Skip to main content
SpringerLink
Log in

Experimental determination and computation of the liquid miscibility gap in the system CaO-MgO-SiO2-TiO2

  • Basic And Applied Research
  • Published:
Journal of Phase Equilibria

Abstract

Coexisting liquids in the CaO-MgO-SiO2-TiO2 system were synthesized and quenched at ambient pressure in air from 1600 °C using a Rh-Pt resistance furnace and from 1800 to 2000 °C using a laser heated air levitation setup. Compositions of quenched glasses determined by electron microprobe analysis are reproduced in detail by weighted extrapolations of binary Margules-type excess functions. Using a generalized Kohler method, the authors illustrate the correlation between the degree of binary excess polynomials and their extrapolation behavior to higher-order systems. The presented extrapolation approach avoids additional ternary parameters in the CaO-SiO2-TiO2 and MgO-SiO2-TiO2 systems and affords a reasonable extrapolation outside of the compositional region of stable liquid immiscibility. In contrast, ternary excess parameters had to be added to binary interaction terms in the CaO-MgO-TiO2 and CaO-MgO-SiO2 systems to reproduce the solvus and liquidus phase relations reported in the literature. The excess entropy terms of the liquid were minimized in order to avoid unjustified stable miscibility gaps of the melt up to at least 3000 °C. The reliability of the authors’ polynomial approximation for the excess Gibbs energy of the melt is reduced only when ternary interaction terms are added to binary terms in the melt. However, the proposed method permits a valuable approximation of the highly complex excess Gibbs energy at solvus compositions in the system CaO-MgO-SiO2-TiO2 with a minimum number of excess terms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J.W. Greig, Immiscibility in Silicate Melts, Am. J. Sci., Vol 13, 1927, p 1–44 & 133–154

    Article  Google Scholar 

  2. I.I. Olshansky, Equilibrium of Two Immiscible Liquids in the Silicate Systems of the Alkaline Earth Metals, Dokl. Akad. Nauk SSSR, Vol 76, 1951, p 93–96 (in Russian)

    Google Scholar 

  3. L.W. Coughanour, R.S. Roth, and V.A. DeProsses, Phase Equilibrium Relations in the Systems Lime-Titania and Zirconia-Titania, J. Res. Natl. Bur. Stand., Vol 52, 1954, p 37–42

    Google Scholar 

  4. R.C. DeVries, R. Roy, and E.F. Osborn, The System TiO2-SiO2, Trans. Br. Ceram. Soc., Vol 53, 1954, p 525–540

    Google Scholar 

  5. R.C. DeVries, R. Roy, and E.F. Osborn, Phase Equilibria in the System CaO-TiO2, J. Phys. Chem., Vol 58, 1954, p 1069–1073

    Article  Google Scholar 

  6. R.C. DeVries, R. Roy, and E.F. Osborn, Phase Equilibria in the System CaO-TiO2-SiO2, J. Am. Ceram. Soc., Vol 38, 1955, p 158–171

    Article  Google Scholar 

  7. G.D. McTaggart and A.I. Andrews, Immiscibility Area in the System TiO2-ZrO2-SiO2, J. Am. Ceram. Soc., Vol 40, 1957, p 167–170

    Article  Google Scholar 

  8. F. Massazza and E. Sirchia, Il sistema MgO-SiO2-TiO2 nota I—revisione dei sistemi binari, Chim. l’Ind., Vol 40, 1958, p 376–380 (in Italian)

    Google Scholar 

  9. F. Massazza and E. Sirchia, Il sistema MgO-SiO2-TiO2 nota II—gli equilibri allo stato solido e alla fusione, Chim. l’Ind., Vol 40, 1958, p 460–467 (in Italian)

    Google Scholar 

  10. R.S. Roth, Revision of the Phase Equilibrium Diagram of the Binary System Calcia-Titania, Showing the Compound Ca4Ti3O10, J. Res. Natl. Bur. Stand., Vol 61, 1958, p 437–440

    Google Scholar 

  11. F. Kohler, Zur Berechnung der thermodynamischen Daten eines ternaeren Systems aus den zugehoerigen binaeren Systemen, Monatsh. Chem., Vol 91, 1960, p 738–740 (in German)

    Article  Google Scholar 

  12. G.W. Toop, Predicting Ternary Activities Using Binary Data, Trans. Metall. Soc. AIME, Vol 233, 1965, p 850–855

    Google Scholar 

  13. I.D. McGregor, The System MgO-SiO2-TiO2 and Its Bearing on the Distribution of TiO2 in Basalts, Am. J. Sci., Vol 267A, 1969, p 342–363

    Google Scholar 

  14. M.A. Rouf, A.H. Cooper, and H.B. Bell A Study of Phase Equilibria in the System CaO-MgO-TiO2, Trans. Brit. Ceram. Soc., Vol 68, 1969, p 263–267

    Google Scholar 

  15. E. Woermann, B. Brezny, and A. Muan, Phase Equilibria in the System MgO-Iron Oxide-TiO2 in Air, Am. J. Sci., Vol 267A, 1969, p 463–479

    Google Scholar 

  16. A. Jongejan and A.L. Wilkins, A Re-examination of the System CaO-TiO2 at Liquidus Temperatures, J. Less-Common Met., Vol 20, 1970, p 273–279

    Article  Google Scholar 

  17. S. Kimura and A. Muan, Phase Relations in the System CaO-Iron Oxide-TiO2 in Air, Am. Min., Vol 56, 1971, p 1332–1346

    Google Scholar 

  18. M.V. Rao, R. Hiskes, and W.A. Tiller, Determination of Solute Interaction Parameters by Analysis of Phase Equilibria Using a Linear Programming Technique, Acta Metall., Vol 21, 1973, p 733–740

    Article  Google Scholar 

  19. R.L. Shultz, Effects of Titanium Oxide on Equilibria among Refractory Phases in the System CaO-MgO-Iron Oxide, J. Am. Ceram. Soc., Vol 56, 1973, p 33–36

    Article  Google Scholar 

  20. F.Y. Galakhov, M.P. Areshev, V.T. Vavilonova, and V.I. Aver’yanov, Determination of the Limits of Metastable Liquidation in the Silica-Rich Region of the System TiO2-SiO2, Bull. Acad. Sci. USSR: Inorganic Mater., Vol 10, 1974, p 153–154

    Google Scholar 

  21. Y.-M. Muggianu, M. Gambino, and J.P. Bros, Enthalpies de formation des alliages liquides bismuth-etain-gallium a 723K. Choix d’un representation analytique des grandeur d’exces integrales et partielles de melange, J. Chim. Phys. Biol., Vol 72, 1975, p 83–88 (in French)

    Google Scholar 

  22. H.E. Tulgar, Solid State Relationships in the System CaO-TiO2, Istanbul Tek. Univers. Bull., Vol 29, 1976, p 111–129

    Google Scholar 

  23. J.D. Tewhey and P.C. Hess, The Two Phase Region in the CaO-SiO2 System: Experimental Data and Thermodynamic Analysis, Phys. Chem. Glasses, Vol 20, 1979, p 41–53

    Google Scholar 

  24. M. Hillert, Empirical Methods of Predicting and Representing Thermodynamic Properties of Ternary Solution Phases, Calphad, Vol 4, 1980, p 1–12

    Article  Google Scholar 

  25. M.I. Wood and P.C. Hess, The Structural Role of Al2O3 and TiO2 in Immiscible Silicate Liquids in the System SiO2-MgO-CaO-FeO-TiO2-Al2O3, Contrib. Min. Petrol., Vol 72, 1980, p 319–328

    Article  ADS  Google Scholar 

  26. R.G. Berman and T.H. Brown, A Thermodynamic Model for Multicomponent Melts with Application to the System CaO-Al2O3-SiO2, Geochim. Cosmochim. Acta, Vol 48, 1984, p 661–678

    Article  ADS  Google Scholar 

  27. M. Hoch and I. Arpshofen, Z. Metallkde., Vol 75, 1984, p 23–29

    Google Scholar 

  28. B. Wechsler and A. Navrotsky, Thermodynamics and Structural Chemistry of Compounds in the System MgO-TiO2, J. Solid State Chem., Vol 55, 1984, p 165–180

    Article  ADS  Google Scholar 

  29. R.G. Berman and T.H. Brown, Heat Capacities of Minerals in the System Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2: Representation, Estimation, and High Temperature Extrapolation, Contrib. Min. Petrol., Vol 89, 1985, p 168–183

    Article  ADS  Google Scholar 

  30. M.W. Chase, C.A. Davies, J.R. Downey, D.J. Frurip, R.A. McDonald, and A.N. Syverud, JANAF Thermochemical Tables, J. Phys. Chem. Ref. Data, Vol 14, 1985

  31. B. Sundman, B. Jansson, and J.-O. Andersson, Calphad, Vol 9, 1985, p 153

    Article  Google Scholar 

  32. R. Berman and T.H. Brown, Erratum: Heat Capacities of Minerals in the System Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2: Representation, Estimation, and High Temperature Extrapolation, Contrib. Min. Petrol., Vol 94, 1986, p 262

    Article  ADS  Google Scholar 

  33. V.B.M. Hageman and H.A.J. Oonk, “Liquid Immiscibility in the SiO2 + MgO, SiO2 + SrO, SiO2 + La2O3, SiO2 + Y2O3 Systems,” Phys. Chem. Glasses, Vol 27, 1986, p 194–198

    Google Scholar 

  34. V.B.M. Hageman, G.J.K. van den Berg, H.J. Jannsen, and H.A.J. Oonk, A Reinvestigation of Liquid Immiscibility in the SiO2-CaO System, Phys. Chem. Glasses, Vol 27, 1986, p 100–106

    Google Scholar 

  35. A.D. Pelton and M. Blander, Thermodynamic Analysis of Ordered Liquid Solutions by a Modified Quasichemical Approach—Application to Silicate Slags, Metall. Trans. B, Vol 17B, 1986, p 805–815

    Article  ADS  Google Scholar 

  36. M. Blander and A.D. Pelton, Thermodynamic Analysis of Binary Liquid Silicates and Prediction of Ternary Solution Properties by Modified Quasichemical Equations, Geochim. Cosmochim. Acta, Vol 51, 1987, p 85–95

    Article  ADS  Google Scholar 

  37. K.-C. Chou, A New Solution Model for Predicting Ternary Thermodynamic Properties, Calphad, Vol 11, 1987, p 293–300

    Article  Google Scholar 

  38. C. DeCapitani and T.H. Brown, The Computation of Chemical Equilibrium in Complex Systems Containing Non-Ideal Solutions, Geochim. Cosmochim. Acta, Vol 51, 1987, p 2639–2652

    Article  ADS  Google Scholar 

  39. R.G. Berman, Internally Consistent Thermodynamic Data for Minerals in the System Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2, J. Petrol., Vol 29, 1988, p 445–522

    Google Scholar 

  40. M. Hillert and X. Wang, Modelling of Asymmetric Immiscibility Gaps, Calphad, Vol 12, 1988, p 255–256

    Article  Google Scholar 

  41. G. Helffrich and B. Wood, Subregular Model for Multicomponent Solutions, Am. Min., Vol 74, 1989, p 1016–1022

    Google Scholar 

  42. S.L. Jackson, Extension of Wohl’s Ternary Asymmetric Solution Model to Four and n Components, Am. Min., Vol 74, 1989, p 14–17

    Google Scholar 

  43. G.F. Bastin and H.J.M. Heijligers, Quantitative Electron Probe Microanalysis of Ultralight Elements (Boron-Oxygen), Scanning, Vol 12, 1990, p 225–236

    Google Scholar 

  44. R.H. Davies, A.T. Dinsdale, T.G. Chart, T.I. Barry, and M.H. Rand, Application of MTDATA to the Modelling of Multicomponent Equilibria, High Temp. Sci., Vol 26, 1990, p 251–262

    Google Scholar 

  45. G. Eriksson and K. Hack, ChemSage—A Computer Program for the Calculation of Complex Chemical Equilibria, Metall. Trans. B, Vol 21B, 1990, p 1013–1023

    Article  ADS  Google Scholar 

  46. J.R. Taylor and A.T. Dinsdale, Thermodynamic and Phase Diagram Data for the CaO-SiO2 System, Calphad, Vol 14, 1990, p 71–88

    Article  Google Scholar 

  47. R.O. Sack and M.S. Ghiorso, An Internally Consistent Model for the Thermodynamic Properties of Fe-Mg-Titanomagnetite-Aluminate Spinels, Contrib. Min. Petrol., Vol 106, 1991, p 474–505

    Article  ADS  Google Scholar 

  48. G. Eriksson and A.D. Pelton, Critical Evaluation and Optimization of the Thermodynamic Properties and Phase Diagrams of the CaO-Al2O3, Al2O3-SiO2 and CaO-Al2O3-SiO2 Systems, Metall. Trans. B, Vol 24, 1993, p 1839–1849

    Google Scholar 

  49. G. Eriksson and A.D. Pelton, Critical Evaluation and Optimization of the Thermodynamic Properties and Phase Diagrams of the MnO-TiO2, MgO-TiO2, FeO-TiO2, Ti2O3-TiO2, Na2O-TiO2, and K2O-TiO2 Systems, Metall. Trans. B, Vol 24, 1993, p 795–805

    Article  Google Scholar 

  50. P. Wu, G. Eriksson, A.D. Pelton, and M. Blander, Prediction of Thermodynamic Properties and Phase Diagrams of Silicate Systems—Evaluation of the FeO-MgO-SiO2 System, ISIJ Int., Vol 33, 1993, p 26–35

    Article  Google Scholar 

  51. W. Cheng and J. Ganguly, Some Aspects of Multicomponent Excess Free Energy Models with Subregular Binaries, Geochim. Cosmochim. Acta, Vol 58, 1994, p 3763–3767

    Article  ADS  Google Scholar 

  52. G. Eriksson, P. Wu, M. Blander, and A.D. Pelton, Critical Evaluation and Optimization of the Thermodynamic Properties and Phase Diagram of the MnO-SiO2 and CaO-SiO2 Systems, Can. Metall. Q., Vol 33, 1994, p 13–21

    Google Scholar 

  53. W. Huang, M. Hillert, and X. Wang, Thermodynamic Assessment of the CaO-MgO-SiO2 System, Metall. Trans. A, Vol 26A, 1994, p 2293–2310

    Google Scholar 

  54. V. Swamy, S. Saxena, and B. Sundman, An Assessment of the One-Bar Liquidus Phase Relations in the MgO-SiO2 System, Calphad, Vol 18, 1994, p 157–164

    Article  Google Scholar 

  55. M.A. Villegas, A. dePablos, and J.M. Fernandez Navarro, Properties of CaO-TiO2-SiO2 Glasses, Glass Technol., Vol 35, 1994, p 276–280

    Google Scholar 

  56. S. Chakraborty, Diffusion in Silicate Melts, Rev. Min., Vol 32, 1995, p 411–503

    Google Scholar 

  57. 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. Min. Petrol., Vol 119, 1995, p 197–212

    Article  ADS  Google Scholar 

  58. T. Ban, S. Hayashi, A. Yasumori, and K. Okada, Calculation of Metastable Immiscibility Region in the Al2O3-SiO2 System, J. Mater. Res., Vol 11, 1996, p 1421–1427

    Article  ADS  Google Scholar 

  59. R.G. Berman and L.Y. Aranovich, Optimized Standard State and Solution Properties of Minerals. I. Model Calibration for Olivine, Orthopyroxene, Cordierite, and Ilmenite in the System FeO-MgO-CaO-Al2O3-TiO2-SiO2, Contrib. Mineral. Petrol., Vol 126, 1996, p 1–24

    Article  ADS  Google Scholar 

  60. N.A. Gokcen, Gibbs-Duhem-Margules Laws, J. Phase Equilibria, Vol 17, 1996, p 50–51

    Article  Google Scholar 

  61. J. Tomiska and A. Neckel, The Margules Concept: The Basis of Modern Algebraic Representations of Thermodynamic Excess Properties, J. Phase Equilibria, Vol 17, 1996, p 11–20

    Article  Google Scholar 

  62. K.-C. Chou, A New Generation Solution Model for Predicting Ternary Thermodynamic Properties of a Multicomponent System from Binaries, Metall. Trans. B, Vol 28B, 1997, p 439–445

    Google Scholar 

  63. M. Selleby, An Assessment of the Ca-Fe-O-Si System, Metall. Trans. B, Vol 28B, 1997, p 577–596

    Google Scholar 

  64. A.I. Zaitsev, A.D. Litvina, N.P. Lyakishev, and B.M. Mogutnov, Thermodynamics of CaO-Al2O3-SiO2 and CaF2-CaO-Al2O3-SiO2 Melts, J. Chem. Soc.—Farad. Trans., Vol 93, 1997, p 3089–3098

    Article  Google Scholar 

  65. C. DeCapitani and M. Kirschen, A Generalized Multicomponent Excess Function with Application to Immiscible Liquids in the System CaO-SiO2-TiO2, Geochim. Cosmochim. Acta, Vol 62, 1998, p 3753–3763

    Article  ADS  Google Scholar 

  66. B.A. Murtagh and M.A. Saunders, “MINOS 5.5. User’s Guide,” Technical Report SOL 83-20R, revised, Stanford University, 1998

  67. M. Kirschen, C. DeCapitani, F. Millot, J.-C. Rifflet, and J.-P. Coutures, Immiscible Silicate Liquids in the System SiO2-TiO2-Al2O3, Eur. J. Min., Vol 11, 1999, p 427–440

    Google Scholar 

Download references

Author information

Author notes

  1. M. Kirschen

    Present address: Centre National de Recherche Scientifique—Centre de Recherches sur la Synthèse et la Chimie des Minéraux CRSCM, 1A rue de la Férollerie, F-45071, Orléans Cedex 2, France

Authors and Affiliations

  1. Mineralogisch-Petrographisches Institut, Bernoullistrasse 30, CH-4056, Basel, Switzerland

    M. Kirschen & C. DeCapitani

Authors
  1. M. Kirschen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. DeCapitani
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kirschen, M., DeCapitani, C. Experimental determination and computation of the liquid miscibility gap in the system CaO-MgO-SiO2-TiO2 . JPE 20, 593–611 (1999). https://doi.org/10.1361/105497199770340581

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1361/105497199770340581

Keywords

Search

Navigation