Home▸Materials Science▸Binary Alloy Phase Diagram: Lever Rule & Cooling Curve (2D)

Binary Alloy Phase Diagram: Lever Rule & Cooling Curve (2D)

2D companion to the 3D binary eutectic phase diagram: the same liquidus/solidus/lever-rule physics on a Canvas2D chart. Drag composition and temperature across four real alloy systems, or switch to a live cooling-curve view that arrests at the eutectic temperature.

Materials Science2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

Details

CategoryMaterials Science

RenderingCanvas 2D

DifficultyModerate

Target FPS60

ControlsButtons switch between four real alloy systems (Cu-Ag, Pb-Sn, Al-Cu, Bi-Sn); sliders (or a direct drag on the diagram) set composition and temperature; a checkbox toggles the lever-rule tie line; and a view toggle switches between the static phase diagram and an animated cooling curve.

phase diagrambinary alloyeutecticliquidussoliduslever rulecooling curvesolidification

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This 2D companion renders the exact same binary-eutectic thermodynamics as the 3D version — liquidus, eutectic solidus, both solvus curves and the lever rule — on a plain Canvas2D chart, so the physics reads cleanly against fixed axes instead of an orthographic WebGL scene. Drag the state point directly on the diagram (or use the composition and temperature sliders) to watch the phase readout and lever-rule tie line update live across four real alloy systems, or switch to the cooling-curve view to see the same composition freeze from the melt, slow through the mushy zone as latent heat is released, and hold isothermal at the eutectic temperature for a duration set by how much liquid remains — the classic thermal-arrest signature used to read eutectic points from real cooling-curve data.

⚙ Under the hood

2D binary eutectic phase diagram on Canvas2D: draggable composition/temperature state point, live lever-rule tie line across four real alloy systems, and an animated cooling curve with a physically motivated eutectic thermal-arrest plateau.

phase diagrambinary alloyeutecticliquidussoliduslever rulecooling curvesolidification

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install

What does the lever-rule tie line show?

Inside a two-phase field (α+L, β+L or α+β), the tie line connects the composition of each phase present at that temperature. The overall composition point divides the tie line into two segments whose lengths give the mass fraction of each phase — the fraction of liquid equals the distance from the state point to the solid-side boundary, divided by the total tie-line length.

Why does the cooling curve go flat at the eutectic temperature?

At the eutectic composition and temperature, liquid transforms into two solid phases simultaneously at a single, fixed temperature (an invariant reaction). While that reaction is in progress, the latent heat it releases exactly balances the heat being extracted, so the temperature holds constant — the plateau — until all the remaining liquid has solidified; only then does the temperature resume falling.