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Size Dependences of the Thermal Physical Properties of Nanoparticles: Entropy and Heat of Melting

  • THERMOPHYSICAL PROPERTIES OF MATERIALS
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High Temperature Aims and scope

Abstract

In the thermodynamic theory of phase equilibria in disperse systems, the size dependences of jumps in entropy and the heat of fusion of particles (including those in the nanometer range) are obtained with strict and consistent consideration of surface phenomena in the approach with separating surfaces. The consideration is carried out taking into account the dimensional dependences of the molar volume, melting temperature, and interfacial tension. Using the obtained relations, calculations were performed for spherical sodium and tin nanoparticles. This implies a decrease in the entropy and heat of fusion with decreasing nanoparticle size. The results are in close agreement with the experimental and calculated data available in the literature.

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REFERENCES

  1. Roduner, E., Nanoscopic Materials: Size-Dependent Phenomena and Growth Principles, London: R. Soc. Chem., 2006.

    Book  Google Scholar 

  2. Jiang, Q. and Shi, F.G., Mater. Lett., 1998, vol. 37, p. 79.

    Article  Google Scholar 

  3. Jiang, Q., Yang, C.C., and Li, J.C., Mater. Lett., 2002, vol. 56, p. 1019.

    Article  Google Scholar 

  4. Shandiz, M.A. and Safaci, A., Mater. Lett., 2008, vol. 62, p. 3954.

    Article  Google Scholar 

  5. Summ, B.D., Osnovy kolloidnoi khimii (Fundamentals of Colloidal Chemistry), Moscow: Akademiya, 2006.

  6. Andrievskii, R.A., Osnovy nanostrukturnogo materialovedeniya (Fundamentals of Nanostructured Materials Science), Moscow: Binom, 2012.

  7. Singh, M., Taele, B.M., and Patel, G., Orient. J. Chem., 2018, vol. 34, no. 5, p. 2282.

    Article  Google Scholar 

  8. Regel, A.R. and Glazov, V.M., Semiconductors, 1995, vol. 29, p. 405.

    ADS  Google Scholar 

  9. Qi, W.H., Wang, M.P., and Liu, Q.H., Mater. Sci., 2005, vol. 40, p. 2737.

    Article  ADS  Google Scholar 

  10. Tsyu, Ya., L’yu, V., Chzhan, V., and Chzhai, Ch., Fiz. Met. Metalloved., 2019, vol. 120, no. 5, p. 451.

    Google Scholar 

  11. Kumar, R., Sharma, G., and Kumar, M., J. Thermodyn., 2013, vol. 5, p. 5.

    Google Scholar 

  12. Sdobnyakov, N.Yu., Komarov, P.V., Kolosov, A.Yu., Novozhilov, N.V., Sokolov, D.N., and Kul’pin, D.A., Kondens. Sredy Mezhfaznye Granitsy, 2013, vol. 15, no. 3, p. 337.

    Google Scholar 

  13. Sdobnyakov, N.Yu., Sokolov, D.N., Myasnichenko, V.S., and Bazulev, A.N., in Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov (Physicochemical Aspects of Studying Clusters, Nanostructures and Nanomaterials), Samsonov, V.M., Ed., Tver: Tversk. Gos. Univ., 2014, vol. 6, p. 342.

  14. Samsonov, V.M., Sdobnyakov, N.Yu., Vasil’ev, S.A., and Sokolov, D.N., Bull. Russ. Acad. Sci.: Phys., 2016, vol. 80, no. 5, p. 494.

    Article  Google Scholar 

  15. Kuzamishev, A.G., Shebzukhova, M.A., Bzhikhatlov, K.Ch., and Shebzukhov, A.A., High Temp., 2022, vol. 60, no. 3, p. 304.

    Article  Google Scholar 

  16. Rusanov, A.I., Fazovye ravnovesiya i poverkhnostnye yavleniya (Phase Equilibria and Surface Phenomena), Leningrad: Khimiya, 1967.

  17. Shebzukhova, M.A. and Shebzukhov, A.A., Bull. Russ. Acad. Sci.: Phys., 2012, vol. 76, no. 7, p. 772.

    Google Scholar 

  18. Shebzukhov, Z.A., Shebzukhova, M.A., and Shebzukhov, A.A., Izv. Kabard.-Balkar. Gos. Univ., 2010, no. 7, p. 17.

  19. Skripov, V.P. and Faizullin, M.Z., Fazovye perekhody kristall-zhidkost’-par i termodinamicheskoe podobie (Phase Transitions Crystal–Liquid–Vapor and Thermodynamic Similarity), Moscow: Fizmatlit, 2003.

  20. Vogelsberger, W.J. and Marx, G., Z. Phys. Chem., 1976, vol. 257, no. 3, p. 580.

    Article  Google Scholar 

  21. Vogelsberger, W.J., Sonnefeld, J., and Rudakoff, G., Z. Phys. Chem., 1985, vol. 226, p. 225.

    Google Scholar 

  22. Skripov, V.P. and Faizullin, M.Z., in Fazovye prevrashcheniya v metastabil’nykh sistemakh (Phase Transformations in Metastable Systems), Yekaterinburg: Akad. Nauk SSSR, 1983, p. 18.

  23. Glazov, V.M., Lazarev, V.B., and Zharov, V.V., Fazovye diagrammy prostykh veshchestv (Phase Diagrams of Simple Substances), Moscow: Nauka, 1980.

  24. Stankus, S.V. and Khairulin, R.A., High Temp., 2006, vol. 44, no. 3, p. 389.

    Article  Google Scholar 

  25. Safaei, A. and Shandiz, M.A., Phys. E (Amsterdam, Neth.), 2009, vol. 41, p. 359.

    Google Scholar 

  26. Lai, S.L., Guo, J.V., Petrova, V., Ramanathal, G., and Allen, L.H., Phys. Rev. Lett., 1996, vol. 77, p. 99.

    Article  ADS  Google Scholar 

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

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  1. Berbekov Kabardino-Balkarian State University, Nalchik, Russia

    A. G. Kuzamishev, M. A. Shebzukhova & K. Ch. Bzhikhatlov

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  1. A. G. Kuzamishev
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  2. M. A. Shebzukhova
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  3. K. Ch. Bzhikhatlov
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Correspondence to M. A. Shebzukhova.

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Kuzamishev, A.G., Shebzukhova, M.A. & Bzhikhatlov, K.C. Size Dependences of the Thermal Physical Properties of Nanoparticles: Entropy and Heat of Melting. High Temp 61, 638–643 (2023). https://doi.org/10.1134/S0018151X23050097

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