Pore Evolution at Reactive Diffusion in Spherical and Cylindrical Nanoparticles

  • O. M. Podolyan Bogdan Khmelnyts’kyi National University of Cherkasy
  • T. V. Zaporozhets Bogdan Khmelnyts’kyi National University of Cherkasy
  • A. M. Gusak Bogdan Khmelnyts’kyi National University of Cherkasy
Keywords: void, nanoshell, diffusion, vacancies, reaction, Kirkendall effect, Gibbs– Thomson effect, intermediate phase


A phenomenological model has been proposed for the description of the pore evolution at the phase formation in spherically and cylindrically symmetric binary systems “core–shell” with different mobilities of components. The dependences of the duration and the efficiency of the pore formation, relative pore stability, and degree of core restoration in the course of pore shrinkage on the initial dimensions of the system, surface tension, thermodynamic gain of
formation/decay of a compound, and diffusion mobilities of components are analyzed. The ratio between the thermodynamic reaction gain and the surface tension is shown to be the governing parameter at the transition from the stage of nanoshell formation to that of its shrinkage; namely, it determines which of the regimes–pore formation and shrinkage with or without restoration of the initial components – will take place.


  1. F. Aldinger, Acta. Metall. 22, 923 (1974). https://doi.org/10.1016/0001-6160(74)90059-5

  2. Ya.E. Geguzin, Diffusion Zone (Nauka, Moscow, 1979) (in Russian).

  3. Y. Yadong, R.M. Rioux, C.K. Erdonmez, S. Hughes, G.A. Somorjai, and A.P. Alivisatos, Science 304, 711 (2004). https://doi.org/10.1126/science.1096566

  4. H.J. Fan, M. Knez, R. Scholz, D. Hesse, K. Nielsch, M. Zacharias, and U. Gosele, Nano Lett. 7, 993 (2007). https://doi.org/10.1021/nl070026p

  5. C.M. Wang, D.R. Baer, L.E. Thomas, J.E. Amonette, J. Antony, Y. Qiang, and G. Duscher, J. Appl. Phys. 98, 094308 (2005). https://doi.org/10.1063/1.2130890

  6. Y. Yin, C.K. Erdonmez, A. Cabot, S. Hughes, and A.P. Alivisatos, Adv. Funct. Mater. 16, 1389 (2006). https://doi.org/10.1002/adfm.200600256

  7. A. Cabot, V.F. Puntes, E. Shevchenko, Y. Yin, L. Balcells, M.A. Marcus, S.M. Hughes, and A.P. Alivisatos, J. Am. Chem. Soc. 129, 10358 (2007). https://doi.org/10.1021/ja072574a

  8. R. Nakamura, D. Tokozakura, J-G. Lee, H. Mori, and H. Nakajima, Acta Mater. 56, 5276 (2008). https://doi.org/10.1016/j.actamat.2008.07.004

  9. R. Nakamura, G. Matsubayashi, H. Tsuchiya, S. Fujimoto, and H. Nakajima, Acta Mater. 57, 4261 (2009). https://doi.org/10.1016/j.actamat.2009.05.023

  10. G. Glod’an, C. Cserh’ati, I. Beszeda, and D.L. Beke, Appl. Phys. Lett. 97, 113109 (2010). https://doi.org/10.1063/1.3490675

  11. G. Glod’an, C. Cserh’ati, and D.L. Beke, Philos. Mag. 92, 3806 (2012). https://doi.org/10.1080/14786435.2012.687841

  12. K.N. Tu and U. G¨osele, Appl. Phys. Lett. 86, 093111 (2005). https://doi.org/10.1063/1.1873044

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

  14. T.V. Zaporozhets, O.M. Podolyan, and A.M. Gusak, Metallofiz. Noveish. Tekhnol. 34, 111 (2012).

  15. A.M. Gusak and K.N. Tu, Acta Mater. 57, 3367 (2009). https://doi.org/10.1016/j.actamat.2009.03.043

  16. T.V. Zaporozhets, A.M. Gusak, and O.N. Podolyan, Usp. Fiz. Metall. 12, 1 (2011). https://doi.org/10.15407/ufm.12.01.001

How to Cite
Podolyan, O., Zaporozhets, T., & Gusak, A. (2018). Pore Evolution at Reactive Diffusion in Spherical and Cylindrical Nanoparticles. Ukrainian Journal of Physics, 58(2), 171. https://doi.org/10.15407/ujpe58.02.0171