Water in the deep Earth: The dielectric constant and the solubilities of quartz and corundum to 60 kb and 1200 °C

Comprehensive quantitative theoretical evaluation of water–rock interactions in the Earth has long been restricted to a pressure of 5.0 kb – too low to address processes involving deep aqueous fluids. Yet such fluids are thought to play an important role in the long-term geologic cycling of many chemical elements. A reason for this restriction is the lack of information on the dielectric constant of water (εH2OεH2O) needed for the revised Helgeson–Kirkham–Flowers (HKF) equations of state for aqueous species. Equation of state coefficients are available for hundreds of aqueous species in SUPCRT92, but calculations using these species can only be made to 5.0 kb (Shock et al., 1992).In the present study, the applicability of the revised HKF equations of state for aqueous species was extended to 60 kb by developing estimates of (εH2OεH2O). We used a statistical mechanically-based equation for the dielectric constant of a hard-sphere fluid applicable to water (Franck et al., 1990). The equation was calibrated with experimental data, and data from a comprehensive analysis of the literature (Fernández et al., 1997), and then used to calculate (εH2OεH2O) to a density of 1.1 g cm−3. The values of ln(εH2Oln(εH2O) were found to be linear with ln(ρH2OρH2O) which enabled empirical extrapolation of (εH2OεH2O) to 60 kb. Values of ρH2OρH2O were computed with a recent comprehensive evaluation consistent with experimental data and a molecular dynamics model for water (Zhang and Duan, 2005).The resulting dielectric constants were tested at 727 °C and 58 kb by comparison with the results of ab initio molecular dynamics calculations ( Pan et al., 2013). Additional testing was carried out by computing standard Gibbs free energies of aqueous species using the new values of (εH2OεH2O) and ρH2OρH2O in the revised HKF equations to predict equilibrium constants which in turn enabled calculation of the solubilities of quartz and corundum for comparison with experimental measurements to 20 kb and 1100 °C. Our results strongly suggest that geochemically useful predictions can now be made that will facilitate analysis of water–rock interactions in the Earth at depths much greater than previously possible.