What is a phase diagram?
A phase is one form of a substance, such as ice, water or steam. Minerals have phases too. Some minerals have the same chemical formula but different crystal structures. These are called polymorphs (poly = many, morph = shape).
A phase diagram is a map. Across the bottom is temperature. Up the side is pressure, and pressure grows with depth. Every point on the map is one set of conditions, and the zone it falls in tells you the form that is stable there. Stable means it will not change if you leave it alone.
- Pressure comes from the weight of the rock above. About 1 GPa is reached at roughly 33 km depth, so 0.03 GPa per km.
- Temperature rises with depth too. Near hot magma or in a collision zone it rises faster.
Reading the AlāSiOā diagram: andalusite, kyanite, sillimanite
The most famous mineral phase diagram is for AlāSiOā . It has three polymorphs. The numbers on our board are simplified so you can see the pattern; real studies give slightly different values, but the shape is the same.
- Andalusite: low pressure, up to about 0.4 GPa (shallow, about 13 km). Often a thick, square-ended crystal.
- Kyanite: high pressure. A flat, blue blade. Common where mountains are being built and rock is buried deep.
- Sillimanite: high temperature. A thin needle or fibre. Common near big magma bodies and in very hot rock.
To read it: find the temperature on the bottom axis, find the pressure on the side axis, and see which colour zone the two meet in.
Geologists use this trio as a thermometer and barometer: the mineral found in a metamorphic rock tells the heat and pressure it once felt.
Boundary lines and the triple point
The black lines are where two forms are equally stable, so both can exist together in balance. Cross a line and one form is no longer stable, so it starts changing into the other.
Where three lines meet is the triple point. On our board it is near 500 Ā°C and 0.4 GPa (about 13 km deep). Only here can andalusite, kyanite and sillimanite all sit side by side.
- The andalusiteākyanite line slopes up to the right: more heat needs more pressure to keep kyanite.
- The kyaniteāsillimanite line also slopes up to the right and is the high-pressure edge of sillimanite.
- The andalusiteāsillimanite line leans the other way: sillimanite wins when it is hotter, even at low pressure.
How minerals transform in real rocks
When a rock is buried, heated or squeezed, its minerals do not melt. They change in the solid state: atoms move a little, and new crystals grow. This is metamorphism. A rock that moves across a line in the diagram, because it sinks deeper or a magma heats it, gets a new mineral.
- Slow changes: atoms in solid rock move slowly. A mineral can survive outside its stable zone for millions of years. Kyanite on the surface was formed deep and carried up. Geologists call this metastable.
- Other minerals use diagrams too: graphite changes to diamond at very high pressure (over about 4 GPa, deeper than 130 km). Quartz becomes a denser form, coesite, at very high pressure such as in meteorite impacts. In the mantle, olivine changes to a denser structure with depth, which is one cause of sudden changes in earthquake wave speed.
- Dense at high pressure: in general, the high-pressure form packs atoms closer together.
Try it: a practical with water and a pencil
1. On squared paper, draw temperature across (0 to 1000) and pressure up (0 to 1.2). 2. Mark the triple point at 500 and 0.4. 3. Draw three lines out from it as on the 3D board and colour the three zones. 4. Choose three rocks, for example (350 Ā°C, 0.15 GPa), (350 Ā°C, 0.9 GPa), (750 Ā°C, 0.35 GPa). Predict the mineral first, then check on the 3D board with the sliders. 5. Ask a friend to pick any point and name the mineral.
Key formulas and definitions
- Phase diagram: x = temperature, y = pressure (depth); each zone = one stable form
- Pressure from depth: P (GPa) ā 0.03 Ć depth (km); depth (km) ā P Ć· 0.03
- On a line: two forms stable together. At the triple point: three forms together
- AlāSiOā : andalusite (low P), kyanite (high P), sillimanite (high T); triple point about 500 Ā°C and 0.4 GPa (simplified)
- Key terms: polymorph, stable, metastable, triple point, metamorphism
Worked examples
1. A rock is at 400 Ā°C and 0.2 GPa. Which AlāSiOā mineral is stable? (Use the board: at 400 Ā°C the andalusiteākyanite line is at about 0.33 GPa.)
The rock is to the left of the triple point (400 Ā°C is less than 500 Ā°C). Its pressure, 0.2 GPa, is below the line value 0.33 GPa. Below that line is the low-pressure zone, so the mineral is andalusite.
2. How deep is a rock where the pressure is 0.6 GPa?
Depth = P Ć· 0.03 = 0.6 Ć· 0.03 = 20 km.
3. A rock at 400 Ā°C and 0.8 GPa. Which mineral?
Pressure 0.8 GPa is well above the andalusiteākyanite line (about 0.33 GPa at 400 Ā°C). Pressure is high, so the mineral is kyanite (flat blade).
4. A rock at 600 Ā°C and 0.3 GPa. Which mineral? (At 600 Ā°C the kyanite line is at about 0.63 GPa and the andalusiteāsillimanite line at that pressure is near 520 Ā°C.)
The pressure 0.3 GPa is below the kyanite line at 600 Ā°C (0.63 GPa), so it is not kyanite. The temperature, 600 Ā°C, is higher than the andalusiteāsillimanite line (about 520 Ā°C at 0.3 GPa). So the mineral is sillimanite.
5. A rock at 300 Ā°C and 0.2 GPa is heated by magma to 700 Ā°C at the same pressure. Describe the change.
At 300 Ā°C and 0.2 GPa the rock sits in the andalusite zone. Moving right at 0.2 GPa we cross the andalusiteāsillimanite line at about 540 Ā°C. After that the stable mineral is sillimanite. So andalusite slowly changes to sillimanite (needle crystals), more completely the hotter it gets.
6. Kyanite is found in a rock at the surface. Does that mean the surface is high pressure?
No. Kyanite grew when the rock was buried deep, at high pressure. Later the rock was uplifted and eroded. Solid changes are slow and the surface is cold, so kyanite did not change back. It is metastable at the surface. It tells us the rock was once deep.
Common mistakes
- Thinking a phase diagram shows melting only. Many diagrams show changes between solid forms, with no melting at all.
- Reading the axes the wrong way round: pressure goes up the side and also means deeper.
- Thinking a mineral must change back when the rock reaches the surface. Slow solid changes leave metastable minerals behind.
- Thinking different minerals have different formulas. Andalusite, kyanite and sillimanite are all AlāSiOā ; only the structure differs.