Thermodynamic Modeling of Silicate Melts

  • Y. Bottinga
  • D. F. Weill
  • P. Richet
Part of the Advances in Physical Geochemistry book series (PHYSICAL GEOCHE, volume 1)


The chemical and physical properties of silicate liquids exhibit a strong dependence on chemical composition as well as temperature and pressure. Physical chemists in the glass, ceramic, and metallurgical industries investigate these dependences in order to increase the efficiency of industrial processes and to discover materials with new and interesting properties required for technological progress. Earth scientists presently constitute another significant segment of the science community with a deep interest in the properties of silicate liquids. There is now perhaps a greater realization than ever before that many features of our planet and some of its solar system neighbors must be understood in the context of igneous processes. Since silicate melts occur in nature in an almost infinite variety of chemical compositions as well as a very large range of pressure-temperature conditions, it is a special concern of the geosciences to achieve sound models for interpolating and eventually extrapolating a limited number of laboratory measurements.


Thermodynamic Modeling Silicate Glass Partial Molar Volume Silicate System Polymer Model 
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  1. Aksay, I. A., and J. A. Pask, 1975, Stable and metastable equilibria in the system SiO2-Al2O3, J. Am. Ceram. Soc., 58, 507–512.CrossRefGoogle Scholar
  2. Aksay, I. A., J. A. Pask, and R. F. Davis, 1979, Densities of SiO2-Al2O3 melts, J. Am., Ceram. Soc., 62, 332–336.CrossRefGoogle Scholar
  3. Baes, C. F., Jr., 1970, A polymer model for BeF2 and SiO2 melts, J. Solid State Chem., 1, 159–169.CrossRefGoogle Scholar
  4. Barin, I., and O. Knacke, 1973, Thermochemical Properties of Inorganic Substances, Springer-Verlag, Berlin.Google Scholar
  5. Bell, R. J., and P. Dean, 1972, The structure of vitreous silica: validity of the random network theory, Philos. Mag., 25, 1381–1398.CrossRefGoogle Scholar
  6. Beveridge, G. S., and R. S. Schlechter, 1970, Optimization: Theory and Practice, McGraw-Hill Kogakusha Ltd., Tokyo.Google Scholar
  7. Bockris, J. O’M., J. A. Kitchner, S. Ignatowicz, and J. W. Tomlinson, 1948, The electrical conductivity of silicate melts: systems containing Ca, Mn, and Al, Discuss. Faraday Soc., 44, 265–281.CrossRefGoogle Scholar
  8. Bockris, J. O’M., J. A. Kitchner, S. Ignatowicz, and J. W. Tomlinson, 1952, Electric conductance in liquid silicates, Trans. Faraday Soc., 48, 75–91.CrossRefGoogle Scholar
  9. Bockris, J. O’M., and D. C. Lowe, 1954, Viscosity and structure of molten silicates, Proc Roy. Soc. London, A226, 423–435.Google Scholar
  10. Bockris, J. O’M., J. D. Mackenzie, and J. A. Kitchner, 1955, Viscous flow in silica and binary silicates, Trans. Faraday Soc., 51, 1734–1748.CrossRefGoogle Scholar
  11. Bockris, J. O’M., J. W. Tomlinson, and J. L. White, 1956, The structure of the liquid silicates: partial molar volumes and expansivities, Trans. Faraday Soc., 52, 299–310.CrossRefGoogle Scholar
  12. Boon, J. A., 1971, Mössbauer investigations in the system Na2O-FeO-SiO2, Chem. Geol., 7, 153–169.CrossRefGoogle Scholar
  13. Bottinga, Y., and D. F. Weill, 1970, Densities of liquid silicate systems calculated from partial molar volumes of oxide components, Am. J. Sci., 269, 169–182.CrossRefGoogle Scholar
  14. Bottinga, Y., and D. F. Weill, 1972, The viscosity of magmatic silicate liquids: a model for calculation, Am. J. Sci., 272, 438–475.CrossRefGoogle Scholar
  15. Bottinga, Y., and P. Richet, 1978, Thermodynamics of liquid silicates, a preliminary report, Earth Planet. Sci. Lett., 40, 382–400.CrossRefGoogle Scholar
  16. Bowen, N. L., and O. Andersen, 1914, The binary system MgO-SiO2, Am. J. Sci., 37, 487–500.CrossRefGoogle Scholar
  17. Brawer, S. A., and W. B. White, 1975, Raman spectroscopic investigation of the structure of silicate glasses, I, The binary alkali silicates, J. Chem. Phys., 63, 2421–2432.Google Scholar
  18. Brawer, S. A., 1975, Theory of the vibrational spectra of some network and molecular glasses, Phys. Rev., B11, 3173–3193.Google Scholar
  19. Brosset, C., 1963, X-ray investigation of the distribution of heavy atoms in glass, Phys. Chem. Glasses, 4, 99–102.Google Scholar
  20. Brückner, R., 1970, Properties and structure of vitreous silica, I, J. Non-Cryst. Solids, 5, 123–175.CrossRefGoogle Scholar
  21. Burnham, C. W., 1974, NaAlSi3O8-H2O solutions: A thermodynamic model for hydrous magmas, Bull. Minéral., 97, 223–230.Google Scholar
  22. Burnham, C. W., 1975a, Water and magmas; a mixing model, Geochim. Cosmochim. Acta, 39, 1077–1084.CrossRefGoogle Scholar
  23. Burnham, C. W., 1975b, Thermodynamics of melting in experimental silica-volatile systems, Fortschr. Mineral., 52, 101–118.Google Scholar
  24. Burnham, C. W., 1979a, The importance of volatile constituents, in The Evolution of the Igneous Rocks, Fiftieth Anniversary Perspectives, pp. 439–478, Princeton University Press, Princeton, N.J.Google Scholar
  25. Burnham, C. W., 1979b, Magmas and hydrothermal fluids, in Geochemistry of Hydrothermal Ore Deposits, 2nd ed., pp. 71–136. Wiley-Interscience, New York.Google Scholar
  26. Burnham, C. W., and R. H. Jahns, 1962, A method of determining the solubility of water in silicate melts, Am. J. Sci., 260, 721–745.CrossRefGoogle Scholar
  27. Burnham, C. W., J. R. Holloway, and N. F. Davis, 1969, Thermodynamic properties of water to 1000°C and 10000 bars, Geol. Soc. Am., Special paper No. 132.Google Scholar
  28. Burnham, C. W., and N. F. Davis, 1971, The role of H2O in silicate melts, I, Am. J. Sci., 270, 54–79.CrossRefGoogle Scholar
  29. Burnham, C. W., and N. F. Davis, 1974, The role of H2O in silicate melts, II, Am. J. Sci., 274, 902–940.Google Scholar
  30. Burnham, C. W., L. S. Darken, and A. C. Lasaga, 1978, Water and magmas: application of the Gibbs-Duhem equation: a response, Geochim. Cosmochim. Acta, 42, 277–280.CrossRefGoogle Scholar
  31. Calas, G., 1979, Les éléments de transition comme sondes ponctuelles dans les liquides silicatés, application au partage des éléments traces, in Haute température et sciences de la terre, pp. 147–160. Edition du C.N.R.S., Paris.Google Scholar
  32. Calas, G., 1980, Contribution à l’étude du comportement des éléments de transition dans les liquides silicatés magmatiques, Thèse Université de Paris VI, Paris.Google Scholar
  33. Camara, B., 1978, Coordination and valence state of iron in glass, Glastechn. Ber., 51, 87–95.Google Scholar
  34. Carmichael, I. S. E., J. Nichols, F. J. Spera, B. J. Wood, and S. A. Nelson, 1977, High temperature properties of silicate liquids: applications to the equilibration and ascent of basic magma, Philos. Trans. Roy. Soc. London, A286, 373–421.Google Scholar
  35. Catchings, R. M., 1977a, Magnetic susceptibility studies of iron-dysprosium sodium borate glasses, Phys. Status Solidi, A39, K71–K74.Google Scholar
  36. Catchings, R. M., 1977b, EPR study of the ferric oxide-nickel oxide sodium lithium low silica glass system, Phys. Status Solidi, A39, K101–K103.Google Scholar
  37. Clark, Jr., S. P. (editor), 1966, Handbook of Physical Constants, Geol. Soc. Am. Memoir, 97.Google Scholar
  38. Day, D. E., and G. E. Rindone, 1962a, Properties of soda aluminosilicate glasses, I, J. Am. Ceram. Soc., 45, 486–496.Google Scholar
  39. Day, D. E., and G. E. Rindone, 1962b, Properties of soda aluminosilicate glasses, II, J. Am. Ceram. Soc., 45, 496–504.CrossRefGoogle Scholar
  40. Day, D. E., and G. E. Rindone, 1962c, Properties of soda aluminosilicate glasses, III, J. Am. Ceram. Soc., 45, 579–581.CrossRefGoogle Scholar
  41. Distin, P. A., S. G. Whiteway, and C. R. Masson, 1971, Thermodynamics and constitution of ferrous silicate melts, Can. Metall. Quart., 10, 73–78.Google Scholar
  42. Doremus, R. H., 1973, Glass Science. Wiley-Interscience, New York.Google Scholar
  43. Endell, K., and J. Hellbrügge, 1942. The effect of the ionic radius and the valence of the cations on the electrical conductivity of silicate melts between 1250 and 1450°C, Glastech. Ber., 20, 277–287.Google Scholar
  44. Esin, O. A., 1946, Elektroliticheskaya priroda zhidkikh shlakov, Izd. Doma Tekhniki Ural’skogo Industr. Inst., Sverdlovsk.Google Scholar
  45. Etchepare, J., 1972, Study by Raman spectroscopy of crystalline and glassy diopside, in Amorphous Materials, Wiley-Interscience, New York.Google Scholar
  46. Fincham, C. J. B., and F. D. Richardson, 1954, The behaviour of sulphur in silicate and aluminate melts, Proc Roy. Soc., A223, 40–62.Google Scholar
  47. Flood, H., T. Förland, and B. Roald, 1947, Acidic and basic properties of oxides, III, Acta Chem. Scand., 1, 790–798.CrossRefGoogle Scholar
  48. Flory, P. J., 1953, Principles of Polymer Chemistry, Cornell University Press, Ithaca, N.Y.Google Scholar
  49. Flory, P. J., 1970, Thermodynamics of polymer solutions, Discuss. Faraday Soc., 49, 7–29.CrossRefGoogle Scholar
  50. Förland, T., 1964, Thermodynamic properties of fused salt systems, in Fused Salts, McGraw-Hill, New York.Google Scholar
  51. Franz, H., and H. Scholze, 1963, Die Löslichkeit von H2O Dampf in Glasschemlzen verschiedener Basizität, Glastechn. Ber., 36, 347–356.Google Scholar
  52. Frischat, G. H., and G. Tomandl, 1969, Mössbaueruntersuchung von Wertigkeitsverhältnis und Koordination des Eisens in Silicatgläsern. Glastechn. Ber., 42, 182–185.Google Scholar
  53. Gaskell, D. R., 1977, Activities and free energies of mixing in binary silicate melts, Metall. Trans., 8B, 131–145.Google Scholar
  54. Goranson, R. W., 1938, Silicate-water systems: Phase equilibria in NaAlSi3O8-H2O and KAlSi3O8-H2O systems at high temperatures and pressures, Am. J. Sci., 35A, 71–91.Google Scholar
  55. Greig, J. W., 1927, Immiscibility in silicate melts, Am. J. Sci., 13, 1–44.CrossRefGoogle Scholar
  56. Guggenheim, E. A., 1952, Mixtures, Oxford University Press, London.Google Scholar
  57. Haller, W., D. H. Blackburn, and J. H. Simmons, 1974, Miscibility gaps in alkali-silicate binaries, data and thermodynamic interpretation, J. Am. Ceram. Soc., 57, 120–126.CrossRefGoogle Scholar
  58. Hamilton, D. L., C. W. Burnham, and E. F. Osborn, 1964, The solubility of water and effects of oxygen fugacity and water content on crystallization in mafic magmas, J. Petrol., 5, 21–39.Google Scholar
  59. Helgeson, H. C., J. M. Delany, H. W. Nesbit, and D. K. Bird, 1978, Summary and critique of the thermodynamic properties of rock forming minerals, Am. J. Sci., 278A, 1–229.Google Scholar
  60. Hess, P. C., 1971, Polymer model of silicate melts, Geochim. Cosmochim. Acta, 35, 289–306.CrossRefGoogle Scholar
  61. Hess, P. C., 1974, PbO-SiO2 melts: structure and thermodynamics of mixing, Geochim. Cosmochim. Acta, 39, 671–688.CrossRefGoogle Scholar
  62. Hess, P. C., 1977, Structure of silicate melts, Can. Mineral., 15, 162–178.Google Scholar
  63. Hildebrand, J. H., and R. L. Scott, 1964, The Solubility of NonElectrotytes, 3rd ed., Dover, New York.Google Scholar
  64. Isard, J. O., 1959, Electrical conductivity in the aluminosilicate glasses, J. Soc. Glass Technol., 43, 113–123T.Google Scholar
  65. Kapoor, M. L., G. M. Mehrotra, and M. G. Frohberg, 1974, Zusammenhang zwischen den thermodynamischen Grössen und der Struktur flüssiger Silicatsysteme, Archiv Eisenhüttenw., 45, 213–218.Google Scholar
  66. Kapoor, M. L., G. M. Mehrotra, and M. G. Frohberg, 1975, Statistical thermodynamic approach to chain polymers in binary silicate melts, Proc. Australas. Inst. Min. Metall., 254, 11–17.Google Scholar
  67. Kayashima, K., N. Sano, and Y. Matsushita, 1978, Electronparamagnetic resonance in R2O-Al2O3-SiO2 glass systems, J. Am. Ceram. Soc., 61, 311–314.CrossRefGoogle Scholar
  68. Kelley, K. K., 1960, Contributions to the data on theoretical metallurgy XIII, U.S. Bur. Mines Bull., 584.Google Scholar
  69. Kennedy, G. C., G. J. Wasserburg, H. C. Heard, and R. C. Newton, 1962, The upper three-phase region in the system SiO2-H2O, Am. J. Sci., 260, 501–521.CrossRefGoogle Scholar
  70. Khitarov, N. I., A. S. Kadik, and E. B. Lebedev, 1963, Estimation of the thermal effect of the separation of water from felsic melts based on data for the system albite-water. Geochemistry, No. 7, 637–649.Google Scholar
  71. Khitarov, N. I., and A. S. Kadik, 1973, Water and carbon dioxide in magmatic melts and peculiarities of melting process, Contrib. Mineral., Petrol., 41, 205–215.CrossRefGoogle Scholar
  72. Kingery, W. D., H. K. B. Bowen, and D. R. Uhlmann, 1976, Introduction to Ceramics, Wiley-Interscience, New York.Google Scholar
  73. Konijnendijk, W. L., and J. M. Stevels, 1976, Raman scattering measurements of silicate glasses and compounds, J. Non-Cryst. Solids, 21, 447–453.CrossRefGoogle Scholar
  74. Konnert, J. H., J. Karle, and G. A. Ferguson, 1973, Crystalline ordering in silica and germania, Science, 179, 177–178.CrossRefGoogle Scholar
  75. Kozakevitch, P., 1960, Viscosité et éléments structuraux des alumino-silicates fondus, laitiers CaO-Al2O3-SiO2 entre 1600 et 2000°C. Rev. Metall, 57, 149–160.Google Scholar
  76. Kracek, F. C., 1930, The cristobalite liquidus in the alkali oxide silica systems and the heat of fusion of cristobalite, J. Am. Chem. Soc., 52, 1436–1442.CrossRefGoogle Scholar
  77. Krupka, K. M., R. A. Robie, and B. S. Hemingway, 1979, High temperature heat capacities of corundum, periclase, anorthite, CaAl2Si2O8 glass, muscovite, pyrophyllite, KAlSi3O8 glass, grossular and NaAlSi3O8, Am. Mineral., 64, 86–101.Google Scholar
  78. Kubaschewski, O., and C. B. Alcock, 1979, Metallurgical Thermochemistry, 5th ed., Pergamon Press, Oxford.Google Scholar
  79. Kurkjian, C. R., and L. E. Russell, 1958, Solubility of water in molten alkali silicates, J. Soc. Glass Technol., 42, 130–144T.Google Scholar
  80. Kushiro, I., 1975, On the nature of the silicate melt and its significance in magma genesis: regularities in the shift of the liquidus boundaries involving olivine, pyroxene, and silica minerals, Am. J. Sci., 275, 411–431.CrossRefGoogle Scholar
  81. Lahiri, A. K., 1971, Free energy of mixing of divalent basic oxide with silica, Trans. Faraday Soc., 67, 2952–2960.CrossRefGoogle Scholar
  82. Lasaga, A. C., and C. W. Burnham, 1979, Water and magma: another reply, Geochim. Cosmochim. Acta, 43, 643–647.CrossRefGoogle Scholar
  83. Lebedev, A. A., 1921, Polymorphism and tempering of glass. Preliminary communication. J. Russ. Chem. Soc., Phys. Sect., 50, 57.Google Scholar
  84. Leventhal, M., and J. P. Bray, 1965, Nuclear and magnetic investigations of compounds and glasses in the systems PbO-B2O3 and PbO-SiO2, Phys. Chem. Glasses, 6, 113–125.Google Scholar
  85. Levy, R. A., C. H. P. Lupis, and P. A. Flinn, 1976, Mössbauer analysis of the valence and coordination of iron cations in SiO2-Na2O-CaO glasses, Phys. Chem. Glasses, 17, 94–103.Google Scholar
  86. Longhi, J., and J. F. Hays, 1979, Phase equilibria and solid solution along the join CaAl2Si2O8-SiO2, Am. J. Sci., 279, 876–890.CrossRefGoogle Scholar
  87. Longuet-Higgins, H. C., 1953, Solutions of chain molecules, a new statistical theory, Discuss. Faraday Soc., 15, 73–80.CrossRefGoogle Scholar
  88. Ludington, S., 1979, Thermodynamics of melting of anorthite deduced from phase equilibrium studies, Am. Mineral., 64, 77–85.Google Scholar
  89. Masson, C. R., 1965, An approach to the problem of ionic distribution in liquid silicates, Proc Roy. Soc. London, A287, 201–221.Google Scholar
  90. Masson, C. R., 1972, Thermodynamics and constitution of silicate slags, J. Iron Steel Inst., 210, 89–96.Google Scholar
  91. Masson, C. R., 1977, Anionic constitution of glass-forming melts, J. Non-Cryst. Solids, 25, 1–41.CrossRefGoogle Scholar
  92. Masson, C. R., I. B. Smith, and S. G. Whiteway, 1970, Activities and ionic distribution in liquid silicates: application of polymer theory, Can. J. Chem., 48, 1456–1464.CrossRefGoogle Scholar
  93. Mathews, J., and R. L. Walker, 1965, Mathematical Methods of Physics, W. A. Benjamin, New York.Google Scholar
  94. Milberg, M. E., and C. R. Peters, 1969, Cation distribution in thallium silicate glasses, Phys. Chem. Glasses, 10, 46–49.Google Scholar
  95. Morse, S. A., 1980, An updating in petrology, Science, 207, 296–297.CrossRefGoogle Scholar
  96. Mott., N. F., 1967, Electrons in disordered structures, Adv. Phys., 16, 49–144.CrossRefGoogle Scholar
  97. Mozzi, R. L., and B. E. Warren, 1969, The structure of vitreous silica, J. Appl. Crystallogr., 2, 164–172.CrossRefGoogle Scholar
  98. Navrotsky, A., R. Hon, D. F. Weill, and D. Henry, 1980, Thermochemistry of glasses and liquids in the systems CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8, SiO2-CaAl2Si2O8-NaAlSi3O8, and SiO2-Al2O3-CaO-Na2O, Geochim. Cosmochim. Acta, 44, 1409–1423.CrossRefGoogle Scholar
  99. Nelson, S. A., and I. S. E. Carmichael, 1980, Partial molar volumes of oxide components in silicate liquids, Contrib. Mineral. Petrol., 71, 117–129.CrossRefGoogle Scholar
  100. Newton, R. C., T. V. Charlu, and O. J. Kleppa, 1980, Thermochemistry of the high structural state plagioclases, Geochim. Cosmochim. Acta, 44, 933–941.CrossRefGoogle Scholar
  101. Orlova, G. P., 1964, The solubility of water in albite melts, Int. Geol. Rev., 6, 254–258.CrossRefGoogle Scholar
  102. Oxtoby, S., and D. L. Hamilton, 1978, The discrete association of water with Na2O and SiO2 in NaAl silicate melts, Contrib. Mineral. Petrol., 66, 185–188.CrossRefGoogle Scholar
  103. Pargamin, L., C. H. P. Lupis, and P. A. Flinn, 1972, Mössbauer analysis of the distribution of iron cations in silicate slags, Metall Trans., 3, 2093–2105.CrossRefGoogle Scholar
  104. Piriou, B., 1979, Etude optique des millieux vitreux et de bain fondus, in Haute température et sciences de la terre, pp. 91–99, Edition C.N.R.S., Paris.Google Scholar
  105. Pretnar, B., 1968, Beitrag zur lonentheorie der Silicatschmelzen, Ber. Bunsenges. Phys. Chem., 72, 773–778.Google Scholar
  106. Prigogine, I., and R. Defay, 1954, Chemical Thermodynamics, Wiley, New York.Google Scholar
  107. Proks, I., M. Eliáşová, and L. Kosa, 1977, The heat of fusion of akermanite, Silikaty, 21, 3–11.Google Scholar
  108. Randall, J. T., H. P. Rooksby, and B. S. Cooper, 1930, Structure of glasses: the evidence of X-ray diffraction, J. Soc. Glass Technol, 14, 219–229T.Google Scholar
  109. Rein, R. H., and J. Chipman, 1965, Activities in the liquid solution SiO2-CaO-MgO-A12O3 at 1600°C, Trans. Metall. Soc. AIME, 233, 415–425.Google Scholar
  110. Richardson, F. D., 1955, The Vitreous State, pp. 63–84, Glass Delegacy of the University of Sheffield, Sheffield, U.K.Google Scholar
  111. Richardson, F. D., 1956, Activities in ternary silicate melts, Trans. Faraday Soc., 52, 1312–1324.CrossRefGoogle Scholar
  112. Richet, P., and Y. Bottinga, 1980, Heat capacity of liquid silicates: new measurements on NaAlSi3O8 and K2Si4O9, Geochim. Cosmochim. Acta, 44, 1535–1541.CrossRefGoogle Scholar
  113. Riebling, E. F., 1966, Structure of sodium aluminosilicate melts containing at least 50 mole % SiO2 at 1500°C, J. Chem. Phys., 44, 2857–2865.CrossRefGoogle Scholar
  114. Robie, R. A., B. S. Hemmingway, and J. R. Fisher, 1978, Thermodynamic properties of minerals and related substances at 298.15K and 1 bar (105 Pascals) pressure and at higher temperature, U.S. Geol. Survey Bull., 1452.Google Scholar
  115. Robie, R. A., and D. R. Waldbaum, 1968, Thermodynamic properties of minerals and related substances at 298.15°K (25.0°C) and one atmosphere (1.013 bars) pressure and at higher temperatures, U.S. Geol. Survey Bull., 1259.Google Scholar
  116. Rossin, R., J. Bersan, and G. Urbain, 1964, Etude de la viscosité de laitiers liquides appartenant au système ternaire SiO2-Al2O3-CaO, Rev. Hautes Temp. Refract., 1, 15–170.Google Scholar
  117. Russell, R. E., 1955, Solubility of water in molten glass, Thesis, Massachusetts Institute of Technology.Google Scholar
  118. Sakka, S., and A. Senga, 1978, Studies on Si-O bonding in silicate and aluminosilicate glasses based on SiKβ emission X-rays, J. Mater. Sci., 13, 505–512.CrossRefGoogle Scholar
  119. Schende, H., 1945, Physico-Chemistry of Steel Making, BISRA Transl., London.Google Scholar
  120. Scholze, H., 1966, Gases and water in glass, Pt. 2, Glass Industry, 622-628.Google Scholar
  121. Schreiber, H. D., H. V. Lauer, Jr., and T. Thanyasin, 1980, The redox state of cerium in basaltic magmas: An experimental study of iron-cerium interactions in silicate melts, Geochim. Cosmochim. Acta.Google Scholar
  122. Segers, L., 1977, Contribution à l’étude des mélanges d’oxydes fondus CaO-SiO2-MnO. Thèse, Université Libre de Bruxelles, Bruxelles.Google Scholar
  123. Shaw, H. R., 1972, Viscosities of magmatic silicate liquids: An empirical method of prediction, Am. J. Sci., 272, 870–892.CrossRefGoogle Scholar
  124. Shiraishi, Y., K. Ikeda, A. Tamura, and T. Saito, 1978. On the viscosity and density of the molten FeO-SiO2 system, Trans. Japanese Inst. Metall., 19, 264–274.Google Scholar
  125. Smart, R. M., and F. P. Glasser, 1978, Silicate anion constitution of lead silicate glasses and crystals, Phys. Chem. Glasses, 19, 95–102.Google Scholar
  126. Spencer, P. J., 1973, The thermodynamic properties of silicates, NPL Rept. Chem. 21, National Physical Laboratory, Teddington, U.K.Google Scholar
  127. Taylor, M., and G. E. Brown, 1979a, Structure of silicate mineral glasses I, Geochim. Cosmochim. Acta, 43, 61–75.CrossRefGoogle Scholar
  128. Taylor, M., and G. E. Brown, 1979b, Structure of silicate mineral glasses II, Geochim. Cosmochim. Acta, 43, 1467–1473.CrossRefGoogle Scholar
  129. Taylor, M., G. E. Brown, and P. M. Fen, 1980, Structure of mineral glasses, III, Geochim. Cosmochim. Acta, 44, 109–118.CrossRefGoogle Scholar
  130. Temkin, M., 1945, Mixtures of fused salts as ionic solutions, Acta Physicochim. URSS, 20, 411–420.Google Scholar
  131. Tewhey, J. D., and P. C. Hess, 1979, The two phase region in the CaO-SiO2 system: experimental data and thermodynamic analysis, Phys. Chem. Glasses, 20, 41–53.Google Scholar
  132. Tomandl, G., G. H. Frischat, and H. J. Oel, 1967, Mössbauer Effekt in Eisen-Alkali-Silicatgläsern, Glastechn. Ber., 40, 293–298.Google Scholar
  133. Tomlinson, J. W., 1956, A note on the solubility of water in a molten sodium silicate, J. Soc. Glass Technol., 40, 25–31T.Google Scholar
  134. Tomazawa, M., and R. A. Obara, 1973, Effect of minor third components on metastable immiscibility boundaries of binary glasses, J. Am. Ceram. Soc., 56, 378–381.CrossRefGoogle Scholar
  135. Toop, G. W., and C. S. Samis, 1962, Activities of ions in silicate melts, Trans. Metall. Soc. AIME, 224, 878–887.Google Scholar
  136. Topping, J. A., and M. K. Murthy, 1973, Effect of small additions of A12O3 and Ga2O3 on the immiscibility temperature of Na2O-SiO2 glasses, J. Am. Ceram. Soc., 56, 270–275.CrossRefGoogle Scholar
  137. Uhrich, D. L., and R. G. Barnes, 1968, Moessbauer effect determination of thulium (III) crystalline electric field parameters in thulium-doped soda-silica glass, Phys. Chem. Glasses, 9, 184–189.Google Scholar
  138. Urnes, S., 1969, Studies of the sodium distribution in sodium silicate glasses by the chemical difference method, Phys. Chem. Glasses, 10, 69–71.Google Scholar
  139. Valenkov, N., and E. Porai-Koshitz, 1936, X-ray investigation of the glassy state, Z. Kristallogr., A95, 195–229.Google Scholar
  140. Venkatadri, A. S., and H. B. Bell, 1969, Use of slag-metal sulfur partition ratio to compute the low iron oxide activities in slags, Trans. AIME, 245, 2319–2323.Google Scholar
  141. Verweij, H., and W. L. Konijnendijk, 1976, Structural units in K2O-PbO-SiO2 glasses by Raman spectroscopy, J. Am. Ceram. Soc., 59, 517–521.CrossRefGoogle Scholar
  142. Waff, H. S., 1975, Pressure-induced coordination changes in magmatic liquids, Geophys. Res. Lett., 2, 193–196.CrossRefGoogle Scholar
  143. Waff, H. S., and D. F. Weill, 1975, Electrical conductivity of magmatic liquids: effect of temperature, oxygen fugacity and composition, Earth Planet. Sci. Lett., 28, 254–260.CrossRefGoogle Scholar
  144. Walsh, J. H., J. Chipman, T. B. King, and N. J. Grant, 1956, Hydrogen in steel making slags, Trans. AIME, J. Metals, 206, 1568–1576.Google Scholar
  145. Waseda, Y., and H. Suito, 1977, The structure of molten alkali metal silicates, Trans. ISO, 17, 82–90.Google Scholar
  146. Waseda, Y., and J. M. Toguri, 1977a, Temperature dependence of the structure of molten silicates, Trans. ISIJ, 17, 601–603.Google Scholar
  147. Waseda, Y., and J. M. Toguri, 1977b, Structure of molten binary silicate systems CaO-SiO2 and MgO-SiO2, Metall. Trans., 8B, 563–568.Google Scholar
  148. Waseda, Y., and J. M. Toguri, 1978, The structure of the molten FeO-SiO2 system. Metall. Trans., 9B, 595-601.Google Scholar
  149. Weill, D. F., J. F. Stebbins, R. Hon, and I. S. E. Carmichael, 1980, The enthalpy of fusion of anorthite, Contrib. Mineral. Petrol., 74, 95–102.CrossRefGoogle Scholar
  150. Weill, D. F., R. Hon, and A. Navortsky, 1980, The system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8: variations on a classical theme by Bowen, in Physics of Magmatic Processes, pp. 49–92, Princeton University Press, Princeton, N.J.Google Scholar
  151. Whiteway, S. G., I. B. Smith, and C. R. Masson, 1970, Theory of molecular size distribution in multichain polymers, Can. J. Chem., 48, 33–45.CrossRefGoogle Scholar
  152. Wong, J., and C. A. Angell, 1976, Glass Structure by Spectroscopy, Dekker, New York.Google Scholar
  153. Zachariasen, W. H., 1932, The atomic arrangement in glass, J. Am. Chem. Soc., 54, 3841–3851.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc 1981

Authors and Affiliations

  • Y. Bottinga
  • D. F. Weill
    • 1
  • P. Richet
  1. 1.Dept. of GeologyUniversity of OregonEugeneUSA

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