Reanalysis of the 3D quasi-stationary grain size distribution based on Hillert's grain growth rate equation

  • Wang Chao 
  • Liu Guoquan 


Based on Hillert's 3D grain growth rate equation, the grain growth continuity equation was solved. The results show that there are an infinite number of 3D quasi-stationary grain size distributions. This conclusion has gained strong supports from results of different computer simulations reported in the literature.


Hillert's grain growth equation continuity equation quasi-stationary state grain size distribution analytical distribution 


  1. 1.
    Feppon, J. M., Hutchinson, W. B., On the growth of grains, Acta Mater., 2002, 50: 3293–3300.CrossRefGoogle Scholar
  2. 2.
    Liu Guoquan, Yu Haibo, Song Xiaoyan et al., A new model of three-dimensional grain growth: Theory and computer simulation of topology-dependency of individual grain growth rate, Materials and Design, 2001, 22:33–38.CrossRefGoogle Scholar
  3. 3.
    Liu Guoquan, Yu Haibo, Qin Xiangge, Three-dimensional grain topology—size relationships in a real metallic polycrystal compared with theoretical models, Materials Science and Engineering A, 2002, 326 276–281.CrossRefGoogle Scholar
  4. 4.
    Hillert, M., On the theory of normal and abnormal grain growth, Acta Metall., 1965, 13(3): 227–238.CrossRefGoogle Scholar
  5. 5.
    Hillert, M., Analytical treatments of normal grain growth, Materials Science Forum, 1996, 202–206: 3–18.CrossRefGoogle Scholar
  6. 6.
    Wagner, C., Thoerie der altering von neiderschlagen durch umlosen, Z. Elektrochem, 1961, 65: 581–591.Google Scholar
  7. 7.
    Brown, L. C., A new reexamination of classical coarsening theory, Acta Metall., 1989, 37(1): 71–77.CrossRefGoogle Scholar
  8. 8.
    Coughlan, S. D., Fortes, M. A., Self-similar size distribution in particle coarsening, Scripta Metall. Mater., 1993, 28: 1471–1476.CrossRefGoogle Scholar
  9. 9.
    Rios, P. R., Comparison between a computer simulated and an analytical grain size distribution, Scripta Mater., 1999, 40(6): 665–668.CrossRefGoogle Scholar
  10. 10.
    Atkinson, H. V., Theories of normal grain growth in pure single phase system, Acta Metal., 1988, 36(3), 469–491.CrossRefGoogle Scholar
  11. 11.
    Weygand, D., Brechet, Y., Three-dimensional grain growth A vertex dynamics simulation, Phil. Mag. B, 1999, 79(5): 703–716.Google Scholar
  12. 12.
    Wakai, F., Enomoto, N., Ogawa, H., Three-dimensional microstructural evolution in ideal grain growth—general statistics, Acta Mater., 2000, 48: 1297–1311.CrossRefGoogle Scholar
  13. 13.
    Krill, III C. E., Chen, L. Q., Computer simulation of 3D grain growth using a phase-field model, Acta Mater., 2002, 50: 3057–3073.Google Scholar
  14. 14.
    Song Xiaoyan, Liu Guoquan, Gu Nanju, Re-analysis on grain size distribution during normal grain growth based on Monte Carlo simulation, Scripta Mater., 2000, 43: 355–359.CrossRefGoogle Scholar

Copyright information

© Science in China Press 2004

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringUniversity of Science and Technology BeijingBeijingChina

Personalised recommendations