What is Phase Rule - Petrology |Geologypage

Phase Equilibrium in Metamorphic Petrology

System: In metamorphic petrology, the arbitrary and hypothetical lump of rock is a system in chemical terms. It is made up of minerals and perhaps also contains an inter-granular fluid. Each of its constituents is known as its phases.

Phase: A phase is defined as the type of physically separable constituent in a system that is distinct from the rest. A phase may be a mineral, liquid, a gas or an amorphous solid such as glass. As an example, the plagioclase and quartz are separable phases in a pelitic schist.

Component: A component may be defined as the minimum number of chemical species required to completely define the system and all its phases. For example, a system that contains only andalusite and kyanite has only one component, Al₂ SiO_5, whereas a system that contains andalusite, corundum and quartz must have two components, Al­₂O­­₃  and SiO₂ , to make all the phases.

The Phase Rule

The phase rule is an expression of the number of variables and equations that can be used to describe a system in equilibrium. In simple terms, the numbers of variables are the number of chemical components in the system plus the intensive variables, temperature and pressure. The number of phases present will depend on the variance or degrees of freedom of the system. The general form of the phase rule is stated as follows:

F = C + 2 –P

Where F is number of degrees of freedom or variance of the system

C is number of components in the system

P is number of Phases

And 2 comes from the number of intensive variables.

To understand, how the phase rule works, let's consider a simple one component system - the system Al₂SiO₅, shown in the Pressure-Temperature phase diagram below.

First look at the point in the field of kyanite stability. Since kyanite is the only phase present, P=1. Now by using phase rule ( F = C + 2 –P), we found F = 2. Hence, this point is called the divariant (divariance) because both the temperature and pressure can be changed without affecting the number of phases present.

Next, look at the point on the phase boundary between kyanite and sillimanite. For any point on such a boundary the number of phases, P, will be 2. Using the phase rule we find that F = 1, or there is one degree of freedom. This means there is only one independent variable. If we change pressure, temperature must also change in order to keep both phases stable. The phase assemblage is said to be univariant in this case, and the phase boundaries are univariant lines (or curves in the more general case.

Finally, we look at the point where all three univariant lines intersect. At this point, 3 phases, kyanite, andalusite, and sillimanite all coexist at equilibrium. Note that this is the only point where all three phases can coexist. For this case, P=3, and F, from the phase rule, is 0. There are no degrees of freedom, meaning that any change in pressure or temperature will result in a change in the number of phases. The three phase assemblage in a one component system is said to be invariant.

References and further readings

Principles of igneous and metamorphic petrology by J.D. Winter

An introduction to metamorphic petrology by Bruce W.D. Yardley

Image by tulane university/earthsciences