A thermodynamic model for determining the surface tension of molten ionic mixtures, derived by considering the ionic radii of the components, was extended to multi-component slag systems. The composition dependence of the surface tension in 6-component systems of the type CaO-SiO 2 -Al 2 O 3 -MgO-Na 2 O-CaF 2 was evaluated with the present model using information based on the surface tension and molar volume of the pure oxide components, and on the anionic and cationic radii. The evaluated results for the surface tension agree well with literature data.KEY WORDS: surface tension; molten slag; mold flux; ionic radius. ISIJ International, Vol. 47 (2007) Subscript i refers to the following components: SiO 2 , CaO, Al 2 O 3 , MgO, Na 2 O or CaF 2 . Subscripts A and X refer to the cations and anions of component i, respectively. Superscripts "Surf " and "Bulk" indicate the surface and bulk, respectively. R is the gas constant, T is the absolute temperature, s i Pure is the surface tension of the pure molten component i, which is treated as a model parameter.,corresponds to the molar surface area in a monolayer of pure molten component i (N 0 : Avogadro's number, V i : molar volume of the pure molten component i). N i P is the mole fraction of the component i in phase P (PϭSurf or Bulk). R A is the radii of the cation, and R X is the radii of the anion. undergo surface relaxation due to spontaneous changes in the ionic distance at the surface, which causes the energetic state of the surface to approach that of the bulk state. Thus, the contribution from excess Gibbs energy terms is neglected in Butler's equation.[2] In ionic substances, it is well known that their ionic structures depend upon the ratio of the cation to anion radii. In order to evaluate the ionic structures and physico-chemical properties of ionic materials, the cation to anion radii ratio should be considered. Data on the ionic radii were obtained from Shannon,9) and the molar volumes of the pure oxides recommended by Mills and Keene 10) were used in the present model. These values are listed in Tables 1 and 2, respectively.Regarding the temperature dependences of the surface tensions for pure SiO 2 and CaF 2 , those recommended by NIST 11) were used for the calculations in this study. The temperature dependences of the surface tension for pure CaO, Al 2 O 3 , MgO and Na 2 O were evaluated in previous work 7,8) and used in the current study. The equations for determining the temperature dependences of surface tension are listed in Table 3.
Results and Discussion
Quaternary SystemThe surface tension of molten slag for the CaO-SiO 2 -CaF 2 system was evaluated in the previous work. 8) Based on these results, 8) the effects of Al 2 O 3 , MgO or Na 2 O addition on the surface tension of the above ternary system were evaluated in this study. The calculated results for the surface tension are shown in Fig. 1. Figure 1(a) is based on the results obtained for the CaO-SiO 2 -CaF 2 system reported by Nakamoto et al. 8) The three lines in this figure indicat...
