Lecture notes for GEOL 3010

Klein (22nd) p. 115-134

Gibbs phase rule

p + f = c + 2

where:

Example with the kyanite-sillimanite-andalusite series

Polymorphs of Al2SiO5

f is the number of variables that must be fixed to define a particular set of conditions in the system.

In the case of the kyanite-sillimanite-andalusite series, like the H2O system, there is a triple point or invariant point in T and P space. It is the unique set of T and P conditions under which all three phases can coexist.

This can be expressed by rearranging the Gibbs phase rule:

f = c - p + 2

In this case:

c = 1 (the component is Al2SiO5)

p = 3 (there are three phases at this point)

Therefore:

f = 1 - 3 + 2 = 0 (zero degrees of freedom)

Along the curve or univariant line there is not one unique set of P and T conditions under which two phases can coexist.

In this case:

c = 1 (the component is Al2SiO5)

p = 2 (there are two phases at this point)

Therefore:

f = 1 - 2 + 2 = 1 (one degree of freedom)

In the divariant or phase regions only one phase can coexist. No unique set of P and T conditions can be defined by the presence of one mineral phase

In this case:

c = 1 (the component is Al2SiO5)

p = 1 (there is one phase at this point)

Therefore:

f = 1 - 1 + 2 = 2 (two degrees of freedom)

Binary Systems are cases with two components in the system, meaning the system can be described by two chemical entities.

Binary systems are usually discussed in terms of temperature and the percentages of the components present (rather than grams of material) at a constant pressure (T-X diagrams).

Examples of binary systems

Water and powdered glass - two components (H2O, SiO2) , two phases - liquid and solid.

Ice and powdered glass - two components (H2O, SiO2) , two phases - both solid.

Water and oil - two components (H2O, HC) , two phases - both liquids but are considered immiscible (no mixing at the molecular level).

Water and alcohol - two components (H2O, CH3OH) , one phase - a miscibile solution.

Water (10 g) and Salt (1g) - two components (H2O, NaCl) , one phase - a solution.

Water (10 g) and Salt (10g) - two components (H2O, NaCl) , two phases - a saturated solution and excess solid.

Olivine - Fosterite/Fayalite series- one phase - miscible solid solution (forsterite can occur with a small fayalite content or fayalite with a small forsterite content).

Plagioclase - Albite/Anorthite series - a partial solid-solution with a miscibility gap between the end-member (i.e., homogeneous plagioclase).

Albite - Silica - Two immiscible solids.