HomeMaterials ScienceBinary Alloy Phase Diagram — Eutectic & Solidification

🧪 Binary Alloy Phase Diagram — Eutectic & Solidification

Explore the equilibrium phase diagram of a two-component alloy: liquidus, solidus, eutectic point, and two-phase regions. Drag the cursor to read phases by the lever rule.

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About Binary Alloy Phase Diagram

A binary alloy phase diagram maps the equilibrium states of a two-component metallic system as a function of composition (x-axis, mol% of component B) and temperature (y-axis). The diagram displays three key boundaries: the liquidus line above which the alloy is entirely molten, the solidus line below which it is entirely solid, and the eutectic isotherm — the unique temperature at which one special composition melts and freezes at a single fixed temperature lower than either pure component. The eutectic point exists because mixing two metals lowers the Gibbs free energy of the liquid phase, depressing the freezing point; the classic example is lead-tin solder (63/37 wt%, 183 °C), used in electronics for over a century.

Click or drag anywhere on the canvas to move the cursor and read off the phase at that (composition, temperature) point. In the two-phase mushy zone the lever rule is drawn automatically: two coloured markers show the liquidus composition x_L and solidus composition x_S, and the HUD displays the fraction of liquid and solid at a glance. Adjust the melting points of both pure components, the eutectic composition, and the eutectic depression with the HUD sliders to explore a wide range of real and hypothetical alloy systems.

Frequently Asked Questions

What is the lever rule and how is it applied?

The lever rule is a mass-balance technique for calculating the fraction of each phase in a two-phase region. If the overall composition is x₀, the liquidus composition at the current temperature is x_L, and the solidus composition is x_S, then the fraction of liquid = (x₀ − x_S)/(x_L − x_S) and the fraction of solid = 1 − fraction liquid. The result is exact at thermodynamic equilibrium and follows directly from conservation of mass.

Why is the eutectic temperature the lowest melting point in the system?

Adding a second component to a pure metal generally lowers the chemical potential of the liquid phase more than that of the solid, depressing the freezing point in both directions. The eutectic point is where the liquidus curves from the two pure components intersect, forming the absolute minimum melting temperature for any composition in that binary system — a property exploited in soldering, brazing, and casting alloys.

What is the Gibbs phase rule and what does it say about the eutectic point?

The Gibbs phase rule states F = C − P + 2, where F is degrees of freedom, C is the number of components, and P is the number of phases. For a binary alloy (C = 2) at constant pressure: in a single-phase region P = 1 so F = 2 (T and x are both free); in the two-phase mushy zone P = 2 so F = 1 (fixing T fixes both x_L and x_S); at the eutectic point P = 3 so F = 0 — the system is invariant, meaning T and both compositions are completely fixed.

What happens during solidification of a hypoeutectic alloy?

A hypoeutectic alloy (composition to the left of the eutectic) first crosses the liquidus on cooling, nucleating primary alpha-phase crystals. As temperature falls, the remaining liquid becomes progressively richer in component B, tracking the liquidus curve toward the eutectic composition. When the temperature reaches the eutectic isotherm, the remaining liquid — now at the eutectic composition — solidifies simultaneously into a fine lamellar mixture of alpha and beta phases.

What are some real binary alloy systems with eutectic diagrams?

Classic examples include lead-tin (Pb-Sn, eutectic at 61.9 wt% Sn, 183 °C — the backbone of traditional electronics solder), silver-copper (Ag-Cu, eutectic at 28.1 wt% Cu, 779 °C — used in silver brazing filler), and bismuth-tin (Bi-Sn, eutectic at 57 wt% Bi, 139 °C — a low-temperature solder used in thermosensitive applications). Modern lead-free SAC305 solder (Sn-Ag-Cu) is a ternary near-eutectic.

How does cooling rate affect the microstructure of a eutectic alloy?

Slow equilibrium cooling gives atoms time to diffuse, producing coarse lamellar microstructure with alternating wide plates of alpha and beta. Rapid quenching suppresses diffusion, producing fine lamellar or even amorphous (glassy) structures. Very fast quenching can create supersaturated solid solutions — the basis of rapidly solidified aluminium alloys used in aircraft, where the fine microstructure dramatically improves strength and corrosion resistance.

What is a hypereutectic alloy?

A hypereutectic alloy has a composition to the right of the eutectic point (more of component B). On cooling it first precipitates primary beta-phase crystals while the liquid moves toward the eutectic composition. Both hypoeutectic and hypereutectic alloys ultimately produce eutectic microstructure in the remaining liquid — the difference is only in which primary phase precipitates first and in what proportion it appears in the final microstructure.

What is the isomorphous phase diagram and how does it differ from the eutectic?

In an isomorphous system (such as copper-nickel) the two components are completely miscible in both liquid and solid phases, so there is no two-solid region and no eutectic point — only a lens-shaped two-phase region between the liquidus and solidus curves. The eutectic type shown here has limited solid solubility; the two components can only partially dissolve in each other, leading to the characteristic V-shaped liquidus and the eutectic reaction.

Can the simulation model non-symmetric eutectic systems?

Yes. Move the eutectic composition slider (x_E) away from 50% to create an asymmetric system where the eutectic lies closer to one pure component. This mimics most real eutectic systems: the Pb-Sn eutectic at 61.9 wt% Sn is strongly asymmetric, as is the Al-Si eutectic at 12.6 wt% Si that is the basis of cast aluminium alloys used in automotive engine blocks.

What is the solidification path shown in the animation?

The orange dashed line traces how the state of a single alloy (at a composition you can set by clicking) evolves as it cools from above the liquidus. In the liquid region the path descends vertically. On crossing the liquidus, the composition of the remaining liquid follows the liquidus curve (moving toward the eutectic), while the overall composition stays fixed — the path therefore appears to bend. At the eutectic isotherm the remaining liquid solidifies completely at constant temperature.

⚙ Under the hood

Drag the cursor across a two-component alloy phase diagram to read liquidus, solidus and phase fractions by the lever rule.

phase diagrameutecticbinary alloysolidificationCanvas 2D

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install

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