Real-time drawing of isomorphous, eutectic, and peritectic phase diagrams. Automatically calculates phase fractions and equilibrium compositions via the lever rule at any temperature and composition.
Parameters
Material Presets
System Type
Component A Melting Point T_mA
°C
Component B Melting Point T_mB
°C
Eutectic Composition x_E (mol%B)
%
Eutectic Temperature T_E
°C
Query Composition x_B
%
Query Temperature T
°C
Results
—
Present Phase(s)
—
Liquid Fraction f_L
—
Solid Fraction f_α
—
Liquidus/Solidus Comp.
Phase
Applications in CAE & Materials Design
Alloy solidification sequence prediction / Initial segregation and macro-segregation assessment / Weld HAZ microstructure prediction / Foundation for multi-component CALPHAD calculations / Preprocessing for solidification simulations coupled with FEM thermal analysis.
where $x_L$: liquidus composition, $x_\alpha$: solidus composition (equilibrium values at temperature T)
Scheil Equation (non-equilibrium solidification):
$$C_S = k\,C_0\,(1-f_S)^{k-1}, \quad k = \frac{x_\alpha}{x_L}$$
$k$: partition coefficient. When $k<1$, solute segregates into the liquid (back-segregation).
What is a Binary Phase Diagram & Lever Rule?
🙋
What exactly is a binary phase diagram? I see the simulator lets me pick types like "isomorphous" or "eutectic".
🎓
Basically, it's a map for two-element alloys, like copper-nickel or aluminum-silicon. It shows what phases—solid, liquid, or mixtures—are stable at a given temperature and composition. In practice, the "System Type" you choose changes the map's shape. For instance, an isomorphous system has complete solid solubility, while a eutectic system has a point where liquid freezes into two different solids.
🙋
Wait, really? So if I pick a "Query Composition" and "Temperature" on the diagram, how do I know how much of each phase is present?
🎓
That's where the lever rule comes in! When your query point lands inside a two-phase region, the diagram gives you the compositions of the two phases at the boundaries. The lever rule is like a seesaw: the phase fractions are inversely proportional to the distances from your query point to each boundary. Try moving the "Query Temperature" slider up and down in a two-phase region and watch the calculated fractions change in real-time.
🙋
That makes sense. But what's "segregation" mentioned in the theory? Is that related to the "k" parameter I see?
🎓
Great question. Segregation is when the composition isn't uniform as the alloy solidifies. The parameter $k = x_\alpha / x_L$ is the partition coefficient. If $k < 1$, the first solid to form is purer in component A, pushing B into the remaining liquid. A common case is in aluminum casting. The simulator uses this in the Scheil equation to predict this non-equilibrium segregation—try setting $k$ to a low value like 0.1 and see how the composition profile steepens.
Physical Model & Key Equations
The lever rule calculates the mass or mole fractions of two coexisting phases (α and Liquid) at equilibrium for a given overall composition $x_0$ and temperature T. It's a mass balance derived from the phase diagram.
$f_\alpha, f_L$: Fraction of α (solid) and Liquid phase. $x_0$: Overall composition of the alloy (mol% B). $x_L, x_\alpha$: Composition of the Liquid and α phase at the temperature T, read from the liquidus and solidus lines.
The Scheil equation models non-equilibrium solidification, where diffusion in the solid is negligible. It predicts how solute builds up in the remaining liquid, leading to segregation.
$$C_S = k\,C_0\,(1-f_S)^{k-1}, \quad k = \frac{x_\alpha}{x_L}$$
$C_S$: Composition of the solid forming at fraction $f_S$. $C_0$: Initial liquid composition ($x_0$). $k$: Partition coefficient. If $k<1$, solute is rejected into the liquid, enriching it as solidification proceeds.
Frequently Asked Questions
No, manual input is not required. This tool incorporates phase diagrams for isomorphous, eutectic, and peritectic systems, and the liquidus and solidus lines are automatically drawn according to the selected system. Simply moving the temperature slider calculates the equilibrium composition at that temperature, and the phase fractions based on the lever rule are displayed immediately.
The lever rule provides phase fractions under equilibrium conditions, which hold true under ideal conditions where the cooling rate is sufficiently slow and diffusion is complete. For non-equilibrium solidification, such as in actual casting, different models like the Scheil equation are required. This tool primarily performs equilibrium calculations, but you can also check the results of the Scheil equation as a reference for non-equilibrium conditions.
When the overall composition crosses a boundary between a single-phase region and a two-phase coexistence region (such as the liquidus or solidus line), the types of phases present change, causing a discontinuous change in the phase fractions. This is the correct behavior when the composition crosses a phase boundary on the phase diagram, and the tool automatically detects these boundaries and switches the calculations accordingly.
Currently, there is no function to save graph images, but you can manually copy the numerical values of the phase fractions and compositions displayed at the bottom of the screen for your use. Additionally, since changes can be observed in real time when varying the temperature or overall composition, it is ideal for educational materials or demonstration purposes to understand phenomena.
Real-World Applications
Alloy Design & Processing: Engineers use these diagrams to select heat treatment temperatures (like for annealing or homogenization) and to predict the melting range of an alloy, which is critical for casting and welding processes.
Casting & Solidification Simulation: The lever rule and Scheil equation are foundational inputs for CAE software that simulates casting. They help predict where shrinkage porosity or severe segregation (like "centerline segregation" in steel ingots) might occur, guiding the design of risers and chills.
Welding Metallurgy: The rapid heating and cooling in a weld's Heat-Affected Zone (HAZ) can be approximated using phase diagrams. Predicting the phases that form helps assess the risk of cracking or corrosion, crucial for welding aerospace or pipeline components.
Foundation for CALPHAD: Binary systems are the building blocks for the CALPHAD method used in sophisticated materials design software. It computationally extrapolates these principles to complex, multi-component alloys used in jet engines or battery materials.
Common Misconceptions and Points to Note
When you start using this tool, there are a few common pitfalls to watch out for. First, be mindful of whether the overall composition is given in weight percent (wt%) or atomic percent (at%). The simulator input is typically mole fraction (similar to at%), but material specification sheets in practice are often written in wt%. For example, the eutectic point of an Al-Si alloy is about 12.6 wt% Si, but it's about 18.6 at% Si. Confusing these units will cause you to completely misplace the point on the phase diagram, so be careful.
Second, remember that the lever rule calculates for "equilibrium conditions". In actual casting, the cooling rate is fast, so the composition of the liquid and solid phases does not become uniform as calculated. Treat the equilibrium calculation result from the tool as an "ideal limit value." The trick is to compare it with the result from the Scheil equation on the non-equilibrium tab to intuitively grasp how much reality deviates. For instance, for an alloy with a partition coefficient k=0.5 at a solid fraction $f_S$ of 0.5, the solid composition $C_S$ returns to $C_0$ under equilibrium. However, under non-equilibrium (Scheil equation), it remains significantly lower at $C_S = 0.5 C_0 (1-0.5)^{-0.5} \approx 0.707 C_0$. This is the essence of segregation.
Third, understand the limitations of "binary systems". Most practical alloys, like Fe-Cr-Ni, are ternary or more complex. The principles you learn with this tool are foundational, but in reality, the presence of a third element can significantly shift liquidus lines and eutectic temperatures. It's risky to directly apply binary system calculation results to practical work; think of this strictly as a "training tool for understanding phase equilibrium concepts."