Activities and volatilities of trace components in silicate melts: a novel use of metal–silicate partitioning data

Abstract

Ian Carmichael spent 45 years thinking about and working on the activities of components in silicate melts and their use to estimate physicochemical conditions at eruption and in the source regions of igneous rocks. These interests, principally in major components such as SiO2, led us to think about possible ways of determining the complementary activity coefficients of trace components in silicate melts. While investigating the conditions of accretion and differentiation of the Earth, a number of authors have determined the partitioning of trace elements such as Co, Ni, Mo and W between liquid Fe metal and liquid silicate. These data have the potential to provide activity information for a large number of trace components in silicate melts. In order to turn the partitioning measurements into activities, however, we need to know the activity coefficient of FeO, γFeO in the silicate. We obtained γFeO as a function of melt composition by fitting a simple model to 83 experimental data for which the authors had measured the FeO content of the silicate melt in equilibrium with metal (Fe-bearing alloy) at known fO2. The compositional dependence of γFeO is weak, but, when calculated in the system Diopside–Anorthite–Forsterite, it decreases towards the Forsterite apex. A similar approach for Ni, for which twice as many data are available, leads to similar composition dependence of activity coefficient and confirms the suggestion that γNiO/γFeO is almost constant over a wide range of silicate melt composition. The activity coefficients for FeO were used in conjunction with measured Mo and W partitioning between Fe-rich metal and silicate melt to estimate activity coefficients for trace MoO2 and WO3 dissolved in silicate melt. When combined with data on Mo- and W-saturated silicate melts a strong dependence of activity coefficient is observed. Calculated in the system Diopside–Anorthite–Forsterite, both MoO2 and WO3 exhibit similar behaviour to FeO and NiO in that activity coefficients decrease as Forsterite content increases. The effect is much larger for Mo and W, however, γMoO2 and γWO3 varying by factors of 20 and nearly 100, respectively, in this system. In order to illustrate the potential applications of the metal–silicate partitioning approach to determine the activity coefficients of volatile elements, we used it to determine activity coefficients of PbO, CuO0.5 and InO1.5 in a silica-saturated melt at 1,650 °C. We find values of 0.22, 3.5 and 0.02, respectively, indicating a strong dependence on cation charge. The value for CuO0.5 is in excellent agreement with experimental data of Holzheid and Lodders (Geochim Cosmochim Acta 65:1933–1951, 2001), which shows that the method is viable. When combined with thermodynamic data on the gas species, we find that Pb is the most volatile of the 3 elements under ‘normal’ terrestrial conditions of oxygen fugacity but that In should become the most volatile under strongly reducing conditions such as those of the solar nebula. The oxygen fugacity dependence of volatility has implications for the high relative abundance of In in silicate Earth. We conclude that metal–silicate partitioning experiments are a viable means for determining activities of trace components in silicate melts and are particularly useful if the metal of the element is unstable or volatile at igneous temperatures.