Binary Alloy Phase Diagram & Solidification Simulator

The core principle is conservation of mass. For an alloy of overall composition $C_0$ that has separated into a solid of composition $C_S$ and a liquid of composition $C_L$, the total amount of component B must be conserved. This leads to the lever rule.

$f_s$: Mass fraction of solid phase.
$C_0$: Overall composition of the alloy (set by the slider).
$C_L$: Composition of the liquid phase (read from the liquidus line).
$C_S$: Composition of the solid phase (read from the solidus line).

The lever rule is only valid under the assumption of equilibrium solidification, meaning diffusion in both solid and liquid is infinitely fast. This ensures the phases maintain uniform compositions ($C_S$ and $C_L$) as defined by the phase boundaries at each temperature.

This simple sum rule states that the mass fractions of all phases must add to one. Combined with the lever rule, it allows you to also solve for the liquid fraction $f_L$.

Casting & Foundry Engineering: Predicting how much solid forms at a given temperature is crucial for designing casting processes. For instance, using the Sn-Pb diagram helps control the solidification of solder to avoid defects like shrinkage pores, which form in the last liquid to freeze.

Alloy Design & Heat Treatment: The Fe-C (steel) phase diagram is the foundation of metallurgy. Engineers use it to design heat treatments like annealing or quenching. By understanding the phases present at different temperatures and carbon contents, they can tailor a steel's strength, hardness, and toughness.

Microstructure Prediction: The lever rule gives the phase fractions, but the assumption of equilibrium solidification often leads to a uniform microstructure. In real, non-equilibrium cooling (like in welding), different microstructures form, but the equilibrium diagram provides the essential starting point for analysis.

Materials Selection: When choosing a corrosion-resistant alloy like Cu-Ni for marine applications, the phase diagram ensures the selected composition will be a single, uniform solid solution at operating temperatures, preventing the formation of weak or corrosive secondary phases.

First, understand that this simulator deals with an equilibrium state. The composition and amount of solid and liquid phases calculated by the lever rule describe an ideal case of "infinitely slow cooling." In actual casting or welding, the cooling rate is faster, so atomic diffusion within the solid cannot keep up, leading to non-equilibrium solidification that differs from the calculation. For example, rapidly cooling a Sn-Pb alloy results in a phenomenon called coring, where the composition differs significantly between the center and surface, rather than the uniform microstructure predicted by the calculation.

Next, be cautious of the oversimplified notion that "a solid fraction of 50% means half of the total is solid." The lever rule yields mass fractions. For alloys where the density of the solid phase and liquid phase differ significantly (like many cast irons), the volume fractions do not match. Since volume change is crucial for predicting shrinkage cavities, confusing these can lead to discrepancies in actual design.

Finally, pay attention to how the behavior changes when you adjust the "initial composition C₀" parameter in the tool. Moving C₀ away from the eutectic point (e.g., 61.9 wt% Sn for Sn-Pb) creates a difference between the temperature where solidification starts (liquidus) and where it ends (solidus). Alloys with a wider temperature range (solidification temperature range) will have a more gradual slope in the solidification curve, making it easier to form a broad, "mushroom-shaped" mushy zone. This means shrinkage porosity tends to be dispersed, making riser design more challenging. The quickest way to understand this is to actually try changing C₀ in the simulator and observe how the shape of the solidification curve changes.