Thermodynamic properties of aluminum, magnesium, and calcium in molten silicon

The thermodynamic properties of aluminum, magnesium, and calcium in molten silicon were investigated using a chemical equilibration technique at 1723 to 1848 K, 1698 to 1798 K, and 1723 to 1823 K, respectively. The activity coefficient of aluminum in molten silicon was determined by equilibrating molten silicon-aluminum alloys with solid Al2O3 and Al6Si2O13, that of magnesium was determined by equilibrating molten silicon-magnesium alloys and MgO-SiO2-Al2O3 melts doubly saturated with MgSiO3 and SiO2, and that of calcium was determined by equilibrating molten silicon-calcium alloys with SiO2-saturated CaO-SiO2 melts. The activity coefficients at infinite dilution relative to the pure liquid state were determined as follows: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{array}{*{20}c} {log \gamma _{Al(l) in Si}^ \circ = - \frac{{1570}}{T} + 0.236 (1723 to 1848 K)} \\ {log \gamma _{Mg(l) in Si}^ \circ = - \frac{{4900}}{T} + 1.96 (1698 to 1798 K)} \\ {log \gamma _{Ca(l) in Si}^ \circ = - \frac{{7670}}{T} + 1.53 (1723 to 1823 K)} \\ \end{array} $$ \end{document}