Binary Alloy Phase Diagrams: Liquidus, Solidus & the Eutectic Reaction

Reading the map: liquidus, solidus and the two-phase region

A binary alloy phase diagram plots composition along the horizontal axis — from 100% element A on the left to 100% element B on the right — against temperature on the vertical axis. The two boundaries that matter most are the liquidus, the upper curve above which the alloy is entirely molten, and the solidus, the lower curve below which it is entirely solid. Between them lies a lens-shaped two-phase region where liquid and solid coexist in equilibrium.

A pure metal melts at a single fixed temperature because its liquidus and solidus meet at one point. An alloy of intermediate composition instead freezes over a range: the first solid crystals appear at the liquidus temperature, and as cooling continues the remaining liquid becomes progressively enriched in the lower-melting element, until the last liquid solidifies at the solidus.

The lever rule

At any temperature inside the two-phase region, a horizontal tie line gives the relative amounts of liquid and solid present. This is the lever rule, a direct consequence of conservation of mass:

f_solid = (C₀ − C_L) / (C_S − C_L)

C₀ = overall alloy composition
C_L, C_S = liquid and solid compositions at the ends of the tie line

The geometry behaves exactly like a balanced lever, hence the name — the fraction of one phase equals the length of the opposite arm divided by the total tie-line length, a detail that trips up many students who reach for the near arm instead.

The eutectic reaction

Many alloy systems have only limited solid solubility, so the two metals cannot dissolve fully into one another as solids. The liquidus then splits into two branches descending from each pure-metal melting point, meeting at a low-temperature minimum called the eutectic point — from the Greek for "easily melted". There, a single liquid transforms simultaneously into two distinct solid phases: Liquid → α + β, at a fixed temperature and fixed composition.

This invariant reaction is fixed by Gibbs' phase rule, F = C − P + 1. With two components and three phases in equilibrium at once, the degrees of freedom F fall to zero — both temperature and all three compositions are uniquely determined. The resulting microstructure is a fine, often lamellar, intergrowth of the two solid phases, because both must crystallise together from the same liquid.

Why engineers design around the eutectic

Tin-lead and tin-silver-copper solders sit near eutectic compositions so they melt and freeze sharply at one low temperature, avoiding a sluggish pasty range that would produce weak joints. Aluminium-silicon casting alloys are chosen close to their eutectic to improve mould fluidity and reduce shrinkage defects — the reason they dominate automotive cylinder blocks. Lead- and tin-based bearing "white metals" exploit a soft eutectic matrix with hard dispersed phases, a balance read directly from the diagram. Even steel heat treatment traces back to the same ideas, via the iron-carbon diagram's eutectoid reaction.

Equilibrium versus real cooling

Phase diagrams describe equilibrium — infinitely slow cooling that gives diffusion time to keep every atom in its ideal place. Real castings cool much faster, producing non-equilibrium effects such as coring, where a grain's centre stays richer in the higher-melting element than its edges because diffusion cannot keep pace. Recognising where the diagram's assumptions break down is as important as reading the diagram itself.

Frequently asked questions

Try it live

Everything above runs in your browser — open Alloy Phase Diagram, pick a Cu-Ag, Pb-Sn, Al-Cu or Bi-Sn preset, drag composition and temperature, and watch the lever rule and eutectic reaction play out on the diagram and cooling curve in real time.