Abstract The solubilities of andalusite, kyanite, sillimanite, mullite, tridymite and quartz are measured in liquids of the Al 2O 3-SiO 2-Na 3AlF 6 system at 1010 and 800°C. It is shown that the Gibbs free energy of solid phases in the Al 2O 3SiO 2- system can be simply related to the activity of silica in the liquid with which they are in equilibrium. When a SiO 2 is calculated according to the model of Temkin for fused salts the free energy relations in calories are as follows. At 1010°C; sillimanite → andalusite, ΔG = 75; sillimanite → 1 3 (mullite + tridymit), ΔG = 345; sillimanite → corundum + tridymite, ΔG = 1273. At 800°C; sillimanite → andalusite, ΔG = 24; sillimanite → 1 3 (mullite + quartz), ΔG = 598; sillimanite → kyanite, ΔG = 1293; sillimanitemanite → corundum + quartz, ΔG = 1341. A pressure-temperature phase equilibrium diagram is calculated for the solid portion of the Al 2O 3-SiO 2 system which gives a triple point, andalusitekyanite-sillimanite at approximately 410°C, 2400 bars. The P H 2 O - T equilibrium curve for the reaction muscovite + quartz ⇆ K-feldspar + sillimanite + H 2O is found to lie approximately 60–80°C below the curve for the simple breakdown of muscovite.