Phase Diagrams of Binary Mixtures

Core Idea

Binary phase diagrams (T-x, P-x) map equilibrium regions (vapor, liquid, solid) and show key features: eutectic points (lowest-melting mixtures), peritectic points, azeotropes (same liquid and vapor composition), and immiscibility regions. These are derived from Gibbs-Duhem relations and activity models. Understanding phase diagrams is essential for distillation, crystallization, and alloy design.

Explainer

A single-component phase diagram maps the stable phase of a pure substance as a function of temperature and pressure. Binary phase diagrams extend this idea to mixtures of two components, adding composition as a third variable. The result is typically displayed as a T-x diagram (temperature vs. mole fraction at constant pressure) or a P-x diagram (pressure vs. mole fraction at constant temperature). These diagrams encode enormous practical information about how mixtures behave when heated, cooled, or partially vaporized.

In a vapor-liquid T-x diagram for a non-ideal system, the key feature is the two-phase envelope defined by the bubble-point curve (below which all liquid) and the dew-point curve (above which all vapor). At any temperature between these curves, liquid and vapor coexist with compositions given by the endpoints of a horizontal tie line. Raoult's Law predicts ideal behavior; real systems deviate because unlike-molecule interactions (A–B) may be stronger or weaker than like-molecule interactions (A–A, B–B). Stronger A–B interactions suppress vapor pressure below ideal predictions (negative deviation), pushing the bubble-point and dew-point curves upward and potentially creating a maximum-boiling azeotrope. Weaker A–B interactions do the opposite, creating a minimum-boiling azeotrope. At an azeotrope, liquid and vapor compositions are identical — the tie line degenerates to a point — and the mixture cannot be further separated by simple distillation.

In solid-liquid T-x diagrams (relevant for alloys, pharmaceuticals, and salt systems), the most important feature is the eutectic point. For two components that are mutually soluble as liquids but insoluble as solids, cooling any liquid mixture causes one solid to crystallize preferentially, shifting the remaining liquid composition toward the eutectic. At the eutectic temperature, the liquid simultaneously solidifies into two solid phases — a process called eutectic solidification — producing a characteristic fine-grained two-phase microstructure. The eutectic is the thermodynamic minimum of the liquidus curve; no liquid of that composition can exist below it. Systems with peritectic points are more complex: one solid phase partially transforms into a different solid plus liquid on heating, which can trap unequilibrated phases during rapid cooling.

Both diagram types are derived from the same thermodynamic foundation: the Gibbs-Duhem equation constrains how the chemical potentials of components in a mixture must vary together, and activity models (Raoult's Law, Margules, van Laar, NRTL) quantify deviations from ideal behavior. The phase boundaries are located by finding conditions where chemical potentials are equal in coexisting phases — exactly the criterion for thermodynamic equilibrium. Familiarity with binary phase diagrams is essential for distillation column design, alloy selection, crystallization purification, and formulating stable pharmaceutical excipients.