Abstract
Determination of the physicochemical properties of solutions is important for industrial applications. Geometrical models, specifically the “mass triangle model” and a new model, have been utilized to calculate the viscosity and surface tension of CaO–SiO2–CaF2 slags based on the corresponding ternary system boundary data within the partially soluble region. The two models are validated with available experimental data in terms of viscosity and surface tension. Results reveal that the models are capable of estimating the physicochemical properties of the ternary system with limited solubility with high accuracy. The new model predicts the viscosity better, but the mass triangle model may perform better for the surface tension predictions. It is expected that these two solution models could be applied to the calculation of physicochemical properties of more ternary systems with limited solubility, especially when the systems are with high melting points or/and volatile components and/or easily oxidized or reduced components.
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References
Chou, K.C.: A general solution model for predicting ternary thermodynamic properties. Calphad 19, 315–325 (1995)
Wang, X.D., Bao, H., Li, W.C.: Estimation of viscosity of ternary-metallic melts. Metall. Mater. Trans. 33A, 3201–3204 (2002)
Arslan, H.: Analytical determination of partial and integral properties of the six components systems Ni–Cr–Co–Al–Mo–Ti and their subsystems. Phys. B: Condens. Matter 438, 48–52 (2014)
Scatchard, G.: Solutions of nonelectrolytes. Annu. Rev. Phys. Chem. 3, 259–274 (1952)
Scatchard, G., Ticknor, L.B., Goates, J.R., McCartney, E.R.: Heats of mixing in some non-electrolyte solutions. J. Am. Chem. Soc. 74, 3721–3724 (1952)
Scatchard, G., Ticknor, L.B.: Vapor–liquid equilibrium. IX. The methanol–carbon tetrachloride–benzene system. J. Am. Chem. Soc. 74, 3724–3729 (1952)
Kohler, F.: Estimation of the thermodynamic data for a ternary system from the corresponding binary systems. Monatsh. Chem. 91, 738–740 (1960)
Bonnier, E., Caboz, R.: Sur l'estimation de l'enthalpie libre de mélange de certains alliages métalliques liquides ternaires. C. R. Hebd. Seances Acad. Sci. 250, 527–529 (1960)
Tsao, C.C., Smith, J.M.: Heat of mixing of liquids. “Applied thermodynamics”. Chem. Eng. Prog. Symp. Ser. 49, 107–117 (1953)
Chou, K.C.: Application of phenomenological theory to chemical metallurgy. ISIJ Int. 58, 785–791 (2018)
Hillert, M.: Empirical methods of predicting and representing thermodynamic properties of ternary solution phases. Calphad 4, 1–12 (1980)
Chou, K.C., Chang, Y.A.: A study of ternary geometrical models. Ber. Bunsenges. Phys. Chem. 93, 735–741 (2010)
Arslan, H., Dogan, A.: Determination of surface tension of liquid ternary Ni–Cu–Fe and sub-binary alloys. Philos. Mag. 99, 1206–1224 (2019)
Colinet, C.: Estimation des grandeurs thermodynamiques des alliages ternaries. University of Grenoble, France (1967)
Muggianu, Y.M., Gambino, M., Bros, J.P.: Enthalpies of formation of liquid alloy bismuth–gallium–tin at 723 K. Choice of an analytical representation of integral and partial excess functions of mixing. J. Chim. Phys. 72, 83–88 (1975)
Lück, R., Gerling, U., Predel, B.: Interpolation algorithms for thermodynamic functions of mixtures in multicomponent systems from binary boundary systems. Z. Metallkd. 77, 442–446 (1986)
Chou, K.C.: A new solution model for predicting ternary thermodynamic properties. Calphad 11, 293–300 (1987)
Toop, G.W.: Predicting ternary activities using binary data. Trans. Metall. Soc. AIME 233, 850–855 (1965)
Chou, K.C., Li, W.C., Li, F.S., He, M.G.: Formalism of new ternary model expressed in terms of binary regular-solution type parameters. Calphad 20, 395–406 (1996)
Gomidželović, L., Živković, D., Balanović, L., Manasijevic, D.: Ternary Au-Ga-Sb system: calculation of thermodynamic properties using general solution model. Rare Met. 35, 262–268 (2016)
Gomidželović, L., Kostov, A., Živković, D., Krstić, V.: Analytic approach to alloys thermodynamics: ternary Cu–Ga–Ni system. Mater. Res. 19, 1026–1032 (2016)
Živković, D., Grgurić, T.H., Gojić, M., Ćubela, D., Šimišić, Z.S., Kostov, A., Kožuh, S.: Calculation of thermodynamic properties of Cu––(Ag, Au) shape memory alloy systems. Trans. Indian Inst. Met. 67, 285–289 (2014)
Maniani, M.E., Chaar, R.M., Moudane, M.E., Sabbar, A.: Comparative study of thermodynamic predicting methods applied to the Au–In–Zn ternary system. Mater. Environ. Sci. 5, 2045–2051 (2014)
Zhang, G.H., Chou, K.C.: General formalism for new generation geometrical model: application to the thermodynamics of liquid mixtures. J. Solution Chem. 39, 1200–1212 (2010)
Chou, K.C., Wei, S.K.: A new generation solution model for predicting thermodynamic properties of a multicomponent system from binaries. Metall. Mater. Trans. 28B, 439–445 (1997)
Chou, K.C., Zhong, X.M., Xu, K.D.: Calculation of physicochemical properties in a ternary system with miscibility gap. Metall. Mater. Trans. 35B, 715–720 (2004)
Chou, K.C., Yu, Z.G.: Calculation of the physicochemical properties for ternary solution with limited solubility. Ceram. Int. 44, 20955–20960 (2018)
Živković, D., Du, Y., Talijan, N., Kostov, A., Balanović, L.: Calculation of thermodynamic properties in liquid phase for ternary Al–Ni–Zn alloys. Trans. Nonferrous Met. Soc. China 22, 3059–3065 (2012)
Wang, L.J., Chou, K.C., Seetharaman, S.: A comparison of traditional geometrical models and mass triangle model in calculating the surface tensions of ternary sulphide melts. Calphad 32, 49–55 (2008)
Yu, Z.G., Leng, H.Y., Wang, L.J., Chou, K.C.: Computational study on various properties of CaO–Al2O3–SiO2 mold flux. Ceram. Int. 45, 7180–7187 (2019)
Yu, Z.G., Luo, Q., Zhang, J.Y., Chou, K.C.: An insight into the viscosity prediction of ternary alloys with limited solubility. Philos. Mag. 99, 2408–2423 (2019)
Yu, Z.G., Leng, H.Y., Luo, Q., Zhang, J.Y., Chou, K.C.: Geometrical modelling of the physicochemical properties of CaO–Al2O3–CaF2 slag at 1873 K. Ceram. Int. 46, 8075–8081 (2020)
Shahbazian, F., Sichen, D., Mills, K.C., Seetharaman, S.: Experimental studies of viscosities of some CaO–CaF2–SiO2 slags. Ironmak. Steelmak. 26, 193–199 (1999)
Park, J.H., Min, D.J., Song, H.S.: The effect of CaF2 on the viscosities and structures of CaO–SiO2(–MgO)–CaF2 slags. Metall. Mater. Trans. 33B, 723–729 (2002)
Herty, C.H., Hartgen, F.A., Frear, G.L., Royer, M.B.: Temperature-viscosity measurement in the systems CaO–SiO2 and CaO–SiO2–CaF2. U. S. Bur. Mines Rep. Invest. R.I. 3232, 1–31 (1934)
Okabe, Y., Tajima, I., Ito, K.: Thermodynamics of chromium oxides in CaO–SiO2–CaF2 slag. Metall. Mater. Trans. 29B, 131–136 (1998)
Shiraishi, Y., Saitô, T.: The viscositys of CaO–SiO2–alkaline earth fluoride systems (on the viscosity of molten slags, (I)). Nippon Kinzoku Gakki 29, 614–622 (1965)
Ejima, A., Shimoji, M.: Effect of alkali and alkaline-earth fluorides on surface tension of molten calcium silicates. Trans. Faraday Soc. 66, 99–106 (1970)
Wang, C., Zhang, J.L., Liu, Z.J., Jiao, K.X., Wang, G.W., Yang, J.Q., Chou, K.C.: Effect of chlorine on the viscosities and structures of CaO–SiO2–CaCl2 slags. Metall. Mater. Trans. 48B, 328–334 (2017)
Acknowledgements
This work was financially supported by the China Postdoctoral Science Foundation (No. 2018M631339), the Fundamental Research Funds for the Central Universities (No. FRF-TP-18-008A1) and the Key Program of the National Natural Science Foundation of China (No. 51734002).
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Wang, C., Chou, KC. & Yu, ZG. Determination of Viscosity and Surface Tension for CaO–SiO2–CaF2 Slags. J Solution Chem 49, 863–874 (2020). https://doi.org/10.1007/s10953-020-00998-w
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DOI: https://doi.org/10.1007/s10953-020-00998-w