A phase of a substance is a form of matter that is uniform throughout in chemical composition and physical state.

Thus we will typically encounter the solid, liquid and gaseous phases of a substance. Allotropes of the solid state, such as graphite and diamond, are also different phases. Processes such as vaporisation, melting and interconversion of allotropes that change one phase into another are thus termed phase changes or phase transitions.

The fundamental thermodynamic principle underlying such processes is the tendency of a system at a given pressure and temperature to minimise its Gibbs energy

Phase transitions occur at a characteristic temperature for a given substance at a given pressure. This temperature is called the transition temperature, T_trs (i.e. for water, at 1 atm, melting takes place at 0ºC /  273.15 K . Above this temperature, liquid water is the most stable phase of water (has the lowest molar Gibbs energy) but below this temperature ice is the most stable phase. At 0ºC , the transition temperature, the two phases are in equilibrium, and their molar Gibbs energies are identical.)
It is convenient at this stage to introduce an extremely important thermodynamic quantity called the chemical potential, denoted μ. For a pure substance, it is defined as follows:

where n is the amount of substance in moles.

i.e. the chemical potential shows how the Gibbs energy of a system changes as a substance is added to it. Since, for a pure substance, G  =  nG_m , it follows that μ  =  G_m   - the chemical potential of a pure substance is equal to the molar Gibbs energy of that substance. (Though this merely appears to be a change of notation, the chemical potential finds wider applications in fields such as equilibrium chemistry, where the chemical potential of a component of a mixture proves to be of crucial importance.)

We could thus rewrite the above example to say that below 0ºC ice is the phase of water with the lowest chemical potential, etc.

Note the tendency of systems is from high to low chemical potential.

The chemical potential (or Gibbs energy) can only tell us about the thermodynamics of the system under consideration, and nothing about the kinetics. It may be the case that a thermodynamically favourable change occurs too slowly to be observed, and is thus not significant. For example, graphite has a lower chemical potential than diamond at normal temperatures and pressures, but diamonds are known to exist under such conditions. The change from diamond to graphite requires the carbon atoms in the solid phases to alter their positions, which is an incredibly slow process.

The thermodynamic instability persists because of a kinetic inertness

Thermodynamically unstable phases that exist because the transition to a more stable phase is kinetically hindered are called metastable phases.

A phase diagram depicts the areas of pressure and temperature at which the different phases of a given substance are stable. The lines on the diagram separating different areas are called phase boundaries, and mark the values of pressure and temperature at which the two phases on either side of the boundary are in equilibrium with each other. i.e. these boundaries show the variation of the transition temperatures with pressure. A typical phase diagram has this general form:

Note phase boundaries are indicated by the green lines. Discussion of the Triple and Critical points will be left until later.