MATS1192 Chap.5 Phase Diagrams and Transformations
Phase Diagrams and Transformations
A binary phase diagram maps equilibrium phase constitution as functions of composition and temperature. Start by locating the state point rather than searching for a formula. A single-phase field gives one stable phase whose composition matches the overall alloy composition.
A two-phase field identifies two stable phases, but their individual compositions must be read at the ends of a horizontal tie line.
Phase composition and phase amount answer different questions. The tie-line endpoints give the composition of each phase. The lever rule uses the segment opposite a phase to calculate that phase fraction.
A sound calculation confirms that the fractions sum to one and that their composition-weighted average returns the overall composition. Those checks catch reversed arms and misread endpoints.
Cooling introduces a transformation path. At a phase boundary, a new phase nucleates and then grows.
Redistribution of solute requires diffusion, so time and temperature determine how closely the developing microstructure approaches equilibrium. The diagram supplies the equilibrium destination, not the transformation rate or final grain morphology.
At a eutectic reaction, one liquid transforms into two solid phases at a particular composition and temperature.
An off-eutectic alloy first develops a primary solid before the remaining liquid reaches the eutectic condition. A complete cooling explanation therefore names the primary phase, follows the liquid composition, identifies the eutectic transformation and describes the final constituents.
Rapid cooling can suppress the redistribution needed for equilibrium.
It may retain a supersaturated phase or preserve composition gradients. This is why a strong materials answer combines diagram reading with kinetics and ends by describing the microstructure that carries the property.
What this chapter covers
- 01
Components, phases and state variables
- 02
Single-phase and two-phase fields
- 03
Tie lines and equilibrium phase compositions
- 04
Lever-rule calculation of phase fractions
- 05
Nucleation, growth and solute redistribution
- 06
Eutectic and off-eutectic cooling paths
- 07
Non-equilibrium structures produced by rapid cooling
Worked example · free
Read a tie line and apply the lever rule
- +1The tie-line length is 55 minus 15 = 40 composition points.
- +1The alpha fraction uses the opposite liquid-side arm: (55 minus 35) divided by 40 = 20 divided by 40 = 0.50.
- +1The liquid fraction uses the opposite alpha-side arm: (35 minus 15) divided by 40 = 20 divided by 40 = 0.50.
- +1The fractions sum to 1.00, and 0.50 times 15 plus 0.50 times 55 = 35 wt% B, so the composition balance closes.
Key terms
- Phase
- A physically and chemically uniform region with a distinct structure or composition.
- Phase field
- A diagram region in which the labelled equilibrium phase constitution is stable.
- Tie line
- A horizontal line used to obtain phase compositions inside a two-phase field.
- Lever rule
- A composition balance that converts opposite tie-line lengths into phase fractions.
- Eutectic reaction
- An invariant transformation in which one liquid forms two solid phases.
- Nucleation
- Formation of a stable small region of a new phase.
- Supersaturated phase
- A phase retaining more solute than its equilibrium solubility permits.
Phase Diagrams and Transformations FAQ
What does a tie-line endpoint represent?
It gives the equilibrium composition of the phase at that boundary and temperature. It is not the fraction of that phase and need not equal the overall composition of the alloy.
Why does each phase use the opposite lever arm?
The relation follows from conservation of composition. Moving the overall composition toward one endpoint increases that phase amount, which makes the distance to the opposite endpoint the appropriate numerator.
How can I check a lever-rule answer?
Both fractions must lie between zero and one and add to one. Their weighted phase compositions must also reproduce the stated overall composition. Any failed check requires the setup to be revisited.
Does the equilibrium diagram show transformation speed?
No. It identifies stable states under equilibrium conditions. Nucleation barriers, diffusion distance, holding time and cooling rate control how quickly phases form and what morphology develops.
What changes under rapid cooling?
Rapid cooling reduces the time available for long-range diffusion. The material may retain supersaturation, composition gradients or another non-equilibrium structure instead of reaching the diagram's predicted equilibrium constitution.
How should an off-eutectic cooling path be described?
Name the primary phase that appears first, track the changing liquid composition toward the eutectic, state the eutectic transformation, and identify the final primary plus eutectic microstructural constituents.
Exam move
Use one fixed reading order for every diagram. Mark composition and temperature, identify the field, name the stable phases, draw the horizontal tie line, read phase compositions and only then calculate amounts. Label each symbol so overall composition cannot be confused with an endpoint. Test every result with fraction and composition balances.
Rehearse cooling paths separately from static calculations: say what nucleates, what grows, which element must diffuse and what the final constituents look like. When cooling is rapid, contrast the equilibrium prediction with the kinetically plausible retained state. Conclude with phase type, fraction, size, shape and distribution because those microstructural features connect processing to properties.
Practise with unlabeled generic diagrams before named alloy systems so the method does not depend on memory. Draw the vertical composition path and horizontal tie line in different colours, then annotate every endpoint with both phase name and composition units. After applying the opposite arms, rebuild the overall composition from the calculated fractions.
If that weighted value misses the starting composition, stop and correct the arms before interpreting the structure. For cooling narratives, mark each boundary crossing and write an event beside it. Finally compare a slow route with a quench at the same overall composition, identifying exactly which diffusion-dependent redistribution is curtailed and which non-equilibrium feature may remain.
