Phase diagram

A phase diagram is a chart of a substance's equilibrium state as a function of thermodynamic variables, most commonly pressure and temperature. Its regions are the single-phase fields — solid, liquid, vapour, and beyond the critical point the supercritical fluid — and its lines are the coexistence curves separating them. Two landmarks organise the picture: the triple point, where all three ordinary phases meet, and the critical point, where the liquid–vapour boundary ends.

Reading a phase diagram along a horizontal line at constant pressure recovers everyday experience: at one atmosphere, water crosses the melting line at 0 °C and the boiling line at 100 °C. Reading it for carbon dioxide explains why dry ice does not melt — CO₂'s triple point sits at 5.2 atmospheres, above room pressure, so a 1 atm isobar never enters the liquid field and the solid sublimes directly at −78.5 °C.

The slopes of the lines are not free: each is fixed by the Clausius–Clapeyron relation from the latent heat and volume change of the transition. The most visible consequence is the tilt of the solid–liquid line, which leans right for almost every substance and left for water, whose solid is less dense than its liquid. Diagrams in other variables — pressure–volume, temperature–composition for alloys and mixtures — follow the same logic with different axes.

Grew out of Andrews's 1869 isotherms of carbon dioxide and Gibbs's phase rule of 1876, which established how many phases can coexist in how many dimensions; James Clerk Maxwell built a plaster model of Gibbs's thermodynamic surface and sent it to him.