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Phase Equilibrium and Surface Properties of a Binary System Containing Nanoparticles

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Abstract

A consistent description of phase equilibrium and surface phenomena in binary systems containing monodisperse spherical nanoparticles of arbitrary (including nanoscale) size is presented in the context of the classical method with separating surfaces. Using the obtained relations, we have calculated the composition of coexisting phases and interface layer, and interfacial tension on the boundary between nanoparticles and the matrix at different temperatures in Ti-Mo system. The results of the calculations are consistent with the available experimental data.

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References

  1. A. I. Rusanov, Phase Equilibria and Surface Phenomena (Khimiya, Leningr. otd, Leningrad, 1967) [in Russian].

    Google Scholar 

  2. A. I. Rusanov, Thermodynamical Principles of Mechanochemistry (Nauka, St. Petersburg, 2006) [in Russian].

    Google Scholar 

  3. A. I. Rusanov, Lectures on Surface Thermodynamics (Lan’, St. Petersburg, 2013) [in Russian].

    Google Scholar 

  4. Nanoscience and Nanotechnologies, Encyclopedy of Life Support Systems (Yunesko, EOLSS, Magistr-Press, Moscow, 2010) [in Russian].

  5. V. K. Grigorovich, High-Temperature Strength and State Diagram (Metallurgiya, Moscow, 1969) [in Russian].

    Google Scholar 

  6. P. E. L’vov, V. V. Svetukhin, and A. V. Obukhov, Phys. Solid State 53, 421 (2011).

    Article  ADS  Google Scholar 

  7. P. E. L’vov and V. V. Svetukhin, Phys. Solid State 55, 2374 (2013).

    Article  ADS  Google Scholar 

  8. P. E. L’vov and V. V. Svetukhin, Phys. Solid State 56, 1889 (2014).

    Article  ADS  Google Scholar 

  9. J. W. Gibbs, The Collected Works (New York, Longmans, Green, 1928).

    MATH  Google Scholar 

  10. M. A. Shebzukhova and A. A. Shebzukhov, Phys. Solid State 59, 1395 (2017).

    Article  ADS  Google Scholar 

  11. Z. A. Shebzukhov, M. A. Shebzukhova, and A. A. Shebzukhov, Poverkhnost’, No. 11, 102 (2009).

    Google Scholar 

  12. A. A. Smirnov, Molecular-Kinetic Theory of Metals (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  13. Z. A. Shebzukhov, M. A. Shebzukhova, and A. A Shebzukhov, Izv. Kab.-Balk. Univ. Kh. M. Berbekova, No. 1, 17 (2010).

    Google Scholar 

  14. M. Hansen and K. Anderko, Structure of Binary Alloys (McGraw-Hill, New York, 1958; Metallurgizdat, Moscow, 1962), Vol. 2.

    Google Scholar 

  15. L. Kaufman and H. Bernstein, Computer Calculasion of Phase Diagrams (Mir, Moscow, 1972; Academic, New York, 1970).

    Google Scholar 

  16. Q. Jiang and H. M. Li, Surf. Sci. Rep. 63, 427 (2008).

    Article  ADS  Google Scholar 

  17. S. V. Stankus, Preprint No. 247-91 (Novosibirsk, 1991).

  18. M. N. Magomedov, Study of Interatomic Interaction, Formation of Vacancies and Self-Diffusion in Crystals (Fizmatlit, Moscow, 2010) [in Russian].

    Google Scholar 

  19. W. Vogelsberger and G. Marx, Z. Phys. Chem. 257, 580 (1976).

    Article  Google Scholar 

  20. V. B. Kogan, Heterogeneous Equilibria (Khimiya, Leningrad, 1968) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Berbekov Kabardino-Balkarian State University, Nal’chik, Russia

    M. A. Shebzukhova & A. A. Shebzukhov

Authors
  1. M. A. Shebzukhova
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  2. A. A. Shebzukhov
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Correspondence to M. A. Shebzukhova.

Additional information

Original Russian Text © M.A. Shebzukhova, A.A. Shebzukhov, 2018, published in Fizika Tverdogo Tela, 2018, Vol. 60, No. 2, pp. 390–395.

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Shebzukhova, M.A., Shebzukhov, A.A. Phase Equilibrium and Surface Properties of a Binary System Containing Nanoparticles. Phys. Solid State 60, 397–403 (2018). https://doi.org/10.1134/S1063783418020245

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  • DOI: https://doi.org/10.1134/S1063783418020245

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