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.
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References
A. R. Ubbelohde, The Molten State of Matter (Wiley, New York 1978; Metallurgiya, Moscow, 1982).
E. A. Moelwin-Hughes, Physical Chemistry (Pergamon, London, New York, Paris, 1961; Inostr. Liter., Moscow, 1962), Vols. 1, 2.
I. Z. Fischer, Statistical Theory of Liquids (Fizmatgiz, Moscow, 1961; Chicago Univ., Chicago, 1964).
G. A. Martunov, Classical Statistical Mechanics, Fundamental Theories of Physics, Vol. 89 (Kluwer, Dordrecht, 1997).
G. N. Sarkisov, Phys. Usp. 45, 597 (2002).
J. E. Lennard-Jones and A. F. Devonshire, Proc. R. Soc. A 169, 317 (1939).
J. Lajzerowicz and J. Siverdiere, Phys. Rev. A 11, 2079 (1975).
Y. Imry and M. Schwartz, Phys. Rev. A 21, 2946 (1980).
L. D. Landau, Zh. Eksp. Teor. Fiz. 5, 627 (1937).
I. Ya. Frenkel’, Introduction to Theory of Metals (GITTL, Moscow, 1950) [in Russian].
N. N. Bogolyubov, Quasimean in Problems of Statistical Mechanics (OIYaI, Dubna, 1963) [in Russian].
I. P. Bazarov, Statistical Theory of the Crystalline State (Mosk. Gos. Univ., Moscow, 1972) [in Russian].
L. S. Kukushkin and A. V. Osipov, Inorg. Mater. 35, 551 (1999).
Yu. K. Tovbin, Russ. J. Phys. Chem. A 80, 1554 (2006).
V. I. Yukalov, Phys. Rev. B 32, 436 (1985).
J. M. Rickman and R. LeSar, Ann. Rev. Mater. Res. 32, 195 (2002).
S. K. Kwak, Y. Cahyana, and J. K. Singh, J. Chem. Phys. 128, 134514 (2008).
A. Donev, F. H. Stillinger, and S. Torquato, J. Comput. Phys. 225, 509 (2007).
Yu. K. Tovbin, Theory of Physicochemical Processes at the Gas-Solid Interface (Nauka, Moscow, 1990) [in Russian].
T. Hill, Statistical Mechanics; Principles and Selected Applications (Dover, New York, 1987; Inostr. Liter., Moscow, 1960).
Yu. K. Tovbin, M. M. Senyavin, and L. K. Zhidkova, Russ. J. Phys. Chem. A 73, 245 (1999).
J. W. Gibbs, Elementary Principles of Statistical Mechanics (Ox Bow Press, 1981; Nauka, Moscow, 1982).
I. Prigogine and R. Defay, Chemical Thermodynamics (Longmans Green, London, 1954).
Yu. K. Tovbin, Zh. Fiz. Khim. 69, 118 (1995).
I. P. Bazarov, Zh. Fiz. Khim. 37, 2545 (1963).
I. P. Bazarov and P. N. Nikolaev, Correlation Theory of Crystal (Mosk. Gos. Univ., Moscow, 1981) [in Russian].
I. A. Kvasnikov, Theory of Equilibrium Systems. Statistical Mechanics (Editorial URSS, Moscow, 2002), Vol. 2 [in Russian].
Yu. K. Tovbin, Russ. J. Phys. Chem. A 86, 1356 (2012).
Yu. K. Tovbin, Zh. Fiz. Khim. 86, 1395 (1992).
V. G. Rostiashvili, V. I. Irzhak, and B. A. Rozenberg, Glass Transitions in Polymers (Khimiya, Leningrad, 1987) [in Russian].
A. M. Kosevich, Principles of Crystal-Lattice Mechanics (Nauka, Moscow, 1972) [in Russian].
P. Dean, in Computational Methods in Solid State Theory (Mir, Moscow, 1975), p. 209 [in Russian].
A. Maradudin, Defects and Vibrational Spectra of Crystals (Mir, Moscow, 1968) [in Russian].
Yu. K. Tovbin, Khim. Fiz. 21(1), 83 (2002).
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).
G. Leibfried and V. Ludwig, Theory of Anharmonic Effects in Crystals (Academic, New York, 1961; Inostr. Liter., Moscow, 1963).
N. M. Plakida, Statistical Physics and Quantum Field Theory (Nauka, Moscow, 1973), p. 205 [in Russian].
C. Heer, Statistical Mechanics, Kinetic Theory and Stochastic Processes (Academic, New York, 1972; Mir, Moscow, 1976).
L. Girifalco, Statistical Physics of Materials (Wiley, New York, 1973).
Ya. I. Frenkel’, Kinetic Theory of Liquids (Akad. Nauk SSSR, Moscow, 1945) [in Russian].
J. Crack, The Mathematics of Diffuion (Oxford Univ. Press, Oxford, 1975).
M. E. Glicksman, Diffusion in Solids (Wiley, New York, 2000).
N. I. Nikolaev, Diffusion in Membranes (Khimiya, Moscow, 1980) [in Russian].
B. S. Bokshtein, S. Z. Bokshtein, and A. A. Zhukho- vitskii, Thermodynamics and Kinetics of Diffusion in Solids (Metallurgiya, Moscow, 1974) [in Russian].
A. F. Andreev, Sov. Phys. Usp. 19, 137 (1976).
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Original Russian Text © Yu.K. Tovbin, 2013, published in Zhurnal Fizicheskoi Khimii, 2013, Vol. 87, No. 7, pp. 1097–1105.
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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
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DOI: https://doi.org/10.1134/S0036024413070340