A phase diagram is a graph that shows the distribution of stable phase assemblages as a function of the values of the intensive variables used to describe the thermodynamic system. If pressure and temperature are the variables of interest then the stable assemblage is the one with the lowest Gibbs free energy, although other thermodynamic potentials may be used if the variables of interest are different, for example, Helmholtz free energy if one is interested in temperature and volume (more on this in Chapter 9). Phase diagrams are powerful analytical tools in many branches of planetary sciences, as they provide a way to quickly visualize how phase assemblages change in response to changes in pressure, temperature, chemical potentials, or any other combination of intensive variables. There are many different types of phase diagrams and it is not the purpose of this book to offer a comprehensive review of all of them. Rather, in this chapter I will focus on the fundamental rules that phase diagrams must abide by in order to be thermodynamically valid. We therefore begin with a discussion of the thermodynamic underpinnings of phase diagrams.

The foundations of phase equilibrium

The Gibbs–Duhem equation

Any extensive thermodynamic property can be written as a sum of products of partial molar properties times mol numbers (equation (5.27)).