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A binary phase diagram maps the equilibrium phases present for all compositions and temperatures of a two-component system. Key features include the liquidus (above which the system is fully liquid), solidus (below which it is fully solid), and special invariant points such as the eutectic (a single liquid transforming simultaneously into two solids). Reading a phase diagram for a given alloy composition and temperature reveals which phases exist, their compositions, and — via the lever rule — their relative amounts. Phase diagrams are the roadmap for heat treatment and solidification processing.
Start with the isomorphous (fully soluble) Cu-Ni system to practice reading single- and two-phase regions, then progress to the eutectic Pb-Sn system. Draw cooling curves for different compositions to connect diagram features to solidification behavior.
A binary phase diagram is a map of a two-component system: one axis is temperature, the other is composition (often expressed as weight percent or mole fraction of one component), and each region of the map tells you which phases are present at equilibrium. You read it like a topographic map — the boundary lines are where phase transitions occur, and the regions between them describe stable coexistence.
The most important lines are the liquidus (above it, everything is liquid) and the solidus (below it, everything is solid). Between them is a two-phase region where liquid and solid coexist. For a given alloy composition and temperature that falls in this region, you can immediately read off two things from the diagram: the *compositions* of each phase (where a horizontal tie-line meets each boundary) and the *amounts* of each phase (from the lever rule). The lever rule is mechanical intuition applied to composition: the fraction of one phase equals how far the overall composition is from that phase's boundary, divided by the total span between the two boundaries.
The eutectic point is the most distinctive feature of many binary diagrams. It is the one composition that melts at the lowest possible temperature for the system, and at that temperature a single liquid transforms into two solid phases simultaneously. The Pb-Sn eutectic (used in solder) is the classic example: at 61.9% Sn and 183 °C, liquid transforms directly into alternating lamellae of Sn-rich and Pb-rich solid. Compositions richer or leaner in Sn pass through a mushy two-phase region during cooling rather than transforming at a sharp temperature.
The critical caveat for all phase diagrams is that they describe equilibrium — what you get if you cool infinitely slowly, giving every atom time to diffuse to its equilibrium position. Real cooling rates are finite, which means diffusion is often incomplete. The result is coring: the first solid to form is enriched in the higher-melting component, while later-solidifying layers are leaner, creating a composition gradient within each grain. The actual microstructure can differ substantially from what the diagram would predict. Homogenization heat treatments exist precisely to drive real alloys back toward equilibrium by allowing solid-state diffusion to proceed.