Equation of state for carbonate liquids and iron oxide- and titanium dioxide-bearing silicate liquids

An equation of state (P-V-T relation) for magmatic liquids is essential for calculations of equilibrium mineral-liquid phase relations at pressure, for determining the direction and velocity of magma transport in the Earth, and in a broad sense, for understanding the differentiation and evolution of the Earth and other planets. One bar density, thermal expansivity, compressibility (beta) or bulk modulus (K = 1/beta), and its pressure dependence (K' = dY/dP) are determined employing double-bob Archimedean method, frequency sweep interferometry, and fusion curve analysis respectively on carbonate liquids and Fe2O3- and TiO2-bearing alkali silicate liquids. The partial molar volume and thermal expansivity for CaCO3 and other alkali carbonate components are derived for the first time, from which densities of carbonate liquids can be calculated at 1 bar. To extrapolate the density calculation to high pressure, it is required to incorporate a K' value in the model. The fusion curve analysis on K2CO3 places a tight constraint on the liquid K' value, which is 14.1 +/- 1.1, a much higher value than that of silicate liquids (< 10). This result suggests that K2CO3 liquid remains strongly buoyant in the deep mantle and is highly unlikely to be a significant carbon sink in the mantle transition zone atop of 410 km seismic discontinuity. It also supports the hypothesis that highly compressible liquids at one bar have correspondingly high K' value (Lange, 2003).; One bar density measurements on the Na(K)2O-Fe2O 3-FeO-SiO2 liquids gave a compositionally independent partial molar volume (V¯Fe 2O3 = 41.52 cm3/mole, reflecting an average Fe3+ coordination number between 4.5 and 5.0) and zero thermal expansivity for the Fe2O3 component. The lack of strong compositional or temperature dependence to V¯Fe2O 3, in contrast to what is observed in the literature for V¯ TiO2 in similar melts, may reflect the different geometries for [5]Fe3+ and [5]Ti4+ (trigonal bipyramid vs. square pyramid). Sound speed measurements on the Na2O-TiO2-SiO2 liquids indicate that TiO2 component is 3--15 times more compressible than SiO2 and Na2O components. The strong correlation between the partial molar sound speed (c¯ TiO2) and thermal expansivity (∂V¯ TiO2/∂T) for TiO 2 component indicate that they do not correspond to the average Ti coordination, but reflect the relative abundance of [5]Ti4+.