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Simulation of molecular mass distributions and evaluation of O2− concentrations in polymerized silicate melts

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Abstract

A new statistical model is proposed for the molecular mass distributions (MMD) of polymerized anions in silicate melts. The model is based on the known distribution of Q n species in the MeO-Me2O-SiO2 system. In this model, chain and ring complexes are regarded as a random series of Q n structons with various concentrations of bridging bonds (1 ≤ n ≤ 4, Q 0 corresponds to SiO 4−4 ). This approach makes it possible to estimate the probability of formation of various ensembles of polymer species corresponding to the general formula (Si i O3i+1−j )2(i+1−j)−, where i is the size of the ion, and j is the cyclization number of intrachain bonds. The statistical model is utilized in the STRUCTON computer model, which makes use of the Monte Carlo method and is intended for the calculation of the composition and proportions of polyanions at a specified degree of polymerization of silicate melts (STRUCTON, version 1.2; 2007). Using this program, we simulated 1200 MMD for polyanions in the range of 0.52 ≤ p ≤98, where p is the fraction of nonbridging bonds in the silicon-oxygen matrix. The average number of types of anions in this range was determined to increase from three (SiO 4−4 , Si2O 6−7 , and Si3O 8−10 ) to 153, and their average size increases from 1 to 7.2. A special option of the STRUCTON program combines MMD reconstructions in silicate melts with the formalism of the Toop-Samis model, which enables the calculation of the mole fraction of the O2− ion relative to all anions in melts of specified composition. It is demonstrated that, with regard for the distribution and average size of anion complexes, the concentration of the O2− ion in the MeO-SiO2 system is characterized by two extrema: a minimum at 40–45 mol % SiO2, which corresponds to the initial stages of the gelenization of the polycondensated silicate matrix, and a maximum, which is predicted for the range of 60–80 mol % SiO2.

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References

  1. M. S. Ghiorso, “Chemical Mass Transfer in Magmatic Processes I. Thermodynamic Relations and Numeric Algorithms,” Contrib. Mineral. Petrol. 90, 107–120 (1985).

    Article  Google Scholar 

  2. M. Ya. Frenkel’ and A. A. Ariskin, “Numeric Algorithm for the Solution of Equilibrium of Crystallizing Basaltic Melt,” Geokhimiya, No. 5, 679–690 (1984).

  3. M. S. Ghiorso and I. S. E. Carmichael, “Modeling Magmatic Systems: Petrologic Applications,” in Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Melts, Rev. Mineral. 17, 467–499 (1987).

    Google Scholar 

  4. M. S. Ghiorso and R. O. Sack, “Chemical Mass Transfer in Magmatic Processes IV. A Revised and Internally Consistent Thermodynamic Model for the Interpolation and Extrapolation of Liquid-Solid Equilibria in Magmatic Systems at Elevated Temperatures and Pressures,” Contrib. Mineral. Petrol. 119, 197–212 (1995).

    Article  Google Scholar 

  5. A. A. Ariskin, G. S. Barmina, M. Ya. Frenkel, and R. L. Nielsen, “COMAGMAT: A Fortran Program to Model Magma Differentiation Processes,” Comput. Geosci. 19, 1155–1170 (1993).

    Article  Google Scholar 

  6. A. A. Ariskin, “Phase Equilibria Modeling in Igneous Petrology: Use of COMAGMAT Model for Simulating Fractionation of Ferro-Basaltic Magmas and the Genesis of High-Alumina Basalt,” J. Volcanol. Geotherm. Res. 90, 115–162 (1999).

    Article  Google Scholar 

  7. A. A. Ariskin and G. S. Barmina, Modeling Phase Equilibria during the Crystallization of Basaltic Magmas (Nauka, Moscow, 2000) [in Russian].

    Google Scholar 

  8. A. A. Ariskin and G. S. Barmina, “COMAGMAT: Development of a Magma Crystallization Model and Its Petrological Applications,” Geochem. Int. 42(Suppl. 1), 1–157 (2004).

    Google Scholar 

  9. M. S. Ghiorso, “Thermodynamic Models of Igneous Processes,” Annu. Rev. Earth Planet. Sci. 25, 221–241 (1997).

    Article  Google Scholar 

  10. R. G. Berman and T. H. Brown, “Development of Models for Multi-Component Melts: Analysis of Synthetic Systems,” in Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Melts, Ed. by I. S. E. Carmichael and H. P. Eugster, Mineral. Soc. Am. Rev. Mineral. 17, 405–442 (1987).

  11. R. G. Berman and T. H. Brown, “A Thermodynamic Model for Multicomponent Melts, with Application to the System CaO-Al2O3-SiO2,” Geochim. Cosmochim. Acta 45, 661–678 (1984).

    Article  Google Scholar 

  12. M. S. Ghiorso, I. S. E. Carmichael, M. L. Rivers, and R. O. Sack, “The Gibbs Free Energy of Mixing of Natural Liquids: An Expanded Regular Solution Approximation for the Calculation of Magmatic Intensive Variables,” Contrib. Mineral. Petrol. 84, 107–145 (1983).

    Article  Google Scholar 

  13. V. A. Solov’ev, E. V. Zhivaeva, and A. O. Kislyuk, “Models of Molecular Associates in the Theories of Thermodynamic Properties of Glass-Forming Melts,” Fiz. Khim. Stekla 24(3), 345–354 (1998).

    Google Scholar 

  14. V. N. Anfilogov, V. N. Bykov, and A. A. Osipov, Silcate Melts (Nauka, Moscow, 2005) [in Russian].

    Google Scholar 

  15. B. A. Shakhmatkin and N. M. Vedishcheva, “Thermodynamic Approach to the Modeling of Physical Properties of Oxide Glasses,” Fiz. Khim. Stekla 24(3), 333–344 (1998).

    Google Scholar 

  16. E. N. Plotnikov and V. L. Stolyarova, “Calculation of Thermodynamic Properties of Melts in the Systems Na2O-SiO2 and B2O-SiO2 Based on the Generalized Lattice Theory of Associated Solutions,” Fiz. Khim. Stekla 31(6), 1048–1086 (2005).

    Google Scholar 

  17. B. Bjorkman, “An Assessment of the System Fe-O-SiO2 Using a Structure Based Model for the Liquid Silicate,” CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 9, 271–282 (1985).

    Google Scholar 

  18. R. L. Nielsen and M. A. Dungan, “Low-Pressure Mineral-Melt Equilibria in Natural Anhydrous Mafic Systems,” Contrib. Mineral. Petrol. 84, 310–326 (1983).

    Article  Google Scholar 

  19. D. Dolejs and D. R. Baker, “Thermodynamic Modeling of Melts in the System Na2O-NaAlO2-SiO2-F2O,” Geochim. Cosmochim. Acta 69, 5537–5556 (2005).

    Article  Google Scholar 

  20. O. A. Esin, “Polymer Model of Molten Silicates,” in Solutions. Melts (Results of Science and Techniques) (VINITI, Moscow, 1975), Vol. 2, pp. 76–107 [in Russian].

    Google Scholar 

  21. D. S. Korzhinskii, “Acid-Base Interaction of Components in the Silicate Melts and Trends of Cotectic Lines,” Dokl. Akad. Nauk SSSR 128(2), 383–386 (1959).

    Google Scholar 

  22. I. B. Bobylev and V. N. Anfilogov, “Features of Crystallization of Silicate Melts and Calculation of Liquidus Lines in Binary Systems,” in Structural Studies of Magmatic Melts (UNO AN SSSR, Sverdlovsk, 1981), pp. 52–61 [in Russian].

    Google Scholar 

  23. R. A. Cruz, S. A. Romero, R. M. Vargas, and L. M. Hallen, “Thermodynamic Analysis of the SiO2-NiO-FeO System,” J. Non-Cryst. Solids 351, 1359–1365 (2005).

    Article  Google Scholar 

  24. G. W. Toop and C. S. Samis, “Activities of Ions in Silicate Melts,” Trans. Metall. Soc. AIME 224, 878–887 (1962).

    Google Scholar 

  25. E. D. Lacy, “A Statistical Model of Polymerisation/Depolymerisation Relationships in Silicate Melts and Glasses,” Phys. Chem. Glasses 6, 171–180 (1965).

    Google Scholar 

  26. D. G. Fraser, “Thermodynamic Properties of Silicate Melts,” in Thermodynamics in Geology (D. Reidel Publ. Company, 1977), pp. 301–325 (1977).

  27. D. G. Fraser, “Acid-Base Properties and Structures: Towards a Structural Model for Predicting the Thermodynamic Properties of Silicate Melts,” Annals Geophysics 48(4/5), 549–559 (2005).

    Google Scholar 

  28. C. R. Masson, “Ionic Equilibria in Liquid Silicates,” J. Am. Ceram. Soc. 51, 134–143 (1968).

    Article  Google Scholar 

  29. C. R. Masson, I. B. Smith, and S. G. Whiteway, “Activities and Ionic Distributions in Liquid Silicates: Application of Polymer Theory,” Can. J. Chem. 48, 1456–1464 (1970).

    Article  Google Scholar 

  30. S. C. Whiteway, I. B. Smith, and C. R. Masson, “Theory of Molecular Size Distribution in Multichain Polymers,” Can. J. Chem. 48, 33–45 (1970).

    Article  Google Scholar 

  31. V. B. Pretnar, “Beitrag zur Ionentheorie der Silikatmelzen,” Ber. Bunsen Ges. Phys. Chem. 72, 773–778 (1968).

    Google Scholar 

  32. C. F. Baes, Jr. “A Polymer Model for BeF2 and SiO2 Melts,” J. Solid State Chem. 1, 159–170 (1970).

    Article  Google Scholar 

  33. O. A. Esin, “Comparison of Estimation Methods of the Degree of Polymerization of Silicate Melts,” in Physical Chemistry of Metallurgical Melts Tr. Inst. Metallurg., Vyp. 28, 76–90 (1972).

    Google Scholar 

  34. O. A. Esin, “On Complex Anions in the Melted Cinder,” in Structure and Properties of Metallurgical Melts, Tr. Inst. Metallurg., Vyp. 28, 76–90 (1974).

    Google Scholar 

  35. “Encyclopedia of Polymers,” Ed. by V. A. Kabanova, in Soviet Encyclopedia (Moscow, 1974), Vol. 2, pp. 286–300 [in Russian].

  36. C. R. Masson, “Anionic Composition of Glass-Forming Melts,” J. Non-Cryst. Solids 25, 3–41 (1977).

    Article  Google Scholar 

  37. P. C. Hess, “Structure of Silicate Melts,” Can. Mineral. 15, 162–178 (1977).

    Google Scholar 

  38. B. O. Mysen, “Experimental, in Situ, High-Temperature Studies of Properties and Structure of Silicate Melts Relevant to Magmatic Processes,” Eur. J. Mineral. 7, 745–766 (1995).

    Google Scholar 

  39. B. O. Mysen, “Structure and Properties of Magmatic Liquids: From Haplobasalt to Haploandesite,” Geochim. Cosmochim. Acta 63, 95–112 (1999).

    Article  Google Scholar 

  40. V. N. Bykov, V. N. Anfilogov, and A. A. Osipov, Spectroscopy and Structure of Silicate Melts and Glasses (IM URO RAN, Miass, 2001) [in Russian].

    Google Scholar 

  41. G. S. Henderson, “The Structure of Silicate Melts: A Glass Perspective,” Can. Mineral. 43, 1921–1958 (2005).

    Article  Google Scholar 

  42. V. G. Konakov, “Study of Oxygen Ion Activity in the Sodium-Silicate Melts,” Fiz. Khim. Stekla 16(5), 753–758 (1990).

    Google Scholar 

  43. V. G. Konakov and M. M. Shul’ts, Studies of Relative Basicities (Oxygen Indicator) of Melts in the Systems M 2 O-SiO 2 (m= Li, Na, K), Fiz. Khim. Stekla 22(6), 715–723 (1996).

    Google Scholar 

  44. G. Ottonello, “Thermodynamic Constraints Arising from the Polymeric Approach to Silicate Slags,” J. Non-Cryst. Solids 282, 72–85 (2001).

    Article  Google Scholar 

  45. J-H. Park and C.-H. Rhee, “Ionic Properties of Oxygen in Slag,” J. Non-Cryst. Solids 282, 7–14 (2001).

    Article  Google Scholar 

  46. G. Ottonello, R. Moretti, L. Marini, and M. V. Zuccolini, “Oxidation State of Iron in Silicate Glasses and Melts: A Thermochemical Model,” Chem. Geol. 174, 159–179 (2001).

    Article  Google Scholar 

  47. R. Moretti and G. Ottonello, “Polymerization and Disproportionation of Iron and Sulfur in Silicate Melts: Insights from an Optical Basicity-Based Approach,” J. Non-Cryst. Solids 323, 111–119 (2003).

    Article  Google Scholar 

  48. R. Moretti and G. Ottonello, “Solubility and Speciation of Sulfur in Silicate Melts: The Conjugated Toop-Samis-Flood-Grjotheim (CTSFG) Model,” Geochim. Cosmochim. Acta 69, 801–823 (2005).

    Article  Google Scholar 

  49. K. W. Semkow and L. A. Haskin, “Concentrations and Behavior of Oxygen and Oxide Ion in Melts of Composition CaO-MgO-xSiO2,” Geochim. Cosmochim. Acta 49, 1897–1908 (1985).

    Article  Google Scholar 

  50. R. O. Colson, C. R. Keedy, and L. A. Haskin, “Diffusion and Activity of NiO in CaO-MgO-Al2O3-SiO2 Melts Considering Effects of a O 2− and γNi 2+,” Geochim. Cosmochim. Acta 59, 909–925 (1995).

    Google Scholar 

  51. R. O. Colson, A. M. Floden, T. R. Haugen, et al., “Activities of NiO, FeO, and O2− in Silicate Melts,” Geochim. Cosmochim. Acta 69, 3061–3073 (2005).

    Article  Google Scholar 

  52. N. V. Borisova, V. G. Konakov, T. G. Kostyreva, and M. M. Shul’ts, “Possibilities of Complex Formation with the Participation of O2− Ions in the Melts and Glasses in the System Na2O-SiO2-CuO2-CuO,” Fiz. Khim. Stekla 29(1), 44–53 (2003).

    Google Scholar 

  53. G. Ottonello, “Chemical Interactions and Configurational Disorder in Silicate Melts,” Annals Geophysics 48(4/5), 561–581 (2005).

    Google Scholar 

  54. R. Moretti, “Polymerization, Basicity, Oxidation State and Their Role in Ionic Modeling of Silicate Melts,” Annals Geophysics 48(4/5), 583–608 (2005).

    Google Scholar 

  55. V. B. Polyakov and A. A. Ariskin, “Simulation of the Composition and Proportions of Anions in Polymerized Silicate Melts,” Glass Phys. Chem., 34, 50–62 (2008).

    Google Scholar 

  56. M. Temkin, “Mixture of Melted Salts as Ionic Solutions,” Zh. Fiz. Khim. 20(1), 105–110 (1946).

    Google Scholar 

  57. R. S. Bradley, “Thermodynamic Calculations on Phase Equilibria Involving Fused Salts, Part II, Solid Solutions and Applications to the Olivines,” Am. J. Sci. 260, 550–554 (1962).

    Google Scholar 

  58. C. T. Herzberg, “The Solubility of Olivine in Basaltic Liquids: An Ionic Model,” Geochim. Cosmochim. Acta 43, 1241–1251 (1979).

    Article  Google Scholar 

  59. O. A. Esin, “Polymerization of Anions in Molten Silicates,” Dokl. Akad. Nauk SSSR 211(2), 341–342 (1973).

    Google Scholar 

  60. O. A. Esin, “Isomeric Species of Anions and Estimation of Activities in Molten Silicates,” Zh. Fiz. Khim. 50(7), 1858–1860 (1976).

    Google Scholar 

  61. O. A. Esin, “Formation Constants and the Structure of Silicate Polymers,” Zh. Fiz. Khim. 52(4), 1073–1074 (1978).

    Google Scholar 

  62. M. Falk and R. E. Thomas, “Molecular Size Distribution in Random Polyfunctional Condensation with or without Ring Formation: Computer Simulation,” Can. J. Chem. 52, 3285–3295 (1974).

    Article  Google Scholar 

  63. J. R. Van Wezer, Phosphorous and Its Compounds (Inostrannaya Literatura, Moscow, 1962) [in Russian].

    Google Scholar 

  64. H. Maekawa, T. Maekawa, K. Kawamura, and T. Yokokawa, “The Structural Groups of Alkali Silicate Glasses Determined from 29Si MAS-NMR,” J. Non-Cryst. Solids 127, 53 (1991).

    Article  Google Scholar 

  65. M. L. Huggins, “The Structure of Amorphous Materials,” J. Phys. Chem. 58, 1141–1146 (1954).

    Article  Google Scholar 

  66. H. St. C. O’Neill and A. J. Berry, “Activity Coefficients at Low Dilution of CrO, NiO and CoO in Melts in the System CaO-MgO-Al2O3-SiO2 at 1400°C: Using the Thermodynamic Behavior of Transition Metal Oxides in Silicate Melts to Probe Their Structure,” Chem. Geol. 231, 77–89 (2006).

    Article  Google Scholar 

  67. A. A. Borisov, “Experimental Study of the Effect of SiO2 on Ni Solubility in Silicate Melts,” Petrologiya 14(6), 564–575 (2006) [Petrology 14, 530–539 (2006)].

    Google Scholar 

  68. A. A. Borisov, “Experimental Study of the Influence of SiO2 on the Solubility of Cobalt and Iron in Silicate Melts,” Petrologiya 15(6), 564–575 (2007) [Petrology 15, 523–529 (2007)].

    Google Scholar 

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  1. Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, ul. Kosygina 19, Moscow, 119991, Russia

    A. A. Ariskin

  2. Institute of Experimental Mineralogy, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia

    V. B. Polyakov

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  1. A. A. Ariskin
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Original Russian Text © A.A. Ariskin, V.B. Polyakov, 2008, published in Geokhimiya, 2008, No. 5, pp. 467–486.

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Ariskin, A.A., Polyakov, V.B. Simulation of molecular mass distributions and evaluation of O2− concentrations in polymerized silicate melts. Geochem. Int. 46, 429–447 (2008). https://doi.org/10.1134/S0016702908050017

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