A model to calculate the viscosity of silicate melts
-
A. Nicholas Grundy
, Honqin Liu , In-Ho Jung , Sergei A. Decterov und Arthur D. Pelton
Abstract
A model has been developed that links the viscosities of silicate melts to their thermodynamic properties. Over the past several years, through critical evaluation of all available thermodynamic and phase equilibrium data, we have developed a quantitative thermodynamic description of multicomponent silicate melts using the Modified Quasichemical Model for short-range ordering. The local structure of the liquid, in terms of the bridging behavior of oxygen, calculated using our thermodynamic model allows us to characterize the structure of the liquid semi-quantitatively using the concepts of Q-species and connectivity of Q-species. The viscosity is modeled by optimizing viscosity parameters that are related to the structure of the liquid. The viscosity of pure liquid silica is modeled using four model parameters and every other unary liquid is modeled using two. The viscosity of all binary liquids is reproduced within experimental accuracy by optimizing one or at most two binary viscosity parameters for each system. In the present article the equations for the viscosity model are derived and analyses for the experimentally well-established systems CaO – SiO2 MgO – SiO2, NaO0.5 – SiO2, KO0.5 – SiO2 and AlO1.5 – SiO2 are presented. This is the first step in the development of a predictive model for the viscosity of multicomponent silicate melts that will be presented in part II.
References
[1] A.D.Pelton, M.Blander: Metall. Trans. B17 (1986) 805–815.10.1007/BF02657144Suche in Google Scholar
[2] M.L.Kapoor, M.G.Frohberg: Proceedings of the International Symposium Chemical Metallurgy of Iron and Steel, Sheffield, England, The Institute of Metals, London (1971) 17–22.Suche in Google Scholar
[3] L.Zhang, S.Jahanshahi: Metall. Mater. Trans. B29 (1998) 177–186.10.1007/s11663-998-0020-3Suche in Google Scholar
[4] A.Kondratiev, E.Jak: Metall. Trans. B36 (2005) 623–638.10.1007/s11663-005-0053-9Suche in Google Scholar
[5] M.Nakamoto, J.Lee, T.Tanaka: ISIJ Int.45 (2005) 651–656.10.2355/isijinternational.45.651Suche in Google Scholar
[6] A.D.Pelton, S.A.Decterov, G.Eriksson, C.Robelin, Y.Dessureault: Metall. Mater. Trans. B31 (2000) 651–659.10.1007/s11663-000-0103-2Suche in Google Scholar
[7] 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)00035-4Suche in Google Scholar
[8] C.J.B.Fincham, F.D.Richardson: Proc. Roy. Soc. (London)223 (1954) 40–62.Suche in Google Scholar
[9] P.Wu, G.Eriksson, A.D.Pelton: J. Am. Ceram. Soc.76 (1993) 2059–64.10.1111/j.1151-2916.1993.tb08333.xSuche in Google Scholar
[10] G.Eriksson, P.Wu, M.Blander, A.D.Pelton: Can. Metall. Q.33 (1994) 13–21.10.1179/cmq.1994.33.1.13Suche in Google Scholar
[11] P.Wu, G.Eriksson, A.D.Pelton, M.Blander: ISIJ Int.33 (1993) 26–35.10.2355/isijinternational.33.26Suche in Google Scholar
[12] G.Eriksson, A.D.Pelton: Metall. Trans. B24 (1993) 807–816.10.1007/BF02663141Suche in Google Scholar
[13] B.Mysen: Eur. J. Mineral.15 (2003) 781–802.10.1127/0935-1221/2003/0015-0781Suche in Google Scholar
[14] P.L.Lin, A.D.Pelton: Metall. Trans. B10 (1979) 667–675.10.1007/BF02662569Suche in Google Scholar
[15] J.D.Frantz, B.O.Mysen: Chem. Geol.121 (1995) 155–176.10.1016/0009-2541(94)00127-TSuche in Google Scholar
[16] H.Maekawa, T.Maekawa, K.Kawamura, T.Yokokawa: J. Non-Cryst. Solids127 (1991) 53–64.10.1016/0022-3093(91)90400-ZSuche in Google Scholar
[17] W.E.Halter, B.O.Mysen: Chem. Geol.213 (2004) 115–123.10.1016/j.chemgeo.2004.08.036Suche in Google Scholar
[18] T.Yano, S.Shibata, T.Maehara: J. Am. Ceram. Soc.89 (2006) 89–95.10.1111/j.1551-2916.2005.00815.xSuche in Google Scholar
[19] J.Machacek, O.Gedeon: Ceramics-Silikaty47 (2003) 45–49.Suche in Google Scholar
[20] J.Machacek, O.Gedeon, M.Liska: J. Non-Cryst. Solids352 (2006) 2173–2179.10.1016/j.jnoncrysol.2006.01.036Suche in Google Scholar
[21] J.F.Bacon, A.A.Hasapis: J. Appl. Phys.30 (1959) 1470–1471.10.1063/1.1735377Suche in Google Scholar
[22] J.F.Bacon, A.A.Hasapis, J.W.Wholley, Jr.: Phys. Chem. Glasses1 (1960) 90–98.Suche in Google Scholar
[23] D.W.Bowen, R.W.Taylor: Am. Ceram. Soc. Bull.57 (1978) 818–819.Suche in Google Scholar
[24] J.O.M.Bockris, J.D.Mackenzie, J. A.Kitchener: Trans. Faraday Soc.51 (1955) 1734–1748.10.1039/tf9555101734Suche in Google Scholar
[25] G.Urbain, Y.Bottinga, P.Richet: Geochim. Cosmochim. Acta46 (1982) 1061–1072.10.1016/0016-7037(82)90059-XSuche in Google Scholar
[26] R.Rossin, J.Bersan, G.Urbain: Rev. Hautes Temp. Refractaires1 (1964) 159–170.Suche in Google Scholar
[27] G.Hofmaier: Berg- und Huettenmaennische Monatshefte113 (1968) 270–81.Suche in Google Scholar
[28] N.V.Solomin: J. Phys. Chem. (U.S.S.R.)14 (1940) 235–243.Suche in Google Scholar
[29] R.Bruckner: Z. Glaskunde37 (1964) 413–425.Suche in Google Scholar
[30] T.Kimura: Japanese J. Appl. Phys.8 (1969) 1397–1403.10.1143/JJAP.8.1397Suche in Google Scholar
[31] E.H.Fontana, W.A.Plummer: Phys. Chem. Glasses7 (1966) 139–146.Suche in Google Scholar
[32] J.Hlavac, T.K.Sen: Silikaty12 (1968) 213–220.Suche in Google Scholar
[33] J.Yovanovitch: Compt. Rend.253 (1961) 853–855.Suche in Google Scholar
[34] S.D.Brown, S.S.Kistler: J. Am. Ceram. Soc.42 (1959) 263–270.10.1111/j.1151-2916.1959.tb12951.xSuche in Google Scholar
[35] M.P.Volarovich, A.A.Leont'eva: J. Soc. Glass Tech.20 (1936) 139–43.Suche in Google Scholar
[36] G.Hetherington, K.H.Jack, J.C.Kennedy: Phys. Chem. Glasses5 (1964) 130–136.Suche in Google Scholar
[37] G.Hofmaier, G.Urbain: Sci. Ceram.4 (1968) 25–32.Suche in Google Scholar
[38] R.H.Doremus: J. Appl. Phys.92 (2002) 7619–7629.10.1063/1.1515132Suche in Google Scholar
[39] G.Urbain: Rev. Int. Hautes Tempér. Réfract., Fr.19 (1982) 55–57.Suche in Google Scholar
[40] P.Kozakevitch: Rev. Métall.57 (1960) 149–160.10.1051/metal/196057020149Suche in Google Scholar
[41] V.P.Elyutin, V.I.Kostikov, B.S.Mitin, Yu.A.Nagibin: Zhurnal Fizicheskoi Khimii43 (1969) 579–83.Suche in Google Scholar
[42] R.A.Blomquist, J.K.Fink, L.Leibowitz: Am. Ceram. Soc. Bull.57 (1978) 522.Suche in Google Scholar
[43] F.-Z.Ji, D.Sichen, S.Seetharaman: Metall. Mater. Trans. B28 (1997) 827–834.10.1007/s11663-997-0010-xSuche in Google Scholar
[44] J.S.Machin, D.L.Hanna: J. Am. Ceram. Soc.28 (1945) 310–316.10.1111/j.1151-2916.1945.tb14500.xSuche in Google Scholar
[45] T.Licko, V.Danek: Phys. Chem. Glasses27 (1986) 22–26.Suche in Google Scholar
[46] I.I.Gul'tyai: Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk, Metall. Toplivo5 (1962) 52–65.Suche in Google Scholar
[47] J.S.Machin, T.B.Yee: J. Am. Ceram. Soc.31 (1948) 200–204.10.1111/j.1151-2916.1948.tb14290.xSuche in Google Scholar
[48] J.S.Machin, T.B.Yee, D.L.Hanna: J. Am. Ceram. Soc.35 (1952) 322–325.10.1111/j.1151-2916.1952.tb13057.xSuche in Google Scholar
[49] J.S.Machin, T.B.Yee: J. Am. Ceram. Soc.37 (1954) 177–185.10.1111/j.1151-2916.1954.tb14019.xSuche in Google Scholar
[50] V.H.Schenck, M.G.Frohberg: Arch. Eisenhuettenwes.33 (1962) 421–425.Suche in Google Scholar
[51] J.O.Bockris, D.C.Lowe: Proc. Roy. Soc. London, Ser. A226 (1954) 423–435.10.1098/rspa.1954.0266Suche in Google Scholar
[52] P.Drissen, H.J.Engell, D.Janke: Metall. Slags Fluxes, Int. Symp., Proc., 2nd (1984), Metall. Soc. AIME, Warrendale, Pa (1984) 583–592.Suche in Google Scholar
[53] D.R.Neuville: Chem. Geol.229 (2006) 28–41.10.1016/j.chemgeo.2006.01.008Suche in Google Scholar
[54] T.Saito, Y.Kawai: Tetsu to Hagane38 (1952) 81–86.10.2355/tetsutohagane1915.38.2_81Suche in Google Scholar
[55] D.J.Lacks, D.B.Rear, J.A.Van Orman: Geochim. Cosmochim. Acta71 (2007) 1312–1323.10.1016/j.gca.2006.11.030Suche in Google Scholar
[56] M.Kawahara, K.Morinaga, T.Yanagase: J. Jpn. Inst. Metals41 (1977) 1047–1052.10.2320/jinstmet1952.41.10_1047Suche in Google Scholar
[57] G.Urbain: Rev. Int. Hautes Tempér. Réfract., Fr.22 (1985) 39–45.Suche in Google Scholar
[58] S.Sumita, H.Takano, K.Morinaga, T.Yanagase: J. Jpn. Inst. Met.46 (1982) 280–285.10.2320/jinstmet1952.46.3_280Suche in Google Scholar
[59] T.Kou, K.Mizoguchi, Y.Suginohara: Nippon Kinzoku Gakkaishi42 (1978) 775–781.Suche in Google Scholar
[60] K.-D.Kim, S.-H.Lee: Journal of the Ceramic Society of Japan105 (1997) 827–832.10.2109/jcersj.105.827Suche in Google Scholar
[61] H.R.Lillie: J. Am. Ceram. Soc.22 (1939) 367–74.10.1111/j.1151-2916.1939.tb19482.xSuche in Google Scholar
[62] G.S.Meiling, D.R.Uhlmann: Phys. Chem. Glasses8 (1967) 62–68.Suche in Google Scholar
[63] K.Hunold, R.Brueckner: Glastechn. Ber.53 (1980) 149–161.Suche in Google Scholar
[64] M.Liska, P.Simurka, J.Antalik, P.Perichta: Chem. Geol.128 (1996) 199–206.10.1016/0009-2541(95)00173-5Suche in Google Scholar
[65] R.Ota, T.Wakasugi, W.Kawamura, B.Tuchiya, J.Fukunaga: J. Non-Cryst. Solids188 (1995) 136–146.10.1016/0022-3093(95)00185-9Suche in Google Scholar
[66] L.Shartsis, S.Spinner, W.Capps: J. Am. Ceram. Soc.35 (1952) 155–60.10.1111/j.1151-2916.1952.tb13090.xSuche in Google Scholar
[67] T.P.Shvaiko-Shvaikovskaya, O.V.Mazurin, Z.S.Bashun: Izvestiya Akademii Nauk SSSR, Neorganicheskie Materialy7 (1971) 128–131.Suche in Google Scholar
[68] G.Heidtkamp, K.Endell: Glastech. Ber.14 (1936) 89–103.Suche in Google Scholar
[69] S.English: Journal of the Society of Glass Technology8 (1924) 205–48.Suche in Google Scholar
[70] E.W.Washburn, G.R.Shelton, E.E.Libman: Bull.140 (1924) 71 pp.Suche in Google Scholar
[71] E.Eipelauer, A.More: Radex Rundsch.4 (1960) 230–238.Suche in Google Scholar
[72] H.J.Pohlmann: Glastech. Ber.49 (1976) 177–182.Suche in Google Scholar
[73] K.Mizoguchi, K.Okamoto, Y.Suginohara: Nippon Kinzoku Gakkaishi46 (1982) 1055–1060.Suche in Google Scholar
[74] E.Asayama, H.Takebe, K.Morinaga: ISIJ Int.33 (1993) 233–238.10.2355/isijinternational.33.233Suche in Google Scholar
[75] A.Kondratiev, P.C.Hayes, E.Jak: ISIJ Int.46 (2006) 359–367.10.2355/isijinternational.46.359Suche in Google Scholar
© 2008, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents
- Contents
- Basic
- A model to calculate the viscosity of silicate melts
- A model to calculate the viscosity of silicate melts
- A note on the application of the phase rule
- Thermodynamic properties of liquid silver–indium–tin alloys determined from emf measurements
- Unconstrained solidification and characterisation of near-eutectic Al–Cu–Ag alloys
- Tensile properties of L12 intermetallic foils fabricated by cold rolling
- Microstructural control of FeB-inoculated mottled low-alloy white iron by a design of experiments approach
- Applied
- Dislocation structure and crystallite size distribution in lath martensite determined by X-ray diffraction peak profile analysis
- Effect of minor addition of Pb upon interfacial reactions and mechanical properties at Sn-3.0Ag-0.5Cu/Cu and Sn-58Bi/Cu solder joints
- Elastic properties of braided ceramic matrix composites
- The influence of microstructural characteristics and contaminants on the mechanical properties and fracture topography of low cost Ti6Al4V alloy
- Microstructure and room temperature mechanical properties of Hf and Sn-doped Nb-20Ti-5Cr-3Al-18Si alloy
- The effect of alloying elements on constrained carbon equilibrium due to a quench and partition process
- Hardfacing behavior of Cr–Ni stainless steel with Co-based super alloys
- Development of SMD 32.768 kHz tuning fork-type crystals
- Notification
- DGM News
Artikel in diesem Heft
- Contents
- Contents
- Basic
- A model to calculate the viscosity of silicate melts
- A model to calculate the viscosity of silicate melts
- A note on the application of the phase rule
- Thermodynamic properties of liquid silver–indium–tin alloys determined from emf measurements
- Unconstrained solidification and characterisation of near-eutectic Al–Cu–Ag alloys
- Tensile properties of L12 intermetallic foils fabricated by cold rolling
- Microstructural control of FeB-inoculated mottled low-alloy white iron by a design of experiments approach
- Applied
- Dislocation structure and crystallite size distribution in lath martensite determined by X-ray diffraction peak profile analysis
- Effect of minor addition of Pb upon interfacial reactions and mechanical properties at Sn-3.0Ag-0.5Cu/Cu and Sn-58Bi/Cu solder joints
- Elastic properties of braided ceramic matrix composites
- The influence of microstructural characteristics and contaminants on the mechanical properties and fracture topography of low cost Ti6Al4V alloy
- Microstructure and room temperature mechanical properties of Hf and Sn-doped Nb-20Ti-5Cr-3Al-18Si alloy
- The effect of alloying elements on constrained carbon equilibrium due to a quench and partition process
- Hardfacing behavior of Cr–Ni stainless steel with Co-based super alloys
- Development of SMD 32.768 kHz tuning fork-type crystals
- Notification
- DGM News