SpringerLink
Log in

Calculation of the Melting Temperatures of Alkali Metal Halides Using the Thermodynamic Perturbation Theory

  • Published:
Russian Metallurgy (Metally) Aims and scope

Abstract

A model is proposed to describe liquid–crystal phase equilibria in order to calculate the melting temperatures of ionic compounds. The dependence of the melting temperatures of alkali metal halides on the cation–anion composition of a salt can be described in terms of ionic radii and polarizabilities when the thermodynamic perturbation theory is used for a molten phase. For the chemical potential of a crystalline phase, the Born–Mayer formulas for electrostatic energy and the Debye formula for taking into account the contribution of vibrations are used. The complete system of equations describing the liquid–solid equilibrium includes not only the equality of chemical potentials, but also self-consistency using an equation of state for calculating the equilibrium melt density at the solidification point. Another equation of the system is derived using the mean spherical model of an ion mixture for self-consistent finding of characteristic Blum’s screening parameter. On this basis, the melting temperatures of fluorides, chlorides, bromides, and iodides of lithium, sodium, potassium, rubidium, and cesium are calculated. A combination of the model of charged hard spheres of different diameters, which is taken as a reference in the mean spherical approximation, and the first correction due to the ion dipoles induced by the point charge of another ion to the chemical potential of a liquid salt is shown to be a good basis for quantitative agreement with the experimental data on the melting temperatures within a few percent. In addition, we also discusses the laws of changing the melting temperature reduced to the Coulomb energy at the minimum cation–anion distance and its dependence on the difference in the ionic radii of salts.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.

REFERENCES

  1. W. M. Haynes, Handbook of Chemistry and Physics, 97th ed. (CRC Press: Taylor & Francis Group, 2017).

  2. L. Pauling, The Nature of the Chemical Bond, 3rd ed. (Cornell University Press, 1960).

    Google Scholar 

  3. A. S. Dworkin and M. A. Bredig, J. Phys. Chem. 64, 269–272 (1960). https://doi.org/10.1021/j100831a023

    Article  CAS  Google Scholar 

  4. T. Forland, “Thermodynamic properties of fused salt systems,” in Fused Salts, Ed by B. R. Sundheim (McGraw-Hill, 1964), pp. 63–164.

    Google Scholar 

  5. H. Kanno, Nature 218, 765–766 (1968). https://doi.org/10.1038/218765b0

    Article  CAS  Google Scholar 

  6. H. Kanno, Bull. Chem. Soc. Jpn. 50, 2799–2800 (1977). https://doi.org/10.1246/bcsj.50.2799

    Article  CAS  Google Scholar 

  7. J. L. Aragones, E. Sanz, C. Valeriani, and C. Vega, J. Chem. Phys. 137, 104507 (2012). https://doi.org/10.1063/L4745205

    Article  CAS  Google Scholar 

  8. X. W. Sun, Y. D. Chu, Z. J. Liu, B. Kong, et al., Phys. B: Condens. Matter. 407, 60–63 (2012). https://doi.org/10.1016/j.physb.2011.09.119

    Article  CAS  Google Scholar 

  9. R. S. DeFever, H. Wang, Y. Zhang, and E. J. Maginn, J. Chem. Phys. 153, 011101 (2020). https://doi.org/10.1063/5.0012253

    Article  CAS  Google Scholar 

  10. P. A. Madden and M. Wilson, Chem. Soc. Rev. 25, 339–350 (1996). https://doi.org/10.1039/cs9962500339

    Article  CAS  Google Scholar 

  11. M. Salanne, C. Simon, P. Turq, and P. A. Madden, J. Fluor. Chem. 130, 38–44 (2008). https://doi.org/10.1016/jjfluchem.2008.07.013

    Article  Google Scholar 

  12. L. C. Dewan, C. Simon, P. A. Madden, L. W. Hobbs, et al., J. Nucl. Mater. 434, 322–327 (2013). https://doi.org/10.1016/jjnucmat.2012.12.006

    Article  CAS  Google Scholar 

  13. M. Salanne and P. A. Madden, Mol. Phys. 109, 2299–2315 (2011). https://doi.org/10.1080/00268976.2011.617523

    Article  CAS  Google Scholar 

  14. D. O. Zakiryanov, M. A. Kobelev, and N. K. Tkachev, J. Phys.: Conf. Ser. 1385, 012050 (2019). https://doi.org/10.1088/1742-6596/1385/1/012050

    Article  CAS  Google Scholar 

  15. D. O. Zakiryanov, M. A. Kobelev, and N. K. Tkachev, Fluid Ph. Equilib. 506, 112369 (2020). https://doi.org/10.1016/j.fluid.2019.112369

    Article  CAS  Google Scholar 

  16. A. G. Davydov and N. K. Tkachev, J. Mol. Liq. 318, 114045 (2020). https://doi.org/10.1016/j.molliq.2020.114045

    Article  CAS  Google Scholar 

  17. A. G. Davydov and N. K. Tkachev, J. Mol. Liq. 356, 119032 (2022). https://doi.org/10.1016/j.molliq.2022.119032

    Article  CAS  Google Scholar 

  18. A. G. Davydov and N. K. Tkachev, J. Phys. Chem. A 126, 3774–3782 (2022). https://doi.org/10.1021/acs.jpca.2c01614

    Article  CAS  Google Scholar 

  19. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Butterworth–Heinemann, 1980), Vol. 5, Part 1.

  20. A. G. Davydov and N. K. Tkachev, J. Mol. Liq. 275, 91–99 (2019). https://doi.org/10.1016/j.molliq.2018.10.133

    Article  CAS  Google Scholar 

  21. L. Blum, “Primitive electrolytes in the mean spherical approximation,” in Theoretical Chemistry: Advances and Perspectives, Ed. by H. Eyring and D. Henderson (Academic Press, 1980), pp. 1–66.

  22. L. Blum and Y. Rosenfeld, J. Stat. Phys. 63, 1177–1190 (1991). https://doi.org/10.1007/bf01030005

    Article  Google Scholar 

  23. N. K. Tkachev, “Phase diagram of a primitive model for a binary mixture of ionic liquids,” Dokl. Akad. Nauk 362, 75–78 (1998).

    Google Scholar 

  24. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt College Publishers, 1976).

  25. D. B. Sirdeshmukh, L. Sirdeshmukh, and K. G. Subhadra, Alkali Halides: A Handbook of Physical Properties (Springer, 2001).

    Book  Google Scholar 

  26. D. K. MacDonald and S. K. Roy, Phys. Rev. 97, 673–676 (1955). https://doi.org/10.1103/physrev.97.673

    Article  CAS  Google Scholar 

  27. I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans Green and Co, 1954).

    Google Scholar 

  28. M. Kucharczyk and S. Olszewski, Phys. Status Solidi B 114, 589–598 (1982). https://doi.org/10.1002/pssb.2221140236

    Article  CAS  Google Scholar 

  29. A. M. Krivtsov and V. A. Kuz’kin, “Derivation of equations of state for ideal crystals with a simple structure,” Izv. Ross. Akad. Nauk, Ser. Mekh. Tverd. Tela, No. 3, 67–72 (2011).

    Google Scholar 

  30. F. H. Stillinger, “Equilibrium theory of pure fused salts,” in Molten Salt Chemistry, Ed. by M. Blander (Interscience Publishers, 1964), pp. 1–108.

    Google Scholar 

  31. M. P. Tosi and F. G. Fumi, J. Phys. Chem. Solids 25, 45–52 (1964). https://doi.org/10.1016/0022-3697(64)90160-x

    Article  CAS  Google Scholar 

  32. S. S. Batsanov and A. S. Batsanov, Introduction to Structural Chemistry (Springer Science + Business Media, 2012).

  33. J. N. Wilson and R. M. Curtis, J. Phys. Chem. 74, 187–196 (1970). https://doi.org/10.1021/j100696a034

    Article  CAS  Google Scholar 

  34. M. N. Magomedov, “Calculation of Debye temperature for alkali halide crystals,” Teplofiz. Vys. Temp. 30, 1110–1117 (1992).

    CAS  Google Scholar 

  35. M. E. Fisher, “The story of Coulombic criticality,” J. Stat. Phys. 75, 1–36 (1994). https://doi.org/10.1007/BF02186278

    Article  Google Scholar 

Download references

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

Author information

Authors and Affiliations

  1. Institute of High-Temperature Electrochemistry, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    A. G. Davydov & N. K. Tkachev

Authors
  1. A. G. Davydov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. K. Tkachev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. G. Davydov.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by K. Shakhlevich

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Davydov, A.G., Tkachev, N.K. Calculation of the Melting Temperatures of Alkali Metal Halides Using the Thermodynamic Perturbation Theory. Russ. Metall. 2023, 977–985 (2023). https://doi.org/10.1134/S0036029523080074

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0036029523080074

Keywords:

Search

Navigation