Journal of Materials Science

, Volume 43, Issue 15, pp 5068–5075 | Cite as

Grain growth in porous two-dimensional nanocrystalline materials

  • Leonid Klinger
  • Eugen RabkinEmail author
  • Lasar S. Shvindlerman
  • Günter Gottstein
Interface Science


Grain growth in two-dimensional polycrystals with mobile pores at the grain boundary triple junctions is considered. The kinetics of grain and pore growth are determined under the assumption that pore sintering and pore mobility are controlled by grain boundary and surface diffusion, respectively. It is shown that a polycrystal can achieve full density in the course of grain growth only when the initial pore size is below a certain critical value which depends on kinetic parameters, interfacial energies, and initial grain size. Larger pores grow without limits with the growing grains, and the corresponding grain growth exponent depends on kinetic parameters and lies between 2 and 4. It is shown that for a polycrystal with subcritical pores the average grain size increases linearly with time during the initial stages of growth, in agreement with recent experimental data on grain growth in thin Cu films and in bulk nanocrystalline Fe.


Triple Junction Nanocrystalline Material Triple Line Residual Porosity Growth Exponent 



This work was supported by the Russell Berrie Nanotechnology Institute (Technion) and by the RWTH Aachen through the Umbrella Cooperation Program.


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Leonid Klinger
    • 1
  • Eugen Rabkin
    • 1
    Email author
  • Lasar S. Shvindlerman
    • 2
    • 3
  • Günter Gottstein
    • 2
  1. 1.Department of Materials EngineeringTechnion-Israel Institute of TechnologyHaifaIsrael
  2. 2.Institute of Physical Metallurgy and Metal PhysicsRWTH Aachen UniversityAachenGermany
  3. 3.Institute of Solid State PhysicsRussian Academy of SciencesChernogolovkaRussia

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