Binary Phase Diagram Simulation

Interactive demonstration of T-x diagrams, lever rule, and microstructure evolution

System Type

Microstructure Evolution

Phase Composition:

Current State

Current Phase(s): --
Liquid Fraction: --
Solid Fraction: --

Lever Rule

w₁·l₁ = w₂·l₂

Parameters

Physical Principles

Lever Rule: w₁·l₁ = w₂·l₂
Liquid Fraction: fₗ = (x - xₛ)/(xₗ - xₛ)
Eutectic Reaction: L ⇌ α + β
Gibbs Phase Rule: F = C - P + 2

Phase Regions

What is a Binary Phase Diagram?

A binary phase diagram is a graphical representation of the equilibrium relationships between phases in a two-component system as a function of temperature and composition. It shows the stable phases at different temperatures and compositions, including liquid, solid solutions, and two-phase regions where multiple phases coexist in equilibrium.

Lever Rule

The lever rule is used to calculate the relative amounts of phases in a two-phase region. It treats the phase diagram as a lever with the fulcrum at the overall composition: the fraction of one phase is proportional to the distance from the overall composition to the other phase boundary. Mathematically, for phases α and β: fₐ·(x - xₐ) = f₆·(x₆ - x), where x is the overall composition and xₐ, x₆ are the compositions of the two phases.

Eutectic Point

The eutectic point is the lowest melting point in a binary system where liquid transforms simultaneously into two solid phases (L ⇌ α + β) at a specific composition and temperature. At this point, the alloy behaves like a pure substance with a sharp melting point. Eutectic alloys are important in soldering, casting, and metallurgy due to their low melting temperatures and fine microstructures.

Microstructure Evolution

As an alloy cools, different microstructures form depending on composition. Off-eutectic compositions develop primary solid (α or β) first, followed by eutectic mixture at the eutectic temperature. The eutectic composition forms a characteristic lamellar or rod-like structure of alternating α and β phases. The morphology and scale of these microstructures affect mechanical properties like strength, ductility, and toughness.

Applications

Binary phase diagrams are essential in materials science and metallurgy: designing alloys with specific properties, predicting microstructure from heat treatment, determining processing temperatures for casting and heat treatment, understanding solder behavior in electronics, developing composite materials, and troubleshooting material failures. Common applications include Pb-Sn solders, Al-Si casting alloys, Fe-C steel systems, and Cu-Ni corrosion-resistant alloys.