Journal of the Korean Crystal Growth and Crystal Technology (한국결정성장학회지)

The Korea Association of Crystal Growth (한국결정성장학회)
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Computer simulation of the effects of anisotropic grain boundary energy on grain growth in 2-D

이방성 결정립 계면에너지의 2차원 결정립 성장에 미치는 효과에 대한 컴퓨터 모사

  • Kim, Shin-Woo (Dept. of Materials Engineering, Hoseo University)
  • 김신우 (호서대학교 신소재공학과)
  • Received : 2012.07.02
  • Accepted : 2012.07.20
  • Published : 2012.08.31
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Abstract

The grain growth is very important because of its great influence on the various materials properties. Therefore, in this study, the effects of anisotropic grain boundary energy on grain growth in 2-D have been investigated with a large scale phase field simulation model on PC. A $2000{\times}2000$ grid system and the initial number of grains of about 73,000 were used in the computer simulation. The anisotropic ratio of grain boundary energy, ${\sigma}_{max}/{\sigma}_{min}$, has been varied from 1 to 3. As the anisotropy increased, the grain growth exponent, n, increased from 2.05 to 2.37. The grain size distribution showed a central plateau in the isotropic case, and was changed into no central plateau and the increasing population of very small grains in the anisotropic case, resulting from slowly disappearing grains. Finally, simulated microstructures were compared according to anisotropy.

결정립 성장은 여러 가지 재료의 성질에 미치는 큰 영향으로 재료공학에서 매우 중요하다. 그래서 본 연구에서는 PC에서 대규모 상장 모델을 사용하여 이방성 결정립 계면에너지의 2차원 결정립 성장에 미치는 효과를 조사하였다. 컴퓨터 모사에서는 $2000{\times}2000$의 그리드 시스템과 약 7300개의 초기 결정립 개수가 사용되었다. 결정립계 에너지의 이방성의 비, ${\sigma}_{max}/{\sigma}_{min}$는 1부터 3까지 변경되었다. 이방성이 증가함에 따라 결정립 성장 지수, n은 2.05에서 2.37로 증가하였다. 결정립 크기의 분포는 등방성인 경우에는 중앙에 평탄한 영역을 보였으나 이방성의 경우에는 중앙의 평탄한 영역이 사라지고 매우 느리게 사라지는 작은 결정립에 기인하여 작은 결정립 크기의 분포가 약간 증가하였다. 마지막으로 모사된 결정립 미세구조가 이방성에 따라 비교, 분석되었다.

Keywords

References

  1. E.A. Holm and S.M. Foiles, "How grain growth stops: A mechanism for grain-growth stagnation in pure materials", Science 328 (2010) 1138. https://doi.org/10.1126/science.1187833
  2. P.R. Rois and M.E. Glicksman, "Polyhedral model for self-similar grain growth", Acta Mater. 56 (2008) 1165. https://doi.org/10.1016/j.actamat.2007.11.010
  3. J. Svoboda and F.D. Fischer, "A new approach to modelling of non-steady grain growth", Acta Mater. 55 (2007) 4467. https://doi.org/10.1016/j.actamat.2007.04.012
  4. T. Wejrzanowski, K. Batorski and K.J. Kurzydlowski, "Grain growth modelling: 3D and 2D correlation", Materials Characterization 56 (2006) 336. https://doi.org/10.1016/j.matchar.2005.09.010
  5. C.S. Pande and A.K. Rajagopal, "Modeling of grain growth in two dimensions", Acta Mater. 50 (2002) 3013. https://doi.org/10.1016/S1359-6454(02)00130-1
  6. A. Kazaryan, B.R. Patton, S.A. Dregia and Y. Wang, "On the theory of grain growth in systems with anisotropic boundary mobility", Acta Mater. 50 (2002) 499. https://doi.org/10.1016/S1359-6454(01)00369-X
  7. P.R. Rios, "Irreversible thermodynamics, parabolic law and self-similar state in grain growth", Acta Mater. 52 (2004) 249. https://doi.org/10.1016/j.actamat.2003.09.010
  8. S. Yoon, J. Kim, B. Shin, S. Park, D. Shin and H. Lee, "Effects of anatase-rutile phase transition and grain growth with $WO_{3}$ on thermal stability for TiO2 SCR catalyst", J. of Kor. Cryst. Growth & Cryst. Tech. 21 (2011) 181. https://doi.org/10.6111/JKCGCT.2011.21.4.181
  9. S. Kim, E. Kang, U. Kim, K. Hwang and W. Cho, "Sintered body characteristics of LAS by addition of $CaCO_{3}$ and $ZrO_{2}$ using a solid-state reaction", J. of Kor. Cryst. Growth & Cryst. Tech. 21 (2011) 218. https://doi.org/10.6111/JKCGCT.2011.21.5.218
  10. N. Moelans, F. Wendler and B. Nestler, "Comparative study of two phase-field models for grain growth", Computational Materials Science 46 (2009) 479. https://doi.org/10.1016/j.commatsci.2009.03.037
  11. N. Moelans, B. Blanpain and P. Wollants, "An introduction to phase-field modeling of microstructure evolution", Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 268. https://doi.org/10.1016/j.calphad.2007.11.003
  12. V.Y. Novikov, "Microstructure stabilization in bulk nanocrystalline materials: Analytical approach and numerical modeling", Mater. Lett. 62 (2008) 3748. https://doi.org/10.1016/j.matlet.2008.04.048
  13. S. Kim, D. Kim, W. Kim and Y. Park, "Computer simulations of 2D and 3D ideal grain growth", Phys. Rev. E 74 (2006) 061605. https://doi.org/10.1103/PhysRevE.74.061605
  14. C.E. Krill and L.Q. Chen, "Computer simulation of 3-D grain growth using a phase-field model", Acta Mater. 50 (2002) 3057.
  15. Q. Yu and S.K. Esche, "Three-dimensional grain growth modeling with a monte carlo algrithm", Mater. Lett. 57 (2003) 4622. https://doi.org/10.1016/S0167-577X(03)00372-0
  16. M.P. Anderson, D.J. Srolovitz, G.S. Grest and P.S. Sahni, "Computer simulation of grain growth-I. kinetics", Acta Mater. 32 (1984) 783. https://doi.org/10.1016/0001-6160(84)90151-2
  17. D.J. Srolovitz, M.P. Anderson, P.S. Sahni and G.S. Grest, "Computer simulation of grain growth-II. Grain size distribution, topology, and local dynamics", Acta Mater. 32 (1984) 793. https://doi.org/10.1016/0001-6160(84)90152-4
  18. F.J. Humphreys and M. Hatherly, "Recrystallization and related annealing phenomena", 2nd Ed., Elsevier, p. 338 (2004).