Skip to main content
Log in

Melting diagrams of quaternary systems with a single compound

  • Physicochemical Analysis of Inorganic Systems
  • Published:
Russian Journal of Inorganic Chemistry Aims and scope Submit manuscript

Abstract

Topological analysis was made of the structure of the melting diagrams of quaternary systems with a single compound. Graphs of phase diagrams were constructed, which show the relative positions of invariant points and monovariant lines on the liquidus hypersurface. It was shown that there exist two types of diagrams with a binary compound and six types of diagrams with a ternary compound. Quaternary compound C can form by congruent crystallization reaction L = C (I) or by the interaction of melt with components: L + K1 = C (II), L + K1 + K2 = C (III), or L + K1 + K2 + K3 = C (IV). There are 23 types of diagrams with reaction (I) and 23 types of diagrams with reaction (II), which described by identical graphs; 25 types of diagrams with reaction (III); and 6 types of diagrams with reaction (IV). Fragments of the obtained diagrams correspond to various topological situations, which may occur in more-component systems.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Hillert, Phase Equilibria, Phase Diagrams and Phase Transformation. Their Thermodynamic Basis (Cambridge University Press, Cambridge, 1998).

    Google Scholar 

  2. H. Lukas, S. G. Fries, and B. Sundman, Computation Thermodynamics: The CALPHAD Method (Cambridge University Press, Cambridge, 2007).

    Book  Google Scholar 

  3. A. B. Mlodzeevskii, Geometric Thermodynamics (MGU, Moscow, 1956) [in Russian].

    Google Scholar 

  4. V. I. Kosyakov, V. A. Shestakov, and E. V. Grachev, Dokl. Phys. Chem. 443 (1), 53 (2012).

    Article  CAS  Google Scholar 

  5. F. N. Rhines, Phase Diagrams in Metallurgy: Their Development and Application (McGraw-Hill, New York, 1956).

    Google Scholar 

  6. A. M. Zakharov, State Diagrams of Quaternary Systems (Metallurgiya, Moscow, 1964) [in Russian].

    Google Scholar 

  7. V. Ya. Anosov, M. I. Ozerova, and Yu. Ya. Fialkov, Fundamentals of Physicochemical Analysis (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  8. D. A. Petrov, Quaternary Systems: A New Approach to Construction and Analysis (Metallurgiya, Moscow, 1991) [in Russian].

    Google Scholar 

  9. V. I. Lutsyk, V. P. Vorob’eva, and O. G. Sumkina, Modeling of Phase Diagrams of Quaternary Systems (Nauka, Sib. Otd-e, Novosibirsk, 1992) [in Russian].

    Google Scholar 

  10. K. A. Khaldoyanidi, Phase Diagrams of Heterogeneous Systems with Transformations (INKh SO RAN, Novosibirsk, 2004) [in Russian].

    Google Scholar 

  11. Melting Diagrams of Salt Systems: Multicomponent Systems, Ed. by V. I. Posypaiko and E. A. Alekseeva (Khimiya, Moscow, 1977) [in Russian].

  12. Minerals: Diagrams of Phase Equilibria, Issue 1: Phase Equilibria Important for Natural Mineral Formation (Nauka, Moscow, 1974) [in Russian].

  13. B. D. Babaev and A. M. Gasanaliev, Inorg. Mater. 36, 954 (2000).

    Article  CAS  Google Scholar 

  14. N. S. Kurnakov, Introduction to Physicochemical Analysis (AN SSSR, Moscow, 1940) [in Russian].

    Google Scholar 

  15. V. I. Kosyakov and E. F. Sinyakova, Russ. J. Inorg. Chem. 62, (2017) (in press).

    Google Scholar 

  16. V. I. Kosyakov and V. A. Shestakov, Russ. J. Inorg. Chem. 62, (2017) (in press).

    Google Scholar 

  17. V. I. Kosyakov, V. A. Shestakov, and E. V. Grachev, Russ. J. Inorg. Chem. 62, 318 (2017).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. I. Kosyakov.

Additional information

Original Russian Text © V.I. Kosyakov, 2017, published in Zhurnal Neorganicheskoi Khimii, 2017, Vol. 62, No. 7, pp. 988–996.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kosyakov, V.I. Melting diagrams of quaternary systems with a single compound. Russ. J. Inorg. Chem. 62, 987–994 (2017). https://doi.org/10.1134/S0036023617070117

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0036023617070117

Navigation