🧊 Eutectic Phase Diagram — Binary Alloy Solidification

The eutectic point is the single composition and temperature at which a liquid alloy solidifies directly into two solid phases simultaneously, without passing through a mushy two-phase region. Mixing two components lowers the freezing point of each, similar to freezing-point depression, so the eutectic composition sits at the minimum of the liquidus curve — it melts and freezes at a lower temperature than either pure component or any other mixture ratio.

The liquidus marks the highest temperature at which solid can exist for a given composition; above it the alloy is fully liquid. The solidus marks the lowest temperature at which liquid can exist; below it the alloy is fully solid. Between the two lies the mushy zone. In this simplified system, the solidus collapses to the horizontal eutectic line plus the vertical lines at the pure components.

In a two-phase region, a horizontal tie line connects the liquid composition (C_liquid) and the solid composition (C_solid) at the current temperature. The lever rule treats the tie line like a balance beam pivoted at the overall composition C₀: fraction solid = (C_liquid − C₀)/(C_liquid − C_solid). It gives the exact relative amounts of each phase present.

Below the eutectic temperature, the remaining eutectic liquid solidifies into fine alternating layers (lamellae) of the two solid phases growing side by side. Each phase rejects the component it does not want into the liquid right next to it, feeding growth of the neighboring lamella — a self-organizing diffusion process producing a very fine, regular striped structure.

An alloy at the exact eutectic composition freezes at a single sharp temperature, like a pure metal. Off-eutectic alloys freeze over a temperature range: primary grains of one solid phase grow first as the liquid cools through the mushy zone, and only the remaining liquid transforms to eutectic solid once it reaches the eutectic temperature.

Classic examples include Pb-Sn solder (eutectic near 61.9% Sn, melting at 183°C), Wood's metal (a low-melting Bi-Pb-Sn-Cd eutectic used in fuses and fire sprinklers), and salt-water or salt-ice mixtures, whose eutectic freezing-point depression is why road salt melts ice.

Eutectic solder freezes at one sharp temperature instead of over a range, avoiding time spent in a partially liquid mushy state while cooling. Off-eutectic solders can be disturbed by vibration during that mushy interval, forming cracked or grainy cold joints; eutectic solder solidifies almost instantly and cleanly.

Just as dissolving a solute in a solvent lowers the solvent's freezing point, a colligative effect, mixing two components in a binary alloy lowers the freezing point along each pure component's liquidus curve. The eutectic point is where both lowered liquidus curves meet.

Moving away from the eutectic composition increases the fraction of primary solid that forms before the eutectic reaction begins, and decreases the fraction of fine eutectic microstructure left over. At the pure-component limits, no eutectic structure forms at all.