PREDICTION OF ACTIVITIES OF OXIDE COMPONENTS IN THE MULTICOMPONENT LIQUID SYSTEM Fe0-MgO-CaO-Na2O-Al01.5-Si02;

Calculation of chemical equilibria involving a liquid requires a full knowledge of chemical potentials (or activities) of all the oxide components present in the liquid phase. This is a rigorous requirement compared to that for solid compounds, where only total free energies need to be known in order to calculate their stabilities relative to other compounds; obviously the difference stems from the lack of a stoichiometric requirement for liquids. The determination (or prediction) of activities of the components in oxide liquids is critical for understanding not only terrestrial and planetary igneous processes, but also chemical fractionations that occurred in the solar nebula. It is plausible that near the midplane of the accretionary disk proportions of rock-forming metallic elements and oxygen were enhanced relative to hydrogen. This would raise the condensation temperatures of oxides [I], possibly above the solidus temperature of oxide mixtures. Chondrules and oncemolten Ca,Al-rich inclusions (CAIs) testify to the existence of liquid phases in the nebula (though of course these might be products formed under non-equilibrium conditions). Activities of oxide components have been measured experimentally for many binary silicate solutions, but in most cases the compositional ranges studied are limited; experimental data are scarce for liquids containing more than two components, with the exception of a few ternary systems such as Ca0-A101.5-SiOz [2]. However, a recent experiment using a CAI-analog liquid [3] is promising. A fourth-degree Margules expansion has been used to predict the thermodynamic properties of mixing in a Mg0-Ca0-Al203-Sia liquid [4]. This model, however, has a rather serious problem: it treats the thermodynamic quantities of simple oxide liquids (i.e. reference values for complex compounds) as adjustable parameters, and the adopted values for them are different from those in literature, beyond the 20 uncertainty limits of the latter. A modified quasichemical model for binary silicate liquids has been developed, and expanded to include a third component [5]. In contrast to the model described above, which is basically mathematical, the latter scheme actually describes interactions between constituents by considering M "particles" (Mg, Ca, etc.) and Si particles to mix in a cationic quasilattice. This model, however, does not include aluminum oxide, which is an essential component of rocks and magmas. I have developed a model for mixing the six oxide components in the liquid system Fe0-Mg0-Ca0Na20-Al01.5-Si02, which is described below. This system can be regarded as a mixture of subsystems that consist of binary solutions of a cationic oxide (MO or M20) with an anionic oxide (SiO2 or AlOl.5). There are two possible ways of assembling these subunits into the final six-component solution. One would be to produce the two quinary systems, Fe0-Mg0-Ca0-Na20-Si02 and Fe0-Mg0-Ca0-Na20-All.5, by forming ideal mixtures of the four binary silicate liquids and the four binary aluminate liquids, respectively. Richardson [6] has shown that the free energy of mixing between the liquids (MnO),.(SiO~)l., and (FeO),.(SiOz)l-, (O<x<l) is well approximated by ideal mixing between Mn and Fe sites. This indicates that the mixing effect is due to a configurational change in M sites; Si%, being common to the two binaries, does not change configuration during mixing. The application of his method to mixing between CaO-Si& and Na2O-Si& liquids [7] and between CaO-Si02 and MgO-Si02 also supports such mixing behavior. One could assume that ideal mixing also holds in cation exchange between binary aluminate liquids. In the next step the mixed silicates and aluminates would be brought into a single solution. In this step, however, ideal mixing is not a good approximation: it is known from existing activity data [2] that Si& and Al01.5 mix nonideally when Ca-silicate and Ca-aluminate are combined, although mixing between Mg-silicate and Mg-aluminate occurs nearly ideally. Since it is difficult to deal with these different effects in the final mixing step, I have not used this procedure. In the alternative method, which was eventually adopted, silicate and aluminate binaries that have a common M cation are first mixed. This enables the effects of different M species on the mixing of Si and A1 to be dealt with separately. Ideal mixing was assumed when M = Fe and Mg, while non-ideal mixing was used for M = Ca and Na. The four alumino-silicate liquids thus produced were then mixed ideally: only cation exchange in the M sites needs to occur, since the four subsystems can be mixed so as to have the same SiIAI ratios from the outset. The modified quasichemical model of [51 was adopted to provide activities of oxide components in the binary silicate solutions that are created at the start of mixing. In the case of binary aluminate solutions, for which the quasichemical model was not intended, I used the conqept of "basicities" of cationic oxides proposed by [a]. Basicity is a measure of the degree of interaction between network-modifying cationic species (MO and MzO) and network-forming anionic species (Si02 and AlO1.5), and is approximately represented by an extremum (the top of a negative cusp) on the free energy surface of mixing of an M-silicate or M-aluminate solution. I assumed that the