Role of basicity and tetrahedral speciation in controlling the thermodynamic properties of silicate liquids, part 1: the system CaO-MgO-Al 2 O 3 -SiO 2

Activity coefficients of oxide components in the system CaO-MgO-Al2O3-SiO2 (CMAS) were calculated with the model of Berman (Berman R. G., “A thermodynamic model for multicomponent melts with application to the system CaO-MgO-Al_2O_3-SiO_2,” Ph.D. dissertation, University of British Columbia, 1983) and used to explore large-scale relationships among these variables and between them and the liquid composition. On the basis of Berman’s model, the natural logarithm of the activity coefficient of MgO, ln(γ_(MgO)^(Liq)), and ln(γ_(MgO)^(Liq)/γ_(SiO)_2^(Liq)) are nearly linear functions of ln(γ_(CaO)^(Liq)). All three of these variables are simple functions of the optical basicity Λ with which they display minima near Λ ∼ 0.54 that are generated by liquids with low ratios of nonbridging to tetrahedral oxygens (NBO/T) (<0.3) and a mole fraction ratio, X_(SiO)_2^(Liq)/X_(Al2O)_3^(Liq), in the range 4 to 20. Variations in ln(γ_(CaO)^(Liq)) at constant Λ near the minimum are due mostly to liquids with (X_(CaO)^(Liq) + X_(MgO)^(Liq))/X_(Al)_2O_3^(Liq) < 1. The correlations with optical basicity imply that the electron donor power is an important factor in determining the thermodynamic properties of aluminosilicate liquids. For a constant NBO/T, ln(γ_(CaO)^(Liq)/γ_(Al)_2O_3^(Liq)) and ln(γ_(MgO)^(Liq)γ_(Al)_2O_3^(Liq)) form curves in terms of X_(SiO)_2^(Liq)/X_(Al)_2O_3^(Liq). The same liquids that generate minima in the Λ plots are also associated with minima in ln(γ_(CaO)^(Liq)γ_(Al)_2O_3^(Liq)) and ln(γ_(MgO)^(Liq)γ_(Al)_2O_3^(Liq)) as a function of X_(SiO)_2^(Liq)/X_(Al)_2O_3^(Liq). In addition, there are maxima or sharp changes in slope for NBO/T > 0.3, which occur for X_(SiO)_2^(Liq)/X_(Al)_2O_3^(Liq) ranging from ∼0 to ∼6 and increase with increasing NBO/T. The systematic variations in activity coefficients as a function of composition and optical basicity reflect underlying shifts in speciation as the composition of the liquid is changed. On the basis of correlations among the activity coefficients, it is likely that the use of CaO, an exchange component such as SiMg_(−1) and two of MgO, CaAl_2O_4, or MgAl_2O_4 would yield significant savings in the number of parameters required to model the excess free energy surface of liquids over large portions of CMAS relative to the use of oxide end members. Systematic behavior of thermodynamic properties extends to small amounts of other elements dissolved in otherwise CMAS liquids. For example, ln(X_(Fe)_(2+)^(Liq)/X_(Fe)_(3+)^(Liq)) at constant oxygen fugacity is linearly correlated with ln(γ_(CaO)^(Liq)). Similarly, ln(CS), where CS is the sulfide capacity is linearly correlated at constant temperature with each of the optical basicity, ln(a_(CaO)^(Liq)) and ln(γ_(CaO)^(Liq)), although the correlation for the latter breaks down for low values of Λ. The well-known systematic behavior of sulfide capacity as a function of optical basicity for systems inside as well as outside CMAS suggests that ln(γ_(CaS)^(Liq)) is also a simple function of optical basicity and that the relationships observed among the activity coefficients in CMAS may hold for more complex systems.