phaseequilibria

Phase equilibria refers to the condition in which two or more phases of a material are in thermodynamic balance with each other. In equilibrium, the chemical potential of each component is the same in all coexisting phases, so there is no net transfer of matter between phases. The stable phase assemblage depends on temperature, pressure, and composition.

The Gibbs phase rule provides a compact relation among the number of components (C), the number of coexisting phases (P), and the degrees of freedom (F) of a system: F = C − P + 2. This rule indicates how many intensive variables (such as temperature, pressure, and compositions) can be varied independently without changing the number of phases present. Phase diagrams visualize these equilibria, showing regions of single-phase stability and multiphase fields, with tie lines that connect the compositions of coexisting phases in two-phase regions.

Common types of phase equilibria include vapor–liquid, liquid–liquid, and solid–liquid interfaces. In binary systems, features such as eutectic or peritectic points mark compositions where multiple phases coexist at a single temperature. For ideal solutions, Raoult’s law describes vapor pressures, P_i = x_i P_i^sat, while real solutions require activity coefficients to account for non-ideality.

Modeling approaches use chemical potentials, fugacity concepts, and equations of state or activity models to describe phase boundaries and compositions. Experimental phase diagrams are determined to obtain accurate phase boundaries and tie lines. Phase equilibria underpin many applications, including distillation, crystallization, alloy design, and polymer blends, guiding separation processes and material synthesis.