Phase Diagrams

A phase diagram is a graphical tool that shows, for any given combination of conditions such as temperature, pressure, and composition, which phase or phases represent the lowest-energy configuration of a given chemical system. ^[1] A phase in this context can be a mineral, a melt, or a gas. Ice is a single phase; ice floating in water is two phases simultaneously. Phase diagrams make it possible to read off which minerals are stable, which melts coexist with them, and precisely where transformations occur - all without having to calculate Gibbs free energies from scratch for every case. ^[1]

Phase diagrams are constructed assuming equilibrium - meaning that kinetic complications such as nucleation delays and growth rates are ignored. In practice, the equilibrium condition must be overstepped to some degree before crystals actually begin to form, but working through the equilibrium case first provides the essential framework for understanding what the system is driving toward. ^[1]

Pressure Units

Pressures in phase diagrams are most commonly expressed in kilobars (kbar). In the Earth’s crust, lithostatic pressure increases by roughly 1 kilobar per 3 kilometres of depth, depending on rock density. Some literature uses the gigapascal (GPa), but the kilobar is more convenient for crustal applications: 1 GPa = 10 kbar. ^[1]

Single-Component Systems: Temperature-Pressure Diagrams

In a single-component system, every phase present can be described using a single chemical composition. The most common way to display stability in such a system is a temperature-pressure (T-P) diagram, with temperature on one axis and pressure on the other. Each field on the diagram is the stability field of one particular phase - the region of T-P space where that phase has the lowest ΔG_f and is therefore the equilibrium mineral. ^[1]

The Aluminum Silicates: A Classic Example

The three aluminum silicate polymorphs - andalusite, sillimanite, and kyanite - all share the same chemical formula AlAlOSiO₄ and are common minerals in mica schists produced by metamorphism of shale. ^[1] Because they share the same composition, the stable polymorph at any given T-P condition is determined entirely by which has the lowest free energy. This can be visualized as three surfaces in temperature-pressure-free energy space; the mineral with the lowest surface at any given T-P point is the stable phase there.

The T-P stability fields of the three aluminum silicates are separated by boundary lines. Along each boundary line, the two minerals on either side have the same ΔG_f - they are in equilibrium. The single T-P point where all three boundary lines meet is the triple point, the unique condition at which all three polymorphs coexist in equilibrium. ^[1]

Reading Metamorphic Conditions from Aluminum Silicates

The aluminum silicate diagram has direct geological utility. When a metamorphic rock contains andalusite, the conditions of metamorphism can be inferred to have been within the andalusite stability field - meaning low pressure and moderate temperature, conditions characteristic of contact metamorphism and low-pressure regional metamorphism. ^[1] If the same rock were subsequently heated to a higher temperature, the andalusite would react and sillimanite would grow in its place, because sillimanite has the lowest free energy under those new conditions. At the boundary between the andalusite and sillimanite stability fields, both minerals have identical ΔG_f and neither spontaneously converts to the other. ^[1] In this way, the mineral assemblage of a metamorphic rock serves as a T-P record of the conditions it has experienced - a geothermobarometer preserved in crystal form.

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