What you must learn:

• The topology of the Al₂SiO₅ phase diagram.
• The physical basis for the relative stabilities of the phases at P and T.

Thermodynamics and Phase stabilities

The stability of a phase at a given pressure P and temperature T is conveniently expressed in terms of its Free Energy:

G = U - TS + PV

Here, U is the internal energy, S is the entropy and V is the volume. From the geochemistry module, you might be more familiar with the enthalpy H rather than U. The two quantities are related by H = U + PV. When atoms come together to make a crystal, they want to make G a large negative number. They can do this by making U (or H) a large negative number. At high temperature, however, they might find that going to a new structure with a slightly higher U but an even larger S may give a decrease in the free energy. At high pressure, they will try to make V as small as possible. The structure which is adopted reflects the compromise between U, TS and PV.

Stabilities of the Al₂SiO₅ Polymorphs

We can apply the ideas discussed above to the Al₂SiO₅ polymorphs. The three Al₂SiO₅ polymorphs minerals are very important in metamorphic petrology as they are indicators of metamorphic grade (i.e., metamorphic facies or isograds).

Structures of the Al₂SiO₅ Polymorphs

We can understand the relative stabilities of the Al₂SiO₅ polymorphs in terms of their structures.

Andalusite		Andalusite, VIAlVAlO[SiO4] has Al in 6 and 5-fold coordination giving the largest molar volume (V= 51.3 cm3/mole) of the three polymorphs; It is stable at the lowest pressures. The entropy (S(298K)= 93.22 J/mol-K) is intermediate between that of kyanite and sillimanite. The unit cell is orthorhombic.
Kyanite		Kyanite, VIAl2O[SiO4] has all of the Al in 6-fold coordination giving the most dense structure (V = 44.09 cm3/mol). Kyanite is stable at high pressure. However, the high density and low symmetry (triclinic) means it has the lowest entropy S(298 K) = 83.22 J/mol-K. If you look carefully at the unit cell, you can see that it is triclinic.
Sillimanite		Sillimanite, VIAl[IVAlSiO4] has the greatest entropy (S(298K) = 96.11 J/mol-K) because it has a high symmetry (orthorhombic). The molar volume is V =49.9 cm3/mole. The unit cell is orthorhombic.

Optical Properties of Al₂SiO₅ Polymorphs

Mineral	Kyanite	Andalusite	Sillimanite
System	Triclinic	Ortho	Ortho
Optic Sign	(-)	(-)	(+)