Quartz Solubility and Thermodynamics Above the Upper Critical End Point

Silica is among the most abundant solutes in crustal and mantle fluids, especially at conditions nearing the upper critical end point of the SiO2-H2O system (~10 kbar, 1080 °C). However, the solubility of silica is not well determined at higher pressures. In addition, the thermodynamic mixing relations of the supercritical SiO2-H2O system are poorly known. We made new measurements on quartz solubility in H2O at 15 and 20 kbar at 900-1100 °C. At SiO2 mole fraction below 0.1, solubility was determined by weight loss of single crystals equilibrated with H2O. At higher SiO2 concentrations, solubility was determined by bracketing the presence of absence of quartz in charges with known bulk SiO2 concentration. The measured solubilities imply that there is a solubility minimum above 1050 °C between 10 and 20 kbar. Quartz solubility measurements from Manning (1994), Newton and Manning (2003; 2008), Nakamura (1975) and this study were fitted to a modified sub-regular solution model. A term representing the Gibbs free energy (ΔGr) of the reaction 1/2 H2O + 1/2 O2- = OH- (the depolymerization reaction that occurs when silica is dissolved in water) was added to the free energy of mixing parameterization. Thirteen independent parameters describe the T and P variation of the weak sub-regular interaction terms (Ws and Wh) and the strong interaction term (ΔGr). Nine of the parameters are linear in T and P, and the other four are quadratic: Ws and ΔGr vary with P2, and ΔGr also varies with T2 and PT. The average error between the data and the model is 5%. Because the Gibbs free energy change of the depolymerization reaction is included in the fit, the model predicts an average state of aqueous silica polymerization of solutions in equilibrium with quartz at P between 10 and 20 kbar and T above 500 °C. The results also highlight what can be inferred from the steep hydrothermal melting curve of quartz - that while pressure does determine whether the system is subcritical or supercritical, it has a comparatively minor effect on the transition from an H2O-rich fluid to an SiO2-rich fluid. Whether due to melting or complete miscibility, the composition of a fluid in equilibrium with quartz increases dramatically between 900 and 1100 °C.