Skip to main content
Log in

Fundamentals of the theory of melting of simple substances with consideration of their defects

  • Chemical Thermodynamics and Thermochemistry
  • Published:
Russian Journal of Physical Chemistry A Aims and scope Submit manuscript

Abstract

Molecular principles of the theory of melting of simple substances are considered with regard to defects caused by vacancies. Equations are derived for the chemical potential of atoms in a defective crystal with allowance for their vibrational motion, enabling the determination of coexisting phases (solid-vapor or solid-liquid) from the condition of the equality of chemical potentials. All three aggregate states of matter are described within a unified molecular approach: a lattice gas model. This makes it possible to combine a description of a cell filling with liquid, or vapor and a solid with phase differences in these states during the cell filling. N.N. Bogolyubov’s concept of quasi-averages, from which the degeneration of the density distribution function in space is removed, is applied to describe the crystals. Questions as to the minimum size of the phase corresponding to the concept of quasi-averages and the criteria for the transition of a defective crystal to the frozen state are discussed.

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. A. R. Ubbelohde, The Molten State of Matter (Wiley, New York 1978; Metallurgiya, Moscow, 1982).

    Google Scholar 

  2. E. A. Moelwin-Hughes, Physical Chemistry (Pergamon, London, New York, Paris, 1961; Inostr. Liter., Moscow, 1962), Vols. 1, 2.

    Google Scholar 

  3. I. Z. Fischer, Statistical Theory of Liquids (Fizmatgiz, Moscow, 1961; Chicago Univ., Chicago, 1964).

    Google Scholar 

  4. G. A. Martunov, Classical Statistical Mechanics, Fundamental Theories of Physics, Vol. 89 (Kluwer, Dordrecht, 1997).

    Book  Google Scholar 

  5. G. N. Sarkisov, Phys. Usp. 45, 597 (2002).

    Article  CAS  Google Scholar 

  6. J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. A 169, 317 (1939).

    Article  CAS  Google Scholar 

  7. J. Lajzerowicz and J. Siverdiere, Phys. Rev. A 11, 2079 (1975).

    Article  Google Scholar 

  8. Y. Imry and M. Schwartz, Phys. Rev. A 21, 2946 (1980).

    CAS  Google Scholar 

  9. L. D. Landau, Zh. Eksp. Teor. Fiz. 5, 627 (1937).

    Google Scholar 

  10. I. Ya. Frenkel’, Introduction to Theory of Metals (GITTL, Moscow, 1950) [in Russian].

    Google Scholar 

  11. N. N. Bogolyubov, Quasimean in Problems of Statistical Mechanics (OIYaI, Dubna, 1963) [in Russian].

    Google Scholar 

  12. I. P. Bazarov, Statistical Theory of the Crystalline State (Mosk. Gos. Univ., Moscow, 1972) [in Russian].

    Google Scholar 

  13. L. S. Kukushkin and A. V. Osipov, Inorg. Mater. 35, 551 (1999).

    CAS  Google Scholar 

  14. Yu. K. Tovbin, Russ. J. Phys. Chem. A 80, 1554 (2006).

    Article  CAS  Google Scholar 

  15. V. I. Yukalov, Phys. Rev. B 32, 436 (1985).

    Article  CAS  Google Scholar 

  16. J. M. Rickman and R. LeSar, Ann. Rev. Mater. Res. 32, 195 (2002).

    Article  CAS  Google Scholar 

  17. S. K. Kwak, Y. Cahyana, and J. K. Singh, J. Chem. Phys. 128, 134514 (2008).

    Article  Google Scholar 

  18. A. Donev, F. H. Stillinger, and S. Torquato, J. Comput. Phys. 225, 509 (2007).

    Article  CAS  Google Scholar 

  19. Yu. K. Tovbin, Theory of Physicochemical Processes at the Gas-Solid Interface (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  20. T. Hill, Statistical Mechanics; Principles and Selected Applications (Dover, New York, 1987; Inostr. Liter., Moscow, 1960).

    Google Scholar 

  21. Yu. K. Tovbin, M. M. Senyavin, and L. K. Zhidkova, Russ. J. Phys. Chem. A 73, 245 (1999).

    Google Scholar 

  22. J. W. Gibbs, Elementary Principles of Statistical Mechanics (Ox Bow Press, 1981; Nauka, Moscow, 1982).

    Google Scholar 

  23. I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans Green, London, 1954).

    Google Scholar 

  24. Yu. K. Tovbin, Zh. Fiz. Khim. 69, 118 (1995).

    CAS  Google Scholar 

  25. I. P. Bazarov, Zh. Fiz. Khim. 37, 2545 (1963).

    CAS  Google Scholar 

  26. I. P. Bazarov and P. N. Nikolaev, Correlation Theory of Crystal (Mosk. Gos. Univ., Moscow, 1981) [in Russian].

    Google Scholar 

  27. I. A. Kvasnikov, Theory of Equilibrium Systems. Statistical Mechanics (Editorial URSS, Moscow, 2002), Vol. 2 [in Russian].

    Google Scholar 

  28. Yu. K. Tovbin, Russ. J. Phys. Chem. A 86, 1356 (2012).

    Article  CAS  Google Scholar 

  29. Yu. K. Tovbin, Zh. Fiz. Khim. 86, 1395 (1992).

    Google Scholar 

  30. V. G. Rostiashvili, V. I. Irzhak, and B. A. Rozenberg, Glass Transitions in Polymers (Khimiya, Leningrad, 1987) [in Russian].

    Google Scholar 

  31. A. M. Kosevich, Principles of Crystal-Lattice Mechanics (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  32. P. Dean, in Computational Methods in Solid State Theory (Mir, Moscow, 1975), p. 209 [in Russian].

    Google Scholar 

  33. A. Maradudin, Defects and Vibrational Spectra of Crystals (Mir, Moscow, 1968) [in Russian].

    Google Scholar 

  34. Yu. K. Tovbin, Khim. Fiz. 21(1), 83 (2002).

    CAS  Google Scholar 

  35. G. Leibfried, Microscopic Theory of Mechanical and Thermal Properties of Crystals, in Handbuch der Physik, Vol. 7, Pt. 1, Ed. by S. Flügge (Springer-Verlag, Berlin, 1978; GIFML, Moscow, 1963).

    Google Scholar 

  36. G. Leibfried and V. Ludwig, Theory of Anharmonic Effects in Crystals (Academic, New York, 1961; Inostr. Liter., Moscow, 1963).

    Google Scholar 

  37. N. M. Plakida, Statistical Physics and Quantum Field Theory (Nauka, Moscow, 1973), p. 205 [in Russian].

    Google Scholar 

  38. C. Heer, Statistical Mechanics, Kinetic Theory and Stochastic Processes (Academic, New York, 1972; Mir, Moscow, 1976).

    Google Scholar 

  39. L. Girifalco, Statistical Physics of Materials (Wiley, New York, 1973).

    Google Scholar 

  40. Ya. I. Frenkel’, Kinetic Theory of Liquids (Akad. Nauk SSSR, Moscow, 1945) [in Russian].

    Google Scholar 

  41. J. Crack, The Mathematics of Diffuion (Oxford Univ. Press, Oxford, 1975).

    Google Scholar 

  42. M. E. Glicksman, Diffusion in Solids (Wiley, New York, 2000).

    Google Scholar 

  43. N. I. Nikolaev, Diffusion in Membranes (Khimiya, Moscow, 1980) [in Russian].

    Google Scholar 

  44. B. S. Bokshtein, S. Z. Bokshtein, and A. A. Zhukho- vitskii, Thermodynamics and Kinetics of Diffusion in Solids (Metallurgiya, Moscow, 1974) [in Russian].

    Google Scholar 

  45. A. F. Andreev, Sov. Phys. Usp. 19, 137 (1976).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © Yu.K. Tovbin, 2013, published in Zhurnal Fizicheskoi Khimii, 2013, Vol. 87, No. 7, pp. 1097–1105.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tovbin, Y.K. Fundamentals of the theory of melting of simple substances with consideration of their defects. Russ. J. Phys. Chem. 87, 1083–1091 (2013). https://doi.org/10.1134/S0036024413070340

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0036024413070340

Keywords

Navigation