The surface tension of CaO-SiO 2 -Al 2 O 3 system at 1 873 K was computed using a modified Butler's equation, and by making use of critically evaluated ionic surface distances of pure oxides involved in the system. For CaO-SiO 2 and CaO-Al 2 O 3 binary systems, the computed results are in good agreement with the experimental results reported by other researchers. For CaO-SiO 2 -Al 2 O 3 ternary system, the surface tension in a wide range of liquid compositional range was computed and the results were favorably compared with the experimental results reported in the literature. It was found that the surface tension increases with decreasing SiO 2 , and with increasing CaO or Al 2 O 3 . For a given SiO 2 content, the surface tension was relatively independent of the CaO/Al 2 O 3 ratio. An iso-surface tension diagram has been suggested for liquid CaO
Excess Free Energy of the SurfaceFor the alkali-halide system, Lumsden 8) calculated the heat of mixing of binary alkali-halide mixtures, and the heat of mixing was found to be proportional to the potential energy of mixing due to the non-polar London force and the polarization energy. Provided that the excess Gibbs free energy is mainly determined by the electric field arising from the polarization which is generated by the different ions having the same or different charge sign, the excess free energy can be obtained by partial differentiation of the heat of mixing and have the following proportionality with ionic distances. According to Lumsden,8) . (5) where k is the proportionality factor, the polarizability, Z coordination number, and z i valency of cation of i.Therefore the excess Gibbs free energy of i in the bulk phase can be expressed by Eq. (6).... (6) If the excess Gibbs free energy in the surface has the same function of temperature and compositions as that in the bulk, the excess Gibbs free energy of i in the surface phase can be expressed in a similar way. (7) where (Z S )Ј is the apparent coordination number in the surface under consideration of surface relaxation and z i is the ratio of the ionic distance in the surface phase to that in the bulk phase () represents the excess free energy if the bulk concentration of B had a value of N B S . Then the ratio of) can be then expressed as follows:.......... (8) whereIf the surface relaxation is not considered in the coordination number and ionic distance, the calculated results on the surface tension of molten ionic solutions including molten slags did not agree with the experimental values. 1) Therefore the surface relaxation structure as well as the coordination number should be considered in order to evaluate the surface tension of molten slag. This was pointed out by Tanaka et al. and almost the same relations in Eqs. (5)- (7) was applied to express the effect of the surface relaxation structure on the excess Gibbs energy in the surface. 1,2) The ratio (b) has the relationship with the heat of evaporation and the surface tension for the pure substance i as seen by Eq. (9). 4)Tanaka et al. 4) found tha...