Abstract
New relationships have been obtained in an integral form for binary systems in the case when one of the phases is dispersed (to nanometer sizes) inside another phase (matrix) in the framework of the thermodynamics of phase equilibrium, including surface phenomena. These relationships are used to construct a size-dependent phase diagram in the binary Mo–Ru system containing solid nanoparticles with bcc and hcp structures and a liquid phase in equilibrium conditions. The calculations are performed with the successive inclusion of the size dependences of the characteristics of pure components and the parameter of the interparticle interaction in the phases. The calculated results agree with the experimental data in the microscopic case.
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References
A. I. Rusanov, Phase Equilibria and Surface Phenomena (Khimiya, Leningrad, 1967) [in Russian].
V. K. Grigorovich, Heat Resistance and State Diagrams (Metallurgiya, Moscow, 1969) [in Russian].
P. E. L’vov, V. V. Svetukhin, and A. V. Obukhov, Phys. Solid State 53, 421 (2011).
A. L. Udovskii, Metally 5, 121 (2011).
A. L. Udovskii and D. A. Vasil’ev, Vestn. Novgor. Univ. 2 (73), 51 (2013).
T. Tanaka, Mater. Sci. Forum 653, 55 (2010).
A. I. Rusanov, Lectures on Surface Thermodynamics (Lan’, St. Petersburg, 2013) [in Russian].
A. G. Morachevskii, Physical Chemistry, Surface Phenomena and Disperse Systems (Lan’, St. Petersburg, 2015) [in Russian].
G. Reza Vakili-Nedzhaad, in Nanoscience and Nanotechnologies (EOLS, Magistr-Press, Moscow, 2010), p. 78 [in Russian].
A. A. Smirnov, The Molecular-Kinetic Theory of Metals (Nauka, Moscow, 1966) [in Russian].
L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams (Academic, New York, 1970, Mir, Moscow, 1972).
Z. A. Shebzukhov, M. A. Shebzukhova, and A. A. Shebzukhov, Poverkhnost’, No. 11, 102 (2009).
Z. A. Shebzukhov, M. A. Shebzukhova, and A. A. Shebzukhov, Poverkhnost’, No. 12, 94 (2009).
M. A. Shebzukhova and A. A. Shebzukhov, Bull. Russ. Acad. Sci.: Phys. 80, 718 (2016).
A. A. Shebzukhov and A. M. Karachaev, Poverkhnost’, Fiz., Khim., Mekh. 58 (5), 58 (1984).
S. I. Popel’, Surface Phenomena in Melts (Metallurgiya, Moscow, 1994, Cambridge International Science, Cambridge, 2003).
Z. A. Shebzukhov, M. A. Shebzukhova, and A. A. Shebzukhov, Izv. Kab.-Balk. Univ. im. Kh. M. Berbekova 1, 17 (2010).
M. A. Shebzukhova and A. A. Shebzukhov, Bull. Russ. Acad. Sci.: Phys. 76, 773 (2012).
A. I. Rusanov, Kolloidn. Zh. 49, 932 (1987).
Zhu Ru-Zeng and Wang Xiao-Song, Chin. Phys. B 19, 076801 (2010).
V. V. Baidov and L. L. Kunin, in Surface Phenomena in Melts and Solid Phases Arising from Them, Ed. by S. N. Zadumkin (Kab.-Balk. Knizhn. Izdat., Nal’chik, 1965), p. 79 [in Russian].
A. I. Frenkel, A. Yevick, Ch. Cooper, and R. Vasic, Ann. Rev. Anal. Chem. 4, 23 (2011).
M. A. Shebzukhova, Z. A. Shebzukhov, and A. A. Shebzukhov, Phys. Solid State 54, 185 (2012).
M. A. Shebzukhova, Z. A. Shebzukhov, and A. A. Shebzukhov, Izv. Kab.-Balk. Univ. im. Kh. M. Berbekova 1 (3), 83 (2011).
M. A. Shebzukhova, Z. A. Shebzukhov, and A. A. Shebzukhov, Bull. Russ. Acad. Sci.: Phys. 74, 697 (2010).
J. Rowlinson and B. Widom, Molecular Theory of Capillarity (Dover, New York, 2003, Mir, Moscow, 1986).
W. Vogelsberger and G. Marx, Z. Phys. Chem. 257, 580 (1976).
Q. Jiang and H. M. Li, Surf. Sci. Rep. 63, 427 (2008).
S. I. Novikova, Thermal Expansion of Solids (Nauka, Moscow, 1974) [in Russian].
V. E. Zinov’ev, E. N. Kelina, and L. I. Komarova, Review on Thermophysical Properties of Substances (IVTAN SSSR, Moscow, 1988), No. 3, p. 71 [in Russian].
S. N. Zadumkin, Fiz. Met. Metalloved. 13, 24 (1962).
L. A. Girifalco and R. I. Cood, J. Phys. Chem. 61, 904 (1957).
S. I. Popel’, M. A. Spiridonov, and L. A. Zhukova, Atomic Ordering in the Melted and Amorphous Metals (Ural. Gos. Tekh. Univ., Yekaterinburg, 1997) [in Russian].
V. P. Skripov and M. Z. Faizullin, Phase Transitions Crystal-Liquid-Gas and Thermodynamic Similarity (Fizmatlit, Moscow, 2003) [in Russian].
H. Kleykamp, J. Less-Common Met. 136, 271 (1988).
R. Gürler, J. Alloys Compd. 285, 133 (1999).
State Diagram of Binary Metal Systems, Ed. by N. P. Lyakishev (Mashinostroenie, Moscow, 2001), Vol. 3, Pt. 1 [in Russian].
N. T. Gladkikh, S. V. Dukarov, A. P. Kryshtal’, V. I. Larin, V. N. Sukhov, and S. I. Bogatyrenko, in Surface Phenomena and Phase Transformations in Condensed Films, Ed. by N. T. Gladkikh (Khark. Nats. Univ. im. V. N. Karazina, Khar’kov, 2004) [in Russian].
J. Sopousek, J. Vrestal, J. Pinkas, P. Broz, J. Bursik, A. Styskalik, D. Skoda, O. Zobac, and J. Lee, CALPHAD 45, 33 (2014).
A. Roshanghias, J. Vrestal, A. Yakymovgech, K. Richter, and H. Ipser, CALPHAD 49, 101 (2015).
S. Bajaj, M. G. Haverty, R. Arroyave, W. A. Goddard, and S. Shankare, Nanoscale 7, 9868 (2015).
P. E. L’vov and V. V. Svetukhin, Tech. Phys. Lett. 35, 1040 (2009).
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Original Russian Text © M.A. Shebzukhova, A.A. Shebzukhov, 2017, published in Fizika Tverdogo Tela, 2017, Vol., No. 7, pp. 1368–1378.
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Shebzukhova, M.A., Shebzukhov, A.A. Influence of the nanodimensional effects on the composition of coexisting phases in a binary system with curved boundaries. Phys. Solid State 59, 1395–1405 (2017). https://doi.org/10.1134/S1063783417070253
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DOI: https://doi.org/10.1134/S1063783417070253