A binary phase diagram shows which phases are stable for a two-component alloy at different temperatures and compositions. Engineers use these diagrams to predict melting, solidification, microstructure, and processing temperatures. Reading the diagram correctly helps you choose casting temperatures, heat treatments, and alloy compositions.
The most common axes are temperature on the vertical axis and composition, often weight percent of component B, on the horizontal axis.
The liquidus line marks where the first solid begins to form during cooling, while the solidus line marks where the last liquid disappears. Between phase boundaries, two phases coexist, such as liquid plus alpha or alpha plus beta. In a two-phase region, a horizontal tie line gives the compositions of the phases, and the lever rule gives their relative amounts.
Eutectic points are special compositions and temperatures where one liquid transforms into two solid phases at the same time.
Understanding Engineering: Reading a Binary Phase Diagram
A phase diagram is an equilibrium map. It describes an alloy that has enough time for atoms to move by diffusion and arrange themselves at each temperature. This condition matters because real cooling is often faster than equilibrium cooling.
To use a diagram, first mark the alloy's overall composition and choose the temperature being studied. In a single phase field, that overall composition is the composition of the material everywhere. In a two phase field, the overall composition is no longer the composition of either phase.
The two phase compositions are found at the ends of the horizontal line through the chosen temperature. Reading those end points carefully is the central skill.
The lever rule gives amounts by mass, not the size of regions in a microscope image. Suppose an alloy contains forty percent component B. At a chosen temperature, the left phase contains twenty percent B and the right phase contains seventy percent B.
The left phase fraction is the distance from forty to seventy divided by the full distance from twenty to seventy. That is thirty divided by fifty, or sixty percent. The right phase makes up the remaining forty percent.
The phase whose composition lies farther from the overall composition has the larger amount. This can feel backwards at first, so it helps to imagine a balance beam. Longer distance on one side means more of the phase at the opposite end.
During slow cooling, the composition of the first solid is usually different from the composition of the liquid it formed from. The remaining liquid therefore becomes richer in one component. As temperature falls, both phase compositions shift along their boundary lines.
The amount of solid increases until the liquid is gone. This changing chemistry creates the final microstructure. Near a eutectic composition, the last liquid can form a fine mixture of two solids.
Away from that composition, larger primary crystals may form first, followed by a eutectic mixture between them. These structures affect hardness, strength, ductility, and resistance to cracking.
Real castings do not always match the ideal diagram exactly. Fast cooling can prevent diffusion inside solid grains. The center of a grain may then have a different composition from its edge.
This effect is called coring or microsegregation. Heat treatment can reduce it by allowing atoms to diffuse after solidification. Students should check the composition scale before making any calculation.
Weight percent and atomic percent give different positions on the horizontal axis. They should also identify whether a boundary is a true phase boundary, a solubility limit, or an invariant horizontal line.
Most classroom diagrams assume only two components, constant pressure, and equilibrium conditions. Those assumptions make the diagram useful, but they set limits on what it can predict in an industrial alloy.
Key Facts
- Liquidus line: above it the alloy is fully liquid, and crossing it during cooling starts solidification.
- Solidus line: below it the alloy is fully solid, and crossing it during cooling finishes solidification.
- Tie line: in a two-phase region, draw a horizontal line at the temperature of interest to find the compositions of each phase.
- Lever rule for phase fraction: fraction of left phase = (C_right - C0) / (C_right - C_left).
- Lever rule for phase fraction: fraction of right phase = (C0 - C_left) / (C_right - C_left).
- Eutectic reaction: L -> alpha + beta at the eutectic temperature and eutectic composition.
Vocabulary
- Binary phase diagram
- A graph that shows the stable phases of a two-component system as a function of temperature and composition.
- Liquidus
- The phase boundary above which the alloy is completely liquid and below which solid first appears during cooling.
- Solidus
- The phase boundary below which the alloy is completely solid and above which some liquid remains.
- Tie line
- A horizontal line drawn across a two-phase region to find the compositions of the phases at a chosen temperature.
- Eutectic point
- The point on a binary phase diagram where a liquid transforms into two solid phases at one fixed temperature and composition.
Common Mistakes to Avoid
- Reading phase composition from the overall alloy composition, which is wrong in a two-phase region because each phase has its own composition found at the ends of the tie line.
- Using the lever rule without drawing a tie line, which is wrong because the lever arm distances must be measured at one constant temperature.
- Confusing liquidus and solidus lines, which is wrong because the liquidus marks the start of solid formation and the solidus marks the end of liquid during cooling.
- Assuming the eutectic composition means the alloy is always two solid phases, which is wrong because above the eutectic temperature the same composition can still be liquid.
Practice Questions
- 1 An alloy has overall composition C0 = 40 wt% B at a temperature where the tie line endpoints are C_alpha = 20 wt% B and C_L = 60 wt% B. Calculate the mass fraction of alpha and liquid.
- 2 At a certain temperature, an alloy with C0 = 70 wt% B lies in the alpha plus beta region. The tie line endpoints are C_alpha = 30 wt% B and C_beta = 90 wt% B. Use the lever rule to find the fraction of beta.
- 3 Explain how the microstructure changes when a liquid alloy of eutectic composition cools slowly through the eutectic temperature, and identify the phases present just above and just below that temperature.