An Equation of State for Silicate Melts. II. Calibration of Volumetric Properties at 10⁵ Pa

Mark S. Ghiorso and Victor C. Kress

American Journal of Science, vol. 304, October/November 2004, p 679-751

The full-text article can be downloaded at M. Ghiorso’s website.

Abstract: Reference pressure (10⁵ Pa) parameters for the silicate liquid equation of state of Ghiorso (2004a) are calibrated from literature data on measurements of densities and sound speeds. A model for the temperature- and compositionally-dependent, reference-pressure volume (density) in the system K₂O-Na₂O-CaO-MgO-FeO-NiO-CoO-Fe₂O₃-Al₂O₃-TiO₂-SiO₂ is obtained. Precision of data recovery is 0.76 percent (one root-mean-square residual). Linear mixing relations for model parameters are utilized in this calibration with the inclusion of quadratic terms between soda and titania and potash and titania to account for the effect of alkali metals on the partial molar volume of TiO₂. Liquids in the system CaO-Al₂O₃-SiO₂ with molar ratios of CaO/SiO₂ < 0.5 are excluded from this analysis in order to avoid the inclusion of additional non-linear terms. Iron-bearing systems are modeled by first "speciating" the liquid to obtain molecular proportions of FeO, FeO_1.5 (Fe₂O₃) and FeO_1.3 (Fe_0.4²⁺Fe_0.6³⁺O_1.3). Partial molar properties are extracted for all three iron oxides. This procedure is followed because (1) it affords an internally consistent means of extrapolating previously calibrated models of iron-redox equilibria in silicate melts to elevated pressure, and (2) it results in significant improvements in model recovery of density measurements on Fe-bearing systems. The model partial molar volume of FeO_1.3 is ~12 percent smaller than a linear combination of the fully oxidized and reduced endmembers. Internally consistent expressions for the reference pressure compressibility and its temperature dependence are formulated from a calibration of sound speeds in molten liquids. A model for the temperature- and compositionallydependent sound speed in the system K₂O-Na₂O-CaO-MgO-FeO-Fe₂O₃-Al₂O₃-TiO₂-SiO₂ is obtained. Precision of data recovery is 1.7 percent. Mixing relations identical to the volume model are adopted for consistency with the inclusion of an additional quadratic composition term in soda and alumina.

Glass Melt Density Calculation by Fluegel et al.