Introduction

The phase rule, derived by Gibbs (1875), is a simple relationship between the composition of a system, the number of phases it has, and something called the variance of the system. It requires no thermodynamic data, just compositions, and although simple in principle, and easily applied to the simple systems usually used to explain it, it can be surprisingly difficult to use when considering geological systems. It is absolutely essential in discussing phase diagrams, as in Chapter 17.

In this chapter we will consider not only the “traditional” Gibbs phase rule, but how it becomes modified or extended when aqueous solutes are included in the phase compositions. We then have a look at buffered systems, which are essentially an application of the phase rule.

Derivation of the phase rule

Some definitions

Phase relations involve a small number of carefully defined terms.

Phases

A phase is defined as a homogeneous body of matter having distinct boundaries with adjacent phases, and so is in principle mechanically separable from them. Each mineral in a rock is therefore a single phase, as is a salt solution, or a mixture of gases.

Components

Each phase therefore has a definite chemical composition, and the various phases in a system may have the same (polymorphs) or different compositions. The compositions are described in terms of chemical formulas, such as SiO2 or CaMgSiO3. The smallest number of chemical formulas needed to describe the composition of all the phases in a system is called the number of components of the system.