**An
Equation of State for Silicate Melts. II. Calibration of Volumetric Properties
at 10**^{5} 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 (10^{5} 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 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. 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 TiO_{2}. Liquids in the system CaO-Al_{2}O_{3}-SiO_{2}
with molar ratios of CaO/SiO_{2} < 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} (Fe_{2}O_{3})
and FeO_{1.3} (Fe_{0.4}^{2+}Fe_{0.6}^{3+}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 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 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.**