HR: 0830h
AN: V41C-0307    [PDF]
TI: Calibration of a new Model for Estimating the Density, Coefficient of Thermal Expansion, Sound Speed, and Compressibility of Multicomponent Silicate Liquids at Reference Pressure
AU: * Ghiorso, M S
EM: ghiorso@geosci.uchicago.edu
AF: University of Chicago, Hinds Geophysical Laboratory 5734 S Ellis Ave, Chicago, IL 60637 United States
AU: Kress, V C
EM: kress@u.washington.edu
AF: University of Washington, Dept Earth and Space Sciences Box 351310, Seattle, WA 98195 United States
AB: Ghiorso (2000, EOS 81[48], F1295) proposed a new equation of state for molten silicate liquids. This equation is designed to facilitate the extrapolation of reference pressure volumetric data to pressures in the Earth corresponding to the base of the mantle transition zone. Extrapolation is performed with a minimal number of adjustable parameters and avoids the singularities and instabilities associated with the Birch-Murnaghan and Vinet equations when these are applied to silicate melts. Here, we calibrate reference pressure (10$^{5}$ Pa) parameters for the proposed silicate liquid equation of state from literature data on measurements of densities and sound speeds of molten liquids and from volumetric measurements on supercooled liquids obtained at their glass transition temperatures. A model for the temperature- and compositionally-dependent, reference-pressure volume (density) in the system K$_{2}$O-Na$_{2}$O-CaO-MgO-FeO-NiO-CoO-Fe$_{2}$O$_{3}$-Al$_{2}$O$_{3}$-TiO$_{2}$-SiO$_{2}$ is obtained for liquids with CaO mole fraction $<$ 0.5. Precision of data recovery is 0.55% for Fe-absent liquids and 0.95% for Fe-bearing liquids. 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 compositionally-dependent relaxed sound speed in the system K$_{2}$O-Na$_{2}$O-CaO-MgO-FeO-Fe$_{2}$O$_{3}$-Al$_{2}$O$_{3}$-TiO$_{2}$-SiO$_{2}$ is obtained. Precision of data recovery is 1.7%. In contrast to previous workers, we find that effect of pressure on the volume of silicate melts ({\it i.e. dV/dP}) is more accurately assessed by first calibrating a model equation for the speed of sound and subsequently using this calibration to calculate a value for {\it dV/dP}, rather than estimating {\it dV/dP} for each experimental datum from the sound speed and modeling the derived quantity directly. Linear mixing relations for model parameters are utilized in calibrations of both the density and the sound speed with the addition of a quadratic composition term in Na$_{2}$O and SiO$_{2}$ required to accurately reproduce sound speed measurements. The resulting mixing relations for {\it dV/dP} at the reference pressure are weakly non-linear. The mathematical structure of the equation of state renders the volume of mixing a non-linear function of composition at elevated pressure.
DE: 3919 Equations of state
DE: 8439 Physics and chemistry of magma bodies
SC: Volcanology, Geochemistry, Petrology [V]
MN: 2003 Fall Meeting