phasediagram

A phase diagram is a graphical representation that shows the stable phases of a material system under given thermodynamic conditions. Typically the axes are temperature and composition, or temperature and pressure, and the diagram delineates regions where a single phase is stable and lines where two or more phases coexist in equilibrium.

In binary phase diagrams, the horizontal axis is the composition of one component and the vertical axis is temperature. Boundaries separate single-phase regions from multiphase regions; at the boundaries, phases are in equilibrium. Invariant reactions such as eutectic or peritectic points occur at fixed temperature and composition.

The Gibbs phase rule, F = C − P + 2, applies to a closed system, where F is the number of degrees of freedom, C the number of components, and P the number of phases. This rule helps explain how many variables must be fixed to maintain equilibrium and how the number of coexisting phases changes with composition and temperature.

Common examples include the water phase diagram (solid–liquid–vapor regions) and the iron–carbon diagram used in metallurgy to understand steel and cast iron properties. Phase diagrams guide alloy design, heat treatment, and solidification processing by predicting which phases form under given conditions.

Diagrams are constructed from experimental data and thermodynamic calculations (CALPHAD). They assume equilibrium and may not capture non-equilibrium or metastable states; many practical diagrams are representative rather than exact for a given processing history.