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Differential equation for the melting temperature of small-size particles

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Abstract

A differential equation for determining the melting temperature of small-size particles has been derived within the framework of a thermodynamic approach. The equation has a rather general form that admits the dependence of physical quantities such as the heat of melting, surface tension, and molar volumes in the solid and liquid state on the particles radius. The result of the integration of the obtained equation in particular cases leads to the well-known formulas.

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References

  1. A. N. Gusev, Nanomaterials, Nanostructures, Nanotechnologies (Fizmatlit, Mocow, 2005) [in Russian].

    Google Scholar 

  2. 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 (Kharkiv National University, Kharkiv, 2004) [in Russian].

    Google Scholar 

  3. G. N. Makarov, Usp. Fiz. Nauk 180, 185 (2010) [Phys. Usp. 53, 179 (2010)].

    Article  Google Scholar 

  4. C. J. Coombes, J. Phys. F: Metal Phys. 2, 411 (1972).

    Article  ADS  Google Scholar 

  5. C. R. M. Wronski, Brit. J. Appl. Phys. 18, 1713 (1967).

    Article  Google Scholar 

  6. P. K. Korotkov, R. A. Musukov, T. A. Orkvasov, and V. A. Sozaev, Zh. Tekh. Fiz. 78(3), 99 (2008) [Tech. Phys. 53, 383 (2008)].

    Google Scholar 

  7. S. L. Gafner, L. V. Redel’, and Yu. Ya. Gafner, Basic Problems of Materials Science, Vol. 5, 21 (2008).

    Google Scholar 

  8. S. L. Lai, A. Carlsson, Jr., and L. H. Allen., Appl. Phys. Lett. 72, 1098 (1998).

    Article  ADS  Google Scholar 

  9. P. Pawlov, Zs. Phys. Chem. 65, 1 (1909).

    Google Scholar 

  10. Yu. I. Petrov, Physics of Small Particles (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  11. K. J. Hanszen, Z. Physik 157, 523 (1960).

    Article  ADS  Google Scholar 

  12. T. M. Taova, M. Kh. Khokonov, R. I. Tegaev, and Kh. B. Khokonov, Proceedings of the Intern. Interdisciplinary Symp. “Melting and Crystallization of Metals and Alloys” (Rostov, 2009), pp. 162–168.

  13. P. K. Korotkov, T. A. Orkvasov, and V. A. Sozaev, Pis’ma Zh. Tekh. Fiz. 32(2), 28 (2006) [Tech. Phys. Lett. 32, 61 (2006)].

    Google Scholar 

  14. S. Sh. Rekhviashvili and E. V. Kishtikova, Pis’ma Zh. Tekh. Fiz. 32(10), 50 (2006) [Tech. Phys. Lett. 32, 439 (2006)].

    Google Scholar 

  15. S. Ono and S. Kondo, Molecular Theory of Surface Tension in Liquids (Springer, Berlin, 1960).

    Google Scholar 

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Correspondence to V. I. Shapovalov.

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Original Russian Text © A.A. Barybin, V.I. Shapovalov, 2010, published in Pis’ma v Zhurnal Tekhnicheskoĭ Fiziki, 2010, Vol. 36, No. 22, pp. 69–75.

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Barybin, A.A., Shapovalov, V.I. Differential equation for the melting temperature of small-size particles. Tech. Phys. Lett. 36, 1058–1060 (2010). https://doi.org/10.1134/S1063785010110258

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  • DOI: https://doi.org/10.1134/S1063785010110258

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