Abstract
Our recently developed model to describe the viscosity of binary silicate melts is extended to describe and predict the viscosities of multicomponent silicate melts. The viscosity of multicomponent melts containing no AlO1.5 is modeled to vary linearly as a function of the mole fractions of the basic oxides at constant SiO2 mole fraction. Systems containing AlO1.5 show a more or less pronounced viscosity maximum close to the charge compensating composition. This maximum is caused by some of the Al3+ taking on the same structural role as Si4+, thereby participating in the formation of the silica network. The network-forming Al3+ must remain associated with either one Na+, or two Al3+ ions must remain associated with one Mg2+ or Ca2+, in order to assure charge neutrality. To take this into account we introduce the associates NaAlO2, CaAl2O4 and MgAl2O4 that correspond to charge compensated network-forming Al3+. The Gibbs energy of formation of these associates determines the amount of Al3+ that takes on the network-forming role. We assume the effect on viscosity of network-forming Al3+ to be the same as Si4+ and optimize the Gibbs energies of the associates to reproduce the experimental viscosity data. Viscosities in ternary silicate systems without AlO1.5 are quantitatively predicted with no additional ternary model parameters. Ternary systems MeOx – SiO2 – AlO1.5 are modeled with only two temperature-independent ternary parameters per system. The model not only reproduces the magnitude of the observed viscosity maximum, but also its complex shape, asymmetry and temperature dependence.
References
[1] A.N.Grundy, H.Liu, I.-H.Jung, S.A.Decterov, A.D.Pelton: Int. J. Mat. Res., this issue.Search in Google Scholar
[2] E.F.Riebling: J. Chem. Phys.44 (1966) 2857–2865.10.1063/1.1727145Search in Google Scholar
[3] M.J.Toplis, D.B.Dingwell, T.Lenci: Geochim. Cosmochim. Acta61 (1997) 2605–2612.10.1016/S0016-7037(97)00126-9Search in Google Scholar
[4] E.F.Riebling: Can. J. Chem.42 (1964) 2811–2820.10.1139/v64-416Search in Google Scholar
[5] P.Kozakevitch: Rev. Métall.57 (1960) 149–160.10.1051/metal/196057020149Search in Google Scholar
[6] M.J.Toplis, D.B.Dingwell: Geochim. Cosmochim. Acta68 (2004) 5169–5188.10.1016/j.gca.2004.05.041Search in Google Scholar
[7] G.Urbain, F.Cambier, M.Deletter, M.R.Anseau: Trans. J. Br. Ceram. Soc.80 (1981) 139–141.Search in Google Scholar
[8] M.Nakamoto, J.Lee, T.Tanaka: ISIJ Int.45 (2005) 651–656.10.2355/isijinternational.45.651Search in Google Scholar
[9] L.Zhang, S.Jahanshahi: Metall. Mater. Trans. B29 (1998) 177–186.10.1007/s11663-998-0020-3Search in Google Scholar
[10] L.Zhang, S.Jahanshahi: Scand. J. Metall.30 (2001) 364–369.10.1034/j.1600-0692.2001.300603.xSearch in Google Scholar
[11] A.Kondratiev, E.Jak: Metall. Trans. B36 (2005) 623–638.10.1007/s11663-005-0053-9Search in Google Scholar
[12] A.Kondratiev, P.C.Hayes, E.Jak: ISIJ Int.46 (2006) 375–384.10.2355/isijinternational.46.375Search in Google Scholar
[13] C.W.Bale, P.Chartrand, S.Decterov, G.Eriksson, K.Hack, R.B.Mahfoud, J.Melançon, A.D.Pelton, S.Petersen: Calphad26 (2002) 189–228; www.factsage.com10.1016/S0364-5916(02)00035-4Search in Google Scholar
[14] A.D.Pelton, M.Blander: Metall. Trans. B17 (1986) 805–815.10.1007/BF02657144Search in Google Scholar
[15] C.M.Scarfe, D.J.Cronin, J.T.Wenzel, D.A.Kaufman: Am. Mineral.68 (1983) 1083–1088.Search in Google Scholar
[16] G.Urbain, Y.Bottinga, P.Richet: Geochim. Cosmochim. Acta46 (1982) 1061–1072.10.1016/0016-7037(82)90059-XSearch in Google Scholar
[17] T.Licko, V.Danek: Phys. Chem. Glasses27 (1986) 22–26.Search in Google Scholar
[18] I.I.Gul'tyai: Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, Metall. Toplivo5 (1962) 52–65.Search in Google Scholar
[19] J.S.Machin, T.B.Yee, D.L.Hanna: J. Am. Ceram. Soc.35 (1952) 322–325.10.1111/j.1151-2916.1952.tb13057.xSearch in Google Scholar
[20] J.S.Machin, T.B.Yee: J. Am. Ceram. Soc.37 (1954) 177–185.10.1111/j.1151-2916.1954.tb14019.xSearch in Google Scholar
[21] V.K.Endell, G.Brinkmann: Ber. Deut. Keram. Ges.20 (1939) 493–507.Search in Google Scholar
[22] P.Drissen, H.J.Engell, D.Janke: Proc. 2nd Int. Symp. on Metall. Slags Fluxes, Metall. Soc. AIME, Warrendale, Pa (1984) 583–592.Search in Google Scholar
[23] D.Sykes, J.E.DickinsonJr., R.W.Luth, C.M.Scarfe: Geochim. Cosmochim. Acta57 (1993) 1291–1295.10.1016/0016-7037(93)90065-5Search in Google Scholar
[24] J.D.Mackenzie: Trans. Faraday Soc.53 (1957) 1488–1493.10.1039/tf9575301488Search in Google Scholar
[25] S.English: Journal of the Society of Glass Technology8 (1924) 205–48.Search in Google Scholar
[26] E.W.Washburn, G.R.Shelton, E.E.Libman: Bull.140 (1924) 71 pp.Search in Google Scholar
[27] D.R.Neuville: Chem. Geol.229 (2006) 28–41.10.1016/j.chemgeo.2006.01.008Search in Google Scholar
[28] T.P.Shvaiko-Shvaikovskaya, N.K.Gusakova, O.V.Mazurin: Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy7 (1971) 620–621.Search in Google Scholar
[29] T.Yasukouchi, K.Nakashima, K.Mori: Tetsu to Hagane85 (1999) 571–577.10.2355/tetsutohagane1955.85.8_571Search in Google Scholar
[30] S.Vargas, F.J.Frandsen, K.Dam-Johansen: Progress in Energy and Combustion Science27 (2001) 237–429.10.1016/S0360-1285(00)00023-XSearch in Google Scholar
[31] D.J.Stein, F.J.Spera: Am. Mineral.78 (1993) 710–723.Search in Google Scholar
[32] K.-D.Kim, S.-H.Lee: Journal of the Ceramic Society of Japan105 (1997) 827–832.10.2109/jcersj.105.827Search in Google Scholar
[33] C.M.Scarfe, D.J.Cronin: Am. Mineral.81 (1986) 767–771.Search in Google Scholar
[34] K.Hunold, R.Brueckner: Glastechn. Ber.53 (1980) 149–161.Search in Google Scholar
[35] T.Iida: Koon Gakkaishi28 (2002) 49–53.Search in Google Scholar
[36] T.Saito, Y.Kawai: Tetsu to Hagane38 (1952) 81–86.10.2355/tetsutohagane1915.38.2_81Search in Google Scholar
[37] J.S.Machin, D.L.Hanna: J. Am. Ceram. Soc.28 (1945) 310–316.10.1111/j.1151-2916.1945.tb14500.xSearch in Google Scholar
[38] J.S.Machin, T.B.Yee: J. Am. Ceram. Soc.31 (1948) 200–204.10.1111/j.1151-2916.1948.tb14290.xSearch in Google Scholar
[39] V.F.Johannsen, H.Brunion: Erzmetall12 (1959) 211–219.Search in Google Scholar
[40] P.M.Bills: J. Iron Steel Inst.201 (1963) 133–140.Search in Google Scholar
[41] J.Boow: Fuel48 (1969) 171–178.Search in Google Scholar
[42] M.Kato, S.Minowa: Trans. Iron Steel Inst. Jpn.9 (1969) 31–38.10.2355/isijinternational1966.9.31Search in Google Scholar
[43] H.Taniguchi: Contrib. Mineral. Petrol.109 (1992) 295–303.10.1007/BF00283319Search in Google Scholar
[44] P.Kozakevitch: Rev. Métall.47 (1950) 201–210.10.1051/metal/195047030201Search in Google Scholar
[45] G.Hofmaier: Berg- und Hüttenmännische Monatshefte113 (1968) 270–81.Search in Google Scholar
[46] R.Rossin, J.Bersan, G.Urbain: Rev. Int. Hautes Tempér. Réfract.1 (1964) 159–170.Search in Google Scholar
[47] G.Urbain: Rev. Int. Hautes Tempér. Réfract.11 (1974) 133–145.Search in Google Scholar
[48] G.Urbain: Rev. Int. Hautes Tempér. Réfract.20 (1983) 135–139.Search in Google Scholar
[49] S.L.Sivkov, S.I.Suchil'nikov, V.A.Pavlov: In: Proiz-vo Ferrosplavov, Moscow4 (1975) 45–52.Search in Google Scholar
[50] G.Handfield, G.G.Charette: Can. Metall. Q.10 (1971) 235–243.10.1179/cmq.1971.10.3.235Search in Google Scholar
[51] K.Mizoguchi, K.Okamoto, Y.Suginohara: Nippon Kinzoku Gakkaishi46 (1982) 1055–1060.Search in Google Scholar
[52] N.L.Zhilo: Izv. Akad. Nauk SSSR, Otdel. Tekh. Nauk, Metallurgiya i Toplivo3 (1961) 17–24.Search in Google Scholar
[53] R.A.Liutikov, L.M.Tsyl'ev: Translation of Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, Met. i Gorn. Delo1 (1963) 12–19.Search in Google Scholar
[54] J.F.Stebbins, Z.Xu: Nature390 (1997) 60–62.10.1038/36312Search in Google Scholar
[55] M.Kawahara, K.Morinaga, T.Yanagase: J. Jpn. Inst. Metals41 (1977) 1047–1052.10.2320/jinstmet1952.41.10_1047Search in Google Scholar
[56] M.Kawahara, K.Morinaga, T.Yanagase: Can. Metall. Q.22 (1983) 143–147.10.1179/cmq.1983.22.2.143Search in Google Scholar
[57] P.Chartrand, A.D.Pelton: Calphad23 (1999) 219–230.10.1016/S0364-5916(99)00026-7Search in Google Scholar
© 2008, Carl Hanser Verlag, München
