the nose of the curve. A continuous cooling curve that just touches the nose defines the critical cooling rate required to avoid transformation before reaching the martensite start temperature.
4. At transformation temperatures below the nose (for common steels around ≈550°C), austenite may transform to bainite rather than pearlite; this is the basis of the austempering process. Bainite is a mixture of α-ferrite and cementite, typically finer than pearlite.
Bainite formation

Heat treatment processes related to TTT curves

Martempering (stepped quenching)

• Martempering is carried out in two main stages: first the steel is quenched rapidly into a medium at a temperature slightly above the martensite start temperature and held until the temperature is uniform; then it is cooled further to room temperature in air or a second medium.
• This stepped quenching reduces thermal gradients and the risk of cracking while allowing the steel to transform to martensite in a more uniform manner.
• Typical practice: quench from the austenitising temperature into water or another medium to a temperature somewhat above the martensite start (e.g., ~240-300°C), hold until the part temperature is uniform, then transfer to air or oil to cool to ambient.

Austempering

• Austempering holds the alloy at a temperature below the nose of the TTT diagram but above the martensite start temperature, for a time long enough to allow austenite to transform isothermally to bainite.
• Austempering is performed in molten salt baths or alkaline media maintained typically between ≈150°C and 450°C depending on steel composition and desired bainite characteristics.
• This process produces bainitic microstructures that combine good strength and toughness with reduced distortion compared to direct quenching to martensite.