Вы здесь

Funct. Mater. 2019; 26 (1): 131-151.


Evolution of vacancy pores in bounded particles

V.V.Yanovsky1,2, M.I.Kopp1, M.A.Ratner1

1Institute for Single Crystals, NAS Ukraine, Nauky Ave. 60, Kharkov 61001, Ukraine
2V.N. Karazin Kharkiv National University 4 Svobody Sq., Kharkov 61022, Ukraine


In the present work, the behavior of vacancy pore inside of spherical particle is investigated. On the assumption of quasistationarity of diffusion fluxes, the nonlinear equation set was obtained analytically, that describes completely pore behavior inside of spherical particle. Limiting cases of small and large pores are considered. The comparison of numerical results with asymptotic behavior of considered limiting cases of small and large pores is discussed.

vacancy pore, diffusion fluxes, nonlinear equation, nanoparticle, evolution.

1. D.L. Schodek, P. Ferreira, M.F. Ashby, Nanomaterials, Nanotechnologies and Design: An Introduction for Engineers and Architects, Elsevier Science and Technology, Oxford, United Kingdom, (2009).

2. C. Altavilla, En. Ciliberto, Inorganic Nanoparticles: Synthesis, Applications, and Perspectives, CRC Press, (2016). https://doi.org/10.1201/b10333

3. S. Myhra, J. C. Riviere , Characterization of Nanostructures, CRC Press, (2012). https://doi.org/10.1201/b12176

4. Y. Yin, R.M. Rioux, C.K. Erdonmez, S. Hughes et al., Science, 304, 711 (2004). https://doi.org/10.1126/science.1096566

5. C.M. Wang, D.R. Baer, L.E. Thomas et al., J. Appl. Phys., 98, 94308 (2005). https://doi.org/10.1063/1.2130890

6. Y. Yin, C.K. Erdonmez, A. Cabot et al., Adv. Funct. Mater., 16, 1389 (2006). https://doi.org/10.1002/adfm.200600256

7. A. Cabot, V. F. Puntes, E. Shevchenko et al., J. Am. Chem. Soc., 129, 10358 (2007). https://doi.org/10.1021/ja072574a

8. H.J. Fan, M. Knez, R. Scholz et al., Nano Lett}., 7, 993 (2007). https://doi.org/10.1021/nl070026p

9. R. Nakamura, J. G. Lee, D. Tokozakura et al., Mater. Lett., 61, 1060 (2007). https://doi.org/10.1016/j.matlet.2006.06.039

10. R. Nakamura, D. Tokozakura, H. Nakajima et al., J. Appl. Phys., 101, 07430 (2007). https://doi.org/10.1063/1.2711383

11. D. Tokozakura, R. Nakamura, H. Nakajima et al., Mater. Res., 22, 2930 (2007). https://doi.org/10.1557/JMR.2007.0362

12. R. Nakamura, J.-G. Lee, H. Morix, and H. Nakajima, Philos. Mag., 88, 257 (2008). https://doi.org/10.1080/14786430701819203

13. R. Nakamura, D. Tokozakura, J.-G. Lee et al., Acta Mater., 56, 5276 (2008). https://doi.org/10.1016/j.actamat.2008.07.004

14. R. Nakamura, G. Matsubayashi, H. Tsuchiya et al., Acta Mater.} 57, 5046 (2009). https://doi.org/10.1016/j.actamat.2009.07.006

15. C.E. Carlton, L. Rabenberg, P.J. Ferreira, Philos. Mag. Lett., 88, 715 (2008). https://doi.org/10.1080/09500830802307641

16. A.V. Ragulia and V.V. Skhorohod, Consolidated Nanostructural Materials, Naukova Dumka, Kiev, (2007) [in Russian].

17. I.M. Lifshits and V.V. Slyozov, JETP 8, 331 (1959).

18. Ja.E. Geguzin and M.A. Krivoglaz, Motion of Macroscopic Inclusions in Solid Matter, Metallurgy, Moscow, 1971 [in Russian].

19. P.G. Cheremskoy, V.V. Slyozov, and V.I. Betehin, Pores in Solid Matter, Energoatomizdat, Moscow, 1990 [in Russian].

20. V.V. Slezov and V.V. Sagalovich, Sov. Phys. Usp., 30, 23 (1987). https://doi.org/10.1070/PU1987v030n01ABEH002792

21. V.G. Baryakhtar, A.V. Tur, and V.V. Yanovsky, Functional Materials, 8, 415 (2001).

22. L.A. Maximov and A.I. Ryazanov, Phys. Met. Metallogr., 41, 284 (1976)[in Russian].

23. V.I. Dubinko, A.V. Tur, A.A.Turkin and V.V. Yanovsky, Phys. Met. Metallogr., 68, 17 (1989).

24. T.V. Zaporozhets, A.M. Gusak, and O.N. Podolyan, Usp. Fiz. Met., 13, 1 (2012). https://doi.org/10.15407/ufm.13.01.001

25. F. D. Fischer, J. Svoboda, Journal of Nanoparticle Research}, 10, 255 (2008). https://doi.org/10.1007/s11051-007-9242-6

26. A. M. Gusak , T. V. Zaporozhets, K. N. Tu and U. Gosele, Philos. Mag., 85, 4445 (2005). https://doi.org/10.1080/14786430500311741

27. G. Arfken, Mathematical methods for physicists, Acad. Press, New York and London, (1970)


Current number: