Abstract:
In order to simplify the computation of phase relations in multicomponent systems, a generalized excess function based on Margules-type polynomials is presented. It includes a versatile extrapolation method to higher order systems. A less-common formulation of the Gibbs-Duhem equation is used to compute the activity coefficient from Gxs, omitting additional constraints on the derivatives such as constant (xn + xm) or (xn/xm). The extrapolation of binary excess functions is applied to the ternary model system CaO-SiO2-TiO2 with emphasis on coexisting liquids. Because very few experimental data are available on the miscibility gaps in this system, we determined the compositions of coexisting liquids at 1600°C and 1 bar. Experimental phase relations are reproduced in detail using the proposed extrapolation of binary excess functions. An additional ternary parameter is not required. Non-ideal contributions to the excess Gibbs free energy of the melt in binary systems are modelled with Margules polynomials. Excess parameters of the melt and thermochemical standard state values of the liquid oxides and some crystalline compounds were determined using linear programming methods.
