Phase transitions

What is a phase?

A phase is a macroscopically distinct form of matter, such as solid, liquid, gas, or plasma. Different phases have different structure, density, symmetry, and response to forces. Phase transitions occur when a system changes from one phase to another.

Common examples include melting, freezing, boiling, condensation, sublimation, and magnetic ordering.

First-order phase transitions

Many familiar phase transitions involve latent heat. During melting or boiling at constant pressure, heat is added while temperature remains constant. The energy changes molecular arrangement rather than average kinetic energy.

The heat required is

$Q=mL$

At constant pressure, this heat is an enthalpy change:

$Delta H=mL$

Such transitions are called first-order transitions because entropy changes discontinuously. Since

Delta S=rac{Q_{rev}}{T}

a latent heat implies an entropy change

Delta S=rac{mL}{T}

Phase diagrams

A phase diagram shows which phase is stable at different temperatures and pressures. Boundaries separate phases. Along a phase boundary, two phases coexist in equilibrium.

The triple point is where solid, liquid, and gas coexist. The critical point marks the end of the liquid-gas coexistence curve. Above the critical point, there is no sharp distinction between liquid and gas; the substance becomes a supercritical fluid.

Microscopic interpretation

Phase transitions reflect competition between energy and entropy. At low temperature, lower-energy ordered states may be favored. At high temperature, higher-entropy disordered states may be favored.

Free energy determines equilibrium. At fixed temperature and pressure, the relevant potential is Gibbs free energy:

$G=H-TS$

The stable phase is the one with lowest $G$.

Order parameters

An order parameter is a quantity that distinguishes phases. For a liquid-gas transition, density difference can serve as an order parameter. For a ferromagnet, magnetization is an order parameter. For a crystal, structural order distinguishes solid from liquid.

An order parameter is often zero in one phase and nonzero in another.

Continuous phase transitions

Some phase transitions do not involve latent heat. These are continuous, or second-order, transitions. Near such transitions, quantities like heat capacity or magnetic susceptibility may change sharply or diverge.

A ferromagnet becoming paramagnetic at its Curie temperature is a classic example. Above the Curie temperature, thermal disorder destroys spontaneous magnetization.

Critical behavior

Near critical points, systems can show fluctuations on many length scales. Details of microscopic interactions become less important than symmetry and dimensionality. This leads to universal behavior, where very different systems share similar critical exponents.

This is a major achievement of modern statistical mechanics.

Nucleation and metastability

Phase transitions may require nucleation. For example, very pure water can be supercooled below its freezing point without immediately freezing. A small stable seed of the new phase must form before the transition rapidly proceeds.

Metastable states are not the lowest free-energy states, but they can persist because a barrier must be overcome.

The big idea

Phase transitions are macroscopic changes that emerge from microscopic interactions and statistical behavior. Latent heat, entropy, free energy, order parameters, and fluctuations provide the language for understanding melting, boiling, magnetism, critical points, and the rich behavior of matter.